Finite Group Databasebeta

← C2×#19148689 #26004814

Subgroups — C2×#19148689 #26004814

Order 11008.

7022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148689C2132yesmaximal, direct product factor
2C2×#14583628C211yesmaximal, characteristic, complemented
3C2×#14583627C211yesmaximal, characteristic, complemented
4C2×#14583626C212yesmaximal, complemented
5C2×#14583619C211yesmaximal, characteristic, complemented
6C2×#14583618C212yesmaximal, complemented
7C2×#14583589C212yesmaximal, complemented
8C2×#14583586C214yesmaximal, complemented
9C2×D4×Dic86C212yesmaximal, complemented
10C2×D4×Dic86C211yesmaximal, characteristic, complemented
11C2×#14583511C212yesmaximal, complemented
12C2×#14583506C214yesmaximal, complemented
13C2×#14583456C211yesmaximal, characteristic, complemented
14C2×#14583451C212yesmaximal, complemented
15C2×#14583430C212yesmaximal
16C2×#14583376C212yesmaximal, complemented
17C22×C4×Dic86C211yesmaximal, characteristic, complemented
18C2×C43×#529C211yesmaximal, characteristic
19C23×Dic86C2212yes—
20C23×Dic86C2211yescharacteristic
21#14583628C22116yescomplemented
22#14583627C22116yescomplemented
23#14583626C22132yescomplemented
24#14583619C22116yescomplemented
25#14583618C22132yescomplemented
26#14583589C22132yescomplemented
27#14583586C22164yescomplemented
28D4×Dic86C22132yescomplemented
29D4×Dic86C22116yescomplemented
30#14583511C22132yescomplemented
31#14583506C22164yescomplemented
32#14583456C22116yescomplemented
33#14583451C22132yescomplemented
34C2×#13063325C2211yescharacteristic
35C2×#13063325C2212yes—
36C2×#13063325C2211yescharacteristic
37C2×#13063324C2212yes—
38C2×#13063324C2214yes—
39C2×#13063323C2212yes—
40#14583430C22132yes—
41C2×#13063318C2214yes—
42C2×#13063318C2214yes—
43C2×#13063318C2214yes—
44C2×#13063318C2214yes—
45C2×#13063317C2212yes—
46C2×#13063317C2212yes—
47C2×#13063316C2214yes—
48C2×#13063316C2212yes—
49C2×#13063315C2214yes—
50C2×#13063315C2214yes—
51C2×#13063315C2214yes—
52C2×#13063315C2214yes—
53C2×#13063312C2212yes—
54C2×#13063306C2214yes—
55C2×#13063304C2212yes—
56C2×#13063304C2212yes—
57C2×#13063304C2212yes—
58C2×#13063304C2212yes—
59C2×#13063302C2214yes—
60C2×#13063302C2214yes—
61C2×#13063302C2214yes—
62#14583376C22132yescomplemented
63C2×Q8×Dic43C2212yes—
64C2×C4×Dic86C2211yescharacteristic
65C2×C4×Dic86C2212yes—
66C2×C4×Dic86C2212yes—
67C2×C4×Dic86C2212yes—
68C2×C4×Dic86C2211yescharacteristic
69C2×C4×Dic86C2212yes—
70C2×C4×Dic86C2212yes—
71C2×C4×Dic86C2211yescharacteristic
72C2×C4×Dic86C2212yes—
73C2×C4×Dic86C2211yescharacteristic
74C2×C4×Dic86C22116yescomplemented
75C2×#13063290C2214yes—
76C2×#13063290C2214yes—
77C2×#13063290C2212yes—
78C2×#13063290C2212yes—
79C2×D4×Dic43C2214yes—
80C2×D4×Dic43C2212yes—
81C2×#13063284C2212yes—
82C2×#13063284C2212yes—
83C2×#13063281C2214yes—
84C2×#13063281C2214yes—
85C2×#13063281C2214yes—
86C22×C4⋊Dic43C2211yescharacteristic
87C22×Dic43⋊C4C2212yes—
88C22×C4×Dic43C2212yes—
89C43×#529C22116yes—
90C2×#126×C43C2212yes—
91C2×#125×C43C2211yescharacteristic
92C2×#124×C43C2211yescharacteristic
93C2×#123×C43C2212yes—
94C2×C22⋊Q8×C43C2211yescharacteristic
95C2×#121×C43C2211yescharacteristic
96C2×C4×Q8×C43C2211yescharacteristic
97C2×C4×D4×C43C2212yes—
98C2×C4×D4×C43C2211yescharacteristic
99C2×#117×C43C2212yes—
100C22×C42×C43C2211yescharacteristic
101C22×Dic86—216no—
102C22×Dic86—28no—
103C22×Dic86C2318yes—
104C22×Dic86C23116yes—
105C22×Dic86C2312yes—
106C22×Dic86C2314yes—
107C22×Dic86C2312yes—
108C22×Dic86C2312yes—
109C22×Dic86C2311yescharacteristic
110C22×Dic86C2311yescharacteristic
111C23×Dic43C2312yes—
112C23×Dic43C2312yes—
113C23×Dic43C2314yes—
114#13063325C2318yes—
115#13063325C23116yes—
116#13063325C2318yes—
117#13063324C23116yes—
118#13063324C23132yes—
119#13063323C23116yes—
120#13063318C23132yes—
121#13063318C23132yes—
122#13063318C23132yes—
123#13063318C23132yes—
124#13063317C23116yes—
125#13063317C23116yes—
126#13063316C23132yes—
127#13063316C23116yes—
128#13063315C23132yes—
129#13063315C23132yes—
130#13063315C23132yes—
131#13063315C23132yes—
132#13063312C23116yes—
133#13063306C23132yes—
134#13063304C23116yes—
135#13063304C23116yes—
136#13063304C23116yes—
137#13063304C23116yes—
138#13063302C23132yes—
139#13063302C23132yes—
140#13063302C23132yes—
141Q8×Dic43C23116yes—
142C4×Dic86C2318yes—
143C4×Dic86C23116yes—
144C4×Dic86C23116yes—
145C4×Dic86C23116yes—
146C4×Dic86C23116yes—
147C4×Dic86C2318yes—
148C4×Dic86C2318yes—
149C4×Dic86C23116yes—
150C4×Dic86C2318yes—
151C4×Dic86C23116yes—
152#13063290C23132yes—
153#13063290C23116yes—
154#13063290C23116yes—
155#13063290C23132yes—
156D4×Dic43C23132yes—
157D4×Dic43C23116yes—
158#13063284C23116yes—
159#13063284C23116yes—
160#13063281C23132yes—
161#13063281C23132yes—
162#13063281C23132yes—
163C2×C4⋊Dic43C2318yes—
164C2×C4⋊Dic43C2311yescharacteristic
165C2×C4⋊Dic43C2311yescharacteristic
166C2×C4⋊Dic43C2312yes—
167C2×C4⋊Dic43C2312yes—
168C2×C4⋊Dic43C2312yes—
169C2×C4⋊Dic43C2312yes—
170C2×C4⋊Dic43C2312yes—
171C2×C4⋊Dic43C2314yes—
172C2×C4⋊Dic43C2314yes—
173C2×Dic43⋊C4C23116yes—
174C2×Dic43⋊C4C2312yes—
175C2×Dic43⋊C4C2312yes—
176C2×Dic43⋊C4C2312yes—
177C2×Dic43⋊C4C2312yes—
178C2×Dic43⋊C4C2314yes—
179C2×Dic43⋊C4C2314yes—
180C2×Dic43⋊C4C2314yes—
181C2×Dic43⋊C4C2314yes—
182C2×Dic43⋊C4C2314yes—
183C2×Dic43⋊C4C2314yes—
184C2×Dic43⋊C4C2314yes—
185C2×Dic43⋊C4C2314yes—
186C2×C22⋊Dic43C2314yes—
187C2×C22⋊Dic43C2314yes—
188C2×C22⋊Dic43C2314yes—
189C2×C22⋊Dic43C2314yes—
190C2×C4×Dic43C2312yes—
191C2×C4×Dic43C2312yes—
192C2×C4×Dic43C2312yes—
193C2×C4×Dic43C2312yes—
194C2×C4×Dic43C23116yes—
195C2×C4×Dic43C2314yes—
196C2×C4×Dic43C2314yes—
197C2×C4×Dic43C2314yes—
198C2×C4×Dic43C2314yes—
199C22×Q8×C43C2311yescharacteristic
200C22×D4×C43C2312yes—
201C22×D4×C43C2311yescharacteristic
202C23×C4×C43C2311yescharacteristic
203C23×C4×C43C2311yescharacteristic
204C23×C4×C43C2311yescharacteristic
205C23×C4×C43C2312yes—
206#126×C43C23116yes—
207#125×C43C2318yes—
208#124×C43C2318yes—
209#123×C43C23116yes—
210C22⋊Q8×C43C2318yes—
211#121×C43C2318yes—
212C4×Q8×C43C2318yes—
213C4×D4×C43C23116yes—
214C4×D4×C43C2318yes—
215#117×C43C23116yes—
216C2×C4⋊C4×C43C2312yes—
217C2×C4⋊C4×C43C2312yes—
218C2×C4⋊C4×C43C2311yescharacteristic
219C2×C4⋊C4×C43C2312yes—
220C2×C4⋊C4×C43C2311yescharacteristic
221C2×C4⋊C4×C43C2312yes—
222C2×C22⋊C4×C43C2312yes—
223C2×C22⋊C4×C43C2312yes—
224C2×C22⋊C4×C43C2312yes—
225C2×C22⋊C4×C43C2312yes—
226C2×C22⋊C4×C43C2312yes—
227C2×C42×C43C2311yescharacteristic
228C2×C42×C43C2311yescharacteristic
229C2×C42×C43C2311yescharacteristic
230C2×C42×C43C2311yescharacteristic
231C2×C42×C43C2318yes—
232C2×C42×C43C2312yes—
233C24×C43C2412yes—
234C24×C43C2411yescharacteristic
235C2×Q8×C43—24no—
236C2×Q8×C43C2414yes—
237C2×D4×C43—24no—
238C2×D4×C43—28no—
239C2×D4×C43C2418yes—
240C2×D4×C43C2414yes—
241C22×C4×C43—24no—
242C22×C4×C43—28no—
243C22×C4×C43—24no—
244C22×C4×C43—24no—
245C22×C4×C43C2411yescharacteristic
246C22×C4×C43C2411yescharacteristic
247C22×C4×C43C2411yescharacteristic
248C22×C4×C43C2411yescharacteristic
249C22×C4×C43C2414yes—
250C22×C4×C43C2414yes—
251C22×C4×C43C2414yes—
252C22×C4×C43C2412yes—
253C22×C4×C43C2412yes—
254C22×C4×C43C2412yes—
255C22×C4×C43C2418yes—
256C22×C4×C43C2411yescharacteristic
257C22×C4×C43C2411yescharacteristic
258C22×Dic43—28no—
259C22×Dic43—216no—
260C22×Dic43—28no—
261C22×Dic43C2412yes—
262C22×Dic43C2414yes—
263C22×Dic43C2412yes—
264C22×Dic43C2412yes—
265C22×Dic43C2414yes—
266C22×Dic43C2418yes—
267C22×Dic43C2418yes—
268C22×Dic43C24116yes—
269C22×Dic43C2412yes—
270C2×Dic86—28no—
271C2×Dic86—24no—
272C2×Dic86—28no—
273C2×Dic86—216no—
274C2×Dic86—28no—
275C2×Dic86—232no—
276C2×Dic86—264no—
277C2×Dic86#4118yes—
278C2×Dic86C2418yes—
279C2×Dic86C24116yes—
280C2×Dic86C2418yes—
281C2×Dic86C2418yes—
282C2×Dic86C2414yes—
283C2×Dic86C2414yes—
284C4⋊C4×C43C2418yes—
285C4⋊C4×C43C2418yes—
286C4⋊C4×C43C2414yes—
287C4⋊C4×C43C2418yes—
288C4⋊C4×C43C2414yes—
289C4⋊C4×C43C2418yes—
290C22⋊C4×C43C2418yes—
291C22⋊C4×C43C2418yes—
292C22⋊C4×C43C2418yes—
293C22⋊C4×C43C2418yes—
294C22⋊C4×C43C2418yes—
295C42×C43C2414yes—
296C42×C43C2414yes—
297C42×C43C2414yes—
298C42×C43C2414yes—
299C42×C43C2418yes—
300C22⋊Dic43C24116yes—
301C22⋊Dic43C24116yes—
302C22⋊Dic43C24116yes—
303C22⋊Dic43C24116yes—
304C4⋊Dic43C2414yes—
305C4⋊Dic43C2414yes—
306C4⋊Dic43C2418yes—
307C4⋊Dic43C2418yes—
308C4⋊Dic43C2418yes—
309C4⋊Dic43C2418yes—
310C4⋊Dic43C2418yes—
311C4⋊Dic43C24116yes—
312C4⋊Dic43C24116yes—
313Dic43⋊C4C2418yes—
314Dic43⋊C4C2418yes—
315Dic43⋊C4C2418yes—
316Dic43⋊C4C2418yes—
317Dic43⋊C4C24116yes—
318Dic43⋊C4C24116yes—
319Dic43⋊C4C24116yes—
320Dic43⋊C4C24116yes—
321Dic43⋊C4C24116yes—
322Dic43⋊C4C24116yes—
323Dic43⋊C4C24116yes—
324Dic43⋊C4C24116yes—
325C4×Dic43C2418yes—
326C4×Dic43C2418yes—
327C4×Dic43C2418yes—
328C4×Dic43C2418yes—
329C4×Dic43C24116yes—
330C4×Dic43C24116yes—
331C4×Dic43C24116yes—
332C4×Dic43C24116yes—
333C23×C43—22no—
334C23×C43—22no—
335C23×C43—24no—
336C23×C43—24no—
337C23×C43—24no—
338C23×C432−1+414yes—
339C23×C43C2514yes—
340C23×C43C2512yes—
341C23×C43C2511yescharacteristic
342Q8×C43—28no—
343D4×C43—216no—
344D4×C43—28no—
345C2×C4×C43—22no—
346C2×C4×C43—24no—
347C2×C4×C43—28no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—24no—
352C2×C4×C43—24no—
353C2×C4×C43—28no—
354C2×C4×C43—216no—
355C2×C4×C43—28no—
356C2×C4×C43C2×#4114yes—
357C2×C4×C432−1+414yes—
358C2×C4×C43C2512yes—
359C2×C4×C43C2512yes—
360C2×C4×C43C2514yes—
361C2×C4×C43C2514yes—
362C2×C4×C43C2514yes—
363C2×C4×C43C2512yes—
364C2×C4×C43C2512yes—
365C2×C4×C43C2512yes—
366C2×C4×C43C2512yes—
367C2×Dic43—28no—
368C2×Dic43—24no—
369C2×Dic43—28no—
370C2×Dic43—216no—
371C2×Dic43—24no—
372C2×Dic43—24no—
373C2×Dic43—216no—
374C2×Dic43—232no—
375C2×Dic43C2×#4118yes—
376C2×Dic43C2514yes—
377C2×Dic43C2518yes—
378C2×Dic43C2514yes—
379C2×Dic43C2514yes—
380C2×Dic43C2518yes—
381C2×Dic43C2514yes—
382Dic86—28no—
383Dic86—216no—
384Dic86—216no—
385Dic86—232no—
386Dic86—216no—
387Dic86C2×#41116yes—
388C2×#3523—431nomaximal, Sylow
389C22×C43—22no—
390C22×C43—22no—
391C22×C43—28no—
392C22×C43—24no—
393C22×C43—24no—
394C22×C43—24no—
395C22×C43—48no—
396C22×C43C22×#4112yes—
397C22×C43C2×2−1+414yes—
398C22×C43C2×2−1+412yes—
399C22×C43C2×2−1+412yes—
400C22×C43C2611yescharacteristic
401C4×C43—24no—
402C4×C43—22no—
403C4×C43—22no—
404C4×C43—22no—
405C4×C43—22no—
406C4×C43—24no—
407C4×C43—24no—
408C4×C43C22×#4114yes—
409C4×C43C2×2−1+414yes—
410Dic43—28no—
411Dic43—24no—
412Dic43—28no—
413Dic43—24no—
414Dic43—24no—
415Dic43C22×#4118yes—
416#3523—4332no—
417C2×#557—432no—
418C2×#557—431no—
419C2×#557—431no—
420C2×#556—432no—
421C2×#556—431no—
422C2×#552—434no—
423C2×#552—432no—
424C2×D4×Q8—432no—
425C2×D4×Q8—431no—
426C2×#541—434no—
427C2×#541—432no—
428C2×#533—431no—
429C2×#533—432no—
430C2×#529—432no—
431C2×#529D4311yescharacteristic
432C2×#519—432no—
433C22×C4×Q8—431no—
434C2×C43—24no—
435C2×C43—44no—
436C2×C43#352314yescomplemented
437C2×C43C23×#4111yescharacteristic
438C2×C43C22×2−1+411yescharacteristic
439C2×C43C22×2−1+411yescharacteristic
440C23×Q8—431no—
441C23×Q8—432no—
442#557—4332no—
443#557—4316no—
444#557—4316no—
445#556—4332no—
446#556—4316no—
447#552—4364no—
448#552—4332no—
449D4×Q8—4332no—
450D4×Q8—4316no—
451#541—4364no—
452#541—4332no—
453#533—4332no—
454#533—4316no—
455C2×C4⋊Q8—432no—
456C2×C4⋊Q8—432no—
457C2×C4⋊Q8—434no—
458C2×C4⋊Q8—431no—
459C2×C4⋊Q8—431no—
460C2×C4⋊Q8—432no—
461#529—4332no—
462#529C2×D43116yes—
463C2×#126—434no—
464C2×#126—434no—
465C2×#126—434no—
466C2×#126—434no—
467C2×#126C2×D4312yes—
468C2×#125—432no—
469C2×#125—434no—
470C2×#125—434no—
471C2×#125—434no—
472C2×#125—434no—
473C2×#125—434no—
474C2×#125—432no—
475C2×#125—432no—
476C2×#125C2×D4311yescharacteristic
477C2×#124—432no—
478C2×#124C2×D4311yescharacteristic
479C2×#123—434no—
480C2×#123C2×D4312yes—
481C2×C22⋊Q8—432no—
482C2×C22⋊Q8—432no—
483C2×C22⋊Q8—432no—
484C2×C22⋊Q8—432no—
485C2×C22⋊Q8—434no—
486C2×C22⋊Q8—434no—
487C2×C22⋊Q8—434no—
488C2×C22⋊Q8C2×D4311yescharacteristic
489C2×#121C2×D4311yescharacteristic
490#519—4332no—
491C2×C4×Q8—432no—
492C2×C4×Q8—434no—
493C2×C4×Q8—434no—
494C2×C4×Q8—432no—
495C2×C4×Q8—432no—
496C2×C4×Q8—431no—
497C2×C4×Q8—432no—
498C2×C4×Q8—431no—
499C2×C4×Q8—431no—
500C2×C4×Q8—432no—
501C2×C4×Q8—431no—
502C2×C4×Q8—432no—
503C2×C4×Q8—432no—
504C2×C4×Q8—432no—
505C2×C4×Q8—432no—
506C2×C4×Q8—4316no—
507C2×C4×Q8C2×D4311yescharacteristic
508C2×C4×D4—434no—
509C2×C4×D4—432no—
510C2×C4×D4C2×D4312yes—
511C2×C4×D4C2×D4311yescharacteristic
512C2×#117—432no—
513C2×#117—432no—
514C2×#117—434no—
515C2×#117—434no—
516C2×#117—434no—
517C2×#117C2×D4312yes—
518C22×C4⋊C4—432no—
519C22×C4⋊C4—431no—
520C22×C42—432no—
521C22×C42C2×D4311yescharacteristic
522C43C2×#352311yescharacteristic, complemented, Sylow
523C22×Q8—431no—
524C22×Q8—432no—
525C22×Q8—434no—
526C22×Q8—432no—
527C22×Q8—431no—
528C22×Q8—432no—
529C22×Q8—438no—
530C22×Q8—4316no—
531C22×Q8—868no—
532C22×Q8—8616no—
533C22×Q8C22×D4311yescharacteristic
534C22×D4C22×D4312yes—
535C22×D4C22×D4311yescharacteristic
536C23×C4—432no—
537C23×C4—432no—
538C23×C4—434no—
539C23×C4C22×D4311yescharacteristic
540C23×C4C22×D4311yescharacteristic
541C23×C4C22×D4312yes—
542C23×C4C22×D4311yescharacteristic
543C4⋊Q8—4316no—
544C4⋊Q8—4316no—
545C4⋊Q8—4332no—
546C4⋊Q8—438no—
547C4⋊Q8—438no—
548C4⋊Q8—4316no—
549#126—4332no—
550#126—4332no—
551#126—4332no—
552#126—4332no—
553#126C22×D43116yes—
554#125—4316no—
555#125—4332no—
556#125—4332no—
557#125—4332no—
558#125—4332no—
559#125—4332no—
560#125—4316no—
561#125—4316no—
562#125C22×D4318yes—
563#124—4316no—
564#124C22×D4318yes—
565#123—4332no—
566#123C22×D43116yes—
567C22⋊Q8—4316no—
568C22⋊Q8—4316no—
569C22⋊Q8—4316no—
570C22⋊Q8—4316no—
571C22⋊Q8—4332no—
572C22⋊Q8—4332no—
573C22⋊Q8—4332no—
574C22⋊Q8C22×D4318yes—
575#121C22×D4318yes—
576C4×Q8—4316no—
577C4×Q8—4332no—
578C4×Q8—4332no—
579C4×Q8—4316no—
580C4×Q8—4316no—
581C4×Q8—438no—
582C4×Q8—4316no—
583C4×Q8—438no—
584C4×Q8—438no—
585C4×Q8—4316no—
586C4×Q8—438no—
587C4×Q8—4316no—
588C4×Q8—4316no—
589C4×Q8—4316no—
590C4×Q8—4316no—
591C4×Q8C22×D4318yes—
592C4×D4—4332no—
593C4×D4—4316no—
594C4×D4C22×D43116yes—
595C4×D4C22×D4318yes—
596#117—4316no—
597#117—4316no—
598#117—4332no—
599#117—4332no—
600#117—4332no—
601#117C22×D43116yes—
602C2×C4⋊C4—432no—
603C2×C4⋊C4—431no—
604C2×C4⋊C4—432no—
605C2×C4⋊C4—431no—
606C2×C4⋊C4—432no—
607C2×C4⋊C4—432no—
608C2×C4⋊C4—432no—
609C2×C4⋊C4—4316no—
610C2×C4⋊C4—438no—
611C2×C4⋊C4—434no—
612C2×C4⋊C4—432no—
613C2×C4⋊C4—434no—
614C2×C4⋊C4—434no—
615C2×C4⋊C4—434no—
616C2×C4⋊C4—432no—
617C2×C4⋊C4—434no—
618C2×C4⋊C4—432no—
619C2×C4⋊C4—432no—
620C2×C4⋊C4—434no—
621C2×C4⋊C4—434no—
622C2×C4⋊C4—434no—
623C2×C4⋊C4—434no—
624C2×C4⋊C4—434no—
625C2×C4⋊C4C22×D4312yes—
626C2×C4⋊C4C22×D4312yes—
627C2×C4⋊C4C22×D4311yescharacteristic
628C2×C4⋊C4C22×D4312yes—
629C2×C4⋊C4C22×D4311yescharacteristic
630C2×C4⋊C4C22×D4312yes—
631C2×C22⋊C4—434no—
632C2×C22⋊C4—434no—
633C2×C22⋊C4—434no—
634C2×C22⋊C4—434no—
635C2×C22⋊C4C22×D4312yes—
636C2×C22⋊C4C22×D4312yes—
637C2×C22⋊C4C22×D4312yes—
638C2×C22⋊C4C22×D4312yes—
639C2×C22⋊C4C22×D4312yes—
640C2×C42—432no—
641C2×C42—434no—
642C2×C42—434no—
643C2×C42—434no—
644C2×C42—434no—
645C2×C42—432no—
646C2×C42—432no—
647C2×C42—432no—
648C2×C42—4316no—
649C2×C42C22×D4311yescharacteristic
650C2×C42C22×D4312yes—
651C2×C42C22×D4311yescharacteristic
652C2×C42C22×D4311yescharacteristic
653C2×C42C22×D4311yescharacteristic
654C2×C42C22×D4318yes—
655C24C23×D4312yes—
656C24C23×D4311yescharacteristic
657C2×Q8—24no—
658C2×Q8—438no—
659C2×Q8—434no—
660C2×Q8—438no—
661C2×Q8—4316no—
662C2×Q8—438no—
663C2×Q8—434no—
664C2×Q8—438no—
665C2×Q8—8616no—
666C2×Q8—868no—
667C2×Q8—8632no—
668C2×Q8—8664no—
669C2×Q8—864no—
670C2×Q8—868no—
671C2×Q8—868no—
672C2×Q8C23×D4314yes—
673C2×D4—28no—
674C2×D4—24no—
675C2×D4C23×D4318yes—
676C2×D4C23×D4314yes—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—28no—
680C22×C4—24no—
681C22×C4—432no—
682C22×C4—438no—
683C22×C4—438no—
684C22×C4—4316no—
685C22×C4—432no—
686C22×C4—434no—
687C22×C4—432no—
688C22×C4—434no—
689C22×C4—432no—
690C22×C4—868no—
691C22×C4—8616no—
692C22×C4—868no—
693C22×C4C23×D4314yes—
694C22×C4C23×D4314yes—
695C22×C4C23×D4314yes—
696C22×C4C23×D4318yes—
697C22×C4C23×D4311yescharacteristic
698C22×C4C23×D4311yescharacteristic
699C22×C4C23×D4312yes—
700C22×C4C23×D4312yes—
701C22×C4C23×D4312yes—
702C22×C4C23×D4311yescharacteristic
703C22×C4C23×D4311yescharacteristic
704C22×C4C23×D4311yescharacteristic
705C22×C4C23×D4311yescharacteristic
706C4⋊C4—438no—
707C4⋊C4—434no—
708C4⋊C4—438no—
709C4⋊C4—434no—
710C4⋊C4—438no—
711C4⋊C4—438no—
712C4⋊C4—438no—
713C4⋊C4—4316no—
714C4⋊C4—438no—
715C4⋊C4—4316no—
716C4⋊C4—4316no—
717C4⋊C4—4316no—
718C4⋊C4—438no—
719C4⋊C4—4316no—
720C4⋊C4—438no—
721C4⋊C4—438no—
722C4⋊C4—4316no—
723C4⋊C4—4316no—
724C4⋊C4—4316no—
725C4⋊C4—4316no—
726C4⋊C4—4316no—
727C4⋊C4C23×D4318yes—
728C4⋊C4C23×D4318yes—
729C4⋊C4C23×D4314yes—
730C4⋊C4C23×D4318yes—
731C4⋊C4C23×D4314yes—
732C4⋊C4C23×D4318yes—
733C22⋊C4—4316no—
734C22⋊C4—4316no—
735C22⋊C4—4316no—
736C22⋊C4—4316no—
737C22⋊C4C23×D4318yes—
738C22⋊C4C23×D4318yes—
739C22⋊C4C23×D4318yes—
740C22⋊C4C23×D4318yes—
741C22⋊C4C23×D4318yes—
742C42—438no—
743C42—438no—
744C42—438no—
745C42—438no—
746C42—4316no—
747C42—4316no—
748C42—4316no—
749C42—4316no—
750C42C23×D4314yes—
751C42C23×D4314yes—
752C42C23×D4314yes—
753C42C23×D4314yes—
754C42C23×D4318yes—
755C23—22no—
756C23—22no—
757C23—24no—
758C23—24no—
759C23—24no—
760C23#1306337214yes—
761C23C24×D4314yes—
762C23C24×D4312yes—
763C23C24×D4311yescharacteristic
764Q8—28no—
765Q8—4316no—
766Q8—8632no—
767Q8—8616no—
768Q8—868no—
769Q8—8616no—
770Q8—8616no—
771D4—216no—
772D4—28no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—28no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—28no—
782C2×C4—216no—
783C2×C4—28no—
784C2×C4—438no—
785C2×C4—434no—
786C2×C4—434no—
787C2×C4—438no—
788C2×C4—434no—
789C2×C4—434no—
790C2×C4—438no—
791C2×C4—8616no—
792C2×C4—8632no—
793C2×C4—868no—
794C2×C4—864no—
795C2×C4—8616no—
796C2×C4—864no—
797C2×C4—864no—
798C2×C4—868no—
799C2×C4#41×D4314yes—
800C2×C4#1306337214yes—
801C2×C4C24×D4312yes—
802C2×C4C24×D4312yes—
803C2×C4C24×D4314yes—
804C2×C4C24×D4314yes—
805C2×C4C24×D4314yes—
806C2×C4C24×D4312yes—
807C2×C4C24×D4312yes—
808C2×C4C24×D4312yes—
809C2×C4C24×D4312yes—
810C22—22no—
811C22—22no—
812C22—28no—
813C22—24no—
814C22—24no—
815C22—24no—
816C22—48no—
817C22C2×#41×D4312yes—
818C22C2×#1306337214yes—
819C22C2×#1306337212yes—
820C22C2×#1306337212yes—
821C22C25×D4311yescharacteristic
822C4—24no—
823C4—22no—
824C4—22no—
825C4—22no—
826C4—22no—
827C4—24no—
828C4—24no—
829C4—438no—
830C4—864no—
831C4—868no—
832C4—864no—
833C4—864no—
834C4—868no—
835C4C2×#41×D4314yes—
836C4C2×#1306337214yes—
837C2—24no—
838C2—44no—
839C2#1914868914yesdirect product factor
840C2C22×#41×D4311yescharacteristic
841C2C22×#1306337211yescharacteristic
842C2C22×#1306337211yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#529C2
socleC23×C43C25
prime radicalC2×#121×C43C22
hypercenterC2×#529D43
hypocenterC43C2×#3523
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #19148689C2direct (N × H)
2. C2×#14583628C2semidirect
3. C2×#14583627C2semidirect
4. C2×#14583626C2semidirect
5. C2×#14583619C2semidirect
6. C2×#14583618C2semidirect
7. C2×#14583589C2semidirect
8. C2×#14583586C2semidirect
9. C2×D4×Dic86C2semidirect
10. C2×D4×Dic86C2semidirect
11. C2×#14583511C2semidirect
12. C2×#14583506C2semidirect
13. C2×#14583456C2semidirect
14. C2×#14583451C2semidirect
16. C2×#14583376C2semidirect
17. C22×C4×Dic86C2semidirect
21. #14583628C22semidirect
22. #14583627C22semidirect
23. #14583626C22semidirect
24. #14583619C22semidirect
25. #14583618C22semidirect
26. #14583589C22semidirect
27. #14583586C22semidirect
28. D4×Dic86C22semidirect
29. D4×Dic86C22semidirect
30. #14583511C22semidirect
31. #14583506C22semidirect
32. #14583456C22semidirect
33. #14583451C22semidirect
62. #14583376C22semidirect
74. C2×C4×Dic86C22semidirect
436. C2×C43#3523semidirect
522. C43C2×#3523semidirect
839. C2#19148689direct (N × H)

Maximal subgroups

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

subgroupindex
#191486892
C2×#145836282
C2×#145836272
C2×#145836262
C2×#145836192
C2×#145836182
C2×#145835892
C2×#145835862
C2×D4×Dic862
C2×#145835112
C2×#145835062
C2×#145834562
C2×#145834512
C2×#145834302
C2×#145833762
C22×C4×Dic862
C2×C43×#5292
C2×#352343