Finite Group Databasebeta

← C31×#26926 #21483685

Subgroups — C31×#26926 #21483685

Order 7936.

1082 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×#480C211yesmaximal, characteristic, complemented
2C2×C31×#459C211yesmaximal, characteristic, complemented
3C31×#2428C211yesmaximal, characteristic, complemented
4C31×#2361C211yesmaximal, characteristic, complemented
5C31×#2086C211yesmaximal, characteristic, complemented
6C31×#2041C211yesmaximal, characteristic, complemented
7C31×#1999C211yesmaximal, characteristic, complemented
8C31×#1999C211yesmaximal, characteristic, complemented
9C31×#1970C211yesmaximal, characteristic, complemented
10C31×#1925C211yesmaximal, characteristic, complemented
11C31×#1923C211yesmaximal, characteristic, complemented
12C31×#1879C211yesmaximal, characteristic, complemented
13C31×#1874C211yesmaximal, characteristic, complemented
14C31×#1862C211yesmaximal, characteristic, complemented
15C4×C31×#102C211yesmaximal, characteristic, complemented
16C22×D8×C31C2211yescharacteristic
17C22×D8×C31C2211yescharacteristic
18C2×C31×#127C2211yescharacteristic
19C2×C31×#121—21no—
20C2×C31×#121C2211yescharacteristic
21C2×C31×#121C2211yescharacteristic
22C2×C31×#121C2211yescharacteristic
23C2×C4×D4×C31—21no—
24C2×C4×D4×C31C2211yescharacteristic
25C2×C4×D4×C31C2211yescharacteristic
26C22×C4⋊C4×C31C2211yescharacteristic
27C31×#480—24no—
28C31×#459—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×C31×C22⋊C8C2211yescharacteristic
41C2×C31×C22⋊C8C2211yescharacteristic
42C2×C4×C8×C31C2211yescharacteristic
43C31×#394—21no—
44C31×#392—21no—
45C31×#390C2211yescharacteristic
46C31×#390C2211yescharacteristic
47C31×#389C2211yescharacteristic
48C31×#389C2211yescharacteristic
49C31×#388—21no—
50C31×#386—21no—
51C31×#386—21no—
52C31×#385—21no—
53C4×C4⋊C4×C31C2211yescharacteristic
54C4×C22⋊C4×C31C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×D4×C31—21no—
62C22×D4×C31—21no—
63C22×D4×C31—21no—
64C22×D4×C31—21no—
65C22×D4×C31—21no—
66C22×D4×C31C2311yescharacteristic
67C22×D4×C31C2311yescharacteristic
68C22×D4×C31C2311yescharacteristic
69C23×C4×C31—21no—
70C23×C4×C31—21no—
71C23×C4×C31—21no—
72C23×C4×C31C2311yescharacteristic
73C2×D8×C31—22no—
74C2×D8×C31—22no—
75C2×D8×C31—22no—
76C2×D8×C31—22no—
77C2×D8×C31—41no—
78C2×D8×C31—41no—
79C22×C8×C31C2311yescharacteristic
80C22×C8×C31C2311yescharacteristic
81C22×C8×C31C2311yescharacteristic
82C22×C8×C31C2311yescharacteristic
83C31×#127—22no—
84C31×#127—41no—
85C31×#121—22no—
86C31×#121—22no—
87C31×#121—22no—
88C31×#121—22no—
89C31×#121—41no—
90C31×#121—41no—
91C31×#121—44no—
92C4×D4×C31—22no—
93C4×D4×C31—22no—
94C4×D4×C31—41no—
95C4×D4×C31—41no—
96C4×D4×C31—44no—
97C2×C4⋊C4×C31—22no—
98C2×C4⋊C4×C31—21no—
99C2×C4⋊C4×C31—21no—
100C2×C4⋊C4×C31—21no—
101C2×C4⋊C4×C31—41no—
102C2×C4⋊C4×C31C2311yescharacteristic
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×C31D411yescharacteristic
117C2×C22⋊C4×C31D411yescharacteristic
118C2×C42×C31—21no—
119C2×C42×C31C2311yescharacteristic
120C2×C42×C31C2311yescharacteristic
121C31×#107—22no—
122C31×#107—22no—
123C31×C4⋊C8—22no—
124C31×#102—22no—
125C31×#102—22no—
126C31×#102—22no—
127C31×#102—22no—
128C31×#102—22no—
129C31×#102—41no—
130C31×#102—41no—
131C31×#102D414yescomplemented
132C31×C22⋊C8—22no—
133C31×C22⋊C8—41no—
134C4×C8×C31—41no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95—21no—
138C31×#95D411yescharacteristic
139C31×#95D411yescharacteristic
140C24×C31—21no—
141C24×C31—21no—
142C24×C31—21no—
143C24×C31C2×D411yescharacteristic
144C2×D4×C31—24no—
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—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—42no—
162C2×D4×C31—42no—
163C2×D4×C31—42no—
164C2×D4×C31—42no—
165C2×D4×C31—42no—
166C2×D4×C31—42no—
167C2×D4×C31—42no—
168C2×D4×C31—42no—
169C2×D4×C31—42no—
170C2×D4×C31—42no—
171C2×D4×C31—81no—
172C2×D4×C31—81no—
173C2×D4×C31—81no—
174C2×D4×C31—81no—
175C2×D4×C31C2×D412yes—
176C2×D4×C31#4112yes—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—42no—
189C22×C4×C31—42no—
190C22×C4×C31—42no—
191C22×C4×C31—42no—
192C22×C4×C31—42no—
193C22×C4×C31—42no—
194C22×C4×C31—81no—
195C22×C4×C31—81no—
196C22×C4×C31—81no—
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2411yescharacteristic
203D8×C31—44no—
204D8×C31—44no—
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×C31—21no—
215C2×C8×C31—21no—
216C2×C8×C31C2×D412yes—
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—21no—
224C4⋊C4×C31—42no—
225C4⋊C4×C31—42no—
226C4⋊C4×C31—42no—
227C4⋊C4×C31C2×D412yes—
228C4⋊C4×C31#4112yes—
229C4⋊C4×C31#4112yes—
230C22⋊C4×C31—24no—
231C22⋊C4×C31—41no—
232C22⋊C4×C31—42no—
233C22⋊C4×C31—42no—
234C22⋊C4×C31—42no—
235C22⋊C4×C31—42no—
236C22⋊C4×C31—42no—
237C22⋊C4×C31—42no—
238C22⋊C4×C31—81no—
239C22⋊C4×C31—81no—
240C22⋊C4×C31D814yescomplemented
241C42×C31—21no—
242C42×C31—21no—
243C42×C31—21no—
244C42×C31—21no—
245C42×C31—42no—
246#26926C3111yesmaximal, characteristic, direct product factor, Sylow
247C23×C31—21no—
248C23×C31—21no—
249C23×C31—21no—
250C23×C31—21no—
251C23×C31—21no—
252C23×C31—21no—
253C23×C31—22no—
254C23×C31—22no—
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×C31C2×D812yes—
275C23×C31C22×D411yescharacteristic
276D4×C31—22no—
277D4×C31—22no—
278D4×C31—22no—
279D4×C31—22no—
280D4×C31—48no—
281D4×C31—41no—
282D4×C31—41no—
283D4×C31—41no—
284D4×C31—41no—
285D4×C31—41no—
286D4×C31—41no—
287D4×C31—41no—
288D4×C31—41no—
289D4×C31—84no—
290D4×C31—84no—
291D4×C31—84no—
292D4×C31—84no—
293C2×C4×C31—21no—
294C2×C4×C31—21no—
295C2×C4×C31—21no—
296C2×C4×C31—21no—
297C2×C4×C31—21no—
298C2×C4×C31—22no—
299C2×C4×C31—21no—
300C2×C4×C31—21no—
301C2×C4×C31—22no—
302C2×C4×C31—21no—
303C2×C4×C31—22no—
304C2×C4×C31—21no—
305C2×C4×C31—21no—
306C2×C4×C31—21no—
307C2×C4×C31—21no—
308C2×C4×C31—21no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—41no—
312C2×C4×C31—41no—
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—41no—
325C2×C4×C31—84no—
326C2×C4×C31—84no—
327C2×C4×C31—84no—
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—41no—
338C8×C31—41no—
339C8×C31—41no—
340C2×#480C2×C3111yescharacteristic, complemented
341C2×#459C2×C3111yescharacteristic, complemented
342#2428C2×C3111yescharacteristic, complemented
343#2361C2×C3111yescharacteristic, complemented
344#2086C2×C3111yescharacteristic, complemented
345#2041C2×C3111yescharacteristic, complemented
346#1999C2×C3111yescharacteristic, complemented
347#1999C2×C3111yescharacteristic, complemented
348#1970C2×C3111yescharacteristic, complemented
349#1925C2×C3111yescharacteristic, complemented
350#1923C2×C3111yescharacteristic, complemented
351#1879C2×C3111yescharacteristic, complemented
352#1874C2×C3111yescharacteristic, complemented
353#1862C2×C3111yescharacteristic, complemented
354C4×#102C2×C3111yescharacteristic, complemented
355C22×C31—22no—
356C22×C31—22no—
357C22×C31—22no—
358C22×C31—41no—
359C22×C31—41no—
360C22×C31—41no—
361C22×C31—41no—
362C22×C31—42no—
363C22×C31—42no—
364C22×C31—42no—
365C22×C31—42no—
366C22×C31—42no—
367C22×C31—42no—
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#54611yescharacteristic
386C22×C31C22×D811yescharacteristic
387C22×C31#57511yescharacteristic
388C22×C31#57611yescharacteristic
389C22×C31#57711yescharacteristic
390C4×C31—22no—
391C4×C31—22no—
392C4×C31—42no—
393C4×C31—41no—
394C4×C31—41no—
395C4×C31—42no—
396C4×C31—42no—
397C4×C31—41no—
398C4×C31—81no—
399C4×C31—81no—
400C4×C31#53211yescharacteristic
401C4×C31#54011yescharacteristic
402C4×C31#54611yescharacteristic
403C4×C31#55311yescharacteristic
404C22×D8C22×C3111yescharacteristic
405C22×D8C22×C3111yescharacteristic
406C2×#127C22×C3111yescharacteristic
407C2×#121—21no—
408C2×#121C22×C3111yescharacteristic
409C2×#121C22×C3111yescharacteristic
410C2×#121C22×C3111yescharacteristic
411C2×C4×D4—21no—
412C2×C4×D4C22×C3111yescharacteristic
413C2×C4×D4C22×C3111yescharacteristic
414C22×C4⋊C4C22×C3111yescharacteristic
415#480—24no—
416#459—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×C22⋊C8C22×C3111yescharacteristic
429C2×C22⋊C8C22×C3111yescharacteristic
430C2×C4×C8C22×C3111yescharacteristic
431#394—21no—
432#392—21no—
433#390C22×C3111yescharacteristic
434#390C22×C3111yescharacteristic
435#389C22×C3111yescharacteristic
436#389C22×C3111yescharacteristic
437#388—21no—
438#386—21no—
439#386—21no—
440#385—21no—
441C4×C4⋊C4C22×C3111yescharacteristic
442C4×C22⋊C4C22×C3111yescharacteristic
443#340C22×C3111yescharacteristic
444#340C22×C3111yescharacteristic
445#340C22×C3111yescharacteristic
446#340C22×C3111yescharacteristic
447#336C22×C3111yescharacteristic
448#336C22×C3111yescharacteristic
449C2×C31—42no—
450C2×C31—82no—
451C2×C31—82no—
452C2×C31—161no—
453C2×C31#246411yescharacteristic
454C2×C31#310011yescharacteristic
455C2×C31#311911yescharacteristic
456C2×C31#327511yescharacteristic
457C2×C31D4×D811yescharacteristic
458C2×C31#329411yescharacteristic
459C2×C31#330911yescharacteristic
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4C23×C3111yescharacteristic
466C22×D4C23×C3111yescharacteristic
467C22×D4C23×C3111yescharacteristic
468C23×C4—21no—
469C23×C4—21no—
470C23×C4—21no—
471C23×C4C23×C3111yescharacteristic
472C2×D8—22no—
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—41no—
477C2×D8—41no—
478C22×C8C23×C3111yescharacteristic
479C22×C8C23×C3111yescharacteristic
480C22×C8C23×C3111yescharacteristic
481C22×C8C23×C3111yescharacteristic
482#127—22no—
483#127—41no—
484#121—22no—
485#121—22no—
486#121—22no—
487#121—22no—
488#121—41no—
489#121—41no—
490#121—44no—
491C4×D4—22no—
492C4×D4—22no—
493C4×D4—41no—
494C4×D4—41no—
495C4×D4—44no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—41no—
501C2×C4⋊C4C23×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⋊C4D4×C3111yescharacteristic
516C2×C22⋊C4D4×C3111yescharacteristic
517C2×C42—21no—
518C2×C42C23×C3111yescharacteristic
519C2×C42C23×C3111yescharacteristic
520#107—22no—
521#107—22no—
522C4⋊C8—22no—
523#102—22no—
524#102—22no—
525#102—22no—
526#102—22no—
527#102—22no—
528#102—41no—
529#102—41no—
530#102D4×C3114yescomplemented
531C22⋊C8—22no—
532C22⋊C8—41no—
533C4×C8—41no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95D4×C3111yescharacteristic
538#95D4×C3111yescharacteristic
539C31#2692611yescharacteristic, direct product factor, Sylow
540C24—21no—
541C24—21no—
542C24—21no—
543C24C2×D4×C3111yescharacteristic
544C2×D4—24no—
545C2×D4—21no—
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—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4C2×D4×C3112yes—
576C2×D4#41×C3112yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—81no—
595C22×C4—81no—
596C22×C4—81no—
597C22×C4C2×D4×C3111yescharacteristic
598C22×C4C2×D4×C3111yescharacteristic
599C22×C4C2×D4×C3111yescharacteristic
600C22×C4C2×D4×C3111yescharacteristic
601C22×C4C2×D4×C3111yescharacteristic
602C22×C4C24×C3111yescharacteristic
603D8—44no—
604D8—44no—
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×C8—21no—
615C2×C8—21no—
616C2×C8C2×D4×C3112yes—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4C2×D4×C3112yes—
628C4⋊C4#41×C3112yes—
629C4⋊C4#41×C3112yes—
630C22⋊C4—24no—
631C22⋊C4—41no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4D8×C3114yescomplemented
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—42no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—22no—
653C23—22no—
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—
673C23C2×D8×C3112yes—
674C23C22×D4×C3111yescharacteristic
675D4—22no—
676D4—22no—
677D4—22no—
678D4—22no—
679D4—48no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—84no—
689D4—84no—
690D4—84no—
691D4—84no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
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—41no—
724C2×C4—84no—
725C2×C4—84no—
726C2×C4—84no—
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—41no—
737C8—41no—
738C8—41no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
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×#54611yescharacteristic
770C22C22×D8×C3111yescharacteristic
771C22C31×#57511yescharacteristic
772C22C31×#57611yescharacteristic
773C22C31×#57711yescharacteristic
774C4—22no—
775C4—22no—
776C4—42no—
777C4—41no—
778C4—41no—
779C4—42no—
780C4—42no—
781C4—41no—
782C4—81no—
783C4—81no—
784C4C31×#53211yescharacteristic
785C4C31×#54011yescharacteristic
786C4C31×#54611yescharacteristic
787C4C31×#55311yescharacteristic
788C2—42no—
789C2—82no—
790C2—82no—
791C2—161no—
792C2C31×#246411yescharacteristic
793C2C31×#310011yescharacteristic
794C2C31×#311911yescharacteristic
795C2C31×#327511yescharacteristic
796C2D4×D8×C3111yescharacteristic
797C2C31×#329411yescharacteristic
798C2C31×#330911yescharacteristic
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×#480C2semidirect
2. C2×C31×#459C2semidirect
3. C31×#2428C2semidirect
4. C31×#2361C2semidirect
5. C31×#2086C2semidirect
6. C31×#2041C2semidirect
7. C31×#1999C2semidirect
8. C31×#1999C2semidirect
9. C31×#1970C2semidirect
10. C31×#1925C2semidirect
11. C31×#1923C2semidirect
12. C31×#1879C2semidirect
13. C31×#1874C2semidirect
14. C31×#1862C2semidirect
15. C4×C31×#102C2semidirect
131. C31×#102D4semidirect
240. C22⋊C4×C31D8semidirect
246. #26926C31direct (N × H)
340. C2×#480C2×C31semidirect
341. C2×#459C2×C31semidirect
342. #2428C2×C31semidirect
343. #2361C2×C31semidirect
344. #2086C2×C31semidirect
345. #2041C2×C31semidirect
346. #1999C2×C31semidirect
347. #1999C2×C31semidirect
348. #1970C2×C31semidirect
349. #1925C2×C31semidirect
350. #1923C2×C31semidirect
351. #1879C2×C31semidirect
352. #1874C2×C31semidirect
353. #1862C2×C31semidirect
354. C4×#102C2×C31semidirect
530. #102D4×C31semidirect
539. C31#26926direct (N × H)
640. C22⋊C4D8×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4802
C2×C31×#4592
C31×#24282
C31×#23612
C31×#20862
C31×#20412
C31×#19992
C31×#19702
C31×#19252
C31×#19232
C31×#18792
C31×#18742
C31×#18622
C4×C31×#1022
#2692631