Finite Group Databasebeta

← C31×#15315 #21472074

Subgroups — C31×#15315 #21472074

Order 7936.

2922 conjugacy classes of subgroups.

The subgroup lattice has 1536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic, complemented
2C2×C31×#396C211yesmaximal, characteristic, complemented
3C2×C31×#394C211yesmaximal, characteristic, complemented
4C2×C31×#392C211yesmaximal, characteristic, complemented
5C2×C31×#392C211yesmaximal, characteristic, complemented
6C2×C31×#392C211yesmaximal, characteristic, complemented
7C2×C31×#390C211yesmaximal, characteristic, complemented
8C2×C31×#390C211yesmaximal, characteristic, complemented
9C2×C31×#386C211yesmaximal, characteristic, complemented
10C2×C31×#385C211yesmaximal, characteristic, complemented
11C31×#1439C211yesmaximal, characteristic, complemented
12C31×#1439C211yesmaximal, characteristic, complemented
13C31×#1438C211yesmaximal, characteristic, complemented
14C31×#1438C211yesmaximal, characteristic, complemented
15C31×#1436C211yesmaximal, 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×C4⋊C4×C31C2211yescharacteristic
29C22×C4⋊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×C22⋊C4×C31C2211yescharacteristic
44C22×C22⋊C4×C31C2211yescharacteristic
45C22×C42×C31C2211yescharacteristic
46C31×#396—24no—
47C31×#394—24no—
48C31×#392—24no—
49C31×#392—24no—
50C31×#392—24no—
51C31×#390—24no—
52C31×#390—24no—
53C31×#386—24no—
54C31×#385—24no—
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—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×C31—41no—
107C22×D4×C31—41no—
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—41no—
115C23×C4×C31—41no—
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
125C23×C4×C31C2311yescharacteristic
126C23×C4×C31C2311yescharacteristic
127C31×#121—232no—
128C2×C4⋊C4×C31—22no—
129C2×C4⋊C4×C31—22no—
130C2×C4⋊C4×C31—22no—
131C2×C4⋊C4×C31—22no—
132C2×C4⋊C4×C31—22no—
133C2×C4⋊C4×C31—22no—
134C2×C4⋊C4×C31—22no—
135C2×C4⋊C4×C31—22no—
136C2×C4⋊C4×C31—22no—
137C2×C4⋊C4×C31—41no—
138C2×C4⋊C4×C31—41no—
139C2×C4⋊C4×C31D414yescomplemented
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—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—22no—
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×C31D414yescomplemented
184C2×C22⋊C4×C31D414yescomplemented
185C2×C42×C31—22no—
186C2×C42×C31—22no—
187C2×C42×C31—41no—
188C31×#95—22no—
189C31×#95—22no—
190C31×#95—22no—
191C31×#95—22no—
192C31×#95—22no—
193C31×#95—41no—
194C31×#95D414yescomplemented
195C31×#95D414yescomplemented
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×C31—21no—
245C24×C31—21no—
246C24×C31—21no—
247C24×C31—21no—
248C24×C31—21no—
249C24×C31—21no—
250C24×C31C2×D412yes—
251C24×C31C2×D412yes—
252C24×C31C2×D412yes—
253C24×C31C2×D412yes—
254C24×C31#4112yes—
255C24×C31#4112yes—
256C24×C31C2411yescharacteristic
257C2×D4×C31—28no—
258C2×D4×C31—28no—
259C2×D4×C31—28no—
260C2×D4×C31—28no—
261C2×D4×C31—28no—
262C2×D4×C31—28no—
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—
293C2×D4×C31—44no—
294C2×D4×C31—44no—
295C2×D4×C31—44no—
296C2×D4×C31—44no—
297C2×D4×C31—44no—
298C2×D4×C31—44no—
299C22×C4×C31—21no—
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—21no—
309C22×C4×C31—21no—
310C22×C4×C31—21no—
311C22×C4×C31—28no—
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—44no—
363C22×C4×C31—44no—
364C22×C4×C31—44no—
365C22×C4×C31—44no—
366C22×C4×C31—44no—
367C22×C4×C31—44no—
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×C31C2×D412yes—
375C22×C4×C31C2×D412yes—
376C22×C4×C31C2×D412yes—
377C22×C4×C31C2×D412yes—
378C22×C4×C31C2×D412yes—
379C22×C4×C31C2×D412yes—
380C22×C4×C31C2×D412yes—
381C22×C4×C31C2×D412yes—
382C22×C4×C31#4112yes—
383C4⋊C4×C31—28no—
384C4⋊C4×C31—44no—
385C4⋊C4×C31—44no—
386C4⋊C4×C31—44no—
387C22⋊C4×C31—28no—
388C22⋊C4×C31—28no—
389C22⋊C4×C31—28no—
390C22⋊C4×C31—44no—
391C22⋊C4×C31—44no—
392C22⋊C4×C31—44no—
393C22⋊C4×C31—44no—
394C22⋊C4×C31—44no—
395C22⋊C4×C31—44no—
396C22⋊C4×C31—44no—
397C22⋊C4×C31—44no—
398C22⋊C4×C31—44no—
399C22⋊C4×C31—44no—
400C22⋊C4×C31—44no—
401C22⋊C4×C31—44no—
402C42×C31—44no—
403#15315C3111yesmaximal, characteristic, direct product factor, Sylow
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—22no—
436C23×C31—22no—
437C23×C31—22no—
438C23×C31—22no—
439C23×C31—22no—
440C23×C31—22no—
441C23×C31—22no—
442C23×C31—22no—
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—41no—
536C23×C31—41no—
537C23×C31—41no—
538C23×C31—41no—
539C23×C31—41no—
540C23×C31—41no—
541C23×C31—41no—
542C23×C31—41no—
543C23×C31#12114yes—
544C23×C31C22×D411yescharacteristic
545C23×C31C22×D411yescharacteristic
546C23×C31C22×D411yescharacteristic
547C23×C31C22×D411yescharacteristic
548C23×C31C22×D411yescharacteristic
549C23×C31C22×D411yescharacteristic
550C23×C31C2×#4111yescharacteristic
551C23×C31C2×#4111yescharacteristic
552C23×C31C2×#4111yescharacteristic
553C23×C31H(5,𝔽2)11yescharacteristic
554C23×C31H(5,𝔽2)11yescharacteristic
555C23×C31H(5,𝔽2)11yescharacteristic
556C23×C31H(5,𝔽2)11yescharacteristic
557C23×C31H(5,𝔽2)11yescharacteristic
558C23×C312−1+411yescharacteristic
559D4×C31—416no—
560D4×C31—416no—
561D4×C31—416no—
562D4×C31—416no—
563D4×C31—416no—
564D4×C31—416no—
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—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—416no—
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—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#12014yes—
641C2×C4×C31#12114yescomplemented
642C2×C4×C31#12714yes—
643C22×#121C2×C3111yescharacteristic, complemented
644C2×#396C2×C3111yescharacteristic, complemented
645C2×#394C2×C3111yescharacteristic, complemented
646C2×#392C2×C3111yescharacteristic, complemented
647C2×#392C2×C3111yescharacteristic, complemented
648C2×#392C2×C3111yescharacteristic, complemented
649C2×#390C2×C3111yescharacteristic, complemented
650C2×#390C2×C3111yescharacteristic, complemented
651C2×#386C2×C3111yescharacteristic, complemented
652C2×#385C2×C3111yescharacteristic, complemented
653#1439C2×C3111yescharacteristic, complemented
654#1439C2×C3111yescharacteristic, complemented
655#1438C2×C3111yescharacteristic, complemented
656#1438C2×C3111yescharacteristic, complemented
657#1436C2×C3111yescharacteristic, complemented
658C22×C31—24no—
659C22×C31—24no—
660C22×C31—24no—
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—42no—
687C22×C31—42no—
688C22×C31—42no—
689C22×C31—42no—
690C22×C31—42no—
691C22×C31—42no—
692C22×C31—42no—
693C22×C31—42no—
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×C31—81no—
711C22×C31—81no—
712C22×C31—81no—
713C22×C31—81no—
714C22×C31—81no—
715C22×C31—81no—
716C22×C31—81no—
717C22×C31—81no—
718C22×C31C2×#12011yescharacteristic
719C22×C31C2×#12111yescharacteristic
720C22×C31C2×#12111yescharacteristic
721C22×C31#52511yescharacteristic
722C22×C31#52511yescharacteristic
723C22×C31C2×#12711yescharacteristic
724C22×C31#53411yescharacteristic
725C22×C31#53511yescharacteristic
726C22×C31#53511yescharacteristic
727C22×C31#53711yescharacteristic
728C22×C31#53711yescharacteristic
729C22×C31#53711yescharacteristic
730C22×C31#53811yescharacteristic
731C22×C31#53811yescharacteristic
732C22×C31#53811yescharacteristic
733C22×C31D4211yescharacteristic
734C22×C31D4211yescharacteristic
735C22×C31D4211yescharacteristic
736C22×C31D4211yescharacteristic
737C22×C31D4211yescharacteristic
738C22×C31D4211yescharacteristic
739C22×C31D4211yescharacteristic
740C22×C31#54611yescharacteristic
741C22×C31#54611yescharacteristic
742C22×C31#54611yescharacteristic
743C22×C31#54611yescharacteristic
744C22×C31#54611yescharacteristic
745C22×C31#54711yescharacteristic
746C22×C31#54811yescharacteristic
747C22×C31#54811yescharacteristic
748C22×C31#55011yescharacteristic
749C22×C31#55011yescharacteristic
750C22×C31#55311yescharacteristic
751C22×C31#56011yescharacteristic
752C22×C31#56211yescharacteristic
753C4×C31—24no—
754C4×C31—24no—
755C4×C31—24no—
756C4×C31—42no—
757C4×C31—42no—
758C4×C31—42no—
759C4×C31—42no—
760C4×C31—42no—
761C4×C31—42no—
762C4×C31—81no—
763C4×C31—81no—
764C23×D4C22×C3111yescharacteristic
765C23×D4C22×C3111yescharacteristic
766C23×D4C22×C3111yescharacteristic
767C23×D4C22×C3111yescharacteristic
768C23×D4C22×C3111yescharacteristic
769C23×D4C22×C3111yescharacteristic
770C24×C4C22×C3111yescharacteristic
771C2×#121—24no—
772C2×#121—24no—
773C2×#121—24no—
774C22×C4⋊C4C22×C3111yescharacteristic
775C22×C4⋊C4C22×C3111yescharacteristic
776C22×C4⋊C4C22×C3111yescharacteristic
777C22×C4⋊C4C22×C3111yescharacteristic
778C22×C22⋊C4C22×C3111yescharacteristic
779C22×C22⋊C4C22×C3111yescharacteristic
780C22×C22⋊C4C22×C3111yescharacteristic
781C22×C22⋊C4C22×C3111yescharacteristic
782C22×C22⋊C4C22×C3111yescharacteristic
783C22×C22⋊C4C22×C3111yescharacteristic
784C22×C22⋊C4C22×C3111yescharacteristic
785C22×C22⋊C4C22×C3111yescharacteristic
786C22×C22⋊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×C42C22×C3111yescharacteristic
794#396—24no—
795#394—24no—
796#392—24no—
797#392—24no—
798#392—24no—
799#390—24no—
800#390—24no—
801#386—24no—
802#385—24no—
803C2×#95C22×C3111yescharacteristic
804C2×#95C22×C3111yescharacteristic
805C2×#95C22×C3111yescharacteristic
806C2×#95C22×C3111yescharacteristic
807C2×#95C22×C3111yescharacteristic
808C2×#95C22×C3111yescharacteristic
809C2×#95C22×C3111yescharacteristic
810C2×#95C22×C3111yescharacteristic
811C2×C31—44no—
812C2×C31—82no—
813C2×C31—82no—
814C2×C31—82no—
815C2×C31#240711yescharacteristic
816C2×C31#241011yescharacteristic
817C2×C31#241611yescharacteristic
818C2×C31#242411yescharacteristic
819C2×C31#242411yescharacteristic
820C2×C31#243311yescharacteristic
821C2×C31#245611yescharacteristic
822C2×C31#254011yescharacteristic
823C2×C31#254111yescharacteristic
824C2×C31#267511yescharacteristic
825C2×C31#267611yescharacteristic
826C2×C31#267611yescharacteristic
827C2×C31#267811yescharacteristic
828C2×C31#268211yescharacteristic
829C2×C31#271411yescharacteristic
830C25C23×C3111yescharacteristic
831C25C23×C3111yescharacteristic
832C25C23×C3111yescharacteristic
833C25C23×C3111yescharacteristic
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—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—41no—
862C22×D4—41no—
863C22×D4—41no—
864C22×D4—41no—
865C22×D4—41no—
866C22×D4—41no—
867C22×D4—41no—
868C22×D4—41no—
869C22×D4—41no—
870C22×D4—41no—
871C22×D4—41no—
872C22×D4—41no—
873C22×D4—41no—
874C22×D4—41no—
875C22×D4D4×C3114yescomplemented
876C23×C4—22no—
877C23×C4—22no—
878C23×C4—22no—
879C23×C4—22no—
880C23×C4—22no—
881C23×C4—41no—
882C23×C4—41no—
883C23×C4C23×C3111yescharacteristic
884C23×C4C23×C3111yescharacteristic
885C23×C4C23×C3111yescharacteristic
886C23×C4C23×C3111yescharacteristic
887C23×C4C23×C3111yescharacteristic
888C23×C4C23×C3111yescharacteristic
889C23×C4C23×C3111yescharacteristic
890C23×C4C23×C3111yescharacteristic
891C23×C4C23×C3111yescharacteristic
892C23×C4C23×C3111yescharacteristic
893C23×C4C23×C3111yescharacteristic
894#121—232no—
895C2×C4⋊C4—22no—
896C2×C4⋊C4—22no—
897C2×C4⋊C4—22no—
898C2×C4⋊C4—22no—
899C2×C4⋊C4—22no—
900C2×C4⋊C4—22no—
901C2×C4⋊C4—22no—
902C2×C4⋊C4—22no—
903C2×C4⋊C4—22no—
904C2×C4⋊C4—41no—
905C2×C4⋊C4—41no—
906C2×C4⋊C4D4×C3114yescomplemented
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—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—41no—
941C2×C22⋊C4—41no—
942C2×C22⋊C4—41no—
943C2×C22⋊C4—41no—
944C2×C22⋊C4—41no—
945C2×C22⋊C4—41no—
946C2×C22⋊C4—41no—
947C2×C22⋊C4—41no—
948C2×C22⋊C4—41no—
949C2×C22⋊C4—41no—
950C2×C22⋊C4D4×C3114yescomplemented
951C2×C22⋊C4D4×C3114yescomplemented
952C2×C42—22no—
953C2×C42—22no—
954C2×C42—41no—
955#95—22no—
956#95—22no—
957#95—22no—
958#95—22no—
959#95—22no—
960#95—41no—
961#95D4×C3114yescomplemented
962#95D4×C3114yescomplemented
963C31#1531511yescharacteristic, direct product factor, Sylow
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—
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—
1018C24C2×D4×C3112yes—
1019C24C2×D4×C3112yes—
1020C24C2×D4×C3112yes—
1021C24C2×D4×C3112yes—
1022C24#41×C3112yes—
1023C24#41×C3112yes—
1024C24C24×C3111yescharacteristic
1025C2×D4—28no—
1026C2×D4—28no—
1027C2×D4—28no—
1028C2×D4—28no—
1029C2×D4—28no—
1030C2×D4—28no—
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—
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—
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—28no—
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—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—44no—
1131C22×C4—44no—
1132C22×C4—44no—
1133C22×C4—44no—
1134C22×C4—44no—
1135C22×C4—44no—
1136C22×C4C2×D4×C3112yes—
1137C22×C4C2×D4×C3112yes—
1138C22×C4C2×D4×C3112yes—
1139C22×C4C2×D4×C3112yes—
1140C22×C4C2×D4×C3112yes—
1141C22×C4C2×D4×C3112yes—
1142C22×C4C2×D4×C3112yes—
1143C22×C4C2×D4×C3112yes—
1144C22×C4C2×D4×C3112yes—
1145C22×C4C2×D4×C3112yes—
1146C22×C4C2×D4×C3112yes—
1147C22×C4C2×D4×C3112yes—
1148C22×C4C2×D4×C3112yes—
1149C22×C4C2×D4×C3112yes—
1150C22×C4#41×C3112yes—
1151C4⋊C4—28no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C22⋊C4—28no—
1156C22⋊C4—28no—
1157C22⋊C4—28no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C42—44no—
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—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—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—
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—
1310C23C31×#12114yes—
1311C23C22×D4×C3111yescharacteristic
1312C23C22×D4×C3111yescharacteristic
1313C23C22×D4×C3111yescharacteristic
1314C23C22×D4×C3111yescharacteristic
1315C23C22×D4×C3111yescharacteristic
1316C23C22×D4×C3111yescharacteristic
1317C23C2×#41×C3111yescharacteristic
1318C23C2×#41×C3111yescharacteristic
1319C23C2×#41×C3111yescharacteristic
1320C23C31×H(5,𝔽2)11yescharacteristic
1321C23C31×H(5,𝔽2)11yescharacteristic
1322C23C31×H(5,𝔽2)11yescharacteristic
1323C23C31×H(5,𝔽2)11yescharacteristic
1324C23C31×H(5,𝔽2)11yescharacteristic
1325C23C31×2−1+411yescharacteristic
1326D4—416no—
1327D4—416no—
1328D4—416no—
1329D4—416no—
1330D4—416no—
1331D4—416no—
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—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—416no—
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×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×C4C31×#12014yes—
1408C2×C4C31×#12114yescomplemented
1409C2×C4C31×#12714yes—
1410C22—24no—
1411C22—24no—
1412C22—24no—
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—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—81no—
1447C22—81no—
1448C22—81no—
1449C22—81no—
1450C22—81no—
1451C22—81no—
1452C22—81no—
1453C22—81no—
1454C22—81no—
1455C22—81no—
1456C22—81no—
1457C22—81no—
1458C22—81no—
1459C22—81no—
1460C22—81no—
1461C22—81no—
1462C22—81no—
1463C22—81no—
1464C22—81no—
1465C22—81no—
1466C22—81no—
1467C22—81no—
1468C22—81no—
1469C22—81no—
1470C22C2×C31×#12011yescharacteristic
1471C22C2×C31×#12111yescharacteristic
1472C22C2×C31×#12111yescharacteristic
1473C22C31×#52511yescharacteristic
1474C22C31×#52511yescharacteristic
1475C22C2×C31×#12711yescharacteristic
1476C22C31×#53411yescharacteristic
1477C22C31×#53511yescharacteristic
1478C22C31×#53511yescharacteristic
1479C22C31×#53711yescharacteristic
1480C22C31×#53711yescharacteristic
1481C22C31×#53711yescharacteristic
1482C22C31×#53811yescharacteristic
1483C22C31×#53811yescharacteristic
1484C22C31×#53811yescharacteristic
1485C22D42×C3111yescharacteristic
1486C22D42×C3111yescharacteristic
1487C22D42×C3111yescharacteristic
1488C22D42×C3111yescharacteristic
1489C22D42×C3111yescharacteristic
1490C22D42×C3111yescharacteristic
1491C22D42×C3111yescharacteristic
1492C22C31×#54611yescharacteristic
1493C22C31×#54611yescharacteristic
1494C22C31×#54611yescharacteristic
1495C22C31×#54611yescharacteristic
1496C22C31×#54611yescharacteristic
1497C22C31×#54711yescharacteristic
1498C22C31×#54811yescharacteristic
1499C22C31×#54811yescharacteristic
1500C22C31×#55011yescharacteristic
1501C22C31×#55011yescharacteristic
1502C22C31×#55311yescharacteristic
1503C22C31×#56011yescharacteristic
1504C22C31×#56211yescharacteristic
1505C4—24no—
1506C4—24no—
1507C4—24no—
1508C4—42no—
1509C4—42no—
1510C4—42no—
1511C4—42no—
1512C4—42no—
1513C4—42no—
1514C4—81no—
1515C4—81no—
1516C2—44no—
1517C2—82no—
1518C2—82no—
1519C2—82no—
1520C2C31×#240711yescharacteristic
1521C2C31×#241011yescharacteristic
1522C2C31×#241611yescharacteristic
1523C2C31×#242411yescharacteristic
1524C2C31×#242411yescharacteristic
1525C2C31×#243311yescharacteristic
1526C2C31×#245611yescharacteristic
1527C2C31×#254011yescharacteristic
1528C2C31×#254111yescharacteristic
1529C2C31×#267511yescharacteristic
1530C2C31×#267611yescharacteristic
1531C2C31×#267611yescharacteristic
1532C2C31×#267811yescharacteristic
1533C2C31×#268211yescharacteristic
1534C2C31×#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×#396C2semidirect
3. C2×C31×#394C2semidirect
4. C2×C31×#392C2semidirect
5. C2×C31×#392C2semidirect
6. C2×C31×#392C2semidirect
7. C2×C31×#390C2semidirect
8. C2×C31×#390C2semidirect
9. C2×C31×#386C2semidirect
10. C2×C31×#385C2semidirect
11. C31×#1439C2semidirect
12. C31×#1439C2semidirect
13. C31×#1438C2semidirect
14. C31×#1438C2semidirect
15. C31×#1436C2semidirect
108. C22×D4×C31D4semidirect
139. C2×C4⋊C4×C31D4semidirect
183. C2×C22⋊C4×C31D4semidirect
184. C2×C22⋊C4×C31D4semidirect
194. C31×#95D4semidirect
195. C31×#95D4semidirect
403. #15315C31direct (N × H)
641. C2×C4×C31#121semidirect
643. C22×#121C2×C31semidirect
644. C2×#396C2×C31semidirect
645. C2×#394C2×C31semidirect
646. C2×#392C2×C31semidirect
647. C2×#392C2×C31semidirect
648. C2×#392C2×C31semidirect
649. C2×#390C2×C31semidirect
650. C2×#390C2×C31semidirect
651. C2×#386C2×C31semidirect
652. C2×#385C2×C31semidirect
653. #1439C2×C31semidirect
654. #1439C2×C31semidirect
655. #1438C2×C31semidirect
656. #1438C2×C31semidirect
657. #1436C2×C31semidirect
875. C22×D4D4×C31semidirect
906. C2×C4⋊C4D4×C31semidirect
950. C2×C22⋊C4D4×C31semidirect
951. C2×C22⋊C4D4×C31semidirect
961. #95D4×C31semidirect
962. #95D4×C31semidirect
963. C31#15315direct (N × H)
1408. 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×#3962
C2×C31×#3942
C2×C31×#3922
C2×C31×#3902
C2×C31×#3862
C2×C31×#3852
C31×#14392
C31×#14382
C31×#14362
#1531531