Finite Group Databasebeta

← C31×#21397 #21478156

Subgroups — C31×#21397 #21478156

Order 7936.

1150 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#542C211yesmaximal, characteristic
2C2×C31×#433C211yesmaximal, characteristic, complemented
3C31×#2274C211yesmaximal, characteristic, complemented
4C31×#1988C211yesmaximal, characteristic, complemented
5C31×#1987C211yesmaximal, characteristic, complemented
6C31×#1983C211yesmaximal, characteristic, complemented
7C31×#1983C211yesmaximal, characteristic, complemented
8C31×#1875C211yesmaximal, characteristic
9C31×#1874C211yesmaximal, characteristic
10C31×#1873C211yesmaximal, characteristic, complemented
11C31×#1872C211yesmaximal, characteristic, complemented
12C31×#1763C211yesmaximal, characteristic, complemented
13C31×#1762C211yesmaximal, characteristic, complemented
14C4×C31×#103C211yesmaximal, characteristic, complemented
15C4×C31×#102C211yesmaximal, characteristic, complemented
16C31×#542—24no—
17C31×#542C418yescomplemented
18C2×C31×C4⋊Q8C2211yescharacteristic
19C2×C31×#126—21no—
20C2×C31×#124—21no—
21C2×C31×#124C2211yescharacteristic
22C2×C31×#123—21no—
23C2×C31×C22⋊Q8—21no—
24C2×C31×C22⋊Q8C2211yescharacteristic
25C2×C31×#121C2211yescharacteristic
26C2×C4×Q8×C31C2211yescharacteristic
27C2×C4×D4×C31C2211yescharacteristic
28C2×C31×#117C2211yescharacteristic
29C2×C31×#117C2211yescharacteristic
30C22×C4⋊C4×C31C2211yescharacteristic
31C31×#433—24no—
32C2×C31×C4⋊C8C2211yescharacteristic
33C2×C31×C4⋊C8C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×C22⋊C8C2211yescharacteristic
43C2×C31×C22⋊C8C2211yescharacteristic
44C2×C31×#97C2211yescharacteristic
45C2×C4×C8×C31C2211yescharacteristic
46C4×C4⋊C4×C31—21no—
47C4×C4⋊C4×C31—21no—
48C4×C4⋊C4×C31C2211yescharacteristic
49C4×C4⋊C4×C31C2211yescharacteristic
50C4×C4⋊C4×C31C2211yescharacteristic
51C4×C4⋊C4×C31C2211yescharacteristic
52C4×C22⋊C4×C31—21no—
53C4×C22⋊C4×C31—21no—
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C22×Q8×C31—21no—
63C22×Q8×C31C2311yescharacteristic
64C22×D4×C31—21no—
65C22×D4×C31C2311yescharacteristic
66C23×C4×C31—21no—
67C23×C4×C31—21no—
68C23×C4×C31C2311yescharacteristic
69C22×C8×C31C2311yescharacteristic
70C22×C8×C31C2311yescharacteristic
71C22×C8×C31C2311yescharacteristic
72C22×C8×C31C2311yescharacteristic
73C31×C4⋊Q8—22no—
74C31×C4⋊Q8C2×C414yescomplemented
75C31×#126—28no—
76C31×#124—28no—
77C31×#124—22no—
78C31×#124C2×C414yescomplemented
79C31×#123—28no—
80C31×C22⋊Q8—22no—
81C31×C22⋊Q8—28no—
82C31×C22⋊Q8C2×C414yes—
83C31×#121—22no—
84C31×#121C2×C414yes—
85C4×Q8×C31—22no—
86C4×Q8×C31C2×C414yescomplemented
87C4×D4×C31—22no—
88C4×D4×C31C2×C414yescomplemented
89C31×#117—22no—
90C31×#117—22no—
91C31×#117C2×C414yes—
92C31×#117D414yes—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31—21no—
96C2×C4⋊C4×C31—21no—
97C2×C4⋊C4×C31—22no—
98C2×C4⋊C4×C31—22no—
99C2×C4⋊C4×C31D411yescharacteristic
100C2×C4⋊C4×C31D411yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C4⋊C4×C31C2311yescharacteristic
104C2×C4⋊C4×C31C2311yescharacteristic
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31—21no—
109C2×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31—21no—
113C2×C22⋊C4×C31D411yescharacteristic
114C2×C22⋊C4×C31D411yescharacteristic
115C2×C42×C31—21no—
116C2×C42×C31—21no—
117C2×C42×C31—21no—
118C2×C42×C31—21no—
119C2×C42×C31—21no—
120C2×C42×C31—21no—
121C2×C42×C31C2311yescharacteristic
122C2×C42×C31C2311yescharacteristic
123C31×C4⋊C8—22no—
124C31×C4⋊C8—22no—
125C31×#103—22no—
126C31×#103—22no—
127C31×#103—22no—
128C31×#103—22no—
129C31×#102—22no—
130C31×#102—22no—
131C31×#102—22no—
132C31×#102—22no—
133C31×C22⋊C8—22no—
134C31×C22⋊C8—22no—
135C31×#97—22no—
136C4×C8×C31—22no—
137C31×#95—21no—
138C31×#95—21no—
139C31×#95—21no—
140C31×#95—21no—
141C24×C31—21no—
142C24×C31C2×D411yescharacteristic
143C2×Q8×C31—24no—
144C2×Q8×C31—21no—
145C2×Q8×C31—21no—
146C2×Q8×C31—21no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31—81no—
150C2×Q8×C31—81no—
151C2×Q8×C31C22×C412yes—
152C2×D4×C31—24no—
153C2×D4×C31—21no—
154C2×D4×C31—21no—
155C2×D4×C31—21no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—81no—
159C2×D4×C31—81no—
160C2×D4×C31C22×C412yes—
161C22×C4×C31—21no—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—21no—
170C22×C4×C31—21no—
171C22×C4×C31—21no—
172C22×C4×C31—24no—
173C22×C4×C31—24no—
174C22×C4×C31—81no—
175C22×C4×C31—81no—
176C22×C4×C31—81no—
177C22×C4×C31—81no—
178C22×C4×C31C22×C412yes—
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2×D411yescharacteristic
181C22×C4×C31C2×D411yescharacteristic
182C22×C4×C31C2×D411yescharacteristic
183C22×C4×C31C2×D411yescharacteristic
184C22×C4×C31C2×D412yes—
185C22×C4×C31C2411yescharacteristic
186C2×C8×C31—21no—
187C2×C8×C31—21no—
188C2×C8×C31—21no—
189C2×C8×C31—21no—
190C2×C8×C31—21no—
191C2×C8×C31—21no—
192C2×C8×C31—21no—
193C2×C8×C31—21no—
194C2×C8×C31—21no—
195C2×C8×C31—21no—
196C2×C8×C31—21no—
197C2×C8×C31—21no—
198C4⋊C4×C31—24no—
199C4⋊C4×C31—24no—
200C4⋊C4×C31—24no—
201C4⋊C4×C31—24no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—21no—
208C4⋊C4×C31C22⋊C414yes—
209C4⋊C4×C31C22⋊C414yes—
210C4⋊C4×C31C22×C412yes—
211C4⋊C4×C31C22×C412yes—
212C4⋊C4×C31#4112yes—
213C4⋊C4×C31#4112yes—
214C4⋊C4×C31#4112yes—
215C4⋊C4×C31#4112yes—
216C22⋊C4×C31—24no—
217C22⋊C4×C31—24no—
218C22⋊C4×C31—24no—
219C22⋊C4×C31—24no—
220C22⋊C4×C31—24no—
221C22⋊C4×C31—24no—
222C22⋊C4×C31C22⋊C414yes—
223C22⋊C4×C31C22⋊C414yes—
224C42×C31—24no—
225C42×C31—24no—
226C42×C31—81no—
227C42×C31—81no—
228C42×C31—81no—
229C42×C31—81no—
230C42×C31C22×C412yes—
231C42×C31C22×C412yes—
232C42×C31C2×D412yes—
233C42×C31C2×D412yes—
234#21397C3111yesmaximal, characteristic, direct product factor, Sylow
235C23×C31—21no—
236C23×C31—21no—
237C23×C31—21no—
238C23×C31—21no—
239C23×C31—21no—
240C23×C31—21no—
241C23×C31—22no—
242C23×C31—41no—
243C23×C31—41no—
244C23×C31—41no—
245C23×C31—41no—
246C23×C31—41no—
247C23×C31—41no—
248C23×C31C2×C22⋊C412yes—
249C23×C31C22×D411yescharacteristic
250Q8×C31—22no—
251Q8×C31—22no—
252Q8×C31—41no—
253Q8×C31—41no—
254Q8×C31—84no—
255D4×C31—22no—
256D4×C31—22no—
257D4×C31—41no—
258D4×C31—41no—
259D4×C31—84no—
260C2×C4×C31—21no—
261C2×C4×C31—21no—
262C2×C4×C31—21no—
263C2×C4×C31—21no—
264C2×C4×C31—21no—
265C2×C4×C31—21no—
266C2×C4×C31—21no—
267C2×C4×C31—21no—
268C2×C4×C31—21no—
269C2×C4×C31—21no—
270C2×C4×C31—22no—
271C2×C4×C31—22no—
272C2×C4×C31—22no—
273C2×C4×C31—22no—
274C2×C4×C31—22no—
275C2×C4×C31—22no—
276C2×C4×C31—22no—
277C2×C4×C31—22no—
278C2×C4×C31—22no—
279C2×C4×C31—22no—
280C2×C4×C31—22no—
281C2×C4×C31—41no—
282C2×C4×C31—41no—
283C2×C4×C31—41no—
284C2×C4×C31—41no—
285C2×C4×C31—41no—
286C2×C4×C31—41no—
287C2×C4×C31—41no—
288C2×C4×C31—41no—
289C2×C4×C31—41no—
290C2×C4×C31—41no—
291C2×C4×C31—41no—
292C2×C4×C31—41no—
293C2×C4×C31—41no—
294C2×C4×C31—41no—
295C2×C4×C31—84no—
296C2×C4×C31—84no—
297C2×C4×C31C2×C22⋊C412yes—
298C2×C4×C31C2×C22⋊C412yes—
299C2×C4×C31C2×C22⋊C412yes—
300C2×C4×C31C2×C22⋊C412yes—
301C2×C4×C31C2×C22⋊C412yes—
302C2×C4×C31C23×C411yescharacteristic
303C2×C4×C31C22×D411yescharacteristic
304C2×C4×C31C2×#4111yescharacteristic
305C2×C4×C31C2×#4111yescharacteristic
306C2×C4×C31C2×#4111yescharacteristic
307C2×C4×C31C2×#4111yescharacteristic
308C8×C31—41no—
309C8×C31—41no—
310C8×C31—41no—
311C8×C31—41no—
312C2×#542C2×C3111yescharacteristic
313C2×#433C2×C3111yescharacteristic, complemented
314#2274C2×C3111yescharacteristic, complemented
315#1988C2×C3111yescharacteristic, complemented
316#1987C2×C3111yescharacteristic, complemented
317#1983C2×C3111yescharacteristic, complemented
318#1983C2×C3111yescharacteristic, complemented
319#1875C2×C3111yescharacteristic
320#1874C2×C3111yescharacteristic
321#1873C2×C3111yescharacteristic, complemented
322#1872C2×C3111yescharacteristic, complemented
323#1763C2×C3111yescharacteristic, complemented
324#1762C2×C3111yescharacteristic, complemented
325C4×#103C2×C3111yescharacteristic, complemented
326C4×#102C2×C3111yescharacteristic, complemented
327C22×C31—22no—
328C22×C31—22no—
329C22×C31—22no—
330C22×C31—41no—
331C22×C31—41no—
332C22×C31—41no—
333C22×C31—41no—
334C22×C31—42no—
335C22×C31—42no—
336C22×C31—42no—
337C22×C31—81no—
338C22×C31—81no—
339C22×C31—81no—
340C22×C31—81no—
341C22×C31C22×C22⋊C411yescharacteristic
342C22×C31#52511yescharacteristic
343C22×C31#52511yescharacteristic
344C22×C31#57611yescharacteristic
345C22×C31#57711yescharacteristic
346C22×C31#57711yescharacteristic
347C22×C31#57811yescharacteristic
348C4×C31—22no—
349C4×C31—22no—
350C4×C31—22no—
351C4×C31—22no—
352C4×C31—22no—
353C4×C31—42no—
354C4×C31—42no—
355C4×C31—42no—
356C4×C31—42no—
357C4×C31—42no—
358C4×C31—42no—
359C4×C31—42no—
360C4×C31C4×#4111yescharacteristic
361C4×C31C4×#4111yescharacteristic
362C4×C31#53211yescharacteristic
363C4×C31#53211yescharacteristic
364#542—24no—
365#542C4×C3118yescomplemented
366C2×C4⋊Q8C22×C3111yescharacteristic
367C2×#126—21no—
368C2×#124—21no—
369C2×#124C22×C3111yescharacteristic
370C2×#123—21no—
371C2×C22⋊Q8—21no—
372C2×C22⋊Q8C22×C3111yescharacteristic
373C2×#121C22×C3111yescharacteristic
374C2×C4×Q8C22×C3111yescharacteristic
375C2×C4×D4C22×C3111yescharacteristic
376C2×#117C22×C3111yescharacteristic
377C2×#117C22×C3111yescharacteristic
378C22×C4⋊C4C22×C3111yescharacteristic
379#433—24no—
380C2×C4⋊C8C22×C3111yescharacteristic
381C2×C4⋊C8C22×C3111yescharacteristic
382C2×#103C22×C3111yescharacteristic
383C2×#103C22×C3111yescharacteristic
384C2×#103C22×C3111yescharacteristic
385C2×#103C22×C3111yescharacteristic
386C2×#102C22×C3111yescharacteristic
387C2×#102C22×C3111yescharacteristic
388C2×#102C22×C3111yescharacteristic
389C2×#102C22×C3111yescharacteristic
390C2×C22⋊C8C22×C3111yescharacteristic
391C2×C22⋊C8C22×C3111yescharacteristic
392C2×#97C22×C3111yescharacteristic
393C2×C4×C8C22×C3111yescharacteristic
394C4×C4⋊C4—21no—
395C4×C4⋊C4—21no—
396C4×C4⋊C4C22×C3111yescharacteristic
397C4×C4⋊C4C22×C3111yescharacteristic
398C4×C4⋊C4C22×C3111yescharacteristic
399C4×C4⋊C4C22×C3111yescharacteristic
400C4×C22⋊C4—21no—
401C4×C22⋊C4—21no—
402#340C22×C3111yescharacteristic
403#340C22×C3111yescharacteristic
404#340C22×C3111yescharacteristic
405#340C22×C3111yescharacteristic
406#340C22×C3111yescharacteristic
407#340C22×C3111yescharacteristic
408#340C22×C3111yescharacteristic
409#340C22×C3111yescharacteristic
410C2×C31—42no—
411C2×C31—82no—
412C2×C31#229711yescharacteristic
413C2×C31#289711yescharacteristic
414C2×C31#289811yescharacteristic
415C2×C31#311811yescharacteristic
416C2×C31#312111yescharacteristic
417C2×C31#312411yescharacteristic
418C2×C31#312511yescharacteristic
419C22×Q8—21no—
420C22×Q8C23×C3111yescharacteristic
421C22×D4—21no—
422C22×D4C23×C3111yescharacteristic
423C23×C4—21no—
424C23×C4—21no—
425C23×C4C23×C3111yescharacteristic
426C22×C8C23×C3111yescharacteristic
427C22×C8C23×C3111yescharacteristic
428C22×C8C23×C3111yescharacteristic
429C22×C8C23×C3111yescharacteristic
430C4⋊Q8—22no—
431C4⋊Q8C2×C4×C3114yescomplemented
432#126—28no—
433#124—28no—
434#124—22no—
435#124C2×C4×C3114yescomplemented
436#123—28no—
437C22⋊Q8—22no—
438C22⋊Q8—28no—
439C22⋊Q8C2×C4×C3114yes—
440#121—22no—
441#121C2×C4×C3114yes—
442C4×Q8—22no—
443C4×Q8C2×C4×C3114yescomplemented
444C4×D4—22no—
445C4×D4C2×C4×C3114yescomplemented
446#117—22no—
447#117—22no—
448#117C2×C4×C3114yes—
449#117D4×C3114yes—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4D4×C3111yescharacteristic
457C2×C4⋊C4D4×C3111yescharacteristic
458C2×C4⋊C4C23×C3111yescharacteristic
459C2×C4⋊C4C23×C3111yescharacteristic
460C2×C4⋊C4C23×C3111yescharacteristic
461C2×C4⋊C4C23×C3111yescharacteristic
462C2×C4⋊C4C23×C3111yescharacteristic
463C2×C4⋊C4C23×C3111yescharacteristic
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4D4×C3111yescharacteristic
471C2×C22⋊C4D4×C3111yescharacteristic
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—21no—
478C2×C42C23×C3111yescharacteristic
479C2×C42C23×C3111yescharacteristic
480C4⋊C8—22no—
481C4⋊C8—22no—
482#103—22no—
483#103—22no—
484#103—22no—
485#103—22no—
486#102—22no—
487#102—22no—
488#102—22no—
489#102—22no—
490C22⋊C8—22no—
491C22⋊C8—22no—
492#97—22no—
493C4×C8—22no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498C31#2139711yescharacteristic, direct product factor, Sylow
499C24—21no—
500C24C2×D4×C3111yescharacteristic
501C2×Q8—24no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—81no—
508C2×Q8—81no—
509C2×Q8C22×C4×C3112yes—
510C2×D4—24no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—81no—
517C2×D4—81no—
518C2×D4C22×C4×C3112yes—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—81no—
535C22×C4—81no—
536C22×C4C22×C4×C3112yes—
537C22×C4C2×D4×C3111yescharacteristic
538C22×C4C2×D4×C3111yescharacteristic
539C22×C4C2×D4×C3111yescharacteristic
540C22×C4C2×D4×C3111yescharacteristic
541C22×C4C2×D4×C3111yescharacteristic
542C22×C4C2×D4×C3112yes—
543C22×C4C24×C3111yescharacteristic
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4C22⋊C4×C3114yes—
567C4⋊C4C22⋊C4×C3114yes—
568C4⋊C4C22×C4×C3112yes—
569C4⋊C4C22×C4×C3112yes—
570C4⋊C4#41×C3112yes—
571C4⋊C4#41×C3112yes—
572C4⋊C4#41×C3112yes—
573C4⋊C4#41×C3112yes—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C22⋊C4C22⋊C4×C3114yes—
581C22⋊C4C22⋊C4×C3114yes—
582C42—24no—
583C42—24no—
584C42—81no—
585C42—81no—
586C42—81no—
587C42—81no—
588C42C22×C4×C3112yes—
589C42C22×C4×C3112yes—
590C42C2×D4×C3112yes—
591C42C2×D4×C3112yes—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—22no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23C2×C22⋊C4×C3112yes—
606C23C22×D4×C3111yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—41no—
610Q8—41no—
611Q8—84no—
612D4—22no—
613D4—22no—
614D4—41no—
615D4—41no—
616D4—84no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—84no—
653C2×C4—84no—
654C2×C4C2×C22⋊C4×C3112yes—
655C2×C4C2×C22⋊C4×C3112yes—
656C2×C4C2×C22⋊C4×C3112yes—
657C2×C4C2×C22⋊C4×C3112yes—
658C2×C4C2×C22⋊C4×C3112yes—
659C2×C4C23×C4×C3111yescharacteristic
660C2×C4C22×D4×C3111yescharacteristic
661C2×C4C2×#41×C3111yescharacteristic
662C2×C4C2×#41×C3111yescharacteristic
663C2×C4C2×#41×C3111yescharacteristic
664C2×C4C2×#41×C3111yescharacteristic
665C8—41no—
666C8—41no—
667C8—41no—
668C8—41no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C22×C22⋊C4×C3111yescharacteristic
684C22C31×#52511yescharacteristic
685C22C31×#52511yescharacteristic
686C22C31×#57611yescharacteristic
687C22C31×#57711yescharacteristic
688C22C31×#57711yescharacteristic
689C22C31×#57811yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4C4×#41×C3111yescharacteristic
703C4C4×#41×C3111yescharacteristic
704C4C31×#53211yescharacteristic
705C4C31×#53211yescharacteristic
706C2—42no—
707C2—82no—
708C2C31×#229711yescharacteristic
709C2C31×#289711yescharacteristic
710C2C31×#289811yescharacteristic
711C2C31×#311811yescharacteristic
712C2C31×#312111yescharacteristic
713C2C31×#312411yescharacteristic
714C2C31×#312511yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#433C2semidirect
3. C31×#2274C2semidirect
4. C31×#1988C2semidirect
5. C31×#1987C2semidirect
6. C31×#1983C2semidirect
7. C31×#1983C2semidirect
10. C31×#1873C2semidirect
11. C31×#1872C2semidirect
12. C31×#1763C2semidirect
13. C31×#1762C2semidirect
14. C4×C31×#103C2semidirect
15. C4×C31×#102C2semidirect
17. C31×#542C4semidirect
74. C31×C4⋊Q8C2×C4semidirect
78. C31×#124C2×C4semidirect
86. C4×Q8×C31C2×C4semidirect
88. C4×D4×C31C2×C4semidirect
234. #21397C31direct (N × H)
313. C2×#433C2×C31semidirect
314. #2274C2×C31semidirect
315. #1988C2×C31semidirect
316. #1987C2×C31semidirect
317. #1983C2×C31semidirect
318. #1983C2×C31semidirect
321. #1873C2×C31semidirect
322. #1872C2×C31semidirect
323. #1763C2×C31semidirect
324. #1762C2×C31semidirect
325. C4×#103C2×C31semidirect
326. C4×#102C2×C31semidirect
365. #542C4×C31semidirect
431. C4⋊Q8C2×C4×C31semidirect
435. #124C2×C4×C31semidirect
443. C4×Q8C2×C4×C31semidirect
445. C4×D4C2×C4×C31semidirect
498. C31#21397direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5422
C2×C31×#4332
C31×#22742
C31×#19882
C31×#19872
C31×#19832
C31×#18752
C31×#18742
C31×#18732
C31×#18722
C31×#17632
C31×#17622
C4×C31×#1032
C4×C31×#1022
#2139731