Finite Group Databasebeta

← C2×#19149071 #26004312

Subgroups — C2×#19149071 #26004312

Order 11008.

6446 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149071C2132yesmaximal, direct product factor
2C2×#14583651C214yesmaximal, complemented
3C2×Q8×Dic86C211yesmaximal, characteristic, complemented
4C2×#14583628C212yesmaximal, complemented
5C2×#14583624C211yesmaximal, characteristic, complemented
6C2×#14583618C212yesmaximal, complemented
7C2×#14583617C212yesmaximal, complemented
8C2×#14583606C211yesmaximal, characteristic, complemented
9C2×#14583591C212yesmaximal, complemented
10C2×#14583527C212yesmaximal, complemented
11C2×#14583518C212yesmaximal
12C2×#14583509C212yesmaximal, complemented
13C2×#14583507C212yesmaximal, complemented
14C2×#14583506C214yesmaximal, complemented
15C2×#14583454C211yesmaximal, characteristic, complemented
16C2×#14583453C211yesmaximal, characteristic, complemented
17C2×#14583431C211yesmaximal, characteristic
18C2×C43×#556C211yesmaximal, characteristic, complemented
19#14583651C22164yescomplemented
20Q8×Dic86C22116yescomplemented
21#14583628C22132yescomplemented
22#14583624C22116yescomplemented
23#14583618C22132yescomplemented
24#14583617C22132yescomplemented
25#14583606C22116yescomplemented
26#14583591C22132yescomplemented
27#14583527C22132yescomplemented
28#14583518C22132yes—
29#14583509C22132yescomplemented
30#14583507C22132yescomplemented
31#14583506C22164yescomplemented
32#14583454C22116yescomplemented
33#14583453C22116yescomplemented
34C2×#13063325C2211yescharacteristic
35C2×#13063325C2212yes—
36C2×#13063325C2214yes—
37C2×#13063324C2211yescharacteristic
38C2×#13063324C2212yes—
39C2×#13063324C2214yes—
40C2×#13063323C2211yescharacteristic
41C2×#13063323C2212yes—
42#14583431C22116yes—
43C2×#13063320C2214yes—
44C2×#13063319C2214yes—
45C2×#13063318C2212yes—
46C2×#13063318C2214yes—
47C2×#13063318C2214yes—
48C2×#13063318C2214yes—
49C2×#13063317C2214yes—
50C2×#13063316C2212yes—
51C2×#13063316C2214yes—
52C2×#13063316C2211yescharacteristic
53C2×#13063316C2212yes—
54C2×#13063316C2212yes—
55C2×#13063316C2214yes—
56C2×#13063315C2212yes—
57C2×#13063315C2214yes—
58C2×#13063315C2214yes—
59C2×#13063312C2211yescharacteristic
60C2×#13063311C2214yes—
61C2×#13063309C2214yes—
62C2×#13063307C2212yes—
63C2×#13063305C2211yescharacteristic
64C2×#13063305C2211yescharacteristic
65C2×#13063305C2212yes—
66C2×#13063304C2212yes—
67C2×#13063303C2212yes—
68C2×#13063302C2214yes—
69C2×#13063302C2214yes—
70C2×#13063302C2214yes—
71C2×#13063301C2211yescharacteristic
72C2×#13063301C2212yes—
73C2×#13063296C2211yescharacteristic
74C2×Q8×Dic43C2212yes—
75C2×Q8×Dic43C2212yes—
76C2×Q8×Dic43C2212yes—
77C2×C4×Dic86C2211yescharacteristic
78C2×C4×Dic86C2211yescharacteristic
79C2×C4×Dic86C2212yes—
80C2×C4×Dic86C2214yes—
81C2×C4×Dic86C2212yes—
82C2×#13063290C2212yes—
83C2×#13063290C2212yes—
84C2×D4×Dic43C2212yes—
85C2×C4×C22⋊D43C2212yes—
86C2×#13063284C2212yes—
87C2×#13063283C2212yes—
88C2×#13063282C2212yes—
89C2×#13063281C2214yes—
90C22×C4⋊Dic43C2212yes—
91C2×C42×D43C2211yescharacteristic
92C43×#556C22116yescomplemented
93C2×C4⋊Q8×C43C2211yescharacteristic
94C2×#126×C43C2214yes—
95C2×#124×C43C2212yes—
96C2×C22⋊Q8×C43C2212yes—
97C2×C4×Q8×C43C2211yescharacteristic
98C2×C4×Q8×C43C2212yes—
99C2×C4×D4×C43C2211yescharacteristic
100C2×#117×C43C2212yes—
101C22×Dic86C2311yescharacteristic
102C22×Dic86C2311yescharacteristic
103C22×Dic86C2312yes—
104C22×Dic86C2312yes—
105C22×Dic86C2314yes—
106C22×C22⋊D43C2312yes—
107C23×Dic43C2314yes—
108C22×C4×D43C2311yescharacteristic
109C22×C4×D43C2311yescharacteristic
110C22×C4×D43C2311yescharacteristic
111#13063325C2318yes—
112#13063325C23116yes—
113#13063325C23132yes—
114#13063324C23116yes—
115#13063324C23132yes—
116#13063324C2318yes—
117#13063323C23116yes—
118#13063323C2318yes—
119#13063320C23132yes—
120#13063319C23132yes—
121#13063318C23132yes—
122#13063318C23132yes—
123#13063318C23116yes—
124#13063318C23132yes—
125#13063317C23132yes—
126#13063316C23116yes—
127#13063316C23132yes—
128#13063316C23116yes—
129#13063316C2318yes—
130#13063316C23132yes—
131#13063316C23116yes—
132#13063315C23132yes—
133#13063315C23116yes—
134#13063315C23132yes—
135#13063312C2318yes—
136#13063311C23132yes—
137#13063309C23132yes—
138#13063307C23116yes—
139#13063305C2318yes—
140#13063305C23116yes—
141#13063305C2318yes—
142#13063304C23116yes—
143#13063303C23116yes—
144#13063302C23132yes—
145#13063302C23132yes—
146#13063302C23132yes—
147#13063301C2318yes—
148#13063301C23116yes—
149#13063296C2318yes—
150Q8×Dic43C23116yes—
151Q8×Dic43C23116yes—
152Q8×Dic43C23116yes—
153C4×Dic86C2318yes—
154C4×Dic86C23132yes—
155C4×Dic86C23116yes—
156C4×Dic86C23116yes—
157C4×Dic86C2318yes—
158#13063290C23116yes—
159#13063290C23116yes—
160D4×Dic43C23116yes—
161C4×C22⋊D43C23116yes—
162#13063284C23116yes—
163#13063283C23116yes—
164#13063282C23116yes—
165#13063281C23132yes—
166C2×C4⋊Dic43C23116yes—
167C2×C4⋊Dic43C2311yescharacteristic
168C2×C4⋊Dic43C2312yes—
169C2×C4⋊Dic43C2314yes—
170C2×C4⋊Dic43C2312yes—
171C2×C4⋊Dic43C2312yes—
172C2×C4⋊Dic43C2312yes—
173C2×C4⋊Dic43C2312yes—
174C2×C4⋊Dic43C2311yescharacteristic
175C2×C4⋊Dic43C2314yes—
176C2×C4⋊Dic43C2314yes—
177C2×C4⋊Dic43C2314yes—
178C2×Dic43⋊C4C2312yes—
179C2×Dic43⋊C4C2314yes—
180C2×Dic43⋊C4C2312yes—
181C2×Dic43⋊C4C2312yes—
182C2×Dic43⋊C4C2312yes—
183C2×Dic43⋊C4C2314yes—
184C2×Dic43⋊C4C2314yes—
185C2×Dic43⋊C4C2312yes—
186C2×Dic43⋊C4C2314yes—
187C2×Dic43⋊C4C2314yes—
188C2×Dic43⋊C4C2312yes—
189C2×Dic43⋊C4C2312yes—
190C2×C22⋊Dic43C2312yes—
191C2×C22⋊Dic43C2312yes—
192C2×C22⋊Dic43C2312yes—
193C2×C22⋊Dic43C2314yes—
194C2×(C2×D43)⋊C4C2312yes—
195C2×(C2×D43)⋊C4C2312yes—
196C2×(C2×D43)⋊C4C2314yes—
197C2×(C2×D43)⋊C4C2312yes—
198C2×C4×Dic43C2311yescharacteristic
199C2×C4×Dic43C2311yescharacteristic
200C2×C4×Dic43C2311yescharacteristic
201C2×C4×Dic43C2314yes—
202C2×C4×Dic43C2314yes—
203C2×C4×Dic43C2312yes—
204C2×C4×Dic43C2312yes—
205C2×C4×Dic43C2314yes—
206C42×D43C2318yes—
207C22×Q8×C43C2311yescharacteristic
208C22×Q8×C43C2312yes—
209C22×D4×C43C2311yescharacteristic
210C23×C4×C43C2312yes—
211C4⋊Q8×C43C2318yes—
212#126×C43C23132yes—
213#124×C43C23116yes—
214C22⋊Q8×C43C23116yes—
215C4×Q8×C43C23116yes—
216C4×Q8×C43C2318yes—
217C4×D4×C43C2318yes—
218#117×C43C23116yes—
219C2×C4⋊C4×C43C2311yescharacteristic
220C2×C4⋊C4×C43C2312yes—
221C2×C4⋊C4×C43C2311yescharacteristic
222C2×C4⋊C4×C43C2314yes—
223C2×C4⋊C4×C43C2312yes—
224C2×C4⋊C4×C43C2312yes—
225C2×C22⋊C4×C43C2314yes—
226C2×C22⋊C4×C43C2312yes—
227C2×C22⋊C4×C43C2314yes—
228C2×C42×C43C2314yes—
229C2×C42×C43C2311yescharacteristic
230C2×C42×C43C2312yes—
231C24×C43C2412yes—
232C23×D43C2411yescharacteristic
233C2×Q8×C43—24no—
234C2×Q8×C43—28no—
235C2×Q8×C43C2414yes—
236C2×Q8×C43C2418yes—
237C2×D4×C43—24no—
238C2×D4×C43C2414yes—
239C22×C4×C43—28no—
240C22×C4×C43C2412yes—
241C22×C4×C43C2412yes—
242C22×C4×C43C2411yescharacteristic
243C22×C4×C43C2414yes—
244C22×C4×C43C2412yes—
245C22×C4×C43C2418yes—
246C22×C4×C43C2411yescharacteristic
247C22×C4×C43C2411yescharacteristic
248C2×C22⋊D43—44no—
249C2×C22⋊D43C2418yes—
250C22×Dic43—48no—
251C22×Dic43C2411yescharacteristic
252C22×Dic43C2412yes—
253C22×Dic43C2412yes—
254C22×Dic43C2412yes—
255C22×Dic43C2414yes—
256C22×Dic43C2411yescharacteristic
257C22×Dic43C2411yescharacteristic
258C22×Dic43C2412yes—
259C22×Dic43C24116yes—
260C2×C4×D43—24no—
261C2×C4×D43—24no—
262C2×C4×D43—42no—
263C2×C4×D43C2414yes—
264C2×C4×D43C2414yes—
265C2×C4×D43C2414yes—
266C2×Dic86—24no—
267C2×Dic86—24no—
268C2×Dic86—44no—
269C2×Dic86—44no—
270C2×Dic86—48no—
271C2×Dic86C2414yes—
272C2×Dic86C2414yes—
273C2×Dic86C2418yes—
274C2×Dic86C2418yes—
275C2×Dic86C24116yes—
276C4⋊C4×C43C2414yes—
277C4⋊C4×C43C2418yes—
278C4⋊C4×C43C2414yes—
279C4⋊C4×C43C24116yes—
280C4⋊C4×C43C2418yes—
281C4⋊C4×C43C2418yes—
282C22⋊C4×C43C24116yes—
283C22⋊C4×C43C2418yes—
284C22⋊C4×C43C24116yes—
285C42×C43C24116yes—
286C42×C43C2414yes—
287C42×C43C2418yes—
288C22⋊Dic43C2418yes—
289C22⋊Dic43C2418yes—
290C22⋊Dic43C2418yes—
291C22⋊Dic43C24116yes—
292(C2×D43)⋊C4C2418yes—
293(C2×D43)⋊C4C2418yes—
294(C2×D43)⋊C4C24116yes—
295(C2×D43)⋊C4C2418yes—
296C4⋊Dic43C2414yes—
297C4⋊Dic43C2418yes—
298C4⋊Dic43C24116yes—
299C4⋊Dic43C2418yes—
300C4⋊Dic43C2418yes—
301C4⋊Dic43C2418yes—
302C4⋊Dic43C2418yes—
303C4⋊Dic43C2414yes—
304C4⋊Dic43C24116yes—
305C4⋊Dic43C24116yes—
306C4⋊Dic43C24116yes—
307Dic43⋊C4C2418yes—
308Dic43⋊C4C24116yes—
309Dic43⋊C4C2418yes—
310Dic43⋊C4C2418yes—
311Dic43⋊C4C2418yes—
312Dic43⋊C4C24116yes—
313Dic43⋊C4C24116yes—
314Dic43⋊C4C2418yes—
315Dic43⋊C4C24116yes—
316Dic43⋊C4C24116yes—
317Dic43⋊C4C2418yes—
318Dic43⋊C4C2418yes—
319C4×Dic43C2414yes—
320C4×Dic43C2414yes—
321C4×Dic43C2414yes—
322C4×Dic43C24116yes—
323C4×Dic43C24116yes—
324C4×Dic43C2418yes—
325C4×Dic43C2418yes—
326C4×Dic43C24116yes—
327C23×C43—24no—
328C23×C43—24no—
329C23×C43—24no—
330C23×C43C2514yes—
331C23×C43C2511yescharacteristic
332C22×D43—22no—
333C22×D43—22no—
334C22×D43—22no—
335C22×D43C2512yes—
336Q8×C43—28no—
337Q8×C43—216no—
338D4×C43—28no—
339C2×C4×C43—24no—
340C2×C4×C43—24no—
341C2×C4×C43—28no—
342C2×C4×C43—24no—
343C2×C4×C43—22no—
344C2×C4×C43—216no—
345C2×C4×C432−1+414yes—
346C2×C4×C432−1+414yes—
347C2×C4×C43C2518yes—
348C2×C4×C43C2514yes—
349C2×C4×C43C2512yes—
350C2×C4×C43C2514yes—
351C2×C4×C43C2514yes—
352C2×C4×C43C2512yes—
353C2×C4×C43C2512yes—
354C22⋊D43—48no—
355C2×Dic43—24no—
356C2×Dic43—24no—
357C2×Dic43—22no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—28no—
361C2×Dic43—24no—
362C2×Dic43—24no—
363C2×Dic43—416no—
364C2×Dic43C2512yes—
365C2×Dic43C2514yes—
366C2×Dic43C2514yes—
367C2×Dic43C2514yes—
368C2×Dic43C2512yes—
369C2×Dic43C2518yes—
370C2×Dic43C2512yes—
371C2×Dic43C2514yes—
372C4×D43—28no—
373C4×D43—28no—
374C4×D43—44no—
375Dic86—28no—
376Dic86—28no—
377Dic86—48no—
378Dic86—48no—
379Dic86—416no—
380C2×#3555—431nomaximal, Sylow
381C22×C43—24no—
382C22×C43—24no—
383C22×C43—24no—
384C22×C43—48no—
385C22×C43C2×2−1+412yes—
386C22×C43C2×2−1+412yes—
387C22×C43#58512yes—
388C22×C43C2611yescharacteristic
389C2×D43—22no—
390C2×D43—22no—
391C2×D43—22no—
392C2×D43—44no—
393C4×C43—24no—
394C4×C43—24no—
395C4×C43—28no—
396C4×C43—24no—
397C4×C43—22no—
398C4×C43C2×2−1+414yes—
399C4×C43C2×2−1+414yes—
400Dic43—24no—
401Dic43—24no—
402Dic43—22no—
403Dic43—22no—
404Dic43—22no—
405Dic43—28no—
406Dic43—24no—
407Dic43—24no—
408#3555—4332no—
409C2×#563—434no—
410C2×Q82—431no—
411C2×#557—431no—
412C2×#557—432no—
413C2×#556—432no—
414C2×#556—432no—
415C2×#556D4311yescharacteristic, complemented
416C2×#554—431no—
417C2×#552—432no—
418C2×#544—432no—
419C2×#542—432no—
420C2×#541—434no—
421C2×#541—432no—
422C2×#541—432no—
423C2×#533—431no—
424C2×#533—431no—
425C2×#529—431no—
426C2×C43—44no—
427C2×C43#355514yescomplemented
428C2×C43C22×2−1+411yescharacteristic
429C2×C43C22×2−1+411yescharacteristic
430C2×C43C2×#58511yescharacteristic
431D43—42no—
432#563—4364no—
433Q82—4316no—
434#557—4316no—
435#557—4332no—
436#556—4332no—
437#556—4332no—
438#556C2×D43116yescomplemented
439#554—4316no—
440#552—4332no—
441#544—4332no—
442#542—4332no—
443#541—4364no—
444#541—4332no—
445#541—4332no—
446#533—4316no—
447#533—4316no—
448C2×C4⋊Q8—431no—
449C2×C4⋊Q8—432no—
450C2×C4⋊Q8—431no—
451C2×C4⋊Q8—434no—
452C2×C4⋊Q8—432no—
453C2×C4⋊Q8—431no—
454C2×C4⋊Q8—432no—
455C2×C4⋊Q8—434no—
456C2×C4⋊Q8C2×D4311yescharacteristic
457#529—4316no—
458C2×#126—434no—
459C2×#126—432no—
460C2×#126—434no—
461C2×#126—434no—
462C2×#126—434no—
463C2×#126—434no—
464C2×#126C2×D4314yes—
465C2×#125—431no—
466C2×#125—432no—
467C2×#125—432no—
468C2×#125—434no—
469C2×#125—434no—
470C2×#125—434no—
471C2×#125—432no—
472C2×#125—434no—
473C2×#125—432no—
474C2×#125—434no—
475C2×#124—431no—
476C2×#124—434no—
477C2×#124C2×D4312yes—
478C2×#123—432no—
479C2×#123—434no—
480C2×C22⋊Q8—432no—
481C2×C22⋊Q8—431no—
482C2×C22⋊Q8—432no—
483C2×C22⋊Q8—432no—
484C2×C22⋊Q8—431no—
485C2×C22⋊Q8—431no—
486C2×C22⋊Q8—432no—
487C2×C22⋊Q8—434no—
488C2×C22⋊Q8—434no—
489C2×C22⋊Q8—434no—
490C2×C22⋊Q8C2×D4312yes—
491C2×#121—431no—
492C2×C4×Q8—432no—
493C2×C4×Q8—432no—
494C2×C4×Q8—432no—
495C2×C4×Q8—432no—
496C2×C4×Q8—432no—
497C2×C4×Q8—431no—
498C2×C4×Q8—431no—
499C2×C4×Q8—432no—
500C2×C4×Q8—434no—
501C2×C4×Q8—432no—
502C2×C4×Q8C2×D4311yescharacteristic
503C2×C4×Q8C2×D4312yes—
504C2×C4×D4—432no—
505C2×C4×D4—432no—
506C2×C4×D4C2×D4311yescharacteristic
507C2×#117—432no—
508C2×#117—432no—
509C2×#117—434no—
510C2×#117—432no—
511C2×#117C2×D4312yes—
512C22×C4⋊C4—432no—
513C22×C42—431no—
514C43C2×#355511yescharacteristic, complemented, Sylow
515C22×Q8—431no—
516C22×Q8—431no—
517C22×Q8—432no—
518C22×Q8—432no—
519C22×Q8—434no—
520C22×Q8C22×D4311yescharacteristic
521C22×Q8C22×D4312yes—
522C22×D4—432no—
523C22×D4C22×D4311yescharacteristic
524C23×C4—434no—
525C23×C4—431no—
526C23×C4—431no—
527C23×C4—431no—
528C23×C4C22×D4312yes—
529C4⋊Q8—438no—
530C4⋊Q8—4316no—
531C4⋊Q8—438no—
532C4⋊Q8—4332no—
533C4⋊Q8—4316no—
534C4⋊Q8—438no—
535C4⋊Q8—4316no—
536C4⋊Q8—4332no—
537C4⋊Q8C22×D4318yes—
538#126—4332no—
539#126—4316no—
540#126—4332no—
541#126—4332no—
542#126—4332no—
543#126—4332no—
544#126C22×D43132yes—
545#125—438no—
546#125—4316no—
547#125—4316no—
548#125—4332no—
549#125—4332no—
550#125—4316no—
551#125—4332no—
552#125—4332no—
553#125—4316no—
554#125—4332no—
555#124—438no—
556#124—4332no—
557#124C22×D43116yes—
558#123—4316no—
559#123—4332no—
560C22⋊Q8—4316no—
561C22⋊Q8—438no—
562C22⋊Q8—4316no—
563C22⋊Q8—438no—
564C22⋊Q8—438no—
565C22⋊Q8—4316no—
566C22⋊Q8—4316no—
567C22⋊Q8—4332no—
568C22⋊Q8—4332no—
569C22⋊Q8—4332no—
570C22⋊Q8C22×D43116yes—
571#121—438no—
572C4×Q8—4316no—
573C4×Q8—4316no—
574C4×Q8—4316no—
575C4×Q8—4316no—
576C4×Q8—4316no—
577C4×Q8—438no—
578C4×Q8—438no—
579C4×Q8—4316no—
580C4×Q8—4332no—
581C4×Q8—4316no—
582C4×Q8C22×D4318yes—
583C4×Q8C22×D43116yes—
584C4×D4—4316no—
585C4×D4—4316no—
586C4×D4C22×D4318yes—
587#117—4316no—
588#117—4316no—
589#117—4332no—
590#117—4316no—
591#117C22×D43116yes—
592C2×C4⋊C4—431no—
593C2×C4⋊C4—432no—
594C2×C4⋊C4—434no—
595C2×C4⋊C4—4316no—
596C2×C4⋊C4—432no—
597C2×C4⋊C4—432no—
598C2×C4⋊C4—432no—
599C2×C4⋊C4—434no—
600C2×C4⋊C4—432no—
601C2×C4⋊C4—432no—
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—434no—
610C2×C4⋊C4—434no—
611C2×C4⋊C4—432no—
612C2×C4⋊C4—434no—
613C2×C4⋊C4—432no—
614C2×C4⋊C4—434no—
615C2×C4⋊C4—434no—
616C2×C4⋊C4C22×D4312yes—
617C2×C4⋊C4C22×D4311yescharacteristic
618C2×C4⋊C4C22×D4311yescharacteristic
619C2×C4⋊C4C22×D4312yes—
620C2×C4⋊C4C22×D4312yes—
621C2×C4⋊C4C22×D4314yes—
622C2×C22⋊C4—432no—
623C2×C22⋊C4—432no—
624C2×C22⋊C4—432no—
625C2×C22⋊C4—434no—
626C2×C22⋊C4—432no—
627C2×C22⋊C4—434no—
628C2×C22⋊C4—432no—
629C2×C22⋊C4—432no—
630C2×C22⋊C4C22×D4314yes—
631C2×C22⋊C4C22×D4314yes—
632C2×C22⋊C4C22×D4312yes—
633C2×C42—434no—
634C2×C42—431no—
635C2×C42—432no—
636C2×C42—432no—
637C2×C42—434no—
638C2×C42—431no—
639C2×C42—434no—
640C2×C42—431no—
641C2×C42—438no—
642C2×C42C22×D4312yes—
643C2×C42C22×D4314yes—
644C2×C42C22×D4311yescharacteristic
645C24—431no—
646C24C23×D4312yes—
647C2×Q8—24no—
648C2×Q8—28no—
649C2×Q8—434no—
650C2×Q8—434no—
651C2×Q8—438no—
652C2×Q8—438no—
653C2×Q8—4316no—
654C2×Q8—864no—
655C2×Q8—864no—
656C2×Q8—1724no—
657C2×Q8—1724no—
658C2×Q8—1728no—
659C2×Q8C23×D4314yes—
660C2×Q8C23×D4318yes—
661C2×D4—24no—
662C2×D4—438no—
663C2×D4—1724no—
664C2×D4C23×D4314yes—
665C22×C4—28no—
666C22×C4—431no—
667C22×C4—432no—
668C22×C4—432no—
669C22×C4—432no—
670C22×C4—431no—
671C22×C4—434no—
672C22×C4—431no—
673C22×C4—432no—
674C22×C4—4316no—
675C22×C4—434no—
676C22×C4—434no—
677C22×C4—434no—
678C22×C4—864no—
679C22×C4—864no—
680C22×C4—1722no—
681C22×C4—1728no—
682C22×C4C23×D4318yes—
683C22×C4C23×D4314yes—
684C22×C4C23×D4312yes—
685C22×C4C23×D4311yescharacteristic
686C22×C4C23×D4312yes—
687C22×C4C23×D4312yes—
688C22×C4C23×D4311yescharacteristic
689C22×C4C23×D4311yescharacteristic
690C4⋊C4—434no—
691C4⋊C4—438no—
692C4⋊C4—4316no—
693C4⋊C4—438no—
694C4⋊C4—438no—
695C4⋊C4—438no—
696C4⋊C4—4316no—
697C4⋊C4—438no—
698C4⋊C4—438no—
699C4⋊C4—438no—
700C4⋊C4—438no—
701C4⋊C4—434no—
702C4⋊C4—438no—
703C4⋊C4—438no—
704C4⋊C4—4316no—
705C4⋊C4—4316no—
706C4⋊C4—4316no—
707C4⋊C4—4316no—
708C4⋊C4—438no—
709C4⋊C4—4316no—
710C4⋊C4—438no—
711C4⋊C4—4316no—
712C4⋊C4—4316no—
713C4⋊C4C23×D4318yes—
714C4⋊C4C23×D4314yes—
715C4⋊C4C23×D4314yes—
716C4⋊C4C23×D4318yes—
717C4⋊C4C23×D4318yes—
718C4⋊C4C23×D43116yes—
719C22⋊C4—438no—
720C22⋊C4—438no—
721C22⋊C4—438no—
722C22⋊C4—4316no—
723C22⋊C4—438no—
724C22⋊C4—4316no—
725C22⋊C4—438no—
726C22⋊C4—438no—
727C22⋊C4C23×D43116yes—
728C22⋊C4C23×D43116yes—
729C22⋊C4C23×D4318yes—
730C42—434no—
731C42—434no—
732C42—434no—
733C42—4316no—
734C42—438no—
735C42—438no—
736C42—4316no—
737C42—4316no—
738C42C23×D4314yes—
739C42C23×D4318yes—
740C42C23×D43116yes—
741C23—24no—
742C23—24no—
743C23—24no—
744C23—432no—
745C23—862no—
746C23—862no—
747C23—862no—
748C23C24×D4314yes—
749C23C24×D4311yescharacteristic
750Q8—28no—
751Q8—216no—
752Q8—868no—
753Q8—868no—
754Q8—1728no—
755Q8—1728no—
756Q8—17216no—
757D4—28no—
758D4—1728no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—28no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—216no—
765C2×C4—432no—
766C2×C4—434no—
767C2×C4—434no—
768C2×C4—434no—
769C2×C4—432no—
770C2×C4—432no—
771C2×C4—438no—
772C2×C4—434no—
773C2×C4—862no—
774C2×C4—862no—
775C2×C4—864no—
776C2×C4—864no—
777C2×C4—864no—
778C2×C4—862no—
779C2×C4—868no—
780C2×C4—864no—
781C2×C4—868no—
782C2×C4—868no—
783C2×C4—1724no—
784C2×C4—17216no—
785C2×C4#1306337214yes—
786C2×C4#1306337214yes—
787C2×C4C24×D4318yes—
788C2×C4C24×D4314yes—
789C2×C4C24×D4312yes—
790C2×C4C24×D4314yes—
791C2×C4C24×D4314yes—
792C2×C4C24×D4312yes—
793C2×C4C24×D4312yes—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—48no—
798C22—862no—
799C22—862no—
800C22—862no—
801C22—1724no—
802C22C2×#1306337212yes—
803C22C2×#1306337212yes—
804C22#1458373612yes—
805C22C25×D4311yescharacteristic
806C4—24no—
807C4—24no—
808C4—28no—
809C4—22no—
810C4—24no—
811C4—862no—
812C4—862no—
813C4—864no—
814C4—864no—
815C4—864no—
816C4—862no—
817C4—868no—
818C4—864no—
819C4C2×#1306337214yes—
820C4C2×#1306337214yes—
821C2—44no—
822C2—1722no—
823C2#1914907114yesdirect product factor
824C2C22×#1306337211yescharacteristic
825C2C22×#1306337211yescharacteristic
826C2C2×#1458373611yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#556C2
socleC23×C43C25
prime radicalC2×#13063296C22
hypercenterC2×#556D43
hypocenterC43C2×#3555
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #19149071C2direct (N × H)
2. C2×#14583651C2semidirect
3. C2×Q8×Dic86C2semidirect
4. C2×#14583628C2semidirect
5. C2×#14583624C2semidirect
6. C2×#14583618C2semidirect
7. C2×#14583617C2semidirect
8. C2×#14583606C2semidirect
9. C2×#14583591C2semidirect
10. C2×#14583527C2semidirect
12. C2×#14583509C2semidirect
13. C2×#14583507C2semidirect
14. C2×#14583506C2semidirect
15. C2×#14583454C2semidirect
16. C2×#14583453C2semidirect
18. C2×C43×#556C2semidirect
19. #14583651C22semidirect
20. Q8×Dic86C22semidirect
21. #14583628C22semidirect
22. #14583624C22semidirect
23. #14583618C22semidirect
24. #14583617C22semidirect
25. #14583606C22semidirect
26. #14583591C22semidirect
27. #14583527C22semidirect
29. #14583509C22semidirect
30. #14583507C22semidirect
31. #14583506C22semidirect
32. #14583454C22semidirect
33. #14583453C22semidirect
92. C43×#556C22semidirect
415. C2×#556D43semidirect
427. C2×C43#3555semidirect
438. #556C2×D43semidirect
514. C43C2×#3555semidirect
823. C2#19149071direct (N × H)

Maximal subgroups

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

subgroupindex
#191490712
C2×#145836512
C2×Q8×Dic862
C2×#145836282
C2×#145836242
C2×#145836182
C2×#145836172
C2×#145836062
C2×#145835912
C2×#145835272
C2×#145835182
C2×#145835092
C2×#145835072
C2×#145835062
C2×#145834542
C2×#145834532
C2×#145834312
C2×C43×#5562
C2×#355543