Finite Group Databasebeta

← C31×#22422 #21479181

Subgroups — C31×#22422 #21479181

Order 7936.

1530 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#550C211yesmaximal, characteristic
2C2×C31×#435C211yesmaximal, characteristic, complemented
3C2×C31×#417C211yesmaximal, characteristic, complemented
4C2×C31×#416C211yesmaximal, characteristic, complemented
5C31×#2352C211yesmaximal, characteristic, complemented
6C31×#1982C211yesmaximal, characteristic, complemented
7C31×#1961C211yesmaximal, characteristic, complemented
8C31×#1895C211yesmaximal, characteristic, complemented
9C31×#1893C211yesmaximal, characteristic, complemented
10C31×#1875C211yesmaximal, characteristic, complemented
11C31×#1874C211yesmaximal, characteristic, complemented
12C31×#1805C211yesmaximal, characteristic, complemented
13C31×#1788C211yesmaximal, characteristic, complemented
14C31×#1788C211yesmaximal, characteristic, complemented
15C31×#1763C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×#41×C31C2211yescharacteristic
18C22×M16×C31C2211yescharacteristic
19C23×C8×C31C2211yescharacteristic
20C31×#550—24no—
21C31×#550C418yescomplemented
22C2×C31×#127—21no—
23C2×C31×#127C2211yescharacteristic
24C2×C31×#121—21no—
25C2×C31×#121—21no—
26C2×C31×#121C2211yescharacteristic
27C2×C31×#121C2211yescharacteristic
28C2×C4×Q8×C31C2211yescharacteristic
29C2×C4×D4×C31—21no—
30C2×C4×D4×C31C2211yescharacteristic
31C2×C31×#117C2211yescharacteristic
32C22×C4⋊C4×C31C2211yescharacteristic
33C31×#435—24no—
34C2×C31×C4⋊C8C2211yescharacteristic
35C31×#417—24no—
36C31×#416—24no—
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
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
51C2×C31×#97C2211yescharacteristic
52C31×#388—21no—
53C31×#387—21no—
54C31×#386—21no—
55C31×#382C2211yescharacteristic
56C31×#380C2211yescharacteristic
57C31×#380C2211yescharacteristic
58C4×C4⋊C4×C31C2211yescharacteristic
59C4×C22⋊C4×C31—21no—
60C31×#340C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C31×#340C2211yescharacteristic
64C2×#41×C31—22no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—22no—
69C2×#41×C31—22no—
70C2×#41×C31—41no—
71C2×#41×C31—41no—
72C2×#41×C31—41no—
73C2×#41×C31—41no—
74C2×#41×C31C2×C414yes—
75C2×#41×C31C2×C414yescomplemented
76C22×Q8×C31C2311yescharacteristic
77C22×D4×C31—21no—
78C22×D4×C31—21no—
79C22×D4×C31—21no—
80C22×D4×C31—21no—
81C22×D4×C31—21no—
82C22×D4×C31—21no—
83C22×D4×C31D411yescharacteristic
84C22×D4×C31C2311yescharacteristic
85C22×D4×C31C2311yescharacteristic
86C23×C4×C31—21no—
87C23×C4×C31—21no—
88C23×C4×C31—21no—
89C23×C4×C31C2311yescharacteristic
90C23×C4×C31C2311yescharacteristic
91C2×M16×C31—22no—
92C2×M16×C31—22no—
93C2×M16×C31—41no—
94C22×C8×C31—22no—
95C22×C8×C31—22no—
96C22×C8×C31—41no—
97C22×C8×C31C2311yescharacteristic
98C22×C8×C31C2311yescharacteristic
99C22×C8×C31C2311yescharacteristic
100C22×C8×C31C2311yescharacteristic
101C31×#127—28no—
102C31×#127—22no—
103C31×#127C2×C414yescomplemented
104C31×#121—22no—
105C31×#121—22no—
106C31×#121—28no—
107C31×#121—28no—
108C31×#121C2×C414yes—
109C31×#121C2×C414yescomplemented
110C4×Q8×C31—22no—
111C4×Q8×C31C2×C414yescomplemented
112C4×D4×C31—28no—
113C4×D4×C31C2×C414yes—
114C4×D4×C31D414yes—
115C31×#117—22no—
116C31×#117—41no—
117C2×C4⋊C4×C31—21no—
118C2×C4⋊C4×C31—22no—
119C2×C4⋊C4×C31—21no—
120C2×C4⋊C4×C31—41no—
121C2×C4⋊C4×C31D411yescharacteristic
122C2×C4⋊C4×C31C2311yescharacteristic
123C2×C4⋊C4×C31C2311yescharacteristic
124C2×C4⋊C4×C31C2311yescharacteristic
125C2×C4⋊C4×C31C2311yescharacteristic
126C2×C4⋊C4×C31C2311yescharacteristic
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31—21no—
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31D411yescharacteristic
133C2×C22⋊C4×C31D411yescharacteristic
134C2×C42×C31—21no—
135C2×C42×C31—21no—
136C2×C42×C31—21no—
137C2×C42×C31C2311yescharacteristic
138C31×C4⋊C8—22no—
139C31×#103—22no—
140C31×#103—22no—
141C31×#103—22no—
142C31×#103D414yescomplemented
143C31×#102—22no—
144C31×#102—22no—
145C31×#102—22no—
146C31×#102—22no—
147C31×#102—41no—
148C31×#102—41no—
149C31×#102—41no—
150C31×#102—41no—
151C31×C22⋊C8—22no—
152C31×C22⋊C8—22no—
153C31×#97—22no—
154C31×#95—21no—
155C31×#95—21no—
156C31×#95—21no—
157C31×#95—21no—
158C31×#95—21no—
159C24×C31—21no—
160C24×C31—21no—
161C24×C31C2×D411yescharacteristic
162C24×C31C2×D411yescharacteristic
163#41×C31—28no—
164#41×C31—28no—
165#41×C31—44no—
166#41×C31—44no—
167#41×C31—44no—
168#41×C31—44no—
169#41×C31—44no—
170#41×C31—44no—
171C2×Q8×C31—21no—
172C2×Q8×C31—21no—
173C2×Q8×C31—21no—
174C2×Q8×C31C22×C412yes—
175C2×Q8×C31C2×D412yes—
176C2×Q8×C31#4112yes—
177C2×D4×C31—24no—
178C2×D4×C31—24no—
179C2×D4×C31—24no—
180C2×D4×C31—24no—
181C2×D4×C31—24no—
182C2×D4×C31—24no—
183C2×D4×C31—21no—
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—21no—
193C2×D4×C31—41no—
194C2×D4×C31—41no—
195C2×D4×C31—42no—
196C2×D4×C31—42no—
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×C31—81no—
204C2×D4×C31—81no—
205C2×D4×C31—81no—
206C2×D4×C31—81no—
207C2×D4×C31C22⋊C414yes—
208C2×D4×C31C22×C412yes—
209C2×D4×C31C22×C412yes—
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—21no—
220C22×C4×C31—21no—
221C22×C4×C31—24no—
222C22×C4×C31—24no—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31—42no—
227C22×C4×C31—42no—
228C22×C4×C31—42no—
229C22×C4×C31—42no—
230C22×C4×C31—42no—
231C22×C4×C31—42no—
232C22×C4×C31—81no—
233C22×C4×C31C22×C412yes—
234C22×C4×C31C22×C412yes—
235C22×C4×C31C2×D411yescharacteristic
236C22×C4×C31C2×D411yescharacteristic
237C22×C4×C31C2×D411yescharacteristic
238C22×C4×C31C2×D411yescharacteristic
239C22×C4×C31C2×D412yes—
240C22×C4×C31C2×D412yes—
241C22×C4×C31C2411yescharacteristic
242M16×C31—44no—
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—21no—
250C2×C8×C31—21no—
251C2×C8×C31—21no—
252C2×C8×C31—21no—
253C2×C8×C31—21no—
254C2×C8×C31—44no—
255C2×C8×C31C2×D412yes—
256C4⋊C4×C31—24no—
257C4⋊C4×C31—21no—
258C4⋊C4×C31—21no—
259C4⋊C4×C31—21no—
260C4⋊C4×C31—21no—
261C4⋊C4×C31—21no—
262C4⋊C4×C31—21no—
263C4⋊C4×C31—21no—
264C4⋊C4×C31—21no—
265C4⋊C4×C31—42no—
266C4⋊C4×C31C22⋊C414yes—
267C4⋊C4×C31C22×C412yes—
268C4⋊C4×C31C2×D412yes—
269C22⋊C4×C31—24no—
270C22⋊C4×C31—24no—
271C22⋊C4×C31—42no—
272C22⋊C4×C31—42no—
273C22⋊C4×C31—81no—
274C22⋊C4×C31C22⋊C414yes—
275C22⋊C4×C31C22⋊C414yes—
276C42×C31—24no—
277C42×C31—42no—
278C42×C31—81no—
279C42×C31C22×C412yes—
280C42×C31C2×D412yes—
281#22422C3111yesmaximal, characteristic, direct product factor, Sylow
282C23×C31—21no—
283C23×C31—21no—
284C23×C31—21no—
285C23×C31—21no—
286C23×C31—21no—
287C23×C31—21no—
288C23×C31—21no—
289C23×C31—21no—
290C23×C31—21no—
291C23×C31—21no—
292C23×C31—21no—
293C23×C31—21no—
294C23×C31—22no—
295C23×C31—22no—
296C23×C31—41no—
297C23×C31—41no—
298C23×C31—41no—
299C23×C31—41no—
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×C31C2×C22⋊C412yes—
309C23×C31C2×C22⋊C412yes—
310C23×C31C22×D411yescharacteristic
311Q8×C31—22no—
312Q8×C31—22no—
313Q8×C31—22no—
314Q8×C31C4×D414yes—
315D4×C31—22no—
316D4×C31—22no—
317D4×C31—22no—
318D4×C31—22no—
319D4×C31—44no—
320D4×C31—48no—
321D4×C31—48no—
322D4×C31—48no—
323D4×C31—41no—
324D4×C31—41no—
325D4×C31—41no—
326D4×C31—41no—
327D4×C31—84no—
328D4×C31—84no—
329D4×C31—84no—
330C2×C4×C31—22no—
331C2×C4×C31—21no—
332C2×C4×C31—21no—
333C2×C4×C31—22no—
334C2×C4×C31—21no—
335C2×C4×C31—21no—
336C2×C4×C31—22no—
337C2×C4×C31—21no—
338C2×C4×C31—21no—
339C2×C4×C31—21no—
340C2×C4×C31—21no—
341C2×C4×C31—22no—
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—48no—
352C2×C4×C31—48no—
353C2×C4×C31—41no—
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—84no—
367C2×C4×C31C2×C22⋊C412yes—
368C2×C4×C31C2×C22⋊C412yes—
369C2×C4×C31C2×C22⋊C412yes—
370C2×C4×C31C2×C22⋊C412yes—
371C2×C4×C31C23×C411yescharacteristic
372C2×C4×C31C22×D411yescharacteristic
373C2×C4×C31C22×D411yescharacteristic
374C2×C4×C31C2×#4111yescharacteristic
375C2×C4×C31H(5,𝔽2)11yescharacteristic
376C2×C4×C31H(5,𝔽2)11yescharacteristic
377C8×C31—22no—
378C8×C31—41no—
379C8×C31—41no—
380C8×C31—41no—
381C2×#550C2×C3111yescharacteristic
382C2×#435C2×C3111yescharacteristic, complemented
383C2×#417C2×C3111yescharacteristic, complemented
384C2×#416C2×C3111yescharacteristic, complemented
385#2352C2×C3111yescharacteristic, complemented
386#1982C2×C3111yescharacteristic, complemented
387#1961C2×C3111yescharacteristic, complemented
388#1895C2×C3111yescharacteristic, complemented
389#1893C2×C3111yescharacteristic, complemented
390#1875C2×C3111yescharacteristic, complemented
391#1874C2×C3111yescharacteristic, complemented
392#1805C2×C3111yescharacteristic, complemented
393#1788C2×C3111yescharacteristic, complemented
394#1788C2×C3111yescharacteristic, complemented
395#1763C2×C3111yescharacteristic, complemented
396C22×C31—22no—
397C22×C31—22no—
398C22×C31—22no—
399C22×C31—22no—
400C22×C31—22no—
401C22×C31—22no—
402C22×C31—41no—
403C22×C31—41no—
404C22×C31—41no—
405C22×C31—41no—
406C22×C31—41no—
407C22×C31—41no—
408C22×C31—41no—
409C22×C31—41no—
410C22×C31—42no—
411C22×C31—42no—
412C22×C31—42no—
413C22×C31—42no—
414C22×C31—42no—
415C22×C31—42no—
416C22×C31—81no—
417C22×C31—81no—
418C22×C31—81no—
419C22×C31—81no—
420C22×C31—81no—
421C22×C31—81no—
422C22×C31—81no—
423C22×C31—81no—
424C22×C31C22×C22⋊C411yescharacteristic
425C22×C31D4211yescharacteristic
426C22×C31#54611yescharacteristic
427C22×C31#57511yescharacteristic
428C22×C31#57511yescharacteristic
429C22×C31#57611yescharacteristic
430C22×C31#57711yescharacteristic
431C4×C31—22no—
432C4×C31—22no—
433C4×C31—24no—
434C4×C31—22no—
435C4×C31—22no—
436C4×C31—42no—
437C4×C31—42no—
438C4×C31—81no—
439C4×C31—81no—
440C4×C31—81no—
441C4×C31C2×C4×D411yescharacteristic
442C4×C31#51811yescharacteristic
443C4×C31D4211yescharacteristic
444C4×C31#54611yescharacteristic
445C22×#41C22×C3111yescharacteristic
446C22×#41C22×C3111yescharacteristic
447C22×M16C22×C3111yescharacteristic
448C23×C8C22×C3111yescharacteristic
449#550—24no—
450#550C4×C3118yescomplemented
451C2×#127—21no—
452C2×#127C22×C3111yescharacteristic
453C2×#121—21no—
454C2×#121—21no—
455C2×#121C22×C3111yescharacteristic
456C2×#121C22×C3111yescharacteristic
457C2×C4×Q8C22×C3111yescharacteristic
458C2×C4×D4—21no—
459C2×C4×D4C22×C3111yescharacteristic
460C2×#117C22×C3111yescharacteristic
461C22×C4⋊C4C22×C3111yescharacteristic
462#435—24no—
463C2×C4⋊C8C22×C3111yescharacteristic
464#417—24no—
465#416—24no—
466C2×#103C22×C3111yescharacteristic
467C2×#103C22×C3111yescharacteristic
468C2×#103C22×C3111yescharacteristic
469C2×#103C22×C3111yescharacteristic
470C2×#102C22×C3111yescharacteristic
471C2×#102C22×C3111yescharacteristic
472C2×#102C22×C3111yescharacteristic
473C2×#102C22×C3111yescharacteristic
474C2×#102C22×C3111yescharacteristic
475C2×#102C22×C3111yescharacteristic
476C2×#102C22×C3111yescharacteristic
477C2×#102C22×C3111yescharacteristic
478C2×C22⋊C8C22×C3111yescharacteristic
479C2×C22⋊C8C22×C3111yescharacteristic
480C2×#97C22×C3111yescharacteristic
481#388—21no—
482#387—21no—
483#386—21no—
484#382C22×C3111yescharacteristic
485#380C22×C3111yescharacteristic
486#380C22×C3111yescharacteristic
487C4×C4⋊C4C22×C3111yescharacteristic
488C4×C22⋊C4—21no—
489#340C22×C3111yescharacteristic
490#340C22×C3111yescharacteristic
491#340C22×C3111yescharacteristic
492#340C22×C3111yescharacteristic
493C2×C31—42no—
494C2×C31—42no—
495C2×C31—82no—
496C2×C31—82no—
497C2×C31D4×C22⋊C411yescharacteristic
498C2×C31#289611yescharacteristic
499C2×C31#289711yescharacteristic
500C2×C31#326811yescharacteristic
501C2×C31#327111yescharacteristic
502C2×C31#330911yescharacteristic
503C2×C31#331711yescharacteristic
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—41no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41C2×C4×C3114yes—
515C2×#41C2×C4×C3114yescomplemented
516C22×Q8C23×C3111yescharacteristic
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4D4×C3111yescharacteristic
524C22×D4C23×C3111yescharacteristic
525C22×D4C23×C3111yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4C23×C3111yescharacteristic
530C23×C4C23×C3111yescharacteristic
531C2×M16—22no—
532C2×M16—22no—
533C2×M16—41no—
534C22×C8—22no—
535C22×C8—22no—
536C22×C8—41no—
537C22×C8C23×C3111yescharacteristic
538C22×C8C23×C3111yescharacteristic
539C22×C8C23×C3111yescharacteristic
540C22×C8C23×C3111yescharacteristic
541#127—28no—
542#127—22no—
543#127C2×C4×C3114yescomplemented
544#121—22no—
545#121—22no—
546#121—28no—
547#121—28no—
548#121C2×C4×C3114yes—
549#121C2×C4×C3114yescomplemented
550C4×Q8—22no—
551C4×Q8C2×C4×C3114yescomplemented
552C4×D4—28no—
553C4×D4C2×C4×C3114yes—
554C4×D4D4×C3114yes—
555#117—22no—
556#117—41no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—41no—
561C2×C4⋊C4D4×C3111yescharacteristic
562C2×C4⋊C4C23×C3111yescharacteristic
563C2×C4⋊C4C23×C3111yescharacteristic
564C2×C4⋊C4C23×C3111yescharacteristic
565C2×C4⋊C4C23×C3111yescharacteristic
566C2×C4⋊C4C23×C3111yescharacteristic
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4D4×C3111yescharacteristic
573C2×C22⋊C4D4×C3111yescharacteristic
574C2×C42—21no—
575C2×C42—21no—
576C2×C42—21no—
577C2×C42C23×C3111yescharacteristic
578C4⋊C8—22no—
579#103—22no—
580#103—22no—
581#103—22no—
582#103D4×C3114yescomplemented
583#102—22no—
584#102—22no—
585#102—22no—
586#102—22no—
587#102—41no—
588#102—41no—
589#102—41no—
590#102—41no—
591C22⋊C8—22no—
592C22⋊C8—22no—
593#97—22no—
594#95—21no—
595#95—21no—
596#95—21no—
597#95—21no—
598#95—21no—
599C31#2242211yescharacteristic, direct product factor, Sylow
600C24—21no—
601C24—21no—
602C24C2×D4×C3111yescharacteristic
603C24C2×D4×C3111yescharacteristic
604#41—28no—
605#41—28no—
606#41—44no—
607#41—44no—
608#41—44no—
609#41—44no—
610#41—44no—
611#41—44no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8C22×C4×C3112yes—
616C2×Q8C2×D4×C3112yes—
617C2×Q8#41×C3112yes—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—24no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—81no—
643C2×D4—81no—
644C2×D4—81no—
645C2×D4—81no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊C4×C3114yes—
649C2×D4C22×C4×C3112yes—
650C2×D4C22×C4×C3112yes—
651C22×C4—21no—
652C22×C4—21no—
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—24no—
663C22×C4—24no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—81no—
674C22×C4C22×C4×C3112yes—
675C22×C4C22×C4×C3112yes—
676C22×C4C2×D4×C3111yescharacteristic
677C22×C4C2×D4×C3111yescharacteristic
678C22×C4C2×D4×C3111yescharacteristic
679C22×C4C2×D4×C3111yescharacteristic
680C22×C4C2×D4×C3112yes—
681C22×C4C2×D4×C3112yes—
682C22×C4C24×C3111yescharacteristic
683M16—44no—
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—21no—
695C2×C8—44no—
696C2×C8C2×D4×C3112yes—
697C4⋊C4—24no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—42no—
707C4⋊C4C22⋊C4×C3114yes—
708C4⋊C4C22×C4×C3112yes—
709C4⋊C4C2×D4×C3112yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—81no—
715C22⋊C4C22⋊C4×C3114yes—
716C22⋊C4C22⋊C4×C3114yes—
717C42—24no—
718C42—42no—
719C42—81no—
720C42C22×C4×C3112yes—
721C42C2×D4×C3112yes—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—22no—
735C23—22no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23C2×C22⋊C4×C3112yes—
749C23C2×C22⋊C4×C3112yes—
750C23C22×D4×C3111yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8C4×D4×C3114yes—
755D4—22no—
756D4—22no—
757D4—22no—
758D4—22no—
759D4—44no—
760D4—48no—
761D4—48no—
762D4—48no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—84no—
768D4—84no—
769D4—84no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—48no—
792C2×C4—48no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
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—84no—
807C2×C4C2×C22⋊C4×C3112yes—
808C2×C4C2×C22⋊C4×C3112yes—
809C2×C4C2×C22⋊C4×C3112yes—
810C2×C4C2×C22⋊C4×C3112yes—
811C2×C4C23×C4×C3111yescharacteristic
812C2×C4C22×D4×C3111yescharacteristic
813C2×C4C22×D4×C3111yescharacteristic
814C2×C4C2×#41×C3111yescharacteristic
815C2×C4C31×H(5,𝔽2)11yescharacteristic
816C2×C4C31×H(5,𝔽2)11yescharacteristic
817C8—22no—
818C8—41no—
819C8—41no—
820C8—41no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22C22×C22⋊C4×C3111yescharacteristic
850C22D42×C3111yescharacteristic
851C22C31×#54611yescharacteristic
852C22C31×#57511yescharacteristic
853C22C31×#57511yescharacteristic
854C22C31×#57611yescharacteristic
855C22C31×#57711yescharacteristic
856C4—22no—
857C4—22no—
858C4—24no—
859C4—22no—
860C4—22no—
861C4—42no—
862C4—42no—
863C4—81no—
864C4—81no—
865C4—81no—
866C4C2×C4×D4×C3111yescharacteristic
867C4C31×#51811yescharacteristic
868C4D42×C3111yescharacteristic
869C4C31×#54611yescharacteristic
870C2—42no—
871C2—42no—
872C2—82no—
873C2—82no—
874C2D4×C22⋊C4×C3111yescharacteristic
875C2C31×#289611yescharacteristic
876C2C31×#289711yescharacteristic
877C2C31×#326811yescharacteristic
878C2C31×#327111yescharacteristic
879C2C31×#330911yescharacteristic
880C2C31×#331711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#550C2
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×#417C2semidirect
4. C2×C31×#416C2semidirect
5. C31×#2352C2semidirect
6. C31×#1982C2semidirect
7. C31×#1961C2semidirect
8. C31×#1895C2semidirect
9. C31×#1893C2semidirect
10. C31×#1875C2semidirect
11. C31×#1874C2semidirect
12. C31×#1805C2semidirect
13. C31×#1788C2semidirect
14. C31×#1788C2semidirect
15. C31×#1763C2semidirect
21. C31×#550C4semidirect
75. C2×#41×C31C2×C4semidirect
103. C31×#127C2×C4semidirect
109. C31×#121C2×C4semidirect
111. C4×Q8×C31C2×C4semidirect
142. C31×#103D4semidirect
281. #22422C31direct (N × H)
382. C2×#435C2×C31semidirect
383. C2×#417C2×C31semidirect
384. C2×#416C2×C31semidirect
385. #2352C2×C31semidirect
386. #1982C2×C31semidirect
387. #1961C2×C31semidirect
388. #1895C2×C31semidirect
389. #1893C2×C31semidirect
390. #1875C2×C31semidirect
391. #1874C2×C31semidirect
392. #1805C2×C31semidirect
393. #1788C2×C31semidirect
394. #1788C2×C31semidirect
395. #1763C2×C31semidirect
450. #550C4×C31semidirect
515. C2×#41C2×C4×C31semidirect
543. #127C2×C4×C31semidirect
549. #121C2×C4×C31semidirect
551. C4×Q8C2×C4×C31semidirect
582. #103D4×C31semidirect
599. C31#22422direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5502
C2×C31×#4352
C2×C31×#4172
C2×C31×#4162
C31×#23522
C31×#19822
C31×#19612
C31×#18952
C31×#18932
C31×#18752
C31×#18742
C31×#18052
C31×#17882
C31×#17632
#2242231