Finite Group Databasebeta

← C2×C31×#2417 #21491442

Subgroups — C2×C31×#2417 #21491442

Order 7936.

3830 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×C31×C22⋊Q8C211yesmaximal, characteristic, complemented
3C22×C4×D4×C31C211yesmaximal, characteristic
4C23×C4⋊C4×C31C211yesmaximal, characteristic, complemented
5C31×#2417C2116yesmaximal, direct product factor
6C2×C31×#398C212yesmaximal, complemented
7C2×C31×#396C212yesmaximal, complemented
8C2×C31×#391C211yesmaximal, characteristic, complemented
9C2×C31×#389C211yesmaximal, characteristic, complemented
10C2×C31×#386C212yesmaximal
11C2×C31×#380C212yesmaximal, complemented
12C2×C31×#380C211yesmaximal, characteristic, complemented
13C23×Q8×C31C2211yescharacteristic
14C23×D4×C31C2211yescharacteristic
15C24×C4×C31C2211yescharacteristic
16C24×C4×C31C2212yes—
17C24×C4×C31C2211yescharacteristic
18C2×C31×C22⋊Q8—28no—
19C2×C31×C22⋊Q8—28no—
20C2×C31×C22⋊Q8C2218yescomplemented
21C2×C31×C22⋊Q8C2218yescomplemented
22C2×C4×D4×C31—28no—
23C2×C4×D4×C31C2218yes—
24C22×C4⋊C4×C31—28no—
25C22×C4⋊C4×C31C2212yes—
26C22×C4⋊C4×C31C2212yes—
27C22×C4⋊C4×C31C2211yescharacteristic
28C22×C4⋊C4×C31C2212yes—
29C22×C4⋊C4×C31C2211yescharacteristic
30C22×C4⋊C4×C31C2211yescharacteristic
31C22×C4⋊C4×C31C2212yes—
32C22×C4⋊C4×C31C2211yescharacteristic
33C22×C4⋊C4×C31C2218yescomplemented
34C22×C22⋊C4×C31C2211yescharacteristic
35C22×C22⋊C4×C31C2212yes—
36C22×C22⋊C4×C31C2211yescharacteristic
37C22×C22⋊C4×C31C2212yes—
38C22×C22⋊C4×C31C2212yes—
39C22×C42×C31C2211yescharacteristic
40C31×#398C22116yescomplemented
41C31×#396C22116yescomplemented
42C31×#391C2218yescomplemented
43C31×#389C2218yescomplemented
44C31×#386C22116yes—
45C31×#380C22116yescomplemented
46C31×#380C2218yescomplemented
47C2×C31×#95C2212yes—
48C2×C31×#95C2212yes—
49C2×C31×#95C2212yes—
50C2×C31×#95C2212yes—
51C25×C31C2311yescharacteristic
52C25×C31C2311yescharacteristic
53C22×Q8×C31—24no—
54C22×Q8×C31—24no—
55C22×Q8×C31—24no—
56C22×Q8×C31C2314yes—
57C22×D4×C31—24no—
58C22×D4×C31—24no—
59C22×D4×C31Q818yescomplemented
60C22×D4×C31C2314yes—
61C23×C4×C31—24no—
62C23×C4×C31—24no—
63C23×C4×C31—28no—
64C23×C4×C31—28no—
65C23×C4×C31—24no—
66C23×C4×C31—24no—
67C23×C4×C31—24no—
68C23×C4×C31—44no—
69C23×C4×C31D418yes—
70C23×C4×C31C2314yes—
71C23×C4×C31C2311yescharacteristic
72C23×C4×C31C2312yes—
73C23×C4×C31C2312yes—
74C23×C4×C31C2311yescharacteristic
75C23×C4×C31C2312yes—
76C23×C4×C31C2318yes—
77C23×C4×C31C2314yes—
78C23×C4×C31C2311yescharacteristic
79C23×C4×C31C2312yes—
80C23×C4×C31C2311yescharacteristic
81C23×C4×C31C2311yescharacteristic
82C31×C22⋊Q8—232no—
83C31×C22⋊Q8—232no—
84C4×D4×C31—232no—
85C2×C4⋊C4×C31—28no—
86C2×C4⋊C4×C31—24no—
87C2×C4⋊C4×C31—24no—
88C2×C4⋊C4×C31—24no—
89C2×C4⋊C4×C31—28no—
90C2×C4⋊C4×C31—28no—
91C2×C4⋊C4×C31—232no—
92C2×C4⋊C4×C31—44no—
93C2×C4⋊C4×C31D418yescomplemented
94C2×C4⋊C4×C31C2318yes—
95C2×C4⋊C4×C31C2318yes—
96C2×C4⋊C4×C31C2314yes—
97C2×C4⋊C4×C31C2318yes—
98C2×C4⋊C4×C31C2314yes—
99C2×C4⋊C4×C31C2314yes—
100C2×C4⋊C4×C31C2318yes—
101C2×C4⋊C4×C31C2314yes—
102C2×C22⋊C4×C31—24no—
103C2×C22⋊C4×C31—28no—
104C2×C22⋊C4×C31—24no—
105C2×C22⋊C4×C31—28no—
106C2×C22⋊C4×C31—44no—
107C2×C22⋊C4×C31C2314yes—
108C2×C22⋊C4×C31C2318yes—
109C2×C22⋊C4×C31C2314yes—
110C2×C22⋊C4×C31C2318yes—
111C2×C22⋊C4×C31C2318yes—
112C2×C42×C31—24no—
113C2×C42×C31C2314yes—
114C31×#95C2318yes—
115C31×#95C2318yes—
116C31×#95C2318yes—
117C31×#95C2318yes—
118C24×C31—22no—
119C24×C31—22no—
120C24×C31—22no—
121C24×C31—22no—
122C24×C31—22no—
123C24×C31—22no—
124C24×C31—22no—
125C24×C31—22no—
126C24×C31—22no—
127C24×C31—22no—
128C24×C31C2×D414yes—
129C24×C31C2×Q814yes—
130C24×C31C2×Q814yes—
131C24×C31#4114yes—
132C24×C31C2412yes—
133C24×C31C2412yes—
134C24×C31C2411yescharacteristic
135C2×Q8×C31—28no—
136C2×Q8×C31—28no—
137C2×Q8×C31—28no—
138C2×Q8×C31—416no—
139C2×D4×C31—232no—
140C2×D4×C31—28no—
141C2×D4×C31—28no—
142C2×D4×C31C2×Q8116yescomplemented
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—24no—
147C22×C4×C31—22no—
148C22×C4×C31—24no—
149C22×C4×C31—232no—
150C22×C4×C31—28no—
151C22×C4×C31—28no—
152C22×C4×C31—22no—
153C22×C4×C31—24no—
154C22×C4×C31—22no—
155C22×C4×C31—24no—
156C22×C4×C31—24no—
157C22×C4×C31—22no—
158C22×C4×C31—24no—
159C22×C4×C31—216no—
160C22×C4×C31—22no—
161C22×C4×C31—24no—
162C22×C4×C31—24no—
163C22×C4×C31—24no—
164C22×C4×C31—24no—
165C22×C4×C31—22no—
166C22×C4×C31—22no—
167C22×C4×C31—24no—
168C22×C4×C31—216no—
169C22×C4×C31—28no—
170C22×C4×C31—28no—
171C22×C4×C31—28no—
172C22×C4×C31—48no—
173C22×C4×C31—432no—
174C22×C4×C31—416no—
175C22×C4×C31C2×D414yes—
176C22×C4×C31C2×D418yes—
177C22×C4×C31C2×D4116yes—
178C22×C4×C31C2×D414yes—
179C22×C4×C31C2×D414yes—
180C22×C4×C31C2×Q814yes—
181C22×C4×C31#4114yes—
182C22×C4×C31C2414yes—
183C22×C4×C31C2412yes—
184C22×C4×C31C2414yes—
185C22×C4×C31C2414yes—
186C22×C4×C31C2412yes—
187C22×C4×C31C2414yes—
188C22×C4×C31C2412yes—
189C22×C4×C31C2412yes—
190C22×C4×C31C2412yes—
191C4⋊C4×C31—216no—
192C4⋊C4×C31—28no—
193C4⋊C4×C31—28no—
194C4⋊C4×C31—28no—
195C4⋊C4×C31—216no—
196C4⋊C4×C31—216no—
197C4⋊C4×C31—48no—
198C4⋊C4×C31C2×D4116yescomplemented
199C22⋊C4×C31—28no—
200C22⋊C4×C31—216no—
201C22⋊C4×C31—28no—
202C22⋊C4×C31—216no—
203C22⋊C4×C31—48no—
204C42×C31—28no—
205C2×#2417C3111yesmaximal, characteristic, direct product factor, Sylow
206C23×C31—28no—
207C23×C31—28no—
208C23×C31—28no—
209C23×C31—28no—
210C23×C31—28no—
211C23×C31—28no—
212C23×C31—22no—
213C23×C31—22no—
214C23×C31—22no—
215C23×C31—22no—
216C23×C31—28no—
217C23×C31—28no—
218C23×C31—28no—
219C23×C31—22no—
220C23×C31—22no—
221C23×C31—22no—
222C23×C31—22no—
223C23×C31—22no—
224C23×C31—22no—
225C23×C31—44no—
226C23×C31—44no—
227C23×C31—44no—
228C23×C31—44no—
229C23×C31C22⋊Q8116yescomplemented
230C23×C31C22×D414yes—
231C23×C31C22×D412yes—
232C23×C31C22×D412yes—
233C23×C31C22×Q814yes—
234C23×C31C22×Q814yes—
235C23×C31C22×Q812yes—
236C23×C31C2×#4114yes—
237C23×C31C2×#4112yes—
238C23×C31C2×#4112yes—
239C23×C31H(5,𝔽2)12yes—
240C23×C312−1+412yes—
241C23×C31C2511yescharacteristic
242Q8×C31—416no—
243D4×C31—232no—
244C2×C4×C31—28no—
245C2×C4×C31—28no—
246C2×C4×C31—216no—
247C2×C4×C31—22no—
248C2×C4×C31—22no—
249C2×C4×C31—22no—
250C2×C4×C31—24no—
251C2×C4×C31—22no—
252C2×C4×C31—24no—
253C2×C4×C31—232no—
254C2×C4×C31—22no—
255C2×C4×C31—24no—
256C2×C4×C31—22no—
257C2×C4×C31—24no—
258C2×C4×C31—24no—
259C2×C4×C31—22no—
260C2×C4×C31—24no—
261C2×C4×C31—22no—
262C2×C4×C31—24no—
263C2×C4×C31—24no—
264C2×C4×C31—24no—
265C2×C4×C31—24no—
266C2×C4×C31—22no—
267C2×C4×C31—22no—
268C2×C4×C31—24no—
269C2×C4×C31—432no—
270C2×C4×C31—44no—
271C2×C4×C31—48no—
272C2×C4×C31—44no—
273C2×C4×C31—48no—
274C2×C4×C31—48no—
275C2×C4×C31—416no—
276C2×C4×C31#121116yes—
277C2×C4×C31C22×D414yes—
278C2×C4×C31C22×D418yes—
279C2×C4×C31C22×D414yes—
280C2×C4×C31C22×D414yes—
281C2×C4×C31C22×Q814yes—
282C2×C4×C31C2×#4114yes—
283C22×C22⋊Q8C2×C3111yescharacteristic, complemented
284C22×C22⋊Q8C2×C3111yescharacteristic, complemented
285C22×C4×D4C2×C3111yescharacteristic
286C23×C4⋊C4C2×C3111yescharacteristic, complemented
287#2417C2×C31116yesdirect product factor
288C2×#398C2×C3112yescomplemented
289C2×#396C2×C3112yescomplemented
290C2×#391C2×C3111yescharacteristic, complemented
291C2×#389C2×C3111yescharacteristic, complemented
292C2×#386C2×C3112yes—
293C2×#380C2×C3112yescomplemented
294C2×#380C2×C3111yescharacteristic, complemented
295C22×C31—24no—
296C22×C31—232no—
297C22×C31—24no—
298C22×C31—24no—
299C22×C31—24no—
300C22×C31—24no—
301C22×C31—24no—
302C22×C31—24no—
303C22×C31—24no—
304C22×C31—24no—
305C22×C31—42no—
306C22×C31—416no—
307C22×C31—42no—
308C22×C31—42no—
309C22×C31—42no—
310C22×C31C2×#12114yes—
311C22×C31C2×C22⋊Q814yes—
312C22×C31C2×C22⋊Q818yescomplemented
313C22×C31#53714yes—
314C22×C31#54614yes—
315C22×C31D4×Q814yes—
316C22×C31#55214yes—
317C22×C31#55414yes—
318C22×C31C23×D411yescharacteristic
319C22×C31C23×D411yescharacteristic
320C22×C31C23×Q811yescharacteristic
321C22×C31C22×#4111yescharacteristic
322C22×C31C22×#4111yescharacteristic
323C22×C31C2×H(5,𝔽2)11yescharacteristic
324C22×C31C2×2−1+411yescharacteristic
325C4×C31—24no—
326C4×C31—24no—
327C4×C31—28no—
328C4×C31—42no—
329C4×C31—44no—
330C4×C31—42no—
331C4×C31—44no—
332C4×C31—44no—
333C4×C31C2×#12118yes—
334C23×Q8C22×C3111yescharacteristic
335C23×D4C22×C3111yescharacteristic
336C24×C4C22×C3111yescharacteristic
337C24×C4C22×C3112yes—
338C24×C4C22×C3111yescharacteristic
339C2×C22⋊Q8—28no—
340C2×C22⋊Q8—28no—
341C2×C22⋊Q8C22×C3118yescomplemented
342C2×C22⋊Q8C22×C3118yescomplemented
343C2×C4×D4—28no—
344C2×C4×D4C22×C3118yes—
345C22×C4⋊C4—28no—
346C22×C4⋊C4C22×C3112yes—
347C22×C4⋊C4C22×C3112yes—
348C22×C4⋊C4C22×C3111yescharacteristic
349C22×C4⋊C4C22×C3112yes—
350C22×C4⋊C4C22×C3111yescharacteristic
351C22×C4⋊C4C22×C3111yescharacteristic
352C22×C4⋊C4C22×C3112yes—
353C22×C4⋊C4C22×C3111yescharacteristic
354C22×C4⋊C4C22×C3118yescomplemented
355C22×C22⋊C4C22×C3111yescharacteristic
356C22×C22⋊C4C22×C3112yes—
357C22×C22⋊C4C22×C3111yescharacteristic
358C22×C22⋊C4C22×C3112yes—
359C22×C22⋊C4C22×C3112yes—
360C22×C42C22×C3111yescharacteristic
361#398C22×C31116yescomplemented
362#396C22×C31116yescomplemented
363#391C22×C3118yescomplemented
364#389C22×C3118yescomplemented
365#386C22×C31116yes—
366#380C22×C3118yescomplemented
367#380C22×C31116yescomplemented
368C2×#95C22×C3112yes—
369C2×#95C22×C3112yes—
370C2×#95C22×C3112yes—
371C2×#95C22×C3112yes—
372C2×C31—28no—
373C2×C31—44no—
374C2×C31#241718yesdirect product factor
375C2×C31C22×#12111yescharacteristic
376C2×C31C22×C22⋊Q811yescharacteristic
377C2×C31C2×#53711yescharacteristic
378C2×C31C2×#54611yescharacteristic
379C2×C31C2×D4×Q811yescharacteristic
380C2×C31C2×#55211yescharacteristic
381C2×C31C2×#55411yescharacteristic
382C25C23×C3111yescharacteristic
383C25C23×C3111yescharacteristic
384C22×Q8—24no—
385C22×Q8—24no—
386C22×Q8—24no—
387C22×Q8C23×C3114yes—
388C22×D4—24no—
389C22×D4—24no—
390C22×D4Q8×C3118yescomplemented
391C22×D4C23×C3114yes—
392C23×C4—24no—
393C23×C4—24no—
394C23×C4—28no—
395C23×C4—28no—
396C23×C4—24no—
397C23×C4—24no—
398C23×C4—24no—
399C23×C4—44no—
400C23×C4D4×C3118yes—
401C23×C4C23×C3112yes—
402C23×C4C23×C3112yes—
403C23×C4C23×C3111yescharacteristic
404C23×C4C23×C3111yescharacteristic
405C23×C4C23×C3112yes—
406C23×C4C23×C3114yes—
407C23×C4C23×C3118yes—
408C23×C4C23×C3111yescharacteristic
409C23×C4C23×C3112yes—
410C23×C4C23×C3114yes—
411C23×C4C23×C3111yescharacteristic
412C23×C4C23×C3111yescharacteristic
413C22⋊Q8—232no—
414C22⋊Q8—232no—
415C4×D4—232no—
416C2×C4⋊C4—28no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—28no—
421C2×C4⋊C4—28no—
422C2×C4⋊C4—232no—
423C2×C4⋊C4—44no—
424C2×C4⋊C4D4×C3118yescomplemented
425C2×C4⋊C4C23×C3114yes—
426C2×C4⋊C4C23×C3118yes—
427C2×C4⋊C4C23×C3114yes—
428C2×C4⋊C4C23×C3114yes—
429C2×C4⋊C4C23×C3118yes—
430C2×C4⋊C4C23×C3118yes—
431C2×C4⋊C4C23×C3118yes—
432C2×C4⋊C4C23×C3114yes—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—28no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—28no—
437C2×C22⋊C4—44no—
438C2×C22⋊C4C23×C3114yes—
439C2×C22⋊C4C23×C3114yes—
440C2×C22⋊C4C23×C3118yes—
441C2×C22⋊C4C23×C3118yes—
442C2×C22⋊C4C23×C3118yes—
443C2×C42—24no—
444C2×C42C23×C3114yes—
445#95C23×C3118yes—
446#95C23×C3118yes—
447#95C23×C3118yes—
448#95C23×C3118yes—
449C31C2×#241711yescharacteristic, direct product factor, Sylow
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24C2×D4×C3114yes—
461C24C2×Q8×C3114yes—
462C24C2×Q8×C3114yes—
463C24#41×C3114yes—
464C24C24×C3112yes—
465C24C24×C3112yes—
466C24C24×C3111yescharacteristic
467C2×Q8—28no—
468C2×Q8—28no—
469C2×Q8—28no—
470C2×Q8—416no—
471C2×D4—232no—
472C2×D4—28no—
473C2×D4—28no—
474C2×D4C2×Q8×C31116yescomplemented
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—232no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—216no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—216no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—48no—
505C22×C4—432no—
506C22×C4—416no—
507C22×C4C2×D4×C3114yes—
508C22×C4C2×D4×C3118yes—
509C22×C4C2×D4×C31116yes—
510C22×C4C2×D4×C3114yes—
511C22×C4C2×D4×C3114yes—
512C22×C4C2×Q8×C3114yes—
513C22×C4#41×C3114yes—
514C22×C4C24×C3114yes—
515C22×C4C24×C3112yes—
516C22×C4C24×C3114yes—
517C22×C4C24×C3114yes—
518C22×C4C24×C3112yes—
519C22×C4C24×C3114yes—
520C22×C4C24×C3112yes—
521C22×C4C24×C3112yes—
522C22×C4C24×C3112yes—
523C4⋊C4—216no—
524C4⋊C4—28no—
525C4⋊C4—28no—
526C4⋊C4—28no—
527C4⋊C4—216no—
528C4⋊C4—216no—
529C4⋊C4—48no—
530C4⋊C4C2×D4×C31116yescomplemented
531C22⋊C4—28no—
532C22⋊C4—216no—
533C22⋊C4—28no—
534C22⋊C4—216no—
535C22⋊C4—48no—
536C42—28no—
537C23—28no—
538C23—28no—
539C23—28no—
540C23—28no—
541C23—28no—
542C23—28no—
543C23—22no—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—28no—
548C23—28no—
549C23—28no—
550C23—22no—
551C23—22no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—22no—
556C23—44no—
557C23—44no—
558C23—44no—
559C23—44no—
560C23C31×C22⋊Q8116yescomplemented
561C23C22×D4×C3114yes—
562C23C22×D4×C3112yes—
563C23C22×D4×C3112yes—
564C23C22×Q8×C3114yes—
565C23C22×Q8×C3114yes—
566C23C22×Q8×C3112yes—
567C23C2×#41×C3114yes—
568C23C2×#41×C3112yes—
569C23C2×#41×C3112yes—
570C23C31×H(5,𝔽2)12yes—
571C23C31×2−1+412yes—
572C23C25×C3111yescharacteristic
573Q8—416no—
574D4—232no—
575C2×C4—28no—
576C2×C4—28no—
577C2×C4—216no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—232no—
585C2×C4—22no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—24no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—24no—
600C2×C4—432no—
601C2×C4—44no—
602C2×C4—48no—
603C2×C4—44no—
604C2×C4—48no—
605C2×C4—48no—
606C2×C4—416no—
607C2×C4C31×#121116yes—
608C2×C4C22×D4×C3114yes—
609C2×C4C22×D4×C3118yes—
610C2×C4C22×D4×C3114yes—
611C2×C4C22×D4×C3114yes—
612C2×C4C22×Q8×C3114yes—
613C2×C4C2×#41×C3114yes—
614C22—24no—
615C22—232no—
616C22—24no—
617C22—24no—
618C22—24no—
619C22—24no—
620C22—24no—
621C22—24no—
622C22—24no—
623C22—24no—
624C22—42no—
625C22—416no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22C2×C31×#12114yes—
630C22C2×C31×C22⋊Q814yes—
631C22C2×C31×C22⋊Q818yescomplemented
632C22C31×#53714yes—
633C22C31×#54614yes—
634C22D4×Q8×C3114yes—
635C22C31×#55214yes—
636C22C31×#55414yes—
637C22C23×D4×C3111yescharacteristic
638C22C23×D4×C3111yescharacteristic
639C22C23×Q8×C3111yescharacteristic
640C22C22×#41×C3111yescharacteristic
641C22C22×#41×C3111yescharacteristic
642C22C2×C31×H(5,𝔽2)11yescharacteristic
643C22C2×C31×2−1+411yescharacteristic
644C4—24no—
645C4—24no—
646C4—28no—
647C4—42no—
648C4—44no—
649C4—42no—
650C4—44no—
651C4—44no—
652C4C2×C31×#12118yes—
653C2—28no—
654C2—44no—
655C2C31×#241718yesdirect product factor
656C2C22×C31×#12111yescharacteristic
657C2C22×C31×C22⋊Q811yescharacteristic
658C2C2×C31×#53711yescharacteristic
659C2C2×C31×#54611yescharacteristic
660C2C2×D4×Q8×C3111yescharacteristic
661C2C2×C31×#55211yescharacteristic
662C2C2×C31×#55411yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC23C25×C31
prime radicalC23×D4×C31C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×C22⋊Q8C2semidirect
2. C22×C31×C22⋊Q8C2semidirect
4. C23×C4⋊C4×C31C2semidirect
5. C31×#2417C2direct (N × H)
6. C2×C31×#398C2semidirect
7. C2×C31×#396C2semidirect
8. C2×C31×#391C2semidirect
9. C2×C31×#389C2semidirect
11. C2×C31×#380C2semidirect
12. C2×C31×#380C2semidirect
20. C2×C31×C22⋊Q8C22semidirect
21. C2×C31×C22⋊Q8C22semidirect
33. C22×C4⋊C4×C31C22semidirect
40. C31×#398C22semidirect
41. C31×#396C22semidirect
42. C31×#391C22semidirect
43. C31×#389C22semidirect
45. C31×#380C22semidirect
46. C31×#380C22semidirect
59. C22×D4×C31Q8semidirect
93. C2×C4⋊C4×C31D4semidirect
142. C2×D4×C31C2×Q8semidirect
198. C4⋊C4×C31C2×D4semidirect
205. C2×#2417C31direct (N × H)
229. C23×C31C22⋊Q8semidirect
283. C22×C22⋊Q8C2×C31semidirect
284. C22×C22⋊Q8C2×C31semidirect
286. C23×C4⋊C4C2×C31semidirect
287. #2417C2×C31direct (N × H)
288. C2×#398C2×C31semidirect
289. C2×#396C2×C31semidirect
290. C2×#391C2×C31semidirect
291. C2×#389C2×C31semidirect
293. C2×#380C2×C31semidirect
294. C2×#380C2×C31semidirect
312. C22×C31C2×C22⋊Q8semidirect
341. C2×C22⋊Q8C22×C31semidirect
342. C2×C22⋊Q8C22×C31semidirect
354. C22×C4⋊C4C22×C31semidirect
361. #398C22×C31semidirect
362. #396C22×C31semidirect
363. #391C22×C31semidirect
364. #389C22×C31semidirect
366. #380C22×C31semidirect
367. #380C22×C31semidirect
374. C2×C31#2417direct (N × H)
390. C22×D4Q8×C31semidirect
424. C2×C4⋊C4D4×C31semidirect
449. C31C2×#2417direct (N × H)
474. C2×D4C2×Q8×C31semidirect
530. C4⋊C4C2×D4×C31semidirect
560. C23C31×C22⋊Q8semidirect
631. C22C2×C31×C22⋊Q8semidirect
655. C2C31×#2417direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×C22⋊Q82
C22×C4×D4×C312
C23×C4⋊C4×C312
C31×#24172
C2×C31×#3982
C2×C31×#3962
C2×C31×#3912
C2×C31×#3892
C2×C31×#3862
C2×C31×#3802
C2×#241731