Finite Group Databasebeta

← C31×#21457 #21478216

Subgroups — C31×#21457 #21478216

Order 7936.

1468 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#41×C31C211yesmaximal, characteristic
2C2×C31×#452C211yesmaximal, characteristic
3C2×C31×#441C211yesmaximal, characteristic, complemented
4C2×C31×#440C211yesmaximal, characteristic, complemented
5C4×C31×C22⋊Q8C211yesmaximal, characteristic, complemented
6C31×#1878C211yesmaximal, characteristic, complemented
7C31×#1877C211yesmaximal, characteristic, complemented
8C31×#1873C211yesmaximal, characteristic, complemented
9C31×#1864C211yesmaximal, characteristic, complemented
10C31×#1863C211yesmaximal, characteristic, complemented
11C31×#1854C211yesmaximal, characteristic, complemented
12C31×#1788C211yesmaximal, characteristic
13C31×#1763C211yesmaximal, characteristic, complemented
14C31×#1762C211yesmaximal, characteristic, complemented
15C31×#1749C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×Q16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C2×C31×C22⋊Q8C2211yescharacteristic
20C4×#41×C31—24no—
21C4×#41×C31—24no—
22C2×C4×Q8×C31C2211yescharacteristic
23C2×C4×Q8×C31C2211yescharacteristic
24C2×C4×Q8×C31C2211yescharacteristic
25C2×C4×D4×C31—21no—
26C2×C4×D4×C31—21no—
27C2×C4×D4×C31C2211yescharacteristic
28C2×C4×D4×C31C2211yescharacteristic
29C2×C31×#117—21no—
30C2×C31×#117C2211yescharacteristic
31C22×C42×C31—21no—
32C22×C42×C31C2211yescharacteristic
33C31×#452C418yescomplemented
34C31×#441—24no—
35C31×#440—24no—
36C2×C31×#107C2211yescharacteristic
37C2×C31×#106C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#103C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C2×C31×#97C2211yescharacteristic
49C2×C31×#97C2211yescharacteristic
50C31×#391C2211yescharacteristic
51C31×#389C2211yescharacteristic
52C31×#387—21no—
53C31×#385—21no—
54C31×#380C2211yescharacteristic
55C4×C4⋊C4×C31—21no—
56C4×C4⋊C4×C31C2211yescharacteristic
57C4×C22⋊C4×C31—21no—
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C31×#336C2211yescharacteristic
64C2×#41×C31—22no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—22no—
69C2×#41×C31C2×C414yes—
70C22×Q8×C31C2311yescharacteristic
71C22×Q8×C31C2311yescharacteristic
72C22×D4×C31—21no—
73C22×D4×C31C2311yescharacteristic
74C23×C4×C31—21no—
75C23×C4×C31—21no—
76C23×C4×C31—21no—
77C23×C4×C31D411yescharacteristic
78C23×C4×C31D411yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C2×Q16×C31—22no—
81C2×Q16×C31—22no—
82C2×Q16×C31C2×C414yescomplemented
83C2×SD16×C31—22no—
84C2×SD16×C31—22no—
85C2×SD16×C31C2×C414yescomplemented
86C22×C8×C31C2311yescharacteristic
87C22×C8×C31C2311yescharacteristic
88C22×C8×C31C2311yescharacteristic
89C22×C8×C31C2311yescharacteristic
90C31×C22⋊Q8—22no—
91C31×C22⋊Q8C2×C414yescomplemented
92C4×Q8×C31—22no—
93C4×Q8×C31—22no—
94C4×Q8×C31—22no—
95C4×Q8×C31—22no—
96C4×Q8×C31—22no—
97C4×Q8×C31D414yes—
98C4×D4×C31—28no—
99C4×D4×C31—28no—
100C4×D4×C31—22no—
101C4×D4×C31—22no—
102C4×D4×C31—22no—
103C4×D4×C31D414yes—
104C31×#117—28no—
105C31×#117—22no—
106C31×#117—22no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C42×C31—28no—
123C2×C42×C31—21no—
124C2×C42×C31—21no—
125C2×C42×C31—21no—
126C2×C42×C31—22no—
127C2×C42×C31—22no—
128C2×C42×C31—21no—
129C2×C42×C31—21no—
130C2×C42×C31D411yescharacteristic
131C2×C42×C31D411yescharacteristic
132C2×C42×C31C2311yescharacteristic
133C2×C42×C31C2311yescharacteristic
134C31×#107—22no—
135C31×#106—22no—
136C31×#103—22no—
137C31×#103—22no—
138C31×#103—22no—
139C31×#103—22no—
140C31×#103C2×C414yescomplemented
141C31×#102—22no—
142C31×#102—22no—
143C31×#102C2×C414yescomplemented
144C31×C22⋊C8—22no—
145C31×C22⋊C8C2×C414yescomplemented
146C31×#97—22no—
147C31×#97—22no—
148C31×#95—21no—
149C31×#95—21no—
150C31×#95—21no—
151C31×#95—21no—
152C31×#95—21no—
153C24×C31—21no—
154C24×C31C2×D411yescharacteristic
155#41×C31—28no—
156#41×C31—28no—
157#41×C31—28no—
158#41×C31—28no—
159C2×Q8×C31—21no—
160C2×Q8×C31—21no—
161C2×Q8×C31—21no—
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31C22×C412yes—
168C2×Q8×C31C22×C412yes—
169C2×Q8×C31C2×D412yes—
170C2×Q8×C31#4112yes—
171C2×D4×C31—24no—
172C2×D4×C31—24no—
173C2×D4×C31—24no—
174C2×D4×C31—21no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31C22×C412yes—
178C2×D4×C31C2×D412yes—
179C2×D4×C31#4112yes—
180C22×C4×C31—24no—
181C22×C4×C31—24no—
182C22×C4×C31—21no—
183C22×C4×C31—24no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—24no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—22no—
194C22×C4×C31—22no—
195C22×C4×C31—24no—
196C22×C4×C31—22no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—41no—
200C22×C4×C31—41no—
201C22×C4×C31—41no—
202C22×C4×C31—42no—
203C22×C4×C31—42no—
204C22×C4×C31—42no—
205C22×C4×C31—42no—
206C22×C4×C31C22×C412yes—
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31C2×D411yescharacteristic
211C22×C4×C31C2×D411yescharacteristic
212C22×C4×C31#4112yes—
213C22×C4×C31C2411yescharacteristic
214Q16×C31—28no—
215SD16×C31—28no—
216C2×C8×C31—21no—
217C2×C8×C31—21no—
218C2×C8×C31—21no—
219C2×C8×C31—21no—
220C2×C8×C31—21no—
221C2×C8×C31—21no—
222C2×C8×C31—21no—
223C2×C8×C31—21no—
224C2×C8×C31—21no—
225C2×C8×C31—21no—
226C2×C8×C31C22×C412yes—
227C2×C8×C31C22×C412yes—
228C4⋊C4×C31—24no—
229C4⋊C4×C31—24no—
230C4⋊C4×C31—24no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—21no—
233C4⋊C4×C31—21no—
234C4⋊C4×C31—21no—
235C4⋊C4×C31—21no—
236C4⋊C4×C31—21no—
237C4⋊C4×C31—21no—
238C4⋊C4×C31—42no—
239C4⋊C4×C31—42no—
240C4⋊C4×C31C22×C412yes—
241C4⋊C4×C31C2×D412yes—
242C4⋊C4×C31C2×D412yes—
243C22⋊C4×C31—24no—
244C22⋊C4×C31—24no—
245C22⋊C4×C31—24no—
246C22⋊C4×C31—24no—
247C22⋊C4×C31—42no—
248C42×C31—24no—
249C42×C31—24no—
250C42×C31—22no—
251C42×C31—24no—
252C42×C31—22no—
253C42×C31—21no—
254C42×C31—21no—
255C42×C31—42no—
256C42×C31—42no—
257C42×C31C2×D412yes—
258C42×C31C2×D412yes—
259#21457C3111yesmaximal, characteristic, direct product factor, Sylow
260C23×C31—22no—
261C23×C31—21no—
262C23×C31—22no—
263C23×C31—21no—
264C23×C31—22no—
265C23×C31—21no—
266C23×C31—21no—
267C23×C31—21no—
268C23×C31—21no—
269C23×C31—41no—
270C23×C31—41no—
271C23×C31—41no—
272C23×C31—41no—
273C23×C31C4×D412yes—
274C23×C31C22×D411yescharacteristic
275Q8×C31—22no—
276Q8×C31—22no—
277Q8×C31—22no—
278Q8×C31—22no—
279Q8×C31—22no—
280Q8×C31—41no—
281Q8×C31—41no—
282Q8×C31C4×D414yes—
283D4×C31—216no—
284D4×C31—22no—
285D4×C31—22no—
286D4×C31—22no—
287D4×C31C4×D414yes—
288C2×C4×C31—216no—
289C2×C4×C31—22no—
290C2×C4×C31—21no—
291C2×C4×C31—21no—
292C2×C4×C31—22no—
293C2×C4×C31—21no—
294C2×C4×C31—22no—
295C2×C4×C31—21no—
296C2×C4×C31—21no—
297C2×C4×C31—21no—
298C2×C4×C31—21no—
299C2×C4×C31—21no—
300C2×C4×C31—22no—
301C2×C4×C31—22no—
302C2×C4×C31—22no—
303C2×C4×C31—22no—
304C2×C4×C31—22no—
305C2×C4×C31—22no—
306C2×C4×C31—21no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—21no—
310C2×C4×C31—21no—
311C2×C4×C31—44no—
312C2×C4×C31—44no—
313C2×C4×C31—48no—
314C2×C4×C31—48no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—41no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
326C2×C4×C31—41no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31C4×D412yes—
330C2×C4×C31#12012yes—
331C2×C4×C31#12012yes—
332C2×C4×C31#13712yes—
333C2×C4×C31C23×C411yescharacteristic
334C2×C4×C31C22×D411yescharacteristic
335C2×C4×C31C22×D411yescharacteristic
336C2×C4×C31C2×#4111yescharacteristic
337C2×C4×C31C2×#4111yescharacteristic
338C2×C4×C31C2×#4111yescharacteristic
339C8×C31—22no—
340C8×C31—22no—
341C8×C31—41no—
342C8×C31—41no—
343C2×C4×#41C2×C3111yescharacteristic
344C2×#452C2×C3111yescharacteristic
345C2×#441C2×C3111yescharacteristic, complemented
346C2×#440C2×C3111yescharacteristic, complemented
347C4×C22⋊Q8C2×C3111yescharacteristic, complemented
348#1878C2×C3111yescharacteristic, complemented
349#1877C2×C3111yescharacteristic, complemented
350#1873C2×C3111yescharacteristic, complemented
351#1864C2×C3111yescharacteristic, complemented
352#1863C2×C3111yescharacteristic, complemented
353#1854C2×C3111yescharacteristic, complemented
354#1788C2×C3111yescharacteristic
355#1763C2×C3111yescharacteristic, complemented
356#1762C2×C3111yescharacteristic, complemented
357#1749C2×C3111yescharacteristic, complemented
358C22×C31—22no—
359C22×C31—22no—
360C22×C31—22no—
361C22×C31—24no—
362C22×C31—41no—
363C22×C31—42no—
364C22×C31—41no—
365C22×C31—42no—
366C22×C31—42no—
367C22×C31—42no—
368C22×C31—41no—
369C22×C31—42no—
370C22×C31—41no—
371C22×C31—42no—
372C22×C31C2×C4×D411yescharacteristic
373C22×C31C2×#12011yescharacteristic
374C22×C31#52511yescharacteristic
375C22×C31C2×#13711yescharacteristic
376C22×C31#57511yescharacteristic
377C22×C31#57511yescharacteristic
378C22×C31#57511yescharacteristic
379C4×C31—22no—
380C4×C31—22no—
381C4×C31—22no—
382C4×C31—22no—
383C4×C31—24no—
384C4×C31—42no—
385C4×C31—41no—
386C4×C31—42no—
387C4×C31—42no—
388C4×C31—42no—
389C4×C31—81no—
390C4×C31—81no—
391C4×C31C2×C4×D411yescharacteristic
392C4×C31C2×C4×D411yescharacteristic
393C4×C31#52511yescharacteristic
394C4×C31#52511yescharacteristic
395C22×#41C22×C3111yescharacteristic
396C22×Q16C22×C3111yescharacteristic
397C22×SD16C22×C3111yescharacteristic
398C2×C22⋊Q8C22×C3111yescharacteristic
399C4×#41—24no—
400C4×#41—24no—
401C2×C4×Q8C22×C3111yescharacteristic
402C2×C4×Q8C22×C3111yescharacteristic
403C2×C4×Q8C22×C3111yescharacteristic
404C2×C4×D4—21no—
405C2×C4×D4—21no—
406C2×C4×D4C22×C3111yescharacteristic
407C2×C4×D4C22×C3111yescharacteristic
408C2×#117—21no—
409C2×#117C22×C3111yescharacteristic
410C22×C42—21no—
411C22×C42C22×C3111yescharacteristic
412#452C4×C3118yescomplemented
413#441—24no—
414#440—24no—
415C2×#107C22×C3111yescharacteristic
416C2×#106C22×C3111yescharacteristic
417C2×#103C22×C3111yescharacteristic
418C2×#103C22×C3111yescharacteristic
419C2×#103C22×C3111yescharacteristic
420C2×#103C22×C3111yescharacteristic
421C2×#103C22×C3111yescharacteristic
422C2×#102C22×C3111yescharacteristic
423C2×#102C22×C3111yescharacteristic
424C2×#102C22×C3111yescharacteristic
425C2×C22⋊C8C22×C3111yescharacteristic
426C2×C22⋊C8C22×C3111yescharacteristic
427C2×#97C22×C3111yescharacteristic
428C2×#97C22×C3111yescharacteristic
429#391C22×C3111yescharacteristic
430#389C22×C3111yescharacteristic
431#387—21no—
432#385—21no—
433#380C22×C3111yescharacteristic
434C4×C4⋊C4—21no—
435C4×C4⋊C4C22×C3111yescharacteristic
436C4×C22⋊C4—21no—
437#340C22×C3111yescharacteristic
438#340C22×C3111yescharacteristic
439#340C22×C3111yescharacteristic
440#340C22×C3111yescharacteristic
441#336C22×C3111yescharacteristic
442#336C22×C3111yescharacteristic
443C2×C31—42no—
444C2×C31—44no—
445C2×C31C4×#12011yescharacteristic
446C2×C31#294311yescharacteristic
447C2×C31C4×#13711yescharacteristic
448C2×C31#300511yescharacteristic
449C2×C31#300711yescharacteristic
450C2×C31#311111yescharacteristic
451C2×C31#311611yescharacteristic
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—22no—
455C2×#41—22no—
456C2×#41—22no—
457C2×#41C2×C4×C3114yes—
458C22×Q8C23×C3111yescharacteristic
459C22×Q8C23×C3111yescharacteristic
460C22×D4—21no—
461C22×D4C23×C3111yescharacteristic
462C23×C4—21no—
463C23×C4—21no—
464C23×C4—21no—
465C23×C4D4×C3111yescharacteristic
466C23×C4D4×C3111yescharacteristic
467C23×C4C23×C3111yescharacteristic
468C2×Q16—22no—
469C2×Q16—22no—
470C2×Q16C2×C4×C3114yescomplemented
471C2×SD16—22no—
472C2×SD16—22no—
473C2×SD16C2×C4×C3114yescomplemented
474C22×C8C23×C3111yescharacteristic
475C22×C8C23×C3111yescharacteristic
476C22×C8C23×C3111yescharacteristic
477C22×C8C23×C3111yescharacteristic
478C22⋊Q8—22no—
479C22⋊Q8C2×C4×C3114yescomplemented
480C4×Q8—22no—
481C4×Q8—22no—
482C4×Q8—22no—
483C4×Q8—22no—
484C4×Q8—22no—
485C4×Q8D4×C3114yes—
486C4×D4—28no—
487C4×D4—28no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4D4×C3114yes—
492#117—28no—
493#117—22no—
494#117—22no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4C23×C3111yescharacteristic
501C2×C4⋊C4C23×C3111yescharacteristic
502C2×C4⋊C4C23×C3111yescharacteristic
503C2×C4⋊C4C23×C3111yescharacteristic
504C2×C4⋊C4C23×C3111yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C42—28no—
511C2×C42—21no—
512C2×C42—21no—
513C2×C42—21no—
514C2×C42—22no—
515C2×C42—22no—
516C2×C42—21no—
517C2×C42—21no—
518C2×C42D4×C3111yescharacteristic
519C2×C42D4×C3111yescharacteristic
520C2×C42C23×C3111yescharacteristic
521C2×C42C23×C3111yescharacteristic
522#107—22no—
523#106—22no—
524#103—22no—
525#103—22no—
526#103—22no—
527#103—22no—
528#103C2×C4×C3114yescomplemented
529#102—22no—
530#102—22no—
531#102C2×C4×C3114yescomplemented
532C22⋊C8—22no—
533C22⋊C8C2×C4×C3114yescomplemented
534#97—22no—
535#97—22no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—21no—
541C31#2145711yescharacteristic, direct product factor, Sylow
542C24—21no—
543C24C2×D4×C3111yescharacteristic
544#41—28no—
545#41—28no—
546#41—28no—
547#41—28no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8C22×C4×C3112yes—
557C2×Q8C22×C4×C3112yes—
558C2×Q8C2×D4×C3112yes—
559C2×Q8#41×C3112yes—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4C22×C4×C3112yes—
567C2×D4C2×D4×C3112yes—
568C2×D4#41×C3112yes—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—21no—
572C22×C4—24no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4C22×C4×C3112yes—
596C22×C4C2×D4×C3111yescharacteristic
597C22×C4C2×D4×C3111yescharacteristic
598C22×C4C2×D4×C3111yescharacteristic
599C22×C4C2×D4×C3111yescharacteristic
600C22×C4C2×D4×C3111yescharacteristic
601C22×C4#41×C3112yes—
602C22×C4C24×C3111yescharacteristic
603Q16—28no—
604SD16—28no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8C22×C4×C3112yes—
616C2×C8C22×C4×C3112yes—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—42no—
628C4⋊C4—42no—
629C4⋊C4C22×C4×C3112yes—
630C4⋊C4C2×D4×C3112yes—
631C4⋊C4C2×D4×C3112yes—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—42no—
637C42—24no—
638C42—24no—
639C42—22no—
640C42—24no—
641C42—22no—
642C42—21no—
643C42—21no—
644C42—42no—
645C42—42no—
646C42C2×D4×C3112yes—
647C42C2×D4×C3112yes—
648C23—22no—
649C23—21no—
650C23—22no—
651C23—21no—
652C23—22no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23C4×D4×C3112yes—
662C23C22×D4×C3111yescharacteristic
663Q8—22no—
664Q8—22no—
665Q8—22no—
666Q8—22no—
667Q8—22no—
668Q8—41no—
669Q8—41no—
670Q8C4×D4×C3114yes—
671D4—216no—
672D4—22no—
673D4—22no—
674D4—22no—
675D4C4×D4×C3114yes—
676C2×C4—216no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—48no—
702C2×C4—48no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4C4×D4×C3112yes—
718C2×C4C31×#12012yes—
719C2×C4C31×#12012yes—
720C2×C4C31×#13712yes—
721C2×C4C23×C4×C3111yescharacteristic
722C2×C4C22×D4×C3111yescharacteristic
723C2×C4C22×D4×C3111yescharacteristic
724C2×C4C2×#41×C3111yescharacteristic
725C2×C4C2×#41×C3111yescharacteristic
726C2×C4C2×#41×C3111yescharacteristic
727C8—22no—
728C8—22no—
729C8—41no—
730C8—41no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—24no—
735C22—41no—
736C22—42no—
737C22—41no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—41no—
742C22—42no—
743C22—41no—
744C22—42no—
745C22C2×C4×D4×C3111yescharacteristic
746C22C2×C31×#12011yescharacteristic
747C22C31×#52511yescharacteristic
748C22C2×C31×#13711yescharacteristic
749C22C31×#57511yescharacteristic
750C22C31×#57511yescharacteristic
751C22C31×#57511yescharacteristic
752C4—22no—
753C4—22no—
754C4—22no—
755C4—22no—
756C4—24no—
757C4—42no—
758C4—41no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—81no—
763C4—81no—
764C4C2×C4×D4×C3111yescharacteristic
765C4C2×C4×D4×C3111yescharacteristic
766C4C31×#52511yescharacteristic
767C4C31×#52511yescharacteristic
768C2—42no—
769C2—44no—
770C2C4×C31×#12011yescharacteristic
771C2C31×#294311yescharacteristic
772C2C4×C31×#13711yescharacteristic
773C2C31×#300511yescharacteristic
774C2C31×#300711yescharacteristic
775C2C31×#311111yescharacteristic
776C2C31×#311611yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC22×#41×C31C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C31×#441C2semidirect
4. C2×C31×#440C2semidirect
5. C4×C31×C22⋊Q8C2semidirect
6. C31×#1878C2semidirect
7. C31×#1877C2semidirect
8. C31×#1873C2semidirect
9. C31×#1864C2semidirect
10. C31×#1863C2semidirect
11. C31×#1854C2semidirect
13. C31×#1763C2semidirect
14. C31×#1762C2semidirect
15. C31×#1749C2semidirect
33. C31×#452C4semidirect
82. C2×Q16×C31C2×C4semidirect
85. C2×SD16×C31C2×C4semidirect
91. C31×C22⋊Q8C2×C4semidirect
140. C31×#103C2×C4semidirect
143. C31×#102C2×C4semidirect
145. C31×C22⋊C8C2×C4semidirect
259. #21457C31direct (N × H)
345. C2×#441C2×C31semidirect
346. C2×#440C2×C31semidirect
347. C4×C22⋊Q8C2×C31semidirect
348. #1878C2×C31semidirect
349. #1877C2×C31semidirect
350. #1873C2×C31semidirect
351. #1864C2×C31semidirect
352. #1863C2×C31semidirect
353. #1854C2×C31semidirect
355. #1763C2×C31semidirect
356. #1762C2×C31semidirect
357. #1749C2×C31semidirect
412. #452C4×C31semidirect
470. C2×Q16C2×C4×C31semidirect
473. C2×SD16C2×C4×C31semidirect
479. C22⋊Q8C2×C4×C31semidirect
528. #103C2×C4×C31semidirect
531. #102C2×C4×C31semidirect
533. C22⋊C8C2×C4×C31semidirect
541. C31#21457direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#41×C312
C2×C31×#4522
C2×C31×#4412
C2×C31×#4402
C4×C31×C22⋊Q82
C31×#18782
C31×#18772
C31×#18732
C31×#18642
C31×#18632
C31×#18542
C31×#17882
C31×#17632
C31×#17622
C31×#17492
#2145731