Finite Group Databasebeta

← C31×#24364 #21481123

Subgroups — C31×#24364 #21481123

Order 7936.

1512 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#135C211yesmaximal, characteristic, complemented
2C2×C31×#463C211yesmaximal, characteristic, complemented
3C2×C31×#459C211yesmaximal, characteristic, complemented
4C2×C31×#449C211yesmaximal, characteristic, complemented
5C31×#2431C211yesmaximal, characteristic, complemented
6C31×#2339C211yesmaximal, characteristic, complemented
7C31×#2056C211yesmaximal, characteristic, complemented
8C31×#2055C211yesmaximal, characteristic, complemented
9C31×#2015C211yesmaximal, characteristic, complemented
10C31×#2014C211yesmaximal, characteristic, complemented
11C31×#1893C211yesmaximal, characteristic, complemented
12C31×#1879C211yesmaximal, characteristic, complemented
13C31×#1877C211yesmaximal, characteristic, complemented
14C31×#1850C211yesmaximal, characteristic, complemented
15C31×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×#41×C31C2211yescharacteristic
18C2×C31×#135—24no—
19C2×C31×#135—24no—
20C2×C31×#135—24no—
21C22×Q16×C31C2211yescharacteristic
22C22×SD16×C31C2211yescharacteristic
23C22×SD16×C31C2211yescharacteristic
24C22×SD16×C31C2211yescharacteristic
25C22×D8×C31C2211yescharacteristic
26C22×D8×C31C2211yescharacteristic
27C23×C8×C31C2211yescharacteristic
28C2×C31×#127C2211yescharacteristic
29C2×C31×#124C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic
31C2×C4×D4×C31C2211yescharacteristic
32C2×C4×D4×C31C2211yescharacteristic
33C31×#463—24no—
34C31×#459—24no—
35C31×#449—24no—
36C2×C31×C4⋊C8C2211yescharacteristic
37C2×C31×C4⋊C8C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C31×#392—21no—
48C31×#392—21no—
49C31×#391C2211yescharacteristic
50C31×#391C2211yescharacteristic
51C31×#391C2211yescharacteristic
52C31×#390C2211yescharacteristic
53C31×#386—21no—
54C31×#386—21no—
55C31×#386—21no—
56C31×#386—21no—
57C31×#381—21no—
58C31×#380C2211yescharacteristic
59C4×C22⋊C4×C31C2211yescharacteristic
60C2×C31×#95—21no—
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C31×#336C2211yescharacteristic
64C31×#336C2211yescharacteristic
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—22no—
69C2×#41×C31—22no—
70C2×#41×C31—22no—
71C2×#41×C31—22no—
72C2×#41×C31—41no—
73C2×#41×C31—41no—
74C2×#41×C31—41no—
75C2×#41×C31—41no—
76C2×#41×C31D414yescomplemented
77C22×Q8×C31C2311yescharacteristic
78C22×Q8×C31C2311yescharacteristic
79C22×D4×C31—21no—
80C22×D4×C31—21no—
81C22×D4×C31—21no—
82C22×D4×C31—21no—
83C22×D4×C31—21no—
84C22×D4×C31C2311yescharacteristic
85C22×D4×C31C2311yescharacteristic
86C22×D4×C31C2311yescharacteristic
87C23×C4×C31—21no—
88C23×C4×C31—21no—
89C23×C4×C31—21no—
90C23×C4×C31—21no—
91C23×C4×C31C2311yescharacteristic
92C31×#135—232no—
93C2×Q16×C31—22no—
94C2×Q16×C31—22no—
95C2×Q16×C31—22no—
96C2×SD16×C31—22no—
97C2×SD16×C31—22no—
98C2×SD16×C31—22no—
99C2×SD16×C31—22no—
100C2×SD16×C31—22no—
101C2×SD16×C31—22no—
102C2×SD16×C31—41no—
103C2×SD16×C31—41no—
104C2×SD16×C31D414yescomplemented
105C2×D8×C31—22no—
106C2×D8×C31—22no—
107C2×D8×C31—22no—
108C2×D8×C31—22no—
109C2×D8×C31—22no—
110C2×D8×C31D414yescomplemented
111C22×C8×C31—22no—
112C22×C8×C31—22no—
113C22×C8×C31—22no—
114C22×C8×C31C2311yescharacteristic
115C22×C8×C31C2311yescharacteristic
116C22×C8×C31C2311yescharacteristic
117C22×C8×C31C2311yescharacteristic
118C31×#127—22no—
119C31×#127—41no—
120C31×#124—22no—
121C31×#124—41no—
122C31×#121—22no—
123C31×#121—22no—
124C4×D4×C31—22no—
125C4×D4×C31—22no—
126C4×D4×C31—41no—
127C4×D4×C31—41no—
128C2×C4⋊C4×C31C2311yescharacteristic
129C2×C4⋊C4×C31C2311yescharacteristic
130C2×C4⋊C4×C31C2311yescharacteristic
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31—21no—
134C2×C22⋊C4×C31—21no—
135C2×C22⋊C4×C31—21no—
136C2×C22⋊C4×C31—21no—
137C2×C22⋊C4×C31—21no—
138C2×C22⋊C4×C31—21no—
139C2×C22⋊C4×C31D411yescharacteristic
140C2×C22⋊C4×C31D411yescharacteristic
141C2×C42×C31C2311yescharacteristic
142C2×C42×C31C2311yescharacteristic
143C31×C4⋊C8—22no—
144C31×C4⋊C8—22no—
145C31×#103—22no—
146C31×#103—22no—
147C31×#103—41no—
148C31×#102—22no—
149C31×#102—22no—
150C31×#102—22no—
151C31×#102—22no—
152C31×#102—41no—
153C31×C22⋊C8—22no—
154C31×#95—21no—
155C31×#95—21no—
156C31×#95—21no—
157C31×#95—21no—
158C31×#95—21no—
159C31×#95—21no—
160C31×#95—21no—
161C31×#95D411yescharacteristic
162C31×#95D411yescharacteristic
163C24×C31—21no—
164C24×C31—21no—
165C24×C31—21no—
166C24×C31C2×D411yescharacteristic
167#41×C31—28no—
168#41×C31—28no—
169#41×C31—44no—
170#41×C31—44no—
171#41×C31—44no—
172#41×C31—44no—
173#41×C31—44no—
174#41×C31—44no—
175C2×Q8×C31—21no—
176C2×Q8×C31—21no—
177C2×Q8×C31—21no—
178C2×Q8×C31—21no—
179C2×Q8×C31—21no—
180C2×Q8×C31—21no—
181C2×Q8×C31—21no—
182C2×Q8×C31—21no—
183C2×Q8×C31—21no—
184C2×Q8×C31—21no—
185C2×Q8×C31C2×D412yes—
186C2×Q8×C31C2×D412yes—
187C2×D4×C31—24no—
188C2×D4×C31—21no—
189C2×D4×C31—21no—
190C2×D4×C31—21no—
191C2×D4×C31—21no—
192C2×D4×C31—21no—
193C2×D4×C31—21no—
194C2×D4×C31—21no—
195C2×D4×C31—21no—
196C2×D4×C31—21no—
197C2×D4×C31—21no—
198C2×D4×C31—21no—
199C2×D4×C31—21no—
200C2×D4×C31—21no—
201C2×D4×C31—21no—
202C2×D4×C31—42no—
203C2×D4×C31—42no—
204C2×D4×C31—42no—
205C2×D4×C31—42no—
206C2×D4×C31—42no—
207C2×D4×C31—42no—
208C2×D4×C31—42no—
209C2×D4×C31—42no—
210C2×D4×C31—42no—
211C2×D4×C31—42no—
212C2×D4×C31—81no—
213C2×D4×C31—81no—
214C2×D4×C31—81no—
215C2×D4×C31—81no—
216C2×D4×C31C2×D412yes—
217C2×D4×C31C2×D412yes—
218C2×D4×C31C2×D412yes—
219C2×D4×C31C2×D412yes—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31—24no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
229C22×C4×C31—21no—
230C22×C4×C31—42no—
231C22×C4×C31—42no—
232C22×C4×C31—42no—
233C22×C4×C31—42no—
234C22×C4×C31—42no—
235C22×C4×C31—42no—
236C22×C4×C31—42no—
237C22×C4×C31—42no—
238C22×C4×C31—42no—
239C22×C4×C31—81no—
240C22×C4×C31—81no—
241C22×C4×C31C2×D411yescharacteristic
242C22×C4×C31C2×D411yescharacteristic
243C22×C4×C31C2×D411yescharacteristic
244C22×C4×C31C2×D411yescharacteristic
245C22×C4×C31C2×D412yes—
246C22×C4×C31C2×D411yescharacteristic
247C22×C4×C31#4112yes—
248C22×C4×C31C2411yescharacteristic
249Q16×C31—28no—
250SD16×C31—28no—
251SD16×C31—28no—
252SD16×C31—44no—
253D8×C31—28no—
254D8×C31—44no—
255C2×C8×C31—28no—
256C2×C8×C31—21no—
257C2×C8×C31—21no—
258C2×C8×C31—21no—
259C2×C8×C31—21no—
260C2×C8×C31—21no—
261C2×C8×C31—21no—
262C2×C8×C31—21no—
263C2×C8×C31—21no—
264C2×C8×C31—21no—
265C2×C8×C31—21no—
266C2×C8×C31C2×D412yes—
267C2×C8×C31C2×D412yes—
268C4⋊C4×C31—21no—
269C4⋊C4×C31—21no—
270C4⋊C4×C31—21no—
271C4⋊C4×C31—21no—
272C4⋊C4×C31—21no—
273C4⋊C4×C31—21no—
274C22⋊C4×C31—22no—
275C22⋊C4×C31—41no—
276C22⋊C4×C31—42no—
277C22⋊C4×C31—42no—
278C22⋊C4×C31—42no—
279C22⋊C4×C31—42no—
280C22⋊C4×C31—42no—
281C22⋊C4×C31—81no—
282C22⋊C4×C31—81no—
283C22⋊C4×C31—81no—
284C42×C31—21no—
285C42×C31—21no—
286C42×C31—21no—
287C42×C31—21no—
288#24364C3111yesmaximal, characteristic, direct product factor, Sylow
289C23×C31—22no—
290C23×C31—22no—
291C23×C31—22no—
292C23×C31—21no—
293C23×C31—21no—
294C23×C31—21no—
295C23×C31—21no—
296C23×C31—21no—
297C23×C31—21no—
298C23×C31—22no—
299C23×C31—41no—
300C23×C31—41no—
301C23×C31—41no—
302C23×C31—41no—
303C23×C31—41no—
304C23×C31—41no—
305C23×C31—41no—
306C23×C31—41no—
307C23×C31—41no—
308C23×C31—41no—
309C23×C31—41no—
310C23×C31—41no—
311C23×C31—41no—
312C23×C31—41no—
313C23×C31—41no—
314C23×C31—41no—
315C23×C31—41no—
316C23×C31#12112yes—
317C23×C31C22×D411yescharacteristic
318Q8×C31—22no—
319Q8×C31—22no—
320Q8×C31—22no—
321Q8×C31—22no—
322Q8×C31—41no—
323Q8×C31—41no—
324Q8×C31—41no—
325Q8×C31—41no—
326D4×C31—22no—
327D4×C31—22no—
328D4×C31—22no—
329D4×C31—22no—
330D4×C31—22no—
331D4×C31—48no—
332D4×C31—48no—
333D4×C31—41no—
334D4×C31—41no—
335D4×C31—41no—
336D4×C31—41no—
337D4×C31—41no—
338D4×C31—41no—
339D4×C31—84no—
340D4×C31—84no—
341D4×C31—84no—
342D4×C31#12014yes—
343C2×C4×C31—21no—
344C2×C4×C31—21no—
345C2×C4×C31—21no—
346C2×C4×C31—21no—
347C2×C4×C31—22no—
348C2×C4×C31—22no—
349C2×C4×C31—22no—
350C2×C4×C31—22no—
351C2×C4×C31—22no—
352C2×C4×C31—21no—
353C2×C4×C31—21no—
354C2×C4×C31—21no—
355C2×C4×C31—22no—
356C2×C4×C31—21no—
357C2×C4×C31—21no—
358C2×C4×C31—21no—
359C2×C4×C31—21no—
360C2×C4×C31—21no—
361C2×C4×C31—21no—
362C2×C4×C31—48no—
363C2×C4×C31—48no—
364C2×C4×C31—41no—
365C2×C4×C31—41no—
366C2×C4×C31—41no—
367C2×C4×C31—41no—
368C2×C4×C31—41no—
369C2×C4×C31—41no—
370C2×C4×C31—41no—
371C2×C4×C31—41no—
372C2×C4×C31—41no—
373C2×C4×C31—41no—
374C2×C4×C31—41no—
375C2×C4×C31—41no—
376C2×C4×C31—41no—
377C2×C4×C31—84no—
378C2×C4×C31—84no—
379C2×C4×C31#12112yes—
380C2×C4×C31#13512yescomplemented
381C2×C4×C31C22×D411yescharacteristic
382C2×C4×C31C22×D411yescharacteristic
383C2×C4×C31C22×D411yescharacteristic
384C2×C4×C31C2×#4111yescharacteristic
385C2×C4×C31H(5,𝔽2)11yescharacteristic
386C2×C4×C31H(5,𝔽2)11yescharacteristic
387C8×C31—22no—
388C8×C31—22no—
389C8×C31—41no—
390C8×C31—41no—
391C22×#135C2×C3111yescharacteristic, complemented
392C2×#463C2×C3111yescharacteristic, complemented
393C2×#459C2×C3111yescharacteristic, complemented
394C2×#449C2×C3111yescharacteristic, complemented
395#2431C2×C3111yescharacteristic, complemented
396#2339C2×C3111yescharacteristic, complemented
397#2056C2×C3111yescharacteristic, complemented
398#2055C2×C3111yescharacteristic, complemented
399#2015C2×C3111yescharacteristic, complemented
400#2014C2×C3111yescharacteristic, complemented
401#1893C2×C3111yescharacteristic, complemented
402#1879C2×C3111yescharacteristic, complemented
403#1877C2×C3111yescharacteristic, complemented
404#1850C2×C3111yescharacteristic, complemented
405#1788C2×C3111yescharacteristic, complemented
406C22×C31—22no—
407C22×C31—24no—
408C22×C31—22no—
409C22×C31—22no—
410C22×C31—41no—
411C22×C31—42no—
412C22×C31—42no—
413C22×C31—41no—
414C22×C31—42no—
415C22×C31—41no—
416C22×C31—41no—
417C22×C31—42no—
418C22×C31—42no—
419C22×C31—42no—
420C22×C31—42no—
421C22×C31—42no—
422C22×C31—42no—
423C22×C31—81no—
424C22×C31—81no—
425C22×C31—81no—
426C22×C31—81no—
427C22×C31—81no—
428C22×C31—81no—
429C22×C31—81no—
430C22×C31—81no—
431C22×C31—81no—
432C22×C31—81no—
433C22×C31—81no—
434C22×C31C2×#12111yescharacteristic
435C22×C31D4211yescharacteristic
436C22×C31D4211yescharacteristic
437C22×C31C2×#13511yescharacteristic
438C22×C31#57511yescharacteristic
439C22×C31#57611yescharacteristic
440C22×C31#57711yescharacteristic
441C4×C31—22no—
442C4×C31—22no—
443C4×C31—42no—
444C4×C31—42no—
445C4×C31—41no—
446C4×C31—41no—
447C4×C31—41no—
448C4×C31—81no—
449C4×C31—81no—
450C4×C31—81no—
451C4×C31C2×#12011yescharacteristic
452C4×C31#53411yescharacteristic
453C4×C31#54611yescharacteristic
454C4×C31#54611yescharacteristic
455C22×#41C22×C3111yescharacteristic
456C22×#41C22×C3111yescharacteristic
457C2×#135—24no—
458C2×#135—24no—
459C2×#135—24no—
460C22×Q16C22×C3111yescharacteristic
461C22×SD16C22×C3111yescharacteristic
462C22×SD16C22×C3111yescharacteristic
463C22×SD16C22×C3111yescharacteristic
464C22×D8C22×C3111yescharacteristic
465C22×D8C22×C3111yescharacteristic
466C23×C8C22×C3111yescharacteristic
467C2×#127C22×C3111yescharacteristic
468C2×#124C22×C3111yescharacteristic
469C2×#121C22×C3111yescharacteristic
470C2×C4×D4C22×C3111yescharacteristic
471C2×C4×D4C22×C3111yescharacteristic
472#463—24no—
473#459—24no—
474#449—24no—
475C2×C4⋊C8C22×C3111yescharacteristic
476C2×C4⋊C8C22×C3111yescharacteristic
477C2×#103C22×C3111yescharacteristic
478C2×#103C22×C3111yescharacteristic
479C2×#103C22×C3111yescharacteristic
480C2×#102C22×C3111yescharacteristic
481C2×#102C22×C3111yescharacteristic
482C2×#102C22×C3111yescharacteristic
483C2×#102C22×C3111yescharacteristic
484C2×#102C22×C3111yescharacteristic
485C2×C22⋊C8C22×C3111yescharacteristic
486#392—21no—
487#392—21no—
488#391C22×C3111yescharacteristic
489#391C22×C3111yescharacteristic
490#391C22×C3111yescharacteristic
491#390C22×C3111yescharacteristic
492#386—21no—
493#386—21no—
494#386—21no—
495#386—21no—
496#381—21no—
497#380C22×C3111yescharacteristic
498C4×C22⋊C4C22×C3111yescharacteristic
499C2×#95—21no—
500#340C22×C3111yescharacteristic
501#340C22×C3111yescharacteristic
502#336C22×C3111yescharacteristic
503#336C22×C3111yescharacteristic
504C2×C31—42no—
505C2×C31—44no—
506C2×C31—82no—
507C2×C31—161no—
508C2×C31#241011yescharacteristic
509C2×C31#303511yescharacteristic
510C2×C31#304511yescharacteristic
511C2×C31#326711yescharacteristic
512C2×C31#326811yescharacteristic
513C2×C31#328011yescharacteristic
514C2×C31#328411yescharacteristic
515C2×#41—22no—
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41—41no—
525C2×#41—41no—
526C2×#41D4×C3114yescomplemented
527C22×Q8C23×C3111yescharacteristic
528C22×Q8C23×C3111yescharacteristic
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4C23×C3111yescharacteristic
535C22×D4C23×C3111yescharacteristic
536C22×D4C23×C3111yescharacteristic
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4C23×C3111yescharacteristic
542#135—232no—
543C2×Q16—22no—
544C2×Q16—22no—
545C2×Q16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16D4×C3114yescomplemented
555C2×D8—22no—
556C2×D8—22no—
557C2×D8—22no—
558C2×D8—22no—
559C2×D8—22no—
560C2×D8D4×C3114yescomplemented
561C22×C8—22no—
562C22×C8—22no—
563C22×C8—22no—
564C22×C8C23×C3111yescharacteristic
565C22×C8C23×C3111yescharacteristic
566C22×C8C23×C3111yescharacteristic
567C22×C8C23×C3111yescharacteristic
568#127—22no—
569#127—41no—
570#124—22no—
571#124—41no—
572#121—22no—
573#121—22no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—41no—
577C4×D4—41no—
578C2×C4⋊C4C23×C3111yescharacteristic
579C2×C4⋊C4C23×C3111yescharacteristic
580C2×C4⋊C4C23×C3111yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4D4×C3111yescharacteristic
590C2×C22⋊C4D4×C3111yescharacteristic
591C2×C42C23×C3111yescharacteristic
592C2×C42C23×C3111yescharacteristic
593C4⋊C8—22no—
594C4⋊C8—22no—
595#103—22no—
596#103—22no—
597#103—41no—
598#102—22no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—41no—
603C22⋊C8—22no—
604#95—21no—
605#95—21no—
606#95—21no—
607#95—21no—
608#95—21no—
609#95—21no—
610#95—21no—
611#95D4×C3111yescharacteristic
612#95D4×C3111yescharacteristic
613C31#2436411yescharacteristic, direct product factor, Sylow
614C24—21no—
615C24—21no—
616C24—21no—
617C24C2×D4×C3111yescharacteristic
618#41—28no—
619#41—28no—
620#41—44no—
621#41—44no—
622#41—44no—
623#41—44no—
624#41—44no—
625#41—44no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8C2×D4×C3112yes—
637C2×Q8C2×D4×C3112yes—
638C2×D4—24no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—81no—
664C2×D4—81no—
665C2×D4—81no—
666C2×D4—81no—
667C2×D4C2×D4×C3112yes—
668C2×D4C2×D4×C3112yes—
669C2×D4C2×D4×C3112yes—
670C2×D4C2×D4×C3112yes—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—24no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—81no—
691C22×C4—81no—
692C22×C4C2×D4×C3111yescharacteristic
693C22×C4C2×D4×C3111yescharacteristic
694C22×C4C2×D4×C3111yescharacteristic
695C22×C4C2×D4×C3111yescharacteristic
696C22×C4C2×D4×C3112yes—
697C22×C4C2×D4×C3111yescharacteristic
698C22×C4#41×C3112yes—
699C22×C4C24×C3111yescharacteristic
700Q16—28no—
701SD16—28no—
702SD16—28no—
703SD16—44no—
704D8—28no—
705D8—44no—
706C2×C8—28no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8C2×D4×C3112yes—
718C2×C8C2×D4×C3112yes—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C22⋊C4—22no—
726C22⋊C4—41no—
727C22⋊C4—42no—
728C22⋊C4—42no—
729C22⋊C4—42no—
730C22⋊C4—42no—
731C22⋊C4—42no—
732C22⋊C4—81no—
733C22⋊C4—81no—
734C22⋊C4—81no—
735C42—21no—
736C42—21no—
737C42—21no—
738C42—21no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—22no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23C31×#12112yes—
767C23C22×D4×C3111yescharacteristic
768Q8—22no—
769Q8—22no—
770Q8—22no—
771Q8—22no—
772Q8—41no—
773Q8—41no—
774Q8—41no—
775Q8—41no—
776D4—22no—
777D4—22no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—48no—
782D4—48no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—84no—
790D4—84no—
791D4—84no—
792D4C31×#12014yes—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—48no—
813C2×C4—48no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—84no—
828C2×C4—84no—
829C2×C4C31×#12112yes—
830C2×C4C31×#13512yescomplemented
831C2×C4C22×D4×C3111yescharacteristic
832C2×C4C22×D4×C3111yescharacteristic
833C2×C4C22×D4×C3111yescharacteristic
834C2×C4C2×#41×C3111yescharacteristic
835C2×C4C31×H(5,𝔽2)11yescharacteristic
836C2×C4C31×H(5,𝔽2)11yescharacteristic
837C8—22no—
838C8—22no—
839C8—41no—
840C8—41no—
841C22—22no—
842C22—24no—
843C22—22no—
844C22—22no—
845C22—41no—
846C22—42no—
847C22—42no—
848C22—41no—
849C22—42no—
850C22—41no—
851C22—41no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22C2×C31×#12111yescharacteristic
870C22D42×C3111yescharacteristic
871C22D42×C3111yescharacteristic
872C22C2×C31×#13511yescharacteristic
873C22C31×#57511yescharacteristic
874C22C31×#57611yescharacteristic
875C22C31×#57711yescharacteristic
876C4—22no—
877C4—22no—
878C4—42no—
879C4—42no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—81no—
884C4—81no—
885C4—81no—
886C4C2×C31×#12011yescharacteristic
887C4C31×#53411yescharacteristic
888C4C31×#54611yescharacteristic
889C4C31×#54611yescharacteristic
890C2—42no—
891C2—44no—
892C2—82no—
893C2—161no—
894C2C31×#241011yescharacteristic
895C2C31×#303511yescharacteristic
896C2C31×#304511yescharacteristic
897C2C31×#326711yescharacteristic
898C2C31×#326811yescharacteristic
899C2C31×#328011yescharacteristic
900C2C31×#328411yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×#135C2semidirect
2. C2×C31×#463C2semidirect
3. C2×C31×#459C2semidirect
4. C2×C31×#449C2semidirect
5. C31×#2431C2semidirect
6. C31×#2339C2semidirect
7. C31×#2056C2semidirect
8. C31×#2055C2semidirect
9. C31×#2015C2semidirect
10. C31×#2014C2semidirect
11. C31×#1893C2semidirect
12. C31×#1879C2semidirect
13. C31×#1877C2semidirect
14. C31×#1850C2semidirect
15. C31×#1788C2semidirect
76. C2×#41×C31D4semidirect
104. C2×SD16×C31D4semidirect
110. C2×D8×C31D4semidirect
288. #24364C31direct (N × H)
380. C2×C4×C31#135semidirect
391. C22×#135C2×C31semidirect
392. C2×#463C2×C31semidirect
393. C2×#459C2×C31semidirect
394. C2×#449C2×C31semidirect
395. #2431C2×C31semidirect
396. #2339C2×C31semidirect
397. #2056C2×C31semidirect
398. #2055C2×C31semidirect
399. #2015C2×C31semidirect
400. #2014C2×C31semidirect
401. #1893C2×C31semidirect
402. #1879C2×C31semidirect
403. #1877C2×C31semidirect
404. #1850C2×C31semidirect
405. #1788C2×C31semidirect
526. C2×#41D4×C31semidirect
554. C2×SD16D4×C31semidirect
560. C2×D8D4×C31semidirect
613. C31#24364direct (N × H)
830. C2×C4C31×#135semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1352
C2×C31×#4632
C2×C31×#4592
C2×C31×#4492
C31×#24312
C31×#23392
C31×#20562
C31×#20552
C31×#20152
C31×#20142
C31×#18932
C31×#18792
C31×#18772
C31×#18502
C31×#17882
#2436431