Finite Group Databasebeta

← C2×#19148690 #26004813

Subgroups — C2×#19148690 #26004813

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#19148690C2132yesmaximal, direct product factor
2C2×#14583627C211yesmaximal, characteristic, complemented
3C2×#14583625C212yesmaximal, complemented
4C2×#14583624C211yesmaximal, characteristic, complemented
5C2×#14583618C212yesmaximal, complemented
6C2×#14583588C212yesmaximal, complemented
7C2×#14583585C214yesmaximal, complemented
8C2×D4×Dic86C211yesmaximal, characteristic, complemented
9C2×#14583562C212yesmaximal, complemented
10C2×#14583509C212yesmaximal, complemented
11C2×#14583506C214yesmaximal, complemented
12C2×#14583454C211yesmaximal, characteristic, complemented
13C2×#14583453C212yesmaximal, complemented
14C2×#14583431C211yesmaximal, characteristic
15C2×#14583428C212yesmaximal
16C2×#14583376C212yesmaximal, complemented
17C2×C4×Q8×D43C211yesmaximal, characteristic, complemented
18C2×C43×#556C211yesmaximal, characteristic, complemented
19C23×Dic86C2212yes—
20C22×Q8×D43C2211yescharacteristic
21#14583627C22116yescomplemented
22#14583625C22132yescomplemented
23#14583624C22116yescomplemented
24#14583618C22132yescomplemented
25#14583588C22132yescomplemented
26#14583585C22164yescomplemented
27D4×Dic86C22116yescomplemented
28#14583562C22132yescomplemented
29#14583509C22132yescomplemented
30#14583506C22164yescomplemented
31#14583454C22116yescomplemented
32#14583453C22132yescomplemented
33C2×#13063325C2211yescharacteristic
34C2×#13063324C2214yes—
35C2×#13063324C2212yes—
36C2×#13063323C2212yes—
37C2×#13063323C2212yes—
38#14583431C22116yes—
39#14583428C22132yes—
40C2×#13063318C2214yes—
41C2×#13063318C2214yes—
42C2×#13063318C2214yes—
43C2×#13063318C2212yes—
44C2×#13063317C2214yes—
45C2×#13063317C2212yes—
46C2×#13063316C2214yes—
47C2×#13063316C2212yes—
48C2×#13063316C2211yescharacteristic
49C2×#13063316C2212yes—
50C2×#13063315C2214yes—
51C2×#13063315C2214yes—
52C2×#13063315C2214yes—
53C2×#13063312C2211yescharacteristic
54C2×#13063307C2212yes—
55C2×#13063307C2214yes—
56C2×#13063305C2212yes—
57C2×#13063305C2211yescharacteristic
58C2×#13063304C2212yes—
59C2×#13063303C2214yes—
60C2×#13063302C2214yes—
61C2×#13063302C2214yes—
62C2×#13063301C2212yes—
63C2×#13063296C2211yescharacteristic
64#14583376C22132yescomplemented
65C2×Q8×Dic43C2212yes—
66C2×Q8×Dic43C2212yes—
67C2×Q8×Dic43C2211yescharacteristic
68C2×C4×Dic86C2214yes—
69C2×C4×Dic86C2214yes—
70C2×C4×Dic86C2211yescharacteristic
71C2×C4×Dic86C2211yescharacteristic
72C2×C4×Dic86C2212yes—
73C2×C4×Dic86C2212yes—
74C2×#13063290C2211yescharacteristic
75C2×#13063290C2212yes—
76C2×#13063290C2212yes—
77C2×#13063290C2212yes—
78C2×#13063290C2212yes—
79C4×Q8×D43C22116yescomplemented
80C2×D4×Dic43C2212yes—
81C2×C4×C22⋊D43C2212yes—
82C2×(C22⋊D43)⋊C4C2214yes—
83C2×#13063284C2212yes—
84C2×#13063283C2212yes—
85C2×#13063282C2214yes—
86C2×#13063281C2214yes—
87C2×#13063281C2214yes—
88C2×C4⋊C4×D43C2212yes—
89C2×C4⋊C4×D43C2211yescharacteristic
90C2×C42×D43C2212yes—
91C2×C42×D43C2211yescharacteristic
92C43×#556C22116yescomplemented
93C2×C4⋊Q8×C43C2211yescharacteristic
94C2×#126×C43C2214yes—
95C2×#124×C43C2212yes—
96C2×C22⋊Q8×C43C2212yes—
97C2×C4×Q8×C43C2212yes—
98C2×C4×Q8×C43C2211yescharacteristic
99C2×C4×D4×C43C2211yescharacteristic
100C2×#117×C43C2212yes—
101C22×Dic86—216no—
102C22×Dic86C23116yes—
103C22×Dic86C2312yes—
104C22×Dic86C2312yes—
105C22×Dic86C2311yescharacteristic
106C22×Dic86C2314yes—
107C22×Dic86C2311yescharacteristic
108C2×Q8×D43—28no—
109C2×Q8×D43C2318yes—
110C22×C22⋊D43C2312yes—
111C23×Dic43C2314yes—
112C22×C4×D43C2311yescharacteristic
113C22×C4×D43C2312yes—
114C22×C4×D43C2311yescharacteristic
115C22×C4×D43C2312yes—
116C22×C4×D43C2311yescharacteristic
117#13063325C2318yes—
118#13063324C23132yes—
119#13063324C23116yes—
120#13063323C23116yes—
121#13063323C23116yes—
122#13063318C23132yes—
123#13063318C23132yes—
124#13063318C23132yes—
125#13063318C23116yes—
126#13063317C23132yes—
127#13063317C23116yes—
128#13063316C23132yes—
129#13063316C23116yes—
130#13063316C2318yes—
131#13063316C23116yes—
132#13063315C23132yes—
133#13063315C23132yes—
134#13063315C23132yes—
135#13063312C2318yes—
136#13063307C23116yes—
137#13063307C23132yes—
138#13063305C23116yes—
139#13063305C2318yes—
140#13063304C23116yes—
141#13063303C23132yes—
142#13063302C23132yes—
143#13063302C23132yes—
144#13063301C23116yes—
145#13063296C2318yes—
146Q8×Dic43C2318yes—
147Q8×Dic43C23116yes—
148Q8×Dic43C23116yes—
149C4×Dic86C2318yes—
150C4×Dic86C23132yes—
151C4×Dic86C23116yes—
152C4×Dic86C23116yes—
153C4×Dic86C2318yes—
154C4×Dic86C23132yes—
155#13063290C23116yes—
156#13063290C23116yes—
157#13063290C2318yes—
158#13063290C23116yes—
159#13063290C23116yes—
160D4×Dic43C23116yes—
161C4×C22⋊D43C23116yes—
162(C22⋊D43)⋊C4C23132yes—
163#13063284C23116yes—
164#13063283C23116yes—
165#13063282C23132yes—
166#13063281C23132yes—
167#13063281C23132yes—
168C2×C4⋊Dic43C2311yescharacteristic
169C2×C4⋊Dic43C2312yes—
170C2×C4⋊Dic43C2312yes—
171C2×C4⋊Dic43C2312yes—
172C2×C4⋊Dic43C2312yes—
173C2×C4⋊Dic43C2312yes—
174C2×C4⋊Dic43C2311yescharacteristic
175C2×C4⋊Dic43C2314yes—
176C2×C4⋊Dic43C2314yes—
177C2×Dic43⋊C4C2312yes—
178C2×Dic43⋊C4C2312yes—
179C2×Dic43⋊C4C2312yes—
180C2×Dic43⋊C4C2314yes—
181C2×Dic43⋊C4C2314yes—
182C2×Dic43⋊C4C2314yes—
183C2×Dic43⋊C4C2314yes—
184C2×Dic43⋊C4C2314yes—
185C2×Dic43⋊C4C2314yes—
186C2×Dic43⋊C4C2312yes—
187C2×Dic43⋊C4C2314yes—
188C2×Dic43⋊C4C2312yes—
189C4⋊C4×D43C23116yes—
190C4⋊C4×D43C2318yes—
191C2×C22⋊Dic43C2312yes—
192C2×C22⋊Dic43C2312yes—
193C2×C22⋊Dic43C2312yes—
194C2×C22⋊Dic43C2314yes—
195C2×(C2×D43)⋊C4C2312yes—
196C2×(C2×D43)⋊C4C2314yes—
197C2×C4×Dic43C2312yes—
198C2×C4×Dic43C2311yescharacteristic
199C2×C4×Dic43C2312yes—
200C2×C4×Dic43C2311yescharacteristic
201C2×C4×Dic43C2312yes—
202C2×C4×Dic43C2311yescharacteristic
203C2×C4×Dic43C2314yes—
204C2×C4×Dic43C2314yes—
205C2×C4×Dic43C2314yes—
206C2×C4×Dic43C2312yes—
207C42×D43C23116yes—
208C42×D43C2318yes—
209C22×Q8×C43C2311yescharacteristic
210C22×Q8×C43C2312yes—
211C22×D4×C43C2311yescharacteristic
212C23×C4×C43C2312yes—
213C4⋊Q8×C43C2318yes—
214#126×C43C23132yes—
215#124×C43C23116yes—
216C22⋊Q8×C43C23116yes—
217C4×Q8×C43C2318yes—
218C4×Q8×C43C23116yes—
219C4×D4×C43C2318yes—
220#117×C43C23116yes—
221C2×C4⋊C4×C43C2311yescharacteristic
222C2×C4⋊C4×C43C2312yes—
223C2×C4⋊C4×C43C2311yescharacteristic
224C2×C4⋊C4×C43C2314yes—
225C2×C4⋊C4×C43C2312yes—
226C2×C4⋊C4×C43C2312yes—
227C2×C22⋊C4×C43C2314yes—
228C2×C22⋊C4×C43C2312yes—
229C2×C22⋊C4×C43C2314yes—
230C2×C42×C43C2314yes—
231C2×C42×C43C2311yescharacteristic
232C2×C42×C43C2312yes—
233C24×C43C2412yes—
234C23×D43C2411yescharacteristic
235C2×Q8×C43—24no—
236C2×Q8×C43—28no—
237C2×Q8×C43C2414yes—
238C2×Q8×C43C2418yes—
239C2×D4×C43—24no—
240C2×D4×C43C2414yes—
241C22×C4×C43—28no—
242C22×C4×C43C2412yes—
243C22×C4×C43C2412yes—
244C22×C4×C43C2411yescharacteristic
245C22×C4×C43C2414yes—
246C22×C4×C43C2412yes—
247C22×C4×C43C2418yes—
248C22×C4×C43C2411yescharacteristic
249C22×C4×C43C2411yescharacteristic
250C2×C22⋊D43—28no—
251C2×C22⋊D43C2418yes—
252C22×Dic43—216no—
253C22×Dic43C2411yescharacteristic
254C22×Dic43C2411yescharacteristic
255C22×Dic43C2412yes—
256C22×Dic43C2412yes—
257C22×Dic43C2414yes—
258C22×Dic43C2412yes—
259C22×Dic43C2411yescharacteristic
260C22×Dic43C24116yes—
261C22×Dic43C2412yes—
262Q8×D43—232no—
263C2×C4×D43—24no—
264C2×C4×D43—24no—
265C2×C4×D43—28no—
266C2×C4×D43—28no—
267C2×C4×D43—24no—
268C2×C4×D43C2414yes—
269C2×C4×D43C2418yes—
270C2×C4×D43C2414yes—
271C2×C4×D43C2418yes—
272C2×C4×D43C2414yes—
273C2×Dic86—28no—
274C2×Dic86—24no—
275C2×Dic86—28no—
276C2×Dic86—216no—
277C2×Dic86—264no—
278C2×Dic86#4118yes—
279C2×Dic86C2418yes—
280C2×Dic86C2418yes—
281C2×Dic86C2414yes—
282C2×Dic86C24116yes—
283C2×Dic86C2414yes—
284C4⋊C4×C43C2414yes—
285C4⋊C4×C43C2418yes—
286C4⋊C4×C43C2414yes—
287C4⋊C4×C43C24116yes—
288C4⋊C4×C43C2418yes—
289C4⋊C4×C43C2418yes—
290C22⋊C4×C43C24116yes—
291C22⋊C4×C43C2418yes—
292C22⋊C4×C43C24116yes—
293C42×C43C24116yes—
294C42×C43C2414yes—
295C42×C43C2418yes—
296C22⋊Dic43C2418yes—
297C22⋊Dic43C2418yes—
298C22⋊Dic43C2418yes—
299C22⋊Dic43C24116yes—
300(C2×D43)⋊C4C2418yes—
301(C2×D43)⋊C4C24116yes—
302C4⋊Dic43C2414yes—
303C4⋊Dic43C2418yes—
304C4⋊Dic43C2418yes—
305C4⋊Dic43C2418yes—
306C4⋊Dic43C2418yes—
307C4⋊Dic43C2418yes—
308C4⋊Dic43C2414yes—
309C4⋊Dic43C24116yes—
310C4⋊Dic43C24116yes—
311Dic43⋊C4C2418yes—
312Dic43⋊C4C2418yes—
313Dic43⋊C4C2418yes—
314Dic43⋊C4C24116yes—
315Dic43⋊C4C24116yes—
316Dic43⋊C4C24116yes—
317Dic43⋊C4C24116yes—
318Dic43⋊C4C24116yes—
319Dic43⋊C4C24116yes—
320Dic43⋊C4C2418yes—
321Dic43⋊C4C24116yes—
322Dic43⋊C4C2418yes—
323C4×Dic43C2418yes—
324C4×Dic43C2414yes—
325C4×Dic43C2418yes—
326C4×Dic43C2414yes—
327C4×Dic43C2418yes—
328C4×Dic43C2414yes—
329C4×Dic43C24116yes—
330C4×Dic43C24116yes—
331C4×Dic43C24116yes—
332C4×Dic43C2418yes—
333C23×C43—24no—
334C23×C43—24no—
335C23×C43—24no—
336C23×C43C2514yes—
337C23×C43C2511yescharacteristic
338C22×D43—22no—
339C22×D43—22no—
340C22×D432−1+414yes—
341C22×D43C2512yes—
342Q8×C43—28no—
343Q8×C43—216no—
344D4×C43—28no—
345C2×C4×C43—24no—
346C2×C4×C43—24no—
347C2×C4×C43—24no—
348C2×C4×C43—22no—
349C2×C4×C43—28no—
350C2×C4×C43—216no—
351C2×C4×C43C2×#4114yes—
352C2×C4×C432−1+414yes—
353C2×C4×C43C2514yes—
354C2×C4×C43C2518yes—
355C2×C4×C43C2512yes—
356C2×C4×C43C2514yes—
357C2×C4×C43C2514yes—
358C2×C4×C43C2512yes—
359C2×C4×C43C2512yes—
360C22⋊D43—216no—
361C2×Dic43—22no—
362C2×Dic43—28no—
363C2×Dic43—24no—
364C2×Dic43—22no—
365C2×Dic43—24no—
366C2×Dic43—22no—
367C2×Dic43—24no—
368C2×Dic43—232no—
369C2×Dic43C2×#4118yes—
370C2×Dic43C2512yes—
371C2×Dic43C2512yes—
372C2×Dic43C2514yes—
373C2×Dic43C2514yes—
374C2×Dic43C2514yes—
375C2×Dic43C2518yes—
376C2×Dic43C2512yes—
377C2×Dic43C2514yes—
378C4×D43—216no—
379C4×D43—28no—
380C4×D43—28no—
381C4×D43—28no—
382C4×D43—216no—
383Dic86—216no—
384Dic86—28no—
385Dic86—232no—
386Dic86—216no—
387Dic86C2×#41116yes—
388C2×#3523—431nomaximal, Sylow
389C22×C43—24no—
390C22×C43—24no—
391C22×C43—24no—
392C22×C43—48no—
393C22×C43C22×#4112yes—
394C22×C43C2×2−1+412yes—
395C22×C43C2×2−1+412yes—
396C22×C43C2611yescharacteristic
397C2×D43—22no—
398C2×D43—22no—
399C2×D43—28no—
400C2×D43C2×2−1+414yes—
401C4×C43—24no—
402C4×C43—24no—
403C4×C43—24no—
404C4×C43—22no—
405C4×C43—28no—
406C4×C43C22×#4114yes—
407C4×C43C2×2−1+414yes—
408Dic43—22no—
409Dic43—28no—
410Dic43—24no—
411Dic43—22no—
412Dic43—24no—
413Dic43—22no—
414Dic43—24no—
415Dic43C22×#4118yes—
416#3523—4332no—
417C2×#557—431no—
418C2×#557—432no—
419C2×#557—431no—
420C2×#556—432no—
421C2×#556D4311yescharacteristic, complemented
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×#529—431no—
432C2×#519—432no—
433C22×C4×Q8—431no—
434C2×C43—44no—
435C2×C43#352314yescomplemented
436C2×C43C23×#4111yescharacteristic
437C2×C43C22×2−1+411yescharacteristic
438C2×C43C22×2−1+411yescharacteristic
439D43—24no—
440C23×Q8—431no—
441C23×Q8—432no—
442#557—4316no—
443#557—4332no—
444#557—4316no—
445#556—4332no—
446#556C2×D43116yescomplemented
447#552—4364no—
448#552—4332no—
449D4×Q8—4332no—
450D4×Q8—4316no—
451#541—4364no—
452#541—4332no—
453#533—4316no—
454#533—4332no—
455C2×C4⋊Q8—432no—
456C2×C4⋊Q8—432no—
457C2×C4⋊Q8—432no—
458C2×C4⋊Q8—434no—
459C2×C4⋊Q8—431no—
460C2×C4⋊Q8C2×D4311yescharacteristic
461#529—4332no—
462#529—4316no—
463C2×#126—434no—
464C2×#126—432no—
465C2×#126—434no—
466C2×#126—434no—
467C2×#126C2×D4314yes—
468C2×#125—431no—
469C2×#125—434no—
470C2×#125—432no—
471C2×#125—434no—
472C2×#125—434no—
473C2×#125—434no—
474C2×#125—432no—
475C2×#125—432no—
476C2×#125—434no—
477C2×#124—431no—
478C2×#124C2×D4312yes—
479C2×#123—432no—
480C2×#123—434no—
481C2×C22⋊Q8—432no—
482C2×C22⋊Q8—432no—
483C2×C22⋊Q8—434no—
484C2×C22⋊Q8—431no—
485C2×C22⋊Q8—432no—
486C2×C22⋊Q8—434no—
487C2×C22⋊Q8—434no—
488C2×C22⋊Q8C2×D4312yes—
489C2×#121—431no—
490#519—4332no—
491C2×C4×Q8—431no—
492C2×C4×Q8—432no—
493C2×C4×Q8—432no—
494C2×C4×Q8—4316no—
495C2×C4×Q8—431no—
496C2×C4×Q8—432no—
497C2×C4×Q8—432no—
498C2×C4×Q8—432no—
499C2×C4×Q8—432no—
500C2×C4×Q8—431no—
501C2×C4×Q8—432no—
502C2×C4×Q8—434no—
503C2×C4×Q8—434no—
504C2×C4×Q8—431no—
505C2×C4×Q8—432no—
506C2×C4×Q8C2×D4311yescharacteristic
507C2×C4×Q8C2×D4312yes—
508C2×C4×D4—432no—
509C2×C4×D4—432no—
510C2×C4×D4—434no—
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×C42—431no—
522C43C2×#352311yescharacteristic, complemented, Sylow
523C22×Q8—438no—
524C22×Q8—431no—
525C22×Q8—431no—
526C22×Q8—432no—
527C22×Q8—434no—
528C22×Q8—432no—
529C22×Q8—4316no—
530C22×Q8—8616no—
531C22×Q8—868no—
532C22×Q8C22×D4312yes—
533C22×Q8C22×D4311yescharacteristic
534C22×D4—432no—
535C22×D4C22×D4311yescharacteristic
536C23×C4—434no—
537C23×C4—431no—
538C23×C4—432no—
539C23×C4—432no—
540C23×C4—431no—
541C23×C4—431no—
542C23×C4C22×D4312yes—
543C4⋊Q8—4316no—
544C4⋊Q8—4316no—
545C4⋊Q8—4316no—
546C4⋊Q8—4332no—
547C4⋊Q8—438no—
548C4⋊Q8C22×D4318yes—
549#126—4332no—
550#126—4316no—
551#126—4332no—
552#126—4332no—
553#126C22×D43132yes—
554#125—438no—
555#125—4332no—
556#125—4316no—
557#125—4332no—
558#125—4332no—
559#125—4332no—
560#125—4316no—
561#125—4316no—
562#125—4332no—
563#124—438no—
564#124C22×D43116yes—
565#123—4316no—
566#123—4332no—
567C22⋊Q8—4316no—
568C22⋊Q8—4316no—
569C22⋊Q8—438no—
570C22⋊Q8—4332no—
571C22⋊Q8—4316no—
572C22⋊Q8—4332no—
573C22⋊Q8—4332no—
574C22⋊Q8C22×D43116yes—
575#121—438no—
576C4×Q8—438no—
577C4×Q8—4316no—
578C4×Q8—4316no—
579C4×Q8—438no—
580C4×Q8—4316no—
581C4×Q8—4316no—
582C4×Q8—4316no—
583C4×Q8—4316no—
584C4×Q8—438no—
585C4×Q8—4316no—
586C4×Q8—4332no—
587C4×Q8—4332no—
588C4×Q8—438no—
589C4×Q8—4316no—
590C4×Q8C22×D4318yes—
591C4×Q8C22×D43116yes—
592C4×D4—4316no—
593C4×D4—4316no—
594C4×D4—4332no—
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—432no—
604C2×C4⋊C4—431no—
605C2×C4⋊C4—432no—
606C2×C4⋊C4—432no—
607C2×C4⋊C4—434no—
608C2×C4⋊C4—434no—
609C2×C4⋊C4—432no—
610C2×C4⋊C4—434no—
611C2×C4⋊C4—432no—
612C2×C4⋊C4—434no—
613C2×C4⋊C4—432no—
614C2×C4⋊C4—434no—
615C2×C4⋊C4—432no—
616C2×C4⋊C4—434no—
617C2×C4⋊C4—432no—
618C2×C4⋊C4—431no—
619C2×C4⋊C4—434no—
620C2×C4⋊C4—434no—
621C2×C4⋊C4—432no—
622C2×C4⋊C4—434no—
623C2×C4⋊C4—4316no—
624C2×C4⋊C4—438no—
625C2×C4⋊C4C22×D4311yescharacteristic
626C2×C4⋊C4C22×D4312yes—
627C2×C4⋊C4C22×D4312yes—
628C2×C4⋊C4C22×D4312yes—
629C2×C4⋊C4C22×D4311yescharacteristic
630C2×C4⋊C4C22×D4314yes—
631C2×C22⋊C4—432no—
632C2×C22⋊C4—432no—
633C2×C22⋊C4—434no—
634C2×C22⋊C4—432no—
635C2×C22⋊C4—432no—
636C2×C22⋊C4—434no—
637C2×C22⋊C4C22×D4314yes—
638C2×C22⋊C4C22×D4314yes—
639C2×C22⋊C4C22×D4312yes—
640C2×C42—432no—
641C2×C42—431no—
642C2×C42—434no—
643C2×C42—434no—
644C2×C42—434no—
645C2×C42—432no—
646C2×C42—432no—
647C2×C42—431no—
648C2×C42—432no—
649C2×C42—431no—
650C2×C42—4316no—
651C2×C42—438no—
652C2×C42C22×D4314yes—
653C2×C42C22×D4311yescharacteristic
654C2×C42C22×D4312yes—
655C24—431no—
656C24C23×D4312yes—
657C2×Q8—24no—
658C2×Q8—28no—
659C2×Q8—438no—
660C2×Q8—434no—
661C2×Q8—434no—
662C2×Q8—438no—
663C2×Q8—4316no—
664C2×Q8—438no—
665C2×Q8—8616no—
666C2×Q8—868no—
667C2×Q8—8664no—
668C2×Q8—8632no—
669C2×Q8—868no—
670C2×Q8—864no—
671C2×Q8C23×D4318yes—
672C2×Q8C23×D4314yes—
673C2×D4—24no—
674C2×D4—438no—
675C2×D4—868no—
676C2×D4C23×D4314yes—
677C22×C4—28no—
678C22×C4—432no—
679C22×C4—4316no—
680C22×C4—431no—
681C22×C4—431no—
682C22×C4—432no—
683C22×C4—432no—
684C22×C4—432no—
685C22×C4—434no—
686C22×C4—431no—
687C22×C4—434no—
688C22×C4—434no—
689C22×C4—438no—
690C22×C4—438no—
691C22×C4—434no—
692C22×C4—868no—
693C22×C4—868no—
694C22×C4—864no—
695C22×C4—8616no—
696C22×C4—864no—
697C22×C4—864no—
698C22×C4C23×D4318yes—
699C22×C4C23×D4312yes—
700C22×C4C23×D4314yes—
701C22×C4C23×D4311yescharacteristic
702C22×C4C23×D4312yes—
703C22×C4C23×D4312yes—
704C22×C4C23×D4311yescharacteristic
705C22×C4C23×D4311yescharacteristic
706C4⋊C4—438no—
707C4⋊C4—438no—
708C4⋊C4—434no—
709C4⋊C4—438no—
710C4⋊C4—438no—
711C4⋊C4—4316no—
712C4⋊C4—4316no—
713C4⋊C4—438no—
714C4⋊C4—4316no—
715C4⋊C4—438no—
716C4⋊C4—4316no—
717C4⋊C4—438no—
718C4⋊C4—4316no—
719C4⋊C4—438no—
720C4⋊C4—4316no—
721C4⋊C4—438no—
722C4⋊C4—434no—
723C4⋊C4—4316no—
724C4⋊C4—4316no—
725C4⋊C4—438no—
726C4⋊C4—4316no—
727C4⋊C4C23×D4314yes—
728C4⋊C4C23×D4318yes—
729C4⋊C4C23×D4318yes—
730C4⋊C4C23×D4318yes—
731C4⋊C4C23×D4314yes—
732C4⋊C4C23×D43116yes—
733C22⋊C4—438no—
734C22⋊C4—438no—
735C22⋊C4—4316no—
736C22⋊C4—438no—
737C22⋊C4—438no—
738C22⋊C4—4316no—
739C22⋊C4C23×D43116yes—
740C22⋊C4C23×D43116yes—
741C22⋊C4C23×D4318yes—
742C42—438no—
743C42—434no—
744C42—438no—
745C42—434no—
746C42—438no—
747C42—434no—
748C42—4316no—
749C42—4316no—
750C42—4316no—
751C42—438no—
752C42C23×D4314yes—
753C42C23×D4318yes—
754C42C23×D43116yes—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—434no—
759C23—432no—
760C23—862no—
761C23—862no—
762C23C24×D4314yes—
763C23C24×D4311yescharacteristic
764Q8—28no—
765Q8—216no—
766Q8—4316no—
767Q8—8632no—
768Q8—8616no—
769Q8—8616no—
770Q8—868no—
771D4—28no—
772D4—8616no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—28no—
778C2×C4—216no—
779C2×C4—438no—
780C2×C4—434no—
781C2×C4—432no—
782C2×C4—432no—
783C2×C4—434no—
784C2×C4—434no—
785C2×C4—434no—
786C2×C4—432no—
787C2×C4—438no—
788C2×C4—8616no—
789C2×C4—8616no—
790C2×C4—868no—
791C2×C4—8632no—
792C2×C4—868no—
793C2×C4—862no—
794C2×C4—862no—
795C2×C4—864no—
796C2×C4—864no—
797C2×C4—862no—
798C2×C4—864no—
799C2×C4—868no—
800C2×C4—868no—
801C2×C4#41×D4314yes—
802C2×C4#1306337214yes—
803C2×C4C24×D4314yes—
804C2×C4C24×D4318yes—
805C2×C4C24×D4312yes—
806C2×C4C24×D4314yes—
807C2×C4C24×D4314yes—
808C2×C4C24×D4312yes—
809C2×C4C24×D4312yes—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—48no—
814C22—434no—
815C22—862no—
816C22—862no—
817C22—868no—
818C22C2×#41×D4312yes—
819C222−1+4×D4312yes—
820C22C2×#1306337212yes—
821C22C25×D4311yescharacteristic
822C4—24no—
823C4—24no—
824C4—24no—
825C4—22no—
826C4—28no—
827C4—438no—
828C4—868no—
829C4—862no—
830C4—862no—
831C4—864no—
832C4—864no—
833C4—862no—
834C4—864no—
835C4C2×#41×D4314yes—
836C4C2×#1306337214yes—
837C2—44no—
838C2—864no—
839C2#1914869014yesdirect product factor
840C2C22×#41×D4311yescharacteristic
841C2C2×2−1+4×D4311yescharacteristic
842C2C22×#1306337211yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#556C2
socleC23×C43C25
prime radicalC2×#13063296C22
hypercenterC2×#556D43
hypocenterC43C2×#3523
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #19148690C2direct (N × H)
2. C2×#14583627C2semidirect
3. C2×#14583625C2semidirect
4. C2×#14583624C2semidirect
5. C2×#14583618C2semidirect
6. C2×#14583588C2semidirect
7. C2×#14583585C2semidirect
8. C2×D4×Dic86C2semidirect
9. C2×#14583562C2semidirect
10. C2×#14583509C2semidirect
11. C2×#14583506C2semidirect
12. C2×#14583454C2semidirect
13. C2×#14583453C2semidirect
16. C2×#14583376C2semidirect
17. C2×C4×Q8×D43C2semidirect
18. C2×C43×#556C2semidirect
21. #14583627C22semidirect
22. #14583625C22semidirect
23. #14583624C22semidirect
24. #14583618C22semidirect
25. #14583588C22semidirect
26. #14583585C22semidirect
27. D4×Dic86C22semidirect
28. #14583562C22semidirect
29. #14583509C22semidirect
30. #14583506C22semidirect
31. #14583454C22semidirect
32. #14583453C22semidirect
64. #14583376C22semidirect
79. C4×Q8×D43C22semidirect
92. C43×#556C22semidirect
421. C2×#556D43semidirect
435. C2×C43#3523semidirect
446. #556C2×D43semidirect
522. C43C2×#3523semidirect
839. C2#19148690direct (N × H)

Maximal subgroups

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

subgroupindex
#191486902
C2×#145836272
C2×#145836252
C2×#145836242
C2×#145836182
C2×#145835882
C2×#145835852
C2×D4×Dic862
C2×#145835622
C2×#145835092
C2×#145835062
C2×#145834542
C2×#145834532
C2×#145834312
C2×#145834282
C2×#145833762
C2×C4×Q8×D432
C2×C43×#5562
C2×#352343