Finite Group Databasebeta

← C31×#25157 #21481916

Subgroups — C31×#25157 #21481916

Order 7936.

1100 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#464C211yesmaximal, characteristic, complemented
2C2×C31×#451C211yesmaximal, characteristic, complemented
3C2×C31×#448C211yesmaximal, characteristic
4C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
5C31×#2427C211yesmaximal, characteristic
6Q8×C22⋊C4×C31C211yesmaximal, characteristic, complemented
7C31×#2066C211yesmaximal, characteristic, complemented
8C31×#2035C211yesmaximal, characteristic, complemented
9C31×#2033C211yesmaximal, characteristic
10C31×#2015C211yesmaximal, characteristic, complemented
11C31×#1969C211yesmaximal, characteristic, complemented
12C31×#1923C211yesmaximal, characteristic, complemented
13C31×#1878C211yesmaximal, characteristic, complemented
14C31×#1877C211yesmaximal, characteristic, complemented
15C31×#1863C211yesmaximal, characteristic, complemented
16C23×Q8×C31C2211yescharacteristic
17C22×Q16×C31C2211yescharacteristic
18C22×Q16×C31C2211yescharacteristic
19C22×SD16×C31C2211yescharacteristic
20C22×SD16×C31C2211yescharacteristic
21C2×C31×#124C2211yescharacteristic
22C2×C31×C22⋊Q8C2211yescharacteristic
23C2×C31×#121C2211yescharacteristic
24C2×C4×Q8×C31C2211yescharacteristic
25C2×C4×Q8×C31C2211yescharacteristic
26C2×C4×D4×C31C2211yescharacteristic
27C31×#464—24no—
28C31×#451—24no—
29C31×#448—24no—
30C4×SD16×C31—24no—
31C2×C31×#107C2211yescharacteristic
32C2×C31×#106C2211yescharacteristic
33C2×C31×C4⋊C8C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×C22⋊C8C2211yescharacteristic
43C2×C31×C22⋊C8C2211yescharacteristic
44C2×C4×C8×C31C2211yescharacteristic
45C31×#397—21no—
46C31×#394—21no—
47C31×#391—21no—
48C31×#391—21no—
49C31×#391C2211yescharacteristic
50C31×#391C2211yescharacteristic
51C31×#391C2211yescharacteristic
52C31×#389C2211yescharacteristic
53C31×#386—21no—
54C31×#380—21no—
55C31×#380—21no—
56C31×#380C2211yescharacteristic
57C4×C22⋊C4×C31—21no—
58C4×C22⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31—22no—
64C22×Q8×C31—22no—
65C22×Q8×C31—21no—
66C22×Q8×C31—22no—
67C22×Q8×C31—22no—
68C22×Q8×C31—41no—
69C22×Q8×C31—41no—
70C22×Q8×C31C2311yescharacteristic
71C22×Q8×C31C2311yescharacteristic
72C22×Q8×C31C2311yescharacteristic
73C22×D4×C31—21no—
74C22×D4×C31C2311yescharacteristic
75C23×C4×C31—21no—
76C23×C4×C31—21no—
77C23×C4×C31C2311yescharacteristic
78C2×Q16×C31—22no—
79C2×Q16×C31—22no—
80C2×Q16×C31—22no—
81C2×Q16×C31—22no—
82C2×Q16×C31—22no—
83C2×Q16×C31—41no—
84C2×SD16×C31—22no—
85C2×SD16×C31—22no—
86C2×SD16×C31—22no—
87C2×SD16×C31—22no—
88C2×SD16×C31—41no—
89C2×SD16×C31D414yes—
90C22×C8×C31C2311yescharacteristic
91C22×C8×C31C2311yescharacteristic
92C22×C8×C31C2311yescharacteristic
93C22×C8×C31C2311yescharacteristic
94C31×#124—22no—
95C31×#124—41no—
96C31×C22⋊Q8—22no—
97C31×C22⋊Q8—41no—
98C31×#121—22no—
99C31×#121—41no—
100C4×Q8×C31—22no—
101C4×Q8×C31—22no—
102C4×Q8×C31—41no—
103C4×Q8×C31—41no—
104C4×D4×C31—22no—
105C4×D4×C31—41no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31C2311yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
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×C22⋊C4×C31D411yescharacteristic
121C2×C22⋊C4×C31D411yescharacteristic
122C2×C42×C31—21no—
123C2×C42×C31—21no—
124C2×C42×C31C2311yescharacteristic
125C2×C42×C31C2311yescharacteristic
126C31×#107—41no—
127C31×#106—22no—
128C31×C4⋊C8—22no—
129C31×#103—22no—
130C31×#103—22no—
131C31×#103—22no—
132C31×#103—22no—
133C31×#103—41no—
134C31×#103D414yescomplemented
135C31×#102—22no—
136C31×#102—22no—
137C31×C22⋊C8—22no—
138C31×C22⋊C8—22no—
139C4×C8×C31—22no—
140C31×#95—21no—
141C31×#95—21no—
142C31×#95—21no—
143C31×#95—21no—
144C31×#95—21no—
145C31×#95—21no—
146C31×#95—21no—
147C31×#95—21no—
148C31×#95D411yescharacteristic
149C31×#95D411yescharacteristic
150C24×C31—21no—
151C24×C31C2×D411yescharacteristic
152C2×Q8×C31—24no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×Q8×C31—21no—
156C2×Q8×C31—21no—
157C2×Q8×C31—21no—
158C2×Q8×C31—21no—
159C2×Q8×C31—21no—
160C2×Q8×C31—21no—
161C2×Q8×C31—21no—
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31—42no—
168C2×Q8×C31—42no—
169C2×Q8×C31—44no—
170C2×Q8×C31—44no—
171C2×Q8×C31—44no—
172C2×Q8×C31—44no—
173C2×Q8×C31C2×D412yes—
174C2×Q8×C31C2×D412yes—
175C2×Q8×C31#4112yes—
176C2×Q8×C31#4112yes—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—21no—
181C2×D4×C31—21no—
182C2×D4×C31—42no—
183C2×D4×C31—42no—
184C2×D4×C31—81no—
185C2×D4×C31C2×D412yes—
186C22×C4×C31—21no—
187C22×C4×C31—24no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—42no—
201C22×C4×C31—42no—
202C22×C4×C31—42no—
203C22×C4×C31—42no—
204C22×C4×C31—81no—
205C22×C4×C31C2×D411yescharacteristic
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31C2411yescharacteristic
211Q16×C31—44no—
212Q16×C31—44no—
213SD16×C31—28no—
214SD16×C31—44no—
215C2×C8×C31—21no—
216C2×C8×C31—21no—
217C2×C8×C31—21no—
218C2×C8×C31—21no—
219C2×C8×C31—21no—
220C2×C8×C31—21no—
221C2×C8×C31—21no—
222C2×C8×C31—21no—
223C2×C8×C31—21no—
224C2×C8×C31—21no—
225C2×C8×C31C2×D412yes—
226C2×C8×C31C2×D412yes—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31—21no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—21no—
233C4⋊C4×C31—21no—
234C4⋊C4×C31—42no—
235C4⋊C4×C31—42no—
236C4⋊C4×C31—42no—
237C4⋊C4×C31—81no—
238C4⋊C4×C31C2×D412yes—
239C22⋊C4×C31—22no—
240C22⋊C4×C31—22no—
241C22⋊C4×C31—42no—
242C22⋊C4×C31—42no—
243C22⋊C4×C31—42no—
244C22⋊C4×C31—42no—
245C22⋊C4×C31—42no—
246C22⋊C4×C31—42no—
247C42×C31—21no—
248C42×C31—21no—
249C42×C31—21no—
250C42×C31—21no—
251C42×C31—42no—
252C42×C31—42no—
253#25157C3111yesmaximal, characteristic, direct product factor, Sylow
254C23×C31—21no—
255C23×C31—21no—
256C23×C31—21no—
257C23×C31—21no—
258C23×C31—21no—
259C23×C31—21no—
260C23×C31—22no—
261C23×C31—41no—
262C23×C31—41no—
263C23×C31—41no—
264C23×C31—41no—
265C23×C31—41no—
266C23×C31—41no—
267C23×C31#13512yes—
268C23×C31C22×D411yescharacteristic
269Q8×C31—22no—
270Q8×C31—22no—
271Q8×C31—22no—
272Q8×C31—22no—
273Q8×C31—22no—
274Q8×C31—48no—
275Q8×C31—41no—
276Q8×C31—41no—
277Q8×C31—41no—
278Q8×C31—41no—
279Q8×C31—41no—
280Q8×C31—41no—
281Q8×C31#12114yes—
282D4×C31—22no—
283D4×C31—22no—
284D4×C31—41no—
285D4×C31—41no—
286D4×C31—84no—
287C2×C4×C31—22no—
288C2×C4×C31—21no—
289C2×C4×C31—22no—
290C2×C4×C31—22no—
291C2×C4×C31—21no—
292C2×C4×C31—22no—
293C2×C4×C31—21no—
294C2×C4×C31—21no—
295C2×C4×C31—21no—
296C2×C4×C31—21no—
297C2×C4×C31—22no—
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—48no—
307C2×C4×C31—41no—
308C2×C4×C31—41no—
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—41no—
326C2×C4×C31—41no—
327C2×C4×C31—84no—
328C2×C4×C31#13712yes—
329C2×C4×C31C22×D411yescharacteristic
330C2×C4×C31C22×D411yescharacteristic
331C2×C4×C31C2×#4111yescharacteristic
332C2×C4×C31C2×#4111yescharacteristic
333C2×C4×C31H(5,𝔽2)11yescharacteristic
334C2×C4×C31H(5,𝔽2)11yescharacteristic
335C8×C31—22no—
336C8×C31—22no—
337C8×C31—41no—
338C8×C31—41no—
339C2×#464C2×C3111yescharacteristic, complemented
340C2×#451C2×C3111yescharacteristic, complemented
341C2×#448C2×C3111yescharacteristic
342C2×C4×SD16C2×C3111yescharacteristic, complemented
343#2427C2×C3111yescharacteristic
344Q8×C22⋊C4C2×C3111yescharacteristic, complemented
345#2066C2×C3111yescharacteristic, complemented
346#2035C2×C3111yescharacteristic, complemented
347#2033C2×C3111yescharacteristic
348#2015C2×C3111yescharacteristic, complemented
349#1969C2×C3111yescharacteristic, complemented
350#1923C2×C3111yescharacteristic, complemented
351#1878C2×C3111yescharacteristic, complemented
352#1877C2×C3111yescharacteristic, complemented
353#1863C2×C3111yescharacteristic, complemented
354C22×C31—22no—
355C22×C31—22no—
356C22×C31—22no—
357C22×C31—41no—
358C22×C31—41no—
359C22×C31—41no—
360C22×C31—41no—
361C22×C31—42no—
362C22×C31—42no—
363C22×C31—42no—
364C22×C31—81no—
365C22×C31—81no—
366C22×C31—81no—
367C22×C31—81no—
368C22×C31#52511yescharacteristic
369C22×C31D4211yescharacteristic
370C22×C31D4211yescharacteristic
371C22×C31C2×#13511yescharacteristic
372C22×C31C2×#13711yescharacteristic
373C22×C31#57711yescharacteristic
374C22×C31#57811yescharacteristic
375C4×C31—24no—
376C4×C31—22no—
377C4×C31—41no—
378C4×C31—42no—
379C4×C31—42no—
380C4×C31—41no—
381C4×C31—41no—
382C4×C31—41no—
383C4×C31—81no—
384C4×C31—81no—
385C4×C31—81no—
386C4×C31—81no—
387C4×C31C2×#12111yescharacteristic
388C4×C31#53811yescharacteristic
389C4×C31#54611yescharacteristic
390C4×C31#54611yescharacteristic
391C23×Q8C22×C3111yescharacteristic
392C22×Q16C22×C3111yescharacteristic
393C22×Q16C22×C3111yescharacteristic
394C22×SD16C22×C3111yescharacteristic
395C22×SD16C22×C3111yescharacteristic
396C2×#124C22×C3111yescharacteristic
397C2×C22⋊Q8C22×C3111yescharacteristic
398C2×#121C22×C3111yescharacteristic
399C2×C4×Q8C22×C3111yescharacteristic
400C2×C4×Q8C22×C3111yescharacteristic
401C2×C4×D4C22×C3111yescharacteristic
402#464—24no—
403#451—24no—
404#448—24no—
405C4×SD16—24no—
406C2×#107C22×C3111yescharacteristic
407C2×#106C22×C3111yescharacteristic
408C2×C4⋊C8C22×C3111yescharacteristic
409C2×#103C22×C3111yescharacteristic
410C2×#103C22×C3111yescharacteristic
411C2×#103C22×C3111yescharacteristic
412C2×#103C22×C3111yescharacteristic
413C2×#103C22×C3111yescharacteristic
414C2×#103C22×C3111yescharacteristic
415C2×#102C22×C3111yescharacteristic
416C2×#102C22×C3111yescharacteristic
417C2×C22⋊C8C22×C3111yescharacteristic
418C2×C22⋊C8C22×C3111yescharacteristic
419C2×C4×C8C22×C3111yescharacteristic
420#397—21no—
421#394—21no—
422#391—21no—
423#391—21no—
424#391C22×C3111yescharacteristic
425#391C22×C3111yescharacteristic
426#391C22×C3111yescharacteristic
427#389C22×C3111yescharacteristic
428#386—21no—
429#380—21no—
430#380—21no—
431#380C22×C3111yescharacteristic
432C4×C22⋊C4—21no—
433C4×C22⋊C4C22×C3111yescharacteristic
434#340C22×C3111yescharacteristic
435#340C22×C3111yescharacteristic
436#336C22×C3111yescharacteristic
437#336C22×C3111yescharacteristic
438C2×C31—42no—
439C2×C31—82no—
440C2×C31#242411yescharacteristic
441C2×C31#310811yescharacteristic
442C2×C31#312111yescharacteristic
443C2×C31#326611yescharacteristic
444C2×C31#327611yescharacteristic
445C2×C31#328211yescharacteristic
446C2×C31#328511yescharacteristic
447C22×Q8—22no—
448C22×Q8—22no—
449C22×Q8—21no—
450C22×Q8—22no—
451C22×Q8—22no—
452C22×Q8—41no—
453C22×Q8—41no—
454C22×Q8C23×C3111yescharacteristic
455C22×Q8C23×C3111yescharacteristic
456C22×Q8C23×C3111yescharacteristic
457C22×D4—21no—
458C22×D4C23×C3111yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4C23×C3111yescharacteristic
462C2×Q16—22no—
463C2×Q16—22no—
464C2×Q16—22no—
465C2×Q16—22no—
466C2×Q16—22no—
467C2×Q16—41no—
468C2×SD16—22no—
469C2×SD16—22no—
470C2×SD16—22no—
471C2×SD16—22no—
472C2×SD16—41no—
473C2×SD16D4×C3114yes—
474C22×C8C23×C3111yescharacteristic
475C22×C8C23×C3111yescharacteristic
476C22×C8C23×C3111yescharacteristic
477C22×C8C23×C3111yescharacteristic
478#124—22no—
479#124—41no—
480C22⋊Q8—22no—
481C22⋊Q8—41no—
482#121—22no—
483#121—41no—
484C4×Q8—22no—
485C4×Q8—22no—
486C4×Q8—41no—
487C4×Q8—41no—
488C4×D4—22no—
489C4×D4—41no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4C23×C3111yescharacteristic
495C2×C4⋊C4C23×C3111yescharacteristic
496C2×C4⋊C4C23×C3111yescharacteristic
497C2×C4⋊C4C23×C3111yescharacteristic
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4D4×C3111yescharacteristic
505C2×C22⋊C4D4×C3111yescharacteristic
506C2×C42—21no—
507C2×C42—21no—
508C2×C42C23×C3111yescharacteristic
509C2×C42C23×C3111yescharacteristic
510#107—41no—
511#106—22no—
512C4⋊C8—22no—
513#103—22no—
514#103—22no—
515#103—22no—
516#103—22no—
517#103—41no—
518#103D4×C3114yescomplemented
519#102—22no—
520#102—22no—
521C22⋊C8—22no—
522C22⋊C8—22no—
523C4×C8—22no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95D4×C3111yescharacteristic
533#95D4×C3111yescharacteristic
534C31#2515711yescharacteristic, direct product factor, Sylow
535C24—21no—
536C24C2×D4×C3111yescharacteristic
537C2×Q8—24no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—42no—
553C2×Q8—42no—
554C2×Q8—44no—
555C2×Q8—44no—
556C2×Q8—44no—
557C2×Q8—44no—
558C2×Q8C2×D4×C3112yes—
559C2×Q8C2×D4×C3112yes—
560C2×Q8#41×C3112yes—
561C2×Q8#41×C3112yes—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—81no—
570C2×D4C2×D4×C3112yes—
571C22×C4—21no—
572C22×C4—24no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
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—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—81no—
590C22×C4C2×D4×C3111yescharacteristic
591C22×C4C2×D4×C3111yescharacteristic
592C22×C4C2×D4×C3111yescharacteristic
593C22×C4C2×D4×C3111yescharacteristic
594C22×C4C2×D4×C3111yescharacteristic
595C22×C4C24×C3111yescharacteristic
596Q16—44no—
597Q16—44no—
598SD16—28no—
599SD16—44no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8C2×D4×C3112yes—
611C2×C8C2×D4×C3112yes—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—81no—
623C4⋊C4C2×D4×C3112yes—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—42no—
637C42—42no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—22no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23C31×#13512yes—
652C23C22×D4×C3111yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—22no—
657Q8—22no—
658Q8—48no—
659Q8—41no—
660Q8—41no—
661Q8—41no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8C31×#12114yes—
666D4—22no—
667D4—22no—
668D4—41no—
669D4—41no—
670D4—84no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—48no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—84no—
712C2×C4C31×#13712yes—
713C2×C4C22×D4×C3111yescharacteristic
714C2×C4C22×D4×C3111yescharacteristic
715C2×C4C2×#41×C3111yescharacteristic
716C2×C4C2×#41×C3111yescharacteristic
717C2×C4C31×H(5,𝔽2)11yescharacteristic
718C2×C4C31×H(5,𝔽2)11yescharacteristic
719C8—22no—
720C8—22no—
721C8—41no—
722C8—41no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22C31×#52511yescharacteristic
738C22D42×C3111yescharacteristic
739C22D42×C3111yescharacteristic
740C22C2×C31×#13511yescharacteristic
741C22C2×C31×#13711yescharacteristic
742C22C31×#57711yescharacteristic
743C22C31×#57811yescharacteristic
744C4—24no—
745C4—22no—
746C4—41no—
747C4—42no—
748C4—42no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—81no—
753C4—81no—
754C4—81no—
755C4—81no—
756C4C2×C31×#12111yescharacteristic
757C4C31×#53811yescharacteristic
758C4C31×#54611yescharacteristic
759C4C31×#54611yescharacteristic
760C2—42no—
761C2—82no—
762C2C31×#242411yescharacteristic
763C2C31×#310811yescharacteristic
764C2C31×#312111yescharacteristic
765C2C31×#326611yescharacteristic
766C2C31×#327611yescharacteristic
767C2C31×#328211yescharacteristic
768C2C31×#328511yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
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×#464C2semidirect
2. C2×C31×#451C2semidirect
4. C2×C4×SD16×C31C2semidirect
6. Q8×C22⋊C4×C31C2semidirect
7. C31×#2066C2semidirect
8. C31×#2035C2semidirect
10. C31×#2015C2semidirect
11. C31×#1969C2semidirect
12. C31×#1923C2semidirect
13. C31×#1878C2semidirect
14. C31×#1877C2semidirect
15. C31×#1863C2semidirect
134. C31×#103D4semidirect
253. #25157C31direct (N × H)
339. C2×#464C2×C31semidirect
340. C2×#451C2×C31semidirect
342. C2×C4×SD16C2×C31semidirect
344. Q8×C22⋊C4C2×C31semidirect
345. #2066C2×C31semidirect
346. #2035C2×C31semidirect
348. #2015C2×C31semidirect
349. #1969C2×C31semidirect
350. #1923C2×C31semidirect
351. #1878C2×C31semidirect
352. #1877C2×C31semidirect
353. #1863C2×C31semidirect
518. #103D4×C31semidirect
534. C31#25157direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4642
C2×C31×#4512
C2×C31×#4482
C2×C4×SD16×C312
C31×#24272
Q8×C22⋊C4×C312
C31×#20662
C31×#20352
C31×#20332
C31×#20152
C31×#19692
C31×#19232
C31×#18782
C31×#18772
C31×#18632
#2515731