Finite Group Databasebeta

← C31×#22424 #21479183

Subgroups — C31×#22424 #21479183

Order 7936.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#546C211yesmaximal, characteristic
2C2×C31×#435C211yesmaximal, characteristic, complemented
3C2×C31×#418C211yesmaximal, characteristic, complemented
4C2×C31×#416C211yesmaximal, characteristic, complemented
5C31×#2354C211yesmaximal, characteristic, complemented
6C31×#1983C211yesmaximal, characteristic, complemented
7C31×#1959C211yesmaximal, characteristic, complemented
8C31×#1894C211yesmaximal, characteristic, complemented
9C31×#1893C211yesmaximal, characteristic, complemented
10C31×#1875C211yesmaximal, characteristic, complemented
11C31×#1873C211yesmaximal, characteristic, complemented
12C31×#1802C211yesmaximal, characteristic, complemented
13C31×#1788C211yesmaximal, characteristic, complemented
14C31×#1786C211yesmaximal, characteristic, complemented
15C31×#1762C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C22×M16×C31C2211yescharacteristic
19C23×C8×C31C2211yescharacteristic, complemented
20C31×#546—24no—
21C31×#546C418yescomplemented
22C2×C31×#124C2211yescharacteristic
23C2×C31×#123—21no—
24C2×C31×C22⋊Q8C2211yescharacteristic
25C2×C31×#121—21no—
26C2×C31×#121C2211yescharacteristic
27C2×C31×#120—21no—
28C2×C4×D4×C31C2211yescharacteristic
29C2×C4×D4×C31C2211yescharacteristic
30C2×C31×#117C2211yescharacteristic
31C2×C31×#117C2211yescharacteristic, complemented
32C22×C22⋊C4×C31—21no—
33C31×#435—24no—
34C2×C31×C4⋊C8C2211yescharacteristic, complemented
35C31×#418—24no—
36C31×#416—24no—
37C2×C31×#103C2211yescharacteristic, complemented
38C2×C31×#103C2211yescharacteristic, complemented
39C2×C31×#103C2211yescharacteristic, complemented
40C2×C31×#103C2211yescharacteristic, complemented
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C31×#102C2211yescharacteristic
48C2×C31×#102C2211yescharacteristic
49C2×C31×C22⋊C8C2211yescharacteristic
50C2×C31×C22⋊C8C2211yescharacteristic, complemented
51C2×C31×#97C2211yescharacteristic, complemented
52C31×#390—21no—
53C31×#388—21no—
54C31×#388—21no—
55C31×#384C2211yescharacteristic, complemented
56C31×#380C2211yescharacteristic
57C31×#380C2211yescharacteristic, complemented
58C4×C4⋊C4×C31—21no—
59C4×C4⋊C4×C31C2211yescharacteristic, complemented
60C31×#340C2211yescharacteristic, complemented
61C31×#340C2211yescharacteristic, complemented
62C31×#340C2211yescharacteristic, complemented
63C31×#340C2211yescharacteristic, complemented
64C25×C31—21no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—41no—
69C2×#41×C31—41no—
70C2×#41×C31C2×C414yes—
71C22×Q8×C31C2311yescharacteristic
72C22×D4×C31—22no—
73C22×D4×C31—22no—
74C22×D4×C31—21no—
75C22×D4×C31—21no—
76C22×D4×C31—21no—
77C22×D4×C31—22no—
78C22×D4×C31—41no—
79C22×D4×C31—41no—
80C22×D4×C31C2×C414yes—
81C22×D4×C31D411yescharacteristic
82C22×D4×C31C2311yescharacteristic
83C22×D4×C31C2311yescharacteristic
84C23×C4×C31—21no—
85C23×C4×C31—21no—
86C23×C4×C31C2311yescharacteristic
87C23×C4×C31C2311yescharacteristic
88C2×M16×C31—22no—
89C2×M16×C31—22no—
90C2×M16×C31—41no—
91C22×C8×C31—22no—
92C22×C8×C31—22no—
93C22×C8×C31—41no—
94C22×C8×C31C2311yescharacteristic
95C22×C8×C31C2311yescharacteristic
96C22×C8×C31C2311yescharacteristic
97C22×C8×C31C2311yescharacteristic
98C31×#124—22no—
99C31×#124C2×C414yes—
100C31×#123—28no—
101C31×C22⋊Q8—22no—
102C31×C22⋊Q8C2×C414yes—
103C31×#121—22no—
104C31×#121—28no—
105C31×#121C2×C414yes—
106C31×#120—28no—
107C4×D4×C31—22no—
108C4×D4×C31C2×C414yes—
109C4×D4×C31C2×C414yes—
110C4×D4×C31D414yes—
111C31×#117—22no—
112C31×#117—22no—
113C31×#117—41no—
114C31×#117—41no—
115C2×C4⋊C4×C31—21no—
116C2×C4⋊C4×C31—21no—
117C2×C4⋊C4×C31—21no—
118C2×C4⋊C4×C31D411yescharacteristic
119C2×C4⋊C4×C31C2311yescharacteristic
120C2×C4⋊C4×C31C2311yescharacteristic
121C2×C4⋊C4×C31C2311yescharacteristic
122C2×C4⋊C4×C31C2311yescharacteristic
123C2×C4⋊C4×C31C2311yescharacteristic
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—28no—
130C2×C22⋊C4×C31—21no—
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31—21no—
134C2×C22⋊C4×C31D411yescharacteristic
135C2×C22⋊C4×C31D411yescharacteristic
136C2×C42×C31—21no—
137C2×C42×C31—21no—
138C2×C42×C31—21no—
139C2×C42×C31C2311yescharacteristic
140C31×C4⋊C8—22no—
141C31×#103—22no—
142C31×#103—22no—
143C31×#103—41no—
144C31×#103—41no—
145C31×#102—22no—
146C31×#102—22no—
147C31×#102—22no—
148C31×#102—22no—
149C31×#102—22no—
150C31×#102—41no—
151C31×#102—41no—
152C31×#102D414yescomplemented
153C31×C22⋊C8—22no—
154C31×C22⋊C8—22no—
155C31×#97—22no—
156C31×#95—21no—
157C31×#95—21no—
158C31×#95—21no—
159C24×C31—21no—
160C24×C31—21no—
161C24×C31—24no—
162C24×C31—42no—
163C24×C31—42no—
164C24×C31—42no—
165C24×C31—42no—
166C24×C31—81no—
167C24×C31—81no—
168C24×C31C2×D411yescharacteristic
169C24×C31C2×D411yescharacteristic
170#41×C31—28no—
171#41×C31—44no—
172#41×C31—44no—
173#41×C31—44no—
174C2×Q8×C31—21no—
175C2×Q8×C31—21no—
176C2×Q8×C31—21no—
177C2×Q8×C31—21no—
178C2×Q8×C31—21no—
179C2×Q8×C31C22×C412yes—
180C2×D4×C31—28no—
181C2×D4×C31—24no—
182C2×D4×C31—24no—
183C2×D4×C31—24no—
184C2×D4×C31—21no—
185C2×D4×C31—21no—
186C2×D4×C31—21no—
187C2×D4×C31—21no—
188C2×D4×C31—21no—
189C2×D4×C31—21no—
190C2×D4×C31—21no—
191C2×D4×C31—21no—
192C2×D4×C31—44no—
193C2×D4×C31—44no—
194C2×D4×C31—44no—
195C2×D4×C31—41no—
196C2×D4×C31—41no—
197C2×D4×C31—42no—
198C2×D4×C31—42no—
199C2×D4×C31—42no—
200C2×D4×C31—42no—
201C2×D4×C31—81no—
202C2×D4×C31—81no—
203C2×D4×C31C22⋊C414yes—
204C2×D4×C31C22×C412yes—
205C2×D4×C31C22×C412yes—
206C2×D4×C31C2×D412yes—
207C2×D4×C31#4112yes—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—21no—
217C22×C4×C31—21no—
218C22×C4×C31—21no—
219C22×C4×C31—24no—
220C22×C4×C31—24no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—42no—
225C22×C4×C31—42no—
226C22×C4×C31—81no—
227C22×C4×C31—81no—
228C22×C4×C31C22×C412yes—
229C22×C4×C31C22×C412yes—
230C22×C4×C31C2×D411yescharacteristic
231C22×C4×C31C2×D411yescharacteristic
232C22×C4×C31C2×D411yescharacteristic
233C22×C4×C31C2×D411yescharacteristic
234C22×C4×C31C2×D412yes—
235C22×C4×C31C2×D412yes—
236C22×C4×C31C2411yescharacteristic
237M16×C31—44no—
238C2×C8×C31—21no—
239C2×C8×C31—21no—
240C2×C8×C31—21no—
241C2×C8×C31—21no—
242C2×C8×C31—21no—
243C2×C8×C31—21no—
244C2×C8×C31—21no—
245C2×C8×C31—21no—
246C2×C8×C31—21no—
247C2×C8×C31—21no—
248C2×C8×C31—21no—
249C2×C8×C31—44no—
250C2×C8×C31C2×D412yes—
251C4⋊C4×C31—24no—
252C4⋊C4×C31—21no—
253C4⋊C4×C31—21no—
254C4⋊C4×C31—21no—
255C4⋊C4×C31—21no—
256C4⋊C4×C31—21no—
257C4⋊C4×C31—21no—
258C4⋊C4×C31—21no—
259C4⋊C4×C31—21no—
260C4⋊C4×C31—42no—
261C4⋊C4×C31—81no—
262C4⋊C4×C31C22⋊C414yes—
263C4⋊C4×C31C22×C412yes—
264C4⋊C4×C31C2×D412yes—
265C22⋊C4×C31—24no—
266C22⋊C4×C31—24no—
267C22⋊C4×C31—24no—
268C22⋊C4×C31—24no—
269C22⋊C4×C31—24no—
270C22⋊C4×C31—42no—
271C22⋊C4×C31—42no—
272C22⋊C4×C31—81no—
273C22⋊C4×C31—81no—
274C22⋊C4×C31C22⋊C414yes—
275C22⋊C4×C31C22⋊C414yes—
276C42×C31—42no—
277C42×C31—42no—
278C42×C31—42no—
279C42×C31C22×C412yes—
280C42×C31C2×D412yes—
281#22424C3111yesmaximal, characteristic, direct product factor, Sylow
282C23×C31—22no—
283C23×C31—21no—
284C23×C31—21no—
285C23×C31—22no—
286C23×C31—21no—
287C23×C31—21no—
288C23×C31—22no—
289C23×C31—21no—
290C23×C31—21no—
291C23×C31—21no—
292C23×C31—21no—
293C23×C31—21no—
294C23×C31—21no—
295C23×C31—21no—
296C23×C31—21no—
297C23×C31—22no—
298C23×C31—48no—
299C23×C31—48no—
300C23×C31—41no—
301C23×C31—41no—
302C23×C31—41no—
303C23×C31—41no—
304C23×C31—41no—
305C23×C31—41no—
306C23×C31—41no—
307C23×C31—41no—
308C23×C31—41no—
309C23×C31—41no—
310C23×C31—84no—
311C23×C31—84no—
312C23×C31—84no—
313C23×C31—84no—
314C23×C31—84no—
315C23×C31C2×C22⋊C412yes—
316C23×C31C2×C22⋊C412yes—
317C23×C31C22×D411yescharacteristic
318Q8×C31—22no—
319Q8×C31—22no—
320Q8×C31—41no—
321Q8×C31—41no—
322D4×C31—22no—
323D4×C31—22no—
324D4×C31—22no—
325D4×C31—22no—
326D4×C31—22no—
327D4×C31—44no—
328D4×C31—48no—
329D4×C31—48no—
330D4×C31—41no—
331D4×C31—41no—
332D4×C31—84no—
333D4×C31C4×D414yes—
334C2×C4×C31—21no—
335C2×C4×C31—21no—
336C2×C4×C31—21no—
337C2×C4×C31—21no—
338C2×C4×C31—21no—
339C2×C4×C31—21no—
340C2×C4×C31—21no—
341C2×C4×C31—21no—
342C2×C4×C31—22no—
343C2×C4×C31—22no—
344C2×C4×C31—22no—
345C2×C4×C31—22no—
346C2×C4×C31—22no—
347C2×C4×C31—22no—
348C2×C4×C31—22no—
349C2×C4×C31—22no—
350C2×C4×C31—22no—
351C2×C4×C31—22no—
352C2×C4×C31—22no—
353C2×C4×C31—48no—
354C2×C4×C31—41no—
355C2×C4×C31—41no—
356C2×C4×C31—41no—
357C2×C4×C31—41no—
358C2×C4×C31—41no—
359C2×C4×C31—41no—
360C2×C4×C31—41no—
361C2×C4×C31—41no—
362C2×C4×C31—41no—
363C2×C4×C31—41no—
364C2×C4×C31—41no—
365C2×C4×C31—41no—
366C2×C4×C31—41no—
367C2×C4×C31—41no—
368C2×C4×C31—41no—
369C2×C4×C31—84no—
370C2×C4×C31C2×C22⋊C412yes—
371C2×C4×C31C2×C22⋊C412yes—
372C2×C4×C31C2×C22⋊C412yes—
373C2×C4×C31C2×C22⋊C412yes—
374C2×C4×C31C23×C411yescharacteristic
375C2×C4×C31C22×D411yescharacteristic
376C2×C4×C31C22×D411yescharacteristic
377C2×C4×C31C2×#4111yescharacteristic
378C2×C4×C31H(5,𝔽2)11yescharacteristic
379C2×C4×C31H(5,𝔽2)11yescharacteristic
380C8×C31—22no—
381C8×C31—41no—
382C8×C31—41no—
383C8×C31—41no—
384C2×#546C2×C3111yescharacteristic
385C2×#435C2×C3111yescharacteristic, complemented
386C2×#418C2×C3111yescharacteristic, complemented
387C2×#416C2×C3111yescharacteristic, complemented
388#2354C2×C3111yescharacteristic, complemented
389#1983C2×C3111yescharacteristic, complemented
390#1959C2×C3111yescharacteristic, complemented
391#1894C2×C3111yescharacteristic, complemented
392#1893C2×C3111yescharacteristic, complemented
393#1875C2×C3111yescharacteristic, complemented
394#1873C2×C3111yescharacteristic, complemented
395#1802C2×C3111yescharacteristic, complemented
396#1788C2×C3111yescharacteristic, complemented
397#1786C2×C3111yescharacteristic, complemented
398#1762C2×C3111yescharacteristic, complemented
399C22×C31—22no—
400C22×C31—22no—
401C22×C31—24no—
402C22×C31—22no—
403C22×C31—22no—
404C22×C31—22no—
405C22×C31—22no—
406C22×C31—42no—
407C22×C31—42no—
408C22×C31—41no—
409C22×C31—41no—
410C22×C31—42no—
411C22×C31—41no—
412C22×C31—41no—
413C22×C31—42no—
414C22×C31—41no—
415C22×C31—41no—
416C22×C31—42no—
417C22×C31—41no—
418C22×C31—41no—
419C22×C31—42no—
420C22×C31—42no—
421C22×C31—42no—
422C22×C31—42no—
423C22×C31—816no—
424C22×C31—81no—
425C22×C31—81no—
426C22×C31—81no—
427C22×C31—81no—
428C22×C31C22×C22⋊C411yescharacteristic
429C22×C31D4211yescharacteristic
430C22×C31#54611yescharacteristic
431C22×C31#57511yescharacteristic
432C22×C31#57511yescharacteristic
433C22×C31#57611yescharacteristic
434C22×C31#57711yescharacteristic
435C4×C31—22no—
436C4×C31—22no—
437C4×C31—22no—
438C4×C31—22no—
439C4×C31—42no—
440C4×C31—42no—
441C4×C31—42no—
442C4×C31—81no—
443C4×C31—81no—
444C4×C31—81no—
445C4×C31C2×C4×D411yescharacteristic
446C4×C31#51811yescharacteristic
447C4×C31D4211yescharacteristic
448C4×C31#54611yescharacteristic
449C22×#41C22×C3111yescharacteristic
450C23×D4C22×C3111yescharacteristic
451C22×M16C22×C3111yescharacteristic
452C23×C8C22×C3111yescharacteristic, complemented
453#546—24no—
454#546C4×C3118yescomplemented
455C2×#124C22×C3111yescharacteristic
456C2×#123—21no—
457C2×C22⋊Q8C22×C3111yescharacteristic
458C2×#121—21no—
459C2×#121C22×C3111yescharacteristic
460C2×#120—21no—
461C2×C4×D4C22×C3111yescharacteristic
462C2×C4×D4C22×C3111yescharacteristic
463C2×#117C22×C3111yescharacteristic
464C2×#117C22×C3111yescharacteristic, complemented
465C22×C22⋊C4—21no—
466#435—24no—
467C2×C4⋊C8C22×C3111yescharacteristic, complemented
468#418—24no—
469#416—24no—
470C2×#103C22×C3111yescharacteristic, complemented
471C2×#103C22×C3111yescharacteristic, complemented
472C2×#103C22×C3111yescharacteristic, complemented
473C2×#103C22×C3111yescharacteristic, complemented
474C2×#102C22×C3111yescharacteristic
475C2×#102C22×C3111yescharacteristic
476C2×#102C22×C3111yescharacteristic
477C2×#102C22×C3111yescharacteristic
478C2×#102C22×C3111yescharacteristic
479C2×#102C22×C3111yescharacteristic
480C2×#102C22×C3111yescharacteristic
481C2×#102C22×C3111yescharacteristic
482C2×C22⋊C8C22×C3111yescharacteristic
483C2×C22⋊C8C22×C3111yescharacteristic, complemented
484C2×#97C22×C3111yescharacteristic, complemented
485#390—21no—
486#388—21no—
487#388—21no—
488#384C22×C3111yescharacteristic, complemented
489#380C22×C3111yescharacteristic
490#380C22×C3111yescharacteristic, complemented
491C4×C4⋊C4—21no—
492C4×C4⋊C4C22×C3111yescharacteristic, complemented
493#340C22×C3111yescharacteristic, complemented
494#340C22×C3111yescharacteristic, complemented
495#340C22×C3111yescharacteristic, complemented
496#340C22×C3111yescharacteristic, complemented
497C2×C31—42no—
498C2×C31—42no—
499C2×C31—44no—
500C2×C31—82no—
501C2×C31D4×C22⋊C411yescharacteristic
502C2×C31#289611yescharacteristic
503C2×C31#289711yescharacteristic
504C2×C31#326711yescharacteristic
505C2×C31#326811yescharacteristic
506C2×C31#331111yescharacteristic
507C2×C31#331911yescharacteristic
508C25—21no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41C2×C4×C3114yes—
515C22×Q8C23×C3111yescharacteristic
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—22no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4C2×C4×C3114yes—
525C22×D4D4×C3111yescharacteristic
526C22×D4C23×C3111yescharacteristic
527C22×D4C23×C3111yescharacteristic
528C23×C4—21no—
529C23×C4—21no—
530C23×C4C23×C3111yescharacteristic
531C23×C4C23×C3111yescharacteristic
532C2×M16—22no—
533C2×M16—22no—
534C2×M16—41no—
535C22×C8—22no—
536C22×C8—22no—
537C22×C8—41no—
538C22×C8C23×C3111yescharacteristic
539C22×C8C23×C3111yescharacteristic
540C22×C8C23×C3111yescharacteristic
541C22×C8C23×C3111yescharacteristic
542#124—22no—
543#124C2×C4×C3114yes—
544#123—28no—
545C22⋊Q8—22no—
546C22⋊Q8C2×C4×C3114yes—
547#121—22no—
548#121—28no—
549#121C2×C4×C3114yes—
550#120—28no—
551C4×D4—22no—
552C4×D4C2×C4×C3114yes—
553C4×D4C2×C4×C3114yes—
554C4×D4D4×C3114yes—
555#117—22no—
556#117—22no—
557#117—41no—
558#117—41no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4D4×C3111yescharacteristic
563C2×C4⋊C4C23×C3111yescharacteristic
564C2×C4⋊C4C23×C3111yescharacteristic
565C2×C4⋊C4C23×C3111yescharacteristic
566C2×C4⋊C4C23×C3111yescharacteristic
567C2×C4⋊C4C23×C3111yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—28no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4D4×C3111yescharacteristic
579C2×C22⋊C4D4×C3111yescharacteristic
580C2×C42—21no—
581C2×C42—21no—
582C2×C42—21no—
583C2×C42C23×C3111yescharacteristic
584C4⋊C8—22no—
585#103—22no—
586#103—22no—
587#103—41no—
588#103—41no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—41no—
595#102—41no—
596#102D4×C3114yescomplemented
597C22⋊C8—22no—
598C22⋊C8—22no—
599#97—22no—
600#95—21no—
601#95—21no—
602#95—21no—
603C31#2242411yescharacteristic, direct product factor, Sylow
604C24—21no—
605C24—21no—
606C24—24no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—81no—
612C24—81no—
613C24C2×D4×C3111yescharacteristic
614C24C2×D4×C3111yescharacteristic
615#41—28no—
616#41—44no—
617#41—44no—
618#41—44no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C22×C4×C3112yes—
625C2×D4—28no—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—41no—
641C2×D4—41no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊C4×C3114yes—
649C2×D4C22×C4×C3112yes—
650C2×D4C22×C4×C3112yes—
651C2×D4C2×D4×C3112yes—
652C2×D4#41×C3112yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—81no—
672C22×C4—81no—
673C22×C4C22×C4×C3112yes—
674C22×C4C22×C4×C3112yes—
675C22×C4C2×D4×C3111yescharacteristic
676C22×C4C2×D4×C3111yescharacteristic
677C22×C4C2×D4×C3111yescharacteristic
678C22×C4C2×D4×C3111yescharacteristic
679C22×C4C2×D4×C3112yes—
680C22×C4C2×D4×C3112yes—
681C22×C4C24×C3111yescharacteristic
682M16—44no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—44no—
695C2×C8C2×D4×C3112yes—
696C4⋊C4—24no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—42no—
706C4⋊C4—81no—
707C4⋊C4C22⋊C4×C3114yes—
708C4⋊C4C22×C4×C3112yes—
709C4⋊C4C2×D4×C3112yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—81no—
718C22⋊C4—81no—
719C22⋊C4C22⋊C4×C3114yes—
720C22⋊C4C22⋊C4×C3114yes—
721C42—42no—
722C42—42no—
723C42—42no—
724C42C22×C4×C3112yes—
725C42C2×D4×C3112yes—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—22no—
742C23—48no—
743C23—48no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23C2×C22⋊C4×C3112yes—
760C23C2×C22⋊C4×C3112yes—
761C23C22×D4×C3111yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—41no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—44no—
772D4—48no—
773D4—48no—
774D4—41no—
775D4—41no—
776D4—84no—
777D4C4×D4×C3114yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—48no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—84no—
814C2×C4C2×C22⋊C4×C3112yes—
815C2×C4C2×C22⋊C4×C3112yes—
816C2×C4C2×C22⋊C4×C3112yes—
817C2×C4C2×C22⋊C4×C3112yes—
818C2×C4C23×C4×C3111yescharacteristic
819C2×C4C22×D4×C3111yescharacteristic
820C2×C4C22×D4×C3111yescharacteristic
821C2×C4C2×#41×C3111yescharacteristic
822C2×C4C31×H(5,𝔽2)11yescharacteristic
823C2×C4C31×H(5,𝔽2)11yescharacteristic
824C8—22no—
825C8—41no—
826C8—41no—
827C8—41no—
828C22—22no—
829C22—22no—
830C22—24no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—42no—
836C22—42no—
837C22—41no—
838C22—41no—
839C22—42no—
840C22—41no—
841C22—41no—
842C22—42no—
843C22—41no—
844C22—41no—
845C22—42no—
846C22—41no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—816no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22C22×C22⋊C4×C3111yescharacteristic
858C22D42×C3111yescharacteristic
859C22C31×#54611yescharacteristic
860C22C31×#57511yescharacteristic
861C22C31×#57511yescharacteristic
862C22C31×#57611yescharacteristic
863C22C31×#57711yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4C2×C4×D4×C3111yescharacteristic
875C4C31×#51811yescharacteristic
876C4D42×C3111yescharacteristic
877C4C31×#54611yescharacteristic
878C2—42no—
879C2—42no—
880C2—44no—
881C2—82no—
882C2D4×C22⋊C4×C3111yescharacteristic
883C2C31×#289611yescharacteristic
884C2C31×#289711yescharacteristic
885C2C31×#326711yescharacteristic
886C2C31×#326811yescharacteristic
887C2C31×#331111yescharacteristic
888C2C31×#331911yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#546C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#435C2semidirect
3. C2×C31×#418C2semidirect
4. C2×C31×#416C2semidirect
5. C31×#2354C2semidirect
6. C31×#1983C2semidirect
7. C31×#1959C2semidirect
8. C31×#1894C2semidirect
9. C31×#1893C2semidirect
10. C31×#1875C2semidirect
11. C31×#1873C2semidirect
12. C31×#1802C2semidirect
13. C31×#1788C2semidirect
14. C31×#1786C2semidirect
15. C31×#1762C2semidirect
19. C23×C8×C31C22semidirect
21. C31×#546C4semidirect
31. C2×C31×#117C22semidirect
34. C2×C31×C4⋊C8C22semidirect
37. C2×C31×#103C22semidirect
38. C2×C31×#103C22semidirect
39. C2×C31×#103C22semidirect
40. C2×C31×#103C22semidirect
50. C2×C31×C22⋊C8C22semidirect
51. C2×C31×#97C22semidirect
55. C31×#384C22semidirect
57. C31×#380C22semidirect
59. C4×C4⋊C4×C31C22semidirect
60. C31×#340C22semidirect
61. C31×#340C22semidirect
62. C31×#340C22semidirect
63. C31×#340C22semidirect
152. C31×#102D4semidirect
281. #22424C31direct (N × H)
385. C2×#435C2×C31semidirect
386. C2×#418C2×C31semidirect
387. C2×#416C2×C31semidirect
388. #2354C2×C31semidirect
389. #1983C2×C31semidirect
390. #1959C2×C31semidirect
391. #1894C2×C31semidirect
392. #1893C2×C31semidirect
393. #1875C2×C31semidirect
394. #1873C2×C31semidirect
395. #1802C2×C31semidirect
396. #1788C2×C31semidirect
397. #1786C2×C31semidirect
398. #1762C2×C31semidirect
452. C23×C8C22×C31semidirect
454. #546C4×C31semidirect
464. C2×#117C22×C31semidirect
467. C2×C4⋊C8C22×C31semidirect
470. C2×#103C22×C31semidirect
471. C2×#103C22×C31semidirect
472. C2×#103C22×C31semidirect
473. C2×#103C22×C31semidirect
483. C2×C22⋊C8C22×C31semidirect
484. C2×#97C22×C31semidirect
488. #384C22×C31semidirect
490. #380C22×C31semidirect
492. C4×C4⋊C4C22×C31semidirect
493. #340C22×C31semidirect
494. #340C22×C31semidirect
495. #340C22×C31semidirect
496. #340C22×C31semidirect
596. #102D4×C31semidirect
603. C31#22424direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5462
C2×C31×#4352
C2×C31×#4182
C2×C31×#4162
C31×#23542
C31×#19832
C31×#19592
C31×#18942
C31×#18932
C31×#18752
C31×#18732
C31×#18022
C31×#17882
C31×#17862
C31×#17622
#2242431