Finite Group Databasebeta

← C2×#19143411 #25960668

Subgroups — C2×#19143411 #25960668

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×#13063357C211yesmaximal, characteristic
2C2×C4×#10621902C211yesmaximal, characteristic
3C2×C4×Q8×D43C211yesmaximal, characteristic, complemented
4#19143411C2116yesmaximal, direct product factor
5C2×#14583004C211yesmaximal, characteristic, complemented
6C2×#14583001C211yesmaximal, characteristic, complemented
7C2×#14582997C211yesmaximal, characteristic, complemented
8C2×Q16×Dic43C211yesmaximal, characteristic, complemented
9C2×#14582991C211yesmaximal, characteristic, complemented
10C2×#14582986C211yesmaximal, characteristic, complemented
11C2×#14582984C211yesmaximal, characteristic, complemented
12C2×#14582938C211yesmaximal, characteristic, complemented
13C2×#14582899C211yesmaximal, characteristic
14C2×#14582906C211yesmaximal, characteristic, complemented
15C2×#14582851C211yesmaximal, characteristic, complemented
16C2×C43×#441C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C2×#13063357C4116yescomplemented
20C2×#13063357C2218yes—
21C22×#10621885C2211yescharacteristic
22C22×#10621873C2211yescharacteristic
23C22×#10621884C2211yescharacteristic
24C22×#10621872C2211yescharacteristic
25C22×#10621872C2211yescharacteristic
26C4×#10621902—24no—
27C4×#10621902C2218yes—
28C2×Q8×Dic43C2211yescharacteristic
29C2×Q8×Dic43C2211yescharacteristic
30C2×C4×Dic86—21no—
31C2×C4×Dic86C2211yescharacteristic
32C2×#13063290—21no—
33C2×#13063290C2211yescharacteristic
34C4×Q8×D43—24no—
35C4×Q8×D43C2218yescomplemented
36C2×C4×D172—21no—
37C2×C4×D172C2211yescharacteristic
38C2×#13063287—21no—
39C2×#13063287C2211yescharacteristic
40C2×#13063283—21no—
41C2×#13063283C2211yescharacteristic
42C2×C4⋊C4×D43—21no—
43C2×C4⋊C4×D43C2211yescharacteristic
44C2×C42×D43—21no—
45C2×C42×D43—21no—
46C2×C42×D43C2211yescharacteristic
47#14583004C2218yescomplemented
48#14583001C2218yescomplemented
49#14582997C2218yescomplemented
50Q16×Dic43C2218yescomplemented
51#14582991C2218yescomplemented
52#14582986C2218yescomplemented
53#14582984C2218yescomplemented
54#14582938C2218yescomplemented
55C2×#13063259C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58#14582906C2218yescomplemented
59#14582899C2218yes—
60C2×#13063250C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66#14582851C2218yescomplemented
67C2×#13063236C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C2×C8×Dic43C2211yescharacteristic
70C22×Q16×C43C2211yescharacteristic
71C2×C4×Q8×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic
73C43×#441C2218yescomplemented
74C2×#106×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#103×C43C2211yescharacteristic
77C2×#97×C43C2211yescharacteristic
78C2×#10621902—22no—
79C2×#10621902—24no—
80C2×#10621902C2×C418yes—
81C2×#10621902C2314yes—
82C22×Dic86—21no—
83C22×Dic86C2311yescharacteristic
84C2×Q8×D43—22no—
85C2×Q8×D43—24no—
86C2×Q8×D43C2×C418yescomplemented
87C2×Q8×D43C2314yes—
88C22×D172—21no—
89C22×D172C2311yescharacteristic
90C22×C4×D43—21no—
91C22×C4×D43—21no—
92C22×C4×D43—21no—
93C22×C4×D43—21no—
94C22×C4×D43—21no—
95C22×C4×D43D411yescharacteristic
96C22×C4×D43D411yescharacteristic
97C22×C4×D43C2311yescharacteristic
98#13063357C2×C4164yescomplemented
99C2×#10621885C2×C418yescomplemented
100C2×#10621885C2314yes—
101C2×#10621873C2×C418yescomplemented
102C2×#10621873C2314yes—
103C2×#10621884C2×C418yescomplemented
104C2×#10621884C2314yes—
105C2×#10621872—24no—
106C2×#10621872C2×C418yescomplemented
107C2×#10621872C2314yes—
108C2×#10621872C2314yes—
109C22×C43⋊C8C2311yescharacteristic
110C22×C43⋊C8C2311yescharacteristic
111Q8×Dic43—22no—
112Q8×Dic43—22no—
113Q8×Dic43C2314yes—
114Q8×Dic43C2314yes—
115C4×Dic86—22no—
116C4×Dic86—28no—
117C4×Dic86C2314yes—
118#13063290—22no—
119#13063290—28no—
120#13063290C2314yes—
121C4×D172—28no—
122C4×D172—22no—
123C4×D172C2314yes—
124#13063287—28no—
125#13063287—22no—
126#13063287C2314yes—
127#13063283—22no—
128#13063283—28no—
129#13063283C2314yes—
130C2×C4⋊Dic43—21no—
131C2×C4⋊Dic43—21no—
132C2×C4⋊Dic43C2311yescharacteristic
133C2×C4⋊Dic43C2311yescharacteristic
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C4⋊C4×D43—28no—
138C4⋊C4×D43—22no—
139C4⋊C4×D43C2314yes—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×C4×Dic43—21no—
144C2×C4×Dic43—21no—
145C2×C4×Dic43—21no—
146C2×C4×Dic43—21no—
147C2×C4×Dic43—21no—
148C2×C4×Dic43D411yescharacteristic
149C2×C4×Dic43D411yescharacteristic
150C2×C4×Dic43C2311yescharacteristic
151C42×D43—28no—
152C42×D43—28no—
153C42×D43D414yes—
154C42×D43C2314yes—
155#13063259C2314yes—
156#13063258C2314yes—
157#13063256C2314yes—
158#13063250C2314yes—
159#13063249C2314yes—
160#13063249C2314yes—
161#13063248C2314yes—
162#13063247C2314yes—
163#13063245C2314yes—
164#13063236C2314yes—
165C8×Dic43C2314yes—
166C8×Dic43C2314yes—
167C22×Q8×C43C2311yescharacteristic
168C22×Q8×C43C2311yescharacteristic
169C2×Q16×C43C2×C418yescomplemented
170C2×Q16×C43C2314yes—
171C22×C8×C43C2311yescharacteristic
172C22×C8×C43C2311yescharacteristic
173C4×Q8×C43—22no—
174C4×Q8×C43—22no—
175C4×Q8×C43C2314yes—
176C4×Q8×C43C2314yes—
177C2×C4⋊C4×C43—21no—
178C2×C4⋊C4×C43—21no—
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C42×C43—21no—
182C2×C42×C43—21no—
183C2×C42×C43C2311yescharacteristic
184#106×C43C2314yes—
185#103×C43C2314yes—
186#103×C43C2314yes—
187#97×C43C2314yes—
188C23×D43—21no—
189C23×D43C2×D411yescharacteristic
190C2×Q8×C43—21no—
191C2×Q8×C43—21no—
192C2×Q8×C43—22no—
193C2×Q8×C43—22no—
194C2×Q8×C43C22×C414yes—
195C2×Q8×C43C22×C414yes—
196C2×Q8×C43C2412yes—
197C2×Q8×C43C2412yes—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2411yescharacteristic
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43C2×D411yescharacteristic
209C22×Dic43C2×D411yescharacteristic
210C22×Dic43C2×D411yescharacteristic
211#10621902—216no—
212#10621902—28no—
213#10621902C22×C4116yes—
214Q8×D43—216no—
215Q8×D43—28no—
216Q8×D43C22×C4116yescomplemented
217C2×D172—21no—
218C2×D172—22no—
219C2×D172—28no—
220C2×D172—24no—
221C2×D172C22×C414yes—
222C2×D172C2412yes—
223C2×C4×D43—28no—
224C2×C4×D43—24no—
225C2×C4×D43—24no—
226C2×C4×D43—24no—
227C2×C4×D43—24no—
228C2×C4×D43—28no—
229C2×C4×D43—24no—
230C2×C4×D43—24no—
231C2×C4×D43—42no—
232C2×C4×D43—44no—
233C2×C4×D43—44no—
234C2×C4×D43—44no—
235C2×C4×D43C22×C414yes—
236C2×C4×D43C2×D414yes—
237C2×C4×D43C2×D414yes—
238C2×C4×D43C2×D412yes—
239C2×C4×D43#4114yes—
240C2×C4×D43C2412yes—
241C2×Dic86—21no—
242C2×Dic86—22no—
243C2×Dic86—28no—
244C2×Dic86—24no—
245C2×Dic86C22×C414yes—
246C2×Dic86C2412yes—
247Q16×C43C22×C4116yescomplemented
248C2×C8×C43—22no—
249C2×C8×C43C22×C414yes—
250C2×C8×C43C2412yes—
251C2×C8×C43C2412yes—
252C4⋊C4×C43—24no—
253C4⋊C4×C43—24no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43C2412yes—
257C4⋊C4×C43C2412yes—
258C42×C43—24no—
259C42×C43—24no—
260C42×C43C2×D412yes—
261C42×C43C2412yes—
262#10621885C22×C4116yescomplemented
263#10621884C22×C4116yescomplemented
264(C2×D43)⋊C4—24no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43—24no—
270C4⋊Dic43—24no—
271C4⋊Dic43C2412yes—
272C4⋊Dic43C2412yes—
273Dic43⋊C4—24no—
274Dic43⋊C4—24no—
275Dic43⋊C4—24no—
276C4×Dic43—24no—
277C4×Dic43—24no—
278C4×Dic43—24no—
279C4×Dic43—24no—
280C4×Dic43—24no—
281C4×Dic43C2×D414yes—
282C4×Dic43C2×D412yes—
283C4×Dic43C2×D414yes—
284C4×Dic43C2412yes—
285C2×C43⋊C8—22no—
286C2×C43⋊C8C22×C414yes—
287C2×C43⋊C8C2412yes—
288C2×C43⋊C8C2412yes—
289#10621873C22×C4116yescomplemented
290#10621872—28no—
291#10621872C22×C4116yescomplemented
292C23×C43C22×D411yescharacteristic
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—24no—
296C22×D43—22no—
297C22×D43—42no—
298C22×D43—42no—
299C22×D43C4×D414yes—
300C22×D43C22×D412yes—
301Q8×C43—24no—
302Q8×C43—24no—
303Q8×C43—22no—
304Q8×C43—22no—
305Q8×C43C23×C414yes—
306Q8×C43C23×C414yes—
307C2×C4×C43—24no—
308C2×C4×C43—24no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43C23×C412yes—
318C2×C4×C43C22×D412yes—
319C2×C4×C43C22×D412yes—
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C2×#4112yes—
322C2×C4×C43C2511yescharacteristic
323C2×Dic43—24no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—42no—
329C2×Dic43—42no—
330C2×Dic43C4×D414yes—
331C2×Dic43#13714yescomplemented
332C2×Dic43C22×D412yes—
333C2×Dic43C22×D412yes—
334C2×Dic43C22×D412yes—
335D172—216no—
336D172—24no—
337D172—22no—
338D172C23×C414yes—
339C4×D43—216no—
340C4×D43—216no—
341C4×D43—28no—
342C4×D43—44no—
343C4×D43—48no—
344C4×D43—48no—
345C4×D43—48no—
346C4×D43C4×D418yes—
347C4×D43C23×C414yes—
348C4×D43C2×#4114yes—
349Dic86—24no—
350Dic86—22no—
351Dic86—216no—
352Dic86C23×C414yes—
353C8×C43—22no—
354C8×C43C23×C414yes—
355C43⋊C8—22no—
356C43⋊C8C23×C414yes—
357C2×C4×#137—431nomaximal, Sylow
358C22×C43C2×C4×D412yes—
359C22×C43C2×#13712yes—
360C22×C43#57512yes—
361C22×C43C23×D411yescharacteristic
362C2×D43—28no—
363C2×D43—22no—
364C2×D43—22no—
365C2×D43—24no—
366C2×D43—48no—
367C2×D43—42no—
368C2×D43—42no—
369C2×D43C2×C4×D414yes—
370C4×C43—24no—
371C4×C43—24no—
372C4×C43—22no—
373C4×C43—22no—
374C4×C43—42no—
375C4×C43—42no—
376C4×C43C2×C4×D412yes—
377C4×C43C24×C411yescharacteristic
378C4×C43C22×#4111yescharacteristic
379Dic43—24no—
380Dic43—22no—
381Dic43—42no—
382Dic43—42no—
383Dic43C2×C4×D414yes—
384Dic43C2×#13714yescomplemented
385C22×#137—431no—
386C2×C4×#41—431no—
387C22×C4×Q8—431no—
388C4×#137—4316no—
389C2×#441—431no—
390C2×#441D4311yescharacteristic, complemented
391C2×#440—431no—
392C2×#440—431no—
393C2×C4×Q16—431no—
394C2×C4×Q16—431no—
395C2×C4×SD16—431no—
396C2×C4×SD16—431no—
397C2×#428—431no—
398C2×#417—431no—
399C2×#419—431no—
400C2×C4×M16—431no—
401C2×C43C4×#13714yescomplemented
402C2×C43C22×C4×D411yescharacteristic
403C2×C43C22×#13711yescharacteristic
404C2×C43C2×#57511yescharacteristic
405D43—24no—
406D43—44no—
407C22×#41—431no—
408C23×Q8—431no—
409C2×#137—438no—
410C2×#137—4316no—
411C22×Q16—431no—
412C22×Q16C2×D4311yescharacteristic
413C22×SD16—431no—
414C22×SD16—431no—
415C22×M16—431no—
416C22×M16—431no—
417C4×#41—438no—
418C4×#41—864no—
419C2×C4×Q8—431no—
420C2×C4×Q8—431no—
421C2×C4×Q8—438no—
422C2×C4×Q8—431no—
423C2×C4×Q8—431no—
424C2×C4×Q8—861no—
425C2×C4×Q8—861no—
426C2×C4×Q8—864no—
427C2×C4×Q8C2×D4311yescharacteristic
428C2×C4×Q8C2×D4311yescharacteristic
429C2×C4×D4—431no—
430C2×C4×D4—431no—
431C2×C4×D4—861no—
432C2×C4×D4—861no—
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#441C2×D4318yescomplemented
442#440—438no—
443#440—438no—
444C4×Q16—438no—
445C4×Q16—438no—
446C4×SD16—438no—
447C4×SD16—438no—
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×#103C2×D4311yescharacteristic
460C2×#103C2×D4311yescharacteristic
461C2×#102—431no—
462C2×#102—431no—
463C4×M16—438no—
464C2×#97—431no—
465C2×#97C2×D4311yescharacteristic
466C2×C4×C8—431no—
467C2×C4×C8—431no—
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—861no—
477C22×Q8—862no—
478C22×Q8—864no—
479C22×Q8C22×D4311yescharacteristic
480C22×Q8C22×D4311yescharacteristic
481C22×D4—431no—
482C22×D4—861no—
483C23×C4—431no—
484C23×C4—431no—
485C23×C4—431no—
486C23×C4—861no—
487C23×C4—861no—
488C23×C4—861no—
489C23×C4—861no—
490C23×C4—861no—
491#137—4364no—
492C2×Q16—438no—
493C2×Q16—434no—
494C2×Q16C4×D4318yescomplemented
495C2×Q16C22×D4314yes—
496C2×SD16—438no—
497C2×SD16—434no—
498C2×SD16—438no—
499C2×SD16—434no—
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—22no—
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×Q8C22×D4314yes—
521C4×Q8C22×D4314yes—
522C4×D4—434no—
523C4×D4—434no—
524C4×D4—868no—
525C4×D4—862no—
526C4×D4—868no—
527C4×D4—862no—
528#117—434no—
529#117—868no—
530#117—862no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—431no—
534C2×C4⋊C4—431no—
535C2×C4⋊C4—434no—
536C2×C4⋊C4—862no—
537C2×C4⋊C4—868no—
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—861no—
546C2×C22⋊C4—861no—
547C2×C22⋊C4—861no—
548C2×C42—21no—
549C2×C42—21no—
550C2×C42—431no—
551C2×C42—431no—
552C2×C42—431no—
553C2×C42—434no—
554C2×C42—434no—
555C2×C42—868no—
556C2×C42—868no—
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#103C22×D4314yes—
572#103C22×D4314yes—
573#102—434no—
574#102—434no—
575#97—434no—
576#97C22×D4314yes—
577C4×C8—434no—
578C4×C8—434no—
579C24—431no—
580C24—861no—
581#41—4316no—
582#41—8616no—
583#41—868no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—4316no—
589C2×Q8—434no—
590C2×Q8—432no—
591C2×Q8—864no—
592C2×Q8—868no—
593C2×Q8—8616no—
594C2×Q8—868no—
595C2×Q8—861no—
596C2×Q8—862no—
597C2×Q8C2×C4×D4314yes—
598C2×Q8C2×C4×D4314yes—
599C2×Q8C23×D4312yes—
600C2×Q8C23×D4312yes—
601C2×D4—434no—
602C2×D4—432no—
603C2×D4—864no—
604C2×D4—868no—
605C2×D4—861no—
606C2×D4—862no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—431no—
612C22×C4—431no—
613C22×C4—434no—
614C22×C4—432no—
615C22×C4—434no—
616C22×C4—432no—
617C22×C4—431no—
618C22×C4—434no—
619C22×C4—434no—
620C22×C4—864no—
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—861no—
630C22×C4—864no—
631C22×C4—1722no—
632C22×C4—1724no—
633C22×C4—1724no—
634C22×C4—1724no—
635C22×C4D4×D4311yescharacteristic
636C22×C4D4×D4311yescharacteristic
637C22×C4C23×D4311yescharacteristic
638Q16—4316no—
639Q16C2×C4×D43116yescomplemented
640SD16—4316no—
641SD16—4316no—
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—24no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—432no—
657C4⋊C4—432no—
658C4⋊C4—864no—
659C4⋊C4—864no—
660C4⋊C4—864no—
661C4⋊C4—864no—
662C4⋊C4—861no—
663C4⋊C4—861no—
664C4⋊C4—864no—
665C4⋊C4C23×D4312yes—
666C4⋊C4C23×D4312yes—
667C22⋊C4—864no—
668C22⋊C4—864no—
669C22⋊C4—864no—
670C42—24no—
671C42—24no—
672C42—434no—
673C42—434no—
674C42—432no—
675C42—432no—
676C42—864no—
677C42—864no—
678C42—864no—
679C42—864no—
680C42—864no—
681C42D4×D4312yes—
682C42C23×D4312yes—
683C23—434no—
684C23—432no—
685C23—862no—
686C23—862no—
687C23—864no—
688C23—862no—
689C23—1722no—
690C23—1722no—
691C23C2×D4×D4311yescharacteristic
692Q8—24no—
693Q8—24no—
694Q8—22no—
695Q8—22no—
696Q8—434no—
697Q8—8616no—
698Q8—864no—
699Q8—862no—
700Q8C22×C4×D4314yes—
701Q8C22×C4×D4314yes—
702D4—434no—
703D4—8616no—
704D4—864no—
705D4—862no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—434no—
717C2×C4—434no—
718C2×C4—432no—
719C2×C4—432no—
720C2×C4—438no—
721C2×C4—434no—
722C2×C4—434no—
723C2×C4—432no—
724C2×C4—868no—
725C2×C4—8616no—
726C2×C4—8616no—
727C2×C4—864no—
728C2×C4—862no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—1724no—
733C2×C4—1728no—
734C2×C4—1728no—
735C2×C4—1728no—
736C2×C4—1722no—
737C2×C4—1722no—
738C2×C4C22×C4×D4312yes—
739C2×C4C2×D4×D4312yes—
740C2×C4C2×D4×D4312yes—
741C2×C4C2×D4×D4311yescharacteristic
742C2×C4#41×D4312yes—
743C2×C4C24×D4311yescharacteristic
744C8—22no—
745C8—434no—
746C8—862no—
747C8C22×C4×D4314yes—
748C22—434no—
749C22—862no—
750C22—862no—
751C22—868no—
752C22—864no—
753C22—1722no—
754C22—1722no—
755C22—1728no—
756C22C4×D4×D4312yes—
757C22#137×D4312yes—
758C22#1458369812yes—
759C22C22×D4×D4311yescharacteristic
760C4—22no—
761C4—22no—
762C4—24no—
763C4—24no—
764C4—42no—
765C4—42no—
766C4—434no—
767C4—434no—
768C4—862no—
769C4—864no—
770C4—1722no—
771C4—1722no—
772C4C4×D4×D4312yes—
773C4C23×C4×D4311yescharacteristic
774C4C2×#41×D4311yescharacteristic
775C2—864no—
776C2—1724no—
777C2#1914341114yesdirect product factor
778C2C2×C4×D4×D4311yescharacteristic
779C2C2×#137×D4311yescharacteristic
780C2C2×#1458369811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C43×#441C2
socleC23×C43C22×D4
prime radicalC22×#10621902C22
cosocleC2×C4×C43C25
hypercenterC2×#441D43
hypocenterC43C2×C4×#137
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. C2×C4×Q8×D43C2semidirect
4. #19143411C2direct (N × H)
5. C2×#14583004C2semidirect
6. C2×#14583001C2semidirect
7. C2×#14582997C2semidirect
8. C2×Q16×Dic43C2semidirect
9. C2×#14582991C2semidirect
10. C2×#14582986C2semidirect
11. C2×#14582984C2semidirect
12. C2×#14582938C2semidirect
14. C2×#14582906C2semidirect
15. C2×#14582851C2semidirect
16. C2×C43×#441C2semidirect
19. C2×#13063357C4semidirect
35. C4×Q8×D43C22semidirect
47. #14583004C22semidirect
48. #14583001C22semidirect
49. #14582997C22semidirect
50. Q16×Dic43C22semidirect
51. #14582991C22semidirect
52. #14582986C22semidirect
53. #14582984C22semidirect
54. #14582938C22semidirect
58. #14582906C22semidirect
66. #14582851C22semidirect
73. C43×#441C22semidirect
86. C2×Q8×D43C2×C4semidirect
98. #13063357C2×C4semidirect
99. C2×#10621885C2×C4semidirect
101. C2×#10621873C2×C4semidirect
103. C2×#10621884C2×C4semidirect
106. C2×#10621872C2×C4semidirect
169. C2×Q16×C43C2×C4semidirect
216. Q8×D43C22×C4semidirect
247. Q16×C43C22×C4semidirect
262. #10621885C22×C4semidirect
263. #10621884C22×C4semidirect
289. #10621873C22×C4semidirect
291. #10621872C22×C4semidirect
331. C2×Dic43#137semidirect
384. Dic43C2×#137semidirect
390. C2×#441D43semidirect
401. C2×C43C4×#137semidirect
441. #441C2×D43semidirect
468. C43C2×C4×#137semidirect
494. C2×Q16C4×D43semidirect
639. Q16C2×C4×D43semidirect
777. C2#19143411direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633572
C2×C4×#106219022
C2×C4×Q8×D432
#191434112
C2×#145830042
C2×#145830012
C2×#145829972
C2×Q16×Dic432
C2×#145829912
C2×#145829862
C2×#145829842
C2×#145829382
C2×#145828992
C2×#145829062
C2×#145828512
C2×C43×#4412
C2×C4×#13743