Finite Group Databasebeta

← C31×#11021 #21467780

Subgroups — C31×#11021 #21467780

Order 7936.

1278 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#137C211yesmaximal, characteristic
2C2×C31×#417C211yesmaximal, characteristic
3C22×C31×#103C211yesmaximal, characteristic, complemented
4C22×C31×#101C211yesmaximal, characteristic, complemented
5C2×C31×#408C211yesmaximal, characteristic
6C2×C31×#343C211yesmaximal, characteristic, complemented
7C2×C31×#341C211yesmaximal, characteristic, complemented
8C22×#41×C31C2211yescharacteristic
9C23×Q8×C31C2211yescharacteristic
10C2×C31×#137—22no—
11C2×C31×#137—22no—
12C2×C31×#137—22no—
13C2×C31×#137—22no—
14C2×C31×#137—22no—
15C2×C31×#137C414yescomplemented
16C22×Q16×C31—21no—
17C22×SD16×C31—21no—
18C22×M16×C31C2211yescharacteristic
19C22×M16×C31C2211yescharacteristic
20C22×M16×C31C2211yescharacteristic
21C23×C8×C31C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C31×#417—22no—
24C31×#417—22no—
25C2×C31×#103—22no—
26C2×C31×#103—21no—
27C2×C31×#103—22no—
28C2×C31×#103—22no—
29C2×C31×#102—21no—
30C2×C31×#101—22no—
31C2×C31×#101—22no—
32C2×C31×#101—22no—
33C31×#408—22no—
34C31×#408—22no—
35C2×C31×C22⋊C8—22no—
36C31×#343—22no—
37C31×#341—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×C31—21no—
70C23×C4×C31C2311yescharacteristic
71C31×#137—28no—
72C31×#137—28no—
73C31×#137—28no—
74C31×#137—28no—
75C2×Q16×C31—24no—
76C2×Q16×C31—24no—
77C2×Q16×C31—24no—
78C2×SD16×C31—24no—
79C2×SD16×C31—24no—
80C2×SD16×C31—24no—
81C2×M16×C31—21no—
82C2×M16×C31—21no—
83C2×M16×C31—21no—
84C2×M16×C31—21no—
85C2×M16×C31—21no—
86C2×M16×C31—21no—
87C2×M16×C31—21no—
88C2×M16×C31—21no—
89C2×M16×C31—21no—
90C2×M16×C31—21no—
91C2×M16×C31—21no—
92C2×M16×C31—21no—
93C2×M16×C31—21no—
94C2×M16×C31C2×C412yes—
95C2×M16×C31D412yes—
96C2×M16×C31D412yes—
97C2×M16×C31D412yes—
98C2×M16×C31D412yes—
99C22×C8×C31—21no—
100C22×C8×C31—21no—
101C22×C8×C31—21no—
102C22×C8×C31—21no—
103C22×C8×C31—21no—
104C22×C8×C31—21no—
105C22×C8×C31—21no—
106C22×C8×C31—21no—
107C22×C8×C31—21no—
108C22×C8×C31D412yes—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31—21no—
114C2×C4⋊C4×C31D412yes—
115C31×#103—28no—
116C31×#103—24no—
117C31×#102—24no—
118C31×#101—28no—
119C31×C22⋊C8—28no—
120C24×C31—21no—
121C24×C31#4111yescharacteristic
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—21no—
148C2×Q8×C31—22no—
149C2×Q8×C31—22no—
150C2×Q8×C31—21no—
151C2×Q8×C31—21no—
152C2×Q8×C31—22no—
153C2×Q8×C31—22no—
154C2×Q8×C31—22no—
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⋊C412yes—
171C2×Q8×C31C22⋊C414yes—
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—21no—
187C22×C4×C31—22no—
188C22×C4×C31—22no—
189C22×C4×C31—22no—
190C22×C4×C31—22no—
191C22×C4×C31—41no—
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×C31—82no—
202C22×C4×C31C22×C411yescharacteristic
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×C31C2×D411yescharacteristic
212C22×C4×C31C2×D411yescharacteristic
213C22×C4×C31#4111yescharacteristic
214C22×C4×C31#4111yescharacteristic
215C22×C4×C31#4111yescharacteristic
216Q16×C31—216no—
217SD16×C31—216no—
218M16×C31—22no—
219M16×C31—22no—
220M16×C31—22no—
221M16×C31—22no—
222M16×C31—22no—
223M16×C31—22no—
224M16×C31—22no—
225M16×C31—41no—
226M16×C31—41no—
227M16×C31—41no—
228M16×C31—41no—
229M16×C31C22⋊C414yes—
230C2×C8×C31—22no—
231C2×C8×C31—22no—
232C2×C8×C31—22no—
233C2×C8×C31—22no—
234C2×C8×C31—22no—
235C2×C8×C31—22no—
236C2×C8×C31—22no—
237C2×C8×C31—22no—
238C2×C8×C31—41no—
239C2×C8×C31—41no—
240C2×C8×C31—41no—
241C2×C8×C31—41no—
242C2×C8×C31—41no—
243C2×C8×C31—41no—
244C2×C8×C31—41no—
245C2×C8×C31—41no—
246C4⋊C4×C31—22no—
247C4⋊C4×C31—22no—
248C4⋊C4×C31—41no—
249C4⋊C4×C31—41no—
250#11021C3111yesmaximal, characteristic, direct product factor, Sylow
251C23×C31—22no—
252C23×C31—22no—
253C23×C31—22no—
254C23×C31—41no—
255C23×C31—41no—
256C23×C31—42no—
257C23×C31—42no—
258C23×C31C4×D411yescharacteristic
259C23×C31#12111yescharacteristic
260C23×C31#12111yescharacteristic
261C23×C31#12111yescharacteristic
262C23×C31#12311yescharacteristic
263C23×C31#12311yescharacteristic
264C23×C31#12411yescharacteristic
265Q8×C31—24no—
266Q8×C31—22no—
267Q8×C31—24no—
268Q8×C31—22no—
269Q8×C31—42no—
270Q8×C31—42no—
271Q8×C31—42no—
272Q8×C31—42no—
273Q8×C31—42no—
274Q8×C31—41no—
275Q8×C31—42no—
276Q8×C31—41no—
277D4×C31—22no—
278D4×C31—22no—
279D4×C31—42no—
280D4×C31—42no—
281D4×C31—42no—
282D4×C31—42no—
283D4×C31—41no—
284D4×C31—41no—
285C2×C4×C31—22no—
286C2×C4×C31—24no—
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×C31—82no—
303C2×C4×C31C2×C22⋊C411yescharacteristic
304C2×C4×C31C2×C22⋊C411yescharacteristic
305C2×C4×C31C2×C22⋊C411yescharacteristic
306C2×C4×C31C4×D411yescharacteristic
307C2×C4×C31C4×D411yescharacteristic
308C2×C4×C31C4×D411yescharacteristic
309C2×C4×C31#12011yescharacteristic
310C2×C4×C31#12011yescharacteristic
311C2×C4×C31#12011yescharacteristic
312C2×C4×C31#12011yescharacteristic
313C2×C4×C31#12011yescharacteristic
314C2×C4×C31#12011yescharacteristic
315C2×C4×C31#12011yescharacteristic
316C2×C4×C31#12011yescharacteristic
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#12111yescharacteristic
325C2×C4×C31#12111yescharacteristic
326C2×C4×C31#12311yescharacteristic
327C2×C4×C31#12311yescharacteristic
328C2×C4×C31#12411yescharacteristic
329C2×C4×C31#12711yescharacteristic
330C2×C4×C31#12711yescharacteristic
331C8×C31—24no—
332C8×C31—42no—
333C8×C31—42no—
334C8×C31—42no—
335C22×#137C2×C3111yescharacteristic
336C2×#417C2×C3111yescharacteristic
337C22×#103C2×C3111yescharacteristic, complemented
338C22×#101C2×C3111yescharacteristic, complemented
339C2×#408C2×C3111yescharacteristic
340C2×#343C2×C3111yescharacteristic, complemented
341C2×#341C2×C3111yescharacteristic, complemented
342C22×C31—22no—
343C22×C31—22no—
344C22×C31—22no—
345C22×C31—22no—
346C22×C31—21no—
347C22×C31—21no—
348C22×C31—21no—
349C22×C31—21no—
350C22×C31—44no—
351C22×C31—42no—
352C22×C31—82no—
353C22×C31—81no—
354C22×C31—81no—
355C22×C31#38611yescharacteristic
356C22×C31#38611yescharacteristic
357C22×C31#39011yescharacteristic
358C22×C31#39211yescharacteristic
359C22×C31#39411yescharacteristic
360C22×C31#39411yescharacteristic
361C22×C31#39411yescharacteristic
362C22×C31#47112yes—
363C22×C31#47312yes—
364C4×C31—42no—
365C4×C31—44no—
366C4×C31—82no—
367C4×C31#37911yescharacteristic
368C4×C31#38611yescharacteristic
369C4×C31#38611yescharacteristic
370C4×C31#39011yescharacteristic
371C4×C31#39211yescharacteristic
372C4×C31#39211yescharacteristic
373C4×C31#39211yescharacteristic
374C4×C31#39411yescharacteristic
375C22×#41C22×C3111yescharacteristic
376C23×Q8C22×C3111yescharacteristic
377C2×#137—22no—
378C2×#137—22no—
379C2×#137—22no—
380C2×#137—22no—
381C2×#137—22no—
382C2×#137C4×C3114yescomplemented
383C22×Q16—21no—
384C22×SD16—21no—
385C22×M16C22×C3111yescharacteristic
386C22×M16C22×C3111yescharacteristic
387C22×M16C22×C3111yescharacteristic
388C23×C8C22×C3111yescharacteristic
389C22×C4⋊C4C22×C3111yescharacteristic
390#417—22no—
391#417—22no—
392C2×#103—22no—
393C2×#103—21no—
394C2×#103—22no—
395C2×#103—22no—
396C2×#102—21no—
397C2×#101—22no—
398C2×#101—22no—
399C2×#101—22no—
400#408—22no—
401#408—22no—
402C2×C22⋊C8—22no—
403#343—22no—
404#341—22no—
405C2×C31—21no—
406C2×C31—21no—
407C2×C31—21no—
408C2×C31—21no—
409C2×C31—82no—
410C2×C31#143811yescharacteristic
411C2×C31#190812yes—
412C2×C31#201911yescharacteristic
413C2×C31#202011yescharacteristic
414C2×C31#205212yes—
415C2×#41—21no—
416C2×#41—21no—
417C2×#41—21no—
418C2×#41—21no—
419C2×#41—21no—
420C2×#41—21no—
421C2×#41—21no—
422C2×#41—21no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41C2×C4×C3112yes—
426C2×#41D4×C3112yes—
427C22×Q8—21no—
428C22×Q8—21no—
429C22×Q8—21no—
430C22×Q8—21no—
431C22×Q8—21no—
432C22×Q8—21no—
433C22×Q8—21no—
434C22×Q8—21no—
435C22×Q8—21no—
436C22×Q8—21no—
437C22×Q8—21no—
438C22×Q8C2×C4×C3112yes—
439C22×Q8D4×C3111yescharacteristic
440C22×Q8D4×C3112yes—
441C22×Q8D4×C3112yes—
442C22×D4—21no—
443C22×D4D4×C3111yescharacteristic
444C23×C4—21no—
445C23×C4—21no—
446C23×C4—21no—
447C23×C4C23×C3111yescharacteristic
448#137—28no—
449#137—28no—
450#137—28no—
451#137—28no—
452C2×Q16—24no—
453C2×Q16—24no—
454C2×Q16—24no—
455C2×SD16—24no—
456C2×SD16—24no—
457C2×SD16—24no—
458C2×M16—21no—
459C2×M16—21no—
460C2×M16—21no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—21no—
465C2×M16—21no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—21no—
470C2×M16—21no—
471C2×M16C2×C4×C3112yes—
472C2×M16D4×C3112yes—
473C2×M16D4×C3112yes—
474C2×M16D4×C3112yes—
475C2×M16D4×C3112yes—
476C22×C8—21no—
477C22×C8—21no—
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—21no—
483C22×C8—21no—
484C22×C8—21no—
485C22×C8D4×C3112yes—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4D4×C3112yes—
492#103—28no—
493#103—24no—
494#102—24no—
495#101—28no—
496C22⋊C8—28no—
497C31#1102111yescharacteristic, direct product factor, Sylow
498C24—21no—
499C24#41×C3111yescharacteristic
500#41—22no—
501#41—22no—
502#41—22no—
503#41—22no—
504#41—22no—
505#41—22no—
506#41—22no—
507#41—22no—
508#41—41no—
509#41—41no—
510#41—41no—
511#41—41no—
512#41—41no—
513#41—41no—
514#41—41no—
515#41—41no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—21no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—21no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—22no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—21no—
536C2×Q8—41no—
537C2×Q8—41no—
538C2×Q8—41no—
539C2×Q8—41no—
540C2×Q8—41no—
541C2×Q8—41no—
542C2×Q8—41no—
543C2×Q8—41no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—41no—
547C2×Q8—41no—
548C2×Q8C22⋊C4×C3112yes—
549C2×Q8C22⋊C4×C3114yes—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4C22⋊C4×C3112yes—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—82no—
580C22×C4C22×C4×C3111yescharacteristic
581C22×C4C2×D4×C3111yescharacteristic
582C22×C4C2×D4×C3111yescharacteristic
583C22×C4C2×D4×C3111yescharacteristic
584C22×C4C2×D4×C3111yescharacteristic
585C22×C4C2×D4×C3111yescharacteristic
586C22×C4C2×D4×C3111yescharacteristic
587C22×C4C2×D4×C3111yescharacteristic
588C22×C4C2×D4×C3111yescharacteristic
589C22×C4C2×D4×C3111yescharacteristic
590C22×C4C2×D4×C3111yescharacteristic
591C22×C4#41×C3111yescharacteristic
592C22×C4#41×C3111yescharacteristic
593C22×C4#41×C3111yescharacteristic
594Q16—216no—
595SD16—216no—
596M16—22no—
597M16—22no—
598M16—22no—
599M16—22no—
600M16—22no—
601M16—22no—
602M16—22no—
603M16—41no—
604M16—41no—
605M16—41no—
606M16—41no—
607M16C22⋊C4×C3114yes—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—41no—
617C2×C8—41no—
618C2×C8—41no—
619C2×C8—41no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—42no—
632C23—42no—
633C23—41no—
634C23—41no—
635C23C4×D4×C3111yescharacteristic
636C23C31×#12111yescharacteristic
637C23C31×#12111yescharacteristic
638C23C31×#12111yescharacteristic
639C23C31×#12311yescharacteristic
640C23C31×#12311yescharacteristic
641C23C31×#12411yescharacteristic
642Q8—24no—
643Q8—22no—
644Q8—24no—
645Q8—22no—
646Q8—42no—
647Q8—42no—
648Q8—42no—
649Q8—42no—
650Q8—42no—
651Q8—41no—
652Q8—42no—
653Q8—41no—
654D4—22no—
655D4—22no—
656D4—42no—
657D4—42no—
658D4—42no—
659D4—42no—
660D4—41no—
661D4—41no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—82no—
678C2×C4—82no—
679C2×C4—82no—
680C2×C4C2×C22⋊C4×C3111yescharacteristic
681C2×C4C2×C22⋊C4×C3111yescharacteristic
682C2×C4C2×C22⋊C4×C3111yescharacteristic
683C2×C4C4×D4×C3111yescharacteristic
684C2×C4C4×D4×C3111yescharacteristic
685C2×C4C4×D4×C3111yescharacteristic
686C2×C4C31×#12011yescharacteristic
687C2×C4C31×#12011yescharacteristic
688C2×C4C31×#12011yescharacteristic
689C2×C4C31×#12011yescharacteristic
690C2×C4C31×#12011yescharacteristic
691C2×C4C31×#12011yescharacteristic
692C2×C4C31×#12011yescharacteristic
693C2×C4C31×#12011yescharacteristic
694C2×C4C31×#12111yescharacteristic
695C2×C4C31×#12111yescharacteristic
696C2×C4C31×#12111yescharacteristic
697C2×C4C31×#12111yescharacteristic
698C2×C4C31×#12111yescharacteristic
699C2×C4C31×#12111yescharacteristic
700C2×C4C31×#12111yescharacteristic
701C2×C4C31×#12111yescharacteristic
702C2×C4C31×#12111yescharacteristic
703C2×C4C31×#12311yescharacteristic
704C2×C4C31×#12311yescharacteristic
705C2×C4C31×#12411yescharacteristic
706C2×C4C31×#12711yescharacteristic
707C2×C4C31×#12711yescharacteristic
708C8—24no—
709C8—42no—
710C8—42no—
711C8—42no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—44no—
721C22—42no—
722C22—82no—
723C22—81no—
724C22—81no—
725C22C31×#38611yescharacteristic
726C22C31×#38611yescharacteristic
727C22C31×#39011yescharacteristic
728C22C31×#39211yescharacteristic
729C22C31×#39411yescharacteristic
730C22C31×#39411yescharacteristic
731C22C31×#39411yescharacteristic
732C22C31×#47112yes—
733C22C31×#47312yes—
734C4—42no—
735C4—44no—
736C4—82no—
737C4C31×#37911yescharacteristic
738C4C31×#38611yescharacteristic
739C4C31×#38611yescharacteristic
740C4C31×#39011yescharacteristic
741C4C31×#39211yescharacteristic
742C4C31×#39211yescharacteristic
743C4C31×#39211yescharacteristic
744C4C31×#39411yescharacteristic
745C2—21no—
746C2—21no—
747C2—21no—
748C2—21no—
749C2—82no—
750C2C31×#143811yescharacteristic
751C2C31×#190812yes—
752C2C31×#201911yescharacteristic
753C2C31×#202011yescharacteristic
754C2C31×#205212yes—
subgroupG/H
center, socleC23×C31#121
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
prime radicalC22×#41×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C22×C31×#103C2semidirect
4. C22×C31×#101C2semidirect
6. C2×C31×#343C2semidirect
7. C2×C31×#341C2semidirect
15. C2×C31×#137C4semidirect
250. #11021C31direct (N × H)
337. C22×#103C2×C31semidirect
338. C22×#101C2×C31semidirect
340. C2×#343C2×C31semidirect
341. C2×#341C2×C31semidirect
382. C2×#137C4×C31semidirect
497. C31#11021direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1372
C2×C31×#4172
C22×C31×#1032
C22×C31×#1012
C2×C31×#4082
C2×C31×#3432
C2×C31×#3412
#1102131