Finite Group Databasebeta

← C2×#19148272 #26004997

Subgroups — C2×#19148272 #26004997

Order 11008.

11438 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063373C211yesmaximal, characteristic, complemented
2C23×#10621902C211yesmaximal, characteristic, complemented
3#19148272C2132yesmaximal, direct product factor
4C2×Q8×C22⋊D43C211yesmaximal, characteristic, complemented
5C2×#14583561C211yesmaximal, characteristic, complemented
6C2×#14583560C211yesmaximal, characteristic, complemented
7C2×#14583552C213yesmaximal, complemented
8C2×#14583551C213yesmaximal, complemented
9C2×#14583545C213yesmaximal, complemented
10C2×#14583540C213yesmaximal, complemented
11C2×#14583479C213yesmaximal, complemented
12C2×#14583474C213yesmaximal, complemented
13C2×#14583408C213yesmaximal, complemented
14C2×C22⋊Q8×D43C213yesmaximal, complemented
15C2×#14583381C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C43C211yesmaximal, characteristic, complemented
17C2×#13063373—216no—
18C2×#13063373C22116yescomplemented
19C22×#10621902—216no—
20C22×#10621902C2213yes—
21C22×#10621902C2211yescharacteristic
22C22×#10621902C2213yes—
23C22×#10621902C2211yescharacteristic
24C22×#10621902C22116yescomplemented
25C22×#10621902C2213yescomplemented
26C22×#10621898C2213yescomplemented
27C22×#10621898C2213yescomplemented
28C22×Q8×D43C2211yescharacteristic, complemented
29C22×Q8×D43C2213yescomplemented
30C23×D172C2213yes—
31C23×C4×D43C2213yes—
32Q8×C22⋊D43C22116yescomplemented
33#14583561C22116yescomplemented
34#14583560C22116yescomplemented
35#14583552C22148yescomplemented
36#14583551C22148yescomplemented
37#14583545C22148yescomplemented
38#14583540C22148yescomplemented
39#14583479C22148yescomplemented
40#14583474C22148yescomplemented
41C2×#13063323C2213yescomplemented
42C2×#13063314C2213yescomplemented
43C2×#13063313C2213yescomplemented
44#14583408C22148yescomplemented
45C2×#13063310C2216yescomplemented
46C2×#13063310C2216yescomplemented
47C2×#13063310C2213yescomplemented
48C2×#13063307C2213yescomplemented
49C2×#13063305C2213yescomplemented
50C2×#13063304C2213yes—
51C2×#13063303C2216yescomplemented
52C2×#13063303C2213yescomplemented
53C2×#13063302C2213yes—
54C2×#13063301C2213yescomplemented
55C2×#13063301C2213yescomplemented
56C22⋊Q8×D43C22148yescomplemented
57C2×#13063300C2216yescomplemented
58C2×#13063300C2213yescomplemented
59C2×#13063299C2213yescomplemented
60C2×#13063298C2216yescomplemented
61C2×#13063298C2213yescomplemented
62C2×#13063297C2211yescharacteristic
63C2×#13063295C2213yes—
64C2×#13063293C2213yes—
65#14583381C22116yescomplemented
66C2×Q8×Dic43C2211yescharacteristic, complemented
67C2×C4×D172C2213yescomplemented
68C2×C4×D172C2213yescomplemented
69C2×#13063287C2213yescomplemented
70C2×C4×C22⋊D43C2213yes—
71C2×C4×C22⋊D43C2213yescomplemented
72C2×#13063282C2213yescomplemented
73C2×C4⋊C4×D43C2213yescomplemented
74C2×C4⋊C4×D43C2216yescomplemented
75C2×C22⋊C4×D43C2216yes—
76C23×Q8×C43C2211yescharacteristic
77C23×Q8×C43C2211yescharacteristic, complemented
78D4×Q8×C43C22116yescomplemented
79C2×C4⋊Q8×C43C2213yescomplemented
80C2×C22⋊Q8×C43C2213yes—
81C2×C22⋊Q8×C43C2213yescomplemented
82C2×C4×Q8×C43C2211yescharacteristic, complemented
83C2×C4×D4×C43C2213yes—
84C24×D43C2313yes—
85#13063373—2128no—
86C2×#10621902—28no—
87C2×#10621902—2128no—
88C2×#10621902—224no—
89C2×#10621902—224no—
90C2×#10621902—224no—
91C2×#10621902D4116yescomplemented
92C2×#10621902C23124yes—
93C2×#10621902C2318yes—
94C2×#10621902C23124yes—
95C2×#10621902C2318yes—
96C2×#10621902C23124yescomplemented
97C2×#10621898—224no—
98C2×#10621898—224no—
99C2×#10621898C23124yescomplemented
100C2×#10621898C23124yescomplemented
101C22×Dic86C2313yes—
102C22×Dic86C2313yes—
103C2×Q8×D43—28no—
104C2×Q8×D43—224no—
105C2×Q8×D43C2318yescomplemented
106C2×Q8×D43C23124yescomplemented
107C22×D172—224no—
108C22×D172C2313yes—
109C22×D172C2316yes—
110C22×D172C2313yes—
111C22×D172C23124yes—
112C22×D172C2313yes—
113C22×D172C2313yes—
114C22×C22⋊D43C2311yescharacteristic
115C22×C22⋊D43C2313yes—
116C22×C22⋊D43C2311yescharacteristic
117C22×C22⋊D43C2313yes—
118C23×Dic43C2311yescharacteristic
119C22×C4×D43—224no—
120C22×C4×D43C2316yes—
121C22×C4×D43C2313yes—
122C22×C4×D43C2313yes—
123C22×C4×D43C2313yes—
124C22×C4×D43C2313yes—
125C22×C4×D43C23124yes—
126C22×C4×D43C2316yes—
127C22×C4×D43C2313yes—
128#13063323C23124yescomplemented
129#13063314C23124yescomplemented
130#13063313C23124yescomplemented
131#13063310C23124yescomplemented
132#13063310C23148yescomplemented
133#13063310C23148yescomplemented
134#13063307C23124yescomplemented
135#13063305C23124yescomplemented
136#13063304C23124yes—
137#13063303C23148yescomplemented
138#13063303C23124yescomplemented
139#13063302C23124yes—
140#13063301C23124yescomplemented
141#13063301C23124yescomplemented
142#13063300C23148yescomplemented
143#13063300C23124yescomplemented
144#13063299C23124yescomplemented
145#13063298C23124yescomplemented
146#13063298C23148yescomplemented
147#13063297C2318yes—
148#13063295C23124yes—
149#13063293C23124yes—
150Q8×Dic43C2318yescomplemented
151C4×D172C23124yescomplemented
152C4×D172C23124yescomplemented
153#13063287C23124yescomplemented
154C4×C22⋊D43C23124yes—
155C4×C22⋊D43C23124yescomplemented
156#13063282C23124yescomplemented
157C2×C4⋊Dic43C2313yes—
158C2×C4⋊Dic43C2313yes—
159C2×Dic43⋊C4C2313yes—
160C2×Dic43⋊C4C2313yes—
161C2×Dic43⋊C4C2316yes—
162C2×Dic43⋊C4C2311yescharacteristic
163C2×Dic43⋊C4C2313yes—
164C4⋊C4×D43C23148yescomplemented
165C4⋊C4×D43C23124yescomplemented
166C2×C22⋊Dic43C2313yes—
167C2×C22⋊Dic43C2311yescharacteristic
168C2×(C2×D43)⋊C4C2316yes—
169C2×(C2×D43)⋊C4C2316yes—
170C2×(C2×D43)⋊C4C2313yes—
171C2×(C2×D43)⋊C4C2313yes—
172C2×(C2×D43)⋊C4C2313yes—
173C2×(C2×D43)⋊C4C2313yes—
174C2×(C2×D43)⋊C4C2311yescharacteristic
175C2×(C2×D43)⋊C4C2313yes—
176C22⋊C4×D43C23148yes—
177C2×C4×Dic43C2313yes—
178C22×Q8×C43—28no—
179C22×Q8×C43—28no—
180C22×Q8×C43C2318yes—
181C22×Q8×C43C2313yes—
182C22×Q8×C43C2313yes—
183C22×Q8×C43C2311yescharacteristic
184C22×Q8×C43C2318yescomplemented
185C22×D4×C43C2311yescharacteristic
186C23×C4×C43C2313yes—
187C23×C4×C43C2313yes—
188C4⋊Q8×C43C23124yescomplemented
189C22⋊Q8×C43C23124yes—
190C22⋊Q8×C43C23124yescomplemented
191C4×Q8×C43C2318yescomplemented
192C4×D4×C43C23124yes—
193C2×C4⋊C4×C43C2313yes—
194C2×C4⋊C4×C43C2313yes—
195C2×C4⋊C4×C43C2316yes—
196C2×C22⋊C4×C43C2313yes—
197C2×C22⋊C4×C43C2313yes—
198C2×C42×C43C2313yes—
199C24×C43C2411yescharacteristic
200C24×C43C2411yescharacteristic
201C23×D43—212no—
202C23×D43—212no—
203C23×D43—46no—
204C23×D43C2413yes—
205C23×D43C2411yescharacteristic
206C23×D43C24112yes—
207C23×D43C2413yes—
208C2×Q8×C43—232no—
209C2×Q8×C43—232no—
210C2×Q8×C43—212no—
211C2×Q8×C43—212no—
212C2×Q8×C43C2×D418yes—
213C2×Q8×C43C24112yes—
214C2×Q8×C43C24112yes—
215C2×Q8×C43C2414yes—
216C2×D4×C43—24no—
217C2×D4×C43C2414yes—
218C22×C4×C43—212no—
219C22×C4×C43—212no—
220C22×C4×C43C2411yescharacteristic
221C22×C4×C43C2413yes—
222C22×C4×C43C2413yes—
223C22×C4×C43C2413yes—
224C22×C4×C43C24112yes—
225C22×C4×C43C24112yes—
226C22×C4×C43C2413yes—
227C2×C22⋊D43—24no—
228C2×C22⋊D43—24no—
229C2×C22⋊D43—212no—
230C2×C22⋊D43—46no—
231C2×C22⋊D43C2414yes—
232C2×C22⋊D43C24112yes—
233C2×C22⋊D43C2414yes—
234C2×C22⋊D43C24112yes—
235C22×Dic43—24no—
236C22×Dic43C2411yescharacteristic
237C22×Dic43C2413yes—
238C22×Dic43C2413yes—
239C22×Dic43C2411yescharacteristic
240C22×Dic43C2414yes—
241C22×Dic43C2411yescharacteristic
242#10621902—232no—
243#10621902—296no—
244#10621902—296no—
245#10621902—296no—
246#10621902C2×D4164yescomplemented
247Q8×D43—232no—
248Q8×D43—296no—
249#10621898—296no—
250#10621898—296no—
251C2×D172—212no—
252C2×D172—296no—
253C2×D172—224no—
254C2×D172—212no—
255C2×D172—46no—
256C2×D172C2×D4124yes—
257C2×D172C24112yes—
258C2×D172C24124yes—
259C2×D172C24112yes—
260C2×D172C24112yes—
261C2×D172C24112yes—
262C2×C4×D43—212no—
263C2×C4×D43—212no—
264C2×C4×D43—212no—
265C2×C4×D43—296no—
266C2×C4×D43—212no—
267C2×C4×D43—224no—
268C2×C4×D43—412no—
269C2×C4×D43C2×D4124yes—
270C2×C4×D43C24124yes—
271C2×C4×D43C24112yes—
272C2×C4×D43C24112yes—
273C2×C4×D43C24112yes—
274C2×C4×D43C24112yes—
275C2×C4×D43C24124yes—
276C2×C4×D43C24112yes—
277C2×Dic86—212no—
278C2×Dic86—212no—
279C2×Dic86C24112yes—
280C2×Dic86C24112yes—
281C4⋊C4×C43C24112yes—
282C4⋊C4×C43C24112yes—
283C4⋊C4×C43C24124yes—
284C22⋊C4×C43C24112yes—
285C22⋊C4×C43C24112yes—
286C42×C43C24112yes—
287C22⋊Dic43C24112yes—
288C22⋊Dic43C2414yes—
289(C2×D43)⋊C4C24124yes—
290(C2×D43)⋊C4C24124yes—
291(C2×D43)⋊C4C24112yes—
292(C2×D43)⋊C4C24112yes—
293(C2×D43)⋊C4C24112yes—
294(C2×D43)⋊C4C24112yes—
295(C2×D43)⋊C4C2414yes—
296(C2×D43)⋊C4C24112yes—
297C4⋊Dic43C24112yes—
298C4⋊Dic43C24112yes—
299Dic43⋊C4C24112yes—
300Dic43⋊C4C24112yes—
301Dic43⋊C4C24124yes—
302Dic43⋊C4C2414yes—
303Dic43⋊C4C24112yes—
304C4×Dic43C24112yes—
305C23×C43—22no—
306C23×C43—22no—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C432−1+414yescomplemented
311C23×C43C2512yes—
312C23×C43C2512yes—
313C23×C43C2511yescharacteristic
314C22×D43—26no—
315C22×D43—26no—
316C22×D43—22no—
317C22×D43—26no—
318C22×D43—22no—
319C22×D43—26no—
320C22×D43—224no—
321C22×D43—22no—
322C22×D43—26no—
323C22×D43—224no—
324C22×D43—412no—
325C22×D43—448no—
326C22×D43C22×D4112yes—
327C22×D43C2516yes—
328C22×D43C2512yes—
329C22×D43C2516yes—
330Q8×C43—224no—
331Q8×C43—224no—
332Q8×C43C22×D4116yes—
333D4×C43—28no—
334C2×C4×C43—26no—
335C2×C4×C43—26no—
336C2×C4×C43—22no—
337C2×C4×C43—26no—
338C2×C4×C43—224no—
339C2×C4×C43—224no—
340C2×C4×C43C22×D4112yes—
341C2×C4×C43C2516yes—
342C2×C4×C43C2516yes—
343C2×C4×C43C2512yes—
344C2×C4×C43C2516yes—
345C2×C4×C43C2516yes—
346C22⋊D43—28no—
347C22⋊D43—224no—
348C22⋊D43—28no—
349C22⋊D43—412no—
350C2×Dic43—26no—
351C2×Dic43—22no—
352C2×Dic43—22no—
353C2×Dic43—26no—
354C2×Dic43—28no—
355C2×Dic43C22×D414yes—
356C2×Dic43C2512yes—
357C2×Dic43C2516yes—
358C2×Dic43C2512yes—
359C2×Dic43C2516yes—
360C2×Dic43C2512yes—
361D172—248no—
362D172—224no—
363D172—224no—
364D172—412no—
365D172C22×D4148yes—
366C4×D43—224no—
367C4×D43—248no—
368C4×D43—224no—
369C4×D43—224no—
370C4×D43—224no—
371C4×D43—424no—
372C4×D43C22×D4148yes—
373Dic86—224no—
374Dic86—224no—
375C2×#3489—431nomaximal, Sylow
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—28no—
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—44no—
383C22×C43C23×D412yes—
384C22×C43C2×2−1+412yes—
385C22×C43C2×2−1+414yescomplemented
386C22×C43#58512yes—
387C22×C43C2611yescharacteristic
388C2×D43—26no—
389C2×D43—26no—
390C2×D43—224no—
391C2×D43—26no—
392C2×D43—22no—
393C2×D43—26no—
394C2×D43—22no—
395C2×D43—26no—
396C2×D43—22no—
397C2×D43—448no—
398C2×D43—44no—
399C2×D43—412no—
400C2×D43C23×D4112yes—
401C4×C43—26no—
402C4×C43—26no—
403C4×C43—22no—
404C4×C43—26no—
405C4×C43C23×D4112yes—
406Dic43—26no—
407Dic43—22no—
408Dic43—22no—
409Dic43—26no—
410Dic43C23×D414yes—
411C22×2−1+4—431no—
412C23×#41—431no—
413#3489—4332no—
414C2×D4×Q8—431no—
415C2×D4×Q8D4311yescharacteristic, complemented
416C2×#548—431no—
417C2×#548—431no—
418C2×#547—433no—
419C2×#547—433no—
420C2×#546—433no—
421C2×#546—433no—
422C2×#537—433no—
423C2×#536—433no—
424C2×#525—433no—
425C22×C22⋊Q8—433no—
426C2×#520—431no—
427C2×C43—24no—
428C2×C43—42no—
429C2×C43#348914yescomplemented
430C2×C43C24×D411yescharacteristic
431C2×C43C22×2−1+411yescharacteristic
432C2×C43C2×#58511yescharacteristic
433D43—212no—
434D43—42no—
435D43—46no—
436C2×2−1+4—4316no—
437C2×2−1+4—8616no—
438C22×#41—431no—
439C22×#41—433no—
440C22×#41—433no—
441C22×#41—431no—
442C22×#41—4316no—
443C22×#41—433no—
444C22×#41—433no—
445C22×#41—433no—
446C22×#41—8616no—
447C23×Q8—433no—
448C23×Q8—431no—
449C23×Q8C2×D4311yescharacteristic
450C23×Q8C2×D4311yescharacteristic, complemented
451C23×D4—433no—
452C24×C4—433no—
453D4×Q8—4316no—
454D4×Q8C2×D43116yescomplemented
455#548—4316no—
456#548—4316no—
457#547—4348no—
458#547—4348no—
459#546—4348no—
460#546—4348no—
461#537—4348no—
462#536—4348no—
463C2×C4⋊Q8—433no—
464C2×C4⋊Q8C2×D4313yescomplemented
465C2×#124—433no—
466C2×#124—433no—
467#525—4348no—
468C2×#123—433no—
469C2×#123—436no—
470C2×#123—436no—
471C2×#123—433no—
472C2×C22⋊Q8—433no—
473C2×C22⋊Q8—433no—
474C2×C22⋊Q8—433no—
475C2×C22⋊Q8—4348no—
476C2×C22⋊Q8—436no—
477C2×C22⋊Q8—433no—
478C2×C22⋊Q8—433no—
479C2×C22⋊Q8—433no—
480C2×C22⋊Q8C2×D4313yes—
481C2×C22⋊Q8C2×D4313yescomplemented
482C2×#121—431no—
483C2×#121—433no—
484C2×#121—436no—
485C2×#121—433no—
486C2×#121—433no—
487C2×#121—436no—
488C2×#120—433no—
489C2×#120—433no—
490#520—4316no—
491C2×C4×Q8—431no—
492C2×C4×Q8C2×D4311yescharacteristic, complemented
493C2×C4×D4—433no—
494C2×C4×D4—433no—
495C2×C4×D4—433no—
496C2×C4×D4—433no—
497C2×C4×D4—433no—
498C2×C4×D4C2×D4313yes—
499C2×#117—433no—
500C22×C4⋊C4—433no—
501C22×C4⋊C4—436no—
502C22×C22⋊C4—436no—
503C43C2×#348911yescharacteristic, complemented, Sylow
504C25—433no—
5052−1+4—86128no—
506C2×#41—4316no—
507C2×#41—438no—
508C2×#41—4324no—
509C2×#41—4324no—
510C2×#41—4324no—
511C2×#41—438no—
512C2×#41—4324no—
513C2×#41—4324no—
514C2×#41—8624no—
515C2×#41—8624no—
516C2×#41—8624no—
517C2×#41—8624no—
518C2×#41—8624no—
519C2×#41—86128no—
520C2×#41—868no—
521C22×Q8—28no—
522C22×Q8—28no—
523C22×Q8—4324no—
524C22×Q8—438no—
525C22×Q8—433no—
526C22×Q8—433no—
527C22×Q8—8624no—
528C22×Q8—868no—
529C22×Q8C22×D4313yes—
530C22×Q8C22×D4313yes—
531C22×Q8C22×D4318yes—
532C22×Q8C22×D4311yescharacteristic
533C22×Q8C22×D4318yescomplemented
534C22×D4—431no—
535C22×D4—433no—
536C22×D4—431no—
537C22×D4—433no—
538C22×D4—433no—
539C22×D4—433no—
540C22×D4—436no—
541C22×D4—433no—
542C22×D4—4324no—
543C22×D4—433no—
544C22×D4—8624no—
545C22×D4C22×D4311yescharacteristic
546C23×C4—433no—
547C23×C4—431no—
548C23×C4—436no—
549C23×C4—433no—
550C23×C4—433no—
551C23×C4—433no—
552C23×C4—433no—
553C23×C4—4324no—
554C23×C4—436no—
555C23×C4—8624no—
556C23×C4C22×D4313yes—
557C23×C4C22×D4313yes—
558C4⋊Q8—4324no—
559C4⋊Q8C22×D43124yescomplemented
560#124—4324no—
561#124—4324no—
562#123—4324no—
563#123—4348no—
564#123—4348no—
565#123—4324no—
566C22⋊Q8—4324no—
567C22⋊Q8—4324no—
568C22⋊Q8—4324no—
569C22⋊Q8—4348no—
570C22⋊Q8—4324no—
571C22⋊Q8—4324no—
572C22⋊Q8—4324no—
573C22⋊Q8C22×D43124yes—
574C22⋊Q8C22×D43124yescomplemented
575#121—438no—
576#121—4324no—
577#121—4348no—
578#121—4324no—
579#121—4324no—
580#121—4348no—
581#120—4324no—
582#120—4324no—
583C4×Q8—438no—
584C4×Q8C22×D4318yescomplemented
585C4×D4—4324no—
586C4×D4—4324no—
587C4×D4—4324no—
588C4×D4—4324no—
589C4×D4—4324no—
590C4×D4C22×D43124yes—
591#117—4324no—
592C2×C4⋊C4—433no—
593C2×C4⋊C4—433no—
594C2×C4⋊C4—433no—
595C2×C4⋊C4—433no—
596C2×C4⋊C4—436no—
597C2×C4⋊C4—431no—
598C2×C4⋊C4—433no—
599C2×C4⋊C4—4324no—
600C2×C4⋊C4—4348no—
601C2×C4⋊C4C22×D4313yes—
602C2×C4⋊C4C22×D4316yes—
603C2×C4⋊C4C22×D4313yes—
604C2×C22⋊C4—433no—
605C2×C22⋊C4—431no—
606C2×C22⋊C4—436no—
607C2×C22⋊C4—436no—
608C2×C22⋊C4—433no—
609C2×C22⋊C4—433no—
610C2×C22⋊C4—431no—
611C2×C22⋊C4—433no—
612C2×C22⋊C4—433no—
613C2×C22⋊C4—433no—
614C2×C22⋊C4—4348no—
615C2×C22⋊C4C22×D4313yes—
616C2×C22⋊C4C22×D4313yes—
617C2×C42—433no—
618C2×C42C22×D4313yes—
619C24—433no—
620C24—433no—
621C24—431no—
622C24—4312no—
623C24—8612no—
624C24—8612no—
625C24—1726no—
626C24C23×D4311yescharacteristic
627C24C23×D4311yescharacteristic
628#41—4364no—
629#41—8696no—
630#41—8696no—
631#41—8696no—
632#41—8696no—
633#41—8696no—
634#41—8632no—
635C2×Q8—232no—
636C2×Q8—232no—
637C2×Q8—212no—
638C2×Q8—212no—
639C2×Q8—4312no—
640C2×Q8—4312no—
641C2×Q8—8612no—
642C2×Q8—8696no—
643C2×Q8—8632no—
644C2×Q8—8612no—
645C2×Q8D4×D4318yes—
646C2×Q8C23×D43112yes—
647C2×Q8C23×D43112yes—
648C2×Q8C23×D4314yes—
649C2×D4—24no—
650C2×D4—434no—
651C2×D4—4312no—
652C2×D4—434no—
653C2×D4—4312no—
654C2×D4—4324no—
655C2×D4—4312no—
656C2×D4—4312no—
657C2×D4—4324no—
658C2×D4—4312no—
659C2×D4—4312no—
660C2×D4—8696no—
661C2×D4—8624no—
662C2×D4—8612no—
663C2×D4—864no—
664C2×D4—8612no—
665C2×D4—864no—
666C2×D4—8612no—
667C2×D4—1726no—
668C2×D4—1726no—
669C2×D4C23×D4314yes—
670C22×C4—212no—
671C22×C4—212no—
672C22×C4—431no—
673C22×C4—4324no—
674C22×C4—4312no—
675C22×C4—434no—
676C22×C4—431no—
677C22×C4—433no—
678C22×C4—433no—
679C22×C4—431no—
680C22×C4—4324no—
681C22×C4—4312no—
682C22×C4—4312no—
683C22×C4—4312no—
684C22×C4—4312no—
685C22×C4—4324no—
686C22×C4—8612no—
687C22×C4—8696no—
688C22×C4—8612no—
689C22×C4—8624no—
690C22×C4—864no—
691C22×C4—8612no—
692C22×C4—8612no—
693C22×C4—17212no—
694C22×C4C23×D43112yes—
695C22×C4C23×D43112yes—
696C22×C4C23×D4311yescharacteristic
697C22×C4C23×D4313yes—
698C22×C4C23×D4313yes—
699C22×C4C23×D4313yes—
700C22×C4C23×D4313yes—
701C4⋊C4—4312no—
702C4⋊C4—4312no—
703C4⋊C4—4312no—
704C4⋊C4—4312no—
705C4⋊C4—4324no—
706C4⋊C4—434no—
707C4⋊C4—4312no—
708C4⋊C4C23×D43112yes—
709C4⋊C4C23×D43124yes—
710C4⋊C4C23×D43112yes—
711C22⋊C4—4312no—
712C22⋊C4—434no—
713C22⋊C4—4324no—
714C22⋊C4—4324no—
715C22⋊C4—4312no—
716C22⋊C4—4312no—
717C22⋊C4—434no—
718C22⋊C4—4312no—
719C22⋊C4—4312no—
720C22⋊C4—4312no—
721C22⋊C4C23×D43112yes—
722C22⋊C4C23×D43112yes—
723C42—4312no—
724C42C23×D43112yes—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—4312no—
731C23—436no—
732C23—436no—
733C23—432no—
734C23—8624no—
735C23—866no—
736C23—866no—
737C23—862no—
738C23—866no—
739C23—862no—
740C23—866no—
741C23—8624no—
742C23—862no—
743C23—866no—
744C23—17212no—
745C23—17248no—
746C23#1306337314yescomplemented
747C23C24×D4312yes—
748C23C24×D4312yes—
749C23C24×D4311yescharacteristic
750Q8—224no—
751Q8—224no—
752Q8—8624no—
753Q8—8624no—
754Q8C2×D4×D43116yes—
755D4—28no—
756D4—4348no—
757D4—8648no—
758D4—8624no—
759D4—868no—
760D4—8624no—
761D4—868no—
762D4—8624no—
763D4—17212no—
764D4—17212no—
765C2×C4—26no—
766C2×C4—26no—
767C2×C4—22no—
768C2×C4—26no—
769C2×C4—224no—
770C2×C4—224no—
771C2×C4—434no—
772C2×C4—432no—
773C2×C4—4348no—
774C2×C4—432no—
775C2×C4—436no—
776C2×C4—436no—
777C2×C4—432no—
778C2×C4—8624no—
779C2×C4—8624no—
780C2×C4—8648no—
781C2×C4—868no—
782C2×C4—862no—
783C2×C4—866no—
784C2×C4—862no—
785C2×C4—866no—
786C2×C4—8624no—
787C2×C4—8624no—
788C2×C4—17224no—
789C2×C4C2×D4×D43112yes—
790C2×C4C24×D4312yes—
791C2×C4C24×D4316yes—
792C2×C4C24×D4316yes—
793C2×C4C24×D4316yes—
794C2×C4C24×D4316yes—
795C22—22no—
796C22—22no—
797C22—28no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—44no—
802C22—4312no—
803C22—866no—
804C22—866no—
805C22—8624no—
806C22—862no—
807C22—866no—
808C22—862no—
809C22—866no—
810C22—862no—
811C22—866no—
812C22—17248no—
813C22—17212no—
814C22—1724no—
815C22C22×D4×D4312yes—
816C22C2×#1306337312yes—
817C22C2×#1306337314yescomplemented
818C22#1458373612yes—
819C22C25×D4311yescharacteristic
820C4—26no—
821C4—26no—
822C4—22no—
823C4—26no—
824C4—434no—
825C4—862no—
826C4—866no—
827C4—862no—
828C4—866no—
829C4C22×D4×D43112yes—
830C2—24no—
831C2—42no—
832C2—8612no—
833C2—1726no—
834C2—1722no—
835C2#1914827214yesdirect product factor
836C2C23×D4×D4311yescharacteristic
837C2C22×#1306337311yescharacteristic
838C2C2×#1458373611yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×D4×Q8×C43C2
socleC23×C43C25
hypercenterC2×D4×Q8D43
hypocenterC43C2×#3489
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#13063373C2semidirect
2. C23×#10621902C2semidirect
3. #19148272C2direct (N × H)
4. C2×Q8×C22⋊D43C2semidirect
5. C2×#14583561C2semidirect
6. C2×#14583560C2semidirect
7. C2×#14583552C2semidirect
8. C2×#14583551C2semidirect
9. C2×#14583545C2semidirect
10. C2×#14583540C2semidirect
11. C2×#14583479C2semidirect
12. C2×#14583474C2semidirect
13. C2×#14583408C2semidirect
14. C2×C22⋊Q8×D43C2semidirect
15. C2×#14583381C2semidirect
16. C2×D4×Q8×C43C2semidirect
18. C2×#13063373C22semidirect
24. C22×#10621902C22semidirect
25. C22×#10621902C22semidirect
26. C22×#10621898C22semidirect
27. C22×#10621898C22semidirect
28. C22×Q8×D43C22semidirect
29. C22×Q8×D43C22semidirect
32. Q8×C22⋊D43C22semidirect
33. #14583561C22semidirect
34. #14583560C22semidirect
35. #14583552C22semidirect
36. #14583551C22semidirect
37. #14583545C22semidirect
38. #14583540C22semidirect
39. #14583479C22semidirect
40. #14583474C22semidirect
41. C2×#13063323C22semidirect
42. C2×#13063314C22semidirect
43. C2×#13063313C22semidirect
44. #14583408C22semidirect
45. C2×#13063310C22semidirect
46. C2×#13063310C22semidirect
47. C2×#13063310C22semidirect
48. C2×#13063307C22semidirect
49. C2×#13063305C22semidirect
51. C2×#13063303C22semidirect
52. C2×#13063303C22semidirect
54. C2×#13063301C22semidirect
55. C2×#13063301C22semidirect
56. C22⋊Q8×D43C22semidirect
57. C2×#13063300C22semidirect
58. C2×#13063300C22semidirect
59. C2×#13063299C22semidirect
60. C2×#13063298C22semidirect
61. C2×#13063298C22semidirect
65. #14583381C22semidirect
66. C2×Q8×Dic43C22semidirect
67. C2×C4×D172C22semidirect
68. C2×C4×D172C22semidirect
69. C2×#13063287C22semidirect
71. C2×C4×C22⋊D43C22semidirect
72. C2×#13063282C22semidirect
73. C2×C4⋊C4×D43C22semidirect
74. C2×C4⋊C4×D43C22semidirect
77. C23×Q8×C43C22semidirect
78. D4×Q8×C43C22semidirect
79. C2×C4⋊Q8×C43C22semidirect
81. C2×C22⋊Q8×C43C22semidirect
82. C2×C4×Q8×C43C22semidirect
91. C2×#10621902D4semidirect
96. C2×#10621902C23semidirect
99. C2×#10621898C23semidirect
100. C2×#10621898C23semidirect
105. C2×Q8×D43C23semidirect
106. C2×Q8×D43C23semidirect
128. #13063323C23semidirect
129. #13063314C23semidirect
130. #13063313C23semidirect
131. #13063310C23semidirect
132. #13063310C23semidirect
133. #13063310C23semidirect
134. #13063307C23semidirect
135. #13063305C23semidirect
137. #13063303C23semidirect
138. #13063303C23semidirect
140. #13063301C23semidirect
141. #13063301C23semidirect
142. #13063300C23semidirect
143. #13063300C23semidirect
144. #13063299C23semidirect
145. #13063298C23semidirect
146. #13063298C23semidirect
150. Q8×Dic43C23semidirect
151. C4×D172C23semidirect
152. C4×D172C23semidirect
153. #13063287C23semidirect
155. C4×C22⋊D43C23semidirect
156. #13063282C23semidirect
164. C4⋊C4×D43C23semidirect
165. C4⋊C4×D43C23semidirect
184. C22×Q8×C43C23semidirect
188. C4⋊Q8×C43C23semidirect
190. C22⋊Q8×C43C23semidirect
191. C4×Q8×C43C23semidirect
246. #10621902C2×D4semidirect
310. C23×C432−1+4semidirect
385. C22×C43C2×2−1+4semidirect
415. C2×D4×Q8D43semidirect
429. C2×C43#3489semidirect
450. C23×Q8C2×D43semidirect
454. D4×Q8C2×D43semidirect
464. C2×C4⋊Q8C2×D43semidirect
481. C2×C22⋊Q8C2×D43semidirect
492. C2×C4×Q8C2×D43semidirect
503. C43C2×#3489semidirect
533. C22×Q8C22×D43semidirect
559. C4⋊Q8C22×D43semidirect
574. C22⋊Q8C22×D43semidirect
584. C4×Q8C22×D43semidirect
746. C23#13063373semidirect
817. C22C2×#13063373semidirect
835. C2#19148272direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633732
C23×#106219022
#191482722
C2×Q8×C22⋊D432
C2×#145835612
C2×#145835602
C2×#145835522
C2×#145835512
C2×#145835452
C2×#145835402
C2×#145834792
C2×#145834742
C2×#145834082
C2×C22⋊Q8×D432
C2×#145833812
C2×D4×Q8×C432
C2×#348943