Finite Group Databasebeta

← C31×#33011 #21489770

Subgroups — C31×#33011 #21489770

Order 7936.

1346 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#41×C31C211yesmaximal, characteristic
2C2×C31×#485C211yesmaximal, characteristic, complemented
3C2×C31×#452C211yesmaximal, characteristic
4C31×#2855C211yesmaximal, characteristic, complemented
5C31×#1878C211yesmaximal, characteristic, complemented
6C31×#1878C211yesmaximal, characteristic, complemented
7C31×#1877C211yesmaximal, characteristic, complemented
8C31×#1877C211yesmaximal, characteristic, complemented
9C31×#1865C211yesmaximal, characteristic, complemented
10C31×#1864C211yesmaximal, characteristic, complemented
11C31×#1863C211yesmaximal, characteristic, complemented
12C31×#1862C211yesmaximal, characteristic, complemented
13C31×#1825C211yesmaximal, characteristic, complemented
14C31×#1817C211yesmaximal, characteristic, complemented
15C31×#1788C211yesmaximal, characteristic
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×D4×C31—21no—
25C2×C4×D4×C31—21no—
26C2×C4×D4×C31C2211yescharacteristic
27C2×C4×D4×C31C2211yescharacteristic
28C2×C31×#117—21no—
29C2×C31×#117C2211yescharacteristic
30C22×C42×C31—21no—
31C22×C42×C31C2211yescharacteristic
32C31×#485—24no—
33C31×#452—24no—
34C2×C31×#107C2211yescharacteristic
35C2×C31×#106C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×C22⋊C8C2211yescharacteristic
45C2×C31×C22⋊C8C2211yescharacteristic
46C31×#391C2211yescharacteristic
47C31×#391C2211yescharacteristic
48C31×#389C2211yescharacteristic
49C31×#389C2211yescharacteristic
50C31×#387—21no—
51C31×#387—21no—
52C31×#385—21no—
53C31×#381—21no—
54C31×#380C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C2×#41×C31—22no—
64C2×#41×C31—22no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31D414yes—
69C22×Q8×C31C2311yescharacteristic
70C22×Q8×C31C2311yescharacteristic
71C22×D4×C31—21no—
72C22×D4×C31C2311yescharacteristic
73C23×C4×C31—21no—
74C23×C4×C31—21no—
75C23×C4×C31—21no—
76C23×C4×C31D411yescharacteristic
77C23×C4×C31D411yescharacteristic
78C23×C4×C31C2311yescharacteristic
79C2×Q16×C31—22no—
80C2×Q16×C31—22no—
81C2×Q16×C31—22no—
82C2×SD16×C31—22no—
83C2×SD16×C31—22no—
84C2×SD16×C31—22no—
85C22×C8×C31C2311yescharacteristic
86C22×C8×C31C2311yescharacteristic
87C22×C8×C31C2311yescharacteristic
88C22×C8×C31C2311yescharacteristic
89C31×C22⋊Q8—22no—
90C31×C22⋊Q8—22no—
91C4×Q8×C31—22no—
92C4×Q8×C31—22no—
93C4×Q8×C31—22no—
94C4×Q8×C31—22no—
95C4×D4×C31—28no—
96C4×D4×C31—28no—
97C4×D4×C31—22no—
98C4×D4×C31—22no—
99C4×D4×C31—22no—
100C4×D4×C31—22no—
101C31×#117—28no—
102C31×#117—22no—
103C31×#117D414yes—
104C2×C4⋊C4×C31—21no—
105C2×C4⋊C4×C31—21no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31C2311yescharacteristic
110C2×C4⋊C4×C31C2311yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C42×C31—28no—
120C2×C42×C31—21no—
121C2×C42×C31—21no—
122C2×C42×C31—21no—
123C2×C42×C31—22no—
124C2×C42×C31—22no—
125C2×C42×C31D411yescharacteristic
126C2×C42×C31D411yescharacteristic
127C2×C42×C31C2311yescharacteristic
128C2×C42×C31C2311yescharacteristic
129C31×#107—22no—
130C31×#106—22no—
131C31×#103—22no—
132C31×#103—22no—
133C31×#103—22no—
134C31×#103—22no—
135C31×#103—22no—
136C31×#102—22no—
137C31×#102—22no—
138C31×#102—22no—
139C31×C22⋊C8—22no—
140C31×C22⋊C8—22no—
141C31×#95—21no—
142C31×#95—21no—
143C31×#95—21no—
144C31×#95—21no—
145C31×#95—21no—
146C31×#95—21no—
147C31×#95—21no—
148C24×C31—21no—
149C24×C31C2×D411yescharacteristic
150#41×C31—28no—
151#41×C31—28no—
152#41×C31—28no—
153#41×C31—28no—
154C2×Q8×C31—21no—
155C2×Q8×C31—21no—
156C2×Q8×C31—21no—
157C2×Q8×C31—21no—
158C2×Q8×C31—21no—
159C2×Q8×C31—21no—
160C2×Q8×C31—21no—
161C2×Q8×C31—21no—
162C2×Q8×C31—21no—
163C2×Q8×C31C2×D412yes—
164C2×Q8×C31#4112yes—
165C2×Q8×C31#4112yes—
166C2×D4×C31—24no—
167C2×D4×C31—24no—
168C2×D4×C31—24no—
169C2×D4×C31—21no—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
172C2×D4×C31C2×D412yes—
173C2×D4×C31#4112yes—
174C2×D4×C31#4112yes—
175C22×C4×C31—24no—
176C22×C4×C31—24no—
177C22×C4×C31—21no—
178C22×C4×C31—24no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—24no—
184C22×C4×C31—24no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—22no—
190C22×C4×C31—22no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—41no—
196C22×C4×C31—41no—
197C22×C4×C31—42no—
198C22×C4×C31—42no—
199C22×C4×C31—42no—
200C22×C4×C31—42no—
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31C2×D411yescharacteristic
204C22×C4×C31C2×D412yes—
205C22×C4×C31C2×D412yes—
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2411yescharacteristic
209Q16×C31—44no—
210SD16×C31—44no—
211C2×C8×C31—21no—
212C2×C8×C31—21no—
213C2×C8×C31—21no—
214C2×C8×C31—21no—
215C2×C8×C31—21no—
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—
223C4⋊C4×C31—24no—
224C4⋊C4×C31—24no—
225C4⋊C4×C31—21no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31—21no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—21no—
233C4⋊C4×C31—42no—
234C4⋊C4×C31—42no—
235C4⋊C4×C31—42no—
236C4⋊C4×C31C2×D412yes—
237C4⋊C4×C31C2×D412yes—
238C22⋊C4×C31—24no—
239C22⋊C4×C31—24no—
240C22⋊C4×C31—24no—
241C22⋊C4×C31—42no—
242C22⋊C4×C31—42no—
243C42×C31—24no—
244C42×C31—24no—
245C42×C31—22no—
246C42×C31—24no—
247C42×C31—22no—
248C42×C31—21no—
249C42×C31—21no—
250C42×C31—21no—
251C42×C31—21no—
252#33011C3111yesmaximal, characteristic, direct product factor, Sylow
253C23×C31—22no—
254C23×C31—21no—
255C23×C31—21no—
256C23×C31—22no—
257C23×C31—22no—
258C23×C31—21no—
259C23×C31—21no—
260C23×C31—21no—
261C23×C31—21no—
262C23×C31—41no—
263C23×C31—41no—
264C23×C31—41no—
265C23×C31—41no—
266C23×C31#12012yes—
267C23×C31C22×D411yescharacteristic
268Q8×C31—22no—
269Q8×C31—22no—
270Q8×C31—22no—
271Q8×C31—41no—
272Q8×C31—41no—
273Q8×C31—41no—
274Q8×C31—41no—
275Q8×C31#12314yes—
276D4×C31—216no—
277D4×C31—22no—
278D4×C31—22no—
279D4×C31—22no—
280D4×C31#12314yes—
281C2×C4×C31—216no—
282C2×C4×C31—21no—
283C2×C4×C31—21no—
284C2×C4×C31—22no—
285C2×C4×C31—21no—
286C2×C4×C31—21no—
287C2×C4×C31—22no—
288C2×C4×C31—22no—
289C2×C4×C31—21no—
290C2×C4×C31—21no—
291C2×C4×C31—22no—
292C2×C4×C31—22no—
293C2×C4×C31—22no—
294C2×C4×C31—22no—
295C2×C4×C31—21no—
296C2×C4×C31—21no—
297C2×C4×C31—22no—
298C2×C4×C31—22no—
299C2×C4×C31—21no—
300C2×C4×C31—21no—
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—44no—
304C2×C4×C31—44no—
305C2×C4×C31—48no—
306C2×C4×C31—48no—
307C2×C4×C31—41no—
308C2×C4×C31—41no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—41no—
312C2×C4×C31—41no—
313C2×C4×C31—41no—
314C2×C4×C31—41no—
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#12012yes—
324C2×C4×C31#13512yes—
325C2×C4×C31#13712yes—
326C2×C4×C31C22×D411yescharacteristic
327C2×C4×C31C22×D411yescharacteristic
328C2×C4×C31C2×#4111yescharacteristic
329C2×C4×C31C2×#4111yescharacteristic
330C2×C4×C31C2×#4111yescharacteristic
331C2×C4×C31C2×#4111yescharacteristic
332C8×C31—41no—
333C8×C31—41no—
334C8×C31—41no—
335C8×C31—41no—
336C2×C4×#41C2×C3111yescharacteristic
337C2×#485C2×C3111yescharacteristic, complemented
338C2×#452C2×C3111yescharacteristic
339#2855C2×C3111yescharacteristic, complemented
340#1878C2×C3111yescharacteristic, complemented
341#1878C2×C3111yescharacteristic, complemented
342#1877C2×C3111yescharacteristic, complemented
343#1877C2×C3111yescharacteristic, complemented
344#1865C2×C3111yescharacteristic, complemented
345#1864C2×C3111yescharacteristic, complemented
346#1863C2×C3111yescharacteristic, complemented
347#1862C2×C3111yescharacteristic, complemented
348#1825C2×C3111yescharacteristic, complemented
349#1817C2×C3111yescharacteristic, complemented
350#1788C2×C3111yescharacteristic
351C22×C31—22no—
352C22×C31—24no—
353C22×C31—22no—
354C22×C31—22no—
355C22×C31—41no—
356C22×C31—42no—
357C22×C31—41no—
358C22×C31—42no—
359C22×C31—41no—
360C22×C31—42no—
361C22×C31—41no—
362C22×C31—42no—
363C22×C31—42no—
364C22×C31—42no—
365C22×C31C2×#12011yescharacteristic
366C22×C31#52511yescharacteristic
367C22×C31#52511yescharacteristic
368C22×C31C2×#13511yescharacteristic
369C22×C31C2×#13711yescharacteristic
370C22×C31#57511yescharacteristic
371C22×C31#57511yescharacteristic
372C4×C31—22no—
373C4×C31—24no—
374C4×C31—22no—
375C4×C31—22no—
376C4×C31—41no—
377C4×C31—42no—
378C4×C31—41no—
379C4×C31—42no—
380C4×C31—81no—
381C4×C31—81no—
382C4×C31—81no—
383C4×C31—81no—
384C4×C31C2×#12311yescharacteristic
385C4×C31C2×#12311yescharacteristic
386C4×C31#52511yescharacteristic
387C4×C31#52511yescharacteristic
388C22×#41C22×C3111yescharacteristic
389C22×Q16C22×C3111yescharacteristic
390C22×SD16C22×C3111yescharacteristic
391C2×C22⋊Q8C22×C3111yescharacteristic
392C4×#41—24no—
393C4×#41—24no—
394C2×C4×Q8C22×C3111yescharacteristic
395C2×C4×Q8C22×C3111yescharacteristic
396C2×C4×D4—21no—
397C2×C4×D4—21no—
398C2×C4×D4C22×C3111yescharacteristic
399C2×C4×D4C22×C3111yescharacteristic
400C2×#117—21no—
401C2×#117C22×C3111yescharacteristic
402C22×C42—21no—
403C22×C42C22×C3111yescharacteristic
404#485—24no—
405#452—24no—
406C2×#107C22×C3111yescharacteristic
407C2×#106C22×C3111yescharacteristic
408C2×#103C22×C3111yescharacteristic
409C2×#103C22×C3111yescharacteristic
410C2×#103C22×C3111yescharacteristic
411C2×#103C22×C3111yescharacteristic
412C2×#103C22×C3111yescharacteristic
413C2×#102C22×C3111yescharacteristic
414C2×#102C22×C3111yescharacteristic
415C2×#102C22×C3111yescharacteristic
416C2×C22⋊C8C22×C3111yescharacteristic
417C2×C22⋊C8C22×C3111yescharacteristic
418#391C22×C3111yescharacteristic
419#391C22×C3111yescharacteristic
420#389C22×C3111yescharacteristic
421#389C22×C3111yescharacteristic
422#387—21no—
423#387—21no—
424#385—21no—
425#381—21no—
426#380C22×C3111yescharacteristic
427#340C22×C3111yescharacteristic
428#340C22×C3111yescharacteristic
429#340C22×C3111yescharacteristic
430#340C22×C3111yescharacteristic
431#336C22×C3111yescharacteristic
432#336C22×C3111yescharacteristic
433#336C22×C3111yescharacteristic
434#336C22×C3111yescharacteristic
435C2×C31—42no—
436C2×C31—44no—
437C2×C31#284911yescharacteristic
438C2×C31#300211yescharacteristic
439C2×C31#300711yescharacteristic
440C2×C31#310211yescharacteristic
441C2×C31#310711yescharacteristic
442C2×C31#311111yescharacteristic
443C2×C31#311611yescharacteristic
444C2×#41—22no—
445C2×#41—22no—
446C2×#41—22no—
447C2×#41—22no—
448C2×#41—22no—
449C2×#41D4×C3114yes—
450C22×Q8C23×C3111yescharacteristic
451C22×Q8C23×C3111yescharacteristic
452C22×D4—21no—
453C22×D4C23×C3111yescharacteristic
454C23×C4—21no—
455C23×C4—21no—
456C23×C4—21no—
457C23×C4D4×C3111yescharacteristic
458C23×C4D4×C3111yescharacteristic
459C23×C4C23×C3111yescharacteristic
460C2×Q16—22no—
461C2×Q16—22no—
462C2×Q16—22no—
463C2×SD16—22no—
464C2×SD16—22no—
465C2×SD16—22no—
466C22×C8C23×C3111yescharacteristic
467C22×C8C23×C3111yescharacteristic
468C22×C8C23×C3111yescharacteristic
469C22×C8C23×C3111yescharacteristic
470C22⋊Q8—22no—
471C22⋊Q8—22no—
472C4×Q8—22no—
473C4×Q8—22no—
474C4×Q8—22no—
475C4×Q8—22no—
476C4×D4—28no—
477C4×D4—28no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—22no—
481C4×D4—22no—
482#117—28no—
483#117—22no—
484#117D4×C3114yes—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4C23×C3111yescharacteristic
491C2×C4⋊C4C23×C3111yescharacteristic
492C2×C4⋊C4C23×C3111yescharacteristic
493C2×C4⋊C4C23×C3111yescharacteristic
494C2×C4⋊C4C23×C3111yescharacteristic
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C42—28no—
501C2×C42—21no—
502C2×C42—21no—
503C2×C42—21no—
504C2×C42—22no—
505C2×C42—22no—
506C2×C42D4×C3111yescharacteristic
507C2×C42D4×C3111yescharacteristic
508C2×C42C23×C3111yescharacteristic
509C2×C42C23×C3111yescharacteristic
510#107—22no—
511#106—22no—
512#103—22no—
513#103—22no—
514#103—22no—
515#103—22no—
516#103—22no—
517#102—22no—
518#102—22no—
519#102—22no—
520C22⋊C8—22no—
521C22⋊C8—22no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529C31#3301111yescharacteristic, direct product factor, Sylow
530C24—21no—
531C24C2×D4×C3111yescharacteristic
532#41—28no—
533#41—28no—
534#41—28no—
535#41—28no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8C2×D4×C3112yes—
546C2×Q8#41×C3112yes—
547C2×Q8#41×C3112yes—
548C2×D4—24no—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4C2×D4×C3112yes—
555C2×D4#41×C3112yes—
556C2×D4#41×C3112yes—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—21no—
560C22×C4—24no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4C2×D4×C3111yescharacteristic
584C22×C4C2×D4×C3111yescharacteristic
585C22×C4C2×D4×C3111yescharacteristic
586C22×C4C2×D4×C3112yes—
587C22×C4C2×D4×C3112yes—
588C22×C4C2×D4×C3111yescharacteristic
589C22×C4C2×D4×C3111yescharacteristic
590C22×C4C24×C3111yescharacteristic
591Q16—44no—
592SD16—44no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4C2×D4×C3112yes—
619C4⋊C4C2×D4×C3112yes—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C42—24no—
626C42—24no—
627C42—22no—
628C42—24no—
629C42—22no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—21no—
634C23—22no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—22no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23C31×#12012yes—
648C23C22×D4×C3111yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—22no—
652Q8—41no—
653Q8—41no—
654Q8—41no—
655Q8—41no—
656Q8C31×#12314yes—
657D4—216no—
658D4—22no—
659D4—22no—
660D4—22no—
661D4C31×#12314yes—
662C2×C4—216no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—48no—
687C2×C4—48no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4C31×#12012yes—
705C2×C4C31×#13512yes—
706C2×C4C31×#13712yes—
707C2×C4C22×D4×C3111yescharacteristic
708C2×C4C22×D4×C3111yescharacteristic
709C2×C4C2×#41×C3111yescharacteristic
710C2×C4C2×#41×C3111yescharacteristic
711C2×C4C2×#41×C3111yescharacteristic
712C2×C4C2×#41×C3111yescharacteristic
713C8—41no—
714C8—41no—
715C8—41no—
716C8—41no—
717C22—22no—
718C22—24no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—41no—
726C22—42no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22C2×C31×#12011yescharacteristic
732C22C31×#52511yescharacteristic
733C22C31×#52511yescharacteristic
734C22C2×C31×#13511yescharacteristic
735C22C2×C31×#13711yescharacteristic
736C22C31×#57511yescharacteristic
737C22C31×#57511yescharacteristic
738C4—22no—
739C4—24no—
740C4—22no—
741C4—22no—
742C4—41no—
743C4—42no—
744C4—41no—
745C4—42no—
746C4—81no—
747C4—81no—
748C4—81no—
749C4—81no—
750C4C2×C31×#12311yescharacteristic
751C4C2×C31×#12311yescharacteristic
752C4C31×#52511yescharacteristic
753C4C31×#52511yescharacteristic
754C2—42no—
755C2—44no—
756C2C31×#284911yescharacteristic
757C2C31×#300211yescharacteristic
758C2C31×#300711yescharacteristic
759C2C31×#310211yescharacteristic
760C2C31×#310711yescharacteristic
761C2C31×#311111yescharacteristic
762C2C31×#311611yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×#41×C31C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#485C2semidirect
4. C31×#2855C2semidirect
5. C31×#1878C2semidirect
6. C31×#1878C2semidirect
7. C31×#1877C2semidirect
8. C31×#1877C2semidirect
9. C31×#1865C2semidirect
10. C31×#1864C2semidirect
11. C31×#1863C2semidirect
12. C31×#1862C2semidirect
13. C31×#1825C2semidirect
14. C31×#1817C2semidirect
252. #33011C31direct (N × H)
337. C2×#485C2×C31semidirect
339. #2855C2×C31semidirect
340. #1878C2×C31semidirect
341. #1878C2×C31semidirect
342. #1877C2×C31semidirect
343. #1877C2×C31semidirect
344. #1865C2×C31semidirect
345. #1864C2×C31semidirect
346. #1863C2×C31semidirect
347. #1862C2×C31semidirect
348. #1825C2×C31semidirect
349. #1817C2×C31semidirect
529. C31#33011direct (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×#4852
C2×C31×#4522
C31×#28552
C31×#18782
C31×#18772
C31×#18652
C31×#18642
C31×#18632
C31×#18622
C31×#18252
C31×#18172
C31×#17882
#3301131