Finite Group Databasebeta

← C2×C31×#3532 #21519477

Subgroups — C2×C31×#3532 #21519477

Order 7936.

9542 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3532C2132yesmaximal, direct product factor
2C2×C31×H(3,𝔽4)C211yesmaximal, characteristic, complemented
3C2×C31×#560C213yesmaximal, complemented
4C2×C31×#551C213yesmaximal, complemented
5C2×C31×#546C216yesmaximal, complemented
6C2×D42×C31C213yesmaximal, complemented
7C2×C31×#538C216yesmaximal, complemented
8C2×C31×#535C213yesmaximal, complemented
9C2×C31×#534C213yesmaximal, complemented
10C22×C31×#120C213yesmaximal, complemented
11C26×C31C2211yescharacteristic, complemented
12C22×#41×C31C2213yescomplemented
13C23×D4×C31C2213yescomplemented
14C23×D4×C31C2216yescomplemented
15C23×D4×C31C2213yescomplemented
16C31×H(3,𝔽4)C22116yescomplemented
17C31×#560C22148yescomplemented
18C31×#551C22148yescomplemented
19C31×#546C22196yescomplemented
20D42×C31C22148yescomplemented
21C31×#538C22196yescomplemented
22C31×#535C22148yescomplemented
23C31×#534C22148yescomplemented
24C2×C31×#127C2211yescharacteristic, complemented
25C2×C31×#127C2213yescomplemented
26C2×C31×#126C2212yescomplemented
27C2×C31×#126C2216yescomplemented
28C2×C31×#124C2213yescomplemented
29C2×C31×#124C2213yescomplemented
30C2×C31×#124C2216yescomplemented
31C2×C31×#123C2213yescomplemented
32C2×C31×#123C2213yescomplemented
33C2×C31×#123C2216yescomplemented
34C2×C31×#123C2216yescomplemented
35C2×C31×C22⋊Q8C2216yescomplemented
36C2×C31×#121C2216yescomplemented
37C2×C31×#121C2216yescomplemented
38C2×C31×#121C2216yescomplemented
39C2×C31×#121C2216yescomplemented
40C2×C31×#121C2216yescomplemented
41C2×C31×#120C2213yes—
42C2×C31×#120C2216yescomplemented
43C2×C31×#120C2216yescomplemented
44C2×C31×#120C2213yescomplemented
45C2×C31×#120C2213yescomplemented
46C2×C31×#120C2213yescomplemented
47C2×C31×#120C2216yescomplemented
48C2×C31×#120C22148yescomplemented
49C2×C31×#120C2211yescharacteristic, complemented
50C2×C31×#120C2213yescomplemented
51C2×C4×D4×C31C2216yescomplemented
52C2×C4×D4×C31C2216yescomplemented
53C2×C31×#117C2213yescomplemented
54C22×C22⋊C4×C31C2213yescomplemented
55C22×C22⋊C4×C31C2216yescomplemented
56C22×C22⋊C4×C31C2213yescomplemented
57C25×C31—412no—
58C25×C31C2313yes—
59C25×C31C2313yes—
60C25×C31C2313yes—
61C25×C31C2311yescharacteristic
62C25×C31C2318yescomplemented
63C25×C31C2311yescharacteristic, complemented
64C2×#41×C31—412no—
65C2×#41×C31C23124yescomplemented
66C22×Q8×C31C2313yescomplemented
67C22×D4×C31—412no—
68C22×D4×C31—424no—
69C22×D4×C31—412no—
70C22×D4×C31C2316yes—
71C22×D4×C31C2316yes—
72C22×D4×C31C2313yes—
73C22×D4×C31C2313yes—
74C22×D4×C31C2316yes—
75C22×D4×C31C2313yes—
76C22×D4×C31C2316yes—
77C22×D4×C31C2313yes—
78C22×D4×C31C23124yescomplemented
79C22×D4×C31C23148yescomplemented
80C22×D4×C31C2313yescomplemented
81C22×D4×C31C2316yescomplemented
82C22×D4×C31C23124yescomplemented
83C23×C4×C31C2313yes—
84C23×C4×C31C2316yes—
85C23×C4×C31C2316yescomplemented
86C23×C4×C31C2313yescomplemented
87C31×#127C2318yescomplemented
88C31×#127C23124yescomplemented
89C31×#126C23116yescomplemented
90C31×#126C23148yescomplemented
91C31×#124C23124yescomplemented
92C31×#124C23124yescomplemented
93C31×#124C23148yescomplemented
94C31×#123C23124yescomplemented
95C31×#123C23124yescomplemented
96C31×#123C23148yescomplemented
97C31×#123C23148yescomplemented
98C31×C22⋊Q8C23148yescomplemented
99C31×#121C23148yescomplemented
100C31×#121C23148yescomplemented
101C31×#121C23148yescomplemented
102C31×#121C23148yescomplemented
103C31×#121C23148yescomplemented
104C31×#120C23124yes—
105C31×#120C23148yescomplemented
106C31×#120C23148yescomplemented
107C31×#120C23124yescomplemented
108C31×#120C23124yescomplemented
109C31×#120C23124yescomplemented
110C31×#120C23148yescomplemented
111C31×#120C2318yescomplemented
112C31×#120C23124yescomplemented
113C4×D4×C31C23148yescomplemented
114C4×D4×C31C23148yescomplemented
115C31×#117C23124yescomplemented
116C2×C4⋊C4×C31C2316yescomplemented
117C2×C4⋊C4×C31C2316yescomplemented
118C2×C4⋊C4×C31C2316yescomplemented
119C2×C22⋊C4×C31C2316yes—
120C2×C22⋊C4×C31C2316yes—
121C2×C22⋊C4×C31C2313yes—
122C2×C22⋊C4×C31C2316yes—
123C2×C22⋊C4×C31C2316yes—
124C2×C22⋊C4×C31C2316yes—
125C2×C22⋊C4×C31C2313yes—
126C2×C22⋊C4×C31C23124yescomplemented
127C2×C22⋊C4×C31C23148yescomplemented
128C2×C22⋊C4×C31C23124yescomplemented
129C2×C22⋊C4×C31C2313yescomplemented
130C2×C22⋊C4×C31C2313yescomplemented
131C2×C22⋊C4×C31C2316yescomplemented
132C2×C22⋊C4×C31C2316yescomplemented
133C2×C42×C31C2311yescharacteristic, complemented
134C2×C42×C31C2313yescomplemented
135C2×C42×C31C2312yescomplemented
136C24×C31—224no—
137C24×C31—212no—
138C24×C31—212no—
139C24×C31—46no—
140C24×C31—412no—
141C24×C31—46no—
142C24×C31—448no—
143C24×C31—412no—
144C24×C31—46no—
145C24×C31—464no—
146C24×C31C2413yes—
147C24×C31C2411yescharacteristic
148C24×C31C2413yes—
149C24×C31C2413yes—
150C24×C31C24112yes—
151C24×C31C2413yes—
152C24×C31C24112yes—
153C24×C31C24112yes—
154C24×C31C2414yes—
155C24×C31C2414yescomplemented
156#41×C31—448no—
157C2×Q8×C31—46no—
158C2×Q8×C31C24112yescomplemented
159C2×D4×C31—224no—
160C2×D4×C31—224no—
161C2×D4×C31—46no—
162C2×D4×C31—46no—
163C2×D4×C31—46no—
164C2×D4×C31—46no—
165C2×D4×C31—412no—
166C2×D4×C31—412no—
167C2×D4×C31—448no—
168C2×D4×C31—412no—
169C2×D4×C31—46no—
170C2×D4×C31—496no—
171C2×D4×C31—448no—
172C2×D4×C31C24124yes—
173C2×D4×C31C24124yes—
174C2×D4×C31C24112yes—
175C2×D4×C31C24112yes—
176C2×D4×C31C24124yes—
177C2×D4×C31C24112yes—
178C2×D4×C31C24124yes—
179C2×D4×C31C24112yes—
180C2×D4×C31C24112yescomplemented
181C2×D4×C31C24124yescomplemented
182C22×C4×C31—212no—
183C22×C4×C31—412no—
184C22×C4×C31—46no—
185C22×C4×C31—412no—
186C22×C4×C31C24112yes—
187C22×C4×C31C2413yes—
188C22×C4×C31C2416yes—
189C22×C4×C31C2416yes—
190C22×C4×C31C2413yes—
191C22×C4×C31C24124yes—
192C22×C4×C31C24124yescomplemented
193C22×C4×C31C24112yescomplemented
194C4⋊C4×C31C24124yescomplemented
195C4⋊C4×C31C24124yescomplemented
196C4⋊C4×C31C24124yescomplemented
197C22⋊C4×C31C24124yes—
198C22⋊C4×C31C24124yes—
199C22⋊C4×C31C24112yes—
200C22⋊C4×C31C24124yes—
201C22⋊C4×C31C24124yes—
202C22⋊C4×C31C24124yes—
203C22⋊C4×C31C24112yes—
204C22⋊C4×C31C24112yescomplemented
205C22⋊C4×C31C24112yescomplemented
206C22⋊C4×C31C24124yescomplemented
207C22⋊C4×C31C24124yescomplemented
208C42×C31C2414yescomplemented
209C42×C31C24112yescomplemented
210C42×C31C2418yescomplemented
211C2×#3532C3111yesmaximal, characteristic, direct product factor, Sylow
212C23×C31—212no—
213C23×C31—212no—
214C23×C31—26no—
215C23×C31—212no—
216C23×C31—26no—
217C23×C31—248no—
218C23×C31—224no—
219C23×C31—26no—
220C23×C31—212no—
221C23×C31—26no—
222C23×C31—224no—
223C23×C31—412no—
224C23×C31—424no—
225C23×C31—412no—
226C23×C31—424no—
227C23×C31—412no—
228C23×C31—448no—
229C23×C31—448no—
230C23×C31—4128no—
231C23×C31—416no—
232C23×C31—824no—
233C23×C31—88no—
234C23×C31H(5,𝔽2)112yes—
235C23×C31C2516yes—
236C23×C31C2512yes—
237C23×C31C2516yes—
238C23×C31C2516yes—
239C23×C31C2516yes—
240C23×C31C2511yescharacteristic
241Q8×C31—412no—
242D4×C31—248no—
243D4×C31—248no—
244D4×C31—412no—
245D4×C31—412no—
246D4×C31—412no—
247D4×C31—412no—
248D4×C31—424no—
249D4×C31—424no—
250D4×C31—424no—
251D4×C31—412no—
252C2×C4×C31—26no—
253C2×C4×C31—26no—
254C2×C4×C31—224no—
255C2×C4×C31—212no—
256C2×C4×C31—212no—
257C2×C4×C31—424no—
258C2×C4×C31—412no—
259C2×C4×C31—424no—
260C2×C4×C31C2516yes—
261C2×C4×C31C25112yes—
262C2×C4×C31C25112yes—
263C2×C4×C31C2516yes—
264#3532C2×C31132yesdirect product factor
265C2×H(3,𝔽4)C2×C3111yescharacteristic, complemented
266C2×#560C2×C3113yescomplemented
267C2×#551C2×C3113yescomplemented
268C2×#546C2×C3116yescomplemented
269C2×D42C2×C3113yescomplemented
270C2×#538C2×C3116yescomplemented
271C2×#535C2×C3113yescomplemented
272C2×#534C2×C3113yescomplemented
273C22×#120C2×C3113yescomplemented
274C22×C31—212no—
275C22×C31—224no—
276C22×C31—212no—
277C22×C31—26no—
278C22×C31—212no—
279C22×C31—26no—
280C22×C31—26no—
281C22×C31—212no—
282C22×C31—26no—
283C22×C31—448no—
284C22×C31—448no—
285C22×C31—416no—
286C22×C31—412no—
287C22×C31—44no—
288C22×C31—412no—
289C22×C31—412no—
290C22×C31—824no—
291C22×C31—88no—
292C22×C31C2×H(5,𝔽2)112yes—
293C22×C31C2×H(5,𝔽2)16yes—
294C22×C31C2611yescharacteristic
295C4×C31—26no—
296C4×C31—26no—
297C4×C31—212no—
298C4×C31—212no—
299C26C22×C3111yescharacteristic, complemented
300C22×#41C22×C3113yescomplemented
301C23×D4C22×C3113yescomplemented
302C23×D4C22×C3116yescomplemented
303C23×D4C22×C3113yescomplemented
304H(3,𝔽4)C22×C31116yescomplemented
305#560C22×C31148yescomplemented
306#551C22×C31148yescomplemented
307#546C22×C31196yescomplemented
308D42C22×C31148yescomplemented
309#538C22×C31196yescomplemented
310#535C22×C31148yescomplemented
311#534C22×C31148yescomplemented
312C2×#127C22×C3111yescharacteristic, complemented
313C2×#127C22×C3113yescomplemented
314C2×#126C22×C3112yescomplemented
315C2×#126C22×C3116yescomplemented
316C2×#124C22×C3113yescomplemented
317C2×#124C22×C3113yescomplemented
318C2×#124C22×C3116yescomplemented
319C2×#123C22×C3113yescomplemented
320C2×#123C22×C3113yescomplemented
321C2×#123C22×C3116yescomplemented
322C2×#123C22×C3116yescomplemented
323C2×C22⋊Q8C22×C3116yescomplemented
324C2×#121C22×C3116yescomplemented
325C2×#121C22×C3116yescomplemented
326C2×#121C22×C3116yescomplemented
327C2×#121C22×C3116yescomplemented
328C2×#121C22×C3116yescomplemented
329C2×#120C22×C3113yes—
330C2×#120C22×C3116yescomplemented
331C2×#120C22×C3116yescomplemented
332C2×#120C22×C3113yescomplemented
333C2×#120C22×C3113yescomplemented
334C2×#120C22×C3113yescomplemented
335C2×#120C22×C3116yescomplemented
336C2×#120C22×C31148yescomplemented
337C2×#120C22×C3111yescharacteristic, complemented
338C2×#120C22×C3113yescomplemented
339C2×C4×D4C22×C3116yescomplemented
340C2×C4×D4C22×C3116yescomplemented
341C2×#117C22×C3113yescomplemented
342C22×C22⋊C4C22×C3113yescomplemented
343C22×C22⋊C4C22×C3116yescomplemented
344C22×C22⋊C4C22×C3113yescomplemented
345C2×C31—212no—
346C2×C31—46no—
347C2×C31—42no—
348C2×C31—46no—
349C2×C31—46no—
350C2×C31#353214yesdirect product factor
351C2×C31C22×H(5,𝔽2)13yes—
352C25—412no—
353C25C23×C3113yes—
354C25C23×C3113yes—
355C25C23×C3113yes—
356C25C23×C3111yescharacteristic
357C25C23×C3118yescomplemented
358C25C23×C3111yescharacteristic, complemented
359C2×#41—412no—
360C2×#41C23×C31124yescomplemented
361C22×Q8C23×C3113yescomplemented
362C22×D4—412no—
363C22×D4—424no—
364C22×D4—412no—
365C22×D4C23×C3116yes—
366C22×D4C23×C3116yes—
367C22×D4C23×C3113yes—
368C22×D4C23×C3113yes—
369C22×D4C23×C3116yes—
370C22×D4C23×C3113yes—
371C22×D4C23×C3116yes—
372C22×D4C23×C3113yes—
373C22×D4C23×C31124yescomplemented
374C22×D4C23×C31148yescomplemented
375C22×D4C23×C3113yescomplemented
376C22×D4C23×C3116yescomplemented
377C22×D4C23×C31124yescomplemented
378C23×C4C23×C3113yes—
379C23×C4C23×C3116yes—
380C23×C4C23×C3116yescomplemented
381C23×C4C23×C3113yescomplemented
382#127C23×C3118yescomplemented
383#127C23×C31124yescomplemented
384#126C23×C31116yescomplemented
385#126C23×C31148yescomplemented
386#124C23×C31124yescomplemented
387#124C23×C31124yescomplemented
388#124C23×C31148yescomplemented
389#123C23×C31124yescomplemented
390#123C23×C31124yescomplemented
391#123C23×C31148yescomplemented
392#123C23×C31148yescomplemented
393C22⋊Q8C23×C31148yescomplemented
394#121C23×C31148yescomplemented
395#121C23×C31148yescomplemented
396#121C23×C31148yescomplemented
397#121C23×C31148yescomplemented
398#121C23×C31148yescomplemented
399#120C23×C31124yes—
400#120C23×C31148yescomplemented
401#120C23×C31148yescomplemented
402#120C23×C31124yescomplemented
403#120C23×C31124yescomplemented
404#120C23×C31124yescomplemented
405#120C23×C31148yescomplemented
406#120C23×C3118yescomplemented
407#120C23×C31124yescomplemented
408C4×D4C23×C31148yescomplemented
409C4×D4C23×C31148yescomplemented
410#117C23×C31124yescomplemented
411C2×C4⋊C4C23×C3116yescomplemented
412C2×C4⋊C4C23×C3116yescomplemented
413C2×C4⋊C4C23×C3116yescomplemented
414C2×C22⋊C4C23×C3116yes—
415C2×C22⋊C4C23×C3116yes—
416C2×C22⋊C4C23×C3113yes—
417C2×C22⋊C4C23×C3116yes—
418C2×C22⋊C4C23×C3116yes—
419C2×C22⋊C4C23×C3116yes—
420C2×C22⋊C4C23×C3113yes—
421C2×C22⋊C4C23×C31124yescomplemented
422C2×C22⋊C4C23×C31148yescomplemented
423C2×C22⋊C4C23×C31124yescomplemented
424C2×C22⋊C4C23×C3113yescomplemented
425C2×C22⋊C4C23×C3113yescomplemented
426C2×C22⋊C4C23×C3116yescomplemented
427C2×C22⋊C4C23×C3116yescomplemented
428C2×C42C23×C3111yescharacteristic, complemented
429C2×C42C23×C3113yescomplemented
430C2×C42C23×C3112yescomplemented
431C31C2×#353211yescharacteristic, direct product factor, Sylow
432C24—224no—
433C24—212no—
434C24—212no—
435C24—46no—
436C24—412no—
437C24—46no—
438C24—448no—
439C24—412no—
440C24—46no—
441C24—464no—
442C24C24×C3113yes—
443C24C24×C3111yescharacteristic
444C24C24×C3113yes—
445C24C24×C3113yes—
446C24C24×C31112yes—
447C24C24×C3113yes—
448C24C24×C31112yes—
449C24C24×C31112yes—
450C24C24×C3114yes—
451C24C24×C3114yescomplemented
452#41—448no—
453C2×Q8—46no—
454C2×Q8C24×C31112yescomplemented
455C2×D4—224no—
456C2×D4—224no—
457C2×D4—46no—
458C2×D4—46no—
459C2×D4—46no—
460C2×D4—46no—
461C2×D4—412no—
462C2×D4—412no—
463C2×D4—448no—
464C2×D4—412no—
465C2×D4—46no—
466C2×D4—496no—
467C2×D4—448no—
468C2×D4C24×C31124yes—
469C2×D4C24×C31124yes—
470C2×D4C24×C31112yes—
471C2×D4C24×C31112yes—
472C2×D4C24×C31124yes—
473C2×D4C24×C31112yes—
474C2×D4C24×C31124yes—
475C2×D4C24×C31112yes—
476C2×D4C24×C31112yescomplemented
477C2×D4C24×C31124yescomplemented
478C22×C4—212no—
479C22×C4—412no—
480C22×C4—46no—
481C22×C4—412no—
482C22×C4C24×C3113yes—
483C22×C4C24×C3116yes—
484C22×C4C24×C3116yes—
485C22×C4C24×C3113yes—
486C22×C4C24×C31112yes—
487C22×C4C24×C31124yes—
488C22×C4C24×C31124yescomplemented
489C22×C4C24×C31112yescomplemented
490C4⋊C4C24×C31124yescomplemented
491C4⋊C4C24×C31124yescomplemented
492C4⋊C4C24×C31124yescomplemented
493C22⋊C4C24×C31124yes—
494C22⋊C4C24×C31124yes—
495C22⋊C4C24×C31112yes—
496C22⋊C4C24×C31124yes—
497C22⋊C4C24×C31124yes—
498C22⋊C4C24×C31124yes—
499C22⋊C4C24×C31112yes—
500C22⋊C4C24×C31112yescomplemented
501C22⋊C4C24×C31112yescomplemented
502C22⋊C4C24×C31124yescomplemented
503C22⋊C4C24×C31124yescomplemented
504C42C24×C3114yescomplemented
505C42C24×C31112yescomplemented
506C42C24×C3118yescomplemented
507C23—212no—
508C23—212no—
509C23—26no—
510C23—212no—
511C23—26no—
512C23—248no—
513C23—224no—
514C23—26no—
515C23—212no—
516C23—26no—
517C23—224no—
518C23—412no—
519C23—424no—
520C23—412no—
521C23—424no—
522C23—412no—
523C23—448no—
524C23—448no—
525C23—4128no—
526C23—416no—
527C23—824no—
528C23—88no—
529C23C31×H(5,𝔽2)112yes—
530C23C25×C3116yes—
531C23C25×C3112yes—
532C23C25×C3116yes—
533C23C25×C3116yes—
534C23C25×C3116yes—
535C23C25×C3111yescharacteristic
536Q8—412no—
537D4—248no—
538D4—248no—
539D4—412no—
540D4—412no—
541D4—412no—
542D4—412no—
543D4—424no—
544D4—424no—
545D4—424no—
546D4—412no—
547C2×C4—26no—
548C2×C4—26no—
549C2×C4—224no—
550C2×C4—212no—
551C2×C4—212no—
552C2×C4—424no—
553C2×C4—412no—
554C2×C4—424no—
555C2×C4C25×C3116yes—
556C2×C4C25×C31112yes—
557C2×C4C25×C31112yes—
558C2×C4C25×C3116yes—
559C22—212no—
560C22—224no—
561C22—212no—
562C22—26no—
563C22—212no—
564C22—26no—
565C22—26no—
566C22—212no—
567C22—26no—
568C22—448no—
569C22—448no—
570C22—416no—
571C22—412no—
572C22—44no—
573C22—412no—
574C22—412no—
575C22—824no—
576C22—88no—
577C22C2×C31×H(5,𝔽2)112yes—
578C22C2×C31×H(5,𝔽2)16yes—
579C22C26×C3111yescharacteristic
580C4—26no—
581C4—26no—
582C4—212no—
583C4—212no—
584C2—212no—
585C2—46no—
586C2—42no—
587C2—46no—
588C2—46no—
589C2C31×#353214yesdirect product factor
590C2C22×C31×H(5,𝔽2)13yes—
subgroupG/H
center, socleC23×C31C25
commutator, Frattini, cosocleC22C26×C31
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3532C2direct (N × H)
2. C2×C31×H(3,𝔽4)C2semidirect
3. C2×C31×#560C2semidirect
4. C2×C31×#551C2semidirect
5. C2×C31×#546C2semidirect
6. C2×D42×C31C2semidirect
7. C2×C31×#538C2semidirect
8. C2×C31×#535C2semidirect
9. C2×C31×#534C2semidirect
10. C22×C31×#120C2semidirect
11. C26×C31C22semidirect
12. C22×#41×C31C22semidirect
13. C23×D4×C31C22semidirect
14. C23×D4×C31C22semidirect
15. C23×D4×C31C22semidirect
16. C31×H(3,𝔽4)C22semidirect
17. C31×#560C22semidirect
18. C31×#551C22semidirect
19. C31×#546C22semidirect
20. D42×C31C22semidirect
21. C31×#538C22semidirect
22. C31×#535C22semidirect
23. C31×#534C22semidirect
24. C2×C31×#127C22semidirect
25. C2×C31×#127C22semidirect
26. C2×C31×#126C22semidirect
27. C2×C31×#126C22semidirect
28. C2×C31×#124C22semidirect
29. C2×C31×#124C22semidirect
30. C2×C31×#124C22semidirect
31. C2×C31×#123C22semidirect
32. C2×C31×#123C22semidirect
33. C2×C31×#123C22semidirect
34. C2×C31×#123C22semidirect
35. C2×C31×C22⋊Q8C22semidirect
36. C2×C31×#121C22semidirect
37. C2×C31×#121C22semidirect
38. C2×C31×#121C22semidirect
39. C2×C31×#121C22semidirect
40. C2×C31×#121C22semidirect
42. C2×C31×#120C22semidirect
43. C2×C31×#120C22semidirect
44. C2×C31×#120C22semidirect
45. C2×C31×#120C22semidirect
46. C2×C31×#120C22semidirect
47. C2×C31×#120C22semidirect
48. C2×C31×#120C22semidirect
49. C2×C31×#120C22semidirect
50. C2×C31×#120C22semidirect
51. C2×C4×D4×C31C22semidirect
52. C2×C4×D4×C31C22semidirect
53. C2×C31×#117C22semidirect
54. C22×C22⋊C4×C31C22semidirect
55. C22×C22⋊C4×C31C22semidirect
56. C22×C22⋊C4×C31C22semidirect
62. C25×C31C23semidirect
63. C25×C31C23semidirect
65. C2×#41×C31C23semidirect
66. C22×Q8×C31C23semidirect
78. C22×D4×C31C23semidirect
79. C22×D4×C31C23semidirect
80. C22×D4×C31C23semidirect
81. C22×D4×C31C23semidirect
82. C22×D4×C31C23semidirect
85. C23×C4×C31C23semidirect
86. C23×C4×C31C23semidirect
87. C31×#127C23semidirect
88. C31×#127C23semidirect
89. C31×#126C23semidirect
90. C31×#126C23semidirect
91. C31×#124C23semidirect
92. C31×#124C23semidirect
93. C31×#124C23semidirect
94. C31×#123C23semidirect
95. C31×#123C23semidirect
96. C31×#123C23semidirect
97. C31×#123C23semidirect
98. C31×C22⋊Q8C23semidirect
99. C31×#121C23semidirect
100. C31×#121C23semidirect
101. C31×#121C23semidirect
102. C31×#121C23semidirect
103. C31×#121C23semidirect
105. C31×#120C23semidirect
106. C31×#120C23semidirect
107. C31×#120C23semidirect
108. C31×#120C23semidirect
109. C31×#120C23semidirect
110. C31×#120C23semidirect
111. C31×#120C23semidirect
112. C31×#120C23semidirect
113. C4×D4×C31C23semidirect
114. C4×D4×C31C23semidirect
115. C31×#117C23semidirect
116. C2×C4⋊C4×C31C23semidirect
117. C2×C4⋊C4×C31C23semidirect
118. C2×C4⋊C4×C31C23semidirect
126. C2×C22⋊C4×C31C23semidirect
127. C2×C22⋊C4×C31C23semidirect
128. C2×C22⋊C4×C31C23semidirect
129. C2×C22⋊C4×C31C23semidirect
130. C2×C22⋊C4×C31C23semidirect
131. C2×C22⋊C4×C31C23semidirect
132. C2×C22⋊C4×C31C23semidirect
133. C2×C42×C31C23semidirect
134. C2×C42×C31C23semidirect
135. C2×C42×C31C23semidirect
155. C24×C31C24semidirect
158. C2×Q8×C31C24semidirect
180. C2×D4×C31C24semidirect
181. C2×D4×C31C24semidirect
192. C22×C4×C31C24semidirect
193. C22×C4×C31C24semidirect
194. C4⋊C4×C31C24semidirect
195. C4⋊C4×C31C24semidirect
196. C4⋊C4×C31C24semidirect
204. C22⋊C4×C31C24semidirect
205. C22⋊C4×C31C24semidirect
206. C22⋊C4×C31C24semidirect
207. C22⋊C4×C31C24semidirect
208. C42×C31C24semidirect
209. C42×C31C24semidirect
210. C42×C31C24semidirect
211. C2×#3532C31direct (N × H)
264. #3532C2×C31direct (N × H)
265. C2×H(3,𝔽4)C2×C31semidirect
266. C2×#560C2×C31semidirect
267. C2×#551C2×C31semidirect
268. C2×#546C2×C31semidirect
269. C2×D42C2×C31semidirect
270. C2×#538C2×C31semidirect
271. C2×#535C2×C31semidirect
272. C2×#534C2×C31semidirect
273. C22×#120C2×C31semidirect
299. C26C22×C31semidirect
300. C22×#41C22×C31semidirect
301. C23×D4C22×C31semidirect
302. C23×D4C22×C31semidirect
303. C23×D4C22×C31semidirect
304. H(3,𝔽4)C22×C31semidirect
305. #560C22×C31semidirect
306. #551C22×C31semidirect
307. #546C22×C31semidirect
308. D42C22×C31semidirect
309. #538C22×C31semidirect
310. #535C22×C31semidirect
311. #534C22×C31semidirect
312. C2×#127C22×C31semidirect
313. C2×#127C22×C31semidirect
314. C2×#126C22×C31semidirect
315. C2×#126C22×C31semidirect
316. C2×#124C22×C31semidirect
317. C2×#124C22×C31semidirect
318. C2×#124C22×C31semidirect
319. C2×#123C22×C31semidirect
320. C2×#123C22×C31semidirect
321. C2×#123C22×C31semidirect
322. C2×#123C22×C31semidirect
323. C2×C22⋊Q8C22×C31semidirect
324. C2×#121C22×C31semidirect
325. C2×#121C22×C31semidirect
326. C2×#121C22×C31semidirect
327. C2×#121C22×C31semidirect
328. C2×#121C22×C31semidirect
330. C2×#120C22×C31semidirect
331. C2×#120C22×C31semidirect
332. C2×#120C22×C31semidirect
333. C2×#120C22×C31semidirect
334. C2×#120C22×C31semidirect
335. C2×#120C22×C31semidirect
336. C2×#120C22×C31semidirect
337. C2×#120C22×C31semidirect
338. C2×#120C22×C31semidirect
339. C2×C4×D4C22×C31semidirect
340. C2×C4×D4C22×C31semidirect
341. C2×#117C22×C31semidirect
342. C22×C22⋊C4C22×C31semidirect
343. C22×C22⋊C4C22×C31semidirect
344. C22×C22⋊C4C22×C31semidirect
350. C2×C31#3532direct (N × H)
357. C25C23×C31semidirect
358. C25C23×C31semidirect
360. C2×#41C23×C31semidirect
361. C22×Q8C23×C31semidirect
373. C22×D4C23×C31semidirect
374. C22×D4C23×C31semidirect
375. C22×D4C23×C31semidirect
376. C22×D4C23×C31semidirect
377. C22×D4C23×C31semidirect
380. C23×C4C23×C31semidirect
381. C23×C4C23×C31semidirect
382. #127C23×C31semidirect
383. #127C23×C31semidirect
384. #126C23×C31semidirect
385. #126C23×C31semidirect
386. #124C23×C31semidirect
387. #124C23×C31semidirect
388. #124C23×C31semidirect
389. #123C23×C31semidirect
390. #123C23×C31semidirect
391. #123C23×C31semidirect
392. #123C23×C31semidirect
393. C22⋊Q8C23×C31semidirect
394. #121C23×C31semidirect
395. #121C23×C31semidirect
396. #121C23×C31semidirect
397. #121C23×C31semidirect
398. #121C23×C31semidirect
400. #120C23×C31semidirect
401. #120C23×C31semidirect
402. #120C23×C31semidirect
403. #120C23×C31semidirect
404. #120C23×C31semidirect
405. #120C23×C31semidirect
406. #120C23×C31semidirect
407. #120C23×C31semidirect
408. C4×D4C23×C31semidirect
409. C4×D4C23×C31semidirect
410. #117C23×C31semidirect
411. C2×C4⋊C4C23×C31semidirect
412. C2×C4⋊C4C23×C31semidirect
413. C2×C4⋊C4C23×C31semidirect
421. C2×C22⋊C4C23×C31semidirect
422. C2×C22⋊C4C23×C31semidirect
423. C2×C22⋊C4C23×C31semidirect
424. C2×C22⋊C4C23×C31semidirect
425. C2×C22⋊C4C23×C31semidirect
426. C2×C22⋊C4C23×C31semidirect
427. C2×C22⋊C4C23×C31semidirect
428. C2×C42C23×C31semidirect
429. C2×C42C23×C31semidirect
430. C2×C42C23×C31semidirect
431. C31C2×#3532direct (N × H)
451. C24C24×C31semidirect
454. C2×Q8C24×C31semidirect
476. C2×D4C24×C31semidirect
477. C2×D4C24×C31semidirect
488. C22×C4C24×C31semidirect
489. C22×C4C24×C31semidirect
490. C4⋊C4C24×C31semidirect
491. C4⋊C4C24×C31semidirect
492. C4⋊C4C24×C31semidirect
500. C22⋊C4C24×C31semidirect
501. C22⋊C4C24×C31semidirect
502. C22⋊C4C24×C31semidirect
503. C22⋊C4C24×C31semidirect
504. C42C24×C31semidirect
505. C42C24×C31semidirect
506. C42C24×C31semidirect
589. C2C31×#3532direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35322
C2×C31×H(3,𝔽4)2
C2×C31×#5602
C2×C31×#5512
C2×C31×#5462
C2×D42×C312
C2×C31×#5382
C2×C31×#5352
C2×C31×#5342
C22×C31×#1202
C2×#353231