Finite Group Databasebeta

← C31×#17400 #21474159

Subgroups — C31×#17400 #21474159

Order 7936.

1406 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#525C211yesmaximal, characteristic
2C2×C31×#407C211yesmaximal, characteristic, complemented
3C2×C31×#407C211yesmaximal, characteristic, complemented
4C31×#1472C212yesmaximal, complemented
5C31×#1471C212yesmaximal, complemented
6C31×#1468C214yesmaximal, complemented
7C31×#1465C214yesmaximal, complemented
8C22×#41×C31C411yescharacteristic
9C24×C4×C31C2211yescharacteristic
10C22×M16×C31—21no—
11C22×M16×C31—21no—
12C31×#525—21no—
13C31×#525—21no—
14C31×#525—21no—
15C31×#525—21no—
16C31×#525—21no—
17C31×#525—21no—
18C31×#525—21no—
19C31×#525—21no—
20C2×C31×#123C2212yes—
21C2×C31×C22⋊Q8C411yescharacteristic
22C2×C31×C22⋊Q8C2211yescharacteristic
23C2×C31×#121C411yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C2×C31×#120C412yes—
26C2×C4×D4×C31C412yes—
27C2×C4×D4×C31C2212yes—
28C2×C31×#117C411yescharacteristic
29C31×#407—21no—
30C31×#407—21no—
31C31×#407—21no—
32C31×#407—21no—
33C31×#407C2212yes—
34C31×#407C2212yes—
35C31×#407C2212yes—
36C31×#407C2212yes—
37C2×C31×C22⋊C8—21no—
38C2×C31×C22⋊C8—21no—
39C2×C31×C22⋊C8C2212yes—
40C2×C31×C22⋊C8C2212yes—
41C31×#324C2218yescomplemented
42C31×#323C2218yescomplemented
43C25×C31C2×C411yescharacteristic
44C2×#41×C31—21no—
45C2×#41×C31—21no—
46C2×#41×C31—21no—
47C2×#41×C31—21no—
48C2×#41×C31—44no—
49C22×Q8×C31C2×C411yescharacteristic
50C22×D4×C31C2×C412yes—
51C22×D4×C31C2×C412yes—
52C22×D4×C31C2×C412yes—
53C22×D4×C31C2×C411yescharacteristic
54C23×C4×C31—44no—
55C23×C4×C31C2×C411yescharacteristic
56C23×C4×C31C2×C412yes—
57C23×C4×C31C2×C411yescharacteristic
58C23×C4×C31C2×C411yescharacteristic
59C23×C4×C31D411yescharacteristic
60C23×C4×C31D411yescharacteristic
61C23×C4×C31D411yescharacteristic
62C23×C4×C31D411yescharacteristic
63C23×C4×C31D411yescharacteristic
64C23×C4×C31D411yescharacteristic
65C23×C4×C31D411yescharacteristic
66C23×C4×C31D411yescharacteristic
67C23×C4×C31C2311yescharacteristic
68C23×C4×C31C2311yescharacteristic
69C23×C4×C31C2311yescharacteristic
70C2×M16×C31—22no—
71C2×M16×C31—22no—
72C2×M16×C31—22no—
73C2×M16×C31—22no—
74C2×M16×C31—44no—
75C2×M16×C31—44no—
76C22×C8×C31—22no—
77C22×C8×C31—22no—
78C31×#123—22no—
79C31×#123—22no—
80C31×#123—22no—
81C31×#123—22no—
82C31×C22⋊Q8—21no—
83C31×C22⋊Q8—21no—
84C31×C22⋊Q8—21no—
85C31×C22⋊Q8—21no—
86C31×C22⋊Q8—21no—
87C31×C22⋊Q8—21no—
88C31×C22⋊Q8—21no—
89C31×C22⋊Q8—21no—
90C31×#121—21no—
91C31×#121—21no—
92C31×#121—21no—
93C31×#121—21no—
94C31×#121—21no—
95C31×#121—21no—
96C31×#121—21no—
97C31×#121—21no—
98C31×#120—22no—
99C31×#120—22no—
100C31×#120—22no—
101C31×#120—22no—
102C4×D4×C31—22no—
103C4×D4×C31—22no—
104C4×D4×C31—22no—
105C4×D4×C31—22no—
106C4×D4×C31—22no—
107C4×D4×C31—22no—
108C4×D4×C31—22no—
109C4×D4×C31—22no—
110C31×#117—21no—
111C31×#117—21no—
112C31×#117—21no—
113C31×#117—21no—
114C2×C4⋊C4×C31C2×C411yescharacteristic
115C2×C4⋊C4×C31C2×C411yescharacteristic
116C2×C4⋊C4×C31C2×C412yes—
117C2×C4⋊C4×C31C2312yes—
118C2×C22⋊C4×C31C2×C412yes—
119C2×C22⋊C4×C31C2×C412yes—
120C2×C22⋊C4×C31C2×C412yes—
121C2×C22⋊C4×C31C2×C412yes—
122C2×C22⋊C4×C31C2312yes—
123C2×C42×C31C2×C412yes—
124C31×C22⋊C8—22no—
125C31×C22⋊C8—22no—
126C31×C22⋊C8—22no—
127C31×C22⋊C8—22no—
128C31×C22⋊C8—22no—
129C31×C22⋊C8—22no—
130C31×C22⋊C8C2314yes—
131C31×C22⋊C8C2314yes—
132C24×C31—42no—
133C24×C31—42no—
134C24×C31—42no—
135C24×C31C22⋊C411yescharacteristic
136C24×C31C22⋊C411yescharacteristic
137C24×C31C22⋊C411yescharacteristic
138C24×C31C22⋊C411yescharacteristic
139C24×C31C22×C411yescharacteristic
140C24×C31C22×C411yescharacteristic
141C24×C31C22×C412yes—
142C24×C31C22×C411yescharacteristic
143#41×C31—44no—
144#41×C31—44no—
145#41×C31—44no—
146#41×C31—44no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31—42no—
150C2×D4×C31—22no—
151C2×D4×C31—22no—
152C2×D4×C31—22no—
153C2×D4×C31—22no—
154C2×D4×C31—22no—
155C2×D4×C31—22no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—44no—
159C2×D4×C31—42no—
160C2×D4×C31—44no—
161C2×D4×C31—44no—
162C22×C4×C31—24no—
163C22×C4×C31—24no—
164C22×C4×C31—24no—
165C22×C4×C31—22no—
166C22×C4×C31—22no—
167C22×C4×C31—42no—
168C22×C4×C31—42no—
169C22×C4×C31—42no—
170C22×C4×C31—42no—
171C22×C4×C31—42no—
172C22×C4×C31—42no—
173C22×C4×C31—42no—
174C22×C4×C31—42no—
175C22×C4×C31—42no—
176C22×C4×C31—42no—
177C22×C4×C31—42no—
178C22×C4×C31—44no—
179C22×C4×C31C22⋊C411yescharacteristic
180C22×C4×C31C22⋊C411yescharacteristic
181C22×C4×C31C22⋊C411yescharacteristic
182C22×C4×C31C22⋊C411yescharacteristic
183C22×C4×C31C22⋊C411yescharacteristic
184C22×C4×C31C22⋊C411yescharacteristic
185C22×C4×C31C22⋊C411yescharacteristic
186C22×C4×C31C22⋊C411yescharacteristic
187C22×C4×C31C22⋊C411yescharacteristic
188C22×C4×C31C22⋊C411yescharacteristic
189C22×C4×C31C22⋊C411yescharacteristic
190C22×C4×C31C22⋊C411yescharacteristic
191C22×C4×C31C22×C412yes—
192C22×C4×C31C22×C411yescharacteristic
193C22×C4×C31C22×C411yescharacteristic
194C22×C4×C31C22×C412yes—
195C22×C4×C31C22×C412yes—
196C22×C4×C31C22×C411yescharacteristic
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31C2×D411yescharacteristic
204C22×C4×C31C2×D411yescharacteristic
205C22×C4×C31C2×D411yescharacteristic
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2411yescharacteristic
210M16×C31—44no—
211M16×C31—44no—
212M16×C31—44no—
213M16×C31—44no—
214C2×C8×C31—24no—
215C2×C8×C31—24no—
216C2×C8×C31—44no—
217C2×C8×C31—44no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—21no—
220C4⋊C4×C31—21no—
221C4⋊C4×C31—21no—
222C4⋊C4×C31—22no—
223C4⋊C4×C31—22no—
224C4⋊C4×C31—22no—
225C4⋊C4×C31—22no—
226C22⋊C4×C31—22no—
227C22⋊C4×C31—22no—
228C22⋊C4×C31—22no—
229C22⋊C4×C31—22no—
230C22⋊C4×C31—22no—
231C22⋊C4×C31—22no—
232C22⋊C4×C31—22no—
233C22⋊C4×C31—22no—
234C22⋊C4×C31—22no—
235C22⋊C4×C31—22no—
236C42×C31—22no—
237C42×C31—22no—
238#17400C3111yesmaximal, characteristic, direct product factor, Sylow
239C23×C31—22no—
240C23×C31—22no—
241C23×C31—22no—
242C23×C31—22no—
243C23×C31—22no—
244C23×C31—22no—
245C23×C31—22no—
246C23×C31—22no—
247C23×C31—22no—
248C23×C31—22no—
249C23×C31—24no—
250C23×C31—41no—
251C23×C31—41no—
252C23×C31—41no—
253C23×C31—41no—
254C23×C31—41no—
255C23×C31—41no—
256C23×C31—41no—
257C23×C31—41no—
258C23×C31—41no—
259C23×C31—41no—
260C23×C31—41no—
261C23×C31—41no—
262C23×C31—42no—
263C23×C31—42no—
264C23×C31—416no—
265C23×C31C2×C22⋊C411yescharacteristic
266C23×C31C2×C22⋊C411yescharacteristic
267C23×C31C2×C22⋊C411yescharacteristic
268C23×C31C2×C22⋊C411yescharacteristic
269C23×C31C2×C22⋊C411yescharacteristic
270C23×C31C2×C22⋊C411yescharacteristic
271C23×C31C23×C411yescharacteristic
272Q8×C31—42no—
273Q8×C31—42no—
274D4×C31—42no—
275D4×C31—44no—
276D4×C31—44no—
277D4×C31—44no—
278D4×C31—44no—
279D4×C31—44no—
280D4×C31—44no—
281D4×C31—42no—
282C2×C4×C31—22no—
283C2×C4×C31—22no—
284C2×C4×C31—22no—
285C2×C4×C31—22no—
286C2×C4×C31—22no—
287C2×C4×C31—22no—
288C2×C4×C31—22no—
289C2×C4×C31—22no—
290C2×C4×C31—22no—
291C2×C4×C31—22no—
292C2×C4×C31—22no—
293C2×C4×C31—22no—
294C2×C4×C31—22no—
295C2×C4×C31—22no—
296C2×C4×C31—22no—
297C2×C4×C31—22no—
298C2×C4×C31—22no—
299C2×C4×C31—22no—
300C2×C4×C31—24no—
301C2×C4×C31—41no—
302C2×C4×C31—41no—
303C2×C4×C31—41no—
304C2×C4×C31—41no—
305C2×C4×C31—41no—
306C2×C4×C31—41no—
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—44no—
314C2×C4×C31—44no—
315C2×C4×C31—42no—
316C2×C4×C31—42no—
317C2×C4×C31#9914yes—
318C2×C4×C31C2×C22⋊C411yescharacteristic
319C2×C4×C31C2×C22⋊C411yescharacteristic
320C2×C4×C31C2×C22⋊C411yescharacteristic
321C2×C4×C31C2×C22⋊C411yescharacteristic
322C2×C4×C31C2×C22⋊C411yescharacteristic
323C2×C4×C31C2×C22⋊C411yescharacteristic
324C2×C4×C31C22×D411yescharacteristic
325C2×C4×C31C22×D411yescharacteristic
326C8×C31—44no—
327C8×C31—44no—
328C2×#525C2×C3111yescharacteristic
329C2×#407C2×C3111yescharacteristic, complemented
330C2×#407C2×C3111yescharacteristic, complemented
331#1472C2×C3112yescomplemented
332#1471C2×C3112yescomplemented
333#1468C2×C3114yescomplemented
334#1465C2×C3114yescomplemented
335C22×C31—21no—
336C22×C31—21no—
337C22×C31—21no—
338C22×C31—21no—
339C22×C31—21no—
340C22×C31—21no—
341C22×C31—21no—
342C22×C31—21no—
343C22×C31—21no—
344C22×C31—21no—
345C22×C31—21no—
346C22×C31—21no—
347C22×C31—21no—
348C22×C31—21no—
349C22×C31—21no—
350C22×C31—21no—
351C22×C31—21no—
352C22×C31—21no—
353C22×C31—44no—
354C22×C31—44no—
355C22×C31—44no—
356C22×C31—44no—
357C22×C31—44no—
358C22×C31—44no—
359C22×C31—44no—
360C22×C31—42no—
361C22×C31—42no—
362C22×C31—42no—
363C22×C31—84no—
364C22×C31C2×#9912yes—
365C22×C31#41312yes—
366C22×C31C22×C22⋊C411yescharacteristic
367C22×C31#56812yes—
368C4×C31—21no—
369C4×C31—21no—
370C4×C31—21no—
371C4×C31—21no—
372C4×C31—21no—
373C4×C31—21no—
374C4×C31—42no—
375C4×C31—42no—
376C4×C31—42no—
377C4×C31C2×#9912yes—
378C4×C31C2×#9912yes—
379C22×#41C4×C3111yescharacteristic
380C24×C4C22×C3111yescharacteristic
381C22×M16—21no—
382C22×M16—21no—
383#525—21no—
384#525—21no—
385#525—21no—
386#525—21no—
387#525—21no—
388#525—21no—
389#525—21no—
390#525—21no—
391C2×#123C22×C3112yes—
392C2×C22⋊Q8C4×C3111yescharacteristic
393C2×C22⋊Q8C22×C3111yescharacteristic
394C2×#121C4×C3111yescharacteristic
395C2×#121C22×C3111yescharacteristic
396C2×#120C4×C3112yes—
397C2×C4×D4C4×C3112yes—
398C2×C4×D4C22×C3112yes—
399C2×#117C4×C3111yescharacteristic
400#407—21no—
401#407—21no—
402#407—21no—
403#407—21no—
404#407C22×C3112yes—
405#407C22×C3112yes—
406#407C22×C3112yes—
407#407C22×C3112yes—
408C2×C22⋊C8—21no—
409C2×C22⋊C8—21no—
410C2×C22⋊C8C22×C3112yes—
411C2×C22⋊C8C22×C3112yes—
412#324C22×C3118yescomplemented
413#323C22×C3118yescomplemented
414C2×C31—22no—
415C2×C31—22no—
416C2×C31—22no—
417C2×C31—41no—
418C2×C31—41no—
419C2×C31—41no—
420C2×C31—41no—
421C2×C31—82no—
422C2×C31#287911yescharacteristic
423C2×C31C22×#9911yescharacteristic
424C2×C31C2×#41311yescharacteristic
425C25C2×C4×C3111yescharacteristic
426C2×#41—21no—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—44no—
431C22×Q8C2×C4×C3111yescharacteristic
432C22×D4C2×C4×C3112yes—
433C22×D4C2×C4×C3112yes—
434C22×D4C2×C4×C3112yes—
435C22×D4C2×C4×C3111yescharacteristic
436C23×C4—44no—
437C23×C4C2×C4×C3111yescharacteristic
438C23×C4C2×C4×C3112yes—
439C23×C4C2×C4×C3111yescharacteristic
440C23×C4C2×C4×C3111yescharacteristic
441C23×C4D4×C3111yescharacteristic
442C23×C4D4×C3111yescharacteristic
443C23×C4D4×C3111yescharacteristic
444C23×C4D4×C3111yescharacteristic
445C23×C4D4×C3111yescharacteristic
446C23×C4D4×C3111yescharacteristic
447C23×C4D4×C3111yescharacteristic
448C23×C4D4×C3111yescharacteristic
449C23×C4C23×C3111yescharacteristic
450C23×C4C23×C3111yescharacteristic
451C23×C4C23×C3111yescharacteristic
452C2×M16—22no—
453C2×M16—22no—
454C2×M16—22no—
455C2×M16—22no—
456C2×M16—44no—
457C2×M16—44no—
458C22×C8—22no—
459C22×C8—22no—
460#123—22no—
461#123—22no—
462#123—22no—
463#123—22no—
464C22⋊Q8—21no—
465C22⋊Q8—21no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—21no—
469C22⋊Q8—21no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472#121—21no—
473#121—21no—
474#121—21no—
475#121—21no—
476#121—21no—
477#121—21no—
478#121—21no—
479#121—21no—
480#120—22no—
481#120—22no—
482#120—22no—
483#120—22no—
484C4×D4—22no—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—22no—
492#117—21no—
493#117—21no—
494#117—21no—
495#117—21no—
496C2×C4⋊C4C2×C4×C3111yescharacteristic
497C2×C4⋊C4C2×C4×C3111yescharacteristic
498C2×C4⋊C4C2×C4×C3112yes—
499C2×C4⋊C4C23×C3112yes—
500C2×C22⋊C4C2×C4×C3112yes—
501C2×C22⋊C4C2×C4×C3112yes—
502C2×C22⋊C4C2×C4×C3112yes—
503C2×C22⋊C4C2×C4×C3112yes—
504C2×C22⋊C4C23×C3112yes—
505C2×C42C2×C4×C3112yes—
506C22⋊C8—22no—
507C22⋊C8—22no—
508C22⋊C8—22no—
509C22⋊C8—22no—
510C22⋊C8—22no—
511C22⋊C8—22no—
512C22⋊C8C23×C3114yes—
513C22⋊C8C23×C3114yes—
514C31#1740011yescharacteristic, direct product factor, Sylow
515C24—42no—
516C24—42no—
517C24—42no—
518C24C22⋊C4×C3111yescharacteristic
519C24C22⋊C4×C3111yescharacteristic
520C24C22⋊C4×C3111yescharacteristic
521C24C22⋊C4×C3111yescharacteristic
522C24C22×C4×C3111yescharacteristic
523C24C22×C4×C3111yescharacteristic
524C24C22×C4×C3112yes—
525C24C22×C4×C3111yescharacteristic
526#41—44no—
527#41—44no—
528#41—44no—
529#41—44no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—42no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—44no—
542C2×D4—42no—
543C2×D4—44no—
544C2×D4—44no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—44no—
562C22×C4C22⋊C4×C3111yescharacteristic
563C22×C4C22⋊C4×C3111yescharacteristic
564C22×C4C22⋊C4×C3111yescharacteristic
565C22×C4C22⋊C4×C3111yescharacteristic
566C22×C4C22⋊C4×C3111yescharacteristic
567C22×C4C22⋊C4×C3111yescharacteristic
568C22×C4C22⋊C4×C3111yescharacteristic
569C22×C4C22⋊C4×C3111yescharacteristic
570C22×C4C22⋊C4×C3111yescharacteristic
571C22×C4C22⋊C4×C3111yescharacteristic
572C22×C4C22⋊C4×C3111yescharacteristic
573C22×C4C22⋊C4×C3111yescharacteristic
574C22×C4C22×C4×C3112yes—
575C22×C4C22×C4×C3111yescharacteristic
576C22×C4C22×C4×C3111yescharacteristic
577C22×C4C22×C4×C3112yes—
578C22×C4C22×C4×C3112yes—
579C22×C4C22×C4×C3111yescharacteristic
580C22×C4C2×D4×C3111yescharacteristic
581C22×C4C2×D4×C3111yescharacteristic
582C22×C4C2×D4×C3111yescharacteristic
583C22×C4C2×D4×C3111yescharacteristic
584C22×C4C2×D4×C3111yescharacteristic
585C22×C4C2×D4×C3111yescharacteristic
586C22×C4C2×D4×C3111yescharacteristic
587C22×C4C2×D4×C3111yescharacteristic
588C22×C4C2×D4×C3111yescharacteristic
589C22×C4C2×D4×C3111yescharacteristic
590C22×C4C2×D4×C3111yescharacteristic
591C22×C4C2×D4×C3111yescharacteristic
592C22×C4C24×C3111yescharacteristic
593M16—44no—
594M16—44no—
595M16—44no—
596M16—44no—
597C2×C8—24no—
598C2×C8—24no—
599C2×C8—44no—
600C2×C8—44no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C42—22no—
620C42—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—42no—
645C23—42no—
646C23—416no—
647C23C2×C22⋊C4×C3111yescharacteristic
648C23C2×C22⋊C4×C3111yescharacteristic
649C23C2×C22⋊C4×C3111yescharacteristic
650C23C2×C22⋊C4×C3111yescharacteristic
651C23C2×C22⋊C4×C3111yescharacteristic
652C23C2×C22⋊C4×C3111yescharacteristic
653C23C23×C4×C3111yescharacteristic
654Q8—42no—
655Q8—42no—
656D4—42no—
657D4—44no—
658D4—44no—
659D4—44no—
660D4—44no—
661D4—44no—
662D4—44no—
663D4—42no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4C31×#9914yes—
700C2×C4C2×C22⋊C4×C3111yescharacteristic
701C2×C4C2×C22⋊C4×C3111yescharacteristic
702C2×C4C2×C22⋊C4×C3111yescharacteristic
703C2×C4C2×C22⋊C4×C3111yescharacteristic
704C2×C4C2×C22⋊C4×C3111yescharacteristic
705C2×C4C2×C22⋊C4×C3111yescharacteristic
706C2×C4C22×D4×C3111yescharacteristic
707C2×C4C22×D4×C3111yescharacteristic
708C8—44no—
709C8—44no—
710C22—21no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—44no—
729C22—44no—
730C22—44no—
731C22—44no—
732C22—44no—
733C22—44no—
734C22—44no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—84no—
739C22C2×C31×#9912yes—
740C22C31×#41312yes—
741C22C22×C22⋊C4×C3111yescharacteristic
742C22C31×#56812yes—
743C4—21no—
744C4—21no—
745C4—21no—
746C4—21no—
747C4—21no—
748C4—21no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4C2×C31×#9912yes—
753C4C2×C31×#9912yes—
754C2—22no—
755C2—22no—
756C2—22no—
757C2—41no—
758C2—41no—
759C2—41no—
760C2—41no—
761C2—82no—
762C2C31×#287911yescharacteristic
763C2C22×C31×#9911yescharacteristic
764C2C2×C31×#41311yescharacteristic
subgroupG/H
center, socleC22×C31C22×C22⋊C4
commutatorC23C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#525C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#407C2semidirect
3. C2×C31×#407C2semidirect
4. C31×#1472C2semidirect
5. C31×#1471C2semidirect
6. C31×#1468C2semidirect
7. C31×#1465C2semidirect
41. C31×#324C22semidirect
42. C31×#323C22semidirect
238. #17400C31direct (N × H)
329. C2×#407C2×C31semidirect
330. C2×#407C2×C31semidirect
331. #1472C2×C31semidirect
332. #1471C2×C31semidirect
333. #1468C2×C31semidirect
334. #1465C2×C31semidirect
412. #324C22×C31semidirect
413. #323C22×C31semidirect
514. C31#17400direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5252
C2×C31×#4072
C31×#14722
C31×#14712
C31×#14682
C31×#14652
#1740031