Finite Group Databasebeta

← C31×#25148 #21481907

Subgroups — C31×#25148 #21481907

Order 7936.

1402 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#459C211yesmaximal, characteristic, complemented
2C2×C31×#447C211yesmaximal, characteristic, complemented
3C2×C31×#447C211yesmaximal, characteristic, complemented
4C2×C4×D8×C31C211yesmaximal, characteristic, complemented
5C31×#2428C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
7C31×#2067C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#2033C211yesmaximal, characteristic, complemented
10C31×#2011C211yesmaximal, characteristic, complemented
11C31×#1970C211yesmaximal, characteristic, complemented
12C31×#1923C211yesmaximal, characteristic, complemented
13C31×#1879C211yesmaximal, characteristic, complemented
14C31×#1879C211yesmaximal, characteristic, complemented
15C31×#1862C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C22×D8×C31C2211yescharacteristic
19C22×D8×C31C2211yescharacteristic
20C22×D8×C31C2211yescharacteristic
21C2×C31×#127C2211yescharacteristic, complemented
22C2×C31×#121—21no—
23C2×C31×#121C2211yescharacteristic
24C2×C31×#121C2211yescharacteristic
25C2×C4×D4×C31C2211yescharacteristic
26C2×C4×D4×C31C2211yescharacteristic
27C2×C4×D4×C31C2211yescharacteristic, complemented
28C22×C22⋊C4×C31—21no—
29C31×#459—24no—
30C31×#447—24no—
31C31×#447—24no—
32C4×D8×C31—24no—
33C2×C31×#107C2211yescharacteristic, complemented
34C2×C31×#107C2211yescharacteristic, complemented
35C2×C31×C4⋊C8C2211yescharacteristic, complemented
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic, complemented
41C2×C31×#102C2211yescharacteristic, complemented
42C2×C31×#102C2211yescharacteristic, complemented
43C2×C31×#102C2211yescharacteristic, complemented
44C2×C31×C22⋊C8C2211yescharacteristic
45C2×C31×C22⋊C8C2211yescharacteristic
46C2×C4×C8×C31C2211yescharacteristic, complemented
47C31×#394—21no—
48C31×#392—21no—
49C31×#390C2211yescharacteristic
50C31×#390C2211yescharacteristic
51C31×#390C2211yescharacteristic, complemented
52C31×#389C2211yescharacteristic, complemented
53C31×#386—21no—
54C31×#386—21no—
55C31×#386—21no—
56C31×#380C2211yescharacteristic
57C31×#379—21no—
58C4×C22⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic, complemented
60C31×#340C2211yescharacteristic, complemented
61C31×#336C2211yescharacteristic, complemented
62C31×#336C2211yescharacteristic, complemented
63C25×C31—21no—
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—22no—
67C22×D4×C31—22no—
68C22×D4×C31—21no—
69C22×D4×C31—21no—
70C22×D4×C31—21no—
71C22×D4×C31—21no—
72C22×D4×C31—21no—
73C22×D4×C31—41no—
74C22×D4×C31—41no—
75C22×D4×C31C2311yescharacteristic
76C22×D4×C31C2311yescharacteristic
77C22×D4×C31C2311yescharacteristic
78C22×D4×C31C2311yescharacteristic
79C23×C4×C31—21no—
80C23×C4×C31—21no—
81C23×C4×C31—21no—
82C23×C4×C31C2311yescharacteristic
83C2×D8×C31—22no—
84C2×D8×C31—22no—
85C2×D8×C31—22no—
86C2×D8×C31—22no—
87C2×D8×C31—22no—
88C2×D8×C31—22no—
89C2×D8×C31—22no—
90C2×D8×C31—22no—
91C2×D8×C31—22no—
92C2×D8×C31—41no—
93C2×D8×C31—41no—
94C2×D8×C31D414yescomplemented
95C22×C8×C31C2311yescharacteristic
96C22×C8×C31C2311yescharacteristic
97C22×C8×C31C2311yescharacteristic
98C22×C8×C31C2311yescharacteristic
99C31×#127—22no—
100C31×#127—41no—
101C31×#121—22no—
102C31×#121—22no—
103C31×#121—41no—
104C31×#121—41no—
105C31×#121—44no—
106C4×D4×C31—22no—
107C4×D4×C31—22no—
108C4×D4×C31—22no—
109C4×D4×C31—41no—
110C4×D4×C31—41no—
111C4×D4×C31—41no—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
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—44no—
130C2×C22⋊C4×C31D411yescharacteristic
131C2×C22⋊C4×C31D411yescharacteristic
132C2×C42×C31C2311yescharacteristic
133C2×C42×C31C2311yescharacteristic
134C31×#107—22no—
135C31×#107—41no—
136C31×C4⋊C8—22no—
137C31×#102—22no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102—22no—
143C31×#102—41no—
144C31×#102D414yescomplemented
145C31×C22⋊C8—22no—
146C31×C22⋊C8—22no—
147C4×C8×C31—22no—
148C31×#95—21no—
149C31×#95—21no—
150C31×#95D411yescharacteristic
151C31×#95D411yescharacteristic
152C24×C31—21no—
153C24×C31—24no—
154C24×C31—21no—
155C24×C31—21no—
156C24×C31—21no—
157C24×C31—42no—
158C24×C31—42no—
159C24×C31—42no—
160C24×C31—42no—
161C24×C31—81no—
162C24×C31—81no—
163C24×C31C2×D411yescharacteristic
164C2×D4×C31—24no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31—21no—
169C2×D4×C31—21no—
170C2×D4×C31—21no—
171C2×D4×C31—21no—
172C2×D4×C31—21no—
173C2×D4×C31—21no—
174C2×D4×C31—21no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—21no—
181C2×D4×C31—21no—
182C2×D4×C31—21no—
183C2×D4×C31—21no—
184C2×D4×C31—42no—
185C2×D4×C31—42no—
186C2×D4×C31—42no—
187C2×D4×C31—42no—
188C2×D4×C31—42no—
189C2×D4×C31—42no—
190C2×D4×C31—44no—
191C2×D4×C31—44no—
192C2×D4×C31—44no—
193C2×D4×C31—44no—
194C2×D4×C31—42no—
195C2×D4×C31—42no—
196C2×D4×C31—42no—
197C2×D4×C31—42no—
198C2×D4×C31—81no—
199C2×D4×C31—81no—
200C2×D4×C31—81no—
201C2×D4×C31—81no—
202C2×D4×C31C2×D412yes—
203C2×D4×C31C2×D412yes—
204C2×D4×C31C2×D412yes—
205C2×D4×C31#4112yes—
206C2×D4×C31#4112yes—
207C22×C4×C31—21no—
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—42no—
218C22×C4×C31—42no—
219C22×C4×C31—42no—
220C22×C4×C31—42no—
221C22×C4×C31—42no—
222C22×C4×C31—42no—
223C22×C4×C31—81no—
224C22×C4×C31—81no—
225C22×C4×C31—81no—
226C22×C4×C31C2×D411yescharacteristic
227C22×C4×C31C2×D411yescharacteristic
228C22×C4×C31C2×D411yescharacteristic
229C22×C4×C31C2×D411yescharacteristic
230C22×C4×C31C2×D411yescharacteristic
231C22×C4×C31C2411yescharacteristic
232D8×C31—28no—
233D8×C31—44no—
234D8×C31—44no—
235D8×C31—44no—
236C2×C8×C31—21no—
237C2×C8×C31—21no—
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×C31C2×D412yes—
247C2×C8×C31C2×D412yes—
248C4⋊C4×C31—21no—
249C4⋊C4×C31—21no—
250C4⋊C4×C31—21no—
251C4⋊C4×C31—21no—
252C4⋊C4×C31—21no—
253C4⋊C4×C31—21no—
254C4⋊C4×C31—21no—
255C4⋊C4×C31—42no—
256C4⋊C4×C31C2×D412yes—
257C22⋊C4×C31—41no—
258C22⋊C4×C31—42no—
259C22⋊C4×C31—42no—
260C22⋊C4×C31—42no—
261C22⋊C4×C31—42no—
262C22⋊C4×C31—42no—
263C22⋊C4×C31—42no—
264C22⋊C4×C31—42no—
265C22⋊C4×C31—42no—
266C22⋊C4×C31—42no—
267C22⋊C4×C31—81no—
268C22⋊C4×C31—81no—
269C22⋊C4×C31—81no—
270C22⋊C4×C31D814yescomplemented
271C42×C31—21no—
272C42×C31—21no—
273C42×C31—21no—
274C42×C31—21no—
275#25148C3111yesmaximal, characteristic, direct product factor, Sylow
276C23×C31—21no—
277C23×C31—22no—
278C23×C31—22no—
279C23×C31—22no—
280C23×C31—21no—
281C23×C31—21no—
282C23×C31—21no—
283C23×C31—21no—
284C23×C31—21no—
285C23×C31—22no—
286C23×C31—22no—
287C23×C31—48no—
288C23×C31—48no—
289C23×C31—41no—
290C23×C31—41no—
291C23×C31—41no—
292C23×C31—41no—
293C23×C31—41no—
294C23×C31—41no—
295C23×C31—41no—
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×C31—41no—
309C23×C31—41no—
310C23×C31—41no—
311C23×C31—41no—
312C23×C31—84no—
313C23×C31—84no—
314C23×C31—84no—
315C23×C31—84no—
316C23×C31—84no—
317C23×C31C2×D812yes—
318C23×C31C22×D411yescharacteristic
319D4×C31—22no—
320D4×C31—22no—
321D4×C31—22no—
322D4×C31—22no—
323D4×C31—22no—
324D4×C31—22no—
325D4×C31—22no—
326D4×C31—48no—
327D4×C31—41no—
328D4×C31—41no—
329D4×C31—41no—
330D4×C31—41no—
331D4×C31—41no—
332D4×C31—41no—
333D4×C31—41no—
334D4×C31—41no—
335D4×C31—84no—
336D4×C31—84no—
337D4×C31—84no—
338D4×C31—84no—
339D4×C31#12114yescomplemented
340C2×C4×C31—21no—
341C2×C4×C31—21no—
342C2×C4×C31—21no—
343C2×C4×C31—21no—
344C2×C4×C31—21no—
345C2×C4×C31—21no—
346C2×C4×C31—21no—
347C2×C4×C31—22no—
348C2×C4×C31—21no—
349C2×C4×C31—21no—
350C2×C4×C31—21no—
351C2×C4×C31—21no—
352C2×C4×C31—21no—
353C2×C4×C31—21no—
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×C31—84no—
371C2×C4×C31—84no—
372C2×C4×C31C2×D812yes—
373C2×C4×C31C2×D812yes—
374C2×C4×C31C22×D411yescharacteristic
375C2×C4×C31C22×D411yescharacteristic
376C2×C4×C31C2×#4111yescharacteristic
377C2×C4×C31C2×#4111yescharacteristic
378C2×C4×C31H(5,𝔽2)11yescharacteristic
379C2×C4×C31H(5,𝔽2)11yescharacteristic
380C8×C31—22no—
381C8×C31—22no—
382C8×C31—41no—
383C8×C31—41no—
384C2×#459C2×C3111yescharacteristic, complemented
385C2×#447C2×C3111yescharacteristic, complemented
386C2×#447C2×C3111yescharacteristic, complemented
387C2×C4×D8C2×C3111yescharacteristic, complemented
388#2428C2×C3111yescharacteristic, complemented
389D4×C22⋊C4C2×C3111yescharacteristic, complemented
390#2067C2×C3111yescharacteristic, complemented
391#2033C2×C3111yescharacteristic, complemented
392#2033C2×C3111yescharacteristic, complemented
393#2011C2×C3111yescharacteristic, complemented
394#1970C2×C3111yescharacteristic, complemented
395#1923C2×C3111yescharacteristic, complemented
396#1879C2×C3111yescharacteristic, complemented
397#1879C2×C3111yescharacteristic, complemented
398#1862C2×C3111yescharacteristic, complemented
399C22×C31—22no—
400C22×C31—24no—
401C22×C31—22no—
402C22×C31—22no—
403C22×C31—42no—
404C22×C31—41no—
405C22×C31—42no—
406C22×C31—41no—
407C22×C31—41no—
408C22×C31—42no—
409C22×C31—41no—
410C22×C31—42no—
411C22×C31—42no—
412C22×C31—42no—
413C22×C31—42no—
414C22×C31—42no—
415C22×C31—42no—
416C22×C31—42no—
417C22×C31—42no—
418C22×C31—42no—
419C22×C31—816no—
420C22×C31—81no—
421C22×C31—81no—
422C22×C31—81no—
423C22×C31—81no—
424C22×C31—81no—
425C22×C31—81no—
426C22×C31—81no—
427C22×C31—81no—
428C22×C31—81no—
429C22×C31—81no—
430C22×C31—81no—
431C22×C31—81no—
432C22×C31—81no—
433C22×C31—81no—
434C22×C31—81no—
435C22×C31#52511yescharacteristic
436C22×C31D4211yescharacteristic
437C22×C31D4211yescharacteristic
438C22×C31C22×D811yescharacteristic
439C22×C31#57511yescharacteristic
440C22×C31#57611yescharacteristic
441C22×C31#57611yescharacteristic
442C4×C31—22no—
443C4×C31—22no—
444C4×C31—41no—
445C4×C31—41no—
446C4×C31—41no—
447C4×C31—42no—
448C4×C31—81no—
449C4×C31—81no—
450C4×C31—81no—
451C4×C31C2×#12111yescharacteristic
452C4×C31#53811yescharacteristic
453C4×C31#54611yescharacteristic
454C4×C31#54611yescharacteristic
455C23×D4C22×C3111yescharacteristic
456C22×D8C22×C3111yescharacteristic
457C22×D8C22×C3111yescharacteristic
458C22×D8C22×C3111yescharacteristic
459C22×D8C22×C3111yescharacteristic
460C2×#127C22×C3111yescharacteristic, complemented
461C2×#121—21no—
462C2×#121C22×C3111yescharacteristic
463C2×#121C22×C3111yescharacteristic
464C2×C4×D4C22×C3111yescharacteristic
465C2×C4×D4C22×C3111yescharacteristic
466C2×C4×D4C22×C3111yescharacteristic, complemented
467C22×C22⋊C4—21no—
468#459—24no—
469#447—24no—
470#447—24no—
471C4×D8—24no—
472C2×#107C22×C3111yescharacteristic, complemented
473C2×#107C22×C3111yescharacteristic, complemented
474C2×C4⋊C8C22×C3111yescharacteristic, complemented
475C2×#102C22×C3111yescharacteristic
476C2×#102C22×C3111yescharacteristic
477C2×#102C22×C3111yescharacteristic
478C2×#102C22×C3111yescharacteristic
479C2×#102C22×C3111yescharacteristic, complemented
480C2×#102C22×C3111yescharacteristic, complemented
481C2×#102C22×C3111yescharacteristic, complemented
482C2×#102C22×C3111yescharacteristic, complemented
483C2×C22⋊C8C22×C3111yescharacteristic
484C2×C22⋊C8C22×C3111yescharacteristic
485C2×C4×C8C22×C3111yescharacteristic, complemented
486#394—21no—
487#392—21no—
488#390C22×C3111yescharacteristic
489#390C22×C3111yescharacteristic
490#390C22×C3111yescharacteristic, complemented
491#389C22×C3111yescharacteristic, complemented
492#386—21no—
493#386—21no—
494#386—21no—
495#380C22×C3111yescharacteristic
496#379—21no—
497C4×C22⋊C4C22×C3111yescharacteristic
498#340C22×C3111yescharacteristic, complemented
499#340C22×C3111yescharacteristic, complemented
500#336C22×C3111yescharacteristic, complemented
501#336C22×C3111yescharacteristic, complemented
502C2×C31—42no—
503C2×C31—44no—
504C2×C31—82no—
505C2×C31—82no—
506C2×C31—161no—
507C2×C31#242411yescharacteristic
508C2×C31#310011yescharacteristic
509C2×C31#312211yescharacteristic
510C2×C31#326811yescharacteristic
511C2×C31#327311yescharacteristic
512C2×C31D4×D811yescharacteristic
513C2×C31D4×D811yescharacteristic
514C25—21no—
515C22×D4—22no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C23×C3111yescharacteristic
527C22×D4C23×C3111yescharacteristic
528C22×D4C23×C3111yescharacteristic
529C22×D4C23×C3111yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C23×C3111yescharacteristic
534C2×D8—22no—
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8D4×C3114yescomplemented
546C22×C8C23×C3111yescharacteristic
547C22×C8C23×C3111yescharacteristic
548C22×C8C23×C3111yescharacteristic
549C22×C8C23×C3111yescharacteristic
550#127—22no—
551#127—41no—
552#121—22no—
553#121—22no—
554#121—41no—
555#121—41no—
556#121—44no—
557C4×D4—22no—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563C2×C4⋊C4—21no—
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—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—44no—
581C2×C22⋊C4D4×C3111yescharacteristic
582C2×C22⋊C4D4×C3111yescharacteristic
583C2×C42C23×C3111yescharacteristic
584C2×C42C23×C3111yescharacteristic
585#107—22no—
586#107—41no—
587C4⋊C8—22no—
588#102—22no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—41no—
595#102D4×C3114yescomplemented
596C22⋊C8—22no—
597C22⋊C8—22no—
598C4×C8—22no—
599#95—21no—
600#95—21no—
601#95D4×C3111yescharacteristic
602#95D4×C3111yescharacteristic
603C31#2514811yescharacteristic, direct product factor, Sylow
604C24—21no—
605C24—24no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—42no—
613C24—81no—
614C24—81no—
615C24C2×D4×C3111yescharacteristic
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
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—21no—
635C2×D4—21no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—44no—
643C2×D4—44no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—81no—
651C2×D4—81no—
652C2×D4—81no—
653C2×D4—81no—
654C2×D4C2×D4×C3112yes—
655C2×D4C2×D4×C3112yes—
656C2×D4C2×D4×C3112yes—
657C2×D4#41×C3112yes—
658C2×D4#41×C3112yes—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—81no—
676C22×C4—81no—
677C22×C4—81no—
678C22×C4C2×D4×C3111yescharacteristic
679C22×C4C2×D4×C3111yescharacteristic
680C22×C4C2×D4×C3111yescharacteristic
681C22×C4C2×D4×C3111yescharacteristic
682C22×C4C2×D4×C3111yescharacteristic
683C22×C4C24×C3111yescharacteristic
684D8—28no—
685D8—44no—
686D8—44no—
687D8—44no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8C2×D4×C3112yes—
699C2×C8C2×D4×C3112yes—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—42no—
708C4⋊C4C2×D4×C3112yes—
709C22⋊C4—41no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—81no—
720C22⋊C4—81no—
721C22⋊C4—81no—
722C22⋊C4D8×C3114yescomplemented
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—22no—
737C23—22no—
738C23—48no—
739C23—48no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—84no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23C2×D8×C3112yes—
769C23C22×D4×C3111yescharacteristic
770D4—22no—
771D4—22no—
772D4—22no—
773D4—22no—
774D4—22no—
775D4—22no—
776D4—22no—
777D4—48no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—84no—
787D4—84no—
788D4—84no—
789D4—84no—
790D4C31×#12114yescomplemented
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
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—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—84no—
821C2×C4—84no—
822C2×C4—84no—
823C2×C4C2×D8×C3112yes—
824C2×C4C2×D8×C3112yes—
825C2×C4C22×D4×C3111yescharacteristic
826C2×C4C22×D4×C3111yescharacteristic
827C2×C4C2×#41×C3111yescharacteristic
828C2×C4C2×#41×C3111yescharacteristic
829C2×C4C31×H(5,𝔽2)11yescharacteristic
830C2×C4C31×H(5,𝔽2)11yescharacteristic
831C8—22no—
832C8—22no—
833C8—41no—
834C8—41no—
835C22—22no—
836C22—24no—
837C22—22no—
838C22—22no—
839C22—42no—
840C22—41no—
841C22—42no—
842C22—41no—
843C22—41no—
844C22—42no—
845C22—41no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—816no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22C31×#52511yescharacteristic
872C22D42×C3111yescharacteristic
873C22D42×C3111yescharacteristic
874C22C22×D8×C3111yescharacteristic
875C22C31×#57511yescharacteristic
876C22C31×#57611yescharacteristic
877C22C31×#57611yescharacteristic
878C4—22no—
879C4—22no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—42no—
884C4—81no—
885C4—81no—
886C4—81no—
887C4C2×C31×#12111yescharacteristic
888C4C31×#53811yescharacteristic
889C4C31×#54611yescharacteristic
890C4C31×#54611yescharacteristic
891C2—42no—
892C2—44no—
893C2—82no—
894C2—82no—
895C2—161no—
896C2C31×#242411yescharacteristic
897C2C31×#310011yescharacteristic
898C2C31×#312211yescharacteristic
899C2C31×#326811yescharacteristic
900C2C31×#327311yescharacteristic
901C2D4×D8×C3111yescharacteristic
902C2D4×D8×C3111yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#459C2semidirect
2. C2×C31×#447C2semidirect
3. C2×C31×#447C2semidirect
4. C2×C4×D8×C31C2semidirect
5. C31×#2428C2semidirect
6. D4×C22⋊C4×C31C2semidirect
7. C31×#2067C2semidirect
8. C31×#2033C2semidirect
9. C31×#2033C2semidirect
10. C31×#2011C2semidirect
11. C31×#1970C2semidirect
12. C31×#1923C2semidirect
13. C31×#1879C2semidirect
14. C31×#1879C2semidirect
15. C31×#1862C2semidirect
21. C2×C31×#127C22semidirect
27. C2×C4×D4×C31C22semidirect
33. C2×C31×#107C22semidirect
34. C2×C31×#107C22semidirect
35. C2×C31×C4⋊C8C22semidirect
40. C2×C31×#102C22semidirect
41. C2×C31×#102C22semidirect
42. C2×C31×#102C22semidirect
43. C2×C31×#102C22semidirect
46. C2×C4×C8×C31C22semidirect
51. C31×#390C22semidirect
52. C31×#389C22semidirect
59. C31×#340C22semidirect
60. C31×#340C22semidirect
61. C31×#336C22semidirect
62. C31×#336C22semidirect
94. C2×D8×C31D4semidirect
144. C31×#102D4semidirect
270. C22⋊C4×C31D8semidirect
275. #25148C31direct (N × H)
339. D4×C31#121semidirect
384. C2×#459C2×C31semidirect
385. C2×#447C2×C31semidirect
386. C2×#447C2×C31semidirect
387. C2×C4×D8C2×C31semidirect
388. #2428C2×C31semidirect
389. D4×C22⋊C4C2×C31semidirect
390. #2067C2×C31semidirect
391. #2033C2×C31semidirect
392. #2033C2×C31semidirect
393. #2011C2×C31semidirect
394. #1970C2×C31semidirect
395. #1923C2×C31semidirect
396. #1879C2×C31semidirect
397. #1879C2×C31semidirect
398. #1862C2×C31semidirect
460. C2×#127C22×C31semidirect
466. C2×C4×D4C22×C31semidirect
472. C2×#107C22×C31semidirect
473. C2×#107C22×C31semidirect
474. C2×C4⋊C8C22×C31semidirect
479. C2×#102C22×C31semidirect
480. C2×#102C22×C31semidirect
481. C2×#102C22×C31semidirect
482. C2×#102C22×C31semidirect
485. C2×C4×C8C22×C31semidirect
490. #390C22×C31semidirect
491. #389C22×C31semidirect
498. #340C22×C31semidirect
499. #340C22×C31semidirect
500. #336C22×C31semidirect
501. #336C22×C31semidirect
545. C2×D8D4×C31semidirect
595. #102D4×C31semidirect
603. C31#25148direct (N × H)
722. C22⋊C4D8×C31semidirect
790. D4C31×#121semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4592
C2×C31×#4472
C2×C4×D8×C312
C31×#24282
D4×C22⋊C4×C312
C31×#20672
C31×#20332
C31×#20112
C31×#19702
C31×#19232
C31×#18792
C31×#18622
#2514831