Finite Group Databasebeta

← C31×#23022 #21479781

Subgroups — C31×#23022 #21479781

Order 7936.

1066 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#465C211yesmaximal, characteristic
2C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
3C22×C31×#106C211yesmaximal, characteristic, complemented
4C31×#2361C211yesmaximal, characteristic
5C31×#2360C211yesmaximal, characteristic, complemented
6C31×#1968C211yesmaximal, characteristic, complemented
7C31×#1941C211yesmaximal, characteristic, complemented
8C31×#1927C211yesmaximal, characteristic, complemented
9C31×#1926C211yesmaximal, characteristic, complemented
10C31×#1874C211yesmaximal, characteristic
11C31×#1872C211yesmaximal, characteristic, complemented
12C31×#1865C211yesmaximal, characteristic, complemented
13C31×#1864C211yesmaximal, characteristic, complemented
14C4×C31×#106C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C31C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C23×C8×C31C2211yescharacteristic
18C2×C31×C22⋊Q8C2211yescharacteristic
19C2×C31×#121C2211yescharacteristic
20C2×C4×Q8×C31C2211yescharacteristic
21C2×C4×D4×C31—21no—
22C2×C4×D4×C31C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2211yescharacteristic
25C31×#465C418yescomplemented
26C4×SD16×C31—24no—
27C2×C31×#106—24no—
28C2×C31×#106C2211yescharacteristic
29C2×C31×#106C2211yescharacteristic
30C2×C31×#106C2211yescharacteristic
31C2×C31×#106C2211yescharacteristic
32C2×C31×#106C2211yescharacteristic
33C2×C31×#103C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×C22⋊C8C2211yescharacteristic
40C2×C4×C8×C31C2211yescharacteristic
41C2×C4×C8×C31C2211yescharacteristic
42C31×#391C2211yescharacteristic
43C31×#390C2211yescharacteristic
44C31×#389—21no—
45C31×#389C2211yescharacteristic
46C31×#389C2211yescharacteristic
47C31×#388—21no—
48C31×#387—21no—
49C31×#386—21no—
50C31×#385—21no—
51C31×#385—21no—
52C4×C4⋊C4×C31C2211yescharacteristic
53C4×C4⋊C4×C31C2211yescharacteristic
54C4×C22⋊C4×C31—21no—
55C4×C22⋊C4×C31C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C22×Q8×C31C2311yescharacteristic
63C22×D4×C31—21no—
64C22×D4×C31C2311yescharacteristic
65C23×C4×C31—21no—
66C23×C4×C31—21no—
67C23×C4×C31—21no—
68C23×C4×C31C2311yescharacteristic
69C2×SD16×C31—22no—
70C2×SD16×C31—22no—
71C2×SD16×C31C2×C414yescomplemented
72C22×C8×C31—22no—
73C22×C8×C31—22no—
74C22×C8×C31C2×C414yescomplemented
75C22×C8×C31C2311yescharacteristic
76C22×C8×C31C2311yescharacteristic
77C22×C8×C31C2311yescharacteristic
78C22×C8×C31C2311yescharacteristic
79C31×C22⋊Q8—22no—
80C31×C22⋊Q8C2×C414yescomplemented
81C31×#121—22no—
82C31×#121C2×C414yes—
83C4×Q8×C31—22no—
84C4×Q8×C31—41no—
85C4×D4×C31—22no—
86C4×D4×C31—41no—
87C4×D4×C31—44no—
88C2×C4⋊C4×C31—21no—
89C2×C4⋊C4×C31—22no—
90C2×C4⋊C4×C31—22no—
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—41no—
97C2×C4⋊C4×C31—41no—
98C2×C4⋊C4×C31C2311yescharacteristic
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×C31D411yescharacteristic
110C2×C22⋊C4×C31D411yescharacteristic
111C2×C42×C31—21no—
112C2×C42×C31—21no—
113C2×C42×C31—21no—
114C2×C42×C31C2311yescharacteristic
115C2×C42×C31C2311yescharacteristic
116C31×#106—22no—
117C31×#106—22no—
118C31×#106—22no—
119C31×#106C2×C414yescomplemented
120C31×#106D414yescomplemented
121C31×#103—22no—
122C31×#103—41no—
123C31×#103C2×C414yescomplemented
124C31×#102—22no—
125C31×#102—41no—
126C31×#102C2×C414yescomplemented
127C31×C22⋊C8—22no—
128C4×C8×C31—22no—
129C4×C8×C31—22no—
130C31×#95—21no—
131C31×#95—21no—
132C31×#95—21no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95D411yescharacteristic
137C31×#95D411yescharacteristic
138C24×C31—21no—
139C24×C31C2×D411yescharacteristic
140C2×Q8×C31—21no—
141C2×Q8×C31—21no—
142C2×Q8×C31—21no—
143C2×Q8×C31—21no—
144C2×Q8×C31—21no—
145C2×Q8×C31C22×C412yes—
146C2×D4×C31—24no—
147C2×D4×C31—21no—
148C2×D4×C31—21no—
149C2×D4×C31—21no—
150C2×D4×C31—21no—
151C2×D4×C31—21no—
152C2×D4×C31—42no—
153C2×D4×C31—42no—
154C2×D4×C31C22×C412yes—
155C22×C4×C31—21no—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—42no—
167C22×C4×C31—42no—
168C22×C4×C31—42no—
169C22×C4×C31—42no—
170C22×C4×C31—42no—
171C22×C4×C31—42no—
172C22×C4×C31—81no—
173C22×C4×C31—81no—
174C22×C4×C31—81no—
175C22×C4×C31C22×C412yes—
176C22×C4×C31C2×D411yescharacteristic
177C22×C4×C31C2×D411yescharacteristic
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2×D411yescharacteristic
181C22×C4×C31#4112yes—
182C22×C4×C31C2411yescharacteristic
183SD16×C31—28no—
184C2×C8×C31—21no—
185C2×C8×C31—21no—
186C2×C8×C31—28no—
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×C31C22×C412yes—
194C2×C8×C31C22×C412yes—
195C2×C8×C31C2×D412yes—
196C2×C8×C31#4112yes—
197C4⋊C4×C31—24no—
198C4⋊C4×C31—21no—
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—42no—
207C4⋊C4×C31—42no—
208C4⋊C4×C31—42no—
209C4⋊C4×C31—42no—
210C4⋊C4×C31—81no—
211C4⋊C4×C31C22×C412yes—
212C4⋊C4×C31C22×C412yes—
213C4⋊C4×C31C2×D412yes—
214C4⋊C4×C31C2×D412yes—
215C22⋊C4×C31—24no—
216C22⋊C4×C31—22no—
217C22⋊C4×C31—24no—
218C22⋊C4×C31—42no—
219C22⋊C4×C31—42no—
220C22⋊C4×C31—81no—
221C22⋊C4×C31SD1614yescomplemented
222C42×C31—21no—
223C42×C31—21no—
224C42×C31—21no—
225C42×C31—21no—
226C42×C31—42no—
227C42×C31—42no—
228C42×C31—81no—
229#23022C3111yesmaximal, characteristic, direct product factor, Sylow
230C23×C31—21no—
231C23×C31—21no—
232C23×C31—21no—
233C23×C31—21no—
234C23×C31—22no—
235C23×C31—41no—
236C23×C31—41no—
237C23×C31—41no—
238C23×C31—41no—
239C23×C31—41no—
240C23×C31—41no—
241C23×C31C4×D412yes—
242C23×C31C2×SD1612yes—
243C23×C31#13512yes—
244C23×C31C22×D411yescharacteristic
245Q8×C31—22no—
246Q8×C31—22no—
247Q8×C31—41no—
248Q8×C31—41no—
249D4×C31—22no—
250D4×C31—22no—
251D4×C31—48no—
252D4×C31—41no—
253D4×C31—41no—
254C2×C4×C31—21no—
255C2×C4×C31—21no—
256C2×C4×C31—21no—
257C2×C4×C31—21no—
258C2×C4×C31—21no—
259C2×C4×C31—21no—
260C2×C4×C31—22no—
261C2×C4×C31—22no—
262C2×C4×C31—22no—
263C2×C4×C31—22no—
264C2×C4×C31—22no—
265C2×C4×C31—22no—
266C2×C4×C31—22no—
267C2×C4×C31—21no—
268C2×C4×C31—22no—
269C2×C4×C31—22no—
270C2×C4×C31—21no—
271C2×C4×C31—21no—
272C2×C4×C31—21no—
273C2×C4×C31—21no—
274C2×C4×C31—21no—
275C2×C4×C31—41no—
276C2×C4×C31—41no—
277C2×C4×C31—41no—
278C2×C4×C31—41no—
279C2×C4×C31—41no—
280C2×C4×C31—41no—
281C2×C4×C31—41no—
282C2×C4×C31—41no—
283C2×C4×C31—41no—
284C2×C4×C31—41no—
285C2×C4×C31—41no—
286C2×C4×C31—41no—
287C2×C4×C31—41no—
288C2×C4×C31—41no—
289C2×C4×C31—41no—
290C2×C4×C31—41no—
291C2×C4×C31—84no—
292C2×C4×C31—84no—
293C2×C4×C31—84no—
294C2×C4×C31C4×D412yes—
295C2×C4×C31C2×SD1612yes—
296C2×C4×C31C2×SD1612yes—
297C2×C4×C31C23×C411yescharacteristic
298C2×C4×C31C22×D411yescharacteristic
299C2×C4×C31C2×#4111yescharacteristic
300C2×C4×C31C2×#4111yescharacteristic
301C2×C4×C31H(5,𝔽2)11yescharacteristic
302C2×C4×C312−1+411yescharacteristic
303C8×C31—22no—
304C8×C31—41no—
305C8×C31—41no—
306C8×C31C4×D414yescomplemented
307C2×#465C2×C3111yescharacteristic
308C2×C4×SD16C2×C3111yescharacteristic, complemented
309C22×#106C2×C3111yescharacteristic, complemented
310#2361C2×C3111yescharacteristic
311#2360C2×C3111yescharacteristic, complemented
312#1968C2×C3111yescharacteristic, complemented
313#1941C2×C3111yescharacteristic, complemented
314#1927C2×C3111yescharacteristic, complemented
315#1926C2×C3111yescharacteristic, complemented
316#1874C2×C3111yescharacteristic
317#1872C2×C3111yescharacteristic, complemented
318#1865C2×C3111yescharacteristic, complemented
319#1864C2×C3111yescharacteristic, complemented
320C4×#106C2×C3111yescharacteristic, complemented
321C8×C22⋊C4C2×C3111yescharacteristic, complemented
322C22×C31—22no—
323C22×C31—22no—
324C22×C31—22no—
325C22×C31—22no—
326C22×C31—22no—
327C22×C31—22no—
328C22×C31—42no—
329C22×C31—42no—
330C22×C31—42no—
331C22×C31—81no—
332C22×C31—81no—
333C22×C31—81no—
334C22×C31—81no—
335C22×C31C4×SD1614yescomplemented
336C22×C31C2×C4×D411yescharacteristic
337C22×C31D4211yescharacteristic
338C22×C31#54711yescharacteristic
339C22×C31C22×SD1611yescharacteristic
340C22×C31C2×#13511yescharacteristic
341C22×C31#57711yescharacteristic
342C22×C31#57711yescharacteristic
343C4×C31—22no—
344C4×C31—22no—
345C4×C31—22no—
346C4×C31—41no—
347C4×C31—42no—
348C4×C31—42no—
349C4×C31—42no—
350C4×C31—42no—
351C4×C31—41no—
352C4×C31—42no—
353C4×C31—81no—
354C4×C31—81no—
355C4×C31C2×C4×D411yescharacteristic
356C4×C31#52011yescharacteristic
357C4×C31#54811yescharacteristic
358C4×C31#55311yescharacteristic
359C22×SD16C22×C3111yescharacteristic
360C23×C8C22×C3111yescharacteristic
361C2×C22⋊Q8C22×C3111yescharacteristic
362C2×#121C22×C3111yescharacteristic
363C2×C4×Q8C22×C3111yescharacteristic
364C2×C4×D4—21no—
365C2×C4×D4C22×C3111yescharacteristic
366C22×C4⋊C4C22×C3111yescharacteristic
367C22×C4⋊C4C22×C3111yescharacteristic
368#465C4×C3118yescomplemented
369C4×SD16—24no—
370C2×#106—24no—
371C2×#106C22×C3111yescharacteristic
372C2×#106C22×C3111yescharacteristic
373C2×#106C22×C3111yescharacteristic
374C2×#106C22×C3111yescharacteristic
375C2×#106C22×C3111yescharacteristic
376C2×#103C22×C3111yescharacteristic
377C2×#103C22×C3111yescharacteristic
378C2×#103C22×C3111yescharacteristic
379C2×#102C22×C3111yescharacteristic
380C2×#102C22×C3111yescharacteristic
381C2×#102C22×C3111yescharacteristic
382C2×C22⋊C8C22×C3111yescharacteristic
383C2×C4×C8C22×C3111yescharacteristic
384C2×C4×C8C22×C3111yescharacteristic
385#391C22×C3111yescharacteristic
386#390C22×C3111yescharacteristic
387#389—21no—
388#389C22×C3111yescharacteristic
389#389C22×C3111yescharacteristic
390#388—21no—
391#387—21no—
392#386—21no—
393#385—21no—
394#385—21no—
395C4×C4⋊C4C22×C3111yescharacteristic
396C4×C4⋊C4C22×C3111yescharacteristic
397C4×C22⋊C4—21no—
398C4×C22⋊C4C22×C3111yescharacteristic
399#340C22×C3111yescharacteristic
400#340C22×C3111yescharacteristic
401#340C22×C3111yescharacteristic
402#340C22×C3111yescharacteristic
403#336C22×C3111yescharacteristic
404#336C22×C3111yescharacteristic
405C2×C31—24no—
406C2×C31—82no—
407C2×C31#236111yescharacteristic
408C2×C31C2×C4×SD1611yescharacteristic
409C2×C31#295211yescharacteristic
410C2×C31D4×SD1611yescharacteristic
411C2×C31#328211yescharacteristic
412C2×C31#333511yescharacteristic
413C2×C31#333711yescharacteristic
414C22×Q8C23×C3111yescharacteristic
415C22×D4—21no—
416C22×D4C23×C3111yescharacteristic
417C23×C4—21no—
418C23×C4—21no—
419C23×C4—21no—
420C23×C4C23×C3111yescharacteristic
421C2×SD16—22no—
422C2×SD16—22no—
423C2×SD16C2×C4×C3114yescomplemented
424C22×C8—22no—
425C22×C8—22no—
426C22×C8C2×C4×C3114yescomplemented
427C22×C8C23×C3111yescharacteristic
428C22×C8C23×C3111yescharacteristic
429C22×C8C23×C3111yescharacteristic
430C22×C8C23×C3111yescharacteristic
431C22⋊Q8—22no—
432C22⋊Q8C2×C4×C3114yescomplemented
433#121—22no—
434#121C2×C4×C3114yes—
435C4×Q8—22no—
436C4×Q8—41no—
437C4×D4—22no—
438C4×D4—41no—
439C4×D4—44no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—41no—
449C2×C4⋊C4—41no—
450C2×C4⋊C4C23×C3111yescharacteristic
451C2×C4⋊C4C23×C3111yescharacteristic
452C2×C4⋊C4C23×C3111yescharacteristic
453C2×C4⋊C4C23×C3111yescharacteristic
454C2×C4⋊C4C23×C3111yescharacteristic
455C2×C4⋊C4C23×C3111yescharacteristic
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4D4×C3111yescharacteristic
462C2×C22⋊C4D4×C3111yescharacteristic
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42C23×C3111yescharacteristic
467C2×C42C23×C3111yescharacteristic
468#106—22no—
469#106—22no—
470#106—22no—
471#106C2×C4×C3114yescomplemented
472#106D4×C3114yescomplemented
473#103—22no—
474#103—41no—
475#103C2×C4×C3114yescomplemented
476#102—22no—
477#102—41no—
478#102C2×C4×C3114yescomplemented
479C22⋊C8—22no—
480C4×C8—22no—
481C4×C8—22no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95D4×C3111yescharacteristic
489#95D4×C3111yescharacteristic
490C31#2302211yescharacteristic, direct product factor, Sylow
491C24—21no—
492C24C2×D4×C3111yescharacteristic
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8C22×C4×C3112yes—
499C2×D4—24no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4C22×C4×C3112yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—81no—
526C22×C4—81no—
527C22×C4—81no—
528C22×C4C22×C4×C3112yes—
529C22×C4C2×D4×C3111yescharacteristic
530C22×C4C2×D4×C3111yescharacteristic
531C22×C4C2×D4×C3111yescharacteristic
532C22×C4C2×D4×C3111yescharacteristic
533C22×C4C2×D4×C3111yescharacteristic
534C22×C4#41×C3112yes—
535C22×C4C24×C3111yescharacteristic
536SD16—28no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—28no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8C22×C4×C3112yes—
547C2×C8C22×C4×C3112yes—
548C2×C8C2×D4×C3112yes—
549C2×C8#41×C3112yes—
550C4⋊C4—24no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—81no—
564C4⋊C4C22×C4×C3112yes—
565C4⋊C4C22×C4×C3112yes—
566C4⋊C4C2×D4×C3112yes—
567C4⋊C4C2×D4×C3112yes—
568C22⋊C4—24no—
569C22⋊C4—22no—
570C22⋊C4—24no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—81no—
574C22⋊C4SD16×C3114yescomplemented
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—42no—
580C42—42no—
581C42—81no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—22no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23C4×D4×C3112yes—
594C23C2×SD16×C3112yes—
595C23C31×#13512yes—
596C23C22×D4×C3111yescharacteristic
597Q8—22no—
598Q8—22no—
599Q8—41no—
600Q8—41no—
601D4—22no—
602D4—22no—
603D4—48no—
604D4—41no—
605D4—41no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—84no—
644C2×C4—84no—
645C2×C4—84no—
646C2×C4C4×D4×C3112yes—
647C2×C4C2×SD16×C3112yes—
648C2×C4C2×SD16×C3112yes—
649C2×C4C23×C4×C3111yescharacteristic
650C2×C4C22×D4×C3111yescharacteristic
651C2×C4C2×#41×C3111yescharacteristic
652C2×C4C2×#41×C3111yescharacteristic
653C2×C4C31×H(5,𝔽2)11yescharacteristic
654C2×C4C31×2−1+411yescharacteristic
655C8—22no—
656C8—41no—
657C8—41no—
658C8C4×D4×C3114yescomplemented
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22C4×SD16×C3114yescomplemented
673C22C2×C4×D4×C3111yescharacteristic
674C22D42×C3111yescharacteristic
675C22C31×#54711yescharacteristic
676C22C22×SD16×C3111yescharacteristic
677C22C2×C31×#13511yescharacteristic
678C22C31×#57711yescharacteristic
679C22C31×#57711yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—41no—
684C4—42no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—41no—
689C4—42no—
690C4—81no—
691C4—81no—
692C4C2×C4×D4×C3111yescharacteristic
693C4C31×#52011yescharacteristic
694C4C31×#54811yescharacteristic
695C4C31×#55311yescharacteristic
696C2—24no—
697C2—82no—
698C2C31×#236111yescharacteristic
699C2C2×C4×SD16×C3111yescharacteristic
700C2C31×#295211yescharacteristic
701C2D4×SD16×C3111yescharacteristic
702C2C31×#328211yescharacteristic
703C2C31×#333511yescharacteristic
704C2C31×#333711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
LCSG ▷ C2×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
2. C2×C4×SD16×C31C2semidirect
3. C22×C31×#106C2semidirect
5. C31×#2360C2semidirect
6. C31×#1968C2semidirect
7. C31×#1941C2semidirect
8. C31×#1927C2semidirect
9. C31×#1926C2semidirect
11. C31×#1872C2semidirect
12. C31×#1865C2semidirect
13. C31×#1864C2semidirect
14. C4×C31×#106C2semidirect
15. C8×C22⋊C4×C31C2semidirect
25. C31×#465C4semidirect
71. C2×SD16×C31C2×C4semidirect
74. C22×C8×C31C2×C4semidirect
80. C31×C22⋊Q8C2×C4semidirect
119. C31×#106C2×C4semidirect
120. C31×#106D4semidirect
123. C31×#103C2×C4semidirect
126. C31×#102C2×C4semidirect
221. C22⋊C4×C31SD16semidirect
229. #23022C31direct (N × H)
306. C8×C31C4×D4semidirect
308. C2×C4×SD16C2×C31semidirect
309. C22×#106C2×C31semidirect
311. #2360C2×C31semidirect
312. #1968C2×C31semidirect
313. #1941C2×C31semidirect
314. #1927C2×C31semidirect
315. #1926C2×C31semidirect
317. #1872C2×C31semidirect
318. #1865C2×C31semidirect
319. #1864C2×C31semidirect
320. C4×#106C2×C31semidirect
321. C8×C22⋊C4C2×C31semidirect
335. C22×C31C4×SD16semidirect
368. #465C4×C31semidirect
423. C2×SD16C2×C4×C31semidirect
426. C22×C8C2×C4×C31semidirect
432. C22⋊Q8C2×C4×C31semidirect
471. #106C2×C4×C31semidirect
472. #106D4×C31semidirect
475. #103C2×C4×C31semidirect
478. #102C2×C4×C31semidirect
490. C31#23022direct (N × H)
574. C22⋊C4SD16×C31semidirect
658. C8C4×D4×C31semidirect
672. C22C4×SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4652
C2×C4×SD16×C312
C22×C31×#1062
C31×#23612
C31×#23602
C31×#19682
C31×#19412
C31×#19272
C31×#19262
C31×#18742
C31×#18722
C31×#18652
C31×#18642
C4×C31×#1062
C8×C22⋊C4×C312
#2302231