Finite Group Databasebeta

← C2×C4×#13094056 #27080353

Subgroups — C2×C4×#13094056 #27080353

Order 12032.

2810 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094056C211yesmaximal, characteristic
2C2×C4×#10625354C211yesmaximal, characteristic
3C2×C4×Q8×D47C211yesmaximal, characteristic, complemented
4C4×#13094056C2116yesmaximal, direct product factor
5C2×#15689230C211yesmaximal, characteristic, complemented
6C2×#15689227C211yesmaximal, characteristic, complemented
7C2×#15689226C211yesmaximal, characteristic, complemented
8C2×#15689222C211yesmaximal, characteristic, complemented
9C2×C4×#10625337C211yesmaximal, characteristic, complemented
10C2×C4×#10625325C211yesmaximal, characteristic, complemented
11C2×C4×#10625336C211yesmaximal, characteristic, complemented
12C2×#15689164C211yesmaximal, characteristic, complemented
13C2×#15689123C211yesmaximal, characteristic
14C2×#15689130C211yesmaximal, characteristic, complemented
15C2×C4×#10625324C211yesmaximal, characteristic, complemented
16C2×C4×Q16×C47C211yesmaximal, characteristic, complemented
17C22×#10625354C2211yescharacteristic
18C22×Q8×D47C2211yescharacteristic
19C2×#13094056C4116yesdirect product factor
20C2×#13094056C2218yes—
21C22×#10625337C2211yescharacteristic
22C22×#10625325C2211yescharacteristic
23C22×#10625336C2211yescharacteristic
24C22×#10625324C2211yescharacteristic
25C22×#10625324C2211yescharacteristic
26C4×#10625354—24no—
27C4×#10625354C2218yes—
28C2×Q8×Dic47C2211yescharacteristic
29C2×Q8×Dic47C2211yescharacteristic
30C2×C4×Dic94—21no—
31C2×C4×Dic94C2211yescharacteristic
32C2×#13093989—21no—
33C2×#13093989C2211yescharacteristic
34C4×Q8×D47—24no—
35C4×Q8×D47C2218yescomplemented
36C2×C4×D188—21no—
37C2×C4×D188C2211yescharacteristic
38C2×#13093986—21no—
39C2×#13093986C2211yescharacteristic
40C2×#13093982—21no—
41C2×#13093982C2211yescharacteristic
42C2×C4⋊C4×D47—21no—
43C2×C4⋊C4×D47C2211yescharacteristic
44C2×C42×D47—21no—
45C2×C42×D47—21no—
46C2×C42×D47C2211yescharacteristic
47#15689230C2218yescomplemented
48#15689227C2218yescomplemented
49#15689226C2218yescomplemented
50#15689222C2218yescomplemented
51C4×#10625337C2218yescomplemented
52C4×#10625325C2218yescomplemented
53C4×#10625336C2218yescomplemented
54#15689164C2218yescomplemented
55C2×#13093957C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58#15689130C2218yescomplemented
59#15689123C2218yes—
60C2×#13093949C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C4×#10625324C2218yescomplemented
67C2×#13093934C2211yescharacteristic
68C2×#13093934C2211yescharacteristic
69C2×C4×C47⋊C8C2211yescharacteristic
70C22×Q16×C47C2211yescharacteristic
71C2×C4×Q8×C47C2211yescharacteristic
72C2×C4×Q8×C47C2211yescharacteristic
73C4×Q16×C47C2218yescomplemented
74C2×#107×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2211yescharacteristic
77C2×C4×C8×C47C2211yescharacteristic
78C2×#10625354—22no—
79C2×#10625354—24no—
80C2×#10625354C2×C418yes—
81C2×#10625354C2314yes—
82C22×Dic94—21no—
83C22×Dic94C2311yescharacteristic
84C2×Q8×D47—22no—
85C2×Q8×D47—24no—
86C2×Q8×D47C2×C418yescomplemented
87C2×Q8×D47C2314yes—
88C22×D188—21no—
89C22×D188C2311yescharacteristic
90C22×C4×D47—21no—
91C22×C4×D47—21no—
92C22×C4×D47—21no—
93C22×C4×D47—21no—
94C22×C4×D47—21no—
95C22×C4×D47D411yescharacteristic
96C22×C4×D47D411yescharacteristic
97C22×C4×D47C2311yescharacteristic
98#13094056C2×C4164yesdirect product factor
99C2×#10625337C2×C418yescomplemented
100C2×#10625337C2314yes—
101C2×#10625325C2×C418yescomplemented
102C2×#10625325C2314yes—
103C2×#10625336C2×C418yescomplemented
104C2×#10625336C2314yes—
105C2×#10625324—24no—
106C2×#10625324C2×C418yescomplemented
107C2×#10625324C2314yes—
108C2×#10625324C2314yes—
109C22×C47⋊C8C2311yescharacteristic
110C22×C47⋊C8C2311yescharacteristic
111Q8×Dic47—22no—
112Q8×Dic47—22no—
113Q8×Dic47C2314yes—
114Q8×Dic47C2314yes—
115C4×Dic94—22no—
116C4×Dic94—28no—
117C4×Dic94C2314yes—
118#13093989—22no—
119#13093989—28no—
120#13093989C2314yes—
121C4×D188—28no—
122C4×D188—22no—
123C4×D188C2314yes—
124#13093986—28no—
125#13093986—22no—
126#13093986C2314yes—
127#13093982—22no—
128#13093982—28no—
129#13093982C2314yes—
130C2×C4⋊Dic47—21no—
131C2×C4⋊Dic47—21no—
132C2×C4⋊Dic47C2311yescharacteristic
133C2×C4⋊Dic47C2311yescharacteristic
134C2×Dic47⋊C4—21no—
135C2×Dic47⋊C4—21no—
136C2×Dic47⋊C4—21no—
137C4⋊C4×D47—28no—
138C4⋊C4×D47—22no—
139C4⋊C4×D47C2314yes—
140C2×(C2×D47)⋊C4—21no—
141C2×(C2×D47)⋊C4—21no—
142C2×(C2×D47)⋊C4—21no—
143C2×C4×Dic47—21no—
144C2×C4×Dic47—21no—
145C2×C4×Dic47—21no—
146C2×C4×Dic47—21no—
147C2×C4×Dic47—21no—
148C2×C4×Dic47D411yescharacteristic
149C2×C4×Dic47D411yescharacteristic
150C2×C4×Dic47C2311yescharacteristic
151C42×D47—28no—
152C42×D47—28no—
153C42×D47D414yes—
154C42×D47C2314yes—
155#13093957C2314yes—
156#13093956C2314yes—
157#13093955C2314yes—
158#13093949C2314yes—
159#13093948C2314yes—
160#13093948C2314yes—
161#13093947C2314yes—
162#13093946C2314yes—
163#13093944C2314yes—
164#13093934C2314yes—
165#13093934C2314yes—
166C4×C47⋊C8C2314yes—
167C22×Q8×C47C2311yescharacteristic
168C22×Q8×C47C2311yescharacteristic
169C2×Q16×C47C2×C418yescomplemented
170C2×Q16×C47C2314yes—
171C22×C8×C47C2311yescharacteristic
172C22×C8×C47C2311yescharacteristic
173C4×Q8×C47—22no—
174C4×Q8×C47—22no—
175C4×Q8×C47C2314yes—
176C4×Q8×C47C2314yes—
177C2×C4⋊C4×C47—21no—
178C2×C4⋊C4×C47—21no—
179C2×C4⋊C4×C47C2311yescharacteristic
180C2×C4⋊C4×C47C2311yescharacteristic
181C2×C42×C47—21no—
182C2×C42×C47—21no—
183C2×C42×C47C2311yescharacteristic
184#107×C47C2314yes—
185#103×C47C2314yes—
186#103×C47C2314yes—
187C4×C8×C47C2314yes—
188C23×D47—21no—
189C23×D47C2×D411yescharacteristic
190C2×Q8×C47—21no—
191C2×Q8×C47—21no—
192C2×Q8×C47—22no—
193C2×Q8×C47—22no—
194C2×Q8×C47C22×C414yes—
195C2×Q8×C47C22×C414yes—
196C2×Q8×C47C2412yes—
197C2×Q8×C47C2412yes—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47—21no—
201C22×C4×C47—21no—
202C22×C4×C47C2×D411yescharacteristic
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2411yescharacteristic
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—21no—
208C22×Dic47C2×D411yescharacteristic
209C22×Dic47C2×D411yescharacteristic
210C22×Dic47C2×D411yescharacteristic
211#10625354—216no—
212#10625354—28no—
213#10625354C22×C4116yes—
214Q8×D47—216no—
215Q8×D47—28no—
216Q8×D47C22×C4116yescomplemented
217C2×D188—28no—
218C2×D188—24no—
219C2×D188—21no—
220C2×D188—22no—
221C2×D188C22×C414yes—
222C2×D188C2412yes—
223C2×C4×D47—28no—
224C2×C4×D47—24no—
225C2×C4×D47—24no—
226C2×C4×D47—28no—
227C2×C4×D47—24no—
228C2×C4×D47—24no—
229C2×C4×D47—24no—
230C2×C4×D47—24no—
231C2×C4×D47—42no—
232C2×C4×D47—44no—
233C2×C4×D47—44no—
234C2×C4×D47—44no—
235C2×C4×D47C22×C414yes—
236C2×C4×D47C2×D414yes—
237C2×C4×D47C2×D414yes—
238C2×C4×D47C2×D412yes—
239C2×C4×D47#4114yes—
240C2×C4×D47C2412yes—
241C2×Dic94—21no—
242C2×Dic94—22no—
243C2×Dic94—28no—
244C2×Dic94—24no—
245C2×Dic94C22×C414yes—
246C2×Dic94C2412yes—
247Q16×C47C22×C4116yescomplemented
248C2×C8×C47—22no—
249C2×C8×C47C22×C414yes—
250C2×C8×C47C2412yes—
251C2×C8×C47C2412yes—
252C4⋊C4×C47—24no—
253C4⋊C4×C47—24no—
254C4⋊C4×C47—21no—
255C4⋊C4×C47—21no—
256C4⋊C4×C47C2412yes—
257C4⋊C4×C47C2412yes—
258C42×C47—24no—
259C42×C47—24no—
260C42×C47C2×D412yes—
261C42×C47C2412yes—
262#10625337C22×C4116yescomplemented
263#10625336C22×C4116yescomplemented
264(C2×D47)⋊C4—24no—
265(C2×D47)⋊C4—24no—
266(C2×D47)⋊C4—24no—
267C4⋊Dic47—21no—
268C4⋊Dic47—21no—
269C4⋊Dic47—24no—
270C4⋊Dic47—24no—
271C4⋊Dic47C2412yes—
272C4⋊Dic47C2412yes—
273Dic47⋊C4—24no—
274Dic47⋊C4—24no—
275Dic47⋊C4—24no—
276C4×Dic47—24no—
277C4×Dic47—24no—
278C4×Dic47—24no—
279C4×Dic47—24no—
280C4×Dic47—24no—
281C4×Dic47C2×D414yes—
282C4×Dic47C2×D412yes—
283C4×Dic47C2×D414yes—
284C4×Dic47C2412yes—
285C2×C47⋊C8—22no—
286C2×C47⋊C8C22×C414yes—
287C2×C47⋊C8C2412yes—
288C2×C47⋊C8C2412yes—
289#10625325C22×C4116yescomplemented
290#10625324—28no—
291#10625324C22×C4116yescomplemented
292C23×C47C22×D411yescharacteristic
293C22×D47—22no—
294C22×D47—22no—
295C22×D47—24no—
296C22×D47—22no—
297C22×D47—42no—
298C22×D47—42no—
299C22×D47C4×D414yes—
300C22×D47C22×D412yes—
301Q8×C47—24no—
302Q8×C47—24no—
303Q8×C47—22no—
304Q8×C47—22no—
305Q8×C47C23×C414yes—
306Q8×C47C23×C414yes—
307C2×C4×C47—24no—
308C2×C4×C47—24no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—42no—
315C2×C4×C47—42no—
316C2×C4×C47#13714yescomplemented
317C2×C4×C47C23×C412yes—
318C2×C4×C47C22×D412yes—
319C2×C4×C47C22×D411yescharacteristic
320C2×C4×C47C22×D412yes—
321C2×C4×C47C2×#4112yes—
322C2×C4×C47C2511yescharacteristic
323C2×Dic47—24no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—42no—
330C2×Dic47—42no—
331C2×Dic47C4×D414yes—
332C2×Dic47C22×D412yes—
333C2×Dic47C22×D412yes—
334C2×Dic47C22×D412yes—
335D188—216no—
336D188—24no—
337D188—22no—
338D188C23×C414yes—
339C4×D47—216no—
340C4×D47—28no—
341C4×D47—216no—
342C4×D47—44no—
343C4×D47—48no—
344C4×D47—48no—
345C4×D47—48no—
346C4×D47C4×D418yes—
347C4×D47C23×C414yes—
348C4×D47C2×#4114yes—
349Dic94—24no—
350Dic94—22no—
351Dic94—216no—
352Dic94C23×C414yes—
353C8×C47—22no—
354C8×C47C23×C414yes—
355C47⋊C8—22no—
356C47⋊C8C23×C414yes—
357C2×C4×#137—471nomaximal, Sylow
358C22×C47C2×C4×D412yes—
359C22×C47C2×#13712yes—
360C22×C47#57512yes—
361C22×C47C23×D411yescharacteristic
362C2×D47—28no—
363C2×D47—22no—
364C2×D47—22no—
365C2×D47—24no—
366C2×D47—48no—
367C2×D47—42no—
368C2×D47—42no—
369C2×D47C2×C4×D414yes—
370C4×C47—24no—
371C4×C47—24no—
372C4×C47—22no—
373C4×C47—42no—
374C4×C47—42no—
375C4×C47C2×C4×D412yes—
376C4×C47C2×#13714yescomplemented
377C4×C47C24×C411yescharacteristic
378C4×C47C22×#4111yescharacteristic
379Dic47—24no—
380Dic47—22no—
381Dic47—22no—
382Dic47—42no—
383Dic47—42no—
384Dic47C2×C4×D414yes—
385C22×#137—471no—
386C2×C4×#41—471no—
387C22×C4×Q8—471no—
388C4×#137—4716no—
389C2×#441—471no—
390C2×#441—471no—
391C2×#440—471no—
392C2×#440—471no—
393C2×C4×Q16—471no—
394C2×C4×Q16D4711yescharacteristic, complemented
395C2×C4×SD16—471no—
396C2×C4×SD16—471no—
397C2×#428—471no—
398C2×#417—471no—
399C2×#419—471no—
400C2×C4×M16—471no—
401C2×C47C4×#13714yescomplemented
402C2×C47C22×C4×D411yescharacteristic
403C2×C47C22×#13711yescharacteristic
404C2×C47C2×#57511yescharacteristic
405D47—24no—
406D47—44no—
407C22×#41—471no—
408C23×Q8—471no—
409C2×#137—4716no—
410C2×#137—478no—
411C22×Q16—471no—
412C22×Q16C2×D4711yescharacteristic
413C22×SD16—471no—
414C22×SD16—471no—
415C22×M16—471no—
416C22×M16—471no—
417C4×#41—478no—
418C4×#41—944no—
419C2×C4×Q8—471no—
420C2×C4×Q8—471no—
421C2×C4×Q8—478no—
422C2×C4×Q8—471no—
423C2×C4×Q8—471no—
424C2×C4×Q8—941no—
425C2×C4×Q8—941no—
426C2×C4×Q8—944no—
427C2×C4×Q8C2×D4711yescharacteristic
428C2×C4×Q8C2×D4711yescharacteristic
429C2×C4×D4—471no—
430C2×C4×D4—471no—
431C2×C4×D4—941no—
432C2×C4×D4—941no—
433C2×#117—471no—
434C2×#117—941no—
435C22×C4⋊C4—471no—
436C22×C4⋊C4—941no—
437C22×C42—471no—
438C22×C42—941no—
439C22×C42—941no—
440#441—478no—
441#441—478no—
442#440—478no—
443#440—478no—
444C4×Q16—478no—
445C4×Q16C2×D4718yescomplemented
446C4×SD16—478no—
447C4×SD16—478no—
448#428—478no—
449C2×#107—471no—
450C2×#107C2×D4711yescharacteristic
451C2×#106—471no—
452C2×#106—471no—
453#419—478no—
454#417—478no—
455C2×#103—471no—
456C2×#103—471no—
457C2×#103—471no—
458C2×#103—471no—
459C2×#103C2×D4711yescharacteristic
460C2×#103C2×D4711yescharacteristic
461C2×#102—471no—
462C2×#102—471no—
463C4×M16—478no—
464C2×#97—471no—
465C2×#97—471no—
466C2×C4×C8—471no—
467C2×C4×C8C2×D4711yescharacteristic
468C47C2×C4×#13711yescharacteristic, complemented, Sylow
469C2×#41—478no—
470C2×#41—474no—
471C2×#41—942no—
472C2×#41—944no—
473C22×Q8—478no—
474C22×Q8—474no—
475C22×Q8—471no—
476C22×Q8—941no—
477C22×Q8—942no—
478C22×Q8—944no—
479C22×Q8C22×D4711yescharacteristic
480C22×Q8C22×D4711yescharacteristic
481C22×D4—471no—
482C22×D4—941no—
483C23×C4—471no—
484C23×C4—471no—
485C23×C4—471no—
486C23×C4—941no—
487C23×C4—941no—
488C23×C4—941no—
489C23×C4—941no—
490C23×C4—941no—
491#137—4764no—
492C2×Q16—478no—
493C2×Q16—474no—
494C2×Q16C4×D4718yescomplemented
495C2×Q16C22×D4714yes—
496C2×SD16—478no—
497C2×SD16—474no—
498C2×SD16—478no—
499C2×SD16—474no—
500C2×M16—478no—
501C2×M16—474no—
502C2×M16—474no—
503C2×M16—944no—
504C22×C8—471no—
505C22×C8—471no—
506C22×C8C22×D4711yescharacteristic
507C22×C8C22×D4711yescharacteristic
508C4×Q8—22no—
509C4×Q8—22no—
510C4×Q8—474no—
511C4×Q8—474no—
512C4×Q8—474no—
513C4×Q8—474no—
514C4×Q8—948no—
515C4×Q8—948no—
516C4×Q8—942no—
517C4×Q8—942no—
518C4×Q8—942no—
519C4×Q8—942no—
520C4×Q8C22×D4714yes—
521C4×Q8C22×D4714yes—
522C4×D4—474no—
523C4×D4—474no—
524C4×D4—948no—
525C4×D4—942no—
526C4×D4—948no—
527C4×D4—942no—
528#117—474no—
529#117—948no—
530#117—942no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—471no—
534C2×C4⋊C4—471no—
535C2×C4⋊C4—474no—
536C2×C4⋊C4—942no—
537C2×C4⋊C4—948no—
538C2×C4⋊C4—941no—
539C2×C4⋊C4—941no—
540C2×C4⋊C4—941no—
541C2×C4⋊C4—941no—
542C2×C4⋊C4—941no—
543C2×C4⋊C4C22×D4711yescharacteristic
544C2×C4⋊C4C22×D4711yescharacteristic
545C2×C22⋊C4—941no—
546C2×C22⋊C4—941no—
547C2×C22⋊C4—941no—
548C2×C42—21no—
549C2×C42—21no—
550C2×C42—471no—
551C2×C42—471no—
552C2×C42—471no—
553C2×C42—474no—
554C2×C42—474no—
555C2×C42—948no—
556C2×C42—948no—
557C2×C42—941no—
558C2×C42—941no—
559C2×C42—941no—
560C2×C42—941no—
561C2×C42—941no—
562C2×C42C22×D4711yescharacteristic
563#107—474no—
564#107C22×D4714yes—
565#106—474no—
566#106—474no—
567#103—474no—
568#103—474no—
569#103—474no—
570#103—474no—
571#103C22×D4714yes—
572#103C22×D4714yes—
573#102—474no—
574#102—474no—
575#97—474no—
576#97—474no—
577C4×C8—474no—
578C4×C8C22×D4714yes—
579C24—471no—
580C24—941no—
581#41—4716no—
582#41—9416no—
583#41—948no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—4716no—
589C2×Q8—474no—
590C2×Q8—472no—
591C2×Q8—944no—
592C2×Q8—948no—
593C2×Q8—9416no—
594C2×Q8—948no—
595C2×Q8—941no—
596C2×Q8—942no—
597C2×Q8C2×C4×D4714yes—
598C2×Q8C2×C4×D4714yes—
599C2×Q8C23×D4712yes—
600C2×Q8C23×D4712yes—
601C2×D4—474no—
602C2×D4—472no—
603C2×D4—944no—
604C2×D4—948no—
605C2×D4—941no—
606C2×D4—942no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—471no—
612C22×C4—474no—
613C22×C4—472no—
614C22×C4—474no—
615C22×C4—472no—
616C22×C4—471no—
617C22×C4—471no—
618C22×C4—474no—
619C22×C4—474no—
620C22×C4—944no—
621C22×C4—948no—
622C22×C4—944no—
623C22×C4—944no—
624C22×C4—948no—
625C22×C4—944no—
626C22×C4—941no—
627C22×C4—944no—
628C22×C4—941no—
629C22×C4—941no—
630C22×C4—944no—
631C22×C4—1882no—
632C22×C4—1884no—
633C22×C4—1884no—
634C22×C4—1884no—
635C22×C4D4×D4711yescharacteristic
636C22×C4D4×D4711yescharacteristic
637C22×C4C23×D4711yescharacteristic
638Q16—4716no—
639Q16C2×C4×D47116yescomplemented
640SD16—4716no—
641SD16—4716no—
642M16—4716no—
643M16—948no—
644C2×C8—22no—
645C2×C8—474no—
646C2×C8—472no—
647C2×C8—472no—
648C2×C8—942no—
649C2×C8C2×C4×D4714yes—
650C2×C8C23×D4712yes—
651C2×C8C23×D4712yes—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—472no—
657C4⋊C4—472no—
658C4⋊C4—944no—
659C4⋊C4—944no—
660C4⋊C4—944no—
661C4⋊C4—944no—
662C4⋊C4—944no—
663C4⋊C4—941no—
664C4⋊C4—941no—
665C4⋊C4C23×D4712yes—
666C4⋊C4C23×D4712yes—
667C22⋊C4—944no—
668C22⋊C4—944no—
669C22⋊C4—944no—
670C42—24no—
671C42—24no—
672C42—474no—
673C42—474no—
674C42—472no—
675C42—472no—
676C42—944no—
677C42—944no—
678C42—944no—
679C42—944no—
680C42—944no—
681C42D4×D4712yes—
682C42C23×D4712yes—
683C23—474no—
684C23—472no—
685C23—942no—
686C23—942no—
687C23—944no—
688C23—942no—
689C23—1882no—
690C23—1882no—
691C23C2×D4×D4711yescharacteristic
692Q8—24no—
693Q8—24no—
694Q8—22no—
695Q8—22no—
696Q8—474no—
697Q8—9416no—
698Q8—944no—
699Q8—942no—
700Q8C22×C4×D4714yes—
701Q8C22×C4×D4714yes—
702D4—474no—
703D4—9416no—
704D4—944no—
705D4—942no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—474no—
716C2×C4—472no—
717C2×C4—478no—
718C2×C4—474no—
719C2×C4—474no—
720C2×C4—472no—
721C2×C4—472no—
722C2×C4—9416no—
723C2×C4—9416no—
724C2×C4—944no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—948no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—1884no—
732C2×C4—1888no—
733C2×C4—1888no—
734C2×C4—1882no—
735C2×C4—1882no—
736C2×C4—1888no—
737C2×C4#1309405614yesdirect product factor
738C2×C4C22×C4×D4712yes—
739C2×C4C2×D4×D4712yes—
740C2×C4C2×D4×D4711yescharacteristic
741C2×C4C2×D4×D4712yes—
742C2×C4#41×D4712yes—
743C2×C4C24×D4711yescharacteristic
744C8—22no—
745C8—474no—
746C8—942no—
747C8C22×C4×D4714yes—
748C22—474no—
749C22—948no—
750C22—942no—
751C22—942no—
752C22—944no—
753C22—1888no—
754C22—1882no—
755C22—1882no—
756C22C4×D4×D4712yes—
757C22C2×#1309405612yes—
758C22#1568992012yes—
759C22C22×D4×D4711yescharacteristic
760C4—24no—
761C4—24no—
762C4—22no—
763C4—42no—
764C4—42no—
765C4—474no—
766C4—944no—
767C4—942no—
768C4—942no—
769C4—1882no—
770C4—1882no—
771C4C4×D4×D4712yes—
772C4C2×#1309405614yesdirect product factor
773C4C23×C4×D4711yescharacteristic
774C4C2×#41×D4711yescharacteristic
775C2—944no—
776C2—1884no—
777C2C4×#1309405614yesdirect product factor
778C2C2×C4×D4×D4711yescharacteristic
779C2C22×#1309405611yescharacteristic
780C2C2×#1568992011yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC4×C47C24×C4
FrattiniC2×C4C24×D47
FittingC2×C4×Q16×C47C2
socleC23×C47C22×D4
prime radicalC22×#10625354C22
cosocleC2×C4×C47C25
hypercenterC2×C4×Q16D47
hypocenterC47C2×C4×#137
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. C2×C4×Q8×D47C2semidirect
4. C4×#13094056C2direct (N × H)
5. C2×#15689230C2semidirect
6. C2×#15689227C2semidirect
7. C2×#15689226C2semidirect
8. C2×#15689222C2semidirect
9. C2×C4×#10625337C2semidirect
10. C2×C4×#10625325C2semidirect
11. C2×C4×#10625336C2semidirect
12. C2×#15689164C2semidirect
14. C2×#15689130C2semidirect
15. C2×C4×#10625324C2semidirect
16. C2×C4×Q16×C47C2semidirect
19. C2×#13094056C4direct (N × H)
35. C4×Q8×D47C22semidirect
47. #15689230C22semidirect
48. #15689227C22semidirect
49. #15689226C22semidirect
50. #15689222C22semidirect
51. C4×#10625337C22semidirect
52. C4×#10625325C22semidirect
53. C4×#10625336C22semidirect
54. #15689164C22semidirect
58. #15689130C22semidirect
66. C4×#10625324C22semidirect
73. C4×Q16×C47C22semidirect
86. C2×Q8×D47C2×C4semidirect
98. #13094056C2×C4direct (N × H)
99. C2×#10625337C2×C4semidirect
101. C2×#10625325C2×C4semidirect
103. C2×#10625336C2×C4semidirect
106. C2×#10625324C2×C4semidirect
169. C2×Q16×C47C2×C4semidirect
216. Q8×D47C22×C4semidirect
247. Q16×C47C22×C4semidirect
262. #10625337C22×C4semidirect
263. #10625336C22×C4semidirect
289. #10625325C22×C4semidirect
291. #10625324C22×C4semidirect
316. C2×C4×C47#137semidirect
376. C4×C47C2×#137semidirect
394. C2×C4×Q16D47semidirect
401. C2×C47C4×#137semidirect
445. C4×Q16C2×D47semidirect
468. C47C2×C4×#137semidirect
494. C2×Q16C4×D47semidirect
639. Q16C2×C4×D47semidirect
737. C2×C4#13094056direct (N × H)
772. C4C2×#13094056direct (N × H)
777. C2C4×#13094056direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940562
C2×C4×#106253542
C2×C4×Q8×D472
C4×#130940562
C2×#156892302
C2×#156892272
C2×#156892262
C2×#156892222
C2×C4×#106253372
C2×C4×#106253252
C2×C4×#106253362
C2×#156891642
C2×#156891232
C2×#156891302
C2×C4×#106253242
C2×C4×Q16×C472
C2×C4×#13747