Finite Group Databasebeta

← C2×#19144048 #25963415

Subgroups — C2×#19144048 #25963415

Order 11008.

2874 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063347C211yesmaximal, characteristic, complemented
2C22×#13063345C211yesmaximal, characteristic, complemented
3C2×#14583445C211yesmaximal, characteristic, complemented
4C2×#14583367C211yesmaximal, characteristic, complemented
5#19144048C2116yesmaximal, direct product factor
6C2×#14583124C211yesmaximal, characteristic, complemented
7C2×#14583120C211yesmaximal, characteristic, complemented
8C2×#14583108C211yesmaximal, characteristic, complemented
9C2×#14583098C211yesmaximal, characteristic, complemented
10C2×#14583117C211yesmaximal, characteristic, complemented
11C2×#14583113C211yesmaximal, characteristic, complemented
12C2×#14583103C211yesmaximal, characteristic, complemented
13C2×#14583093C211yesmaximal, characteristic, complemented
14C22×Dic43⋊C8C211yesmaximal, characteristic, complemented
15C2×#14582893C211yesmaximal, characteristic, complemented
16C2×C43×#416C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×#10621898C2211yescharacteristic
19C2×#13063347—28no—
20C2×#13063347C2218yescomplemented
21C2×#13063345—28no—
22C2×#13063345C2218yescomplemented
23C22×Dic172C2211yescharacteristic
24C22×#10621885C2211yescharacteristic
25C22×#10621873C2211yescharacteristic
26C22×#10621873C2211yescharacteristic
27C22×#10621883C2211yescharacteristic
28C22×#10621884C2211yescharacteristic
29C22×D344C2211yescharacteristic
30C22×#10621882C2211yescharacteristic
31C23×C43⋊C8C2211yescharacteristic
32#14583445—24no—
33#14583445C2218yescomplemented
34C2×#13063323C2211yescharacteristic
35C2×#13063321C2211yescharacteristic
36C2×#13063314C2211yescharacteristic
37C2×#13063312C2211yescharacteristic
38C2×#13063297—21no—
39C2×#13063297—21no—
40#14583367—24no—
41#14583367C2218yescomplemented
42C2×#13063290C2211yescharacteristic
43C2×#13063290C2211yescharacteristic
44C2×#13063287C2211yescharacteristic
45C2×#13063287C2211yescharacteristic
46C2×C4×C22⋊D43—21no—
47C2×C4×C22⋊D43—21no—
48C2×(C22⋊D43)⋊C4—21no—
49C2×(C22⋊D43)⋊C4—21no—
50C2×#13063282—21no—
51C22×C4×Dic43C2211yescharacteristic
52C2×C42×D43—21no—
53#14583124C2218yescomplemented
54#14583120C2218yescomplemented
55#14583117C2218yescomplemented
56#14583113C2218yescomplemented
57#14583108C2218yescomplemented
58#14583103C2218yescomplemented
59#14583098C2218yescomplemented
60#14583093C2218yescomplemented
61C2×Dic43⋊C8C2211yescharacteristic
62C2×Dic43⋊C8C2211yescharacteristic
63C2×Dic43⋊C8C2211yescharacteristic
64C2×Dic43⋊C8C2211yescharacteristic
65C2×Dic43⋊C8C2218yescomplemented
66#14582893C2218yescomplemented
67C2×#13063248C2211yescharacteristic
68C2×#13063248C2211yescharacteristic
69C2×#13063245C2211yescharacteristic
70C2×#13063245C2211yescharacteristic
71C22×#41×C43C2211yescharacteristic
72C23×C8×C43C2211yescharacteristic
73C2×#117×C43C2211yescharacteristic
74C43×#416C2218yescomplemented
75C2×#103×C43C2211yescharacteristic
76C2×#103×C43C2211yescharacteristic
77C2×#102×C43C2211yescharacteristic
78C2×#102×C43C2211yescharacteristic
79C2×#10621898—22no—
80C2×#10621898—24no—
81C2×#10621898—22no—
82C2×#10621898—24no—
83C2×#10621898—24no—
84C2×#10621898D418yescomplemented
85C2×#10621898C2314yes—
86C2×#10621898C2314yes—
87C22×Dic86C2311yescharacteristic
88C22×Dic86C2311yescharacteristic
89C22×D172C2311yescharacteristic
90C22×D172C2311yescharacteristic
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C22×C22⋊D43—21no—
94C22×C22⋊D43—21no—
95C23×Dic43D411yescharacteristic
96C23×Dic43D411yescharacteristic
97C22×C4×D43—21no—
98C22×C4×D43—21no—
99C22×C4×D43—21no—
100C22×C4×D43—21no—
101#13063347—232no—
102#13063345—232no—
103C2×Dic172—24no—
104C2×Dic172C2314yes—
105C2×#10621885—24no—
106C2×#10621885C2314yes—
107C2×#10621873—24no—
108C2×#10621873—24no—
109C2×#10621873C2314yes—
110C2×#10621873C2314yes—
111C2×#10621883—24no—
112C2×#10621883C2314yes—
113C2×#10621884—24no—
114C2×#10621884C2314yes—
115C2×D344—24no—
116C2×D344C2314yes—
117C2×#10621882—24no—
118C2×#10621882C2314yes—
119C22×C43⋊C8—24no—
120C22×C43⋊C8C2311yescharacteristic
121C22×C43⋊C8C2311yescharacteristic
122C22×C43⋊C8C2314yes—
123#13063323—22no—
124#13063323C2314yes—
125#13063321—22no—
126#13063321C2314yes—
127#13063314—22no—
128#13063314C2314yes—
129#13063312—22no—
130#13063312C2314yes—
131#13063297—28no—
132#13063297—28no—
133#13063290—22no—
134#13063290—22no—
135#13063290C2314yes—
136#13063290C2314yes—
137#13063287—22no—
138#13063287—22no—
139#13063287C2314yes—
140#13063287C2314yes—
141C4×C22⋊D43—28no—
142C4×C22⋊D43—28no—
143(C22⋊D43)⋊C4—28no—
144(C22⋊D43)⋊C4—28no—
145#13063282—28no—
146C2×Dic43⋊C4—21no—
147C2×Dic43⋊C4—21no—
148C2×Dic43⋊C4—21no—
149C2×Dic43⋊C4—21no—
150C2×C22⋊Dic43—21no—
151C2×C22⋊Dic43—21no—
152C2×(C2×D43)⋊C4—21no—
153C2×(C2×D43)⋊C4—21no—
154C2×(C2×D43)⋊C4—21no—
155C2×(C2×D43)⋊C4—21no—
156C2×C4×Dic43—21no—
157C2×C4×Dic43—21no—
158C2×C4×Dic43D411yescharacteristic
159C2×C4×Dic43D411yescharacteristic
160C2×C4×Dic43D414yes—
161C2×C4×Dic43C2311yescharacteristic
162C2×C4×Dic43C2311yescharacteristic
163C2×C4×Dic43C2314yes—
164C42×D43—28no—
165Dic43⋊C8C2314yes—
166Dic43⋊C8C2314yes—
167Dic43⋊C8C2314yes—
168Dic43⋊C8C2314yes—
169#13063248C2314yes—
170#13063248C2314yes—
171#13063245C2314yes—
172#13063245C2314yes—
173C2×#41×C43—22no—
174C2×#41×C43—24no—
175C2×#41×C43—24no—
176C2×#41×C43C2314yes—
177C22×Q8×C43C2311yescharacteristic
178C22×D4×C43—21no—
179C22×D4×C43C2311yescharacteristic
180C23×C4×C43—21no—
181C23×C4×C43C2311yescharacteristic
182C22×C8×C43—24no—
183C22×C8×C43C2311yescharacteristic
184C22×C8×C43C2311yescharacteristic
185C22×C8×C43C2314yes—
186#117×C43—22no—
187#117×C43C2314yes—
188C2×C4⋊C4×C43C2311yescharacteristic
189C2×C4⋊C4×C43C2311yescharacteristic
190C2×C22⋊C4×C43—21no—
191C2×C42×C43—21no—
192#103×C43C2314yes—
193#103×C43C2314yes—
194#102×C43C2314yes—
195#102×C43C2314yes—
196C24×C43—21no—
197C24×C43C2×D411yescharacteristic
198C23×D43—21no—
199C23×D43—21no—
200#41×C43—28no—
201#41×C43—28no—
202#41×C43—48no—
203C2×Q8×C43—21no—
204C2×Q8×C43—22no—
205C2×Q8×C43—22no—
206C2×Q8×C43C2412yes—
207C2×D4×C43—21no—
208C2×D4×C43—24no—
209C2×D4×C43—22no—
210C2×D4×C43—22no—
211C2×D4×C43—44no—
212C2×D4×C43C2412yes—
213C22×C4×C43—24no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—44no—
218C22×C4×C43C2×D414yes—
219C22×C4×C43C2×D412yes—
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43#4114yes—
222C22×C4×C43C2411yescharacteristic
223C22×C4×C43C2412yes—
224C2×C22⋊D43—24no—
225C2×C22⋊D43—24no—
226C2×C22⋊D43—28no—
227C2×C22⋊D43—24no—
228C2×C22⋊D43—24no—
229C2×C22⋊D43—44no—
230C2×C22⋊D43—44no—
231C2×C22⋊D43—44no—
232C22×Dic43—24no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—42no—
236C22×Dic43C2×D411yescharacteristic
237C22×Dic43C2×D411yescharacteristic
238C22×Dic43C2×D411yescharacteristic
239C22×Dic43C2×D414yes—
240C22×Dic43C2×D414yes—
241C22×Dic43C2×D411yescharacteristic
242#10621898—216no—
243#10621898—28no—
244#10621898—28no—
245#10621898—28no—
246#10621898—48no—
247#10621898C2×D4116yescomplemented
248C2×D172—21no—
249C2×D172—22no—
250C2×D172—21no—
251C2×D172—22no—
252C2×D172—22no—
253C2×D172C2×D414yes—
254C2×D172C2412yes—
255C2×D172C2412yes—
256C2×C4×D43—28no—
257C2×C4×D43—24no—
258C2×C4×D43—24no—
259C2×C4×D43—24no—
260C2×C4×D43—24no—
261C2×C4×D43—44no—
262C2×C4×D43—44no—
263C2×C4×D43—44no—
264C2×Dic86—21no—
265C2×Dic86—22no—
266C2×Dic86—22no—
267C2×Dic86—22no—
268C2×Dic86—21no—
269C2×Dic86C2×D414yes—
270C2×Dic86C2412yes—
271C2×Dic86C2412yes—
272C2×C8×C43—22no—
273C2×C8×C43—22no—
274C2×C8×C43—28no—
275C2×C8×C43C2412yes—
276C2×C8×C43C2412yes—
277C4⋊C4×C43—21no—
278C4⋊C4×C43—21no—
279C4⋊C4×C43C2412yes—
280C4⋊C4×C43C2412yes—
281C22⋊C4×C43—24no—
282C42×C43—24no—
283C22⋊Dic43—24no—
284C22⋊Dic43—24no—
285#10621885—28no—
286#10621884—28no—
287#10621883—28no—
288#10621882—28no—
289(C2×D43)⋊C4—24no—
290(C2×D43)⋊C4—24no—
291(C2×D43)⋊C4—24no—
292(C2×D43)⋊C4—24no—
293Dic43⋊C4—24no—
294Dic43⋊C4—24no—
295Dic43⋊C4—24no—
296Dic43⋊C4—24no—
297C4×Dic43—24no—
298C4×Dic43—24no—
299C4×Dic43C2×D414yes—
300C4×Dic43C2×D414yes—
301C4×Dic43C2×D412yes—
302C4×Dic43C2×D412yes—
303C4×Dic43C2412yes—
304C4×Dic43C2412yes—
305C2×C43⋊C8—22no—
306C2×C43⋊C8—22no—
307C2×C43⋊C8—28no—
308C2×C43⋊C8C2412yes—
309C2×C43⋊C8C2412yes—
310Dic172—28no—
311D344—28no—
312#10621873—28no—
313#10621873—28no—
314C23×C43—22no—
315C23×C43—22no—
316C23×C43—22no—
317C23×C43—42no—
318C23×C43—42no—
319C23×C43—42no—
320C23×C43#12114yes—
321C23×C43C22×D412yes—
322C23×C43C22×D411yescharacteristic
323C22×D43—24no—
324C22×D43—22no—
325C22×D43—22no—
326C22×D43—42no—
327C22×D43—42no—
328C22×D43—42no—
329C22×D43—42no—
330C22×D43—42no—
331Q8×C43—22no—
332Q8×C43—22no—
333Q8×C43—42no—
334D4×C43—22no—
335D4×C43—22no—
336D4×C43—48no—
337D4×C43—42no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—42no—
342C2×C4×C43—42no—
343C2×C4×C43—42no—
344C2×C4×C43—48no—
345C2×C4×C43#12114yes—
346C2×C4×C43#12118yes—
347C2×C4×C43C22×D412yes—
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43C22×D412yes—
350C2×C4×C43C22×D414yes—
351C2×C4×C43C2×#4112yes—
352C2×C4×C43C2×#4114yes—
353C2×C4×C43C2511yescharacteristic
354C22⋊D43—216no—
355C22⋊D43—48no—
356C22⋊D43—48no—
357C22⋊D43—48no—
358C2×Dic43—24no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—22no—
363C2×Dic43—28no—
364C2×Dic43—22no—
365C2×Dic43—44no—
366C2×Dic43—42no—
367C2×Dic43#13514yescomplemented
368C2×Dic43C22×D412yes—
369C2×Dic43C22×D412yes—
370C2×Dic43C22×D412yes—
371C2×Dic43C22×D412yes—
372D172—24no—
373D172—22no—
374D172—22no—
375D172—22no—
376D172—42no—
377D172C22×D414yes—
378C4×D43—216no—
379C4×D43—48no—
380C4×D43—48no—
381C4×D43—48no—
382Dic86—24no—
383Dic86—22no—
384Dic86—22no—
385Dic86—22no—
386Dic86—42no—
387Dic86C22×D414yes—
388C8×C43—22no—
389C8×C43—22no—
390C43⋊C8—22no—
391C43⋊C8—22no—
392C2×#3035—431nomaximal, Sylow
393C22×C43—28no—
394C22×C43—22no—
395C22×C43—22no—
396C22×C43—42no—
397C22×C43—42no—
398C22×C43—42no—
399C22×C43—84no—
400C22×C43C2×#12114yes—
401C22×C43C2×#12112yes—
402C22×C43C2×#13512yes—
403C22×C43#57512yes—
404C22×C43C23×D411yescharacteristic
405C2×D43—24no—
406C2×D43—48no—
407C2×D43—42no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—42no—
412C2×D43—84no—
413C4×C43—42no—
414C4×C43—42no—
415C4×C43—42no—
416C4×C43C2×#12112yes—
417C4×C43C2×#12114yes—
418C4×C43C23×D411yescharacteristic
419C4×C43C22×#4111yescharacteristic
420Dic43—24no—
421Dic43—22no—
422Dic43—22no—
423Dic43—22no—
424Dic43—42no—
425Dic43C2×#13514yescomplemented
426C22×#135—431no—
427C22×#135—431no—
428C2×#532—431no—
429C2×C4×#41—431no—
430#3035—4316no—
431C2×#464—431no—
432C2×#464—431no—
433C2×#462—431no—
434C2×#460—431no—
435C2×#463—431no—
436C2×#463—431no—
437C2×#461—431no—
438C2×#459—431no—
439C22×C4⋊C8—431no—
440C2×#416—431no—
441C2×#416D4311yescharacteristic, complemented
442C2×C43—24no—
443C2×C43—82no—
444C2×C43#303514yescomplemented
445C2×C43C22×#12111yescharacteristic
446C2×C43C22×#13511yescharacteristic
447C2×C43C2×#57511yescharacteristic
448D43—44no—
449D43—82no—
450C22×#41—431no—
451C22×#41—431no—
452C22×#41C2×D4311yescharacteristic
453C2×#135—438no—
454C2×#135—438no—
455C2×#135—868no—
456C2×#135—868no—
457C22×Q16—431no—
458C22×Q16—431no—
459C22×SD16—431no—
460C22×SD16—431no—
461C22×SD16—431no—
462C22×SD16—431no—
463C22×D8—431no—
464C22×D8—431no—
465C23×C8—431no—
466C23×C8C2×D4311yescharacteristic
467#532—438no—
468#532—864no—
469C2×C4⋊Q8—431no—
470C2×#127—431no—
471C2×#124—431no—
472C2×#124—431no—
473C2×#121—861no—
474C2×#121—861no—
475C4×#41—438no—
476C4×#41—864no—
477C2×C4×Q8—431no—
478C2×C4×Q8—431no—
479C2×C4×D4—431no—
480C2×C4×D4—431no—
481C2×C4×D4—861no—
482C2×C4×D4—861no—
483C2×C4×D4—861no—
484C2×C4×D4—861no—
485C2×#117—861no—
486C2×#117C2×D4311yescharacteristic
487C22×C42—431no—
488C22×C42—861no—
489#464—438no—
490#464—438no—
491#463—438no—
492#463—438no—
493#462—438no—
494#461—438no—
495#460—438no—
496#459—438no—
497C2×C4⋊C8—431no—
498C2×C4⋊C8—431no—
499C2×C4⋊C8—431no—
500C2×C4⋊C8—431no—
501C2×C4⋊C8—438no—
502#416—438no—
503#416C2×D4318yescomplemented
504C2×#103—431no—
505C2×#103—431no—
506C2×#103C2×D4311yescharacteristic
507C2×#103C2×D4311yescharacteristic
508C2×#102—431no—
509C2×#102—431no—
510C2×#102C2×D4311yescharacteristic
511C2×#102C2×D4311yescharacteristic
512C43C2×#303511yescharacteristic, complemented, Sylow
513C2×#41—22no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—438no—
517C2×#41—434no—
518C2×#41—434no—
519C2×#41—864no—
520C2×#41—862no—
521C2×#41—862no—
522C2×#41—864no—
523C2×#41—864no—
524C2×#41C22×D4314yes—
525C22×Q8—431no—
526C22×Q8—431no—
527C22×Q8C22×D4311yescharacteristic
528C22×D4—21no—
529C22×D4—431no—
530C22×D4—431no—
531C22×D4—861no—
532C22×D4—861no—
533C22×D4—861no—
534C22×D4—861no—
535C22×D4C22×D4311yescharacteristic
536C23×C4—21no—
537C23×C4—431no—
538C23×C4—431no—
539C23×C4—861no—
540C23×C4—861no—
541C23×C4—861no—
542C23×C4—861no—
543C23×C4C22×D4311yescharacteristic
544#135—8632no—
545#135—8632no—
546C2×Q16—434no—
547C2×Q16—434no—
548C2×Q16—864no—
549C2×Q16—864no—
550C2×SD16—434no—
551C2×SD16—434no—
552C2×SD16—434no—
553C2×SD16—434no—
554C2×SD16—864no—
555C2×SD16—864no—
556C2×SD16—864no—
557C2×SD16—864no—
558C2×D8—434no—
559C2×D8—434no—
560C2×D8—864no—
561C2×D8—864no—
562C22×C8—24no—
563C22×C8—431no—
564C22×C8—431no—
565C22×C8—434no—
566C22×C8—864no—
567C22×C8C22×D4311yescharacteristic
568C22×C8C22×D4311yescharacteristic
569C22×C8C22×D4314yes—
570C4⋊Q8—434no—
571C4⋊Q8—862no—
572#127—434no—
573#127—862no—
574#124—434no—
575#124—434no—
576#124—862no—
577#124—862no—
578#121—868no—
579#121—868no—
580C4×Q8—434no—
581C4×Q8—434no—
582C4×Q8—862no—
583C4×Q8—862no—
584C4×D4—434no—
585C4×D4—434no—
586C4×D4—862no—
587C4×D4—862no—
588C4×D4—868no—
589C4×D4—868no—
590C4×D4—868no—
591C4×D4—868no—
592#117—22no—
593#117—868no—
594#117C22×D4314yes—
595C2×C4⋊C4—861no—
596C2×C4⋊C4—861no—
597C2×C4⋊C4—861no—
598C2×C4⋊C4—861no—
599C2×C4⋊C4C22×D4311yescharacteristic
600C2×C4⋊C4C22×D4311yescharacteristic
601C2×C22⋊C4—21no—
602C2×C22⋊C4—861no—
603C2×C22⋊C4—861no—
604C2×C22⋊C4—861no—
605C2×C22⋊C4—861no—
606C2×C22⋊C4—861no—
607C2×C22⋊C4—861no—
608C2×C42—21no—
609C2×C42—434no—
610C2×C42—431no—
611C2×C42—431no—
612C2×C42—431no—
613C2×C42—431no—
614C2×C42—434no—
615C2×C42—868no—
616C2×C42—861no—
617C2×C42—861no—
618C4⋊C8—434no—
619C4⋊C8—434no—
620C4⋊C8—434no—
621C4⋊C8—434no—
622#103—434no—
623#103—434no—
624#103C22×D4314yes—
625#103C22×D4314yes—
626#102—434no—
627#102—434no—
628#102C22×D4314yes—
629#102C22×D4314yes—
630C24—21no—
631C24—861no—
632C24—861no—
633C24D4×D4311yescharacteristic
634#41—28no—
635#41—28no—
636#41—48no—
637#41—4316no—
638#41—8616no—
639#41—868no—
640#41—868no—
641#41—868no—
642#41—1728no—
643C2×Q8—21no—
644C2×Q8—22no—
645C2×Q8—22no—
646C2×Q8—434no—
647C2×Q8—432no—
648C2×Q8—432no—
649C2×Q8—861no—
650C2×Q8—861no—
651C2×Q8—862no—
652C2×Q8—862no—
653C2×Q8—862no—
654C2×Q8C23×D4312yes—
655C2×D4—24no—
656C2×D4—22no—
657C2×D4—21no—
658C2×D4—22no—
659C2×D4—44no—
660C2×D4—434no—
661C2×D4—432no—
662C2×D4—432no—
663C2×D4—864no—
664C2×D4—864no—
665C2×D4—868no—
666C2×D4—864no—
667C2×D4—864no—
668C2×D4—861no—
669C2×D4—862no—
670C2×D4—861no—
671C2×D4—862no—
672C2×D4—862no—
673C2×D4—1724no—
674C2×D4—1724no—
675C2×D4—1724no—
676C2×D4C23×D4312yes—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—24no—
681C22×C4—44no—
682C22×C4—431no—
683C22×C4—431no—
684C22×C4—431no—
685C22×C4—431no—
686C22×C4—434no—
687C22×C4—434no—
688C22×C4—864no—
689C22×C4—864no—
690C22×C4—864no—
691C22×C4—861no—
692C22×C4—868no—
693C22×C4—864no—
694C22×C4—861no—
695C22×C4—864no—
696C22×C4—1724no—
697C22×C4—1724no—
698C22×C4—1722no—
699C22×C4—1724no—
700C22×C4#1062189814yes—
701C22×C4D4×D4312yes—
702C22×C4D4×D4314yes—
703C22×C4D4×D4311yescharacteristic
704C22×C4C23×D4311yescharacteristic
705C22×C4C23×D4312yes—
706Q16—868no—
707Q16—868no—
708SD16—868no—
709SD16—868no—
710SD16—868no—
711SD16—868no—
712D8—868no—
713D8—868no—
714C2×C8—22no—
715C2×C8—22no—
716C2×C8—28no—
717C2×C8—432no—
718C2×C8—432no—
719C2×C8—862no—
720C2×C8—862no—
721C2×C8—868no—
722C2×C8C23×D4312yes—
723C2×C8C23×D4312yes—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—864no—
727C4⋊C4—864no—
728C4⋊C4—864no—
729C4⋊C4—864no—
730C4⋊C4C23×D4312yes—
731C4⋊C4C23×D4312yes—
732C22⋊C4—24no—
733C22⋊C4—864no—
734C22⋊C4—864no—
735C22⋊C4—864no—
736C22⋊C4—864no—
737C22⋊C4—864no—
738C22⋊C4—864no—
739C42—24no—
740C42—434no—
741C42—434no—
742C42—432no—
743C42—432no—
744C42—432no—
745C42—432no—
746C42—864no—
747C42—864no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—864no—
755C23—862no—
756C23—862no—
757C23—1722no—
758C23—1722no—
759C23—1722no—
760C23—1722no—
761C23—1722no—
762C23#1306329814yes—
763C23C2×D4×D4312yes—
764C23C2×D4×D4311yescharacteristic
765Q8—22no—
766Q8—22no—
767Q8—42no—
768Q8—434no—
769Q8—864no—
770Q8—862no—
771Q8—862no—
772Q8—862no—
773Q8—1722no—
774D4—22no—
775D4—22no—
776D4—48no—
777D4—42no—
778D4—434no—
779D4—8616no—
780D4—864no—
781D4—862no—
782D4—862no—
783D4—862no—
784D4—1728no—
785D4—1728no—
786D4—1728no—
787D4—1722no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—48no—
795C2×C4—434no—
796C2×C4—432no—
797C2×C4—432no—
798C2×C4—432no—
799C2×C4—432no—
800C2×C4—868no—
801C2×C4—864no—
802C2×C4—862no—
803C2×C4—862no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—8616no—
807C2×C4—862no—
808C2×C4—1728no—
809C2×C4—1728no—
810C2×C4—1724no—
811C2×C4—1722no—
812C2×C4—1728no—
813C2×C4#1306329814yes—
814C2×C4#1306329818yes—
815C2×C4C2×D4×D4312yes—
816C2×C4C2×D4×D4311yescharacteristic
817C2×C4C2×D4×D4312yes—
818C2×C4C2×D4×D4314yes—
819C2×C4C2×#1062189812yes—
820C2×C4C2×#1062189814yes—
821C2×C4C24×D4311yescharacteristic
822C8—22no—
823C8—22no—
824C8—862no—
825C8—862no—
826C22—22no—
827C22—22no—
828C22—28no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—84no—
833C22—864no—
834C22—3444no—
835C22—1722no—
836C22—1722no—
837C22—1722no—
838C22—1722no—
839C22—1722no—
840C22—1728no—
841C22C2×#1306329814yes—
842C22C2×#1306329812yes—
843C22#135×D4312yes—
844C22#1458369612yes—
845C22C22×D4×D4311yescharacteristic
846C4—42no—
847C4—42no—
848C4—42no—
849C4—434no—
850C4—862no—
851C4—862no—
852C4—862no—
853C4—864no—
854C4—1722no—
855C4C2×#1306329814yes—
856C4C2×#1306329812yes—
857C4C22×D4×D4311yescharacteristic
858C4C22×#1062189811yescharacteristic
859C2—24no—
860C2—82no—
861C2—3442no—
862C2—1724no—
863C2#1914404814yesdirect product factor
864C2C22×#1306329811yescharacteristic
865C2C2×#135×D4311yescharacteristic
866C2C2×#1458369611yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#416C2
socleC23×C43C22×D4
hypercenterC2×#416D43
hypocenterC43C2×#3035
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C22×#13063347C2semidirect
2. C22×#13063345C2semidirect
3. C2×#14583445C2semidirect
4. C2×#14583367C2semidirect
5. #19144048C2direct (N × H)
6. C2×#14583124C2semidirect
7. C2×#14583120C2semidirect
8. C2×#14583108C2semidirect
9. C2×#14583098C2semidirect
10. C2×#14583117C2semidirect
11. C2×#14583113C2semidirect
12. C2×#14583103C2semidirect
13. C2×#14583093C2semidirect
14. C22×Dic43⋊C8C2semidirect
15. C2×#14582893C2semidirect
16. C2×C43×#416C2semidirect
20. C2×#13063347C22semidirect
22. C2×#13063345C22semidirect
33. #14583445C22semidirect
41. #14583367C22semidirect
53. #14583124C22semidirect
54. #14583120C22semidirect
55. #14583117C22semidirect
56. #14583113C22semidirect
57. #14583108C22semidirect
58. #14583103C22semidirect
59. #14583098C22semidirect
60. #14583093C22semidirect
65. C2×Dic43⋊C8C22semidirect
66. #14582893C22semidirect
74. C43×#416C22semidirect
84. C2×#10621898D4semidirect
247. #10621898C2×D4semidirect
367. C2×Dic43#135semidirect
425. Dic43C2×#135semidirect
441. C2×#416D43semidirect
444. C2×C43#3035semidirect
503. #416C2×D43semidirect
512. C43C2×#3035semidirect
863. C2#19144048direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633472
C22×#130633452
C2×#145834452
C2×#145833672
#191440482
C2×#145831242
C2×#145831202
C2×#145831082
C2×#145830982
C2×#145831172
C2×#145831132
C2×#145831032
C2×#145830932
C22×Dic43⋊C82
C2×#145828932
C2×C43×#4162
C2×#303543