Finite Group Databasebeta

← C31×#15263 #21472022

Subgroups — C31×#15263 #21472022

Order 7936.

3142 conjugacy classes of subgroups.

The subgroup lattice has 1548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic, complemented
2C22×C31×#121C211yesmaximal, characteristic, complemented
3C2×C31×#394C211yesmaximal, characteristic, complemented
4C2×C31×#392C211yesmaximal, characteristic, complemented
5C2×C31×#392C211yesmaximal, characteristic, complemented
6C2×C31×#386C211yesmaximal, characteristic, complemented
7C2×C31×#386C211yesmaximal, characteristic, complemented
8C2×C31×#385C211yesmaximal, characteristic, complemented
9C31×#1441C211yesmaximal, characteristic, complemented
10C31×#1439C211yesmaximal, characteristic, complemented
11C31×#1439C211yesmaximal, characteristic, complemented
12C31×#1438C211yesmaximal, characteristic, complemented
13C31×#1438C211yesmaximal, characteristic, complemented
14C31×#1438C211yesmaximal, characteristic, complemented
15C31×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C23×D4×C31C2211yescharacteristic
20C23×D4×C31C2211yescharacteristic
21C23×D4×C31C2211yescharacteristic
22C24×C4×C31C2211yescharacteristic
23C24×C4×C31C2211yescharacteristic
24C2×C31×#121—24no—
25C2×C31×#121—24no—
26C2×C31×#121—24no—
27C2×C31×#121—24no—
28C2×C31×#121—24no—
29C2×C31×#121—24no—
30C22×C4⋊C4×C31C2211yescharacteristic
31C22×C4⋊C4×C31C2211yescharacteristic
32C22×C4⋊C4×C31C2211yescharacteristic
33C22×C22⋊C4×C31C2211yescharacteristic
34C22×C22⋊C4×C31C2211yescharacteristic
35C22×C22⋊C4×C31C2211yescharacteristic
36C22×C22⋊C4×C31C2211yescharacteristic
37C22×C22⋊C4×C31C2211yescharacteristic
38C22×C22⋊C4×C31C2211yescharacteristic
39C22×C22⋊C4×C31C2211yescharacteristic
40C22×C22⋊C4×C31C2211yescharacteristic
41C22×C22⋊C4×C31C2211yescharacteristic
42C22×C22⋊C4×C31C2211yescharacteristic
43C22×C22⋊C4×C31C2211yescharacteristic
44C22×C22⋊C4×C31C2211yescharacteristic
45C22×C22⋊C4×C31C2211yescharacteristic
46C22×C22⋊C4×C31C2211yescharacteristic
47C31×#394—24no—
48C31×#392—24no—
49C31×#392—24no—
50C31×#386—24no—
51C31×#386—24no—
52C31×#385—24no—
53C2×C31×#95C2211yescharacteristic
54C2×C31×#95C2211yescharacteristic
55C2×C31×#95C2211yescharacteristic
56C2×C31×#95C2211yescharacteristic
57C2×C31×#95C2211yescharacteristic
58C2×C31×#95C2211yescharacteristic
59C2×C31×#95C2211yescharacteristic
60C2×C31×#95C2211yescharacteristic
61C2×C31×#95C2211yescharacteristic
62C2×C31×#95C2211yescharacteristic
63C25×C31C2311yescharacteristic
64C25×C31C2311yescharacteristic
65C25×C31C2311yescharacteristic
66C25×C31C2311yescharacteristic
67C22×D4×C31—22no—
68C22×D4×C31—22no—
69C22×D4×C31—22no—
70C22×D4×C31—22no—
71C22×D4×C31—22no—
72C22×D4×C31—22no—
73C22×D4×C31—22no—
74C22×D4×C31—22no—
75C22×D4×C31—22no—
76C22×D4×C31—22no—
77C22×D4×C31—22no—
78C22×D4×C31—22no—
79C22×D4×C31—22no—
80C22×D4×C31—22no—
81C22×D4×C31—22no—
82C22×D4×C31—22no—
83C22×D4×C31—22no—
84C22×D4×C31—22no—
85C22×D4×C31—22no—
86C22×D4×C31—22no—
87C22×D4×C31—22no—
88C22×D4×C31—22no—
89C22×D4×C31—22no—
90C22×D4×C31—22no—
91C22×D4×C31—22no—
92C22×D4×C31—22no—
93C22×D4×C31—22no—
94C22×D4×C31—22no—
95C22×D4×C31—41no—
96C22×D4×C31—41no—
97C22×D4×C31—41no—
98C22×D4×C31—41no—
99C22×D4×C31—41no—
100C22×D4×C31—41no—
101C22×D4×C31—41no—
102C22×D4×C31—41no—
103C22×D4×C31—41no—
104C22×D4×C31—41no—
105C22×D4×C31—41no—
106C22×D4×C31—41no—
107C22×D4×C31D414yescomplemented
108C22×D4×C31D414yescomplemented
109C23×C4×C31—22no—
110C23×C4×C31—22no—
111C23×C4×C31—22no—
112C23×C4×C31—22no—
113C23×C4×C31—22no—
114C23×C4×C31—22no—
115C23×C4×C31—22no—
116C23×C4×C31—22no—
117C23×C4×C31—22no—
118C23×C4×C31—22no—
119C23×C4×C31—41no—
120C23×C4×C31—41no—
121C23×C4×C31—41no—
122C23×C4×C31—41no—
123C23×C4×C31C2311yescharacteristic
124C23×C4×C31C2311yescharacteristic
125C23×C4×C31C2311yescharacteristic
126C23×C4×C31C2311yescharacteristic
127C23×C4×C31C2311yescharacteristic
128C23×C4×C31C2311yescharacteristic
129C23×C4×C31C2311yescharacteristic
130C23×C4×C31C2311yescharacteristic
131C23×C4×C31C2311yescharacteristic
132C23×C4×C31C2311yescharacteristic
133C23×C4×C31C2311yescharacteristic
134C31×#121—232no—
135C31×#121—232no—
136C2×C4⋊C4×C31—22no—
137C2×C4⋊C4×C31—22no—
138C2×C4⋊C4×C31—22no—
139C2×C4⋊C4×C31—22no—
140C2×C4⋊C4×C31—22no—
141C2×C4⋊C4×C31—22no—
142C2×C4⋊C4×C31—22no—
143C2×C4⋊C4×C31—41no—
144C2×C4⋊C4×C31D414yescomplemented
145C2×C22⋊C4×C31—22no—
146C2×C22⋊C4×C31—22no—
147C2×C22⋊C4×C31—22no—
148C2×C22⋊C4×C31—22no—
149C2×C22⋊C4×C31—22no—
150C2×C22⋊C4×C31—22no—
151C2×C22⋊C4×C31—22no—
152C2×C22⋊C4×C31—22no—
153C2×C22⋊C4×C31—22no—
154C2×C22⋊C4×C31—22no—
155C2×C22⋊C4×C31—22no—
156C2×C22⋊C4×C31—22no—
157C2×C22⋊C4×C31—22no—
158C2×C22⋊C4×C31—22no—
159C2×C22⋊C4×C31—22no—
160C2×C22⋊C4×C31—22no—
161C2×C22⋊C4×C31—22no—
162C2×C22⋊C4×C31—22no—
163C2×C22⋊C4×C31—22no—
164C2×C22⋊C4×C31—22no—
165C2×C22⋊C4×C31—22no—
166C2×C22⋊C4×C31—22no—
167C2×C22⋊C4×C31—22no—
168C2×C22⋊C4×C31—22no—
169C2×C22⋊C4×C31—22no—
170C2×C22⋊C4×C31—22no—
171C2×C22⋊C4×C31—22no—
172C2×C22⋊C4×C31—41no—
173C2×C22⋊C4×C31—41no—
174C2×C22⋊C4×C31—41no—
175C2×C22⋊C4×C31—41no—
176C2×C22⋊C4×C31—41no—
177C2×C22⋊C4×C31—41no—
178C2×C22⋊C4×C31—41no—
179C2×C22⋊C4×C31—41no—
180C2×C22⋊C4×C31—41no—
181C2×C22⋊C4×C31—41no—
182C2×C22⋊C4×C31—41no—
183C2×C22⋊C4×C31—41no—
184C2×C22⋊C4×C31D414yescomplemented
185C2×C22⋊C4×C31D414yescomplemented
186C2×C22⋊C4×C31D414yescomplemented
187C31×#95—22no—
188C31×#95—22no—
189C31×#95—22no—
190C31×#95—22no—
191C31×#95—22no—
192C31×#95—22no—
193C31×#95—22no—
194C31×#95—22no—
195C31×#95—22no—
196C31×#95—41no—
197C24×C31—21no—
198C24×C31—21no—
199C24×C31—21no—
200C24×C31—21no—
201C24×C31—21no—
202C24×C31—21no—
203C24×C31—21no—
204C24×C31—21no—
205C24×C31—21no—
206C24×C31—21no—
207C24×C31—21no—
208C24×C31—21no—
209C24×C31—21no—
210C24×C31—21no—
211C24×C31—21no—
212C24×C31—21no—
213C24×C31—21no—
214C24×C31—21no—
215C24×C31—21no—
216C24×C31—21no—
217C24×C31—21no—
218C24×C31—21no—
219C24×C31—21no—
220C24×C31—21no—
221C24×C31—21no—
222C24×C31—21no—
223C24×C31—21no—
224C24×C31—21no—
225C24×C31—21no—
226C24×C31—21no—
227C24×C31—21no—
228C24×C31—21no—
229C24×C31—21no—
230C24×C31—21no—
231C24×C31—21no—
232C24×C31—21no—
233C24×C31—21no—
234C24×C31—21no—
235C24×C31—21no—
236C24×C31—21no—
237C24×C31—21no—
238C24×C31—21no—
239C24×C31—21no—
240C24×C31—21no—
241C24×C31—21no—
242C24×C31—21no—
243C24×C31—21no—
244C24×C31—21no—
245C24×C31—21no—
246C24×C31—21no—
247C24×C31—21no—
248C24×C31—21no—
249C24×C31C2×D412yes—
250C24×C31C2×D412yes—
251C24×C31C2×D412yes—
252C24×C31C2×D412yes—
253C24×C31C2×D412yes—
254C24×C31C2×D412yes—
255C24×C31C2×D412yes—
256C24×C31#4112yes—
257C24×C31C2411yescharacteristic
258C2×D4×C31—28no—
259C2×D4×C31—28no—
260C2×D4×C31—28no—
261C2×D4×C31—28no—
262C2×D4×C31—28no—
263C2×D4×C31—28no—
264C2×D4×C31—28no—
265C2×D4×C31—28no—
266C2×D4×C31—44no—
267C2×D4×C31—44no—
268C2×D4×C31—44no—
269C2×D4×C31—44no—
270C2×D4×C31—44no—
271C2×D4×C31—44no—
272C2×D4×C31—44no—
273C2×D4×C31—44no—
274C2×D4×C31—44no—
275C2×D4×C31—44no—
276C2×D4×C31—44no—
277C2×D4×C31—44no—
278C2×D4×C31—44no—
279C2×D4×C31—44no—
280C2×D4×C31—44no—
281C2×D4×C31—44no—
282C2×D4×C31—44no—
283C2×D4×C31—44no—
284C2×D4×C31—44no—
285C2×D4×C31—44no—
286C2×D4×C31—44no—
287C2×D4×C31—44no—
288C2×D4×C31—44no—
289C2×D4×C31—44no—
290C2×D4×C31—44no—
291C2×D4×C31—44no—
292C2×D4×C31—44no—
293C2×D4×C31—44no—
294C2×D4×C31—44no—
295C2×D4×C31—44no—
296C2×D4×C31—44no—
297C2×D4×C31—44no—
298C2×D4×C31—44no—
299C2×D4×C31—44no—
300C22×C4×C31—21no—
301C22×C4×C31—21no—
302C22×C4×C31—21no—
303C22×C4×C31—21no—
304C22×C4×C31—21no—
305C22×C4×C31—21no—
306C22×C4×C31—21no—
307C22×C4×C31—21no—
308C22×C4×C31—28no—
309C22×C4×C31—28no—
310C22×C4×C31—21no—
311C22×C4×C31—21no—
312C22×C4×C31—21no—
313C22×C4×C31—21no—
314C22×C4×C31—21no—
315C22×C4×C31—21no—
316C22×C4×C31—21no—
317C22×C4×C31—21no—
318C22×C4×C31—21no—
319C22×C4×C31—21no—
320C22×C4×C31—21no—
321C22×C4×C31—21no—
322C22×C4×C31—21no—
323C22×C4×C31—21no—
324C22×C4×C31—21no—
325C22×C4×C31—21no—
326C22×C4×C31—21no—
327C22×C4×C31—21no—
328C22×C4×C31—21no—
329C22×C4×C31—21no—
330C22×C4×C31—21no—
331C22×C4×C31—21no—
332C22×C4×C31—21no—
333C22×C4×C31—21no—
334C22×C4×C31—21no—
335C22×C4×C31—21no—
336C22×C4×C31—21no—
337C22×C4×C31—21no—
338C22×C4×C31—21no—
339C22×C4×C31—21no—
340C22×C4×C31—21no—
341C22×C4×C31—21no—
342C22×C4×C31—21no—
343C22×C4×C31—21no—
344C22×C4×C31—21no—
345C22×C4×C31—21no—
346C22×C4×C31—21no—
347C22×C4×C31—21no—
348C22×C4×C31—21no—
349C22×C4×C31—21no—
350C22×C4×C31—21no—
351C22×C4×C31—21no—
352C22×C4×C31—21no—
353C22×C4×C31—21no—
354C22×C4×C31—21no—
355C22×C4×C31—21no—
356C22×C4×C31—21no—
357C22×C4×C31—21no—
358C22×C4×C31—21no—
359C22×C4×C31—21no—
360C22×C4×C31—21no—
361C22×C4×C31—21no—
362C22×C4×C31—21no—
363C22×C4×C31—21no—
364C22×C4×C31—21no—
365C22×C4×C31—21no—
366C22×C4×C31—44no—
367C22×C4×C31—44no—
368C22×C4×C31—44no—
369C22×C4×C31—44no—
370C22×C4×C31—44no—
371C22×C4×C31—44no—
372C22×C4×C31—44no—
373C22×C4×C31—44no—
374C22×C4×C31—44no—
375C22×C4×C31—44no—
376C22×C4×C31—44no—
377C22×C4×C31—44no—
378C22×C4×C31C2×D412yes—
379C22×C4×C31C2×D412yes—
380C22×C4×C31C2×D412yes—
381C22×C4×C31C2×D412yes—
382C22×C4×C31C2×D412yes—
383C22×C4×C31C2×D412yes—
384C22×C4×C31C2×D412yes—
385C22×C4×C31C2×D412yes—
386C22×C4×C31C2×D412yes—
387C22×C4×C31C2×D412yes—
388C22×C4×C31C2×D412yes—
389C22×C4×C31#4112yes—
390C22×C4×C31#4112yes—
391C4⋊C4×C31—28no—
392C4⋊C4×C31—28no—
393C4⋊C4×C31—44no—
394C22⋊C4×C31—28no—
395C22⋊C4×C31—28no—
396C22⋊C4×C31—28no—
397C22⋊C4×C31—28no—
398C22⋊C4×C31—28no—
399C22⋊C4×C31—44no—
400C22⋊C4×C31—44no—
401C22⋊C4×C31—44no—
402C22⋊C4×C31—44no—
403C22⋊C4×C31—44no—
404C22⋊C4×C31—44no—
405C22⋊C4×C31—44no—
406C22⋊C4×C31—44no—
407C22⋊C4×C31—44no—
408#15263C3111yesmaximal, characteristic, direct product factor, Sylow
409C23×C31—22no—
410C23×C31—22no—
411C23×C31—22no—
412C23×C31—22no—
413C23×C31—22no—
414C23×C31—22no—
415C23×C31—22no—
416C23×C31—22no—
417C23×C31—22no—
418C23×C31—22no—
419C23×C31—22no—
420C23×C31—22no—
421C23×C31—22no—
422C23×C31—22no—
423C23×C31—22no—
424C23×C31—22no—
425C23×C31—22no—
426C23×C31—22no—
427C23×C31—22no—
428C23×C31—22no—
429C23×C31—22no—
430C23×C31—22no—
431C23×C31—22no—
432C23×C31—22no—
433C23×C31—22no—
434C23×C31—22no—
435C23×C31—22no—
436C23×C31—22no—
437C23×C31—22no—
438C23×C31—22no—
439C23×C31—22no—
440C23×C31—22no—
441C23×C31—22no—
442C23×C31—22no—
443C23×C31—22no—
444C23×C31—22no—
445C23×C31—22no—
446C23×C31—22no—
447C23×C31—22no—
448C23×C31—22no—
449C23×C31—22no—
450C23×C31—22no—
451C23×C31—22no—
452C23×C31—22no—
453C23×C31—22no—
454C23×C31—22no—
455C23×C31—22no—
456C23×C31—22no—
457C23×C31—22no—
458C23×C31—22no—
459C23×C31—41no—
460C23×C31—41no—
461C23×C31—41no—
462C23×C31—41no—
463C23×C31—41no—
464C23×C31—41no—
465C23×C31—41no—
466C23×C31—41no—
467C23×C31—41no—
468C23×C31—41no—
469C23×C31—41no—
470C23×C31—41no—
471C23×C31—41no—
472C23×C31—41no—
473C23×C31—41no—
474C23×C31—41no—
475C23×C31—41no—
476C23×C31—41no—
477C23×C31—41no—
478C23×C31—41no—
479C23×C31—41no—
480C23×C31—41no—
481C23×C31—41no—
482C23×C31—41no—
483C23×C31—41no—
484C23×C31—41no—
485C23×C31—41no—
486C23×C31—41no—
487C23×C31—41no—
488C23×C31—41no—
489C23×C31—41no—
490C23×C31—41no—
491C23×C31—41no—
492C23×C31—41no—
493C23×C31—41no—
494C23×C31—41no—
495C23×C31—41no—
496C23×C31—41no—
497C23×C31—41no—
498C23×C31—41no—
499C23×C31—41no—
500C23×C31—41no—
501C23×C31—41no—
502C23×C31—41no—
503C23×C31—41no—
504C23×C31—41no—
505C23×C31—41no—
506C23×C31—41no—
507C23×C31—41no—
508C23×C31—41no—
509C23×C31—41no—
510C23×C31—41no—
511C23×C31—41no—
512C23×C31—41no—
513C23×C31—41no—
514C23×C31—41no—
515C23×C31—41no—
516C23×C31—41no—
517C23×C31—41no—
518C23×C31—41no—
519C23×C31—41no—
520C23×C31—41no—
521C23×C31—41no—
522C23×C31—41no—
523C23×C31—41no—
524C23×C31—41no—
525C23×C31—41no—
526C23×C31—41no—
527C23×C31—41no—
528C23×C31—41no—
529C23×C31—41no—
530C23×C31—41no—
531C23×C31—41no—
532C23×C31—41no—
533C23×C31—41no—
534C23×C31—41no—
535C23×C31—41no—
536C23×C31—41no—
537C23×C31—41no—
538C23×C31—41no—
539C23×C31—41no—
540C23×C31—41no—
541C23×C31—41no—
542C23×C31—41no—
543C23×C31—41no—
544C23×C31—41no—
545C23×C31—41no—
546C23×C31—41no—
547C23×C31#12014yes—
548C23×C31#12114yescomplemented
549C23×C31C22×D411yescharacteristic
550C23×C31C22×D411yescharacteristic
551C23×C31C22×D411yescharacteristic
552C23×C31C22×D411yescharacteristic
553C23×C31C22×D411yescharacteristic
554C23×C31C22×D411yescharacteristic
555C23×C31C2×#4111yescharacteristic
556C23×C31C2×#4111yescharacteristic
557C23×C31C2×#4111yescharacteristic
558C23×C31H(5,𝔽2)11yescharacteristic
559C23×C31H(5,𝔽2)11yescharacteristic
560C23×C31H(5,𝔽2)11yescharacteristic
561C23×C31H(5,𝔽2)11yescharacteristic
562C23×C31H(5,𝔽2)11yescharacteristic
563C23×C312−1+411yescharacteristic
564D4×C31—416no—
565D4×C31—416no—
566D4×C31—416no—
567D4×C31—416no—
568D4×C31—416no—
569D4×C31—416no—
570C2×C4×C31—22no—
571C2×C4×C31—22no—
572C2×C4×C31—22no—
573C2×C4×C31—22no—
574C2×C4×C31—22no—
575C2×C4×C31—22no—
576C2×C4×C31—22no—
577C2×C4×C31—22no—
578C2×C4×C31—22no—
579C2×C4×C31—22no—
580C2×C4×C31—22no—
581C2×C4×C31—22no—
582C2×C4×C31—22no—
583C2×C4×C31—22no—
584C2×C4×C31—22no—
585C2×C4×C31—22no—
586C2×C4×C31—22no—
587C2×C4×C31—22no—
588C2×C4×C31—22no—
589C2×C4×C31—22no—
590C2×C4×C31—22no—
591C2×C4×C31—22no—
592C2×C4×C31—22no—
593C2×C4×C31—22no—
594C2×C4×C31—22no—
595C2×C4×C31—22no—
596C2×C4×C31—22no—
597C2×C4×C31—22no—
598C2×C4×C31—22no—
599C2×C4×C31—22no—
600C2×C4×C31—22no—
601C2×C4×C31—22no—
602C2×C4×C31—22no—
603C2×C4×C31—416no—
604C2×C4×C31—416no—
605C2×C4×C31—41no—
606C2×C4×C31—41no—
607C2×C4×C31—41no—
608C2×C4×C31—41no—
609C2×C4×C31—41no—
610C2×C4×C31—41no—
611C2×C4×C31—41no—
612C2×C4×C31—41no—
613C2×C4×C31—41no—
614C2×C4×C31—41no—
615C2×C4×C31—41no—
616C2×C4×C31—41no—
617C2×C4×C31—41no—
618C2×C4×C31—41no—
619C2×C4×C31—41no—
620C2×C4×C31—41no—
621C2×C4×C31—41no—
622C2×C4×C31—41no—
623C2×C4×C31—41no—
624C2×C4×C31—41no—
625C2×C4×C31—41no—
626C2×C4×C31—41no—
627C2×C4×C31—41no—
628C2×C4×C31—41no—
629C2×C4×C31—41no—
630C2×C4×C31—41no—
631C2×C4×C31—41no—
632C2×C4×C31—41no—
633C2×C4×C31—41no—
634C2×C4×C31—41no—
635C2×C4×C31—41no—
636C2×C4×C31—41no—
637C2×C4×C31—41no—
638C2×C4×C31—41no—
639C2×C4×C31—41no—
640C2×C4×C31—41no—
641C2×C4×C31—41no—
642C2×C4×C31—41no—
643C2×C4×C31—41no—
644C2×C4×C31—41no—
645C2×C4×C31—41no—
646C2×C4×C31—41no—
647C2×C4×C31#12014yes—
648C2×C4×C31#12114yescomplemented
649C22×#121C2×C3111yescharacteristic, complemented
650C22×#121C2×C3111yescharacteristic, complemented
651C2×#394C2×C3111yescharacteristic, complemented
652C2×#392C2×C3111yescharacteristic, complemented
653C2×#392C2×C3111yescharacteristic, complemented
654C2×#386C2×C3111yescharacteristic, complemented
655C2×#386C2×C3111yescharacteristic, complemented
656C2×#385C2×C3111yescharacteristic, complemented
657#1441C2×C3111yescharacteristic, complemented
658#1439C2×C3111yescharacteristic, complemented
659#1439C2×C3111yescharacteristic, complemented
660#1438C2×C3111yescharacteristic, complemented
661#1438C2×C3111yescharacteristic, complemented
662#1438C2×C3111yescharacteristic, complemented
663C22⋊#95C2×C3111yescharacteristic, complemented
664C22×C31—24no—
665C22×C31—24no—
666C22×C31—24no—
667C22×C31—24no—
668C22×C31—24no—
669C22×C31—24no—
670C22×C31—42no—
671C22×C31—42no—
672C22×C31—42no—
673C22×C31—42no—
674C22×C31—42no—
675C22×C31—42no—
676C22×C31—42no—
677C22×C31—42no—
678C22×C31—42no—
679C22×C31—42no—
680C22×C31—42no—
681C22×C31—42no—
682C22×C31—42no—
683C22×C31—42no—
684C22×C31—42no—
685C22×C31—42no—
686C22×C31—42no—
687C22×C31—42no—
688C22×C31—42no—
689C22×C31—42no—
690C22×C31—42no—
691C22×C31—42no—
692C22×C31—42no—
693C22×C31—42no—
694C22×C31—42no—
695C22×C31—42no—
696C22×C31—42no—
697C22×C31—42no—
698C22×C31—42no—
699C22×C31—42no—
700C22×C31—42no—
701C22×C31—42no—
702C22×C31—42no—
703C22×C31—42no—
704C22×C31—42no—
705C22×C31—42no—
706C22×C31—42no—
707C22×C31—42no—
708C22×C31—81no—
709C22×C31—81no—
710C22×C31—81no—
711C22×C31—81no—
712C22×C31—81no—
713C22×C31—81no—
714C22×C31—81no—
715C22×C31—81no—
716C22×C31—81no—
717C22×C31—81no—
718C22×C31—81no—
719C22×C31—81no—
720C22×C31—81no—
721C22×C31—81no—
722C22×C31—81no—
723C22×C31—81no—
724C22×C31C2×#12011yescharacteristic
725C22×C31C2×#12011yescharacteristic
726C22×C31C2×#12111yescharacteristic
727C22×C31C2×#12111yescharacteristic
728C22×C31#52511yescharacteristic
729C22×C31#53211yescharacteristic
730C22×C31#53411yescharacteristic
731C22×C31#53411yescharacteristic
732C22×C31#53511yescharacteristic
733C22×C31#53711yescharacteristic
734C22×C31#53711yescharacteristic
735C22×C31#53711yescharacteristic
736C22×C31#53811yescharacteristic
737C22×C31#54011yescharacteristic
738C22×C31#54011yescharacteristic
739C22×C31D4211yescharacteristic
740C22×C31D4211yescharacteristic
741C22×C31D4211yescharacteristic
742C22×C31D4211yescharacteristic
743C22×C31D4211yescharacteristic
744C22×C31D4211yescharacteristic
745C22×C31D4211yescharacteristic
746C22×C31#54611yescharacteristic
747C22×C31#54611yescharacteristic
748C22×C31#54611yescharacteristic
749C22×C31#54611yescharacteristic
750C22×C31#54611yescharacteristic
751C22×C31#54611yescharacteristic
752C22×C31#54711yescharacteristic
753C22×C31#54711yescharacteristic
754C22×C31#54811yescharacteristic
755C22×C31#55011yescharacteristic
756C22×C31#55311yescharacteristic
757C22×C31#56011yescharacteristic
758C22×C31#56211yescharacteristic
759C4×C31—24no—
760C4×C31—24no—
761C4×C31—42no—
762C4×C31—42no—
763C4×C31—42no—
764C4×C31—42no—
765C4×C31—42no—
766C4×C31—42no—
767C4×C31—42no—
768C4×C31—81no—
769C4×C31—81no—
770C23×D4C22×C3111yescharacteristic
771C23×D4C22×C3111yescharacteristic
772C23×D4C22×C3111yescharacteristic
773C23×D4C22×C3111yescharacteristic
774C23×D4C22×C3111yescharacteristic
775C23×D4C22×C3111yescharacteristic
776C24×C4C22×C3111yescharacteristic
777C24×C4C22×C3111yescharacteristic
778C2×#121—24no—
779C2×#121—24no—
780C2×#121—24no—
781C2×#121—24no—
782C2×#121—24no—
783C2×#121—24no—
784C22×C4⋊C4C22×C3111yescharacteristic
785C22×C4⋊C4C22×C3111yescharacteristic
786C22×C4⋊C4C22×C3111yescharacteristic
787C22×C22⋊C4C22×C3111yescharacteristic
788C22×C22⋊C4C22×C3111yescharacteristic
789C22×C22⋊C4C22×C3111yescharacteristic
790C22×C22⋊C4C22×C3111yescharacteristic
791C22×C22⋊C4C22×C3111yescharacteristic
792C22×C22⋊C4C22×C3111yescharacteristic
793C22×C22⋊C4C22×C3111yescharacteristic
794C22×C22⋊C4C22×C3111yescharacteristic
795C22×C22⋊C4C22×C3111yescharacteristic
796C22×C22⋊C4C22×C3111yescharacteristic
797C22×C22⋊C4C22×C3111yescharacteristic
798C22×C22⋊C4C22×C3111yescharacteristic
799C22×C22⋊C4C22×C3111yescharacteristic
800C22×C22⋊C4C22×C3111yescharacteristic
801#394—24no—
802#392—24no—
803#392—24no—
804#386—24no—
805#386—24no—
806#385—24no—
807C2×#95C22×C3111yescharacteristic
808C2×#95C22×C3111yescharacteristic
809C2×#95C22×C3111yescharacteristic
810C2×#95C22×C3111yescharacteristic
811C2×#95C22×C3111yescharacteristic
812C2×#95C22×C3111yescharacteristic
813C2×#95C22×C3111yescharacteristic
814C2×#95C22×C3111yescharacteristic
815C2×#95C22×C3111yescharacteristic
816C2×#95C22×C3111yescharacteristic
817C2×C31—44no—
818C2×C31—44no—
819C2×C31—82no—
820C2×C31—82no—
821C2×C31#240311yescharacteristic
822C2×C31#240711yescharacteristic
823C2×C31#240811yescharacteristic
824C2×C31#241011yescharacteristic
825C2×C31#241611yescharacteristic
826C2×C31#242411yescharacteristic
827C2×C31#242811yescharacteristic
828C2×C31#243011yescharacteristic
829C2×C31#246411yescharacteristic
830C2×C31#267111yescharacteristic
831C2×C31#267111yescharacteristic
832C2×C31#267311yescharacteristic
833C2×C31#267511yescharacteristic
834C2×C31#267611yescharacteristic
835C2×C31#268811yescharacteristic
836C25C23×C3111yescharacteristic
837C25C23×C3111yescharacteristic
838C25C23×C3111yescharacteristic
839C25C23×C3111yescharacteristic
840C22×D4—22no—
841C22×D4—22no—
842C22×D4—22no—
843C22×D4—22no—
844C22×D4—22no—
845C22×D4—22no—
846C22×D4—22no—
847C22×D4—22no—
848C22×D4—22no—
849C22×D4—22no—
850C22×D4—22no—
851C22×D4—22no—
852C22×D4—22no—
853C22×D4—22no—
854C22×D4—22no—
855C22×D4—22no—
856C22×D4—22no—
857C22×D4—22no—
858C22×D4—22no—
859C22×D4—22no—
860C22×D4—22no—
861C22×D4—22no—
862C22×D4—22no—
863C22×D4—22no—
864C22×D4—22no—
865C22×D4—22no—
866C22×D4—22no—
867C22×D4—22no—
868C22×D4—41no—
869C22×D4—41no—
870C22×D4—41no—
871C22×D4—41no—
872C22×D4—41no—
873C22×D4—41no—
874C22×D4—41no—
875C22×D4—41no—
876C22×D4—41no—
877C22×D4—41no—
878C22×D4—41no—
879C22×D4—41no—
880C22×D4D4×C3114yescomplemented
881C22×D4D4×C3114yescomplemented
882C23×C4—22no—
883C23×C4—22no—
884C23×C4—22no—
885C23×C4—22no—
886C23×C4—22no—
887C23×C4—22no—
888C23×C4—22no—
889C23×C4—22no—
890C23×C4—22no—
891C23×C4—22no—
892C23×C4—41no—
893C23×C4—41no—
894C23×C4—41no—
895C23×C4—41no—
896C23×C4C23×C3111yescharacteristic
897C23×C4C23×C3111yescharacteristic
898C23×C4C23×C3111yescharacteristic
899C23×C4C23×C3111yescharacteristic
900C23×C4C23×C3111yescharacteristic
901C23×C4C23×C3111yescharacteristic
902C23×C4C23×C3111yescharacteristic
903C23×C4C23×C3111yescharacteristic
904C23×C4C23×C3111yescharacteristic
905C23×C4C23×C3111yescharacteristic
906C23×C4C23×C3111yescharacteristic
907#121—232no—
908#121—232no—
909C2×C4⋊C4—22no—
910C2×C4⋊C4—22no—
911C2×C4⋊C4—22no—
912C2×C4⋊C4—22no—
913C2×C4⋊C4—22no—
914C2×C4⋊C4—22no—
915C2×C4⋊C4—22no—
916C2×C4⋊C4—41no—
917C2×C4⋊C4D4×C3114yescomplemented
918C2×C22⋊C4—22no—
919C2×C22⋊C4—22no—
920C2×C22⋊C4—22no—
921C2×C22⋊C4—22no—
922C2×C22⋊C4—22no—
923C2×C22⋊C4—22no—
924C2×C22⋊C4—22no—
925C2×C22⋊C4—22no—
926C2×C22⋊C4—22no—
927C2×C22⋊C4—22no—
928C2×C22⋊C4—22no—
929C2×C22⋊C4—22no—
930C2×C22⋊C4—22no—
931C2×C22⋊C4—22no—
932C2×C22⋊C4—22no—
933C2×C22⋊C4—22no—
934C2×C22⋊C4—22no—
935C2×C22⋊C4—22no—
936C2×C22⋊C4—22no—
937C2×C22⋊C4—22no—
938C2×C22⋊C4—22no—
939C2×C22⋊C4—22no—
940C2×C22⋊C4—22no—
941C2×C22⋊C4—22no—
942C2×C22⋊C4—22no—
943C2×C22⋊C4—22no—
944C2×C22⋊C4—22no—
945C2×C22⋊C4—41no—
946C2×C22⋊C4—41no—
947C2×C22⋊C4—41no—
948C2×C22⋊C4—41no—
949C2×C22⋊C4—41no—
950C2×C22⋊C4—41no—
951C2×C22⋊C4—41no—
952C2×C22⋊C4—41no—
953C2×C22⋊C4—41no—
954C2×C22⋊C4—41no—
955C2×C22⋊C4—41no—
956C2×C22⋊C4—41no—
957C2×C22⋊C4D4×C3114yescomplemented
958C2×C22⋊C4D4×C3114yescomplemented
959C2×C22⋊C4D4×C3114yescomplemented
960#95—22no—
961#95—22no—
962#95—22no—
963#95—22no—
964#95—22no—
965#95—22no—
966#95—22no—
967#95—22no—
968#95—22no—
969#95—41no—
970C31#1526311yescharacteristic, direct product factor, Sylow
971C24—21no—
972C24—21no—
973C24—21no—
974C24—21no—
975C24—21no—
976C24—21no—
977C24—21no—
978C24—21no—
979C24—21no—
980C24—21no—
981C24—21no—
982C24—21no—
983C24—21no—
984C24—21no—
985C24—21no—
986C24—21no—
987C24—21no—
988C24—21no—
989C24—21no—
990C24—21no—
991C24—21no—
992C24—21no—
993C24—21no—
994C24—21no—
995C24—21no—
996C24—21no—
997C24—21no—
998C24—21no—
999C24—21no—
1000C24—21no—
1001C24—21no—
1002C24—21no—
1003C24—21no—
1004C24—21no—
1005C24—21no—
1006C24—21no—
1007C24—21no—
1008C24—21no—
1009C24—21no—
1010C24—21no—
1011C24—21no—
1012C24—21no—
1013C24—21no—
1014C24—21no—
1015C24—21no—
1016C24—21no—
1017C24—21no—
1018C24—21no—
1019C24—21no—
1020C24—21no—
1021C24—21no—
1022C24—21no—
1023C24C2×D4×C3112yes—
1024C24C2×D4×C3112yes—
1025C24C2×D4×C3112yes—
1026C24C2×D4×C3112yes—
1027C24C2×D4×C3112yes—
1028C24C2×D4×C3112yes—
1029C24C2×D4×C3112yes—
1030C24#41×C3112yes—
1031C24C24×C3111yescharacteristic
1032C2×D4—28no—
1033C2×D4—28no—
1034C2×D4—28no—
1035C2×D4—28no—
1036C2×D4—28no—
1037C2×D4—28no—
1038C2×D4—28no—
1039C2×D4—28no—
1040C2×D4—44no—
1041C2×D4—44no—
1042C2×D4—44no—
1043C2×D4—44no—
1044C2×D4—44no—
1045C2×D4—44no—
1046C2×D4—44no—
1047C2×D4—44no—
1048C2×D4—44no—
1049C2×D4—44no—
1050C2×D4—44no—
1051C2×D4—44no—
1052C2×D4—44no—
1053C2×D4—44no—
1054C2×D4—44no—
1055C2×D4—44no—
1056C2×D4—44no—
1057C2×D4—44no—
1058C2×D4—44no—
1059C2×D4—44no—
1060C2×D4—44no—
1061C2×D4—44no—
1062C2×D4—44no—
1063C2×D4—44no—
1064C2×D4—44no—
1065C2×D4—44no—
1066C2×D4—44no—
1067C2×D4—44no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—44no—
1071C2×D4—44no—
1072C2×D4—44no—
1073C2×D4—44no—
1074C22×C4—21no—
1075C22×C4—21no—
1076C22×C4—21no—
1077C22×C4—21no—
1078C22×C4—21no—
1079C22×C4—21no—
1080C22×C4—21no—
1081C22×C4—21no—
1082C22×C4—28no—
1083C22×C4—28no—
1084C22×C4—21no—
1085C22×C4—21no—
1086C22×C4—21no—
1087C22×C4—21no—
1088C22×C4—21no—
1089C22×C4—21no—
1090C22×C4—21no—
1091C22×C4—21no—
1092C22×C4—21no—
1093C22×C4—21no—
1094C22×C4—21no—
1095C22×C4—21no—
1096C22×C4—21no—
1097C22×C4—21no—
1098C22×C4—21no—
1099C22×C4—21no—
1100C22×C4—21no—
1101C22×C4—21no—
1102C22×C4—21no—
1103C22×C4—21no—
1104C22×C4—21no—
1105C22×C4—21no—
1106C22×C4—21no—
1107C22×C4—21no—
1108C22×C4—21no—
1109C22×C4—21no—
1110C22×C4—21no—
1111C22×C4—21no—
1112C22×C4—21no—
1113C22×C4—21no—
1114C22×C4—21no—
1115C22×C4—21no—
1116C22×C4—21no—
1117C22×C4—21no—
1118C22×C4—21no—
1119C22×C4—21no—
1120C22×C4—21no—
1121C22×C4—21no—
1122C22×C4—21no—
1123C22×C4—21no—
1124C22×C4—21no—
1125C22×C4—21no—
1126C22×C4—21no—
1127C22×C4—21no—
1128C22×C4—21no—
1129C22×C4—21no—
1130C22×C4—21no—
1131C22×C4—21no—
1132C22×C4—21no—
1133C22×C4—21no—
1134C22×C4—21no—
1135C22×C4—21no—
1136C22×C4—21no—
1137C22×C4—21no—
1138C22×C4—21no—
1139C22×C4—21no—
1140C22×C4—44no—
1141C22×C4—44no—
1142C22×C4—44no—
1143C22×C4—44no—
1144C22×C4—44no—
1145C22×C4—44no—
1146C22×C4—44no—
1147C22×C4—44no—
1148C22×C4—44no—
1149C22×C4—44no—
1150C22×C4—44no—
1151C22×C4—44no—
1152C22×C4C2×D4×C3112yes—
1153C22×C4C2×D4×C3112yes—
1154C22×C4C2×D4×C3112yes—
1155C22×C4C2×D4×C3112yes—
1156C22×C4C2×D4×C3112yes—
1157C22×C4C2×D4×C3112yes—
1158C22×C4C2×D4×C3112yes—
1159C22×C4C2×D4×C3112yes—
1160C22×C4C2×D4×C3112yes—
1161C22×C4C2×D4×C3112yes—
1162C22×C4C2×D4×C3112yes—
1163C22×C4#41×C3112yes—
1164C22×C4#41×C3112yes—
1165C4⋊C4—28no—
1166C4⋊C4—28no—
1167C4⋊C4—44no—
1168C22⋊C4—28no—
1169C22⋊C4—28no—
1170C22⋊C4—28no—
1171C22⋊C4—28no—
1172C22⋊C4—28no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C23—22no—
1183C23—22no—
1184C23—22no—
1185C23—22no—
1186C23—22no—
1187C23—22no—
1188C23—22no—
1189C23—22no—
1190C23—22no—
1191C23—22no—
1192C23—22no—
1193C23—22no—
1194C23—22no—
1195C23—22no—
1196C23—22no—
1197C23—22no—
1198C23—22no—
1199C23—22no—
1200C23—22no—
1201C23—22no—
1202C23—22no—
1203C23—22no—
1204C23—22no—
1205C23—22no—
1206C23—22no—
1207C23—22no—
1208C23—22no—
1209C23—22no—
1210C23—22no—
1211C23—22no—
1212C23—22no—
1213C23—22no—
1214C23—22no—
1215C23—22no—
1216C23—22no—
1217C23—22no—
1218C23—22no—
1219C23—22no—
1220C23—22no—
1221C23—22no—
1222C23—22no—
1223C23—22no—
1224C23—22no—
1225C23—22no—
1226C23—22no—
1227C23—22no—
1228C23—22no—
1229C23—22no—
1230C23—22no—
1231C23—22no—
1232C23—41no—
1233C23—41no—
1234C23—41no—
1235C23—41no—
1236C23—41no—
1237C23—41no—
1238C23—41no—
1239C23—41no—
1240C23—41no—
1241C23—41no—
1242C23—41no—
1243C23—41no—
1244C23—41no—
1245C23—41no—
1246C23—41no—
1247C23—41no—
1248C23—41no—
1249C23—41no—
1250C23—41no—
1251C23—41no—
1252C23—41no—
1253C23—41no—
1254C23—41no—
1255C23—41no—
1256C23—41no—
1257C23—41no—
1258C23—41no—
1259C23—41no—
1260C23—41no—
1261C23—41no—
1262C23—41no—
1263C23—41no—
1264C23—41no—
1265C23—41no—
1266C23—41no—
1267C23—41no—
1268C23—41no—
1269C23—41no—
1270C23—41no—
1271C23—41no—
1272C23—41no—
1273C23—41no—
1274C23—41no—
1275C23—41no—
1276C23—41no—
1277C23—41no—
1278C23—41no—
1279C23—41no—
1280C23—41no—
1281C23—41no—
1282C23—41no—
1283C23—41no—
1284C23—41no—
1285C23—41no—
1286C23—41no—
1287C23—41no—
1288C23—41no—
1289C23—41no—
1290C23—41no—
1291C23—41no—
1292C23—41no—
1293C23—41no—
1294C23—41no—
1295C23—41no—
1296C23—41no—
1297C23—41no—
1298C23—41no—
1299C23—41no—
1300C23—41no—
1301C23—41no—
1302C23—41no—
1303C23—41no—
1304C23—41no—
1305C23—41no—
1306C23—41no—
1307C23—41no—
1308C23—41no—
1309C23—41no—
1310C23—41no—
1311C23—41no—
1312C23—41no—
1313C23—41no—
1314C23—41no—
1315C23—41no—
1316C23—41no—
1317C23—41no—
1318C23—41no—
1319C23—41no—
1320C23C31×#12014yes—
1321C23C31×#12114yescomplemented
1322C23C22×D4×C3111yescharacteristic
1323C23C22×D4×C3111yescharacteristic
1324C23C22×D4×C3111yescharacteristic
1325C23C22×D4×C3111yescharacteristic
1326C23C22×D4×C3111yescharacteristic
1327C23C22×D4×C3111yescharacteristic
1328C23C2×#41×C3111yescharacteristic
1329C23C2×#41×C3111yescharacteristic
1330C23C2×#41×C3111yescharacteristic
1331C23C31×H(5,𝔽2)11yescharacteristic
1332C23C31×H(5,𝔽2)11yescharacteristic
1333C23C31×H(5,𝔽2)11yescharacteristic
1334C23C31×H(5,𝔽2)11yescharacteristic
1335C23C31×H(5,𝔽2)11yescharacteristic
1336C23C31×2−1+411yescharacteristic
1337D4—416no—
1338D4—416no—
1339D4—416no—
1340D4—416no—
1341D4—416no—
1342D4—416no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—416no—
1377C2×C4—416no—
1378C2×C4—41no—
1379C2×C4—41no—
1380C2×C4—41no—
1381C2×C4—41no—
1382C2×C4—41no—
1383C2×C4—41no—
1384C2×C4—41no—
1385C2×C4—41no—
1386C2×C4—41no—
1387C2×C4—41no—
1388C2×C4—41no—
1389C2×C4—41no—
1390C2×C4—41no—
1391C2×C4—41no—
1392C2×C4—41no—
1393C2×C4—41no—
1394C2×C4—41no—
1395C2×C4—41no—
1396C2×C4—41no—
1397C2×C4—41no—
1398C2×C4—41no—
1399C2×C4—41no—
1400C2×C4—41no—
1401C2×C4—41no—
1402C2×C4—41no—
1403C2×C4—41no—
1404C2×C4—41no—
1405C2×C4—41no—
1406C2×C4—41no—
1407C2×C4—41no—
1408C2×C4—41no—
1409C2×C4—41no—
1410C2×C4—41no—
1411C2×C4—41no—
1412C2×C4—41no—
1413C2×C4—41no—
1414C2×C4—41no—
1415C2×C4—41no—
1416C2×C4—41no—
1417C2×C4—41no—
1418C2×C4—41no—
1419C2×C4—41no—
1420C2×C4C31×#12014yes—
1421C2×C4C31×#12114yescomplemented
1422C22—24no—
1423C22—24no—
1424C22—24no—
1425C22—24no—
1426C22—24no—
1427C22—24no—
1428C22—42no—
1429C22—42no—
1430C22—42no—
1431C22—42no—
1432C22—42no—
1433C22—42no—
1434C22—42no—
1435C22—42no—
1436C22—42no—
1437C22—42no—
1438C22—42no—
1439C22—42no—
1440C22—42no—
1441C22—42no—
1442C22—42no—
1443C22—42no—
1444C22—42no—
1445C22—42no—
1446C22—42no—
1447C22—42no—
1448C22—42no—
1449C22—42no—
1450C22—42no—
1451C22—42no—
1452C22—42no—
1453C22—42no—
1454C22—42no—
1455C22—42no—
1456C22—42no—
1457C22—42no—
1458C22—42no—
1459C22—42no—
1460C22—42no—
1461C22—42no—
1462C22—42no—
1463C22—42no—
1464C22—42no—
1465C22—42no—
1466C22—81no—
1467C22—81no—
1468C22—81no—
1469C22—81no—
1470C22—81no—
1471C22—81no—
1472C22—81no—
1473C22—81no—
1474C22—81no—
1475C22—81no—
1476C22—81no—
1477C22—81no—
1478C22—81no—
1479C22—81no—
1480C22—81no—
1481C22—81no—
1482C22C2×C31×#12011yescharacteristic
1483C22C2×C31×#12011yescharacteristic
1484C22C2×C31×#12111yescharacteristic
1485C22C2×C31×#12111yescharacteristic
1486C22C31×#52511yescharacteristic
1487C22C31×#53211yescharacteristic
1488C22C31×#53411yescharacteristic
1489C22C31×#53411yescharacteristic
1490C22C31×#53511yescharacteristic
1491C22C31×#53711yescharacteristic
1492C22C31×#53711yescharacteristic
1493C22C31×#53711yescharacteristic
1494C22C31×#53811yescharacteristic
1495C22C31×#54011yescharacteristic
1496C22C31×#54011yescharacteristic
1497C22D42×C3111yescharacteristic
1498C22D42×C3111yescharacteristic
1499C22D42×C3111yescharacteristic
1500C22D42×C3111yescharacteristic
1501C22D42×C3111yescharacteristic
1502C22D42×C3111yescharacteristic
1503C22D42×C3111yescharacteristic
1504C22C31×#54611yescharacteristic
1505C22C31×#54611yescharacteristic
1506C22C31×#54611yescharacteristic
1507C22C31×#54611yescharacteristic
1508C22C31×#54611yescharacteristic
1509C22C31×#54611yescharacteristic
1510C22C31×#54711yescharacteristic
1511C22C31×#54711yescharacteristic
1512C22C31×#54811yescharacteristic
1513C22C31×#55011yescharacteristic
1514C22C31×#55311yescharacteristic
1515C22C31×#56011yescharacteristic
1516C22C31×#56211yescharacteristic
1517C4—24no—
1518C4—24no—
1519C4—42no—
1520C4—42no—
1521C4—42no—
1522C4—42no—
1523C4—42no—
1524C4—42no—
1525C4—42no—
1526C4—81no—
1527C4—81no—
1528C2—44no—
1529C2—44no—
1530C2—82no—
1531C2—82no—
1532C2C31×#240311yescharacteristic
1533C2C31×#240711yescharacteristic
1534C2C31×#240811yescharacteristic
1535C2C31×#241011yescharacteristic
1536C2C31×#241611yescharacteristic
1537C2C31×#242411yescharacteristic
1538C2C31×#242811yescharacteristic
1539C2C31×#243011yescharacteristic
1540C2C31×#246411yescharacteristic
1541C2C31×#267111yescharacteristic
1542C2C31×#267111yescharacteristic
1543C2C31×#267311yescharacteristic
1544C2C31×#267511yescharacteristic
1545C2C31×#267611yescharacteristic
1546C2C31×#268811yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×C31×#121C2semidirect
2. C22×C31×#121C2semidirect
3. C2×C31×#394C2semidirect
4. C2×C31×#392C2semidirect
5. C2×C31×#392C2semidirect
6. C2×C31×#386C2semidirect
7. C2×C31×#386C2semidirect
8. C2×C31×#385C2semidirect
9. C31×#1441C2semidirect
10. C31×#1439C2semidirect
11. C31×#1439C2semidirect
12. C31×#1438C2semidirect
13. C31×#1438C2semidirect
14. C31×#1438C2semidirect
15. C31×C22⋊#95C2semidirect
107. C22×D4×C31D4semidirect
108. C22×D4×C31D4semidirect
144. C2×C4⋊C4×C31D4semidirect
184. C2×C22⋊C4×C31D4semidirect
185. C2×C22⋊C4×C31D4semidirect
186. C2×C22⋊C4×C31D4semidirect
408. #15263C31direct (N × H)
548. C23×C31#121semidirect
648. C2×C4×C31#121semidirect
649. C22×#121C2×C31semidirect
650. C22×#121C2×C31semidirect
651. C2×#394C2×C31semidirect
652. C2×#392C2×C31semidirect
653. C2×#392C2×C31semidirect
654. C2×#386C2×C31semidirect
655. C2×#386C2×C31semidirect
656. C2×#385C2×C31semidirect
657. #1441C2×C31semidirect
658. #1439C2×C31semidirect
659. #1439C2×C31semidirect
660. #1438C2×C31semidirect
661. #1438C2×C31semidirect
662. #1438C2×C31semidirect
663. C22⋊#95C2×C31semidirect
880. C22×D4D4×C31semidirect
881. C22×D4D4×C31semidirect
917. C2×C4⋊C4D4×C31semidirect
957. C2×C22⋊C4D4×C31semidirect
958. C2×C22⋊C4D4×C31semidirect
959. C2×C22⋊C4D4×C31semidirect
970. C31#15263direct (N × H)
1321. C23C31×#121semidirect
1421. C2×C4C31×#121semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C31×#1212
C2×C31×#3942
C2×C31×#3922
C2×C31×#3862
C2×C31×#3852
C31×#14412
C31×#14392
C31×#14382
C31×C22⋊#952
#1526331