Finite Group Databasebeta

← C2×#19149008 #26004408

Subgroups — C2×#19149008 #26004408

Order 11008.

7074 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149008C2132yesmaximal, direct product factor
2C2×#14583651C214yesmaximal, complemented
3C2×#14583631C212yesmaximal, complemented
4C2×Q8×Dic86C212yesmaximal, complemented
5C2×#14583623C211yesmaximal, characteristic, complemented
6C2×#14583617C212yesmaximal, complemented
7C2×Q8×D172C211yesmaximal, characteristic, complemented
8C2×D4×Dic86C211yesmaximal, characteristic, complemented
9C2×#14583562C212yesmaximal, complemented
10C2×#14583521C212yesmaximal, complemented
11C2×#14583518C212yesmaximal, complemented
12C2×#14583515C214yesmaximal, complemented
13C2×#14583475C212yesmaximal, complemented
14C2×#14583472C212yesmaximal, complemented
15C2×#14583454C211yesmaximal, characteristic, complemented
16C2×#14583453C211yesmaximal, characteristic, complemented
17C2×#14583446C211yesmaximal, characteristic
18C2×C43×#556C211yesmaximal, characteristic, complemented
19C22×#10621898C2212yes—
20C23×Dic86C2212yes—
21C22×Q8×D43C2212yes—
22#14583651C22164yescomplemented
23#14583631C22132yescomplemented
24Q8×Dic86C22132yescomplemented
25#14583623C22116yescomplemented
26#14583617C22132yescomplemented
27Q8×D172C22116yescomplemented
28D4×Dic86C22116yescomplemented
29#14583562C22132yescomplemented
30#14583521C22132yescomplemented
31#14583518C22132yescomplemented
32#14583515C22164yescomplemented
33#14583475C22132yescomplemented
34#14583472C22132yescomplemented
35#14583454C22116yescomplemented
36#14583453C22116yescomplemented
37#14583446C22116yes—
38C2×#13063325C2211yescharacteristic
39C2×#13063325C2212yes—
40C2×#13063325C2214yes—
41C2×#13063324C2214yes—
42C2×#13063324C2212yes—
43C2×#13063324C2211yescharacteristic
44C2×#13063324C2211yescharacteristic
45C2×#13063324C2214yes—
46C2×#13063323C2211yescharacteristic
47C2×#13063321C2211yescharacteristic
48C2×#13063320C2214yes—
49C2×#13063319C2214yes—
50C2×#13063318C2214yes—
51C2×#13063316C2212yes—
52C2×#13063315C2212yes—
53C2×#13063314C2212yes—
54C2×#13063313C2214yes—
55C2×#13063311C2212yes—
56C2×#13063311C2214yes—
57C2×#13063311C2214yes—
58C2×#13063310C2214yes—
59C2×#13063309C2214yes—
60C2×#13063309C2214yes—
61C2×#13063307C2214yes—
62C2×#13063305C2212yes—
63C2×#13063305C2212yes—
64C2×#13063305C2214yes—
65C2×#13063305C2211yescharacteristic
66C2×#13063305C2212yes—
67C2×#13063304C2212yes—
68C2×#13063303C2214yes—
69C2×#13063303C2212yes—
70C2×#13063302C2214yes—
71C2×#13063302C2214yes—
72C2×#13063301C2211yescharacteristic
73C2×#13063301C2212yes—
74C2×#13063300C2211yescharacteristic
75C2×#13063298C2212yes—
76C2×#13063296C2211yescharacteristic
77C2×Q8×Dic43C2212yes—
78C2×Q8×Dic43C2212yes—
79C2×C4×Dic86C2211yescharacteristic
80C2×C4×Dic86C2212yes—
81C2×C4×Dic86C2214yes—
82C2×#13063290C2212yes—
83C2×C4×D172C2211yescharacteristic
84C2×C4×D172C2212yes—
85C2×D4×Dic43C2212yes—
86C2×C4×C22⋊D43C2212yes—
87C2×(C22⋊D43)⋊C4C2214yes—
88C2×#13063283C2212yes—
89C2×#13063283C2212yes—
90C2×#13063282C2212yes—
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—
101C2×#10621898—48no—
102C2×#10621898C23116yes—
103C22×Dic86—48no—
104C22×Dic86C2312yes—
105C22×Dic86C2312yes—
106C22×Dic86C2311yescharacteristic
107C22×Dic86C23116yes—
108C22×Dic86C2314yes—
109C22×Dic86C2314yes—
110C22×Dic86C2312yes—
111C2×Q8×D43—48no—
112C2×Q8×D43C23116yes—
113C22×D172C2311yescharacteristic
114C22×D172C2312yes—
115C22×C22⋊D43C2312yes—
116C22×C22⋊D43C2312yes—
117C22×C22⋊D43C2312yes—
118C23×Dic43C2314yes—
119C22×C4×D43C2311yescharacteristic
120C22×C4×D43C2311yescharacteristic
121C22×C4×D43C2311yescharacteristic
122C22×C4×D43C2312yes—
123C22×C4×D43C2314yes—
124#13063325C2318yes—
125#13063325C23116yes—
126#13063325C23132yes—
127#13063324C23132yes—
128#13063324C23116yes—
129#13063324C2318yes—
130#13063324C2318yes—
131#13063324C23132yes—
132#13063323C2318yes—
133#13063321C2318yes—
134#13063320C23132yes—
135#13063319C23132yes—
136#13063318C23132yes—
137#13063316C23116yes—
138#13063315C23116yes—
139#13063314C23116yes—
140#13063313C23132yes—
141#13063311C23132yes—
142#13063311C23116yes—
143#13063311C23132yes—
144#13063310C23132yes—
145#13063309C23132yes—
146#13063309C23132yes—
147#13063307C23132yes—
148#13063305C23116yes—
149#13063305C23116yes—
150#13063305C23132yes—
151#13063305C2318yes—
152#13063305C23116yes—
153#13063304C23116yes—
154#13063303C23132yes—
155#13063303C23116yes—
156#13063302C23132yes—
157#13063302C23132yes—
158#13063301C2318yes—
159#13063301C23116yes—
160#13063300C2318yes—
161#13063298C23116yes—
162#13063296C2318yes—
163Q8×Dic43C23116yes—
164Q8×Dic43C23116yes—
165C4×Dic86C2318yes—
166C4×Dic86C23132yes—
167C4×Dic86C23116yes—
168#13063290C23116yes—
169C4×D172C2318yes—
170C4×D172C23116yes—
171D4×Dic43C23116yes—
172C4×C22⋊D43C23116yes—
173(C22⋊D43)⋊C4C23132yes—
174#13063283C23116yes—
175#13063283C23116yes—
176#13063282C23116yes—
177C2×C4⋊Dic43C2311yescharacteristic
178C2×C4⋊Dic43C2312yes—
179C2×C4⋊Dic43C2312yes—
180C2×C4⋊Dic43C2311yescharacteristic
181C2×C4⋊Dic43C2314yes—
182C2×C4⋊Dic43C2312yes—
183C2×C4⋊Dic43C2314yes—
184C2×C4⋊Dic43C2314yes—
185C2×Dic43⋊C4C2312yes—
186C2×Dic43⋊C4C2312yes—
187C2×Dic43⋊C4C2312yes—
188C2×Dic43⋊C4C2312yes—
189C2×Dic43⋊C4C2314yes—
190C2×Dic43⋊C4C2312yes—
191C2×Dic43⋊C4C2312yes—
192C2×Dic43⋊C4C2314yes—
193C2×C22⋊Dic43C2312yes—
194C2×C22⋊Dic43C2314yes—
195C2×(C2×D43)⋊C4C2312yes—
196C2×(C2×D43)⋊C4C2312yes—
197C2×(C2×D43)⋊C4C2314yes—
198C2×(C2×D43)⋊C4C2314yes—
199C2×(C2×D43)⋊C4C2314yes—
200C2×(C2×D43)⋊C4C2312yes—
201C2×(C2×D43)⋊C4C2312yes—
202C2×(C2×D43)⋊C4C2314yes—
203C2×C4×Dic43C2311yescharacteristic
204C2×C4×Dic43C2311yescharacteristic
205C2×C4×Dic43C2311yescharacteristic
206C2×C4×Dic43C2312yes—
207C2×C4×Dic43C2314yes—
208C2×C4×Dic43C2314yes—
209C42×D43C2318yes—
210C22×Q8×C43C2311yescharacteristic
211C22×Q8×C43C2312yes—
212C22×D4×C43C2311yescharacteristic
213C23×C4×C43C2312yes—
214C4⋊Q8×C43C2318yes—
215#126×C43C23132yes—
216#124×C43C23116yes—
217C22⋊Q8×C43C23116yes—
218C4×Q8×C43C2318yes—
219C4×Q8×C43C23116yes—
220C4×D4×C43C2318yes—
221#117×C43C23116yes—
222C2×C4⋊C4×C43C2311yescharacteristic
223C2×C4⋊C4×C43C2312yes—
224C2×C4⋊C4×C43C2311yescharacteristic
225C2×C4⋊C4×C43C2314yes—
226C2×C4⋊C4×C43C2312yes—
227C2×C4⋊C4×C43C2312yes—
228C2×C22⋊C4×C43C2314yes—
229C2×C22⋊C4×C43C2312yes—
230C2×C22⋊C4×C43C2314yes—
231C2×C42×C43C2314yes—
232C2×C42×C43C2311yescharacteristic
233C2×C42×C43C2312yes—
234C24×C43C2412yes—
235C23×D43C2412yes—
236C23×D43C2411yescharacteristic
237C2×Q8×C43—24no—
238C2×Q8×C43—28no—
239C2×Q8×C43C2414yes—
240C2×Q8×C43C2418yes—
241C2×D4×C43—24no—
242C2×D4×C43C2414yes—
243C22×C4×C43—28no—
244C22×C4×C43C2412yes—
245C22×C4×C43C2412yes—
246C22×C4×C43C2411yescharacteristic
247C22×C4×C43C2414yes—
248C22×C4×C43C2412yes—
249C22×C4×C43C2418yes—
250C22×C4×C43C2411yescharacteristic
251C22×C4×C43C2411yescharacteristic
252C2×C22⋊D43—28no—
253C2×C22⋊D43—44no—
254C2×C22⋊D43—44no—
255C2×C22⋊D43C2418yes—
256C2×C22⋊D43C2418yes—
257C2×C22⋊D43C2418yes—
258C22×Dic43—48no—
259C22×Dic43C2412yes—
260C22×Dic43C2411yescharacteristic
261C22×Dic43C2412yes—
262C22×Dic43C2411yescharacteristic
263C22×Dic43C2412yes—
264C22×Dic43C2414yes—
265C22×Dic43C24116yes—
266C22×Dic43C2411yescharacteristic
267Q8×D43—432no—
268#10621898—432no—
269C2×D172—24no—
270C2×D172—44no—
271C2×D172C2414yes—
272C2×D172C2418yes—
273C2×C4×D43—28no—
274C2×C4×D43—24no—
275C2×C4×D43—24no—
276C2×C4×D43—24no—
277C2×C4×D43—48no—
278C2×C4×D43C2414yes—
279C2×C4×D43C2414yes—
280C2×C4×D43C2414yes—
281C2×C4×D43C2418yes—
282C2×C4×D43C24116yes—
283C2×Dic86—28no—
284C2×Dic86—24no—
285C2×Dic86—28no—
286C2×Dic86—432no—
287C2×Dic86—48no—
288C2×Dic86—48no—
289C2×Dic86—44no—
290C2×Dic86C2418yes—
291C2×Dic86C2418yes—
292C2×Dic86C2414yes—
293C2×Dic86C24116yes—
294C2×Dic86C24116yes—
295C2×Dic86C2418yes—
296C4⋊C4×C43C2414yes—
297C4⋊C4×C43C2418yes—
298C4⋊C4×C43C2414yes—
299C4⋊C4×C43C24116yes—
300C4⋊C4×C43C2418yes—
301C4⋊C4×C43C2418yes—
302C22⋊C4×C43C24116yes—
303C22⋊C4×C43C2418yes—
304C22⋊C4×C43C24116yes—
305C42×C43C24116yes—
306C42×C43C2414yes—
307C42×C43C2418yes—
308C22⋊Dic43C2418yes—
309C22⋊Dic43C24116yes—
310(C2×D43)⋊C4C2418yes—
311(C2×D43)⋊C4C2418yes—
312(C2×D43)⋊C4C24116yes—
313(C2×D43)⋊C4C24116yes—
314(C2×D43)⋊C4C24116yes—
315(C2×D43)⋊C4C2418yes—
316(C2×D43)⋊C4C2418yes—
317(C2×D43)⋊C4C24116yes—
318C4⋊Dic43C2414yes—
319C4⋊Dic43C2418yes—
320C4⋊Dic43C2418yes—
321C4⋊Dic43C2414yes—
322C4⋊Dic43C24116yes—
323C4⋊Dic43C2418yes—
324C4⋊Dic43C24116yes—
325C4⋊Dic43C24116yes—
326Dic43⋊C4C2418yes—
327Dic43⋊C4C2418yes—
328Dic43⋊C4C2418yes—
329Dic43⋊C4C2418yes—
330Dic43⋊C4C24116yes—
331Dic43⋊C4C2418yes—
332Dic43⋊C4C2418yes—
333Dic43⋊C4C24116yes—
334C4×Dic43C2414yes—
335C4×Dic43C2414yes—
336C4×Dic43C2414yes—
337C4×Dic43C2418yes—
338C4×Dic43C24116yes—
339C4×Dic43C24116yes—
340C23×C43—24no—
341C23×C43—24no—
342C23×C43—24no—
343C23×C43C2514yes—
344C23×C43C2511yescharacteristic
345C22×D43—24no—
346C22×D43—22no—
347C22×D43—22no—
348C22×D43—22no—
349C22×D43—24no—
350C22×D43—24no—
351C22×D43C2514yes—
352C22×D43C2512yes—
353Q8×C43—28no—
354Q8×C43—216no—
355D4×C43—28no—
356C2×C4×C43—24no—
357C2×C4×C43—24no—
358C2×C4×C43—24no—
359C2×C4×C43—22no—
360C2×C4×C43—28no—
361C2×C4×C43—216no—
362C2×C4×C43H(5,𝔽2)14yes—
363C2×C4×C432−1+414yes—
364C2×C4×C43C2518yes—
365C2×C4×C43C2512yes—
366C2×C4×C43C2514yes—
367C2×C4×C43C2514yes—
368C2×C4×C43C2514yes—
369C2×C4×C43C2512yes—
370C2×C4×C43C2512yes—
371C22⋊D43—216no—
372C22⋊D43—48no—
373C22⋊D43—48no—
374C2×Dic43—28no—
375C2×Dic43—24no—
376C2×Dic43—24no—
377C2×Dic43—22no—
378C2×Dic43—24no—
379C2×Dic43—22no—
380C2×Dic43—416no—
381C2×Dic432−1+414yes—
382C2×Dic43C2514yes—
383C2×Dic43C2512yes—
384C2×Dic43C2512yes—
385C2×Dic43C2514yes—
386C2×Dic43C2514yes—
387C2×Dic43C2518yes—
388C2×Dic43C2512yes—
389D172—28no—
390D172—48no—
391C4×D43—28no—
392C4×D43—216no—
393C4×D43—28no—
394C4×D43—28no—
395C4×D43—416no—
396Dic86—28no—
397Dic86—216no—
398Dic86—216no—
399Dic86—416no—
400Dic86—48no—
401Dic86—416no—
402C2×#3550—431nomaximal, Sylow
403C22×C43—24no—
404C22×C43—24no—
405C22×C43—24no—
406C22×C43—48no—
407C22×C43C2×H(5,𝔽2)12yes—
408C22×C43C2×2−1+412yes—
409C22×C43C2×2−1+412yes—
410C22×C43C2611yescharacteristic
411C2×D43—24no—
412C2×D43—22no—
413C2×D43—22no—
414C2×D43—22no—
415C2×D43—24no—
416C2×D43—24no—
417C2×D43—48no—
418C2×D43—44no—
419C4×C43—24no—
420C4×C43—24no—
421C4×C43—24no—
422C4×C43—22no—
423C4×C43—28no—
424C4×C43C2×H(5,𝔽2)14yes—
425C4×C43C2×2−1+414yes—
426Dic43—28no—
427Dic43—24no—
428Dic43—24no—
429Dic43—22no—
430Dic43—24no—
431Dic43—22no—
432Dic43C2×2−1+414yes—
433#3550—4332no—
434C2×#563—434no—
435C2×#559—432no—
436C2×Q82—432no—
437C2×#556—431no—
438C2×#556—432no—
439C2×#556D4311yescharacteristic, complemented
440C2×D4×Q8—432no—
441C2×D4×Q8—431no—
442C2×D4×Q8—431no—
443C2×#542—434no—
444C2×#542—432no—
445C2×#542—432no—
446C2×#536—432no—
447C2×#536—432no—
448C2×#533—431no—
449C2×#533—431no—
450C2×#532—431no—
451C2×C43—44no—
452C2×C43#355014yescomplemented
453C2×C43C22×H(5,𝔽2)11yescharacteristic
454C2×C43C22×2−1+411yescharacteristic
455C2×C43C22×2−1+411yescharacteristic
456D43—44no—
457D43—42no—
458C22×#41—432no—
459C23×Q8—432no—
460C23×Q8—432no—
461#563—4364no—
462#559—4332no—
463Q82—4332no—
464#556—4316no—
465#556—4332no—
466#556C2×D43116yescomplemented
467D4×Q8—4332no—
468D4×Q8—4316no—
469D4×Q8—4316no—
470#542—4364no—
471#542—4332no—
472#542—4332no—
473#536—4332no—
474#536—4332no—
475#533—4316no—
476#533—4316no—
477#532—4316no—
478C2×C4⋊Q8—431no—
479C2×C4⋊Q8—431no—
480C2×C4⋊Q8—431no—
481C2×C4⋊Q8—434no—
482C2×C4⋊Q8—434no—
483C2×C4⋊Q8—432no—
484C2×C4⋊Q8—431no—
485C2×C4⋊Q8—434no—
486C2×C4⋊Q8—432no—
487C2×C4⋊Q8C2×D4311yescharacteristic
488C2×#127—431no—
489C2×#126—434no—
490C2×#126—434no—
491C2×#126—434no—
492C2×#126C2×D4314yes—
493C2×#125—432no—
494C2×#125—432no—
495C2×#124—432no—
496C2×#124—432no—
497C2×#124—434no—
498C2×#124—434no—
499C2×#124—434no—
500C2×#124C2×D4312yes—
501C2×#123—434no—
502C2×#123—434no—
503C2×#123—434no—
504C2×#123—434no—
505C2×C22⋊Q8—431no—
506C2×C22⋊Q8—432no—
507C2×C22⋊Q8—432no—
508C2×C22⋊Q8—432no—
509C2×C22⋊Q8—434no—
510C2×C22⋊Q8—432no—
511C2×C22⋊Q8—431no—
512C2×C22⋊Q8—432no—
513C2×C22⋊Q8—432no—
514C2×C22⋊Q8—434no—
515C2×C22⋊Q8—434no—
516C2×C22⋊Q8—434no—
517C2×C22⋊Q8C2×D4312yes—
518C2×#121—431no—
519C2×#121—431no—
520C2×#121—432no—
521C2×C4×Q8—432no—
522C2×C4×Q8—432no—
523C2×C4×Q8—432no—
524C2×C4×Q8—431no—
525C2×C4×Q8—432no—
526C2×C4×Q8—434no—
527C2×C4×Q8C2×D4311yescharacteristic
528C2×C4×Q8C2×D4312yes—
529C2×C4×D4—432no—
530C2×C4×D4—432no—
531C2×C4×D4—434no—
532C2×C4×D4—431no—
533C2×C4×D4—432no—
534C2×C4×D4C2×D4311yescharacteristic
535C2×#117—432no—
536C2×#117—432no—
537C2×#117—432no—
538C2×#117C2×D4312yes—
539C22×C42—431no—
540C43C2×#355011yescharacteristic, complemented, Sylow
541C2×#41—4316no—
542C2×#41—1728no—
543C22×Q8—4316no—
544C22×Q8—432no—
545C22×Q8—432no—
546C22×Q8—431no—
547C22×Q8—434no—
548C22×Q8—434no—
549C22×Q8—432no—
550C22×Q8—4316no—
551C22×Q8—1728no—
552C22×Q8—1728no—
553C22×Q8C22×D4312yes—
554C22×Q8C22×D4311yescharacteristic
555C22×D4—432no—
556C22×D4—432no—
557C22×D4—432no—
558C22×D4—431no—
559C22×D4—432no—
560C22×D4C22×D4311yescharacteristic
561C23×C4—434no—
562C23×C4—431no—
563C23×C4—431no—
564C23×C4—432no—
565C23×C4—431no—
566C23×C4—434no—
567C23×C4C22×D4312yes—
568C4⋊Q8—438no—
569C4⋊Q8—438no—
570C4⋊Q8—438no—
571C4⋊Q8—4332no—
572C4⋊Q8—4332no—
573C4⋊Q8—4316no—
574C4⋊Q8—438no—
575C4⋊Q8—4332no—
576C4⋊Q8—4316no—
577C4⋊Q8C22×D4318yes—
578#127—438no—
579#126—4332no—
580#126—4332no—
581#126—4332no—
582#126C22×D43132yes—
583#125—4316no—
584#125—4316no—
585#124—4316no—
586#124—4316no—
587#124—4332no—
588#124—4332no—
589#124—4332no—
590#124C22×D43116yes—
591#123—4332no—
592#123—4332no—
593#123—4332no—
594#123—4332no—
595C22⋊Q8—438no—
596C22⋊Q8—4316no—
597C22⋊Q8—4316no—
598C22⋊Q8—4316no—
599C22⋊Q8—438no—
600C22⋊Q8—4316no—
601C22⋊Q8—4316no—
602C22⋊Q8—4316no—
603C22⋊Q8—4332no—
604C22⋊Q8—4332no—
605C22⋊Q8—4332no—
606C22⋊Q8—4332no—
607C22⋊Q8C22×D43116yes—
608#121—438no—
609#121—438no—
610#121—4316no—
611C4×Q8—4316no—
612C4×Q8—4316no—
613C4×Q8—4316no—
614C4×Q8—438no—
615C4×Q8—4316no—
616C4×Q8—4332no—
617C4×Q8C22×D4318yes—
618C4×Q8C22×D43116yes—
619C4×D4—4316no—
620C4×D4—4316no—
621C4×D4—4332no—
622C4×D4—438no—
623C4×D4—4316no—
624C4×D4C22×D4318yes—
625#117—4316no—
626#117—4316no—
627#117—4316no—
628#117C22×D43116yes—
629C2×C4⋊C4—431no—
630C2×C4⋊C4—432no—
631C2×C4⋊C4—432no—
632C2×C4⋊C4—432no—
633C2×C4⋊C4—432no—
634C2×C4⋊C4—432no—
635C2×C4⋊C4—432no—
636C2×C4⋊C4—431no—
637C2×C4⋊C4—432no—
638C2×C4⋊C4—434no—
639C2×C4⋊C4—434no—
640C2×C4⋊C4—434no—
641C2×C4⋊C4—434no—
642C2×C4⋊C4—432no—
643C2×C4⋊C4—434no—
644C2×C4⋊C4—432no—
645C2×C4⋊C4C22×D4312yes—
646C2×C4⋊C4C22×D4312yes—
647C2×C4⋊C4C22×D4311yescharacteristic
648C2×C4⋊C4C22×D4311yescharacteristic
649C2×C4⋊C4C22×D4312yes—
650C2×C4⋊C4C22×D4314yes—
651C2×C22⋊C4—432no—
652C2×C22⋊C4—434no—
653C2×C22⋊C4—432no—
654C2×C22⋊C4—434no—
655C2×C22⋊C4—432no—
656C2×C22⋊C4—434no—
657C2×C22⋊C4—432no—
658C2×C22⋊C4—432no—
659C2×C22⋊C4—434no—
660C2×C22⋊C4—434no—
661C2×C22⋊C4C22×D4314yes—
662C2×C22⋊C4C22×D4314yes—
663C2×C22⋊C4C22×D4312yes—
664C2×C42—434no—
665C2×C42—432no—
666C2×C42—434no—
667C2×C42—431no—
668C2×C42—431no—
669C2×C42—431no—
670C2×C42—438no—
671C2×C42C22×D4312yes—
672C2×C42C22×D4314yes—
673C2×C42C22×D4311yescharacteristic
674C24—432no—
675C24—431no—
676C24C23×D4312yes—
677#41—17232no—
678C2×Q8—24no—
679C2×Q8—28no—
680C2×Q8—438no—
681C2×Q8—438no—
682C2×Q8—434no—
683C2×Q8—4316no—
684C2×Q8—4316no—
685C2×Q8—438no—
686C2×Q8—868no—
687C2×Q8—864no—
688C2×Q8—868no—
689C2×Q8—1728no—
690C2×Q8—1728no—
691C2×Q8—1724no—
692C2×Q8—17232no—
693C2×Q8—17232no—
694C2×Q8C23×D4318yes—
695C2×Q8C23×D4314yes—
696C2×D4—24no—
697C2×D4—438no—
698C2×D4—438no—
699C2×D4—438no—
700C2×D4—434no—
701C2×D4—438no—
702C2×D4—868no—
703C2×D4—864no—
704C2×D4—1724no—
705C2×D4—1724no—
706C2×D4—1724no—
707C2×D4C23×D4314yes—
708C22×C4—28no—
709C22×C4—431no—
710C22×C4—432no—
711C22×C4—431no—
712C22×C4—432no—
713C22×C4—431no—
714C22×C4—434no—
715C22×C4—432no—
716C22×C4—4316no—
717C22×C4—434no—
718C22×C4—434no—
719C22×C4—434no—
720C22×C4—438no—
721C22×C4—4316no—
722C22×C4—864no—
723C22×C4—868no—
724C22×C4—864no—
725C22×C4—864no—
726C22×C4—1728no—
727C22×C4—1728no—
728C22×C4C23×D4318yes—
729C22×C4C23×D4314yes—
730C22×C4C23×D4311yescharacteristic
731C22×C4C23×D4312yes—
732C22×C4C23×D4312yes—
733C22×C4C23×D4312yes—
734C22×C4C23×D4311yescharacteristic
735C22×C4C23×D4311yescharacteristic
736C4⋊C4—434no—
737C4⋊C4—438no—
738C4⋊C4—438no—
739C4⋊C4—438no—
740C4⋊C4—438no—
741C4⋊C4—438no—
742C4⋊C4—438no—
743C4⋊C4—434no—
744C4⋊C4—438no—
745C4⋊C4—4316no—
746C4⋊C4—4316no—
747C4⋊C4—4316no—
748C4⋊C4—4316no—
749C4⋊C4—438no—
750C4⋊C4—4316no—
751C4⋊C4—438no—
752C4⋊C4C23×D4318yes—
753C4⋊C4C23×D4318yes—
754C4⋊C4C23×D4314yes—
755C4⋊C4C23×D4314yes—
756C4⋊C4C23×D4318yes—
757C4⋊C4C23×D43116yes—
758C22⋊C4—438no—
759C22⋊C4—4316no—
760C22⋊C4—438no—
761C22⋊C4—4316no—
762C22⋊C4—438no—
763C22⋊C4—4316no—
764C22⋊C4—438no—
765C22⋊C4—438no—
766C22⋊C4—4316no—
767C22⋊C4—4316no—
768C22⋊C4C23×D43116yes—
769C22⋊C4C23×D43116yes—
770C22⋊C4C23×D4318yes—
771C42—434no—
772C42—434no—
773C42—434no—
774C42—4316no—
775C42—438no—
776C42—4316no—
777C42C23×D4314yes—
778C42C23×D4318yes—
779C42C23×D43116yes—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—434no—
784C23—432no—
785C23—864no—
786C23—862no—
787C23—862no—
788C23—864no—
789C23—862no—
790C23—864no—
791C23C24×D4314yes—
792C23C24×D4311yescharacteristic
793Q8—28no—
794Q8—216no—
795Q8—8616no—
796Q8—868no—
797Q8—8616no—
798Q8—17216no—
799Q8—17216no—
800Q8—1728no—
801D4—28no—
802D4—8616no—
803D4—868no—
804D4—1728no—
805D4—1728no—
806D4—1728no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—22no—
810C2×C4—24no—
811C2×C4—28no—
812C2×C4—216no—
813C2×C4—434no—
814C2×C4—432no—
815C2×C4—434no—
816C2×C4—432no—
817C2×C4—434no—
818C2×C4—432no—
819C2×C4—438no—
820C2×C4—434no—
821C2×C4—868no—
822C2×C4—862no—
823C2×C4—864no—
824C2×C4—868no—
825C2×C4—864no—
826C2×C4—864no—
827C2×C4—862no—
828C2×C4—8616no—
829C2×C4—868no—
830C2×C4—868no—
831C2×C4—17216no—
832C2×C4—17216no—
833C2×C4#1306337114yes—
834C2×C4#1306337214yes—
835C2×C4C24×D4318yes—
836C2×C4C24×D4312yes—
837C2×C4C24×D4314yes—
838C2×C4C24×D4314yes—
839C2×C4C24×D4314yes—
840C2×C4C24×D4312yes—
841C2×C4C24×D4312yes—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—48no—
846C22—864no—
847C22—862no—
848C22—862no—
849C22—864no—
850C22—862no—
851C22—864no—
852C22—1728no—
853C22—1724no—
854C22C2×#1306337112yes—
855C222−1+4×D4312yes—
856C22C2×#1306337212yes—
857C22C25×D4311yescharacteristic
858C4—24no—
859C4—24no—
860C4—22no—
861C4—24no—
862C4—28no—
863C4—434no—
864C4—862no—
865C4—864no—
866C4—868no—
867C4—864no—
868C4—864no—
869C4—862no—
870C4C2×#1306337114yes—
871C4C2×#1306337214yes—
872C2—44no—
873C2—1724no—
874C2—1722no—
875C2#1914900814yesdirect product factor
876C2C22×#1306337111yescharacteristic
877C2C2×2−1+4×D4311yescharacteristic
878C2C22×#1306337211yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#556C2
socleC23×C43C25
prime radicalC2×#14583446C2
hypercenterC2×#556D43
hypocenterC43C2×#3550
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #19149008C2direct (N × H)
2. C2×#14583651C2semidirect
3. C2×#14583631C2semidirect
4. C2×Q8×Dic86C2semidirect
5. C2×#14583623C2semidirect
6. C2×#14583617C2semidirect
7. C2×Q8×D172C2semidirect
8. C2×D4×Dic86C2semidirect
9. C2×#14583562C2semidirect
10. C2×#14583521C2semidirect
11. C2×#14583518C2semidirect
12. C2×#14583515C2semidirect
13. C2×#14583475C2semidirect
14. C2×#14583472C2semidirect
15. C2×#14583454C2semidirect
16. C2×#14583453C2semidirect
18. C2×C43×#556C2semidirect
22. #14583651C22semidirect
23. #14583631C22semidirect
24. Q8×Dic86C22semidirect
25. #14583623C22semidirect
26. #14583617C22semidirect
27. Q8×D172C22semidirect
28. D4×Dic86C22semidirect
29. #14583562C22semidirect
30. #14583521C22semidirect
31. #14583518C22semidirect
32. #14583515C22semidirect
33. #14583475C22semidirect
34. #14583472C22semidirect
35. #14583454C22semidirect
36. #14583453C22semidirect
92. C43×#556C22semidirect
439. C2×#556D43semidirect
452. C2×C43#3550semidirect
466. #556C2×D43semidirect
540. C43C2×#3550semidirect
875. C2#19149008direct (N × H)

Maximal subgroups

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

subgroupindex
#191490082
C2×#145836512
C2×#145836312
C2×Q8×Dic862
C2×#145836232
C2×#145836172
C2×Q8×D1722
C2×D4×Dic862
C2×#145835622
C2×#145835212
C2×#145835182
C2×#145835152
C2×#145834752
C2×#145834722
C2×#145834542
C2×#145834532
C2×#145834462
C2×C43×#5562
C2×#355043