Finite Group Databasebeta

← C2×#19148706 #26004883

Subgroups — C2×#19148706 #26004883

Order 11008.

7226 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148706C2132yesmaximal, direct product factor
2C2×#14583634C213yesmaximal, complemented
3C2×#14583625C211yesmaximal, characteristic, complemented
4C2×#14583612C213yesmaximal, complemented
5C2×#14583593C213yesmaximal, complemented
6C2×#14583590C213yesmaximal, complemented
7C2×#14583571C211yesmaximal, characteristic, complemented
8C2×#14583560C211yesmaximal, characteristic, complemented
9C2×#14583560C211yesmaximal, characteristic, complemented
10C2×#14583521C213yesmaximal, complemented
11C2×#14583504C213yesmaximal, complemented
12C2×#14583436C213yesmaximal, complemented
13C2×#14583427C213yesmaximal, complemented
14C2×#14583381C211yesmaximal, characteristic, complemented
15C2×C4×#10621902C211yesmaximal, characteristic, complemented
16C2×C43×#519C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621902C2211yescharacteristic
19#14583634C22148yescomplemented
20#14583625C22116yescomplemented
21#14583612C22148yescomplemented
22#14583593C22148yescomplemented
23#14583590C22148yescomplemented
24#14583571C22116yescomplemented
25#14583560C22116yescomplemented
26#14583560C22116yescomplemented
27#14583521C22148yescomplemented
28#14583504C22148yescomplemented
29C2×#13063324C2213yes—
30C2×#13063322C2213yes—
31#14583436C22148yescomplemented
32#14583427C22148yescomplemented
33C2×#13063320C2213yes—
34C2×#13063319C2216yes—
35C2×#13063318C2211yescharacteristic
36C2×#13063317C2213yes—
37C2×#13063316C2213yes—
38C2×#13063315C2213yes—
39C2×#13063314C2213yes—
40C2×#13063314C2213yes—
41C2×#13063313C2216yes—
42C2×#13063311C2213yes—
43C2×#13063310C2216yes—
44C2×#13063310C2213yes—
45C2×#13063310C2216yes—
46C2×#13063307C2213yes—
47C2×#13063303C2213yes—
48C2×#13063301C2213yes—
49C2×#13063301C2213yes—
50C2×#13063300C2213yes—
51C2×#13063300C2213yes—
52C2×#13063299C2213yes—
53C2×#13063299C2213yes—
54C2×#13063298C2213yes—
55C2×#13063298C2216yes—
56#14583381C22116yescomplemented
57C4×#10621902C22116yescomplemented
58C2×Q8×Dic43C2211yescharacteristic
59C2×Q8×Dic43C2211yescharacteristic
60C2×C4×Dic86C2213yes—
61C2×C4×D172C2213yes—
62C2×C4×D172C2213yes—
63C2×C4×D172C2213yes—
64C2×C4×D172C2216yes—
65C2×#13063287C2213yes—
66C2×#13063287C2213yes—
67C2×C4×C22⋊D43C2213yes—
68C2×C4×C22⋊D43C2213yes—
69C2×#13063283C2213yes—
70C2×#13063282C2213yes—
71C2×#13063282C2216yes—
72C2×C4⋊C4×D43C2213yes—
73C2×C42×D43C2213yes—
74C23×Q8×C43C2211yescharacteristic
75C43×#519C22116yescomplemented
76C2×C4×Q8×C43C2211yescharacteristic
77C2×C4×Q8×C43C2211yescharacteristic
78C2×C4×Q8×C43C2213yes—
79C2×C4×Q8×C43C2213yes—
80C2×#117×C43C2213yes—
81C2×#117×C43C2213yes—
82C2×#10621902—28no—
83C2×#10621902—28no—
84C2×#10621902C2318yes—
85C2×#10621902C2318yes—
86C22×Dic86C2313yes—
87C22×D172C2313yes—
88C22×D172C2313yes—
89C22×D172C2316yes—
90C22×D172C2313yes—
91C22×C22⋊D43C2313yes—
92C22×C22⋊D43C2313yes—
93C22×C4×D43C2313yes—
94C22×C4×D43C2313yes—
95C22×C4×D43C2313yes—
96C22×C4×D43C2313yes—
97C22×C4×D43C2316yes—
98#13063324C23124yes—
99#13063322C23124yes—
100#13063320C23124yes—
101#13063319C23148yes—
102#13063318C2318yes—
103#13063317C23124yes—
104#13063316C23124yes—
105#13063315C23124yes—
106#13063314C23124yes—
107#13063314C23124yes—
108#13063313C23148yes—
109#13063311C23124yes—
110#13063310C23148yes—
111#13063310C23124yes—
112#13063310C23148yes—
113#13063307C23124yes—
114#13063303C23124yes—
115#13063301C23124yes—
116#13063301C23124yes—
117#13063300C23124yes—
118#13063300C23124yes—
119#13063299C23124yes—
120#13063299C23124yes—
121#13063298C23148yes—
122#13063298C23124yes—
123Q8×Dic43C2318yes—
124Q8×Dic43C2318yes—
125C4×Dic86C23124yes—
126C4×D172C23124yes—
127C4×D172C23148yes—
128C4×D172C23124yes—
129C4×D172C23124yes—
130#13063287C23124yes—
131#13063287C23124yes—
132C4×C22⋊D43C23124yes—
133C4×C22⋊D43C23124yes—
134#13063283C23124yes—
135#13063282C23148yes—
136#13063282C23124yes—
137C2×C4⋊Dic43C2313yes—
138C2×C4⋊Dic43C2313yes—
139C2×C4⋊Dic43C2311yescharacteristic
140C2×C4⋊Dic43C2313yes—
141C2×Dic43⋊C4C2313yes—
142C2×Dic43⋊C4C2311yescharacteristic
143C2×Dic43⋊C4C2313yes—
144C2×Dic43⋊C4C2316yes—
145C2×Dic43⋊C4C2313yes—
146C2×Dic43⋊C4C2311yescharacteristic
147C2×Dic43⋊C4C2313yes—
148C4⋊C4×D43C23124yes—
149C2×C22⋊Dic43C2311yescharacteristic
150C2×C22⋊Dic43C2311yescharacteristic
151C2×(C2×D43)⋊C4C2313yes—
152C2×(C2×D43)⋊C4C2313yes—
153C2×(C2×D43)⋊C4C2313yes—
154C2×(C2×D43)⋊C4C2316yes—
155C2×(C2×D43)⋊C4C2316yes—
156C2×(C2×D43)⋊C4C2313yes—
157C2×(C2×D43)⋊C4C2313yes—
158C2×(C2×D43)⋊C4C2316yes—
159C2×(C2×D43)⋊C4C2313yes—
160C2×C4×Dic43C2311yescharacteristic
161C2×C4×Dic43C2313yes—
162C2×C4×Dic43C2313yes—
163C2×C4×Dic43C2313yes—
164C42×D43C23124yes—
165C22×Q8×C43—28no—
166C22×Q8×C43C2318yes—
167C22×Q8×C43C2313yes—
168C22×Q8×C43C2311yescharacteristic
169C23×C4×C43C2313yes—
170C4×Q8×C43C2318yes—
171C4×Q8×C43C23124yes—
172C4×Q8×C43C2318yes—
173C4×Q8×C43C23124yes—
174#117×C43C23124yes—
175#117×C43C23124yes—
176C2×C4⋊C4×C43C2313yes—
177C2×C4⋊C4×C43C2313yes—
178C2×C4⋊C4×C43C2313yes—
179C2×C4⋊C4×C43C2313yes—
180C2×C22⋊C4×C43C2311yescharacteristic
181C2×C22⋊C4×C43C2313yes—
182C2×C42×C43C2313yes—
183C2×C42×C43C2316yes—
184C2×C42×C43C2313yes—
185C24×C43C2411yescharacteristic
186C23×D43C2413yes—
187C23×D43C2413yes—
188C2×Q8×C43—232no—
189C2×Q8×C43—212no—
190C2×Q8×C43#4118yes—
191C2×Q8×C43C24112yes—
192C2×Q8×C43C2414yes—
193C22×C4×C43—212no—
194C22×C4×C43C2411yescharacteristic
195C22×C4×C43C2413yes—
196C22×C4×C43C2413yes—
197C22×C4×C43C2411yescharacteristic
198C22×C4×C43C2413yes—
199C22×C4×C43C24112yes—
200C22×C4×C43C2413yes—
201C2×C22⋊D43—46no—
202C2×C22⋊D43—46no—
203C2×C22⋊D43C24112yes—
204C2×C22⋊D43C24112yes—
205C22×Dic43C2411yescharacteristic
206C22×Dic43C2411yescharacteristic
207C22×Dic43C2411yescharacteristic
208C22×Dic43C2413yes—
209C22×Dic43C2413yes—
210C22×Dic43C2411yescharacteristic
211#10621902—232no—
212#10621902—232no—
213C2×D172—212no—
214C2×D172—212no—
215C2×D172—46no—
216C2×D172—412no—
217C2×D172C24112yes—
218C2×D172C24112yes—
219C2×D172C24124yes—
220C2×D172C24112yes—
221C2×C4×D43—212no—
222C2×C4×D43—212no—
223C2×C4×D43—412no—
224C2×C4×D43—46no—
225C2×C4×D43—46no—
226C2×C4×D43C24112yes—
227C2×C4×D43C24112yes—
228C2×C4×D43C24112yes—
229C2×C4×D43C24112yes—
230C2×C4×D43C24124yes—
231C2×Dic86—46no—
232C2×Dic86C24112yes—
233C4⋊C4×C43C24112yes—
234C4⋊C4×C43C24112yes—
235C4⋊C4×C43C24112yes—
236C4⋊C4×C43C24112yes—
237C22⋊C4×C43C2414yes—
238C22⋊C4×C43C24112yes—
239C42×C43C24112yes—
240C42×C43C24124yes—
241C42×C43C24112yes—
242C22⋊Dic43C2414yes—
243C22⋊Dic43C2414yes—
244(C2×D43)⋊C4C24112yes—
245(C2×D43)⋊C4C24112yes—
246(C2×D43)⋊C4C24112yes—
247(C2×D43)⋊C4C24124yes—
248(C2×D43)⋊C4C24124yes—
249(C2×D43)⋊C4C24112yes—
250(C2×D43)⋊C4C24112yes—
251(C2×D43)⋊C4C24124yes—
252(C2×D43)⋊C4C24112yes—
253C4⋊Dic43C24112yes—
254C4⋊Dic43C24112yes—
255C4⋊Dic43C2414yes—
256C4⋊Dic43C24112yes—
257Dic43⋊C4C24112yes—
258Dic43⋊C4C2414yes—
259Dic43⋊C4C24112yes—
260Dic43⋊C4C24124yes—
261Dic43⋊C4C24112yes—
262Dic43⋊C4C2414yes—
263Dic43⋊C4C24112yes—
264C4×Dic43C2414yes—
265C4×Dic43C24112yes—
266C4×Dic43C24112yes—
267C4×Dic43C24112yes—
268C23×C43—22no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43C2512yes—
272C23×C43C2511yescharacteristic
273C22×D43—26no—
274C22×D43—26no—
275C22×D43—26no—
276C22×D43—26no—
277C22×D43—26no—
278C22×D43—26no—
279C22×D43C2516yes—
280C22×D43C2516yes—
281Q8×C43—224no—
282Q8×C43C2×#41116yes—
283C2×C4×C43—26no—
284C2×C4×C43—26no—
285C2×C4×C43—26no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—224no—
289C2×C4×C43C2×#41112yes—
290C2×C4×C43C2512yes—
291C2×C4×C43C2516yes—
292C2×C4×C43C2512yes—
293C2×C4×C43C2516yes—
294C2×C4×C43C2516yes—
295C2×C4×C43C2516yes—
296C22⋊D43—412no—
297C22⋊D43—412no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—26no—
302C2×Dic43—22no—
303C2×Dic43—26no—
304C2×Dic43C2512yes—
305C2×Dic43C2512yes—
306C2×Dic43C2512yes—
307C2×Dic43C2516yes—
308C2×Dic43C2516yes—
309C2×Dic43C2512yes—
310D172—224no—
311D172—224no—
312D172—424no—
313D172—412no—
314C4×D43—224no—
315C4×D43—224no—
316C4×D43—412no—
317C4×D43—412no—
318C4×D43—424no—
319Dic86—412no—
320C2×#3524—431nomaximal, Sylow
321C22×C43—22no—
322C22×C43—22no—
323C22×C43—22no—
324C22×C43—44no—
325C22×C43C22×#4112yes—
326C22×C43#58512yes—
327C22×C43#58512yes—
328C22×C43C2611yescharacteristic
329C2×D43—26no—
330C2×D43—26no—
331C2×D43—26no—
332C2×D43—26no—
333C2×D43—26no—
334C2×D43—26no—
335C2×D43—412no—
336C2×D43—412no—
337C4×C43—26no—
338C4×C43—26no—
339C4×C43—22no—
340C4×C43—26no—
341C4×C43—22no—
342C4×C43C22×#41112yes—
343Dic43—22no—
344Dic43—22no—
345Dic43—22no—
346Dic43—26no—
347Dic43—22no—
348Dic43—26no—
349#3524—4332no—
350C2×#559—433no—
351C2×#557—431no—
352C2×#555—433no—
353C2×#553—433no—
354C2×#552—433no—
355C2×#550—431no—
356C2×#548—431no—
357C2×#548—431no—
358C2×#542—433no—
359C2×#540—433no—
360C2×#529—433no—
361C2×#529—433no—
362C2×#520—431no—
363C2×#519D4311yescharacteristic, complemented
364C2×C4×#41—431no—
365C2×C43—42no—
366C2×C43#352414yescomplemented
367C2×C43C23×#4111yescharacteristic
368C2×C43C2×#58511yescharacteristic
369C2×C43C2×#58511yescharacteristic
370D43—46no—
371D43—46no—
372C22×#41—431no—
373C22×#41—431no—
374C23×Q8C2×D4311yescharacteristic
375#559—4348no—
376#557—4316no—
377#555—4348no—
378#553—4348no—
379#552—4348no—
380#550—4316no—
381#548—4316no—
382#548—4316no—
383#542—4348no—
384#540—4348no—
385C2×C4⋊Q8—433no—
386C2×#127—433no—
387#529—4348no—
388#529—4348no—
389C2×#126—433no—
390C2×#126—431no—
391C2×#126—436no—
392C2×#125—433no—
393C2×#125—433no—
394C2×#125—433no—
395C2×#124—433no—
396C2×#124—433no—
397C2×#124—433no—
398C2×#124—436no—
399C2×#123—436no—
400C2×#123—433no—
401C2×#123—436no—
402C2×#123—433no—
403C2×C22⋊Q8—433no—
404C2×C22⋊Q8—433no—
405C2×C22⋊Q8—433no—
406C2×#121—433no—
407C2×#121—433no—
408C2×#121—433no—
409C2×#121—433no—
410C2×#121—433no—
411C2×#121—436no—
412#520—4316no—
413#519C2×D43116yescomplemented
414C4×#41—4316no—
415C2×C4×Q8—431no—
416C2×C4×Q8—431no—
417C2×C4×Q8—433no—
418C2×C4×Q8C2×D4311yescharacteristic
419C2×C4×Q8C2×D4313yes—
420C2×C4×Q8C2×D4311yescharacteristic
421C2×C4×Q8C2×D4313yes—
422C2×C4×D4—433no—
423C2×C4×D4—433no—
424C2×C4×D4—433no—
425C2×C4×D4—433no—
426C2×C4×D4—433no—
427C2×C4×D4—433no—
428C2×C4×D4—433no—
429C2×C4×D4—436no—
430C2×#117—433no—
431C2×#117—433no—
432C2×#117—436no—
433C2×#117C2×D4313yes—
434C2×#117C2×D4313yes—
435C22×C4⋊C4—433no—
436C22×C42—433no—
437C43C2×#352411yescharacteristic, complemented, Sylow
438C2×#41—438no—
439C2×#41—438no—
440C2×#41—868no—
441C2×#41—868no—
442C22×Q8—28no—
443C22×Q8—433no—
444C22×Q8C22×D4313yes—
445C22×Q8C22×D4318yes—
446C22×Q8C22×D4311yescharacteristic
447C22×D4—433no—
448C22×D4—433no—
449C22×D4—433no—
450C22×D4—433no—
451C22×D4—436no—
452C22×D4—433no—
453C23×C4—433no—
454C23×C4—433no—
455C23×C4—436no—
456C23×C4—433no—
457C23×C4—433no—
458C23×C4C22×D4313yes—
459C4⋊Q8—4324no—
460#127—4324no—
461#126—4324no—
462#126—438no—
463#126—4348no—
464#125—4324no—
465#125—4324no—
466#125—4324no—
467#124—4324no—
468#124—4324no—
469#124—4324no—
470#124—4348no—
471#123—4348no—
472#123—4324no—
473#123—4348no—
474#123—4324no—
475C22⋊Q8—4324no—
476C22⋊Q8—4324no—
477C22⋊Q8—4324no—
478#121—4324no—
479#121—4324no—
480#121—4324no—
481#121—4324no—
482#121—4324no—
483#121—4348no—
484C4×Q8—438no—
485C4×Q8—438no—
486C4×Q8—4324no—
487C4×Q8C22×D4318yes—
488C4×Q8C22×D43124yes—
489C4×Q8C22×D4318yes—
490C4×Q8C22×D43124yes—
491C4×D4—4324no—
492C4×D4—4324no—
493C4×D4—4324no—
494C4×D4—4324no—
495C4×D4—4324no—
496C4×D4—4324no—
497C4×D4—4324no—
498C4×D4—4348no—
499#117—4324no—
500#117—4324no—
501#117—4348no—
502#117C22×D43124yes—
503#117C22×D43124yes—
504C2×C4⋊C4—433no—
505C2×C4⋊C4—433no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—433no—
508C2×C4⋊C4—433no—
509C2×C4⋊C4—436no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—433no—
512C2×C4⋊C4—433no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4—433no—
515C2×C4⋊C4—4324no—
516C2×C4⋊C4C22×D4313yes—
517C2×C4⋊C4C22×D4313yes—
518C2×C4⋊C4C22×D4313yes—
519C2×C4⋊C4C22×D4313yes—
520C2×C22⋊C4—431no—
521C2×C22⋊C4—431no—
522C2×C22⋊C4—433no—
523C2×C22⋊C4—433no—
524C2×C22⋊C4—436no—
525C2×C22⋊C4—433no—
526C2×C22⋊C4—436no—
527C2×C22⋊C4—433no—
528C2×C22⋊C4—433no—
529C2×C22⋊C4—436no—
530C2×C22⋊C4—433no—
531C2×C22⋊C4C22×D4311yescharacteristic
532C2×C22⋊C4C22×D4313yes—
533C2×C42—433no—
534C2×C42—433no—
535C2×C42—433no—
536C2×C42—431no—
537C2×C42—4324no—
538C2×C42C22×D4313yes—
539C2×C42C22×D4316yes—
540C2×C42C22×D4313yes—
541C24—433no—
542C24—433no—
543C24C23×D4311yescharacteristic
544#41—8632no—
545#41—8632no—
546C2×Q8—232no—
547C2×Q8—212no—
548C2×Q8—4312no—
549C2×Q8—1726no—
550C2×Q8#1062189818yes—
551C2×Q8C23×D43112yes—
552C2×Q8C23×D4314yes—
553C2×D4—4312no—
554C2×D4—4312no—
555C2×D4—4312no—
556C2×D4—4312no—
557C2×D4—4324no—
558C2×D4—4312no—
559C2×D4—8612no—
560C2×D4—8612no—
561C2×D4—1726no—
562C2×D4—17212no—
563C2×D4—1726no—
564C2×D4—1726no—
565C22×C4—212no—
566C22×C4—431no—
567C22×C4—431no—
568C22×C4—431no—
569C22×C4—433no—
570C22×C4—433no—
571C22×C4—431no—
572C22×C4—4312no—
573C22×C4—4312no—
574C22×C4—4312no—
575C22×C4—4312no—
576C22×C4—4324no—
577C22×C4—8612no—
578C22×C4—8612no—
579C22×C4—1726no—
580C22×C4—17212no—
581C22×C4—1726no—
582C22×C4C23×D43112yes—
583C22×C4C23×D4313yes—
584C22×C4C23×D4311yescharacteristic
585C22×C4C23×D4313yes—
586C22×C4C23×D4311yescharacteristic
587C22×C4C23×D4313yes—
588C22×C4C23×D4313yes—
589C4⋊C4—4312no—
590C4⋊C4—4312no—
591C4⋊C4—434no—
592C4⋊C4—4312no—
593C4⋊C4—4312no—
594C4⋊C4—4324no—
595C4⋊C4—434no—
596C4⋊C4—4312no—
597C4⋊C4—4312no—
598C4⋊C4—434no—
599C4⋊C4—4312no—
600C4⋊C4C23×D43112yes—
601C4⋊C4C23×D43112yes—
602C4⋊C4C23×D43112yes—
603C4⋊C4C23×D43112yes—
604C22⋊C4—434no—
605C22⋊C4—434no—
606C22⋊C4—4312no—
607C22⋊C4—4312no—
608C22⋊C4—4324no—
609C22⋊C4—4312no—
610C22⋊C4—4324no—
611C22⋊C4—4312no—
612C22⋊C4—4312no—
613C22⋊C4—4324no—
614C22⋊C4—4312no—
615C22⋊C4C23×D4314yes—
616C22⋊C4C23×D43112yes—
617C42—434no—
618C42—4312no—
619C42—4312no—
620C42—4312no—
621C42C23×D43112yes—
622C42C23×D43124yes—
623C42C23×D43112yes—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—436no—
628C23—436no—
629C23—866no—
630C23—866no—
631C23—866no—
632C23—866no—
633C23—866no—
634C23—866no—
635C23C24×D4312yes—
636C23C24×D4311yescharacteristic
637Q8—224no—
638Q8—17212no—
639Q8C2×#10621898116yes—
640D4—8624no—
641D4—8624no—
642D4—17212no—
643D4—17224no—
644D4—17212no—
645D4—17212no—
646C2×C4—26no—
647C2×C4—26no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—26no—
651C2×C4—224no—
652C2×C4—432no—
653C2×C4—432no—
654C2×C4—432no—
655C2×C4—436no—
656C2×C4—436no—
657C2×C4—432no—
658C2×C4—862no—
659C2×C4—862no—
660C2×C4—862no—
661C2×C4—866no—
662C2×C4—866no—
663C2×C4—862no—
664C2×C4—8624no—
665C2×C4—8624no—
666C2×C4—17212no—
667C2×C4—17224no—
668C2×C4—17212no—
669C2×C4C2×#10621898112yes—
670C2×C4C24×D4312yes—
671C2×C4C24×D4316yes—
672C2×C4C24×D4316yes—
673C2×C4C24×D4312yes—
674C2×C4C24×D4316yes—
675C2×C4C24×D4316yes—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—44no—
680C22—866no—
681C22—866no—
682C22—866no—
683C22—866no—
684C22—866no—
685C22—866no—
686C22—17212no—
687C22—17212no—
688C22C22×#1062189812yes—
689C22#1458373612yes—
690C22#1458373612yes—
691C22C25×D4311yescharacteristic
692C4—26no—
693C4—26no—
694C4—22no—
695C4—22no—
696C4—26no—
697C4—862no—
698C4—862no—
699C4—862no—
700C4—866no—
701C4—866no—
702C4—862no—
703C4C22×#10621898112yes—
704C2—42no—
705C2—1726no—
706C2—1726no—
707C2#1914870614yesdirect product factor
708C2C23×#1062189811yescharacteristic
709C2C2×#1458373611yescharacteristic
710C2C2×#1458373611yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#519C2
socleC23×C43C25
hypercenterC2×#519D43
hypocenterC43C2×#3524
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
1. #19148706C2direct (N × H)
2. C2×#14583634C2semidirect
3. C2×#14583625C2semidirect
4. C2×#14583612C2semidirect
5. C2×#14583593C2semidirect
6. C2×#14583590C2semidirect
7. C2×#14583571C2semidirect
8. C2×#14583560C2semidirect
9. C2×#14583560C2semidirect
10. C2×#14583521C2semidirect
11. C2×#14583504C2semidirect
12. C2×#14583436C2semidirect
13. C2×#14583427C2semidirect
14. C2×#14583381C2semidirect
15. C2×C4×#10621902C2semidirect
16. C2×C43×#519C2semidirect
19. #14583634C22semidirect
20. #14583625C22semidirect
21. #14583612C22semidirect
22. #14583593C22semidirect
23. #14583590C22semidirect
24. #14583571C22semidirect
25. #14583560C22semidirect
26. #14583560C22semidirect
27. #14583521C22semidirect
28. #14583504C22semidirect
31. #14583436C22semidirect
32. #14583427C22semidirect
56. #14583381C22semidirect
57. C4×#10621902C22semidirect
75. C43×#519C22semidirect
363. C2×#519D43semidirect
366. C2×C43#3524semidirect
413. #519C2×D43semidirect
437. C43C2×#3524semidirect
707. C2#19148706direct (N × H)

Maximal subgroups

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

subgroupindex
#191487062
C2×#145836342
C2×#145836252
C2×#145836122
C2×#145835932
C2×#145835902
C2×#145835712
C2×#145835602
C2×#145835212
C2×#145835042
C2×#145834362
C2×#145834272
C2×#145833812
C2×C4×#106219022
C2×C43×#5192
C2×#352443