Finite Group Databasebeta

← C2×C4×#13063354 #25960666

Subgroups — C2×C4×#13063354 #25960666

Order 11008.

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×#13063354C211yesmaximal, characteristic
2C2×C4×#10621900C211yesmaximal, characteristic
3C2×C4×Q8×D43C211yesmaximal, characteristic, complemented
4C4×#13063354C2116yesmaximal, direct product factor
5C2×#14583005C211yesmaximal, characteristic, complemented
6C2×#14583003C211yesmaximal, characteristic, complemented
7C2×#14583000C211yesmaximal, characteristic, complemented
8C2×#14582996C211yesmaximal, characteristic, complemented
9C2×C4×Dic172C211yesmaximal, characteristic, complemented
10C2×C4×#10621885C211yesmaximal, characteristic, complemented
11C2×C4×#10621883C211yesmaximal, characteristic, complemented
12C2×#14582938C211yesmaximal, characteristic, complemented
13C2×#14582897C211yesmaximal, characteristic
14C2×#14582906C211yesmaximal, characteristic, complemented
15C2×C4×#10621872C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C43C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C2×#13063354C4116yesdirect product factor
20C2×#13063354C2218yes—
21C22×Dic172C2211yescharacteristic
22C22×#10621885C2211yescharacteristic
23C22×#10621883C2211yescharacteristic
24C22×#10621872C2211yescharacteristic
25C22×#10621872C2211yescharacteristic
26C4×#10621900—24no—
27C4×#10621900C2218yes—
28C2×Q8×Dic43C2211yescharacteristic
29C2×C4×Dic86—21no—
30C2×C4×Dic86C2211yescharacteristic
31C2×C4×Dic86C2211yescharacteristic
32C2×#13063290—21no—
33C2×#13063290C2211yescharacteristic
34C2×#13063290C2211yescharacteristic
35C4×Q8×D43—24no—
36C4×Q8×D43C2218yescomplemented
37C2×D4×Dic43C2211yescharacteristic
38C2×C4×C22⋊D43—21no—
39C2×(C22⋊D43)⋊C4—21no—
40C2×#13063283C2211yescharacteristic
41C2×#13063281—21no—
42C2×C4⋊C4×D43—21no—
43C2×C4⋊C4×D43C2211yescharacteristic
44C22×C4×Dic43—21no—
45C2×C42×D43—21no—
46C2×C42×D43C2211yescharacteristic
47#14583005C2218yescomplemented
48#14583003C2218yescomplemented
49#14583000C2218yescomplemented
50#14582996C2218yescomplemented
51C4×Dic172C2218yescomplemented
52C4×#10621885C2218yescomplemented
53C4×#10621883C2218yescomplemented
54#14582938C2218yescomplemented
55C2×#13063259C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58#14582906C2218yescomplemented
59#14582897C2218yes—
60C2×#13063250C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C4×#10621872C2218yescomplemented
67C2×#13063235C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C2×C4×C43⋊C8C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic
71C2×C4×Q8×C43C2211yescharacteristic
72C2×C4×D4×C43C2211yescharacteristic
73C4×SD16×C43C2218yescomplemented
74C2×#106×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C2×C4×C8×C43C2211yescharacteristic
78C2×#10621900—22no—
79C2×#10621900—24no—
80C2×#10621900C2×C418yes—
81C2×#10621900C2314yes—
82C22×Dic86—21no—
83C22×Dic86C2311yescharacteristic
84C22×Dic86C2311yescharacteristic
85C2×Q8×D43—22no—
86C2×Q8×D43—24no—
87C2×Q8×D43C2×C418yescomplemented
88C2×Q8×D43C2314yes—
89C22×C22⋊D43—21no—
90C23×Dic43—21no—
91C23×Dic43—21no—
92C22×C4×D43—21no—
93C22×C4×D43—21no—
94C22×C4×D43D411yescharacteristic
95C22×C4×D43D411yescharacteristic
96C22×C4×D43C2311yescharacteristic
97#13063354C2×C4164yesdirect product factor
98C2×Dic172C2×C418yescomplemented
99C2×Dic172C2314yes—
100C2×#10621885C2×C418yescomplemented
101C2×#10621885C2314yes—
102C2×#10621883C2×C418yescomplemented
103C2×#10621883C2314yes—
104C2×#10621872—24no—
105C2×#10621872C2×C418yescomplemented
106C2×#10621872C2314yes—
107C2×#10621872C2314yes—
108C22×C43⋊C8C2311yescharacteristic
109C22×C43⋊C8C2311yescharacteristic
110Q8×Dic43—22no—
111Q8×Dic43C2314yes—
112C4×Dic86—22no—
113C4×Dic86—22no—
114C4×Dic86—28no—
115C4×Dic86C2314yes—
116C4×Dic86C2314yes—
117#13063290—22no—
118#13063290—28no—
119#13063290—22no—
120#13063290C2314yes—
121#13063290C2314yes—
122D4×Dic43—22no—
123D4×Dic43C2314yes—
124C4×C22⋊D43—28no—
125(C22⋊D43)⋊C4—28no—
126#13063283—22no—
127#13063283C2314yes—
128#13063281—28no—
129C2×C4⋊Dic43—21no—
130C2×C4⋊Dic43C2311yescharacteristic
131C2×C4⋊Dic43C2311yescharacteristic
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C4⋊C4×D43—28no—
138C4⋊C4×D43—22no—
139C4⋊C4×D43C2314yes—
140C2×C22⋊Dic43—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×C4×Dic43—21no—
143C2×C4×Dic43—21no—
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43—21no—
147C2×C4×Dic43—21no—
148C2×C4×Dic43—28no—
149C2×C4×Dic43D411yescharacteristic
150C2×C4×Dic43D411yescharacteristic
151C2×C4×Dic43C2311yescharacteristic
152C42×D43—28no—
153C42×D43D414yes—
154C42×D43C2314yes—
155#13063259C2314yes—
156#13063258C2314yes—
157#13063256C2314yes—
158#13063250C2314yes—
159#13063250C2314yes—
160#13063249C2314yes—
161#13063248C2314yes—
162#13063248C2314yes—
163#13063246C2314yes—
164#13063235C2314yes—
165#13063235C2314yes—
166C4×C43⋊C8C2314yes—
167C22×Q8×C43C2311yescharacteristic
168C22×D4×C43C2311yescharacteristic
169C23×C4×C43—21no—
170C2×SD16×C43C2×C418yescomplemented
171C2×SD16×C43C2314yes—
172C22×C8×C43C2311yescharacteristic
173C22×C8×C43C2311yescharacteristic
174C4×Q8×C43—22no—
175C4×Q8×C43C2314yes—
176C4×D4×C43—22no—
177C4×D4×C43C2314yes—
178C2×C4⋊C4×C43—21no—
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C22⋊C4×C43—21no—
182C2×C42×C43—21no—
183C2×C42×C43C2311yescharacteristic
184#106×C43C2314yes—
185#103×C43C2314yes—
186#102×C43C2314yes—
187C4×C8×C43C2314yes—
188C24×C43—21no—
189C23×D43C2×D411yescharacteristic
190C2×Q8×C43—21no—
191C2×Q8×C43—22no—
192C2×Q8×C43C22×C414yes—
193C2×Q8×C43C2412yes—
194C2×D4×C43—21no—
195C2×D4×C43—22no—
196C2×D4×C43C22×C414yes—
197C2×D4×C43C2412yes—
198C22×C4×C43—24no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—44no—
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2411yescharacteristic
206C2×C22⋊D43—28no—
207C2×C22⋊D43—24no—
208C22×Dic43—28no—
209C22×Dic43—24no—
210C22×Dic43—24no—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—44no—
216C22×Dic43C2×D411yescharacteristic
217C22×Dic43C2×D411yescharacteristic
218C22×Dic43C2×D411yescharacteristic
219Q8×D43—216no—
220Q8×D43—28no—
221Q8×D43C22×C4116yescomplemented
222#10621900—216no—
223#10621900—28no—
224#10621900C22×C4116yes—
225C2×C4×D43—24no—
226C2×C4×D43—28no—
227C2×C4×D43—24no—
228C2×C4×D43—24no—
229C2×C4×D43—42no—
230C2×C4×D43—44no—
231C2×C4×D43C22×C414yes—
232C2×C4×D43C2×D414yes—
233C2×C4×D43C2×D414yes—
234C2×C4×D43C2×D412yes—
235C2×C4×D43#4114yes—
236C2×C4×D43C2412yes—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86—22no—
240C2×Dic86—22no—
241C2×Dic86—28no—
242C2×Dic86—24no—
243C2×Dic86C22×C414yes—
244C2×Dic86C22×C414yes—
245C2×Dic86C2412yes—
246C2×Dic86C2412yes—
247SD16×C43C22×C4116yescomplemented
248C2×C8×C43—22no—
249C2×C8×C43C22×C414yes—
250C2×C8×C43C2412yes—
251C2×C8×C43C2412yes—
252C4⋊C4×C43—24no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43C2412yes—
256C4⋊C4×C43C2412yes—
257C22⋊C4×C43—24no—
258C42×C43—24no—
259C42×C43C2×D412yes—
260C42×C43C2412yes—
261C22⋊Dic43—24no—
262#10621885C22×C4116yescomplemented
263#10621883C22×C4116yescomplemented
264(C2×D43)⋊C4—24no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—24no—
268C4⋊Dic43C2412yes—
269C4⋊Dic43C2412yes—
270Dic43⋊C4—24no—
271Dic43⋊C4—24no—
272Dic43⋊C4—24no—
273Dic43⋊C4—24no—
274Dic43⋊C4—24no—
275C4×Dic43—24no—
276C4×Dic43—24no—
277C4×Dic43—24no—
278C4×Dic43—24no—
279C4×Dic43—24no—
280C4×Dic43—24no—
281C4×Dic43C2×D412yes—
282C4×Dic43C2×D414yes—
283C4×Dic43C2×D414yes—
284C4×Dic43C2412yes—
285C2×C43⋊C8—22no—
286C2×C43⋊C8C22×C414yes—
287C2×C43⋊C8C2412yes—
288C2×C43⋊C8C2412yes—
289Dic172C22×C4116yescomplemented
290#10621872—28no—
291#10621872C22×C4116yescomplemented
292C23×C43—24no—
293C23×C43—22no—
294C23×C43—42no—
295C23×C43—42no—
296C23×C43C22×D411yescharacteristic
297C22×D43—22no—
298C22×D43—22no—
299C22×D43C4×D414yes—
300C22×D43C22×D412yes—
301Q8×C43—24no—
302Q8×C43—22no—
303Q8×C43C23×C414yes—
304D4×C43—24no—
305D4×C43—22no—
306D4×C43C23×C414yes—
307C2×C4×C43—24no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—42no—
313C2×C4×C43—42no—
314C2×C4×C43—48no—
315C2×C4×C43#13714yescomplemented
316C2×C4×C43C23×C412yes—
317C2×C4×C43C22×D412yes—
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C22×D412yes—
320C2×C4×C43C2×#4112yes—
321C2×C4×C43C2511yescharacteristic
322C22⋊D43—216no—
323C2×Dic43—24no—
324C2×Dic43—24no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—216no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—48no—
333C2×Dic43—42no—
334C2×Dic43—42no—
335C2×Dic43C4×D414yes—
336C2×Dic43C22×D412yes—
337C2×Dic43C22×D412yes—
338C2×Dic43C22×D412yes—
339C4×D43—216no—
340C4×D43—28no—
341C4×D43—44no—
342C4×D43—48no—
343C4×D43C4×D418yes—
344C4×D43C23×C414yes—
345C4×D43C2×#4114yes—
346Dic86—24no—
347Dic86—24no—
348Dic86—22no—
349Dic86—22no—
350Dic86—216no—
351Dic86C23×C414yes—
352Dic86C23×C414yes—
353C8×C43—22no—
354C8×C43C23×C414yes—
355C43⋊C8—22no—
356C43⋊C8C23×C414yes—
357C2×C4×#137—431nomaximal, Sylow
358C22×C43—24no—
359C22×C43—48no—
360C22×C43—42no—
361C22×C43—42no—
362C22×C43C2×C4×D412yes—
363C22×C43C2×#13712yes—
364C22×C43#57512yes—
365C22×C43C23×D411yescharacteristic
366C2×D43—28no—
367C2×D43—22no—
368C2×D43—22no—
369C2×D43C2×C4×D414yes—
370C4×C43—24no—
371C4×C43—22no—
372C4×C43—42no—
373C4×C43—42no—
374C4×C43C2×C4×D412yes—
375C4×C43C2×#13714yescomplemented
376C4×C43C24×C411yescharacteristic
377C4×C43C22×#4111yescharacteristic
378Dic43—24no—
379Dic43—24no—
380Dic43—22no—
381Dic43—22no—
382Dic43—42no—
383Dic43—42no—
384Dic43C2×C4×D414yes—
385C22×#137—431no—
386C2×C4×#41—431no—
387C22×C4×Q8—431no—
388C4×#137—4316no—
389C2×#441—431no—
390C2×#441—431no—
391C2×#440—431no—
392C2×#440—431no—
393C2×C4×Q16—431no—
394C2×C4×Q16—431no—
395C2×C4×SD16—431no—
396C2×C4×SD16D4311yescharacteristic, complemented
397C2×#428—431no—
398C2×#417—431no—
399C2×#419—431no—
400C2×C4×M16—431no—
401C2×C43—44no—
402C2×C43C4×#13714yescomplemented
403C2×C43C22×C4×D411yescharacteristic
404C2×C43C22×#13711yescharacteristic
405C2×C43C2×#57511yescharacteristic
406D43—24no—
407C22×#41—431no—
408C23×Q8—431no—
409C2×#137—438no—
410C2×#137—4316no—
411C22×Q16—431no—
412C22×Q16—431no—
413C22×SD16—431no—
414C22×SD16C2×D4311yescharacteristic
415C22×M16—431no—
416C22×M16—431no—
417C4×#41—438no—
418C4×#41—864no—
419C2×C4×Q8—431no—
420C2×C4×Q8—438no—
421C2×C4×Q8—431no—
422C2×C4×Q8—431no—
423C2×C4×Q8—431no—
424C2×C4×Q8—431no—
425C2×C4×Q8—861no—
426C2×C4×Q8—861no—
427C2×C4×Q8—864no—
428C2×C4×Q8C2×D4311yescharacteristic
429C2×C4×D4—431no—
430C2×C4×D4—861no—
431C2×C4×D4—861no—
432C2×C4×D4C2×D4311yescharacteristic
433C2×#117—431no—
434C2×#117—861no—
435C22×C4⋊C4—431no—
436C22×C4⋊C4—861no—
437C22×C42—431no—
438C22×C42—861no—
439C22×C42—861no—
440#441—438no—
441#441—438no—
442#440—438no—
443#440—438no—
444C4×Q16—438no—
445C4×Q16—438no—
446C4×SD16—438no—
447C4×SD16C2×D4318yescomplemented
448#428—438no—
449C2×#107—431no—
450C2×#107—431no—
451C2×#106—431no—
452C2×#106C2×D4311yescharacteristic
453#419—438no—
454#417—438no—
455C2×#103—431no—
456C2×#103—431no—
457C2×#103—431no—
458C2×#103—431no—
459C2×#103—431no—
460C2×#103C2×D4311yescharacteristic
461C2×#102—431no—
462C2×#102C2×D4311yescharacteristic
463C4×M16—438no—
464C2×#97—431no—
465C2×#97—431no—
466C2×C4×C8—431no—
467C2×C4×C8C2×D4311yescharacteristic
468C43C2×C4×#13711yescharacteristic, complemented, Sylow
469C2×#41—438no—
470C2×#41—434no—
471C2×#41—862no—
472C2×#41—864no—
473C22×Q8—438no—
474C22×Q8—434no—
475C22×Q8—431no—
476C22×Q8—431no—
477C22×Q8—861no—
478C22×Q8—862no—
479C22×Q8—864no—
480C22×Q8C22×D4311yescharacteristic
481C22×D4—861no—
482C22×D4C22×D4311yescharacteristic
483C23×C4—21no—
484C23×C4—431no—
485C23×C4—431no—
486C23×C4—431no—
487C23×C4—861no—
488C23×C4—861no—
489C23×C4—861no—
490C23×C4—861no—
491#137—4364no—
492C2×Q16—438no—
493C2×Q16—434no—
494C2×Q16—438no—
495C2×Q16—434no—
496C2×SD16—438no—
497C2×SD16—434no—
498C2×SD16C4×D4318yescomplemented
499C2×SD16C22×D4314yes—
500C2×M16—438no—
501C2×M16—434no—
502C2×M16—434no—
503C2×M16—864no—
504C22×C8—431no—
505C22×C8—431no—
506C22×C8C22×D4311yescharacteristic
507C22×C8C22×D4311yescharacteristic
508C4×Q8—22no—
509C4×Q8—434no—
510C4×Q8—434no—
511C4×Q8—434no—
512C4×Q8—434no—
513C4×Q8—434no—
514C4×Q8—868no—
515C4×Q8—868no—
516C4×Q8—862no—
517C4×Q8—862no—
518C4×Q8—862no—
519C4×Q8—862no—
520C4×Q8—862no—
521C4×Q8C22×D4314yes—
522C4×D4—22no—
523C4×D4—434no—
524C4×D4—862no—
525C4×D4—868no—
526C4×D4—868no—
527C4×D4C22×D4314yes—
528#117—434no—
529#117—868no—
530#117—862no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—431no—
533C2×C4⋊C4—431no—
534C2×C4⋊C4—434no—
535C2×C4⋊C4—862no—
536C2×C4⋊C4—868no—
537C2×C4⋊C4—861no—
538C2×C4⋊C4—861no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4C22×D4311yescharacteristic
544C2×C4⋊C4C22×D4311yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—861no—
547C2×C22⋊C4—861no—
548C2×C42—21no—
549C2×C42—431no—
550C2×C42—431no—
551C2×C42—431no—
552C2×C42—434no—
553C2×C42—434no—
554C2×C42—868no—
555C2×C42—868no—
556C2×C42—861no—
557C2×C42—861no—
558C2×C42—861no—
559C2×C42—861no—
560C2×C42—861no—
561C2×C42—861no—
562C2×C42C22×D4311yescharacteristic
563#107—434no—
564#107—434no—
565#106—434no—
566#106C22×D4314yes—
567#103—434no—
568#103—434no—
569#103—434no—
570#103—434no—
571#103—434no—
572#103C22×D4314yes—
573#102—434no—
574#102C22×D4314yes—
575#97—434no—
576#97—434no—
577C4×C8—434no—
578C4×C8C22×D4314yes—
579C24—21no—
580C24—431no—
581#41—4316no—
582#41—8616no—
583#41—868no—
584C2×Q8—21no—
585C2×Q8—22no—
586C2×Q8—4316no—
587C2×Q8—434no—
588C2×Q8—434no—
589C2×Q8—432no—
590C2×Q8—432no—
591C2×Q8—864no—
592C2×Q8—868no—
593C2×Q8—8616no—
594C2×Q8—868no—
595C2×Q8—861no—
596C2×Q8—861no—
597C2×Q8—862no—
598C2×Q8—862no—
599C2×Q8C2×C4×D4314yes—
600C2×Q8C23×D4312yes—
601C2×D4—21no—
602C2×D4—22no—
603C2×D4—864no—
604C2×D4—868no—
605C2×D4C2×C4×D4314yes—
606C2×D4C23×D4312yes—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—24no—
611C22×C4—44no—
612C22×C4—431no—
613C22×C4—434no—
614C22×C4—432no—
615C22×C4—434no—
616C22×C4—432no—
617C22×C4—431no—
618C22×C4—431no—
619C22×C4—434no—
620C22×C4—434no—
621C22×C4—864no—
622C22×C4—868no—
623C22×C4—864no—
624C22×C4—864no—
625C22×C4—868no—
626C22×C4—864no—
627C22×C4—861no—
628C22×C4—861no—
629C22×C4—864no—
630C22×C4—861no—
631C22×C4—861no—
632C22×C4—1722no—
633C22×C4—1724no—
634C22×C4—1724no—
635C22×C4D4×D4311yescharacteristic
636C22×C4D4×D4311yescharacteristic
637C22×C4C23×D4311yescharacteristic
638Q16—4316no—
639Q16—4316no—
640SD16—4316no—
641SD16C2×C4×D43116yescomplemented
642M16—4316no—
643M16—868no—
644C2×C8—22no—
645C2×C8—434no—
646C2×C8—432no—
647C2×C8—432no—
648C2×C8—862no—
649C2×C8C2×C4×D4314yes—
650C2×C8C23×D4312yes—
651C2×C8C23×D4312yes—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—432no—
656C4⋊C4—432no—
657C4⋊C4—864no—
658C4⋊C4—864no—
659C4⋊C4—864no—
660C4⋊C4—864no—
661C4⋊C4—861no—
662C4⋊C4—861no—
663C4⋊C4—864no—
664C4⋊C4—864no—
665C4⋊C4C23×D4312yes—
666C4⋊C4C23×D4312yes—
667C22⋊C4—24no—
668C22⋊C4—864no—
669C22⋊C4—864no—
670C42—24no—
671C42—434no—
672C42—434no—
673C42—432no—
674C42—432no—
675C42—864no—
676C42—864no—
677C42—864no—
678C42—864no—
679C42—864no—
680C42—864no—
681C42D4×D4312yes—
682C42C23×D4312yes—
683C23—24no—
684C23—22no—
685C23—42no—
686C23—42no—
687C23—434no—
688C23—432no—
689C23—862no—
690C23—862no—
691C23C2×D4×D4311yescharacteristic
692Q8—24no—
693Q8—22no—
694Q8—434no—
695Q8—434no—
696Q8—8616no—
697Q8—864no—
698Q8—864no—
699Q8—862no—
700Q8—862no—
701Q8C22×C4×D4314yes—
702D4—24no—
703D4—22no—
704D4—8616no—
705D4C22×C4×D4314yes—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—48no—
714C2×C4—434no—
715C2×C4—432no—
716C2×C4—438no—
717C2×C4—434no—
718C2×C4—434no—
719C2×C4—432no—
720C2×C4—432no—
721C2×C4—8616no—
722C2×C4—8616no—
723C2×C4—864no—
724C2×C4—864no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—868no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—1724no—
733C2×C4—1728no—
734C2×C4—1728no—
735C2×C4—1722no—
736C2×C4—1722no—
737C2×C4#1306335414yesdirect product factor
738C2×C4C22×C4×D4312yes—
739C2×C4C2×D4×D4312yes—
740C2×C4C2×D4×D4311yescharacteristic
741C2×C4C2×D4×D4312yes—
742C2×C4#41×D4312yes—
743C2×C4C24×D4311yescharacteristic
744C8—22no—
745C8—434no—
746C8—862no—
747C8C22×C4×D4314yes—
748C22—24no—
749C22—42no—
750C22—42no—
751C22—48no—
752C22—434no—
753C22—862no—
754C22—862no—
755C22—868no—
756C22C4×D4×D4312yes—
757C22C2×#1306335412yes—
758C22#1458369612yes—
759C22C22×D4×D4311yescharacteristic
760C4—22no—
761C4—24no—
762C4—42no—
763C4—42no—
764C4—434no—
765C4—862no—
766C4—862no—
767C4—864no—
768C4—864no—
769C4—1722no—
770C4—1722no—
771C4C4×D4×D4312yes—
772C4C2×#1306335414yesdirect product factor
773C4C23×C4×D4311yescharacteristic
774C4C2×#41×D4311yescharacteristic
775C2—44no—
776C2—864no—
777C2C4×#1306335414yesdirect product factor
778C2C2×C4×D4×D4311yescharacteristic
779C2C22×#1306335411yescharacteristic
780C2C2×#1458369611yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C4×SD16×C43C2
socleC23×C43C22×D4
prime radicalC22×#10621900C22
cosocleC2×C4×C43C25
hypercenterC2×C4×SD16D43
hypocenterC43C2×C4×#137
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
3. C2×C4×Q8×D43C2semidirect
4. C4×#13063354C2direct (N × H)
5. C2×#14583005C2semidirect
6. C2×#14583003C2semidirect
7. C2×#14583000C2semidirect
8. C2×#14582996C2semidirect
9. C2×C4×Dic172C2semidirect
10. C2×C4×#10621885C2semidirect
11. C2×C4×#10621883C2semidirect
12. C2×#14582938C2semidirect
14. C2×#14582906C2semidirect
15. C2×C4×#10621872C2semidirect
16. C2×C4×SD16×C43C2semidirect
19. C2×#13063354C4direct (N × H)
36. C4×Q8×D43C22semidirect
47. #14583005C22semidirect
48. #14583003C22semidirect
49. #14583000C22semidirect
50. #14582996C22semidirect
51. C4×Dic172C22semidirect
52. C4×#10621885C22semidirect
53. C4×#10621883C22semidirect
54. #14582938C22semidirect
58. #14582906C22semidirect
66. C4×#10621872C22semidirect
73. C4×SD16×C43C22semidirect
87. C2×Q8×D43C2×C4semidirect
97. #13063354C2×C4direct (N × H)
98. C2×Dic172C2×C4semidirect
100. C2×#10621885C2×C4semidirect
102. C2×#10621883C2×C4semidirect
105. C2×#10621872C2×C4semidirect
170. C2×SD16×C43C2×C4semidirect
221. Q8×D43C22×C4semidirect
247. SD16×C43C22×C4semidirect
262. #10621885C22×C4semidirect
263. #10621883C22×C4semidirect
289. Dic172C22×C4semidirect
291. #10621872C22×C4semidirect
315. C2×C4×C43#137semidirect
375. C4×C43C2×#137semidirect
396. C2×C4×SD16D43semidirect
402. C2×C43C4×#137semidirect
447. C4×SD16C2×D43semidirect
468. C43C2×C4×#137semidirect
498. C2×SD16C4×D43semidirect
641. SD16C2×C4×D43semidirect
737. C2×C4#13063354direct (N × H)
772. C4C2×#13063354direct (N × H)
777. C2C4×#13063354direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633542
C2×C4×#106219002
C2×C4×Q8×D432
C4×#130633542
C2×#145830052
C2×#145830032
C2×#145830002
C2×#145829962
C2×C4×Dic1722
C2×C4×#106218852
C2×C4×#106218832
C2×#145829382
C2×#145828972
C2×#145829062
C2×C4×#106218722
C2×C4×SD16×C432
C2×C4×#13743