Finite Group Databasebeta

← C31×#15320 #21472079

Subgroups — C31×#15320 #21472079

Order 7936.

2830 conjugacy classes of subgroups.

The subgroup lattice has 1520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic, complemented
2C2×C31×#394C211yesmaximal, characteristic, complemented
3C2×C31×#392C211yesmaximal, characteristic, complemented
4C2×C31×#392C211yesmaximal, characteristic, complemented
5C2×C31×#392C211yesmaximal, characteristic, complemented
6C2×C31×#390C211yesmaximal, characteristic, complemented
7C2×C31×#388C211yesmaximal, characteristic, complemented
8C2×C31×#386C211yesmaximal, characteristic, complemented
9C31×#1441C211yesmaximal, characteristic, complemented
10C31×#1440C211yesmaximal, characteristic, complemented
11C31×#1438C211yesmaximal, characteristic, complemented
12C31×#1438C211yesmaximal, characteristic, complemented
13C31×#1438C211yesmaximal, characteristic, complemented
14C31×#1437C211yesmaximal, 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
23C2×C31×#121—24no—
24C2×C31×#121—24no—
25C2×C31×#121—24no—
26C22×C4⋊C4×C31C2211yescharacteristic
27C22×C4⋊C4×C31C2211yescharacteristic
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2211yescharacteristic
30C22×C22⋊C4×C31C2211yescharacteristic
31C22×C22⋊C4×C31C2211yescharacteristic
32C22×C22⋊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×C42×C31C2211yescharacteristic
44C31×#394—24no—
45C31×#392—24no—
46C31×#392—24no—
47C31×#392—24no—
48C31×#390—24no—
49C31×#388—24no—
50C31×#386—24no—
51C2×C31×#95C2211yescharacteristic
52C2×C31×#95C2211yescharacteristic
53C2×C31×#95C2211yescharacteristic
54C2×C31×#95C2211yescharacteristic
55C2×C31×#95C2211yescharacteristic
56C2×C31×#95C2211yescharacteristic
57C2×C31×#95C2211yescharacteristic
58C2×C31×#95C2211yescharacteristic
59C2×C31×#95C2211yescharacteristic
60C2×C31×#95C2211yescharacteristic
61C25×C31C2311yescharacteristic
62C25×C31C2311yescharacteristic
63C25×C31C2311yescharacteristic
64C25×C31C2311yescharacteristic
65C22×D4×C31—22no—
66C22×D4×C31—22no—
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—41no—
91C22×D4×C31—41no—
92C22×D4×C31—41no—
93C22×D4×C31—41no—
94C22×D4×C31—41no—
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×C31D414yescomplemented
107C23×C4×C31—22no—
108C23×C4×C31—22no—
109C23×C4×C31—22no—
110C23×C4×C31—22no—
111C23×C4×C31—22no—
112C23×C4×C31—41no—
113C23×C4×C31—41no—
114C23×C4×C31C2311yescharacteristic
115C23×C4×C31C2311yescharacteristic
116C23×C4×C31C2311yescharacteristic
117C23×C4×C31C2311yescharacteristic
118C23×C4×C31C2311yescharacteristic
119C23×C4×C31C2311yescharacteristic
120C23×C4×C31C2311yescharacteristic
121C23×C4×C31C2311yescharacteristic
122C23×C4×C31C2311yescharacteristic
123C23×C4×C31C2311yescharacteristic
124C23×C4×C31C2311yescharacteristic
125C31×#121—232no—
126C2×C4⋊C4×C31—22no—
127C2×C4⋊C4×C31—22no—
128C2×C4⋊C4×C31—22no—
129C2×C4⋊C4×C31—22no—
130C2×C4⋊C4×C31—41no—
131C2×C4⋊C4×C31D414yescomplemented
132C2×C22⋊C4×C31—22no—
133C2×C22⋊C4×C31—22no—
134C2×C22⋊C4×C31—22no—
135C2×C22⋊C4×C31—22no—
136C2×C22⋊C4×C31—22no—
137C2×C22⋊C4×C31—22no—
138C2×C22⋊C4×C31—22no—
139C2×C22⋊C4×C31—22no—
140C2×C22⋊C4×C31—22no—
141C2×C22⋊C4×C31—22no—
142C2×C22⋊C4×C31—22no—
143C2×C22⋊C4×C31—22no—
144C2×C22⋊C4×C31—22no—
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—41no—
161C2×C22⋊C4×C31—41no—
162C2×C22⋊C4×C31—41no—
163C2×C22⋊C4×C31—41no—
164C2×C22⋊C4×C31—41no—
165C2×C22⋊C4×C31—41no—
166C2×C22⋊C4×C31—41no—
167C2×C22⋊C4×C31—41no—
168C2×C22⋊C4×C31—41no—
169C2×C22⋊C4×C31—41no—
170C2×C22⋊C4×C31—41no—
171C2×C22⋊C4×C31—41no—
172C2×C22⋊C4×C31—41no—
173C2×C22⋊C4×C31—41no—
174C2×C22⋊C4×C31D414yescomplemented
175C2×C22⋊C4×C31D414yescomplemented
176C2×C22⋊C4×C31D414yescomplemented
177C2×C42×C31—22no—
178C2×C42×C31—22no—
179C2×C42×C31—41no—
180C31×#95—22no—
181C31×#95—22no—
182C31×#95—22no—
183C31×#95—22no—
184C31×#95—22no—
185C31×#95—22no—
186C31×#95—22no—
187C31×#95—22no—
188C31×#95—41no—
189C31×#95—41no—
190C24×C31—21no—
191C24×C31—21no—
192C24×C31—21no—
193C24×C31—21no—
194C24×C31—21no—
195C24×C31—21no—
196C24×C31—21no—
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×C31C2×D412yes—
245C24×C31C2×D412yes—
246C24×C31C2×D412yes—
247C24×C31C2×D412yes—
248C24×C31C2×D412yes—
249C24×C31#4112yes—
250C24×C31C2411yescharacteristic
251C2×D4×C31—28no—
252C2×D4×C31—28no—
253C2×D4×C31—28no—
254C2×D4×C31—28no—
255C2×D4×C31—28no—
256C2×D4×C31—44no—
257C2×D4×C31—44no—
258C2×D4×C31—44no—
259C2×D4×C31—44no—
260C2×D4×C31—44no—
261C2×D4×C31—44no—
262C2×D4×C31—44no—
263C2×D4×C31—44no—
264C2×D4×C31—44no—
265C2×D4×C31—44no—
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—
293C22×C4×C31—21no—
294C22×C4×C31—21no—
295C22×C4×C31—21no—
296C22×C4×C31—21no—
297C22×C4×C31—21no—
298C22×C4×C31—21no—
299C22×C4×C31—21no—
300C22×C4×C31—21no—
301C22×C4×C31—28no—
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—21no—
309C22×C4×C31—21no—
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—44no—
359C22×C4×C31—44no—
360C22×C4×C31—44no—
361C22×C4×C31—44no—
362C22×C4×C31—44no—
363C22×C4×C31—44no—
364C22×C4×C31C2×D412yes—
365C22×C4×C31C2×D412yes—
366C22×C4×C31C2×D412yes—
367C22×C4×C31C2×D412yes—
368C22×C4×C31C2×D412yes—
369C22×C4×C31C2×D412yes—
370C22×C4×C31C2×D412yes—
371C22×C4×C31C2×D412yes—
372C22×C4×C31C2×D412yes—
373C22×C4×C31C2×D412yes—
374C22×C4×C31#4112yes—
375C22×C4×C31#4112yes—
376C22×C4×C31#4112yes—
377C4⋊C4×C31—28no—
378C4⋊C4×C31—44no—
379C22⋊C4×C31—28no—
380C22⋊C4×C31—28no—
381C22⋊C4×C31—28no—
382C22⋊C4×C31—44no—
383C22⋊C4×C31—44no—
384C22⋊C4×C31—44no—
385C22⋊C4×C31—44no—
386C22⋊C4×C31—44no—
387C22⋊C4×C31—44no—
388C22⋊C4×C31—44no—
389C22⋊C4×C31—44no—
390C22⋊C4×C31—44no—
391C22⋊C4×C31—44no—
392C22⋊C4×C31—44no—
393C22⋊C4×C31—44no—
394C42×C31—44no—
395#15320C3111yesmaximal, characteristic, direct product factor, Sylow
396C23×C31—22no—
397C23×C31—22no—
398C23×C31—22no—
399C23×C31—22no—
400C23×C31—22no—
401C23×C31—22no—
402C23×C31—22no—
403C23×C31—22no—
404C23×C31—22no—
405C23×C31—22no—
406C23×C31—22no—
407C23×C31—22no—
408C23×C31—22no—
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—41no—
436C23×C31—41no—
437C23×C31—41no—
438C23×C31—41no—
439C23×C31—41no—
440C23×C31—41no—
441C23×C31—41no—
442C23×C31—41no—
443C23×C31—41no—
444C23×C31—41no—
445C23×C31—41no—
446C23×C31—41no—
447C23×C31—41no—
448C23×C31—41no—
449C23×C31—41no—
450C23×C31—41no—
451C23×C31—41no—
452C23×C31—41no—
453C23×C31—41no—
454C23×C31—41no—
455C23×C31—41no—
456C23×C31—41no—
457C23×C31—41no—
458C23×C31—41no—
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#12114yes—
536C23×C31C22×D411yescharacteristic
537C23×C31C22×D411yescharacteristic
538C23×C31C22×D411yescharacteristic
539C23×C31C22×D411yescharacteristic
540C23×C31C22×D411yescharacteristic
541C23×C31C2×#4111yescharacteristic
542C23×C31C2×#4111yescharacteristic
543C23×C31C2×#4111yescharacteristic
544C23×C31C2×#4111yescharacteristic
545C23×C31H(5,𝔽2)11yescharacteristic
546C23×C31H(5,𝔽2)11yescharacteristic
547C23×C31H(5,𝔽2)11yescharacteristic
548C23×C31H(5,𝔽2)11yescharacteristic
549C23×C31H(5,𝔽2)11yescharacteristic
550C23×C31H(5,𝔽2)11yescharacteristic
551D4×C31—416no—
552D4×C31—416no—
553D4×C31—416no—
554D4×C31—416no—
555D4×C31—416no—
556D4×C31—416no—
557C2×C4×C31—22no—
558C2×C4×C31—22no—
559C2×C4×C31—22no—
560C2×C4×C31—22no—
561C2×C4×C31—22no—
562C2×C4×C31—22no—
563C2×C4×C31—22no—
564C2×C4×C31—22no—
565C2×C4×C31—22no—
566C2×C4×C31—22no—
567C2×C4×C31—22no—
568C2×C4×C31—22no—
569C2×C4×C31—22no—
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—416no—
591C2×C4×C31—41no—
592C2×C4×C31—41no—
593C2×C4×C31—41no—
594C2×C4×C31—41no—
595C2×C4×C31—41no—
596C2×C4×C31—41no—
597C2×C4×C31—41no—
598C2×C4×C31—41no—
599C2×C4×C31—41no—
600C2×C4×C31—41no—
601C2×C4×C31—41no—
602C2×C4×C31—41no—
603C2×C4×C31—41no—
604C2×C4×C31—41no—
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#12014yes—
634C2×C4×C31#12114yes—
635C22×#121C2×C3111yescharacteristic, complemented
636C2×#394C2×C3111yescharacteristic, complemented
637C2×#392C2×C3111yescharacteristic, complemented
638C2×#392C2×C3111yescharacteristic, complemented
639C2×#392C2×C3111yescharacteristic, complemented
640C2×#390C2×C3111yescharacteristic, complemented
641C2×#388C2×C3111yescharacteristic, complemented
642C2×#386C2×C3111yescharacteristic, complemented
643#1441C2×C3111yescharacteristic, complemented
644#1440C2×C3111yescharacteristic, complemented
645#1438C2×C3111yescharacteristic, complemented
646#1438C2×C3111yescharacteristic, complemented
647#1438C2×C3111yescharacteristic, complemented
648#1437C2×C3111yescharacteristic, complemented
649C22⋊#95C2×C3111yescharacteristic, complemented
650C22×C31—24no—
651C22×C31—24no—
652C22×C31—24no—
653C22×C31—42no—
654C22×C31—42no—
655C22×C31—42no—
656C22×C31—42no—
657C22×C31—42no—
658C22×C31—42no—
659C22×C31—42no—
660C22×C31—42no—
661C22×C31—42no—
662C22×C31—42no—
663C22×C31—42no—
664C22×C31—42no—
665C22×C31—42no—
666C22×C31—42no—
667C22×C31—42no—
668C22×C31—42no—
669C22×C31—42no—
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—81no—
687C22×C31—81no—
688C22×C31—81no—
689C22×C31—81no—
690C22×C31—81no—
691C22×C31—81no—
692C22×C31—81no—
693C22×C31—81no—
694C22×C31—81no—
695C22×C31—81no—
696C22×C31—81no—
697C22×C31—81no—
698C22×C31—81no—
699C22×C31—81no—
700C22×C31—81no—
701C22×C31—81no—
702C22×C31—81no—
703C22×C31—81no—
704C22×C31—81no—
705C22×C31—81no—
706C22×C31—81no—
707C22×C31—81no—
708C22×C31—81no—
709C22×C31—81no—
710C22×C31C2×#12011yescharacteristic
711C22×C31C2×#12111yescharacteristic
712C22×C31C2×#12111yescharacteristic
713C22×C31#52511yescharacteristic
714C22×C31#53211yescharacteristic
715C22×C31#53211yescharacteristic
716C22×C31#53411yescharacteristic
717C22×C31#53411yescharacteristic
718C22×C31#53511yescharacteristic
719C22×C31#53511yescharacteristic
720C22×C31#53511yescharacteristic
721C22×C31#53811yescharacteristic
722C22×C31#53811yescharacteristic
723C22×C31#54011yescharacteristic
724C22×C31#54011yescharacteristic
725C22×C31D4211yescharacteristic
726C22×C31D4211yescharacteristic
727C22×C31D4211yescharacteristic
728C22×C31D4211yescharacteristic
729C22×C31D4211yescharacteristic
730C22×C31#54611yescharacteristic
731C22×C31#54611yescharacteristic
732C22×C31#54611yescharacteristic
733C22×C31#54611yescharacteristic
734C22×C31#54611yescharacteristic
735C22×C31#54611yescharacteristic
736C22×C31#54611yescharacteristic
737C22×C31#54611yescharacteristic
738C22×C31#55011yescharacteristic
739C22×C31#55011yescharacteristic
740C22×C31#55311yescharacteristic
741C22×C31#55311yescharacteristic
742C22×C31#55511yescharacteristic
743C22×C31#56011yescharacteristic
744C22×C31#56011yescharacteristic
745C4×C31—24no—
746C4×C31—24no—
747C4×C31—42no—
748C4×C31—42no—
749C4×C31—42no—
750C4×C31—42no—
751C4×C31—42no—
752C4×C31—42no—
753C4×C31—42no—
754C4×C31—81no—
755C4×C31—81no—
756C23×D4C22×C3111yescharacteristic
757C23×D4C22×C3111yescharacteristic
758C23×D4C22×C3111yescharacteristic
759C23×D4C22×C3111yescharacteristic
760C23×D4C22×C3111yescharacteristic
761C23×D4C22×C3111yescharacteristic
762C24×C4C22×C3111yescharacteristic
763C2×#121—24no—
764C2×#121—24no—
765C2×#121—24no—
766C22×C4⋊C4C22×C3111yescharacteristic
767C22×C4⋊C4C22×C3111yescharacteristic
768C22×C22⋊C4C22×C3111yescharacteristic
769C22×C22⋊C4C22×C3111yescharacteristic
770C22×C22⋊C4C22×C3111yescharacteristic
771C22×C22⋊C4C22×C3111yescharacteristic
772C22×C22⋊C4C22×C3111yescharacteristic
773C22×C22⋊C4C22×C3111yescharacteristic
774C22×C22⋊C4C22×C3111yescharacteristic
775C22×C22⋊C4C22×C3111yescharacteristic
776C22×C22⋊C4C22×C3111yescharacteristic
777C22×C22⋊C4C22×C3111yescharacteristic
778C22×C22⋊C4C22×C3111yescharacteristic
779C22×C22⋊C4C22×C3111yescharacteristic
780C22×C22⋊C4C22×C3111yescharacteristic
781C22×C22⋊C4C22×C3111yescharacteristic
782C22×C22⋊C4C22×C3111yescharacteristic
783C22×C42C22×C3111yescharacteristic
784#394—24no—
785#392—24no—
786#392—24no—
787#392—24no—
788#390—24no—
789#388—24no—
790#386—24no—
791C2×#95C22×C3111yescharacteristic
792C2×#95C22×C3111yescharacteristic
793C2×#95C22×C3111yescharacteristic
794C2×#95C22×C3111yescharacteristic
795C2×#95C22×C3111yescharacteristic
796C2×#95C22×C3111yescharacteristic
797C2×#95C22×C3111yescharacteristic
798C2×#95C22×C3111yescharacteristic
799C2×#95C22×C3111yescharacteristic
800C2×#95C22×C3111yescharacteristic
801C2×C31—44no—
802C2×C31—82no—
803C2×C31—82no—
804C2×C31—82no—
805C2×C31#240811yescharacteristic
806C2×C31#241011yescharacteristic
807C2×C31#241411yescharacteristic
808C2×C31#242411yescharacteristic
809C2×C31#242811yescharacteristic
810C2×C31#243111yescharacteristic
811C2×C31#246411yescharacteristic
812C2×C31#254311yescharacteristic
813C2×C31#255511yescharacteristic
814C2×C31#266911yescharacteristic
815C2×C31#267311yescharacteristic
816C2×C31#267811yescharacteristic
817C2×C31#269911yescharacteristic
818C2×C31#270311yescharacteristic
819C2×C31#271411yescharacteristic
820C25C23×C3111yescharacteristic
821C25C23×C3111yescharacteristic
822C25C23×C3111yescharacteristic
823C25C23×C3111yescharacteristic
824C22×D4—22no—
825C22×D4—22no—
826C22×D4—22no—
827C22×D4—22no—
828C22×D4—22no—
829C22×D4—22no—
830C22×D4—22no—
831C22×D4—22no—
832C22×D4—22no—
833C22×D4—22no—
834C22×D4—22no—
835C22×D4—22no—
836C22×D4—22no—
837C22×D4—22no—
838C22×D4—22no—
839C22×D4—22no—
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—41no—
850C22×D4—41no—
851C22×D4—41no—
852C22×D4—41no—
853C22×D4—41no—
854C22×D4—41no—
855C22×D4—41no—
856C22×D4—41no—
857C22×D4—41no—
858C22×D4—41no—
859C22×D4—41no—
860C22×D4—41no—
861C22×D4—41no—
862C22×D4—41no—
863C22×D4—41no—
864C22×D4—41no—
865C22×D4D4×C3114yescomplemented
866C23×C4—22no—
867C23×C4—22no—
868C23×C4—22no—
869C23×C4—22no—
870C23×C4—22no—
871C23×C4—41no—
872C23×C4—41no—
873C23×C4C23×C3111yescharacteristic
874C23×C4C23×C3111yescharacteristic
875C23×C4C23×C3111yescharacteristic
876C23×C4C23×C3111yescharacteristic
877C23×C4C23×C3111yescharacteristic
878C23×C4C23×C3111yescharacteristic
879C23×C4C23×C3111yescharacteristic
880C23×C4C23×C3111yescharacteristic
881C23×C4C23×C3111yescharacteristic
882C23×C4C23×C3111yescharacteristic
883C23×C4C23×C3111yescharacteristic
884#121—232no—
885C2×C4⋊C4—22no—
886C2×C4⋊C4—22no—
887C2×C4⋊C4—22no—
888C2×C4⋊C4—22no—
889C2×C4⋊C4—41no—
890C2×C4⋊C4D4×C3114yescomplemented
891C2×C22⋊C4—22no—
892C2×C22⋊C4—22no—
893C2×C22⋊C4—22no—
894C2×C22⋊C4—22no—
895C2×C22⋊C4—22no—
896C2×C22⋊C4—22no—
897C2×C22⋊C4—22no—
898C2×C22⋊C4—22no—
899C2×C22⋊C4—22no—
900C2×C22⋊C4—22no—
901C2×C22⋊C4—22no—
902C2×C22⋊C4—22no—
903C2×C22⋊C4—22no—
904C2×C22⋊C4—22no—
905C2×C22⋊C4—22no—
906C2×C22⋊C4—22no—
907C2×C22⋊C4—22no—
908C2×C22⋊C4—22no—
909C2×C22⋊C4—22no—
910C2×C22⋊C4—22no—
911C2×C22⋊C4—22no—
912C2×C22⋊C4—22no—
913C2×C22⋊C4—22no—
914C2×C22⋊C4—22no—
915C2×C22⋊C4—22no—
916C2×C22⋊C4—22no—
917C2×C22⋊C4—22no—
918C2×C22⋊C4—22no—
919C2×C22⋊C4—41no—
920C2×C22⋊C4—41no—
921C2×C22⋊C4—41no—
922C2×C22⋊C4—41no—
923C2×C22⋊C4—41no—
924C2×C22⋊C4—41no—
925C2×C22⋊C4—41no—
926C2×C22⋊C4—41no—
927C2×C22⋊C4—41no—
928C2×C22⋊C4—41no—
929C2×C22⋊C4—41no—
930C2×C22⋊C4—41no—
931C2×C22⋊C4—41no—
932C2×C22⋊C4—41no—
933C2×C22⋊C4D4×C3114yescomplemented
934C2×C22⋊C4D4×C3114yescomplemented
935C2×C22⋊C4D4×C3114yescomplemented
936C2×C42—22no—
937C2×C42—22no—
938C2×C42—41no—
939#95—22no—
940#95—22no—
941#95—22no—
942#95—22no—
943#95—22no—
944#95—22no—
945#95—22no—
946#95—22no—
947#95—41no—
948#95—41no—
949C31#1532011yescharacteristic, direct product factor, Sylow
950C24—21no—
951C24—21no—
952C24—21no—
953C24—21no—
954C24—21no—
955C24—21no—
956C24—21no—
957C24—21no—
958C24—21no—
959C24—21no—
960C24—21no—
961C24—21no—
962C24—21no—
963C24—21no—
964C24—21no—
965C24—21no—
966C24—21no—
967C24—21no—
968C24—21no—
969C24—21no—
970C24—21no—
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—
1004C24C2×D4×C3112yes—
1005C24C2×D4×C3112yes—
1006C24C2×D4×C3112yes—
1007C24C2×D4×C3112yes—
1008C24C2×D4×C3112yes—
1009C24#41×C3112yes—
1010C24C24×C3111yescharacteristic
1011C2×D4—28no—
1012C2×D4—28no—
1013C2×D4—28no—
1014C2×D4—28no—
1015C2×D4—28no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—44no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—44no—
1031C2×D4—44no—
1032C2×D4—44no—
1033C2×D4—44no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—44no—
1037C2×D4—44no—
1038C2×D4—44no—
1039C2×D4—44no—
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—
1053C22×C4—21no—
1054C22×C4—21no—
1055C22×C4—21no—
1056C22×C4—21no—
1057C22×C4—21no—
1058C22×C4—21no—
1059C22×C4—21no—
1060C22×C4—21no—
1061C22×C4—28no—
1062C22×C4—21no—
1063C22×C4—21no—
1064C22×C4—21no—
1065C22×C4—21no—
1066C22×C4—21no—
1067C22×C4—21no—
1068C22×C4—21no—
1069C22×C4—21no—
1070C22×C4—21no—
1071C22×C4—21no—
1072C22×C4—21no—
1073C22×C4—21no—
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—21no—
1083C22×C4—21no—
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—44no—
1119C22×C4—44no—
1120C22×C4—44no—
1121C22×C4—44no—
1122C22×C4—44no—
1123C22×C4—44no—
1124C22×C4C2×D4×C3112yes—
1125C22×C4C2×D4×C3112yes—
1126C22×C4C2×D4×C3112yes—
1127C22×C4C2×D4×C3112yes—
1128C22×C4C2×D4×C3112yes—
1129C22×C4C2×D4×C3112yes—
1130C22×C4C2×D4×C3112yes—
1131C22×C4C2×D4×C3112yes—
1132C22×C4C2×D4×C3112yes—
1133C22×C4C2×D4×C3112yes—
1134C22×C4#41×C3112yes—
1135C22×C4#41×C3112yes—
1136C22×C4#41×C3112yes—
1137C4⋊C4—28no—
1138C4⋊C4—44no—
1139C22⋊C4—28no—
1140C22⋊C4—28no—
1141C22⋊C4—28no—
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⋊C4—44no—
1153C22⋊C4—44no—
1154C42—44no—
1155C23—22no—
1156C23—22no—
1157C23—22no—
1158C23—22no—
1159C23—22no—
1160C23—22no—
1161C23—22no—
1162C23—22no—
1163C23—22no—
1164C23—22no—
1165C23—22no—
1166C23—22no—
1167C23—22no—
1168C23—22no—
1169C23—22no—
1170C23—22no—
1171C23—22no—
1172C23—22no—
1173C23—22no—
1174C23—22no—
1175C23—22no—
1176C23—22no—
1177C23—22no—
1178C23—22no—
1179C23—22no—
1180C23—22no—
1181C23—22no—
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—41no—
1195C23—41no—
1196C23—41no—
1197C23—41no—
1198C23—41no—
1199C23—41no—
1200C23—41no—
1201C23—41no—
1202C23—41no—
1203C23—41no—
1204C23—41no—
1205C23—41no—
1206C23—41no—
1207C23—41no—
1208C23—41no—
1209C23—41no—
1210C23—41no—
1211C23—41no—
1212C23—41no—
1213C23—41no—
1214C23—41no—
1215C23—41no—
1216C23—41no—
1217C23—41no—
1218C23—41no—
1219C23—41no—
1220C23—41no—
1221C23—41no—
1222C23—41no—
1223C23—41no—
1224C23—41no—
1225C23—41no—
1226C23—41no—
1227C23—41no—
1228C23—41no—
1229C23—41no—
1230C23—41no—
1231C23—41no—
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—
1294C23C31×#12114yes—
1295C23C22×D4×C3111yescharacteristic
1296C23C22×D4×C3111yescharacteristic
1297C23C22×D4×C3111yescharacteristic
1298C23C22×D4×C3111yescharacteristic
1299C23C22×D4×C3111yescharacteristic
1300C23C2×#41×C3111yescharacteristic
1301C23C2×#41×C3111yescharacteristic
1302C23C2×#41×C3111yescharacteristic
1303C23C2×#41×C3111yescharacteristic
1304C23C31×H(5,𝔽2)11yescharacteristic
1305C23C31×H(5,𝔽2)11yescharacteristic
1306C23C31×H(5,𝔽2)11yescharacteristic
1307C23C31×H(5,𝔽2)11yescharacteristic
1308C23C31×H(5,𝔽2)11yescharacteristic
1309C23C31×H(5,𝔽2)11yescharacteristic
1310D4—416no—
1311D4—416no—
1312D4—416no—
1313D4—416no—
1314D4—416no—
1315D4—416no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—416no—
1350C2×C4—41no—
1351C2×C4—41no—
1352C2×C4—41no—
1353C2×C4—41no—
1354C2×C4—41no—
1355C2×C4—41no—
1356C2×C4—41no—
1357C2×C4—41no—
1358C2×C4—41no—
1359C2×C4—41no—
1360C2×C4—41no—
1361C2×C4—41no—
1362C2×C4—41no—
1363C2×C4—41no—
1364C2×C4—41no—
1365C2×C4—41no—
1366C2×C4—41no—
1367C2×C4—41no—
1368C2×C4—41no—
1369C2×C4—41no—
1370C2×C4—41no—
1371C2×C4—41no—
1372C2×C4—41no—
1373C2×C4—41no—
1374C2×C4—41no—
1375C2×C4—41no—
1376C2×C4—41no—
1377C2×C4—41no—
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×C4C31×#12014yes—
1393C2×C4C31×#12114yes—
1394C22—24no—
1395C22—24no—
1396C22—24no—
1397C22—42no—
1398C22—42no—
1399C22—42no—
1400C22—42no—
1401C22—42no—
1402C22—42no—
1403C22—42no—
1404C22—42no—
1405C22—42no—
1406C22—42no—
1407C22—42no—
1408C22—42no—
1409C22—42no—
1410C22—42no—
1411C22—42no—
1412C22—42no—
1413C22—42no—
1414C22—42no—
1415C22—42no—
1416C22—42no—
1417C22—42no—
1418C22—42no—
1419C22—42no—
1420C22—42no—
1421C22—42no—
1422C22—42no—
1423C22—42no—
1424C22—42no—
1425C22—42no—
1426C22—42no—
1427C22—42no—
1428C22—42no—
1429C22—42no—
1430C22—81no—
1431C22—81no—
1432C22—81no—
1433C22—81no—
1434C22—81no—
1435C22—81no—
1436C22—81no—
1437C22—81no—
1438C22—81no—
1439C22—81no—
1440C22—81no—
1441C22—81no—
1442C22—81no—
1443C22—81no—
1444C22—81no—
1445C22—81no—
1446C22—81no—
1447C22—81no—
1448C22—81no—
1449C22—81no—
1450C22—81no—
1451C22—81no—
1452C22—81no—
1453C22—81no—
1454C22C2×C31×#12011yescharacteristic
1455C22C2×C31×#12111yescharacteristic
1456C22C2×C31×#12111yescharacteristic
1457C22C31×#52511yescharacteristic
1458C22C31×#53211yescharacteristic
1459C22C31×#53211yescharacteristic
1460C22C31×#53411yescharacteristic
1461C22C31×#53411yescharacteristic
1462C22C31×#53511yescharacteristic
1463C22C31×#53511yescharacteristic
1464C22C31×#53511yescharacteristic
1465C22C31×#53811yescharacteristic
1466C22C31×#53811yescharacteristic
1467C22C31×#54011yescharacteristic
1468C22C31×#54011yescharacteristic
1469C22D42×C3111yescharacteristic
1470C22D42×C3111yescharacteristic
1471C22D42×C3111yescharacteristic
1472C22D42×C3111yescharacteristic
1473C22D42×C3111yescharacteristic
1474C22C31×#54611yescharacteristic
1475C22C31×#54611yescharacteristic
1476C22C31×#54611yescharacteristic
1477C22C31×#54611yescharacteristic
1478C22C31×#54611yescharacteristic
1479C22C31×#54611yescharacteristic
1480C22C31×#54611yescharacteristic
1481C22C31×#54611yescharacteristic
1482C22C31×#55011yescharacteristic
1483C22C31×#55011yescharacteristic
1484C22C31×#55311yescharacteristic
1485C22C31×#55311yescharacteristic
1486C22C31×#55511yescharacteristic
1487C22C31×#56011yescharacteristic
1488C22C31×#56011yescharacteristic
1489C4—24no—
1490C4—24no—
1491C4—42no—
1492C4—42no—
1493C4—42no—
1494C4—42no—
1495C4—42no—
1496C4—42no—
1497C4—42no—
1498C4—81no—
1499C4—81no—
1500C2—44no—
1501C2—82no—
1502C2—82no—
1503C2—82no—
1504C2C31×#240811yescharacteristic
1505C2C31×#241011yescharacteristic
1506C2C31×#241411yescharacteristic
1507C2C31×#242411yescharacteristic
1508C2C31×#242811yescharacteristic
1509C2C31×#243111yescharacteristic
1510C2C31×#246411yescharacteristic
1511C2C31×#254311yescharacteristic
1512C2C31×#255511yescharacteristic
1513C2C31×#266911yescharacteristic
1514C2C31×#267311yescharacteristic
1515C2C31×#267811yescharacteristic
1516C2C31×#269911yescharacteristic
1517C2C31×#270311yescharacteristic
1518C2C31×#271411yescharacteristic
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. C2×C31×#394C2semidirect
3. C2×C31×#392C2semidirect
4. C2×C31×#392C2semidirect
5. C2×C31×#392C2semidirect
6. C2×C31×#390C2semidirect
7. C2×C31×#388C2semidirect
8. C2×C31×#386C2semidirect
9. C31×#1441C2semidirect
10. C31×#1440C2semidirect
11. C31×#1438C2semidirect
12. C31×#1438C2semidirect
13. C31×#1438C2semidirect
14. C31×#1437C2semidirect
15. C31×C22⋊#95C2semidirect
106. C22×D4×C31D4semidirect
131. C2×C4⋊C4×C31D4semidirect
174. C2×C22⋊C4×C31D4semidirect
175. C2×C22⋊C4×C31D4semidirect
176. C2×C22⋊C4×C31D4semidirect
395. #15320C31direct (N × H)
635. C22×#121C2×C31semidirect
636. C2×#394C2×C31semidirect
637. C2×#392C2×C31semidirect
638. C2×#392C2×C31semidirect
639. C2×#392C2×C31semidirect
640. C2×#390C2×C31semidirect
641. C2×#388C2×C31semidirect
642. C2×#386C2×C31semidirect
643. #1441C2×C31semidirect
644. #1440C2×C31semidirect
645. #1438C2×C31semidirect
646. #1438C2×C31semidirect
647. #1438C2×C31semidirect
648. #1437C2×C31semidirect
649. C22⋊#95C2×C31semidirect
865. C22×D4D4×C31semidirect
890. C2×C4⋊C4D4×C31semidirect
933. C2×C22⋊C4D4×C31semidirect
934. C2×C22⋊C4D4×C31semidirect
935. C2×C22⋊C4D4×C31semidirect
949. C31#15320direct (N × H)

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×#3902
C2×C31×#3882
C2×C31×#3862
C31×#14412
C31×#14402
C31×#14382
C31×#14372
C31×C22⋊#952
#1532031