Finite Group Databasebeta

← C31×#11005 #21467764

Subgroups — C31×#11005 #21467764

Order 7936.

1270 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#536C211yesmaximal, characteristic
2C2×C31×#421C211yesmaximal, characteristic
3C31×#2896C211yesmaximal, characteristic
4C2×C31×#419C211yesmaximal, characteristic, complemented
5C2×C31×#419C211yesmaximal, characteristic, complemented
6C2×C31×#344C211yesmaximal, characteristic, complemented
7C31×#1740C211yesmaximal, characteristic, complemented
8C22×#41×C31C2211yescharacteristic
9C23×Q8×C31C2211yescharacteristic
10C22×M16×C31C2211yescharacteristic
11C22×M16×C31C2211yescharacteristic
12C31×#536—22no—
13C31×#536—22no—
14C31×#536—22no—
15C31×#536C414yescomplemented
16C2×C31×C4⋊Q8—21no—
17C2×C31×#124—21no—
18C2×C31×#123—22no—
19C2×C31×C22⋊Q8—22no—
20C2×C31×#117C2211yescharacteristic
21C2×C31×#117C2211yescharacteristic
22C2×C31×#117C2211yescharacteristic
23C31×#421—22no—
24C31×#421—22no—
25C2×C31×#104—22no—
26C31×#419—22no—
27C31×#419—22no—
28C31×#419—21no—
29C31×#419—22no—
30C31×#419—22no—
31C31×#418—21no—
32C31×#417—22no—
33C31×#416—22no—
34C2×C31×#103—22no—
35C2×C31×#103—22no—
36C31×#344—22no—
37C31×#342—22no—
38C2×#41×C31—21no—
39C2×#41×C31—21no—
40C2×#41×C31—21no—
41C2×#41×C31—21no—
42C2×#41×C31—21no—
43C2×#41×C31—21no—
44C2×#41×C31—21no—
45C2×#41×C31—21no—
46C2×#41×C31—21no—
47C2×#41×C31—21no—
48C2×#41×C31C2×C412yes—
49C2×#41×C31D412yes—
50C22×Q8×C31—21no—
51C22×Q8×C31—21no—
52C22×Q8×C31—21no—
53C22×Q8×C31—21no—
54C22×Q8×C31—21no—
55C22×Q8×C31—21no—
56C22×Q8×C31—21no—
57C22×Q8×C31—21no—
58C22×Q8×C31—21no—
59C22×Q8×C31—21no—
60C22×Q8×C31—21no—
61C22×Q8×C31C2×C412yes—
62C22×Q8×C31D412yes—
63C22×Q8×C31D411yescharacteristic
64C22×Q8×C31D412yes—
65C22×D4×C31—21no—
66C22×D4×C31D411yescharacteristic
67C23×C4×C31—21no—
68C23×C4×C31—21no—
69C23×C4×C31C2311yescharacteristic
70C2×M16×C31—21no—
71C2×M16×C31—21no—
72C2×M16×C31—21no—
73C2×M16×C31—21no—
74C2×M16×C31—21no—
75C2×M16×C31—21no—
76C2×M16×C31—21no—
77C2×M16×C31—21no—
78C2×M16×C31—21no—
79C2×M16×C31—21no—
80C2×M16×C31—21no—
81C2×M16×C31D412yes—
82C22×C8×C31—21no—
83C22×C8×C31D412yes—
84C31×C4⋊Q8—24no—
85C31×C4⋊Q8—24no—
86C31×#124—24no—
87C31×#124—24no—
88C31×#123—28no—
89C31×#123—28no—
90C31×C22⋊Q8—28no—
91C31×C22⋊Q8—28no—
92C31×#117—21no—
93C31×#117—21no—
94C31×#117—21no—
95C31×#117—21no—
96C31×#117—21no—
97C31×#117—21no—
98C31×#117—21no—
99C31×#117—21no—
100C31×#117—21no—
101C31×#117C2×C412yes—
102C31×#117D412yes—
103C31×#117D412yes—
104C2×C4⋊C4×C31—24no—
105C2×C4⋊C4×C31—21no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31D412yes—
108C2×C22⋊C4×C31—24no—
109C2×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31D412yes—
112C2×C42×C31—21no—
113C2×C42×C31—21no—
114C2×C42×C31—21no—
115C31×#104—28no—
116C31×#103—28no—
117C31×#103—28no—
118C31×#103—24no—
119C31×#102—24no—
120C24×C31—21no—
121C24×C31C2×D411yescharacteristic
122#41×C31—22no—
123#41×C31—22no—
124#41×C31—22no—
125#41×C31—22no—
126#41×C31—22no—
127#41×C31—22no—
128#41×C31—22no—
129#41×C31—22no—
130#41×C31—41no—
131#41×C31—41no—
132#41×C31—41no—
133#41×C31—41no—
134#41×C31—41no—
135#41×C31—41no—
136#41×C31—41no—
137#41×C31—41no—
138C2×Q8×C31—22no—
139C2×Q8×C31—22no—
140C2×Q8×C31—22no—
141C2×Q8×C31—21no—
142C2×Q8×C31—22no—
143C2×Q8×C31—22no—
144C2×Q8×C31—22no—
145C2×Q8×C31—22no—
146C2×Q8×C31—22no—
147C2×Q8×C31—22no—
148C2×Q8×C31—21no—
149C2×Q8×C31—22no—
150C2×Q8×C31—22no—
151C2×Q8×C31—22no—
152C2×Q8×C31—22no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×Q8×C31—22no—
156C2×Q8×C31—22no—
157C2×Q8×C31—21no—
158C2×Q8×C31—41no—
159C2×Q8×C31—41no—
160C2×Q8×C31—41no—
161C2×Q8×C31—41no—
162C2×Q8×C31—41no—
163C2×Q8×C31—41no—
164C2×Q8×C31—41no—
165C2×Q8×C31—41no—
166C2×Q8×C31—41no—
167C2×Q8×C31—41no—
168C2×Q8×C31—41no—
169C2×Q8×C31—41no—
170C2×Q8×C31C22⋊C414yes—
171C2×Q8×C31C22⋊C412yes—
172C2×D4×C31—22no—
173C2×D4×C31—22no—
174C2×D4×C31—21no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—41no—
180C2×D4×C31—41no—
181C2×D4×C31—41no—
182C2×D4×C31—41no—
183C2×D4×C31C22⋊C412yes—
184C22×C4×C31—22no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—21no—
188C22×C4×C31—22no—
189C22×C4×C31—22no—
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—41no—
193C22×C4×C31—41no—
194C22×C4×C31—41no—
195C22×C4×C31—41no—
196C22×C4×C31—41no—
197C22×C4×C31—41no—
198C22×C4×C31—41no—
199C22×C4×C31—41no—
200C22×C4×C31—41no—
201C22×C4×C31C22×C411yescharacteristic
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31C2×D411yescharacteristic
204C22×C4×C31C2×D411yescharacteristic
205C22×C4×C31C2×D411yescharacteristic
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31C2×D411yescharacteristic
211C22×C4×C31#4111yescharacteristic
212C22×C4×C31#4111yescharacteristic
213C22×C4×C31#4111yescharacteristic
214C22×C4×C31#4111yescharacteristic
215M16×C31—22no—
216M16×C31—22no—
217M16×C31—41no—
218M16×C31—41no—
219M16×C31—41no—
220M16×C31—41no—
221M16×C31—41no—
222M16×C31—41no—
223C2×C8×C31—22no—
224C2×C8×C31—22no—
225C2×C8×C31—22no—
226C2×C8×C31—22no—
227C2×C8×C31—41no—
228C2×C8×C31—41no—
229C4⋊C4×C31—216no—
230C4⋊C4×C31—22no—
231C4⋊C4×C31—22no—
232C4⋊C4×C31—22no—
233C4⋊C4×C31—22no—
234C4⋊C4×C31—22no—
235C4⋊C4×C31—41no—
236C22⋊C4×C31—216no—
237C22⋊C4×C31—22no—
238C22⋊C4×C31—22no—
239C22⋊C4×C31—41no—
240C22⋊C4×C31—41no—
241C22⋊C4×C31—41no—
242C22⋊C4×C31C22⋊C414yes—
243C42×C31—22no—
244C42×C31—22no—
245C42×C31—22no—
246C42×C31—41no—
247C42×C31—41no—
248C42×C31—41no—
249#11005C3111yesmaximal, characteristic, direct product factor, Sylow
250C23×C31—22no—
251C23×C31—42no—
252C23×C31—44no—
253C23×C31—41no—
254C23×C31—41no—
255C23×C31C2×C22⋊C411yescharacteristic
256C23×C31#12011yescharacteristic
257C23×C31#12011yescharacteristic
258C23×C31#12111yescharacteristic
259C23×C31#12111yescharacteristic
260C23×C31#12411yescharacteristic
261C23×C31#12711yescharacteristic
262Q8×C31—24no—
263Q8×C31—24no—
264Q8×C31—22no—
265Q8×C31—22no—
266Q8×C31—42no—
267Q8×C31—42no—
268Q8×C31—42no—
269Q8×C31—42no—
270Q8×C31—41no—
271Q8×C31—42no—
272Q8×C31—42no—
273Q8×C31—41no—
274D4×C31—22no—
275D4×C31—22no—
276D4×C31—42no—
277D4×C31—42no—
278D4×C31—42no—
279D4×C31—42no—
280D4×C31—41no—
281D4×C31—41no—
282C2×C4×C31—24no—
283C2×C4×C31—24no—
284C2×C4×C31—22no—
285C2×C4×C31—44no—
286C2×C4×C31—42no—
287C2×C4×C31—42no—
288C2×C4×C31—42no—
289C2×C4×C31—41no—
290C2×C4×C31—42no—
291C2×C4×C31—41no—
292C2×C4×C31—42no—
293C2×C4×C31—42no—
294C2×C4×C31—42no—
295C2×C4×C31—42no—
296C2×C4×C31—42no—
297C2×C4×C31—42no—
298C2×C4×C31—42no—
299C2×C4×C31—42no—
300C2×C4×C31—82no—
301C2×C4×C31—82no—
302C2×C4×C31C2×C22⋊C411yescharacteristic
303C2×C4×C31C2×C22⋊C411yescharacteristic
304C2×C4×C31C4×D411yescharacteristic
305C2×C4×C31C4×D411yescharacteristic
306C2×C4×C31C4×D411yescharacteristic
307C2×C4×C31C4×D411yescharacteristic
308C2×C4×C31#12011yescharacteristic
309C2×C4×C31#12011yescharacteristic
310C2×C4×C31#12011yescharacteristic
311C2×C4×C31#12011yescharacteristic
312C2×C4×C31#12011yescharacteristic
313C2×C4×C31#12011yescharacteristic
314C2×C4×C31#12111yescharacteristic
315C2×C4×C31#12111yescharacteristic
316C2×C4×C31#12111yescharacteristic
317C2×C4×C31#12111yescharacteristic
318C2×C4×C31#12111yescharacteristic
319C2×C4×C31#12111yescharacteristic
320C2×C4×C31#12111yescharacteristic
321C2×C4×C31#12111yescharacteristic
322C2×C4×C31#12111yescharacteristic
323C2×C4×C31#12111yescharacteristic
324C2×C4×C31#12311yescharacteristic
325C2×C4×C31#12311yescharacteristic
326C2×C4×C31#12311yescharacteristic
327C2×C4×C31#12311yescharacteristic
328C2×C4×C31#12411yescharacteristic
329C2×C4×C31#12711yescharacteristic
330C8×C31—42no—
331C8×C31—42no—
332C2×#536C2×C3111yescharacteristic
333C2×#421C2×C3111yescharacteristic
334#2896C2×C3111yescharacteristic
335C2×#419C2×C3111yescharacteristic, complemented
336C2×#419C2×C3111yescharacteristic, complemented
337C2×#344C2×C3111yescharacteristic, complemented
338#1740C2×C3111yescharacteristic, complemented
339C22×C31—22no—
340C22×C31—22no—
341C22×C31—22no—
342C22×C31—41no—
343C22×C31—41no—
344C22×C31—41no—
345C22×C31—41no—
346C22×C31—44no—
347C22×C31—42no—
348C22×C31—82no—
349C22×C31—82no—
350C22×C31#37911yescharacteristic
351C22×C31#39011yescharacteristic
352C22×C31#39011yescharacteristic
353C22×C31#39211yescharacteristic
354C22×C31#39211yescharacteristic
355C22×C31#39411yescharacteristic
356C22×C31#39411yescharacteristic
357C4×C31—44no—
358C4×C31—42no—
359C4×C31—44no—
360C4×C31—82no—
361C4×C31—82no—
362C4×C31#38611yescharacteristic
363C4×C31#38611yescharacteristic
364C4×C31#38611yescharacteristic
365C4×C31#38611yescharacteristic
366C4×C31#39211yescharacteristic
367C4×C31#39211yescharacteristic
368C4×C31#39411yescharacteristic
369C4×C31#39411yescharacteristic
370C22×#41C22×C3111yescharacteristic
371C23×Q8C22×C3111yescharacteristic
372C22×M16C22×C3111yescharacteristic
373C22×M16C22×C3111yescharacteristic
374#536—22no—
375#536—22no—
376#536—22no—
377#536C4×C3114yescomplemented
378C2×C4⋊Q8—21no—
379C2×#124—21no—
380C2×#123—22no—
381C2×C22⋊Q8—22no—
382C2×#117C22×C3111yescharacteristic
383C2×#117C22×C3111yescharacteristic
384C2×#117C22×C3111yescharacteristic
385#421—22no—
386#421—22no—
387C2×#104—22no—
388#419—22no—
389#419—22no—
390#419—21no—
391#419—22no—
392#419—22no—
393#418—21no—
394#417—22no—
395#416—22no—
396C2×#103—22no—
397C2×#103—22no—
398#344—22no—
399#342—22no—
400C2×C31—21no—
401C2×C31—21no—
402C2×C31—21no—
403C2×C31—21no—
404C2×C31—21no—
405C2×C31—21no—
406C2×C31—82no—
407C2×C31#143811yescharacteristic
408C2×C31#200912yes—
409C2×#41—21no—
410C2×#41—21no—
411C2×#41—21no—
412C2×#41—21no—
413C2×#41—21no—
414C2×#41—21no—
415C2×#41—21no—
416C2×#41—21no—
417C2×#41—21no—
418C2×#41—21no—
419C2×#41C2×C4×C3112yes—
420C2×#41D4×C3112yes—
421C22×Q8—21no—
422C22×Q8—21no—
423C22×Q8—21no—
424C22×Q8—21no—
425C22×Q8—21no—
426C22×Q8—21no—
427C22×Q8—21no—
428C22×Q8—21no—
429C22×Q8—21no—
430C22×Q8—21no—
431C22×Q8—21no—
432C22×Q8C2×C4×C3112yes—
433C22×Q8D4×C3112yes—
434C22×Q8D4×C3111yescharacteristic
435C22×Q8D4×C3112yes—
436C22×D4—21no—
437C22×D4D4×C3111yescharacteristic
438C23×C4—21no—
439C23×C4—21no—
440C23×C4C23×C3111yescharacteristic
441C2×M16—21no—
442C2×M16—21no—
443C2×M16—21no—
444C2×M16—21no—
445C2×M16—21no—
446C2×M16—21no—
447C2×M16—21no—
448C2×M16—21no—
449C2×M16—21no—
450C2×M16—21no—
451C2×M16—21no—
452C2×M16D4×C3112yes—
453C22×C8—21no—
454C22×C8D4×C3112yes—
455C4⋊Q8—24no—
456C4⋊Q8—24no—
457#124—24no—
458#124—24no—
459#123—28no—
460#123—28no—
461C22⋊Q8—28no—
462C22⋊Q8—28no—
463#117—21no—
464#117—21no—
465#117—21no—
466#117—21no—
467#117—21no—
468#117—21no—
469#117—21no—
470#117—21no—
471#117—21no—
472#117C2×C4×C3112yes—
473#117D4×C3112yes—
474#117D4×C3112yes—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4D4×C3112yes—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4D4×C3112yes—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42—21no—
486#104—28no—
487#103—28no—
488#103—28no—
489#103—24no—
490#102—24no—
491C31#1100511yescharacteristic, direct product factor, Sylow
492C24—21no—
493C24C2×D4×C3111yescharacteristic
494#41—22no—
495#41—22no—
496#41—22no—
497#41—22no—
498#41—22no—
499#41—22no—
500#41—22no—
501#41—22no—
502#41—41no—
503#41—41no—
504#41—41no—
505#41—41no—
506#41—41no—
507#41—41no—
508#41—41no—
509#41—41no—
510C2×Q8—22no—
511C2×Q8—22no—
512C2×Q8—22no—
513C2×Q8—21no—
514C2×Q8—22no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—21no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—21no—
530C2×Q8—41no—
531C2×Q8—41no—
532C2×Q8—41no—
533C2×Q8—41no—
534C2×Q8—41no—
535C2×Q8—41no—
536C2×Q8—41no—
537C2×Q8—41no—
538C2×Q8—41no—
539C2×Q8—41no—
540C2×Q8—41no—
541C2×Q8—41no—
542C2×Q8C22⋊C4×C3114yes—
543C2×Q8C22⋊C4×C3112yes—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—41no—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4C22⋊C4×C3112yes—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4C22×C4×C3111yescharacteristic
574C22×C4C2×D4×C3111yescharacteristic
575C22×C4C2×D4×C3111yescharacteristic
576C22×C4C2×D4×C3111yescharacteristic
577C22×C4C2×D4×C3111yescharacteristic
578C22×C4C2×D4×C3111yescharacteristic
579C22×C4C2×D4×C3111yescharacteristic
580C22×C4C2×D4×C3111yescharacteristic
581C22×C4C2×D4×C3111yescharacteristic
582C22×C4C2×D4×C3111yescharacteristic
583C22×C4#41×C3111yescharacteristic
584C22×C4#41×C3111yescharacteristic
585C22×C4#41×C3111yescharacteristic
586C22×C4#41×C3111yescharacteristic
587M16—22no—
588M16—22no—
589M16—41no—
590M16—41no—
591M16—41no—
592M16—41no—
593M16—41no—
594M16—41no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—41no—
600C2×C8—41no—
601C4⋊C4—216no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—41no—
608C22⋊C4—216no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—41no—
612C22⋊C4—41no—
613C22⋊C4—41no—
614C22⋊C4C22⋊C4×C3114yes—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—41no—
619C42—41no—
620C42—41no—
621C23—22no—
622C23—42no—
623C23—44no—
624C23—41no—
625C23—41no—
626C23C2×C22⋊C4×C3111yescharacteristic
627C23C31×#12011yescharacteristic
628C23C31×#12011yescharacteristic
629C23C31×#12111yescharacteristic
630C23C31×#12111yescharacteristic
631C23C31×#12411yescharacteristic
632C23C31×#12711yescharacteristic
633Q8—24no—
634Q8—24no—
635Q8—22no—
636Q8—22no—
637Q8—42no—
638Q8—42no—
639Q8—42no—
640Q8—42no—
641Q8—41no—
642Q8—42no—
643Q8—42no—
644Q8—41no—
645D4—22no—
646D4—22no—
647D4—42no—
648D4—42no—
649D4—42no—
650D4—42no—
651D4—41no—
652D4—41no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—44no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—82no—
672C2×C4—82no—
673C2×C4C2×C22⋊C4×C3111yescharacteristic
674C2×C4C2×C22⋊C4×C3111yescharacteristic
675C2×C4C4×D4×C3111yescharacteristic
676C2×C4C4×D4×C3111yescharacteristic
677C2×C4C4×D4×C3111yescharacteristic
678C2×C4C4×D4×C3111yescharacteristic
679C2×C4C31×#12011yescharacteristic
680C2×C4C31×#12011yescharacteristic
681C2×C4C31×#12011yescharacteristic
682C2×C4C31×#12011yescharacteristic
683C2×C4C31×#12011yescharacteristic
684C2×C4C31×#12011yescharacteristic
685C2×C4C31×#12111yescharacteristic
686C2×C4C31×#12111yescharacteristic
687C2×C4C31×#12111yescharacteristic
688C2×C4C31×#12111yescharacteristic
689C2×C4C31×#12111yescharacteristic
690C2×C4C31×#12111yescharacteristic
691C2×C4C31×#12111yescharacteristic
692C2×C4C31×#12111yescharacteristic
693C2×C4C31×#12111yescharacteristic
694C2×C4C31×#12111yescharacteristic
695C2×C4C31×#12311yescharacteristic
696C2×C4C31×#12311yescharacteristic
697C2×C4C31×#12311yescharacteristic
698C2×C4C31×#12311yescharacteristic
699C2×C4C31×#12411yescharacteristic
700C2×C4C31×#12711yescharacteristic
701C8—42no—
702C8—42no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—44no—
711C22—42no—
712C22—82no—
713C22—82no—
714C22C31×#37911yescharacteristic
715C22C31×#39011yescharacteristic
716C22C31×#39011yescharacteristic
717C22C31×#39211yescharacteristic
718C22C31×#39211yescharacteristic
719C22C31×#39411yescharacteristic
720C22C31×#39411yescharacteristic
721C4—44no—
722C4—42no—
723C4—44no—
724C4—82no—
725C4—82no—
726C4C31×#38611yescharacteristic
727C4C31×#38611yescharacteristic
728C4C31×#38611yescharacteristic
729C4C31×#38611yescharacteristic
730C4C31×#39211yescharacteristic
731C4C31×#39211yescharacteristic
732C4C31×#39411yescharacteristic
733C4C31×#39411yescharacteristic
734C2—21no—
735C2—21no—
736C2—21no—
737C2—21no—
738C2—21no—
739C2—21no—
740C2—82no—
741C2C31×#143811yescharacteristic
742C2C31×#200912yes—
subgroupG/H
center, socleC22×C31#392
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC22×#41×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C31×#419C2semidirect
5. C2×C31×#419C2semidirect
6. C2×C31×#344C2semidirect
7. C31×#1740C2semidirect
15. C31×#536C4semidirect
249. #11005C31direct (N × H)
335. C2×#419C2×C31semidirect
336. C2×#419C2×C31semidirect
337. C2×#344C2×C31semidirect
338. #1740C2×C31semidirect
377. #536C4×C31semidirect
491. C31#11005direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5362
C2×C31×#4212
C31×#28962
C2×C31×#4192
C2×C31×#3442
C31×#17402
#1100531