Finite Group Databasebeta

← C31×#17597 #21474356

Subgroups — C31×#17597 #21474356

Order 7936.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3519C211yesmaximal, characteristic
2C31×#2974C211yesmaximal, characteristic, complemented
3C31×#2318C211yesmaximal, characteristic, complemented
4C31×#1521C211yesmaximal, characteristic, complemented
5C31×#1519C211yesmaximal, characteristic, complemented
6C31×#1517C211yesmaximal, characteristic, complemented
7C31×#1516C211yesmaximal, characteristic, complemented
8C31×#1514C211yesmaximal, characteristic, complemented
9C31×#1513C211yesmaximal, characteristic, complemented
10C31×#1512C211yesmaximal, characteristic, complemented
11C31×#1510C211yesmaximal, characteristic, complemented
12C31×#1507C211yesmaximal, characteristic, complemented
13C31×#1504C211yesmaximal, characteristic, complemented
14C31×#1501C211yesmaximal, characteristic, complemented
15C2×C31×#327C211yesmaximal, characteristic, complemented
16C31×#555C411yescharacteristic, complemented
17C31×#554C411yescharacteristic, complemented
18C31×#553—21no—
19C31×#553C411yescharacteristic, complemented
20C31×#553C411yescharacteristic, complemented
21C31×#550C411yescharacteristic, complemented
22C31×#546—21no—
23C31×#546—21no—
24C31×#546C411yescharacteristic, complemented
25C31×#546C411yescharacteristic, complemented
26D42×C31—21no—
27D42×C31C411yescharacteristic, complemented
28C31×#540—21no—
29C31×#538—21no—
30C31×#538—21no—
31C31×#532C2211yescharacteristic
32C31×#529C2211yescharacteristic
33C31×#525C2211yescharacteristic
34C31×#525C2211yescharacteristic
35C2×C31×#121C2211yescharacteristic
36C2×C31×#121C2211yescharacteristic
37C31×#518—21no—
38C2×C4×D4×C31C2211yescharacteristic
39C31×#436—21no—
40C31×#435—21no—
41C31×#435—21no—
42C8×D4×C31—21no—
43C31×#432C2211yescharacteristic, complemented
44C31×#431C2211yescharacteristic, complemented
45C31×#407C2211yescharacteristic, complemented
46C31×#407C2211yescharacteristic, complemented
47C2×C31×C22⋊C8C2211yescharacteristic, complemented
48C2×C31×C22⋊C8C2211yescharacteristic, complemented
49C31×#388—21no—
50C31×#387—21no—
51C31×#386—21no—
52C31×#385—21no—
53C31×#383C2211yescharacteristic, complemented
54C31×#382C2211yescharacteristic, complemented
55C31×#381C2211yescharacteristic, complemented
56C31×#380C2211yescharacteristic, complemented
57C4×C22⋊C4×C31C2211yescharacteristic, complemented
58C2×C31×#95C2211yescharacteristic, complemented
59C31×#328C2211yescharacteristic, complemented
60C31×#328C2211yescharacteristic, complemented
61C31×#328C2211yescharacteristic, complemented
62C31×#328C2211yescharacteristic, complemented
63C31×#327C2211yescharacteristic
64C31×#327C2211yescharacteristic
65C31×#327C2211yescharacteristic
66C31×#327C2211yescharacteristic
67C31×#327C2211yescharacteristic, complemented
68C31×#327C2211yescharacteristic, complemented
69C31×#327C2211yescharacteristic, complemented
70C31×#327C2211yescharacteristic, complemented
71C31×#327C2211yescharacteristic, complemented
72C31×#327C2211yescharacteristic, complemented
73C31×#327C2211yescharacteristic, complemented
74C31×#327C2211yescharacteristic, complemented
75C2×#41×C31—21no—
76C2×#41×C31C2×C411yescharacteristic
77C2×#41×C31C2×C411yescharacteristic, complemented
78C22×D4×C31—21no—
79C22×D4×C31—21no—
80C22×D4×C31—21no—
81C22×D4×C31C2×C411yescharacteristic
82C22×D4×C31C2×C411yescharacteristic, complemented
83C22×D4×C31D411yescharacteristic
84C23×C4×C31—21no—
85C23×C4×C31C2311yescharacteristic
86C23×C4×C31C2311yescharacteristic
87C2×M16×C31—21no—
88C2×M16×C31—21no—
89C22×C8×C31—21no—
90C22×C8×C31—21no—
91C31×C4⋊Q8C2×C411yescharacteristic, complemented
92C31×#127—21no—
93C31×#127C2×C411yescharacteristic, complemented
94C31×#126—21no—
95C31×#126—21no—
96C31×#126—21no—
97C31×#125—21no—
98C31×#125C2×C411yescharacteristic, complemented
99C31×#124—21no—
100C31×#124—21no—
101C31×#124—21no—
102C31×#124C2×C411yescharacteristic, complemented
103C31×#123—21no—
104C31×#123—21no—
105C31×#123—21no—
106C31×#123—21no—
107C31×#123—21no—
108C31×#123—21no—
109C31×#123—21no—
110C31×C22⋊Q8—21no—
111C31×C22⋊Q8—21no—
112C31×C22⋊Q8C2×C411yescharacteristic
113C31×C22⋊Q8C2×C411yescharacteristic, complemented
114C31×C22⋊Q8C2311yescharacteristic
115C31×#121—21no—
116C31×#121—21no—
117C31×#121—21no—
118C31×#121—21no—
119C31×#121—21no—
120C31×#121—21no—
121C31×#121—21no—
122C31×#121—21no—
123C31×#121—21no—
124C31×#121—21no—
125C31×#121—21no—
126C31×#121—21no—
127C31×#121—21no—
128C31×#121C2×C411yescharacteristic
129C31×#121C2×C411yescharacteristic
130C31×#121C2×C411yescharacteristic
131C31×#121C2×C411yescharacteristic, complemented
132C31×#121C2×C411yescharacteristic, complemented
133C31×#121C2×C411yescharacteristic, complemented
134C31×#121C2311yescharacteristic
135C31×#121C2311yescharacteristic
136C31×#121C2311yescharacteristic
137C31×#120—21no—
138C31×#120—21no—
139C31×#120—21no—
140C31×#120—21no—
141C31×#120—21no—
142C31×#120—21no—
143C4×Q8×C31C2×C411yescharacteristic, complemented
144C4×D4×C31—21no—
145C4×D4×C31—21no—
146C4×D4×C31—21no—
147C4×D4×C31—21no—
148C4×D4×C31—21no—
149C4×D4×C31—21no—
150C4×D4×C31—21no—
151C4×D4×C31—21no—
152C4×D4×C31—21no—
153C4×D4×C31—21no—
154C4×D4×C31C2×C411yescharacteristic
155C4×D4×C31C2×C411yescharacteristic
156C4×D4×C31C2×C411yescharacteristic
157C4×D4×C31C2×C411yescharacteristic
158C4×D4×C31C2×C411yescharacteristic, complemented
159C4×D4×C31C2×C411yescharacteristic, complemented
160C4×D4×C31C2×C411yescharacteristic, complemented
161C4×D4×C31D411yescharacteristic
162C4×D4×C31D411yescharacteristic
163C4×D4×C31D411yescharacteristic
164C4×D4×C31D411yescharacteristic
165C31×#117—21no—
166C31×#117—21no—
167C31×#117C2×C411yescharacteristic
168C31×#117C2×C411yescharacteristic, complemented
169C2×C4⋊C4×C31—21no—
170C2×C4⋊C4×C31—21no—
171C2×C4⋊C4×C31C2×C411yescharacteristic
172C2×C4⋊C4×C31C2×C411yescharacteristic, complemented
173C2×C4⋊C4×C31D411yescharacteristic
174C2×C22⋊C4×C31—21no—
175C2×C22⋊C4×C31—21no—
176C2×C22⋊C4×C31—21no—
177C2×C22⋊C4×C31—21no—
178C2×C22⋊C4×C31—21no—
179C2×C22⋊C4×C31—21no—
180C2×C22⋊C4×C31—21no—
181C2×C22⋊C4×C31D411yescharacteristic
182C2×C22⋊C4×C31D411yescharacteristic
183C2×C42×C31—21no—
184C2×C42×C31C2311yescharacteristic
185C31×C4⋊C8—21no—
186C31×C4⋊C8—21no—
187C31×C22⋊C8—21no—
188C31×C22⋊C8—21no—
189C31×C22⋊C8—21no—
190C31×C22⋊C8—21no—
191C31×C22⋊C8C2311yescharacteristic
192C31×C22⋊C8C2311yescharacteristic
193C31×C22⋊C8C2311yescharacteristic
194C31×C22⋊C8C2311yescharacteristic
195C31×#97—21no—
196C4×C8×C31—21no—
197C31×#95—21no—
198C31×#95—21no—
199C31×#95—21no—
200C31×#95—21no—
201C31×#95—21no—
202C31×#95C2311yescharacteristic
203C31×#95C2311yescharacteristic
204C31×#95C2311yescharacteristic
205C31×#95C2311yescharacteristic
206C24×C31—21no—
207C24×C31—21no—
208C24×C31C2×D411yescharacteristic
209C24×C31C2×D411yescharacteristic
210#41×C31—81no—
211#41×C31—81no—
212#41×C31—81no—
213#41×C31—81no—
214C2×Q8×C31—21no—
215C2×Q8×C31C22×C411yescharacteristic
216C2×D4×C31—21no—
217C2×D4×C31—21no—
218C2×D4×C31—21no—
219C2×D4×C31—21no—
220C2×D4×C31—21no—
221C2×D4×C31—21no—
222C2×D4×C31—21no—
223C2×D4×C31—21no—
224C2×D4×C31—21no—
225C2×D4×C31—21no—
226C2×D4×C31—21no—
227C2×D4×C31—21no—
228C2×D4×C31—21no—
229C2×D4×C31—21no—
230C2×D4×C31—21no—
231C2×D4×C31—42no—
232C2×D4×C31—44no—
233C2×D4×C31—81no—
234C2×D4×C31—81no—
235C2×D4×C31—81no—
236C2×D4×C31—81no—
237C2×D4×C31—81no—
238C2×D4×C31—81no—
239C2×D4×C31C22⋊C411yescharacteristic
240C2×D4×C31C22⋊C411yescharacteristic
241C2×D4×C31C22⋊C411yescharacteristic
242C2×D4×C31C22⋊C411yescharacteristic
243C2×D4×C31C22×C411yescharacteristic
244C2×D4×C31C22×C411yescharacteristic
245C2×D4×C31C22×C411yescharacteristic
246C22×C4×C31—21no—
247C22×C4×C31—21no—
248C22×C4×C31—21no—
249C22×C4×C31—21no—
250C22×C4×C31—21no—
251C22×C4×C31—21no—
252C22×C4×C31—21no—
253C22×C4×C31—21no—
254C22×C4×C31—21no—
255C22×C4×C31—21no—
256C22×C4×C31—21no—
257C22×C4×C31—42no—
258C22×C4×C31—81no—
259C22×C4×C31—81no—
260C22×C4×C31—81no—
261C22×C4×C31—81no—
262C22×C4×C31C22×C411yescharacteristic
263C22×C4×C31C22×C411yescharacteristic
264C22×C4×C31C22×C411yescharacteristic
265C22×C4×C31C22×C411yescharacteristic
266C22×C4×C31C2×D411yescharacteristic
267C22×C4×C31C2×D411yescharacteristic
268C22×C4×C31C2×D411yescharacteristic
269C22×C4×C31C2×D411yescharacteristic
270C22×C4×C31C2×D411yescharacteristic
271C22×C4×C31C2×D411yescharacteristic
272C22×C4×C31C2×D411yescharacteristic
273C22×C4×C31C2×D411yescharacteristic
274C22×C4×C31C2411yescharacteristic
275M16×C31—81no—
276M16×C31—81no—
277C2×C8×C31—21no—
278C2×C8×C31—21no—
279C2×C8×C31—21no—
280C2×C8×C31—21no—
281C2×C8×C31—81no—
282C2×C8×C31—81no—
283C4⋊C4×C31—21no—
284C4⋊C4×C31—21no—
285C4⋊C4×C31—21no—
286C4⋊C4×C31—21no—
287C4⋊C4×C31—21no—
288C4⋊C4×C31—21no—
289C4⋊C4×C31—21no—
290C4⋊C4×C31—21no—
291C4⋊C4×C31—21no—
292C4⋊C4×C31—81no—
293C4⋊C4×C31—81no—
294C4⋊C4×C31C22⋊C411yescharacteristic
295C4⋊C4×C31C22⋊C411yescharacteristic
296C4⋊C4×C31C22⋊C411yescharacteristic
297C4⋊C4×C31C22⋊C411yescharacteristic
298C4⋊C4×C31C22×C411yescharacteristic
299C4⋊C4×C31C22×C411yescharacteristic
300C4⋊C4×C31C22×C411yescharacteristic
301C4⋊C4×C31C22×C411yescharacteristic
302C22⋊C4×C31—21no—
303C22⋊C4×C31—21no—
304C22⋊C4×C31—21no—
305C22⋊C4×C31—21no—
306C22⋊C4×C31—21no—
307C22⋊C4×C31—21no—
308C22⋊C4×C31—21no—
309C22⋊C4×C31—21no—
310C22⋊C4×C31—21no—
311C22⋊C4×C31—21no—
312C22⋊C4×C31—21no—
313C22⋊C4×C31—21no—
314C22⋊C4×C31—21no—
315C22⋊C4×C31—21no—
316C22⋊C4×C31—21no—
317C22⋊C4×C31—21no—
318C22⋊C4×C31—21no—
319C22⋊C4×C31—21no—
320C22⋊C4×C31—21no—
321C22⋊C4×C31—42no—
322C22⋊C4×C31—81no—
323C22⋊C4×C31—81no—
324C22⋊C4×C31C22⋊C411yescharacteristic
325C22⋊C4×C31C22⋊C411yescharacteristic
326C22⋊C4×C31C22⋊C411yescharacteristic
327C22⋊C4×C31C22⋊C411yescharacteristic
328C22⋊C4×C31C22⋊C411yescharacteristic
329C22⋊C4×C31C22⋊C411yescharacteristic
330C22⋊C4×C31C22⋊C411yescharacteristic
331C22⋊C4×C31C22⋊C411yescharacteristic
332C42×C31—21no—
333C42×C31—21no—
334C42×C31—21no—
335C42×C31—81no—
336C42×C31C22×C411yescharacteristic
337C42×C31C22×C411yescharacteristic
338C42×C31C2×D411yescharacteristic
339C42×C31C2×D411yescharacteristic
340#17597C3111yesmaximal, characteristic, direct product factor, Sylow
341C23×C31—21no—
342C23×C31—21no—
343C23×C31—22no—
344C23×C31—21no—
345C23×C31—21no—
346C23×C31—21no—
347C23×C31—21no—
348C23×C31—21no—
349C23×C31—41no—
350C23×C31—41no—
351C23×C31—41no—
352C23×C31—42no—
353C23×C31—42no—
354C23×C31—81no—
355C23×C31—81no—
356C23×C31—81no—
357C23×C31—81no—
358C23×C31C2×C22⋊C411yescharacteristic
359C23×C31C2×C22⋊C411yescharacteristic
360C23×C31C2×C22⋊C411yescharacteristic
361C23×C31C2×C22⋊C411yescharacteristic
362C23×C31C22×D411yescharacteristic
363Q8×C31—41no—
364Q8×C31—81no—
365D4×C31—22no—
366D4×C31—22no—
367D4×C31—41no—
368D4×C31—41no—
369D4×C31—41no—
370D4×C31—41no—
371D4×C31—41no—
372D4×C31—42no—
373D4×C31—42no—
374D4×C31—41no—
375D4×C31—41no—
376D4×C31—41no—
377D4×C31—41no—
378D4×C31—41no—
379D4×C31—41no—
380D4×C31—42no—
381D4×C31—81no—
382D4×C31—81no—
383D4×C31—81no—
384D4×C31—81no—
385D4×C31—81no—
386D4×C31—81no—
387D4×C31—81no—
388D4×C31—81no—
389D4×C31—81no—
390C2×C4×C31—21no—
391C2×C4×C31—21no—
392C2×C4×C31—21no—
393C2×C4×C31—21no—
394C2×C4×C31—21no—
395C2×C4×C31—21no—
396C2×C4×C31—21no—
397C2×C4×C31—41no—
398C2×C4×C31—41no—
399C2×C4×C31—41no—
400C2×C4×C31—41no—
401C2×C4×C31—41no—
402C2×C4×C31—41no—
403C2×C4×C31—41no—
404C2×C4×C31—41no—
405C2×C4×C31—41no—
406C2×C4×C31—41no—
407C2×C4×C31—41no—
408C2×C4×C31—41no—
409C2×C4×C31—42no—
410C2×C4×C31—41no—
411C2×C4×C31—41no—
412C2×C4×C31—41no—
413C2×C4×C31—41no—
414C2×C4×C31—41no—
415C2×C4×C31—41no—
416C2×C4×C31—41no—
417C2×C4×C31—41no—
418C2×C4×C31—41no—
419C2×C4×C31—41no—
420C2×C4×C31—41no—
421C2×C4×C31—41no—
422C2×C4×C31—81no—
423C2×C4×C31—81no—
424C2×C4×C31—81no—
425C2×C4×C31—81no—
426C2×C4×C31—81no—
427C2×C4×C31—81no—
428C2×C4×C31—84no—
429C2×C4×C31C2×C22⋊C411yescharacteristic
430C2×C4×C31C2×C22⋊C411yescharacteristic
431C2×C4×C31C2×C22⋊C411yescharacteristic
432C2×C4×C31C2×C22⋊C411yescharacteristic
433C2×C4×C31C2×C22⋊C411yescharacteristic
434C2×C4×C31C2×C22⋊C411yescharacteristic
435C2×C4×C31C2×C22⋊C411yescharacteristic
436C2×C4×C31C2×C22⋊C411yescharacteristic
437C2×C4×C31C23×C411yescharacteristic
438C2×C4×C31C22×D411yescharacteristic
439C8×C31—41no—
440C8×C31—41no—
441C8×C31—41no—
442C8×C31—41no—
443#3519C2×C3111yescharacteristic
444#2974C2×C3111yescharacteristic, complemented
445#2318C2×C3111yescharacteristic, complemented
446#1521C2×C3111yescharacteristic, complemented
447#1519C2×C3111yescharacteristic, complemented
448#1517C2×C3111yescharacteristic, complemented
449#1516C2×C3111yescharacteristic, complemented
450#1514C2×C3111yescharacteristic, complemented
451#1513C2×C3111yescharacteristic, complemented
452#1512C2×C3111yescharacteristic, complemented
453#1510C2×C3111yescharacteristic, complemented
454#1507C2×C3111yescharacteristic, complemented
455#1504C2×C3111yescharacteristic, complemented
456#1501C2×C3111yescharacteristic, complemented
457C2×#327C2×C3111yescharacteristic, complemented
458C22×C31—21no—
459C22×C31—21no—
460C22×C31—21no—
461C22×C31—21no—
462C22×C31—21no—
463C22×C31—21no—
464C22×C31—21no—
465C22×C31—21no—
466C22×C31—21no—
467C22×C31—21no—
468C22×C31—21no—
469C22×C31—21no—
470C22×C31—21no—
471C22×C31—42no—
472C22×C31—42no—
473C22×C31—41no—
474C22×C31—41no—
475C22×C31—41no—
476C22×C31—41no—
477C22×C31—41no—
478C22×C31—41no—
479C22×C31—41no—
480C22×C31—41no—
481C22×C31—41no—
482C22×C31—81no—
483C22×C31—81no—
484C22×C31—162no—
485C22×C31—162no—
486C22×C31#42112yes—
487C22×C31C22×C22⋊C411yescharacteristic
488C22×C31#57611yescharacteristic
489C22×C31#57711yescharacteristic
490C4×C31—21no—
491C4×C31—21no—
492C4×C31—21no—
493C4×C31—21no—
494C4×C31—21no—
495C4×C31—21no—
496C4×C31—21no—
497C4×C31—21no—
498C4×C31—21no—
499C4×C31—21no—
500C4×C31—41no—
501C4×C31—41no—
502C4×C31—41no—
503C4×C31—41no—
504C4×C31—41no—
505C4×C31—81no—
506C4×C31—81no—
507C4×C31—81no—
508C4×C31—81no—
509#555C4×C3111yescharacteristic, complemented
510#554C4×C3111yescharacteristic, complemented
511#553—21no—
512#553C4×C3111yescharacteristic, complemented
513#553C4×C3111yescharacteristic, complemented
514#550C4×C3111yescharacteristic, complemented
515#546—21no—
516#546—21no—
517#546C4×C3111yescharacteristic, complemented
518#546C4×C3111yescharacteristic, complemented
519D42—21no—
520D42C4×C3111yescharacteristic, complemented
521#540—21no—
522#538—21no—
523#538—21no—
524#532C22×C3111yescharacteristic
525#529C22×C3111yescharacteristic
526#525C22×C3111yescharacteristic
527#525C22×C3111yescharacteristic
528C2×#121C22×C3111yescharacteristic
529C2×#121C22×C3111yescharacteristic
530#518—21no—
531C2×C4×D4C22×C3111yescharacteristic
532#436—21no—
533#435—21no—
534#435—21no—
535C8×D4—21no—
536#432C22×C3111yescharacteristic, complemented
537#431C22×C3111yescharacteristic, complemented
538#407C22×C3111yescharacteristic, complemented
539#407C22×C3111yescharacteristic, complemented
540C2×C22⋊C8C22×C3111yescharacteristic, complemented
541C2×C22⋊C8C22×C3111yescharacteristic, complemented
542#388—21no—
543#387—21no—
544#386—21no—
545#385—21no—
546#383C22×C3111yescharacteristic, complemented
547#382C22×C3111yescharacteristic, complemented
548#381C22×C3111yescharacteristic, complemented
549#380C22×C3111yescharacteristic, complemented
550C4×C22⋊C4C22×C3111yescharacteristic, complemented
551C2×#95C22×C3111yescharacteristic, complemented
552#328C22×C3111yescharacteristic, complemented
553#328C22×C3111yescharacteristic, complemented
554#328C22×C3111yescharacteristic, complemented
555#328C22×C3111yescharacteristic, complemented
556#327C22×C3111yescharacteristic
557#327C22×C3111yescharacteristic
558#327C22×C3111yescharacteristic
559#327C22×C3111yescharacteristic
560#327C22×C3111yescharacteristic, complemented
561#327C22×C3111yescharacteristic, complemented
562#327C22×C3111yescharacteristic, complemented
563#327C22×C3111yescharacteristic, complemented
564#327C22×C3111yescharacteristic, complemented
565#327C22×C3111yescharacteristic, complemented
566#327C22×C3111yescharacteristic, complemented
567#327C22×C3111yescharacteristic, complemented
568C2×C31—21no—
569C2×C31—21no—
570C2×C31—22no—
571C2×C31—41no—
572C2×C31—41no—
573C2×C31—41no—
574C2×C31—81no—
575C2×C31—81no—
576C2×C31—81no—
577C2×C31#288311yescharacteristic
578C2×C31#289711yescharacteristic
579C2×C31C2×#42111yescharacteristic
580C2×#41—21no—
581C2×#41C2×C4×C3111yescharacteristic
582C2×#41C2×C4×C3111yescharacteristic, complemented
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4C2×C4×C3111yescharacteristic
587C22×D4C2×C4×C3111yescharacteristic, complemented
588C22×D4D4×C3111yescharacteristic
589C23×C4—21no—
590C23×C4C23×C3111yescharacteristic
591C23×C4C23×C3111yescharacteristic
592C2×M16—21no—
593C2×M16—21no—
594C22×C8—21no—
595C22×C8—21no—
596C4⋊Q8C2×C4×C3111yescharacteristic, complemented
597#127—21no—
598#127C2×C4×C3111yescharacteristic, complemented
599#126—21no—
600#126—21no—
601#126—21no—
602#125—21no—
603#125C2×C4×C3111yescharacteristic, complemented
604#124—21no—
605#124—21no—
606#124—21no—
607#124C2×C4×C3111yescharacteristic, complemented
608#123—21no—
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615C22⋊Q8—21no—
616C22⋊Q8—21no—
617C22⋊Q8C2×C4×C3111yescharacteristic
618C22⋊Q8C2×C4×C3111yescharacteristic, complemented
619C22⋊Q8C23×C3111yescharacteristic
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121C2×C4×C3111yescharacteristic
634#121C2×C4×C3111yescharacteristic
635#121C2×C4×C3111yescharacteristic
636#121C2×C4×C3111yescharacteristic, complemented
637#121C2×C4×C3111yescharacteristic, complemented
638#121C2×C4×C3111yescharacteristic, complemented
639#121C23×C3111yescharacteristic
640#121C23×C3111yescharacteristic
641#121C23×C3111yescharacteristic
642#120—21no—
643#120—21no—
644#120—21no—
645#120—21no—
646#120—21no—
647#120—21no—
648C4×Q8C2×C4×C3111yescharacteristic, complemented
649C4×D4—21no—
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—21no—
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—21no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4C2×C4×C3111yescharacteristic
660C4×D4C2×C4×C3111yescharacteristic
661C4×D4C2×C4×C3111yescharacteristic
662C4×D4C2×C4×C3111yescharacteristic
663C4×D4C2×C4×C3111yescharacteristic, complemented
664C4×D4C2×C4×C3111yescharacteristic, complemented
665C4×D4C2×C4×C3111yescharacteristic, complemented
666C4×D4D4×C3111yescharacteristic
667C4×D4D4×C3111yescharacteristic
668C4×D4D4×C3111yescharacteristic
669C4×D4D4×C3111yescharacteristic
670#117—21no—
671#117—21no—
672#117C2×C4×C3111yescharacteristic
673#117C2×C4×C3111yescharacteristic, complemented
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4C2×C4×C3111yescharacteristic
677C2×C4⋊C4C2×C4×C3111yescharacteristic, complemented
678C2×C4⋊C4D4×C3111yescharacteristic
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4D4×C3111yescharacteristic
687C2×C22⋊C4D4×C3111yescharacteristic
688C2×C42—21no—
689C2×C42C23×C3111yescharacteristic
690C4⋊C8—21no—
691C4⋊C8—21no—
692C22⋊C8—21no—
693C22⋊C8—21no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696C22⋊C8C23×C3111yescharacteristic
697C22⋊C8C23×C3111yescharacteristic
698C22⋊C8C23×C3111yescharacteristic
699C22⋊C8C23×C3111yescharacteristic
700#97—21no—
701C4×C8—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95C23×C3111yescharacteristic
708#95C23×C3111yescharacteristic
709#95C23×C3111yescharacteristic
710#95C23×C3111yescharacteristic
711C31#1759711yescharacteristic, direct product factor, Sylow
712C24—21no—
713C24—21no—
714C24C2×D4×C3111yescharacteristic
715C24C2×D4×C3111yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719#41—81no—
720C2×Q8—21no—
721C2×Q8C22×C4×C3111yescharacteristic
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—42no—
738C2×D4—44no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4—81no—
742C2×D4—81no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4C22⋊C4×C3111yescharacteristic
746C2×D4C22⋊C4×C3111yescharacteristic
747C2×D4C22⋊C4×C3111yescharacteristic
748C2×D4C22⋊C4×C3111yescharacteristic
749C2×D4C22×C4×C3111yescharacteristic
750C2×D4C22×C4×C3111yescharacteristic
751C2×D4C22×C4×C3111yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—42no—
764C22×C4—81no—
765C22×C4—81no—
766C22×C4—81no—
767C22×C4—81no—
768C22×C4C22×C4×C3111yescharacteristic
769C22×C4C22×C4×C3111yescharacteristic
770C22×C4C22×C4×C3111yescharacteristic
771C22×C4C22×C4×C3111yescharacteristic
772C22×C4C2×D4×C3111yescharacteristic
773C22×C4C2×D4×C3111yescharacteristic
774C22×C4C2×D4×C3111yescharacteristic
775C22×C4C2×D4×C3111yescharacteristic
776C22×C4C2×D4×C3111yescharacteristic
777C22×C4C2×D4×C3111yescharacteristic
778C22×C4C2×D4×C3111yescharacteristic
779C22×C4C2×D4×C3111yescharacteristic
780C22×C4C24×C3111yescharacteristic
781M16—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C2×C8—81no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—81no—
799C4⋊C4—81no—
800C4⋊C4C22⋊C4×C3111yescharacteristic
801C4⋊C4C22⋊C4×C3111yescharacteristic
802C4⋊C4C22⋊C4×C3111yescharacteristic
803C4⋊C4C22⋊C4×C3111yescharacteristic
804C4⋊C4C22×C4×C3111yescharacteristic
805C4⋊C4C22×C4×C3111yescharacteristic
806C4⋊C4C22×C4×C3111yescharacteristic
807C4⋊C4C22×C4×C3111yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—42no—
828C22⋊C4—81no—
829C22⋊C4—81no—
830C22⋊C4C22⋊C4×C3111yescharacteristic
831C22⋊C4C22⋊C4×C3111yescharacteristic
832C22⋊C4C22⋊C4×C3111yescharacteristic
833C22⋊C4C22⋊C4×C3111yescharacteristic
834C22⋊C4C22⋊C4×C3111yescharacteristic
835C22⋊C4C22⋊C4×C3111yescharacteristic
836C22⋊C4C22⋊C4×C3111yescharacteristic
837C22⋊C4C22⋊C4×C3111yescharacteristic
838C42—21no—
839C42—21no—
840C42—21no—
841C42—81no—
842C42C22×C4×C3111yescharacteristic
843C42C22×C4×C3111yescharacteristic
844C42C2×D4×C3111yescharacteristic
845C42C2×D4×C3111yescharacteristic
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—81no—
860C23—81no—
861C23—81no—
862C23—81no—
863C23C2×C22⋊C4×C3111yescharacteristic
864C23C2×C22⋊C4×C3111yescharacteristic
865C23C2×C22⋊C4×C3111yescharacteristic
866C23C2×C22⋊C4×C3111yescharacteristic
867C23C22×D4×C3111yescharacteristic
868Q8—41no—
869Q8—81no—
870D4—22no—
871D4—22no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—42no—
878D4—42no—
879D4—42no—
880D4—41no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—81no—
887D4—81no—
888D4—81no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—42no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—81no—
928C2×C4—81no—
929C2×C4—81no—
930C2×C4—81no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—84no—
934C2×C4C2×C22⋊C4×C3111yescharacteristic
935C2×C4C2×C22⋊C4×C3111yescharacteristic
936C2×C4C2×C22⋊C4×C3111yescharacteristic
937C2×C4C2×C22⋊C4×C3111yescharacteristic
938C2×C4C2×C22⋊C4×C3111yescharacteristic
939C2×C4C2×C22⋊C4×C3111yescharacteristic
940C2×C4C2×C22⋊C4×C3111yescharacteristic
941C2×C4C2×C22⋊C4×C3111yescharacteristic
942C2×C4C23×C4×C3111yescharacteristic
943C2×C4C22×D4×C3111yescharacteristic
944C8—41no—
945C8—41no—
946C8—41no—
947C8—41no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—42no—
962C22—42no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—81no—
973C22—81no—
974C22—162no—
975C22—162no—
976C22C31×#42112yes—
977C22C22×C22⋊C4×C3111yescharacteristic
978C22C31×#57611yescharacteristic
979C22C31×#57711yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C4—81no—
998C4—81no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—41no—
1005C2—81no—
1006C2—81no—
1007C2—81no—
1008C2C31×#288311yescharacteristic
1009C2C31×#289711yescharacteristic
1010C2C2×C31×#42111yescharacteristic
subgroupG/H
center, socleC22×C31C22×C22⋊C4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC31×#3519C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2974C2semidirect
3. C31×#2318C2semidirect
4. C31×#1521C2semidirect
5. C31×#1519C2semidirect
6. C31×#1517C2semidirect
7. C31×#1516C2semidirect
8. C31×#1514C2semidirect
9. C31×#1513C2semidirect
10. C31×#1512C2semidirect
11. C31×#1510C2semidirect
12. C31×#1507C2semidirect
13. C31×#1504C2semidirect
14. C31×#1501C2semidirect
15. C2×C31×#327C2semidirect
16. C31×#555C4semidirect
17. C31×#554C4semidirect
19. C31×#553C4semidirect
20. C31×#553C4semidirect
21. C31×#550C4semidirect
24. C31×#546C4semidirect
25. C31×#546C4semidirect
27. D42×C31C4semidirect
43. C31×#432C22semidirect
44. C31×#431C22semidirect
45. C31×#407C22semidirect
46. C31×#407C22semidirect
47. C2×C31×C22⋊C8C22semidirect
48. C2×C31×C22⋊C8C22semidirect
53. C31×#383C22semidirect
54. C31×#382C22semidirect
55. C31×#381C22semidirect
56. C31×#380C22semidirect
57. C4×C22⋊C4×C31C22semidirect
58. C2×C31×#95C22semidirect
59. C31×#328C22semidirect
60. C31×#328C22semidirect
61. C31×#328C22semidirect
62. C31×#328C22semidirect
67. C31×#327C22semidirect
68. C31×#327C22semidirect
69. C31×#327C22semidirect
70. C31×#327C22semidirect
71. C31×#327C22semidirect
72. C31×#327C22semidirect
73. C31×#327C22semidirect
74. C31×#327C22semidirect
77. C2×#41×C31C2×C4semidirect
82. C22×D4×C31C2×C4semidirect
91. C31×C4⋊Q8C2×C4semidirect
93. C31×#127C2×C4semidirect
98. C31×#125C2×C4semidirect
102. C31×#124C2×C4semidirect
113. C31×C22⋊Q8C2×C4semidirect
131. C31×#121C2×C4semidirect
132. C31×#121C2×C4semidirect
133. C31×#121C2×C4semidirect
143. C4×Q8×C31C2×C4semidirect
158. C4×D4×C31C2×C4semidirect
159. C4×D4×C31C2×C4semidirect
160. C4×D4×C31C2×C4semidirect
168. C31×#117C2×C4semidirect
172. C2×C4⋊C4×C31C2×C4semidirect
340. #17597C31direct (N × H)
444. #2974C2×C31semidirect
445. #2318C2×C31semidirect
446. #1521C2×C31semidirect
447. #1519C2×C31semidirect
448. #1517C2×C31semidirect
449. #1516C2×C31semidirect
450. #1514C2×C31semidirect
451. #1513C2×C31semidirect
452. #1512C2×C31semidirect
453. #1510C2×C31semidirect
454. #1507C2×C31semidirect
455. #1504C2×C31semidirect
456. #1501C2×C31semidirect
457. C2×#327C2×C31semidirect
509. #555C4×C31semidirect
510. #554C4×C31semidirect
512. #553C4×C31semidirect
513. #553C4×C31semidirect
514. #550C4×C31semidirect
517. #546C4×C31semidirect
518. #546C4×C31semidirect
520. D42C4×C31semidirect
536. #432C22×C31semidirect
537. #431C22×C31semidirect
538. #407C22×C31semidirect
539. #407C22×C31semidirect
540. C2×C22⋊C8C22×C31semidirect
541. C2×C22⋊C8C22×C31semidirect
546. #383C22×C31semidirect
547. #382C22×C31semidirect
548. #381C22×C31semidirect
549. #380C22×C31semidirect
550. C4×C22⋊C4C22×C31semidirect
551. C2×#95C22×C31semidirect
552. #328C22×C31semidirect
553. #328C22×C31semidirect
554. #328C22×C31semidirect
555. #328C22×C31semidirect
560. #327C22×C31semidirect
561. #327C22×C31semidirect
562. #327C22×C31semidirect
563. #327C22×C31semidirect
564. #327C22×C31semidirect
565. #327C22×C31semidirect
566. #327C22×C31semidirect
567. #327C22×C31semidirect
582. C2×#41C2×C4×C31semidirect
587. C22×D4C2×C4×C31semidirect
596. C4⋊Q8C2×C4×C31semidirect
598. #127C2×C4×C31semidirect
603. #125C2×C4×C31semidirect
607. #124C2×C4×C31semidirect
618. C22⋊Q8C2×C4×C31semidirect
636. #121C2×C4×C31semidirect
637. #121C2×C4×C31semidirect
638. #121C2×C4×C31semidirect
648. C4×Q8C2×C4×C31semidirect
663. C4×D4C2×C4×C31semidirect
664. C4×D4C2×C4×C31semidirect
665. C4×D4C2×C4×C31semidirect
673. #117C2×C4×C31semidirect
677. C2×C4⋊C4C2×C4×C31semidirect
711. C31#17597direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35192
C31×#29742
C31×#23182
C31×#15212
C31×#15192
C31×#15172
C31×#15162
C31×#15142
C31×#15132
C31×#15122
C31×#15102
C31×#15072
C31×#15042
C31×#15012
C2×C31×#3272
#1759731