Finite Group Databasebeta

← C31×#26158 #21482917

Subgroups — C31×#26158 #21482917

Order 7936.

1022 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#459C211yesmaximal, characteristic
2C2×C4×D8×C31C211yesmaximal, characteristic, complemented
3C31×#2445C211yesmaximal, characteristic, complemented
4D4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
5C31×#2093C211yesmaximal, characteristic, complemented
6C31×#2086C211yesmaximal, characteristic, complemented
7C31×#2071C211yesmaximal, characteristic, complemented
8C31×#2041C211yesmaximal, characteristic, complemented
9C31×#1934C211yesmaximal, characteristic, complemented
10C31×#1916C211yesmaximal, characteristic, complemented
11C31×#1879C211yesmaximal, characteristic, complemented
12C31×#1879C211yesmaximal, characteristic, complemented
13C31×#1879C211yesmaximal, characteristic, complemented
14C31×#1862C211yesmaximal, characteristic, complemented
15C31×#1862C211yesmaximal, characteristic, complemented
16C22×D8×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C2×C31×#127C2211yescharacteristic
19C2×C31×#123—21no—
20C2×C4×D4×C31C2211yescharacteristic
21C2×C4×D4×C31C2211yescharacteristic
22C2×C4×D4×C31C2211yescharacteristic
23C2×C4×D4×C31C2211yescharacteristic
24C22×C4⋊C4×C31—21no—
25C31×#459—24no—
26C4×D8×C31—24no—
27C2×C31×#107C2211yescharacteristic
28C2×C31×#107C2211yescharacteristic
29C2×C31×C4⋊C8C2211yescharacteristic
30C2×C31×#102C2211yescharacteristic
31C2×C31×#102C2211yescharacteristic
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C4×C8×C31C2211yescharacteristic
39C31×#394—21no—
40C31×#394—21no—
41C31×#390C2211yescharacteristic
42C31×#390C2211yescharacteristic
43C31×#390C2211yescharacteristic
44C31×#389C2211yescharacteristic
45C31×#389C2211yescharacteristic
46C31×#389C2211yescharacteristic
47C31×#386—21no—
48C31×#385—21no—
49C31×#385—21no—
50C31×#384C2211yescharacteristic
51C31×#380—21no—
52C4×C4⋊C4×C31C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#336C2211yescharacteristic
58C31×#336C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×D4×C31—21no—
62C22×D4×C31—21no—
63C22×D4×C31C2311yescharacteristic
64C22×D4×C31C2311yescharacteristic
65C22×D4×C31C2311yescharacteristic
66C23×C4×C31—21no—
67C23×C4×C31—21no—
68C23×C4×C31—21no—
69C23×C4×C31—21no—
70C2×D8×C31—22no—
71C2×D8×C31—22no—
72C2×D8×C31—22no—
73C2×D8×C31—22no—
74C2×D8×C31—22no—
75C2×D8×C31D414yes—
76C22×C8×C31C2311yescharacteristic
77C22×C8×C31C2311yescharacteristic
78C22×C8×C31C2311yescharacteristic
79C22×C8×C31C2311yescharacteristic
80C31×#127—22no—
81C31×#127—41no—
82C31×#123—44no—
83C4×D4×C31—22no—
84C4×D4×C31—22no—
85C4×D4×C31—22no—
86C4×D4×C31—22no—
87C4×D4×C31—22no—
88C4×D4×C31—41no—
89C4×D4×C31—41no—
90C4×D4×C31—41no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31—21no—
96C2×C4⋊C4×C31—44no—
97C2×C4⋊C4×C31D411yescharacteristic
98C2×C4⋊C4×C31D411yescharacteristic
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C4⋊C4×C31C2311yescharacteristic
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31—21no—
109C2×C22⋊C4×C31—21no—
110C2×C22⋊C4×C31—21no—
111C2×C22⋊C4×C31—21no—
112C2×C22⋊C4×C31—21no—
113C2×C22⋊C4×C31—21no—
114C2×C42×C31C2311yescharacteristic
115C2×C42×C31C2311yescharacteristic
116C2×C42×C31C2311yescharacteristic
117C31×#107—22no—
118C31×#107—41no—
119C31×C4⋊C8—22no—
120C31×#102—22no—
121C31×#102—22no—
122C31×#102—22no—
123C31×#102—22no—
124C31×#102—22no—
125C31×#102—22no—
126C31×#102—22no—
127C31×#102—41no—
128C4×C8×C31—22no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95—21no—
132C31×#95D411yescharacteristic
133C31×#95D411yescharacteristic
134C24×C31—21no—
135C24×C31—21no—
136C24×C31—21no—
137C2×D4×C31—21no—
138C2×D4×C31—21no—
139C2×D4×C31—21no—
140C2×D4×C31—21no—
141C2×D4×C31—21no—
142C2×D4×C31—21no—
143C2×D4×C31—21no—
144C2×D4×C31—21no—
145C2×D4×C31—21no—
146C2×D4×C31—21no—
147C2×D4×C31—21no—
148C2×D4×C31—21no—
149C2×D4×C31—21no—
150C2×D4×C31—21no—
151C2×D4×C31—42no—
152C2×D4×C31—42no—
153C2×D4×C31—42no—
154C2×D4×C31—42no—
155C2×D4×C31—81no—
156C2×D4×C31—81no—
157C2×D4×C31C2×D412yes—
158C2×D4×C31C2×D412yes—
159C2×D4×C31#4112yes—
160C2×D4×C31#4112yes—
161C22×C4×C31—24no—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—42no—
168C22×C4×C31—42no—
169C22×C4×C31—42no—
170C22×C4×C31—42no—
171C22×C4×C31—42no—
172C22×C4×C31—42no—
173C22×C4×C31—42no—
174C22×C4×C31—42no—
175C22×C4×C31—81no—
176C22×C4×C31—81no—
177C22×C4×C31—81no—
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2×D411yescharacteristic
181C22×C4×C31C2×D411yescharacteristic
182C22×C4×C31C2×D411yescharacteristic
183C22×C4×C31C2×D411yescharacteristic
184C22×C4×C31C2411yescharacteristic
185D8×C31—28no—
186D8×C31—44no—
187C2×C8×C31—21no—
188C2×C8×C31—21no—
189C2×C8×C31—21no—
190C2×C8×C31—21no—
191C2×C8×C31—21no—
192C2×C8×C31—21no—
193C2×C8×C31—21no—
194C2×C8×C31—21no—
195C2×C8×C31—21no—
196C2×C8×C31—21no—
197C2×C8×C31—21no—
198C2×C8×C31C2×D412yes—
199C4⋊C4×C31—21no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—21no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—21no—
208C4⋊C4×C31—41no—
209C4⋊C4×C31—42no—
210C4⋊C4×C31—42no—
211C4⋊C4×C31—42no—
212C4⋊C4×C31—42no—
213C4⋊C4×C31—81no—
214C4⋊C4×C31D814yescomplemented
215C4⋊C4×C31#4112yes—
216C22⋊C4×C31—24no—
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—
226C42×C31—21no—
227C42×C31—21no—
228C42×C31—21no—
229C42×C31—21no—
230C42×C31—21no—
231C42×C31—21no—
232#26158C3111yesmaximal, characteristic, direct product factor, Sylow
233C23×C31—22no—
234C23×C31—22no—
235C23×C31—22no—
236C23×C31—22no—
237C23×C31—41no—
238C23×C31—41no—
239C23×C31—41no—
240C23×C31—41no—
241C23×C31—41no—
242C23×C31—41no—
243C23×C31—41no—
244C23×C31—41no—
245C23×C31—41no—
246C23×C31—41no—
247C23×C31—41no—
248C23×C31—41no—
249C23×C31—41no—
250C23×C31—41no—
251C23×C31—41no—
252C23×C31—41no—
253C23×C31—41no—
254C23×C31C22×D411yescharacteristic
255D4×C31—22no—
256D4×C31—22no—
257D4×C31—22no—
258D4×C31—22no—
259D4×C31—22no—
260D4×C31—41no—
261D4×C31—41no—
262D4×C31—41no—
263D4×C31—41no—
264D4×C31—41no—
265D4×C31—41no—
266D4×C31—84no—
267D4×C31—84no—
268D4×C31#12314yescomplemented
269C2×C4×C31—21no—
270C2×C4×C31—21no—
271C2×C4×C31—21no—
272C2×C4×C31—21no—
273C2×C4×C31—21no—
274C2×C4×C31—21no—
275C2×C4×C31—21no—
276C2×C4×C31—22no—
277C2×C4×C31—21no—
278C2×C4×C31—21no—
279C2×C4×C31—21no—
280C2×C4×C31—21no—
281C2×C4×C31—21no—
282C2×C4×C31—21no—
283C2×C4×C31—21no—
284C2×C4×C31—21no—
285C2×C4×C31—48no—
286C2×C4×C31—41no—
287C2×C4×C31—41no—
288C2×C4×C31—41no—
289C2×C4×C31—41no—
290C2×C4×C31—41no—
291C2×C4×C31—41no—
292C2×C4×C31—41no—
293C2×C4×C31—41no—
294C2×C4×C31—41no—
295C2×C4×C31—41no—
296C2×C4×C31—41no—
297C2×C4×C31—41no—
298C2×C4×C31—41no—
299C2×C4×C31—41no—
300C2×C4×C31—84no—
301C2×C4×C31—84no—
302C2×C4×C31—84no—
303C2×C4×C31C2×D812yes—
304C2×C4×C31C2×D812yes—
305C2×C4×C31C2×D812yes—
306C2×C4×C31C22×D411yescharacteristic
307C2×C4×C31C2×#4111yescharacteristic
308C2×C4×C31C2×#4111yescharacteristic
309C2×C4×C31C2×#4111yescharacteristic
310C2×C4×C31H(5,𝔽2)11yescharacteristic
311C2×C4×C312−1+411yescharacteristic
312C8×C31—22no—
313C8×C31—41no—
314C8×C31—41no—
315C8×C31—41no—
316C2×#459C2×C3111yescharacteristic
317C2×C4×D8C2×C3111yescharacteristic, complemented
318#2445C2×C3111yescharacteristic, complemented
319D4×C4⋊C4C2×C3111yescharacteristic, complemented
320#2093C2×C3111yescharacteristic, complemented
321#2086C2×C3111yescharacteristic, complemented
322#2071C2×C3111yescharacteristic, complemented
323#2041C2×C3111yescharacteristic, complemented
324#1934C2×C3111yescharacteristic, complemented
325#1916C2×C3111yescharacteristic, complemented
326#1879C2×C3111yescharacteristic, complemented
327#1879C2×C3111yescharacteristic, complemented
328#1879C2×C3111yescharacteristic, complemented
329#1862C2×C3111yescharacteristic, complemented
330#1862C2×C3111yescharacteristic, complemented
331C22×C31—24no—
332C22×C31—42no—
333C22×C31—42no—
334C22×C31—42no—
335C22×C31—42no—
336C22×C31—42no—
337C22×C31—42no—
338C22×C31—42no—
339C22×C31—42no—
340C22×C31—42no—
341C22×C31—81no—
342C22×C31—81no—
343C22×C31—81no—
344C22×C31—81no—
345C22×C31—81no—
346C22×C31—81no—
347C22×C31—81no—
348C22×C31—81no—
349C22×C31—81no—
350C22×C31—81no—
351C22×C31—81no—
352C22×C31#52511yescharacteristic
353C22×C31D4211yescharacteristic
354C22×C31#54811yescharacteristic
355C22×C31C22×D811yescharacteristic
356C22×C31#57511yescharacteristic
357C22×C31#57611yescharacteristic
358C22×C31#57711yescharacteristic
359C4×C31—22no—
360C4×C31—22no—
361C4×C31—22no—
362C4×C31—42no—
363C4×C31—41no—
364C4×C31—41no—
365C4×C31—41no—
366C4×C31—81no—
367C4×C31—81no—
368C4×C31—81no—
369C4×C31—81no—
370C4×C31C2×#12311yescharacteristic
371C4×C31#53911yescharacteristic
372C4×C31#54711yescharacteristic
373C4×C31#55311yescharacteristic
374C22×D8C22×C3111yescharacteristic
375C22×D8C22×C3111yescharacteristic
376C2×#127C22×C3111yescharacteristic
377C2×#123—21no—
378C2×C4×D4C22×C3111yescharacteristic
379C2×C4×D4C22×C3111yescharacteristic
380C2×C4×D4C22×C3111yescharacteristic
381C2×C4×D4C22×C3111yescharacteristic
382C22×C4⋊C4—21no—
383#459—24no—
384C4×D8—24no—
385C2×#107C22×C3111yescharacteristic
386C2×#107C22×C3111yescharacteristic
387C2×C4⋊C8C22×C3111yescharacteristic
388C2×#102C22×C3111yescharacteristic
389C2×#102C22×C3111yescharacteristic
390C2×#102C22×C3111yescharacteristic
391C2×#102C22×C3111yescharacteristic
392C2×#102C22×C3111yescharacteristic
393C2×#102C22×C3111yescharacteristic
394C2×#102C22×C3111yescharacteristic
395C2×#102C22×C3111yescharacteristic
396C2×C4×C8C22×C3111yescharacteristic
397#394—21no—
398#394—21no—
399#390C22×C3111yescharacteristic
400#390C22×C3111yescharacteristic
401#390C22×C3111yescharacteristic
402#389C22×C3111yescharacteristic
403#389C22×C3111yescharacteristic
404#389C22×C3111yescharacteristic
405#386—21no—
406#385—21no—
407#385—21no—
408#384C22×C3111yescharacteristic
409#380—21no—
410C4×C4⋊C4C22×C3111yescharacteristic
411#340C22×C3111yescharacteristic
412#340C22×C3111yescharacteristic
413#340C22×C3111yescharacteristic
414#340C22×C3111yescharacteristic
415#336C22×C3111yescharacteristic
416#336C22×C3111yescharacteristic
417#336C22×C3111yescharacteristic
418#336C22×C3111yescharacteristic
419C2×C31—44no—
420C2×C31—82no—
421C2×C31—161no—
422C2×C31#244311yescharacteristic
423C2×C31#310011yescharacteristic
424C2×C31#311911yescharacteristic
425C2×C31#326711yescharacteristic
426C2×C31D4×D811yescharacteristic
427C2×C31#335811yescharacteristic
428C2×C31#337011yescharacteristic
429C22×D4—21no—
430C22×D4—21no—
431C22×D4C23×C3111yescharacteristic
432C22×D4C23×C3111yescharacteristic
433C22×D4C23×C3111yescharacteristic
434C23×C4—21no—
435C23×C4—21no—
436C23×C4—21no—
437C23×C4—21no—
438C2×D8—22no—
439C2×D8—22no—
440C2×D8—22no—
441C2×D8—22no—
442C2×D8—22no—
443C2×D8D4×C3114yes—
444C22×C8C23×C3111yescharacteristic
445C22×C8C23×C3111yescharacteristic
446C22×C8C23×C3111yescharacteristic
447C22×C8C23×C3111yescharacteristic
448#127—22no—
449#127—41no—
450#123—44no—
451C4×D4—22no—
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—22no—
455C4×D4—22no—
456C4×D4—41no—
457C4×D4—41no—
458C4×D4—41no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—44no—
465C2×C4⋊C4D4×C3111yescharacteristic
466C2×C4⋊C4D4×C3111yescharacteristic
467C2×C4⋊C4C23×C3111yescharacteristic
468C2×C4⋊C4C23×C3111yescharacteristic
469C2×C4⋊C4C23×C3111yescharacteristic
470C2×C4⋊C4C23×C3111yescharacteristic
471C2×C4⋊C4C23×C3111yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C42C23×C3111yescharacteristic
483C2×C42C23×C3111yescharacteristic
484C2×C42C23×C3111yescharacteristic
485#107—22no—
486#107—41no—
487C4⋊C8—22no—
488#102—22no—
489#102—22no—
490#102—22no—
491#102—22no—
492#102—22no—
493#102—22no—
494#102—22no—
495#102—41no—
496C4×C8—22no—
497#95—21no—
498#95—21no—
499#95—21no—
500#95D4×C3111yescharacteristic
501#95D4×C3111yescharacteristic
502C31#2615811yescharacteristic, direct product factor, Sylow
503C24—21no—
504C24—21no—
505C24—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—81no—
525C2×D4—81no—
526C2×D4C2×D4×C3112yes—
527C2×D4C2×D4×C3112yes—
528C2×D4#41×C3112yes—
529C2×D4#41×C3112yes—
530C22×C4—24no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—81no—
545C22×C4—81no—
546C22×C4—81no—
547C22×C4C2×D4×C3111yescharacteristic
548C22×C4C2×D4×C3111yescharacteristic
549C22×C4C2×D4×C3111yescharacteristic
550C22×C4C2×D4×C3111yescharacteristic
551C22×C4C2×D4×C3111yescharacteristic
552C22×C4C2×D4×C3111yescharacteristic
553C22×C4C24×C3111yescharacteristic
554D8—28no—
555D8—44no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8C2×D4×C3112yes—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—41no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—81no—
583C4⋊C4D8×C3114yescomplemented
584C4⋊C4#41×C3112yes—
585C22⋊C4—24no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—81no—
593C22⋊C4—81no—
594C22⋊C4—81no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23C22×D4×C3111yescharacteristic
623D4—22no—
624D4—22no—
625D4—22no—
626D4—22no—
627D4—22no—
628D4—41no—
629D4—41no—
630D4—41no—
631D4—41no—
632D4—41no—
633D4—41no—
634D4—84no—
635D4—84no—
636D4C31×#12314yescomplemented
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—48no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—84no—
669C2×C4—84no—
670C2×C4—84no—
671C2×C4C2×D8×C3112yes—
672C2×C4C2×D8×C3112yes—
673C2×C4C2×D8×C3112yes—
674C2×C4C22×D4×C3111yescharacteristic
675C2×C4C2×#41×C3111yescharacteristic
676C2×C4C2×#41×C3111yescharacteristic
677C2×C4C2×#41×C3111yescharacteristic
678C2×C4C31×H(5,𝔽2)11yescharacteristic
679C2×C4C31×2−1+411yescharacteristic
680C8—22no—
681C8—41no—
682C8—41no—
683C8—41no—
684C22—24no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22C31×#52511yescharacteristic
706C22D42×C3111yescharacteristic
707C22C31×#54811yescharacteristic
708C22C22×D8×C3111yescharacteristic
709C22C31×#57511yescharacteristic
710C22C31×#57611yescharacteristic
711C22C31×#57711yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—42no—
716C4—41no—
717C4—41no—
718C4—41no—
719C4—81no—
720C4—81no—
721C4—81no—
722C4—81no—
723C4C2×C31×#12311yescharacteristic
724C4C31×#53911yescharacteristic
725C4C31×#54711yescharacteristic
726C4C31×#55311yescharacteristic
727C2—44no—
728C2—82no—
729C2—161no—
730C2C31×#244311yescharacteristic
731C2C31×#310011yescharacteristic
732C2C31×#311911yescharacteristic
733C2C31×#326711yescharacteristic
734C2D4×D8×C3111yescharacteristic
735C2C31×#335811yescharacteristic
736C2C31×#337011yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#459C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×D8×C31C2semidirect
3. C31×#2445C2semidirect
4. D4×C4⋊C4×C31C2semidirect
5. C31×#2093C2semidirect
6. C31×#2086C2semidirect
7. C31×#2071C2semidirect
8. C31×#2041C2semidirect
9. C31×#1934C2semidirect
10. C31×#1916C2semidirect
11. C31×#1879C2semidirect
12. C31×#1879C2semidirect
13. C31×#1879C2semidirect
14. C31×#1862C2semidirect
15. C31×#1862C2semidirect
214. C4⋊C4×C31D8semidirect
232. #26158C31direct (N × H)
268. D4×C31#123semidirect
317. C2×C4×D8C2×C31semidirect
318. #2445C2×C31semidirect
319. D4×C4⋊C4C2×C31semidirect
320. #2093C2×C31semidirect
321. #2086C2×C31semidirect
322. #2071C2×C31semidirect
323. #2041C2×C31semidirect
324. #1934C2×C31semidirect
325. #1916C2×C31semidirect
326. #1879C2×C31semidirect
327. #1879C2×C31semidirect
328. #1879C2×C31semidirect
329. #1862C2×C31semidirect
330. #1862C2×C31semidirect
502. C31#26158direct (N × H)
583. C4⋊C4D8×C31semidirect
636. D4C31×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4592
C2×C4×D8×C312
C31×#24452
D4×C4⋊C4×C312
C31×#20932
C31×#20862
C31×#20712
C31×#20412
C31×#19342
C31×#19162
C31×#18792
C31×#18622
#2615831