Finite Group Databasebeta

← C2×#19146703 #25973184

Subgroups — C2×#19146703 #25973184

Order 11008.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583610C211yesmaximal, characteristic, complemented
2C2×#14583561C211yesmaximal, characteristic
3#19146703C2116yesmaximal, direct product factor
4C2×#14583261C211yesmaximal, characteristic, complemented
5C2×#14583219C211yesmaximal, characteristic, complemented
6C2×#14583231C211yesmaximal, characteristic, complemented
7C2×#14583158C211yesmaximal, characteristic, complemented
8C2×#14583129C211yesmaximal, characteristic, complemented
9C2×#14583122C211yesmaximal, characteristic, complemented
10C2×#14583064C211yesmaximal, characteristic, complemented
11C2×#14583056C211yesmaximal, characteristic, complemented
12C2×#14583004C211yesmaximal, characteristic, complemented
13C2×#14582969C211yesmaximal, characteristic, complemented
14C2×#14582899C211yesmaximal, characteristic, complemented
15C2×#103×D43C211yesmaximal, characteristic, complemented
16C2×C43×#475C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C22×Dic172C2211yescharacteristic
20C22×#10621885C2211yescharacteristic
21C22×#10621873C2211yescharacteristic
22C22×#10621872C2211yescharacteristic
23C22×C8×D43C2211yescharacteristic
24#14583610—24no—
25#14583610C2218yescomplemented
26#14583561—24no—
27#14583561C2218yes—
28C2×#13063316—21no—
29C2×#13063313—21no—
30C2×#13063313C2211yescharacteristic
31C2×#13063305—21no—
32C2×#13063305C2211yescharacteristic
33C2×#13063305C2211yescharacteristic
34C2×#13063305C2211yescharacteristic
35C2×#13063301—21no—
36C2×#13063301—21no—
37C2×#13063300—21no—
38C2×#13063300C2211yescharacteristic
39C2×C4×Dic86C2211yescharacteristic
40C2×C4×D172—21no—
41C2×C4×D172C2211yescharacteristic
42C2×#13063287—21no—
43C2×C4⋊C4×D43C2211yescharacteristic
44C2×C4⋊C4×D43C2211yescharacteristic
45#14583261C2218yescomplemented
46#14583231C2218yescomplemented
47#14583219C2218yescomplemented
48#14583158C2218yescomplemented
49#14583129C2218yescomplemented
50#14583122C2218yescomplemented
51#14583064C2218yescomplemented
52#14583056C2218yescomplemented
53#14583004C2218yescomplemented
54#14582969C2218yescomplemented
55C2×#13063256C2211yescharacteristic
56#14582899C2218yescomplemented
57C2×#13063250C2211yescharacteristic
58C2×#13063249C2211yescharacteristic
59C2×#13063248C2211yescharacteristic
60C2×#13063248C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62#103×D43C2218yescomplemented
63C2×#13063247C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063236C2211yescharacteristic
69C2×C4⋊Q8×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C43×#475C2218yescomplemented
72C2×#106×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#103×C43C2211yescharacteristic
77C2×#10621902—22no—
78C2×#10621902—24no—
79C2×#10621902—42no—
80C2×#10621902C2314yes—
81C22×Dic86—21no—
82C22×Dic86C2311yescharacteristic
83C22×Dic86C2311yescharacteristic
84C2×Q8×D43—22no—
85C2×Q8×D43—24no—
86C2×Q8×D43—42no—
87C2×Q8×D43C2314yes—
88C22×D172—21no—
89C22×D172—21no—
90C22×D172D411yescharacteristic
91C22×D172C2311yescharacteristic
92C22×C4×D43—21no—
93C22×C4×D43—21no—
94C22×C4×D43—21no—
95C22×C4×D43—21no—
96C22×C4×D43C2311yescharacteristic
97C22×C4×D43C2311yescharacteristic
98C2×Dic172—42no—
99C2×Dic172C2314yes—
100C2×#10621885—24no—
101C2×#10621885C2314yes—
102C2×#10621873—42no—
103C2×#10621873C2314yes—
104C2×#10621872—42no—
105C2×#10621872C2314yes—
106C22×C43⋊C8C2311yescharacteristic
107C22×C43⋊C8C2311yescharacteristic
108C2×C8×D43—42no—
109C2×C8×D43C2314yes—
110#13063316—28no—
111#13063313—22no—
112#13063313—28no—
113#13063313C2314yes—
114#13063305—22no—
115#13063305—22no—
116#13063305—22no—
117#13063305—28no—
118#13063305C2314yes—
119#13063305C2314yes—
120#13063305C2314yes—
121#13063301—28no—
122#13063301—28no—
123#13063300—28no—
124#13063300—22no—
125#13063300C2314yes—
126C4×Dic86—22no—
127C4×Dic86C2314yes—
128C4×D172—28no—
129C4×D172D414yes—
130C4×D172C2314yes—
131#13063287—28no—
132C2×C4⋊Dic43—21no—
133C2×C4⋊Dic43—21no—
134C2×C4⋊Dic43—21no—
135C2×C4⋊Dic43D411yescharacteristic
136C2×C4⋊Dic43C2311yescharacteristic
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C4⋊C4×D43—22no—
141C4⋊C4×D43—22no—
142C4⋊C4×D43C2314yes—
143C4⋊C4×D43C2314yes—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4D411yescharacteristic
151C2×(C2×D43)⋊C4D411yescharacteristic
152C2×C4×Dic43—21no—
153#13063256C2314yes—
154#13063250C2314yes—
155#13063249C2314yes—
156#13063248C2314yes—
157#13063248C2314yes—
158#13063248C2314yes—
159#13063247C2314yes—
160#13063245C2314yes—
161#13063245C2314yes—
162(C2×D43)⋊C8C2314yes—
163(C2×D43)⋊C8C2314yes—
164#13063236C2314yes—
165C22×Q8×C43—21no—
166C22×Q8×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C4⋊Q8×C43—22no—
170C4⋊Q8×C43C2314yes—
171C4×Q8×C43—22no—
172C4×Q8×C43C2314yes—
173C2×C4⋊C4×C43—21no—
174C2×C4⋊C4×C43—21no—
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C42×C43—21no—
179C2×C42×C43C2311yescharacteristic
180#106×C43C2314yes—
181#106×C43C2314yes—
182C4⋊C8×C43C2314yes—
183#103×C43C2314yes—
184#103×C43C2314yes—
185C23×D43—21no—
186C23×D43C2×D411yescharacteristic
187C23×D43C2×D411yescharacteristic
188C2×Q8×C43—21no—
189C2×Q8×C43—24no—
190C2×Q8×C43—22no—
191C2×Q8×C43—82no—
192C2×Q8×C43#4114yes—
193C2×Q8×C43C2412yes—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2411yescharacteristic
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43C2×D411yescharacteristic
205C22×Dic43C2×D411yescharacteristic
206#10621902—28no—
207#10621902—44no—
208#10621902—48no—
209Q8×D43—28no—
210Q8×D43—44no—
211Q8×D43—48no—
212C2×D172—21no—
213C2×D172—24no—
214C2×D172—24no—
215C2×D172—24no—
216C2×D172—22no—
217C2×D172—22no—
218C2×D172—44no—
219C2×D172—44no—
220C2×D172C2×D414yes—
221C2×D172C2412yes—
222C2×C4×D43—22no—
223C2×C4×D43—22no—
224C2×C4×D43—22no—
225C2×C4×D43—22no—
226C2×C4×D43—24no—
227C2×C4×D43—24no—
228C2×C4×D43—24no—
229C2×C4×D43—24no—
230C2×C4×D43—44no—
231C2×C4×D43—44no—
232C2×C4×D43—82no—
233C2×C4×D43—82no—
234C2×C4×D43C2×D412yes—
235C2×C4×D43C2×D412yes—
236C2×C4×D43C2412yes—
237C2×C4×D43C2412yes—
238C2×Dic86—22no—
239C2×Dic86—22no—
240C2×Dic86—22no—
241C2×Dic86—22no—
242C2×Dic86—21no—
243C2×Dic86—21no—
244C2×Dic86—24no—
245C2×Dic86—44no—
246C2×Dic86C2412yes—
247C2×Dic86C2412yes—
248C2×C8×C43—22no—
249C2×C8×C43—22no—
250C2×C8×C43C2412yes—
251C2×C8×C43C2412yes—
252C4⋊C4×C43—24no—
253C4⋊C4×C43—24no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43C2412yes—
258C4⋊C4×C43C2412yes—
259C4⋊C4×C43C2412yes—
260C42×C43—24no—
261C42×C43C2×D412yes—
262C42×C43C2412yes—
263#10621885—28no—
264(C2×D43)⋊C4—24no—
265(C2×D43)⋊C4—24no—
266(C2×D43)⋊C4—24no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—24no—
269(C2×D43)⋊C4—24no—
270(C2×D43)⋊C4C2×D414yes—
271(C2×D43)⋊C4C2×D414yes—
272C4⋊Dic43—21no—
273C4⋊Dic43—24no—
274C4⋊Dic43—24no—
275C4⋊Dic43—24no—
276C4⋊Dic43C2×D414yes—
277C4⋊Dic43C2412yes—
278Dic43⋊C4—24no—
279Dic43⋊C4—24no—
280Dic43⋊C4—24no—
281C4×Dic43—24no—
282C2×C43⋊C8—22no—
283C2×C43⋊C8—22no—
284C2×C43⋊C8C2412yes—
285C2×C43⋊C8C2412yes—
286Dic172—44no—
287#10621873—44no—
288#10621872—44no—
289C8×D43—44no—
290C23×C43C22×D411yescharacteristic
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—42no—
298C22×D43—42no—
299C22×D43—42no—
300C22×D43#13714yes—
301C22×D43C22×D412yes—
302C22×D43C22×D412yes—
303Q8×C43—24no—
304Q8×C43—22no—
305Q8×C43—84no—
306Q8×C43C2×#4114yes—
307C2×C4×C43—24no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—42no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43C22×D412yes—
318C2×C4×C43C22×D412yes—
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C2×#4112yes—
321C2×C4×C43H(5,𝔽2)12yes—
322C2×C4×C43C2511yescharacteristic
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—42no—
329C2×Dic43—42no—
330C2×Dic43—42no—
331C2×Dic43C22×D412yes—
332C2×Dic43C22×D412yes—
333D172—28no—
334D172—22no—
335D172—22no—
336D172—48no—
337D172—48no—
338D172—42no—
339C4×D43—24no—
340C4×D43—24no—
341C4×D43—22no—
342C4×D43—22no—
343C4×D43—22no—
344C4×D43—22no—
345C4×D43—48no—
346C4×D43—48no—
347C4×D43—84no—
348C4×D43—84no—
349Dic86—22no—
350Dic86—22no—
351Dic86—22no—
352Dic86—22no—
353Dic86—48no—
354Dic86—42no—
355Dic86—42no—
356C8×C43—22no—
357C8×C43—22no—
358C43⋊C8—22no—
359C43⋊C8—22no—
360C2×#3316—431nomaximal, Sylow
361C22×C43#54612yes—
362C22×C43C2×#13712yes—
363C22×C43#57712yes—
364C22×C43C23×D411yescharacteristic
365C2×D43—22no—
366C2×D43—28no—
367C2×D43—22no—
368C2×D43—22no—
369C2×D43—22no—
370C2×D43—22no—
371C2×D43—44no—
372C2×D43—42no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—84no—
376C2×D43C2×#13714yes—
377C4×C43—24no—
378C4×C43—22no—
379C4×C43—22no—
380C4×C43—42no—
381C4×C43—42no—
382C4×C43—42no—
383C4×C43#54612yes—
384C4×C43C22×#4111yescharacteristic
385C4×C43C2×H(5,𝔽2)11yescharacteristic
386Dic43—22no—
387Dic43—22no—
388Dic43—42no—
389Dic43—42no—
390Dic43—42no—
391C2×#554—431no—
392C2×#548—431no—
393#3316—4316no—
394C2×#489—431no—
395C2×#481—431no—
396C2×#483—431no—
397C2×#475D4311yescharacteristic, complemented
398C2×#470—431no—
399C2×#465—431no—
400C2×#464—431no—
401C2×#452—431no—
402C2×#451—431no—
403C2×#441—431no—
404C2×#435—431no—
405C2×#417—431no—
406C22×#103—431no—
407C2×C43#331614yescomplemented
408C2×C43C2×#54611yescharacteristic
409C2×C43C22×#13711yescharacteristic
410C2×C43C2×#57711yescharacteristic
411D43—24no—
412D43—42no—
413D43—82no—
414C22×#41—431no—
415C23×Q8—431no—
416C22×Q16—431no—
417C22×Q16—431no—
418C22×SD16—431no—
419C22×M16—431no—
420C23×C8—431no—
421#554—438no—
422#554—864no—
423#548—438no—
424#548—864no—
425C2×C4⋊Q8C2×D4311yescharacteristic
426C2×#125—861no—
427C2×#124—431no—
428C2×#124—861no—
429C2×C22⋊Q8—431no—
430C2×C22⋊Q8—431no—
431C2×C22⋊Q8—431no—
432C2×C22⋊Q8—861no—
433C2×C22⋊Q8—861no—
434C2×C22⋊Q8—861no—
435C2×#121—431no—
436C2×#121—861no—
437C2×C4×Q8—431no—
438C2×C4×Q8C2×D4311yescharacteristic
439C2×C4×D4—431no—
440C2×C4×D4—861no—
441C2×C4×D4—861no—
442C22×C4⋊C4—431no—
443C22×C4⋊C4—431no—
444#489—438no—
445#483—438no—
446#481—438no—
447#475C2×D4318yescomplemented
448#470—438no—
449#465—438no—
450#464—438no—
451#452—438no—
452#451—438no—
453#441—438no—
454#435—438no—
455C2×#106—431no—
456C2×#106C2×D4311yescharacteristic
457C2×#106C2×D4311yescharacteristic
458C2×C4⋊C8C2×D4311yescharacteristic
459#417—438no—
460C2×#103—431no—
461C2×#103—431no—
462C2×#103—431no—
463C2×#103—431no—
464C2×#103—431no—
465C2×#103—438no—
466C2×#103C2×D4311yescharacteristic
467C2×#103C2×D4311yescharacteristic
468C2×#102—431no—
469C2×#102—431no—
470C2×#102—431no—
471C2×C22⋊C8—431no—
472C2×C22⋊C8—431no—
473C2×#97—431no—
474C43C2×#331611yescharacteristic, complemented, Sylow
475C2×#41—434no—
476C2×#41—862no—
477C2×#41—864no—
478C2×#41—1722no—
479C22×Q8—21no—
480C22×Q8—434no—
481C22×Q8—431no—
482C22×Q8—431no—
483C22×Q8—861no—
484C22×Q8—862no—
485C22×Q8—864no—
486C22×Q8—1722no—
487C22×Q8C22×D4311yescharacteristic
488C22×D4—431no—
489C22×D4—431no—
490C22×D4—861no—
491C22×D4—861no—
492C23×C4—431no—
493C23×C4—431no—
494C23×C4—861no—
495C23×C4—861no—
496C23×C4—861no—
497C23×C4—861no—
498C2×Q16—434no—
499C2×Q16—434no—
500C2×Q16—864no—
501C2×Q16—1722no—
502C2×SD16—434no—
503C2×SD16—1722no—
504C2×M16—434no—
505C2×M16—1722no—
506C22×C8—431no—
507C22×C8—431no—
508C22×C8—434no—
509C22×C8—1722no—
510C22×C8C22×D4311yescharacteristic
511C22×C8C22×D4311yescharacteristic
512C4⋊Q8—22no—
513C4⋊Q8C22×D4314yes—
514#125—868no—
515#124—434no—
516#124—868no—
517#124—862no—
518C22⋊Q8—434no—
519C22⋊Q8—434no—
520C22⋊Q8—434no—
521C22⋊Q8—868no—
522C22⋊Q8—868no—
523C22⋊Q8—868no—
524C22⋊Q8—862no—
525C22⋊Q8—862no—
526C22⋊Q8—862no—
527#121—434no—
528#121—862no—
529#121—868no—
530C4×Q8—22no—
531C4×Q8—434no—
532C4×Q8—862no—
533C4×Q8C22×D4314yes—
534C4×D4—434no—
535C4×D4—434no—
536C4×D4—868no—
537C4×D4—868no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—431no—
541C2×C4⋊C4—431no—
542C2×C4⋊C4—434no—
543C2×C4⋊C4—434no—
544C2×C4⋊C4—862no—
545C2×C4⋊C4—862no—
546C2×C4⋊C4—861no—
547C2×C4⋊C4—861no—
548C2×C4⋊C4—861no—
549C2×C4⋊C4—861no—
550C2×C4⋊C4—861no—
551C2×C4⋊C4—861no—
552C2×C4⋊C4C22×D4311yescharacteristic
553C2×C4⋊C4C22×D4311yescharacteristic
554C2×C4⋊C4C22×D4311yescharacteristic
555C2×C22⋊C4—431no—
556C2×C22⋊C4—431no—
557C2×C22⋊C4—861no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—861no—
563C2×C42—21no—
564C2×C42—861no—
565C2×C42C22×D4311yescharacteristic
566#106—434no—
567#106C22×D4314yes—
568#106C22×D4314yes—
569C4⋊C8C22×D4314yes—
570#103—434no—
571#103—434no—
572#103—434no—
573#103—434no—
574#103—434no—
575#103C22×D4314yes—
576#103C22×D4314yes—
577#102—434no—
578#102—434no—
579#102—434no—
580C22⋊C8—434no—
581C22⋊C8—434no—
582#97—434no—
583C24—431no—
584C24—431no—
585C24—861no—
586#41—868no—
587#41—1724no—
588#41—1728no—
589C2×Q8—21no—
590C2×Q8—24no—
591C2×Q8—22no—
592C2×Q8—82no—
593C2×Q8—432no—
594C2×Q8—432no—
595C2×Q8—864no—
596C2×Q8—861no—
597C2×Q8—861no—
598C2×Q8—868no—
599C2×Q8—862no—
600C2×Q8—862no—
601C2×Q8—862no—
602C2×Q8—862no—
603C2×Q8—1724no—
604C2×Q8—1724no—
605C2×Q8—1728no—
606C2×Q8#1062190214yes—
607C2×Q8C23×D4312yes—
608C2×D4—434no—
609C2×D4—432no—
610C2×D4—864no—
611C2×D4—864no—
612C2×D4—864no—
613C2×D4—861no—
614C2×D4—862no—
615C2×D4—862no—
616C2×D4—1724no—
617C2×D4—1724no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—431no—
623C22×C4—431no—
624C22×C4—432no—
625C22×C4—432no—
626C22×C4—432no—
627C22×C4—432no—
628C22×C4—864no—
629C22×C4—864no—
630C22×C4—864no—
631C22×C4—864no—
632C22×C4—862no—
633C22×C4—862no—
634C22×C4—862no—
635C22×C4—862no—
636C22×C4—861no—
637C22×C4—861no—
638C22×C4—861no—
639C22×C4—3442no—
640C22×C4—3442no—
641C22×C4—1724no—
642C22×C4—1724no—
643C22×C4D4×D4311yescharacteristic
644C22×C4D4×D4311yescharacteristic
645C22×C4C23×D4311yescharacteristic
646Q16—868no—
647Q16—1724no—
648SD16—1724no—
649M16—1724no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—432no—
653C2×C8—432no—
654C2×C8—862no—
655C2×C8—862no—
656C2×C8—1724no—
657C2×C8C23×D4312yes—
658C2×C8C23×D4312yes—
659C4⋊C4—24no—
660C4⋊C4—24no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—434no—
665C4⋊C4—432no—
666C4⋊C4—864no—
667C4⋊C4—864no—
668C4⋊C4—864no—
669C4⋊C4—864no—
670C4⋊C4—864no—
671C4⋊C4—861no—
672C4⋊C4—864no—
673C4⋊C4C23×D4312yes—
674C4⋊C4C23×D4312yes—
675C4⋊C4C23×D4312yes—
676C22⋊C4—434no—
677C22⋊C4—434no—
678C22⋊C4—864no—
679C22⋊C4—864no—
680C22⋊C4—864no—
681C22⋊C4—864no—
682C22⋊C4—864no—
683C22⋊C4—864no—
684C42—24no—
685C42—864no—
686C42D4×D4312yes—
687C42C23×D4312yes—
688C23—434no—
689C23—432no—
690C23—432no—
691C23—862no—
692C23—862no—
693C23—862no—
694C23—862no—
695C23—862no—
696C23—862no—
697C23—1722no—
698C23—1722no—
699C23—1722no—
700C23C2×D4×D4311yescharacteristic
701Q8—22no—
702Q8—24no—
703Q8—84no—
704Q8—862no—
705Q8—862no—
706Q8—862no—
707Q8—862no—
708Q8—1728no—
709Q8—1722no—
710Q8—1722no—
711Q8C2×#1062190214yes—
712D4—868no—
713D4—862no—
714D4—862no—
715D4—1728no—
716D4—1728no—
717D4—1722no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—432no—
729C2×C4—432no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—864no—
737C2×C4—864no—
738C2×C4—862no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—3444no—
742C2×C4—3444no—
743C2×C4—1728no—
744C2×C4—1728no—
745C2×C4—1722no—
746C2×C4—1722no—
747C2×C4—1722no—
748C2×C4C2×D4×D4312yes—
749C2×C4C2×D4×D4312yes—
750C2×C4C2×D4×D4311yescharacteristic
751C2×C4C2×#1062190212yes—
752C2×C4#1306337112yes—
753C2×C4C24×D4311yescharacteristic
754C8—22no—
755C8—22no—
756C8—862no—
757C8—862no—
758C22—434no—
759C22—862no—
760C22—862no—
761C22—868no—
762C22—862no—
763C22—862no—
764C22—862no—
765C22—3444no—
766C22—1722no—
767C22—1722no—
768C22—1722no—
769C22—1724no—
770C22#1458354012yes—
771C22#137×D4312yes—
772C22#1458370512yes—
773C22C22×D4×D4311yescharacteristic
774C4—24no—
775C4—22no—
776C4—22no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—862no—
781C4—862no—
782C4—1722no—
783C4—1722no—
784C4—1722no—
785C4#1458354012yes—
786C4C22×#1062190211yescharacteristic
787C4C2×#1306337111yescharacteristic
788C2—864no—
789C2—3442no—
790C2—1722no—
791C2#1914670314yesdirect product factor
792C2C2×#1458354011yescharacteristic
793C2C2×#137×D4311yescharacteristic
794C2C2×#1458370511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#475C2
socleC23×C43C22×D4
prime radicalC2×#14583561C2
hypercenterC2×#475D43
hypocenterC43C2×#3316
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
1. C2×#14583610C2semidirect
3. #19146703C2direct (N × H)
4. C2×#14583261C2semidirect
5. C2×#14583219C2semidirect
6. C2×#14583231C2semidirect
7. C2×#14583158C2semidirect
8. C2×#14583129C2semidirect
9. C2×#14583122C2semidirect
10. C2×#14583064C2semidirect
11. C2×#14583056C2semidirect
12. C2×#14583004C2semidirect
13. C2×#14582969C2semidirect
14. C2×#14582899C2semidirect
15. C2×#103×D43C2semidirect
16. C2×C43×#475C2semidirect
25. #14583610C22semidirect
45. #14583261C22semidirect
46. #14583231C22semidirect
47. #14583219C22semidirect
48. #14583158C22semidirect
49. #14583129C22semidirect
50. #14583122C22semidirect
51. #14583064C22semidirect
52. #14583056C22semidirect
53. #14583004C22semidirect
54. #14582969C22semidirect
56. #14582899C22semidirect
62. #103×D43C22semidirect
71. C43×#475C22semidirect
397. C2×#475D43semidirect
407. C2×C43#3316semidirect
447. #475C2×D43semidirect
474. C43C2×#3316semidirect
791. C2#19146703direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836102
C2×#145835612
#191467032
C2×#145832612
C2×#145832192
C2×#145832312
C2×#145831582
C2×#145831292
C2×#145831222
C2×#145830642
C2×#145830562
C2×#145830042
C2×#145829692
C2×#145828992
C2×#103×D432
C2×C43×#4752
C2×#331643