Finite Group Databasebeta

← C2×#19146715 #25973309

Subgroups — C2×#19146715 #25973309

Order 11008.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583570C211yesmaximal, characteristic
2#19146715C2116yesmaximal, direct product factor
3C2×#14583265C211yesmaximal, characteristic, complemented
4C2×#14583217C211yesmaximal, characteristic, complemented
5C2×#14583223C211yesmaximal, characteristic, complemented
6C2×#14583203C211yesmaximal, characteristic, complemented
7C2×#14583147C211yesmaximal, characteristic, complemented
8C2×#14583130C211yesmaximal, characteristic, complemented
9C2×#14583099C211yesmaximal, characteristic, complemented
10C2×#14583059C211yesmaximal, characteristic, complemented
11C2×#14583059C211yesmaximal, characteristic, complemented
12C2×#14583004C211yesmaximal, characteristic, complemented
13C2×#14582971C211yesmaximal, characteristic, complemented
14C2×#14582898C211yesmaximal, characteristic, complemented
15C2×#14582893C211yesmaximal, characteristic, complemented
16C2×C43×#552C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×#10621898C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621884C2211yescharacteristic
21C22×#10621884C2211yescharacteristic
22C22×#10621877C2211yescharacteristic
23C23×C43⋊C8C2211yescharacteristic
24#14583570—24no—
25#14583570C2218yes—
26C2×#13063322C2211yescharacteristic
27C2×#13063321—21no—
28C2×#13063299C2211yescharacteristic
29C2×#13063299C2211yescharacteristic
30C2×#13063298—21no—
31C2×#13063298—21no—
32C2×C4×Dic86C2211yescharacteristic
33C2×#13063287—21no—
34#14583265C2218yescomplemented
35#14583223C2218yescomplemented
36#14583217C2218yescomplemented
37#14583203C2218yescomplemented
38#14583147C2218yescomplemented
39#14583130C2218yescomplemented
40#14583099C2218yescomplemented
41#14583059C2218yescomplemented
42#14583059C2218yescomplemented
43#14583004C2218yescomplemented
44#14582971C2218yescomplemented
45C2×#13063258C2211yescharacteristic
46C2×#13063256C2211yescharacteristic
47C2×#13063256C2211yescharacteristic
48C2×C4⋊(C43⋊C8)C2211yescharacteristic
49#14582898C2218yescomplemented
50#14582893C2218yescomplemented
51C2×#13063249C2211yescharacteristic
52C2×#13063248C2211yescharacteristic
53C2×#13063248C2211yescharacteristic
54C2×#13063248C2211yescharacteristic
55C2×#13063245C2211yescharacteristic
56C2×#13063245C2211yescharacteristic
57C2×#13063245C2211yescharacteristic
58C2×#13063245C2211yescharacteristic
59C2×#13063245C2211yescharacteristic
60C2×#13063245C2211yescharacteristic
61C2×C22⋊(C43⋊C8)C2211yescharacteristic
62C2×C22⋊(C43⋊C8)C2211yescharacteristic
63C2×#13063236C2211yescharacteristic
64C43×#552—24no—
65C43×#552C2218yescomplemented
66C2×#126×C43—21no—
67C2×#125×C43—21no—
68C2×#125×C43C2211yescharacteristic
69C2×#123×C43—21no—
70C2×C22⋊Q8×C43C2211yescharacteristic
71C2×C22⋊Q8×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic
73C2×C4×D4×C43C2211yescharacteristic
74C2×#117×C43—21no—
75C2×#117×C43C2211yescharacteristic
76C22×C4⋊C4×C43C2211yescharacteristic
77C2×#10621898—22no—
78C2×#10621898—22no—
79C2×#10621898—24no—
80C2×#10621898—24no—
81C2×#10621898—42no—
82C2×#10621898—42no—
83C2×#10621898C2314yes—
84C2×#10621898C2314yes—
85C22×Dic86C2311yescharacteristic
86C22×D172—21no—
87C22×D172—21no—
88C22×D172C2311yescharacteristic
89C22×D172C2311yescharacteristic
90C22×C22⋊D43—21no—
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C22×C22⋊D43—21no—
94C22×C4×D43—21no—
95C22×C4×D43—21no—
96C2×#10621885—24no—
97C2×#10621885C2314yes—
98C2×#10621884—42no—
99C2×#10621884—42no—
100C2×#10621884C2314yes—
101C2×#10621884C2314yes—
102C2×#10621877—42no—
103C2×#10621877C2314yes—
104C22×C43⋊C8—42no—
105C22×C43⋊C8C2311yescharacteristic
106C22×C43⋊C8C2311yescharacteristic
107C22×C43⋊C8C2311yescharacteristic
108C22×C43⋊C8C2311yescharacteristic
109C22×C43⋊C8C2314yes—
110#13063322—22no—
111#13063322C2314yes—
112#13063321—28no—
113#13063299—22no—
114#13063299—22no—
115#13063299C2314yes—
116#13063299C2314yes—
117#13063298—28no—
118#13063298—28no—
119C4×Dic86—22no—
120C4×Dic86C2314yes—
121#13063287—28no—
122C2×C4⋊Dic43C2311yescharacteristic
123C2×Dic43⋊C4—21no—
124C2×(C2×D43)⋊C4—21no—
125C2×(C2×D43)⋊C4—21no—
126C2×C4×Dic43—21no—
127#13063258C2314yes—
128#13063256C2314yes—
129#13063256C2314yes—
130C4⋊(C43⋊C8)C2314yes—
131#13063249C2314yes—
132#13063248C2314yes—
133#13063248C2314yes—
134#13063248C2314yes—
135#13063245C2314yes—
136#13063245C2314yes—
137#13063245C2314yes—
138#13063245C2314yes—
139#13063245C2314yes—
140#13063245C2314yes—
141C22⋊(C43⋊C8)C2314yes—
142C22⋊(C43⋊C8)C2314yes—
143#13063236C2314yes—
144C22×Q8×C43C2311yescharacteristic
145C22×D4×C43D411yescharacteristic
146C23×C4×C43—21no—
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149#126×C43—28no—
150#125×C43—28no—
151#125×C43—22no—
152#125×C43C2314yes—
153#123×C43—28no—
154C22⋊Q8×C43—22no—
155C22⋊Q8×C43—22no—
156C22⋊Q8×C43C2314yes—
157C22⋊Q8×C43C2314yes—
158C4×Q8×C43—22no—
159C4×Q8×C43C2314yes—
160C4×D4×C43D414yes—
161C4×D4×C43C2314yes—
162#117×C43—22no—
163#117×C43—28no—
164#117×C43C2314yes—
165C2×C4⋊C4×C43—21no—
166C2×C4⋊C4×C43—22no—
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43—21no—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43D411yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C4⋊C4×C43C2314yes—
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C22⋊C4×C43—21no—
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C2×C22⋊C4×C43D411yescharacteristic
181C2×C22⋊C4×C43D411yescharacteristic
182C2×C42×C43—21no—
183C2×C42×C43—21no—
184C2×C42×C43C2311yescharacteristic
185C24×C43C2×D411yescharacteristic
186C24×C43C2×D411yescharacteristic
187C23×D43—21no—
188C23×D43—21no—
189C2×Q8×C43—21no—
190C2×Q8×C43—22no—
191C2×Q8×C43—22no—
192C2×Q8×C43C2412yes—
193C2×D4×C43—42no—
194C2×D4×C43C2×D414yes—
195C22×C4×C43—22no—
196C22×C4×C43—22no—
197C22×C4×C43—22no—
198C22×C4×C43—22no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—24no—
204C22×C4×C43—44no—
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2×D412yes—
210C22×C4×C43C2×D412yes—
211C22×C4×C43C2412yes—
212C22×C4×C43C2412yes—
213C22×C4×C43C2411yescharacteristic
214C2×C22⋊D43—24no—
215C2×C22⋊D43—24no—
216C2×C22⋊D43—24no—
217C2×C22⋊D43—24no—
218C2×C22⋊D43—44no—
219C2×C22⋊D43—44no—
220C2×C22⋊D43—82no—
221C2×C22⋊D43—82no—
222C22×Dic43—21no—
223C22×Dic43—21no—
224#10621898—28no—
225#10621898—28no—
226#10621898—44no—
227#10621898—44no—
228#10621898—48no—
229#10621898—48no—
230C2×D172—24no—
231C2×D172—21no—
232C2×D172—21no—
233C2×D172—24no—
234C2×D172—22no—
235C2×D172—22no—
236C2×D172—22no—
237C2×D172—22no—
238C2×D172—44no—
239C2×D172—82no—
240C2×D172C2412yes—
241C2×D172C2412yes—
242C2×C4×D43—24no—
243C2×C4×D43—24no—
244C2×C4×D43—44no—
245C2×C4×D43—44no—
246C2×Dic86—21no—
247C2×Dic86—22no—
248C2×Dic86#4114yes—
249C2×Dic86C2412yes—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—24no—
253C4⋊C4×C43—24no—
254C4⋊C4×C43—24no—
255C4⋊C4×C43—24no—
256C4⋊C4×C43—24no—
257C4⋊C4×C43—24no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43C2×D414yes—
260C4⋊C4×C43C2412yes—
261C4⋊C4×C43C2412yes—
262C4⋊C4×C43C2412yes—
263C22⋊C4×C43—24no—
264C22⋊C4×C43—24no—
265C22⋊C4×C43—24no—
266C22⋊C4×C43C2×D414yes—
267C22⋊C4×C43C2×D414yes—
268C42×C43—24no—
269C42×C43—24no—
270C42×C43C2×D412yes—
271C42×C43C2412yes—
272#10621885—28no—
273#10621884—44no—
274#10621884—44no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4—24no—
277C4⋊Dic43—21no—
278C4⋊Dic43C2412yes—
279Dic43⋊C4—24no—
280C4×Dic43—24no—
281#10621877—44no—
282C2×C43⋊C8—22no—
283C2×C43⋊C8—22no—
284C2×C43⋊C8—22no—
285C2×C43⋊C8—22no—
286C2×C43⋊C8—44no—
287C2×C43⋊C8C2412yes—
288C2×C43⋊C8C2412yes—
289C2×C43⋊C8C2412yes—
290C2×C43⋊C8C2412yes—
291C23×C43—22no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43C22×D412yes—
298C23×C43C22×D412yes—
299C23×C43C22×D411yescharacteristic
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—42no—
303C22×D43—42no—
304C22×D43—42no—
305C22×D43—42no—
306C22×D43—42no—
307C22×D43—42no—
308Q8×C43—22no—
309Q8×C43—22no—
310Q8×C43—42no—
311D4×C43—44no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—24no—
317C2×C4×C43—24no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—48no—
327C2×C4×C43—42no—
328C2×C4×C43—42no—
329C2×C4×C43—42no—
330C2×C4×C43—42no—
331C2×C4×C43C22×D412yes—
332C2×C4×C43C22×D412yes—
333C2×C4×C43C22×D412yes—
334C2×C4×C43C22×D412yes—
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43C2×#4112yes—
337C2×C4×C43H(5,𝔽2)12yes—
338C2×C4×C43C2511yescharacteristic
339C22⋊D43—48no—
340C22⋊D43—48no—
341C22⋊D43—84no—
342C22⋊D43—84no—
343C2×Dic43—24no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—42no—
347D172—22no—
348D172—22no—
349D172—22no—
350D172—22no—
351D172—48no—
352D172—42no—
353D172—42no—
354D172—84no—
355C4×D43—48no—
356C4×D43—48no—
357Dic86—24no—
358Dic86—22no—
359Dic86C2×#4114yes—
360C43⋊C8—22no—
361C43⋊C8—22no—
362C43⋊C8—22no—
363C43⋊C8—22no—
364C2×#3317—431nomaximal, Sylow
365C22×C43—22no—
366C22×C43—22no—
367C22×C43—22no—
368C22×C43—22no—
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—44no—
372C22×C43—44no—
373C22×C43#54612yes—
374C22×C43#57512yes—
375C22×C43#57712yes—
376C22×C43C23×D411yescharacteristic
377C2×D43—42no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—84no—
384C2×D43—84no—
385C4×C43—22no—
386C4×C43—22no—
387C4×C43—22no—
388C4×C43—22no—
389C4×C43—42no—
390C4×C43—42no—
391C4×C43—42no—
392C4×C43—42no—
393C4×C43#54612yes—
394C4×C43C22×#4111yescharacteristic
395C4×C43C2×H(5,𝔽2)11yescharacteristic
396Dic43—24no—
397Dic43—42no—
398C2×#552D4311yescharacteristic, complemented
399C2×#550—431no—
400#3317—4316no—
401C2×#490—431no—
402C2×#481—431no—
403C2×#482—431no—
404C2×#479—431no—
405C2×#468—431no—
406C2×#465—431no—
407C2×#460—431no—
408C2×#452—431no—
409C2×#452—431no—
410C2×#441—431no—
411C2×#435—431no—
412C2×#417—431no—
413C2×#416—431no—
414C2×C43—42no—
415C2×C43—42no—
416C2×C43#331714yescomplemented
417C2×C43C2×#54611yescharacteristic
418C2×C43C2×#57511yescharacteristic
419C2×C43C2×#57711yescharacteristic
420D43—82no—
421D43—82no—
422C22×#41—431no—
423C22×#41—431no—
424C22×Q16—431no—
425C22×SD16—431no—
426C22×SD16—431no—
427C22×M16—431no—
428C23×C8—431no—
429#552—24no—
430#552C2×D4318yescomplemented
431#550—438no—
432#550—864no—
433C2×#127—431no—
434C2×#127—861no—
435C2×#126—21no—
436C2×#125—21no—
437C2×#125C2×D4311yescharacteristic
438C2×#123—21no—
439C2×C22⋊Q8C2×D4311yescharacteristic
440C2×C22⋊Q8C2×D4311yescharacteristic
441C2×#121—431no—
442C2×#121—431no—
443C2×#121—861no—
444C2×#121—861no—
445C2×C4×Q8—431no—
446C2×C4×Q8C2×D4311yescharacteristic
447C2×C4×D4—861no—
448C2×C4×D4C2×D4311yescharacteristic
449C2×#117—21no—
450C2×#117C2×D4311yescharacteristic
451C22×C4⋊C4C2×D4311yescharacteristic
452#490—438no—
453#482—438no—
454#481—438no—
455#479—438no—
456#468—438no—
457#465—438no—
458#460—438no—
459#452—438no—
460#452—438no—
461#441—438no—
462#435—438no—
463C2×#107—431no—
464C2×#106—431no—
465C2×#106—431no—
466C2×C4⋊C8—431no—
467#417—438no—
468#416—438no—
469C2×#103—431no—
470C2×#103—431no—
471C2×#103—431no—
472C2×#103—431no—
473C2×#102—431no—
474C2×#102—431no—
475C2×#102—431no—
476C2×#102—431no—
477C2×#102—431no—
478C2×#102—431no—
479C2×C22⋊C8—431no—
480C2×C22⋊C8—431no—
481C2×#97—431no—
482C43C2×#331711yescharacteristic, complemented, Sylow
483C2×#41—434no—
484C2×#41—434no—
485C2×#41—864no—
486C2×#41—864no—
487C2×#41—862no—
488C2×#41—862no—
489C2×#41—1722no—
490C2×#41—1722no—
491C22×Q8—431no—
492C22×Q8C22×D4311yescharacteristic
493C22×D4—431no—
494C22×D4—431no—
495C22×D4—861no—
496C22×D4—861no—
497C22×D4—861no—
498C22×D4—861no—
499C22×D4—861no—
500C22×D4—861no—
501C22×D4C22⋊D4311yescharacteristic
502C23×C4—21no—
503C23×C4—861no—
504C23×C4—861no—
505C23×C4C22×D4311yescharacteristic
506C23×C4C22×D4311yescharacteristic
507C2×Q16—434no—
508C2×Q16—864no—
509C2×SD16—434no—
510C2×SD16—434no—
511C2×SD16—1722no—
512C2×SD16—1722no—
513C2×M16—434no—
514C2×M16—1722no—
515C22×C8—431no—
516C22×C8—431no—
517C22×C8—431no—
518C22×C8—431no—
519C22×C8—434no—
520C22×C8—1722no—
521#127—434no—
522#127—868no—
523#127—862no—
524#126—28no—
525#125—28no—
526#125—22no—
527#125C22×D4314yes—
528#123—28no—
529C22⋊Q8—22no—
530C22⋊Q8—22no—
531C22⋊Q8C22×D4314yes—
532C22⋊Q8C22×D4314yes—
533#121—434no—
534#121—434no—
535#121—862no—
536#121—862no—
537#121—868no—
538#121—868no—
539C4×Q8—22no—
540C4×Q8—434no—
541C4×Q8—862no—
542C4×Q8C22×D4314yes—
543C4×D4—868no—
544C4×D4C22⋊D4314yes—
545C4×D4C22×D4314yes—
546#117—22no—
547#117—28no—
548#117C22×D4314yes—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—431no—
557C2×C4⋊C4—861no—
558C2×C4⋊C4C22⋊D4311yescharacteristic
559C2×C4⋊C4C22×D4311yescharacteristic
560C2×C4⋊C4C22×D4311yescharacteristic
561C2×C4⋊C4C22×D4314yes—
562C2×C4⋊C4C22×D4311yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4C22⋊D4311yescharacteristic
569C2×C22⋊C4C22⋊D4311yescharacteristic
570C2×C42—21no—
571C2×C42—21no—
572C2×C42—861no—
573C2×C42C22×D4311yescharacteristic
574#107—434no—
575#106—434no—
576#106—434no—
577C4⋊C8—434no—
578#103—434no—
579#103—434no—
580#103—434no—
581#103—434no—
582#102—434no—
583#102—434no—
584#102—434no—
585#102—434no—
586#102—434no—
587#102—434no—
588C22⋊C8—434no—
589C22⋊C8—434no—
590#97—434no—
591C24—861no—
592C24—861no—
593C24C2×C22⋊D4311yescharacteristic
594C24C2×C22⋊D4311yescharacteristic
595#41—868no—
596#41—868no—
597#41—1724no—
598#41—1724no—
599#41—1728no—
600#41—1728no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—434no—
605C2×Q8—432no—
606C2×Q8—861no—
607C2×Q8—862no—
608C2×Q8C23×D4312yes—
609C2×D4—42no—
610C2×D4—432no—
611C2×D4—432no—
612C2×D4—864no—
613C2×D4—864no—
614C2×D4—864no—
615C2×D4—864no—
616C2×D4—864no—
617C2×D4—864no—
618C2×D4—861no—
619C2×D4—861no—
620C2×D4—862no—
621C2×D4—862no—
622C2×D4—862no—
623C2×D4—862no—
624C2×D4—3442no—
625C2×D4—3442no—
626C2×D4—3442no—
627C2×D4—1724no—
628C2×D4—1724no—
629C2×D4—1724no—
630C2×D4C2×C22⋊D4314yes—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—24no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—44no—
641C22×C4—861no—
642C22×C4—861no—
643C22×C4—864no—
644C22×C4—864no—
645C22×C4—1724no—
646C22×C4—1724no—
647C22×C4C2×C22⋊D4312yes—
648C22×C4C2×C22⋊D4312yes—
649C22×C4C2×C22⋊D4311yescharacteristic
650C22×C4C2×C22⋊D4311yescharacteristic
651C22×C4C2×C22⋊D4311yescharacteristic
652C22×C4C2×C22⋊D4311yescharacteristic
653C22×C4C23×D4312yes—
654C22×C4C23×D4312yes—
655C22×C4C23×D4311yescharacteristic
656Q16—868no—
657SD16—1724no—
658SD16—1724no—
659M16—1724no—
660C2×C8—432no—
661C2×C8—432no—
662C2×C8—432no—
663C2×C8—432no—
664C2×C8—862no—
665C2×C8—862no—
666C2×C8—862no—
667C2×C8—862no—
668C2×C8—1724no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—24no—
677C4⋊C4—21no—
678C4⋊C4—432no—
679C4⋊C4—861no—
680C4⋊C4—864no—
681C4⋊C4C2×C22⋊D4314yes—
682C4⋊C4C23×D4312yes—
683C4⋊C4C23×D4312yes—
684C4⋊C4C23×D4312yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—864no—
689C22⋊C4—864no—
690C22⋊C4C2×C22⋊D4314yes—
691C22⋊C4C2×C22⋊D4314yes—
692C42—24no—
693C42—24no—
694C42—864no—
695C42C2×C22⋊D4312yes—
696C42C23×D4312yes—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—862no—
704C23—862no—
705C23—1722no—
706C23—1722no—
707C23—1722no—
708C23—1722no—
709C23—1722no—
710C23—1722no—
711C23C22×C22⋊D4312yes—
712C23C22×C22⋊D4312yes—
713C23C22×C22⋊D4311yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—434no—
718Q8—862no—
719Q8—864no—
720D4—44no—
721D4—862no—
722D4—862no—
723D4—862no—
724D4—862no—
725D4—3444no—
726D4—3444no—
727D4—3444no—
728D4—1728no—
729D4—1728no—
730D4—1728no—
731D4—1722no—
732D4—1722no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—48no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—862no—
753C2×C4—864no—
754C2×C4—862no—
755C2×C4—1728no—
756C2×C4—1728no—
757C2×C4—1722no—
758C2×C4C22×C22⋊D4312yes—
759C2×C4C22×C22⋊D4312yes—
760C2×C4C22×C22⋊D4312yes—
761C2×C4C22×C22⋊D4312yes—
762C2×C4C22×C22⋊D4311yescharacteristic
763C2×C4#41×D4312yes—
764C2×C4#1306337112yes—
765C2×C4C24×D4311yescharacteristic
766C8—862no—
767C8—862no—
768C8—862no—
769C8—862no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—3444no—
779C22—3444no—
780C22—1722no—
781C22—1722no—
782C22—1722no—
783C22—1722no—
784C22—1722no—
785C22—1722no—
786C22#1458353712yes—
787C22#1458369712yes—
788C22#1458370712yes—
789C22C23×C22⋊D4311yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—864no—
799C4—1722no—
800C4#1458353712yes—
801C4C2×#41×D4311yescharacteristic
802C4C2×#1306337111yescharacteristic
803C2—42no—
804C2—42no—
805C2—3442no—
806C2—3442no—
807C2#1914671514yesdirect product factor
808C2C2×#1458353711yescharacteristic
809C2C2×#1458369711yescharacteristic
810C2C2×#1458370711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#552C2
socleC23×C43C22×D4
prime radicalC2×#14583570C2
hypercenterC2×#552D43
hypocenterC43C2×#3317
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #19146715C2direct (N × H)
3. C2×#14583265C2semidirect
4. C2×#14583217C2semidirect
5. C2×#14583223C2semidirect
6. C2×#14583203C2semidirect
7. C2×#14583147C2semidirect
8. C2×#14583130C2semidirect
9. C2×#14583099C2semidirect
10. C2×#14583059C2semidirect
11. C2×#14583059C2semidirect
12. C2×#14583004C2semidirect
13. C2×#14582971C2semidirect
14. C2×#14582898C2semidirect
15. C2×#14582893C2semidirect
16. C2×C43×#552C2semidirect
34. #14583265C22semidirect
35. #14583223C22semidirect
36. #14583217C22semidirect
37. #14583203C22semidirect
38. #14583147C22semidirect
39. #14583130C22semidirect
40. #14583099C22semidirect
41. #14583059C22semidirect
42. #14583059C22semidirect
43. #14583004C22semidirect
44. #14582971C22semidirect
49. #14582898C22semidirect
50. #14582893C22semidirect
65. C43×#552C22semidirect
398. C2×#552D43semidirect
416. C2×C43#3317semidirect
430. #552C2×D43semidirect
482. C43C2×#3317semidirect
807. C2#19146715direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835702
#191467152
C2×#145832652
C2×#145832172
C2×#145832232
C2×#145832032
C2×#145831472
C2×#145831302
C2×#145830992
C2×#145830592
C2×#145830042
C2×#145829712
C2×#145828982
C2×#145828932
C2×C43×#5522
C2×#331743