Finite Group Databasebeta

← C31×#26584 #21483343

Subgroups — C31×#26584 #21483343

Order 7936.

1090 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#459C211yesmaximal, characteristic, complemented
2C2×C4×D8×C31C211yesmaximal, characteristic, complemented
3C31×#2445C211yesmaximal, characteristic, complemented
4C31×#2366C211yesmaximal, characteristic, complemented
5C31×#2067C211yesmaximal, characteristic, complemented
6C31×#2011C211yesmaximal, characteristic, complemented
7C31×#2011C211yesmaximal, characteristic, complemented
8C31×#2011C211yesmaximal, characteristic, complemented
9C31×#1970C211yesmaximal, characteristic, complemented
10C31×#1925C211yesmaximal, characteristic, complemented
11C31×#1925C211yesmaximal, characteristic, complemented
12C31×#1916C211yesmaximal, characteristic, complemented
13C31×#1879C211yesmaximal, characteristic, complemented
14C31×#1879C211yesmaximal, characteristic, complemented
15C31×#1862C211yesmaximal, characteristic, complemented
16C22×D8×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C22×D8×C31C2211yescharacteristic
19C22×D8×C31C2211yescharacteristic
20C2×C31×#127C2211yescharacteristic
21C2×C31×#127C2211yescharacteristic
22C2×C31×#123—21no—
23C2×C4×D4×C31—21no—
24C2×C4×D4×C31C2211yescharacteristic
25C2×C4×D4×C31C2211yescharacteristic
26C2×C4×D4×C31C2211yescharacteristic
27C31×#459—24no—
28C4×D8×C31—24no—
29C2×C31×#107C2211yescharacteristic
30C2×C31×#107C2211yescharacteristic
31C2×C31×C4⋊C8C2211yescharacteristic
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C4×C8×C31C2211yescharacteristic
41C31×#394—21no—
42C31×#394—21no—
43C31×#390—21no—
44C31×#390C2211yescharacteristic
45C31×#390C2211yescharacteristic
46C31×#390C2211yescharacteristic
47C31×#390C2211yescharacteristic
48C31×#390C2211yescharacteristic
49C31×#389C2211yescharacteristic
50C31×#386—21no—
51C31×#386—21no—
52C31×#386—21no—
53C4×C4⋊C4×C31C2211yescharacteristic
54C4×C4⋊C4×C31C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#336C2211yescharacteristic
58C31×#336C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×D4×C31—21no—
62C22×D4×C31—21no—
63C22×D4×C31—21no—
64C22×D4×C31—21no—
65C22×D4×C31C2311yescharacteristic
66C22×D4×C31C2311yescharacteristic
67C22×D4×C31C2311yescharacteristic
68C22×D4×C31C2311yescharacteristic
69C23×C4×C31—21no—
70C23×C4×C31—21no—
71C23×C4×C31—21no—
72C2×D8×C31—22no—
73C2×D8×C31—22no—
74C2×D8×C31—22no—
75C2×D8×C31—22no—
76C2×D8×C31—22no—
77C2×D8×C31—22no—
78C2×D8×C31—22no—
79C2×D8×C31—22no—
80C2×D8×C31—41no—
81C2×D8×C31—41no—
82C2×D8×C31—41no—
83C2×D8×C31—41no—
84C22×C8×C31C2311yescharacteristic
85C22×C8×C31C2311yescharacteristic
86C22×C8×C31C2311yescharacteristic
87C22×C8×C31C2311yescharacteristic
88C31×#127—22no—
89C31×#127—22no—
90C31×#127—22no—
91C31×#127—41no—
92C31×#123—44no—
93C4×D4×C31—22no—
94C4×D4×C31—22no—
95C4×D4×C31—22no—
96C4×D4×C31—41no—
97C4×D4×C31—41no—
98C4×D4×C31—41no—
99C4×D4×C31—44no—
100C2×C4⋊C4×C31—21no—
101C2×C4⋊C4×C31D411yescharacteristic
102C2×C4⋊C4×C31D411yescharacteristic
103C2×C4⋊C4×C31C2311yescharacteristic
104C2×C4⋊C4×C31C2311yescharacteristic
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
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×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C42×C31—21no—
121C2×C42×C31C2311yescharacteristic
122C2×C42×C31C2311yescharacteristic
123C2×C42×C31C2311yescharacteristic
124C31×#107—22no—
125C31×#107—41no—
126C31×C4⋊C8—22no—
127C31×#102—22no—
128C31×#102—22no—
129C31×#102—22no—
130C31×#102—22no—
131C31×#102—41no—
132C31×#102—41no—
133C31×#102—41no—
134C31×#102D414yescomplemented
135C4×C8×C31—22no—
136C31×#95—21no—
137C31×#95—21no—
138C31×#95D411yescharacteristic
139C31×#95D411yescharacteristic
140C24×C31—21no—
141C24×C31—21no—
142C24×C31—21no—
143C24×C31—21no—
144C2×D4×C31—24no—
145C2×D4×C31—24no—
146C2×D4×C31—21no—
147C2×D4×C31—21no—
148C2×D4×C31—21no—
149C2×D4×C31—21no—
150C2×D4×C31—21no—
151C2×D4×C31—21no—
152C2×D4×C31—21no—
153C2×D4×C31—21no—
154C2×D4×C31—21no—
155C2×D4×C31—21no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—42no—
168C2×D4×C31—42no—
169C2×D4×C31—42no—
170C2×D4×C31—42no—
171C2×D4×C31—42no—
172C2×D4×C31—42no—
173C2×D4×C31—81no—
174C2×D4×C31—81no—
175C2×D4×C31—81no—
176C2×D4×C31—81no—
177C2×D4×C31C2×D412yes—
178C2×D4×C31#4112yes—
179C2×D4×C31#4112yes—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—42no—
185C22×C4×C31—42no—
186C22×C4×C31—42no—
187C22×C4×C31—42no—
188C22×C4×C31—42no—
189C22×C4×C31—42no—
190C22×C4×C31—81no—
191C22×C4×C31—81no—
192C22×C4×C31—81no—
193C22×C4×C31C2×D411yescharacteristic
194C22×C4×C31C2×D411yescharacteristic
195C22×C4×C31C2×D411yescharacteristic
196C22×C4×C31C2×D411yescharacteristic
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2411yescharacteristic
200D8×C31—28no—
201D8×C31—44no—
202D8×C31—44no—
203D8×C31—44no—
204C2×C8×C31—21no—
205C2×C8×C31—21no—
206C2×C8×C31—21no—
207C2×C8×C31—21no—
208C2×C8×C31—21no—
209C2×C8×C31—21no—
210C2×C8×C31—21no—
211C2×C8×C31—21no—
212C2×C8×C31—21no—
213C2×C8×C31—21no—
214C2×C8×C31C2×D412yes—
215C2×C8×C31#4112yes—
216C4⋊C4×C31—21no—
217C4⋊C4×C31—21no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—21no—
220C4⋊C4×C31—21no—
221C4⋊C4×C31—21no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—41no—
224C4⋊C4×C31—42no—
225C4⋊C4×C31D814yescomplemented
226C4⋊C4×C31C2×D412yes—
227C22⋊C4×C31—42no—
228C22⋊C4×C31—42no—
229C22⋊C4×C31—42no—
230C22⋊C4×C31—42no—
231C22⋊C4×C31—42no—
232C22⋊C4×C31—42no—
233C22⋊C4×C31—42no—
234C22⋊C4×C31—42no—
235C22⋊C4×C31—81no—
236C22⋊C4×C31—81no—
237C22⋊C4×C31—81no—
238C22⋊C4×C31—81no—
239C22⋊C4×C31—81no—
240C42×C31—21no—
241C42×C31—21no—
242C42×C31—21no—
243C42×C31—21no—
244C42×C31—21no—
245C42×C31—21no—
246C42×C31—42no—
247#26584C3111yesmaximal, characteristic, direct product factor, Sylow
248C23×C31—22no—
249C23×C31—22no—
250C23×C31—22no—
251C23×C31—41no—
252C23×C31—41no—
253C23×C31—41no—
254C23×C31—41no—
255C23×C31—41no—
256C23×C31—41no—
257C23×C31—41no—
258C23×C31—41no—
259C23×C31—41no—
260C23×C31—41no—
261C23×C31—41no—
262C23×C31—41no—
263C23×C31—41no—
264C23×C31—41no—
265C23×C31—41no—
266C23×C31—41no—
267C23×C31—41no—
268C23×C31—41no—
269C23×C31—41no—
270C23×C31—41no—
271C23×C31—41no—
272C23×C31—41no—
273C23×C31—41no—
274C23×C31—41no—
275C23×C31—41no—
276C23×C31C22×D411yescharacteristic
277D4×C31—22no—
278D4×C31—22no—
279D4×C31—22no—
280D4×C31—22no—
281D4×C31—22no—
282D4×C31—22no—
283D4×C31—48no—
284D4×C31—41no—
285D4×C31—41no—
286D4×C31—41no—
287D4×C31—41no—
288D4×C31—41no—
289D4×C31—41no—
290D4×C31—41no—
291D4×C31—41no—
292D4×C31—41no—
293D4×C31—41no—
294D4×C31—84no—
295D4×C31—84no—
296D4×C31—84no—
297C2×C4×C31—21no—
298C2×C4×C31—21no—
299C2×C4×C31—21no—
300C2×C4×C31—21no—
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—21no—
306C2×C4×C31—22no—
307C2×C4×C31—21no—
308C2×C4×C31—21no—
309C2×C4×C31—21no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
312C2×C4×C31—21no—
313C2×C4×C31—41no—
314C2×C4×C31—41no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—41no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—84no—
325C2×C4×C31—84no—
326C2×C4×C31—84no—
327C2×C4×C31C2×D812yes—
328C2×C4×C31C2×D812yes—
329C2×C4×C31C2×D812yes—
330C2×C4×C31C22×D411yescharacteristic
331C2×C4×C31C2×#4111yescharacteristic
332C2×C4×C31C2×#4111yescharacteristic
333C2×C4×C31C2×#4111yescharacteristic
334C2×C4×C31H(5,𝔽2)11yescharacteristic
335C2×C4×C31H(5,𝔽2)11yescharacteristic
336C8×C31—22no—
337C8×C31—22no—
338C8×C31—41no—
339C8×C31—41no—
340C2×#459C2×C3111yescharacteristic, complemented
341C2×C4×D8C2×C3111yescharacteristic, complemented
342#2445C2×C3111yescharacteristic, complemented
343#2366C2×C3111yescharacteristic, complemented
344#2067C2×C3111yescharacteristic, complemented
345#2011C2×C3111yescharacteristic, complemented
346#2011C2×C3111yescharacteristic, complemented
347#2011C2×C3111yescharacteristic, complemented
348#1970C2×C3111yescharacteristic, complemented
349#1925C2×C3111yescharacteristic, complemented
350#1925C2×C3111yescharacteristic, complemented
351#1916C2×C3111yescharacteristic, complemented
352#1879C2×C3111yescharacteristic, complemented
353#1879C2×C3111yescharacteristic, complemented
354#1862C2×C3111yescharacteristic, complemented
355C22×C31—42no—
356C22×C31—42no—
357C22×C31—42no—
358C22×C31—42no—
359C22×C31—42no—
360C22×C31—42no—
361C22×C31—42no—
362C22×C31—42no—
363C22×C31—42no—
364C22×C31—81no—
365C22×C31—81no—
366C22×C31—81no—
367C22×C31—81no—
368C22×C31—81no—
369C22×C31—81no—
370C22×C31—81no—
371C22×C31—81no—
372C22×C31—81no—
373C22×C31—81no—
374C22×C31—81no—
375C22×C31—81no—
376C22×C31—81no—
377C22×C31—81no—
378C22×C31—81no—
379C22×C31—81no—
380C22×C31—81no—
381C22×C31—81no—
382C22×C31—81no—
383C22×C31#52511yescharacteristic
384C22×C31D4211yescharacteristic
385C22×C31#55011yescharacteristic
386C22×C31C22×D811yescharacteristic
387C22×C31#57511yescharacteristic
388C22×C31#57611yescharacteristic
389C22×C31#57611yescharacteristic
390C4×C31—22no—
391C4×C31—22no—
392C4×C31—22no—
393C4×C31—41no—
394C4×C31—41no—
395C4×C31—41no—
396C4×C31—42no—
397C4×C31—81no—
398C4×C31—81no—
399C4×C31—81no—
400C4×C31#52511yescharacteristic
401C4×C31#53811yescharacteristic
402C4×C31#54611yescharacteristic
403C4×C31#55311yescharacteristic
404C22×D8C22×C3111yescharacteristic
405C22×D8C22×C3111yescharacteristic
406C22×D8C22×C3111yescharacteristic
407C22×D8C22×C3111yescharacteristic
408C2×#127C22×C3111yescharacteristic
409C2×#127C22×C3111yescharacteristic
410C2×#123—21no—
411C2×C4×D4—21no—
412C2×C4×D4C22×C3111yescharacteristic
413C2×C4×D4C22×C3111yescharacteristic
414C2×C4×D4C22×C3111yescharacteristic
415#459—24no—
416C4×D8—24no—
417C2×#107C22×C3111yescharacteristic
418C2×#107C22×C3111yescharacteristic
419C2×C4⋊C8C22×C3111yescharacteristic
420C2×#102C22×C3111yescharacteristic
421C2×#102C22×C3111yescharacteristic
422C2×#102C22×C3111yescharacteristic
423C2×#102C22×C3111yescharacteristic
424C2×#102C22×C3111yescharacteristic
425C2×#102C22×C3111yescharacteristic
426C2×#102C22×C3111yescharacteristic
427C2×#102C22×C3111yescharacteristic
428C2×C4×C8C22×C3111yescharacteristic
429#394—21no—
430#394—21no—
431#390—21no—
432#390C22×C3111yescharacteristic
433#390C22×C3111yescharacteristic
434#390C22×C3111yescharacteristic
435#390C22×C3111yescharacteristic
436#390C22×C3111yescharacteristic
437#389C22×C3111yescharacteristic
438#386—21no—
439#386—21no—
440#386—21no—
441C4×C4⋊C4C22×C3111yescharacteristic
442C4×C4⋊C4C22×C3111yescharacteristic
443#340C22×C3111yescharacteristic
444#340C22×C3111yescharacteristic
445#336C22×C3111yescharacteristic
446#336C22×C3111yescharacteristic
447#336C22×C3111yescharacteristic
448#336C22×C3111yescharacteristic
449C2×C31—82no—
450C2×C31—82no—
451C2×C31—82no—
452C2×C31—161no—
453C2×C31#245611yescharacteristic
454C2×C31#310011yescharacteristic
455C2×C31#312211yescharacteristic
456C2×C31#326811yescharacteristic
457C2×C31D4×D811yescharacteristic
458C2×C31#339111yescharacteristic
459C2×C31#340311yescharacteristic
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4C23×C3111yescharacteristic
465C22×D4C23×C3111yescharacteristic
466C22×D4C23×C3111yescharacteristic
467C22×D4C23×C3111yescharacteristic
468C23×C4—21no—
469C23×C4—21no—
470C23×C4—21no—
471C2×D8—22no—
472C2×D8—22no—
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×D8—22no—
478C2×D8—22no—
479C2×D8—41no—
480C2×D8—41no—
481C2×D8—41no—
482C2×D8—41no—
483C22×C8C23×C3111yescharacteristic
484C22×C8C23×C3111yescharacteristic
485C22×C8C23×C3111yescharacteristic
486C22×C8C23×C3111yescharacteristic
487#127—22no—
488#127—22no—
489#127—22no—
490#127—41no—
491#123—44no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—41no—
496C4×D4—41no—
497C4×D4—41no—
498C4×D4—44no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4D4×C3111yescharacteristic
501C2×C4⋊C4D4×C3111yescharacteristic
502C2×C4⋊C4C23×C3111yescharacteristic
503C2×C4⋊C4C23×C3111yescharacteristic
504C2×C4⋊C4C23×C3111yescharacteristic
505C2×C4⋊C4C23×C3111yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C42—21no—
520C2×C42C23×C3111yescharacteristic
521C2×C42C23×C3111yescharacteristic
522C2×C42C23×C3111yescharacteristic
523#107—22no—
524#107—41no—
525C4⋊C8—22no—
526#102—22no—
527#102—22no—
528#102—22no—
529#102—22no—
530#102—41no—
531#102—41no—
532#102—41no—
533#102D4×C3114yescomplemented
534C4×C8—22no—
535#95—21no—
536#95—21no—
537#95D4×C3111yescharacteristic
538#95D4×C3111yescharacteristic
539C31#2658411yescharacteristic, direct product factor, Sylow
540C24—21no—
541C24—21no—
542C24—21no—
543C24—21no—
544C2×D4—24no—
545C2×D4—24no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4—81no—
576C2×D4—81no—
577C2×D4C2×D4×C3112yes—
578C2×D4#41×C3112yes—
579C2×D4#41×C3112yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—81no—
591C22×C4—81no—
592C22×C4—81no—
593C22×C4C2×D4×C3111yescharacteristic
594C22×C4C2×D4×C3111yescharacteristic
595C22×C4C2×D4×C3111yescharacteristic
596C22×C4C2×D4×C3111yescharacteristic
597C22×C4C2×D4×C3111yescharacteristic
598C22×C4C2×D4×C3111yescharacteristic
599C22×C4C24×C3111yescharacteristic
600D8—28no—
601D8—44no—
602D8—44no—
603D8—44no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8C2×D4×C3112yes—
615C2×C8#41×C3112yes—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—41no—
624C4⋊C4—42no—
625C4⋊C4D8×C3114yescomplemented
626C4⋊C4C2×D4×C3112yes—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—81no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—42no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23C22×D4×C3111yescharacteristic
676D4—22no—
677D4—22no—
678D4—22no—
679D4—22no—
680D4—22no—
681D4—22no—
682D4—48no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—84no—
694D4—84no—
695D4—84no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—84no—
724C2×C4—84no—
725C2×C4—84no—
726C2×C4C2×D8×C3112yes—
727C2×C4C2×D8×C3112yes—
728C2×C4C2×D8×C3112yes—
729C2×C4C22×D4×C3111yescharacteristic
730C2×C4C2×#41×C3111yescharacteristic
731C2×C4C2×#41×C3111yescharacteristic
732C2×C4C2×#41×C3111yescharacteristic
733C2×C4C31×H(5,𝔽2)11yescharacteristic
734C2×C4C31×H(5,𝔽2)11yescharacteristic
735C8—22no—
736C8—22no—
737C8—41no—
738C8—41no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C31×#52511yescharacteristic
768C22D42×C3111yescharacteristic
769C22C31×#55011yescharacteristic
770C22C22×D8×C3111yescharacteristic
771C22C31×#57511yescharacteristic
772C22C31×#57611yescharacteristic
773C22C31×#57611yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—42no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4C31×#52511yescharacteristic
785C4C31×#53811yescharacteristic
786C4C31×#54611yescharacteristic
787C4C31×#55311yescharacteristic
788C2—82no—
789C2—82no—
790C2—82no—
791C2—161no—
792C2C31×#245611yescharacteristic
793C2C31×#310011yescharacteristic
794C2C31×#312211yescharacteristic
795C2C31×#326811yescharacteristic
796C2D4×D8×C3111yescharacteristic
797C2C31×#339111yescharacteristic
798C2C31×#340311yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
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
1. C2×C31×#459C2semidirect
2. C2×C4×D8×C31C2semidirect
3. C31×#2445C2semidirect
4. C31×#2366C2semidirect
5. C31×#2067C2semidirect
6. C31×#2011C2semidirect
7. C31×#2011C2semidirect
8. C31×#2011C2semidirect
9. C31×#1970C2semidirect
10. C31×#1925C2semidirect
11. C31×#1925C2semidirect
12. C31×#1916C2semidirect
13. C31×#1879C2semidirect
14. C31×#1879C2semidirect
15. C31×#1862C2semidirect
134. C31×#102D4semidirect
225. C4⋊C4×C31D8semidirect
247. #26584C31direct (N × H)
340. C2×#459C2×C31semidirect
341. C2×C4×D8C2×C31semidirect
342. #2445C2×C31semidirect
343. #2366C2×C31semidirect
344. #2067C2×C31semidirect
345. #2011C2×C31semidirect
346. #2011C2×C31semidirect
347. #2011C2×C31semidirect
348. #1970C2×C31semidirect
349. #1925C2×C31semidirect
350. #1925C2×C31semidirect
351. #1916C2×C31semidirect
352. #1879C2×C31semidirect
353. #1879C2×C31semidirect
354. #1862C2×C31semidirect
533. #102D4×C31semidirect
539. C31#26584direct (N × H)
625. C4⋊C4D8×C31semidirect

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
C31×#23662
C31×#20672
C31×#20112
C31×#19702
C31×#19252
C31×#19162
C31×#18792
C31×#18622
#2658431