Finite Group Databasebeta

← C2×#19149129 #26003964

Subgroups — C2×#19149129 #26003964

Order 11008.

7194 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149129C2132yesmaximal, direct product factor
2C2×#14583653C212yesmaximal, complemented
3C2×#14583647C212yesmaximal, complemented
4C2×#14583605C212yesmaximal, complemented
5C2×#14583602C212yesmaximal, complemented
6C2×#14583597C212yesmaximal, complemented
7C2×#14583550C212yesmaximal, complemented
8C2×#14583550C214yesmaximal, complemented
9C2×#14583529C212yesmaximal, complemented
10C2×#14583505C212yesmaximal, complemented
11C2×#14583497C214yesmaximal, complemented
12C2×#14583496C212yesmaximal, complemented
13C2×#14583480C212yesmaximal, complemented
14C2×#14583449C211yesmaximal, characteristic, complemented
15C2×#14583433C211yesmaximal, characteristic, complemented
16C22×#125×C43C211yesmaximal, characteristic, complemented
17C22×#10621898C2212yes—
18C22×#10621898C2214yes—
19#14583653C22132yescomplemented
20#14583647C22132yescomplemented
21#14583605C22132yescomplemented
22#14583602C22132yescomplemented
23#14583597C22132yescomplemented
24#14583550C22132yescomplemented
25#14583550C22164yescomplemented
26#14583529C22132yescomplemented
27#14583505C22132yescomplemented
28#14583497C22164yescomplemented
29#14583496C22132yescomplemented
30#14583480C22132yescomplemented
31#14583449C22116yescomplemented
32C2×#13063325C2211yescharacteristic
33C2×#13063324C2212yes—
34C2×#13063324C2214yes—
35C2×#13063322C2211yescharacteristic
36#14583433C22116yescomplemented
37C2×#13063320C2214yes—
38C2×#13063320C2214yes—
39C2×#13063319C2212yes—
40C2×#13063317C2211yescharacteristic
41C2×#13063316C2212yes—
42C2×#13063315C2214yes—
43C2×#13063313C2211yescharacteristic
44C2×#13063313C2212yes—
45C2×#13063310C2214yes—
46C2×#13063310C2214yes—
47C2×#13063310C2214yes—
48C2×#13063310C2214yes—
49C2×#13063310C2214yes—
50C2×#13063308C2212yes—
51C2×#13063308C2214yes—
52C2×#13063305C2214yes—
53C2×#13063305C2214yes—
54C2×#13063304C2211yescharacteristic
55C2×#13063303C2214yes—
56C2×#13063303C2214yes—
57C2×#13063303C2214yes—
58C2×#13063303C2214yes—
59C2×#13063300C2212yes—
60C2×#13063300C2214yes—
61C2×#13063300C2212yes—
62C2×#13063300C2214yes—
63C2×#13063300C2214yes—
64C2×#13063299C2212yes—
65C2×#13063299C2214yes—
66C2×#13063299C2211yescharacteristic
67C2×#13063299C2212yes—
68C2×C4×Dic86C2211yescharacteristic
69C2×C4×D172C2211yescharacteristic
70C2×C4×D172C2212yes—
71C2×C4×D172C2212yes—
72C2×#13063287C2214yes—
73C2×#13063287C2212yes—
74C2×#13063287C2212yes—
75C2×C4×C22⋊D43C2212yes—
76C2×C4×C22⋊D43C2214yes—
77C2×#13063283C2212yes—
78C2×#13063282C2212yes—
79C2×C4⋊C4×D43C2212yes—
80C2×C4⋊C4×D43C2214yes—
81C2×#125×C43C2212yes—
82C2×#125×C43C2212yes—
83C2×#125×C43C2212yes—
84C2×#125×C43C2212yes—
85C2×#125×C43C22116yescomplemented
86C22×C4⋊C4×C43C2211yescharacteristic
87C22×C4⋊C4×C43C2212yes—
88C22×C4⋊C4×C43C2211yescharacteristic
89C22×C4⋊C4×C43C2212yes—
90C22×C42×C43C2211yescharacteristic
91C2×#10621898—48no—
92C2×#10621898—416no—
93C2×#10621898C23116yes—
94C2×#10621898C23132yes—
95C22×Dic86C2311yescharacteristic
96C22×Dic86C2314yes—
97C22×Dic86C2312yes—
98C22×D172C2312yes—
99C22×D172C2314yes—
100C22×D172C2311yescharacteristic
101C22×D172C2312yes—
102C22×D172C2314yes—
103C22×D172C2312yes—
104C22×C22⋊D43C2312yes—
105C22×C22⋊D43C2314yes—
106C22×C4×D43C2312yes—
107C22×C4×D43C2314yes—
108C22×C4×D43C2314yes—
109C22×C4×D43C2314yes—
110C22×C4×D43C2314yes—
111#13063325C2318yes—
112#13063324C23116yes—
113#13063324C23132yes—
114#13063322C2318yes—
115#13063320C23132yes—
116#13063320C23132yes—
117#13063319C23116yes—
118#13063317C2318yes—
119#13063316C23116yes—
120#13063315C23132yes—
121#13063313C2318yes—
122#13063313C23116yes—
123#13063310C23132yes—
124#13063310C23132yes—
125#13063310C23132yes—
126#13063310C23132yes—
127#13063310C23132yes—
128#13063308C23116yes—
129#13063308C23132yes—
130#13063305C23132yes—
131#13063305C23132yes—
132#13063304C2318yes—
133#13063303C23132yes—
134#13063303C23132yes—
135#13063303C23132yes—
136#13063303C23132yes—
137#13063300C23116yes—
138#13063300C23132yes—
139#13063300C23116yes—
140#13063300C23132yes—
141#13063300C23132yes—
142#13063299C23116yes—
143#13063299C23132yes—
144#13063299C2318yes—
145#13063299C23116yes—
146C4×Dic86C2318yes—
147C4×D172C2318yes—
148C4×D172C23116yes—
149C4×D172C23116yes—
150#13063287C23116yes—
151#13063287C23132yes—
152#13063287C23116yes—
153C4×C22⋊D43C23116yes—
154C4×C22⋊D43C23132yes—
155#13063283C23116yes—
156#13063282C23116yes—
157C2×C4⋊Dic43C2312yes—
158C2×C4⋊Dic43C2314yes—
159C2×C4⋊Dic43C2312yes—
160C2×C4⋊Dic43C2311yescharacteristic
161C2×C4⋊Dic43C2311yescharacteristic
162C2×Dic43⋊C4C2312yes—
163C2×Dic43⋊C4C2314yes—
164C2×Dic43⋊C4C2314yes—
165C2×Dic43⋊C4C2312yes—
166C2×Dic43⋊C4C2312yes—
167C2×Dic43⋊C4C2314yes—
168C2×Dic43⋊C4C2312yes—
169C4⋊C4×D43C23116yes—
170C4⋊C4×D43C23132yes—
171C2×C22⋊Dic43C2312yes—
172C2×(C2×D43)⋊C4C2312yes—
173C2×(C2×D43)⋊C4C2312yes—
174C2×(C2×D43)⋊C4C2314yes—
175C2×(C2×D43)⋊C4C2314yes—
176C2×(C2×D43)⋊C4C2312yes—
177C2×(C2×D43)⋊C4C2312yes—
178C2×(C2×D43)⋊C4C2314yes—
179C2×(C2×D43)⋊C4C2314yes—
180C2×(C2×D43)⋊C4C2314yes—
181C2×(C2×D43)⋊C4C2314yes—
182C2×(C2×D43)⋊C4C2314yes—
183C2×C4×Dic43C2312yes—
184C2×C4×Dic43C2314yes—
185C23×C4×C43C2311yescharacteristic
186C23×C4×C43C2311yescharacteristic
187C23×C4×C43C2312yes—
188C23×C4×C43C2311yescharacteristic
189C23×C4×C43C2312yes—
190#125×C43C23116yes—
191#125×C43C23116yes—
192#125×C43C23116yes—
193#125×C43C23116yes—
194C2×C4⋊C4×C43C2312yes—
195C2×C4⋊C4×C43C2314yes—
196C2×C4⋊C4×C43C2312yes—
197C2×C4⋊C4×C43C2314yes—
198C2×C4⋊C4×C43C2314yes—
199C2×C4⋊C4×C43C2314yes—
200C2×C4⋊C4×C43C2312yes—
201C2×C4⋊C4×C43C2312yes—
202C2×C4⋊C4×C43C2318yes—
203C2×C4⋊C4×C43C23116yes—
204C2×C4⋊C4×C43C2318yes—
205C2×C4⋊C4×C43C23116yes—
206C2×C42×C43C2311yescharacteristic
207C2×C42×C43C2311yescharacteristic
208C2×C42×C43C2311yescharacteristic
209C2×C42×C43C2311yescharacteristic
210C2×C42×C43C2318yes—
211C24×C43C2411yescharacteristic
212C23×D43C2412yes—
213C23×D43C2414yes—
214C22×C4×C43—24no—
215C22×C4×C43—24no—
216C22×C4×C43—28no—
217C22×C4×C43—42no—
218C22×C4×C43—44no—
219C22×C4×C43C2411yescharacteristic
220C22×C4×C43C2411yescharacteristic
221C22×C4×C43C2411yescharacteristic
222C22×C4×C43C2411yescharacteristic
223C22×C4×C43C2411yescharacteristic
224C22×C4×C43C2414yes—
225C22×C4×C43C2414yes—
226C22×C4×C43C2414yes—
227C22×C4×C43C2414yes—
228C22×C4×C43C2418yes—
229C22×C4×C43C2414yes—
230C22×C4×C43C2418yes—
231C22×C4×C43C2411yescharacteristic
232C2×C22⋊D43—28no—
233C2×C22⋊D43—216no—
234C2×C22⋊D43C2418yes—
235C2×C22⋊D43C24116yes—
236C22×Dic43C2412yes—
237C22×Dic43C2412yes—
238C22×Dic43C2412yes—
239C22×Dic43C2414yes—
240#10621898—432no—
241#10621898—464no—
242C2×D172—28no—
243C2×D172—44no—
244C2×D172—48no—
245C2×D172—42no—
246C2×D172—44no—
247C2×D172—48no—
248C2×D172C2418yes—
249C2×D172C24116yes—
250C2×D172C2414yes—
251C2×D172C2418yes—
252C2×D172C24116yes—
253C2×D172C2418yes—
254C2×C4×D43—28no—
255C2×C4×D43—48no—
256C2×C4×D43—48no—
257C2×C4×D43—48no—
258C2×C4×D43—48no—
259C2×C4×D43C2418yes—
260C2×C4×D43C24116yes—
261C2×C4×D43C24116yes—
262C2×C4×D43C24116yes—
263C2×C4×D43C24116yes—
264C2×Dic86—42no—
265C2×Dic86—44no—
266C2×Dic86—48no—
267C2×Dic86C2414yes—
268C2×Dic86C24116yes—
269C2×Dic86C2418yes—
270C4⋊C4×C43C2418yes—
271C4⋊C4×C43C24116yes—
272C4⋊C4×C43C2418yes—
273C4⋊C4×C43C24116yes—
274C4⋊C4×C43C24116yes—
275C4⋊C4×C43C24116yes—
276C4⋊C4×C43C2418yes—
277C4⋊C4×C43C2418yes—
278C42×C43C2414yes—
279C42×C43C2414yes—
280C42×C43C2414yes—
281C42×C43C2414yes—
282C22⋊Dic43C2418yes—
283(C2×D43)⋊C4C2418yes—
284(C2×D43)⋊C4C2418yes—
285(C2×D43)⋊C4C24116yes—
286(C2×D43)⋊C4C24116yes—
287(C2×D43)⋊C4C2418yes—
288(C2×D43)⋊C4C2418yes—
289(C2×D43)⋊C4C24116yes—
290(C2×D43)⋊C4C24116yes—
291(C2×D43)⋊C4C24116yes—
292(C2×D43)⋊C4C24116yes—
293(C2×D43)⋊C4C24116yes—
294C4⋊Dic43C2418yes—
295C4⋊Dic43C24116yes—
296C4⋊Dic43C2418yes—
297C4⋊Dic43C2414yes—
298C4⋊Dic43C2414yes—
299Dic43⋊C4C2418yes—
300Dic43⋊C4C24116yes—
301Dic43⋊C4C24116yes—
302Dic43⋊C4C2418yes—
303Dic43⋊C4C2418yes—
304Dic43⋊C4C24116yes—
305Dic43⋊C4C2418yes—
306C4×Dic43C2418yes—
307C4×Dic43C24116yes—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43H(5,𝔽2)14yes—
311C23×C43C2512yes—
312C23×C43C2511yescharacteristic
313C22×D43—24no—
314C22×D43—28no—
315C22×D43—24no—
316C22×D43—28no—
317C22×D43—28no—
318C22×D43—24no—
319C22×D43C2514yes—
320C22×D43C2518yes—
321C2×C4×C43—22no—
322C2×C4×C43—28no—
323C2×C4×C43—22no—
324C2×C4×C43—28no—
325C2×C4×C43—216no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—28no—
329C2×C4×C43—22no—
330C2×C4×C43—28no—
331C2×C4×C43—44no—
332C2×C4×C43—48no—
333C2×C4×C432−1+414yes—
334C2×C4×C43C2518yes—
335C2×C4×C43C2512yes—
336C2×C4×C43C2512yes—
337C2×C4×C43C2512yes—
338C2×C4×C43C2512yes—
339C2×C4×C43C2518yes—
340C2×C4×C43C2512yes—
341C2×C4×C43C2512yes—
342C22⋊D43—232no—
343C22⋊D43—216no—
344C2×Dic43—28no—
345C2×Dic43—24no—
346C2×Dic43—24no—
347C2×Dic43—24no—
348C2×Dic43C2514yes—
349C2×Dic43C2514yes—
350C2×Dic43C2514yes—
351C2×Dic43C2518yes—
352D172—216no—
353D172—44no—
354D172—416no—
355D172—48no—
356D172—48no—
357D172—416no—
358C4×D43—216no—
359C4×D43—416no—
360C4×D43—416no—
361C4×D43—416no—
362C4×D43—416no—
363Dic86—44no—
364Dic86—48no—
365Dic86—416no—
366C2×#3559—431nomaximal, Sylow
367C22×C43—22no—
368C22×C43—22no—
369C22×C43—28no—
370C22×C43C2×H(5,𝔽2)14yes—
371C22×C43C2×H(5,𝔽2)12yes—
372C22×C43C2×2−1+412yes—
373C22×C43#58512yes—
374C22×C43C2611yescharacteristic
375C2×D43—24no—
376C2×D43—28no—
377C2×D43—24no—
378C2×D43—28no—
379C2×D43—28no—
380C2×D43—24no—
381C2×D43—48no—
382C2×D43—416no—
383C4×C43—22no—
384C4×C43—28no—
385C4×C43—22no—
386C4×C43—22no—
387C4×C43—22no—
388C4×C43—28no—
389C4×C43—22no—
390C4×C43C2×2−1+414yes—
391Dic43—28no—
392Dic43—24no—
393Dic43—24no—
394Dic43—24no—
395#3559—4332no—
396C2×#563—432no—
397C2×#562—432no—
398C2×#554—432no—
399C2×#553—432no—
400C2×#553—432no—
401C2×#547—434no—
402C2×#547—432no—
403C2×#544—432no—
404C2×#540—432no—
405C2×#539—434no—
406C2×#539—432no—
407C2×#537—432no—
408C2×#532—431no—
409C2×#529—431no—
410C22×#125D4311yescharacteristic, complemented
411C2×C43—24no—
412C2×C43#355914yescomplemented
413C2×C43C22×H(5,𝔽2)11yescharacteristic
414C2×C43C22×2−1+411yescharacteristic
415C2×C43C2×#58511yescharacteristic
416D43—44no—
417D43—48no—
418C22×#41—432no—
419C22×#41—434no—
420#563—4332no—
421#562—4332no—
422#554—4332no—
423#553—4332no—
424#553—4332no—
425#547—4364no—
426#547—4332no—
427#544—4332no—
428#540—4332no—
429#539—4364no—
430#539—4332no—
431#537—4332no—
432#532—4316no—
433C2×C4⋊Q8—432no—
434C2×C4⋊Q8—434no—
435C2×C4⋊Q8—431no—
436C2×#127—431no—
437#529—4316no—
438C2×#126—434no—
439C2×#126—434no—
440C2×#126—432no—
441C2×#125—434no—
442C2×#125—432no—
443C2×#125—431no—
444C2×#125C2×D4312yes—
445C2×#125C2×D4312yes—
446C2×#125C2×D4312yes—
447C2×#125C2×D4312yes—
448C2×#125C2×D43116yescomplemented
449C2×#124—431no—
450C2×#124—432no—
451C2×#123—432no—
452C2×#123—434no—
453C2×#123—434no—
454C2×#123—434no—
455C2×#123—434no—
456C2×#123—434no—
457C2×#123—434no—
458C2×C22⋊Q8—431no—
459C2×C22⋊Q8—434no—
460C2×C22⋊Q8—434no—
461C2×C22⋊Q8—434no—
462C2×C22⋊Q8—434no—
463C2×C22⋊Q8—434no—
464C2×C22⋊Q8—434no—
465C2×#121—431no—
466C2×#121—432no—
467C2×#121—432no—
468C2×#121—434no—
469C2×#121—434no—
470C2×#121—434no—
471C2×#121—432no—
472C2×#121—434no—
473C2×#121—432no—
474C2×C4×Q8—431no—
475C2×C4×D4—432no—
476C2×C4×D4—434no—
477C2×C4×D4—434no—
478C2×C4×D4—432no—
479C2×C4×D4—432no—
480C2×C4×D4—431no—
481C2×C4×D4—432no—
482C2×C4×D4—432no—
483C2×#117—432no—
484C2×#117—432no—
485C22×C4⋊C4—434no—
486C22×C4⋊C4—432no—
487C22×C4⋊C4C2×D4312yes—
488C22×C4⋊C4C2×D4311yescharacteristic
489C22×C4⋊C4C2×D4312yes—
490C22×C4⋊C4C2×D4311yescharacteristic
491C22×C42C2×D4311yescharacteristic
492C43C2×#355911yescharacteristic, complemented, Sylow
493C2×#41—4316no—
494C2×#41—4332no—
495C2×#41—1728no—
496C2×#41—17216no—
497C22×Q8—431no—
498C22×Q8—434no—
499C22×Q8—432no—
500C22×D4—432no—
501C22×D4—434no—
502C22×D4—432no—
503C22×D4—434no—
504C22×D4—431no—
505C22×D4—432no—
506C22×D4—434no—
507C22×D4—432no—
508C23×C4—432no—
509C23×C4—434no—
510C23×C4—434no—
511C23×C4—434no—
512C23×C4—434no—
513C23×C4C22×D4312yes—
514C23×C4C22×D4311yescharacteristic
515C23×C4C22×D4311yescharacteristic
516C23×C4C22×D4312yes—
517C23×C4C22×D4311yescharacteristic
518C4⋊Q8—4316no—
519C4⋊Q8—4332no—
520C4⋊Q8—438no—
521#127—438no—
522#126—4332no—
523#126—4332no—
524#126—4316no—
525#125—4332no—
526#125—4316no—
527#125—438no—
528#125C22×D43116yes—
529#125C22×D43116yes—
530#125C22×D43116yes—
531#125C22×D43116yes—
532#124—438no—
533#124—4316no—
534#123—4316no—
535#123—4332no—
536#123—4332no—
537#123—4332no—
538#123—4332no—
539#123—4332no—
540#123—4332no—
541C22⋊Q8—438no—
542C22⋊Q8—4332no—
543C22⋊Q8—4332no—
544C22⋊Q8—4332no—
545C22⋊Q8—4332no—
546C22⋊Q8—4332no—
547C22⋊Q8—4332no—
548#121—438no—
549#121—4316no—
550#121—4316no—
551#121—4332no—
552#121—4332no—
553#121—4332no—
554#121—4316no—
555#121—4332no—
556#121—4316no—
557C4×Q8—438no—
558C4×D4—4316no—
559C4×D4—4332no—
560C4×D4—4332no—
561C4×D4—4316no—
562C4×D4—4316no—
563C4×D4—438no—
564C4×D4—4316no—
565C4×D4—4316no—
566#117—4316no—
567#117—4316no—
568C2×C4⋊C4—432no—
569C2×C4⋊C4—432no—
570C2×C4⋊C4—434no—
571C2×C4⋊C4—434no—
572C2×C4⋊C4—434no—
573C2×C4⋊C4—432no—
574C2×C4⋊C4—432no—
575C2×C4⋊C4—432no—
576C2×C4⋊C4—434no—
577C2×C4⋊C4—432no—
578C2×C4⋊C4—431no—
579C2×C4⋊C4—431no—
580C2×C4⋊C4—4332no—
581C2×C4⋊C4—4316no—
582C2×C4⋊C4C22×D4312yes—
583C2×C4⋊C4C22×D4314yes—
584C2×C4⋊C4C22×D4312yes—
585C2×C4⋊C4C22×D4314yes—
586C2×C4⋊C4C22×D4314yes—
587C2×C4⋊C4C22×D4314yes—
588C2×C4⋊C4C22×D4312yes—
589C2×C4⋊C4C22×D4312yes—
590C2×C4⋊C4C22×D43116yes—
591C2×C4⋊C4C22×D4318yes—
592C2×C4⋊C4C22×D43116yes—
593C2×C4⋊C4C22×D4318yes—
594C2×C22⋊C4—432no—
595C2×C22⋊C4—432no—
596C2×C22⋊C4—434no—
597C2×C22⋊C4—432no—
598C2×C22⋊C4—432no—
599C2×C22⋊C4—434no—
600C2×C22⋊C4—434no—
601C2×C22⋊C4—434no—
602C2×C22⋊C4—434no—
603C2×C22⋊C4—434no—
604C2×C22⋊C4—434no—
605C2×C22⋊C4—432no—
606C2×C42—432no—
607C2×C42—434no—
608C2×C42C22×D4311yescharacteristic
609C2×C42C22×D4311yescharacteristic
610C2×C42C22×D4311yescharacteristic
611C2×C42C22×D4311yescharacteristic
612C2×C42C22×D4318yes—
613C24—432no—
614C24—434no—
615C24C23×D4311yescharacteristic
616#41—17232no—
617#41—17264no—
618C2×Q8—434no—
619C2×Q8—4316no—
620C2×Q8—438no—
621C2×Q8—1728no—
622C2×Q8—1724no—
623C2×Q8—1722no—
624C2×D4—438no—
625C2×D4—4316no—
626C2×D4—438no—
627C2×D4—4316no—
628C2×D4—434no—
629C2×D4—438no—
630C2×D4—4316no—
631C2×D4—438no—
632C2×D4—868no—
633C2×D4—8616no—
634C2×D4—868no—
635C2×D4—1728no—
636C2×D4—1724no—
637C2×D4—1728no—
638C2×D4—1724no—
639C2×D4—1722no—
640C22×C4—24no—
641C22×C4—28no—
642C22×C4—24no—
643C22×C4—44no—
644C22×C4—42no—
645C22×C4—432no—
646C22×C4—432no—
647C22×C4—432no—
648C22×C4—434no—
649C22×C4—438no—
650C22×C4—4316no—
651C22×C4—4316no—
652C22×C4—4316no—
653C22×C4—4316no—
654C22×C4—868no—
655C22×C4—1728no—
656C22×C4—1728no—
657C22×C4—1728no—
658C22×C4—1728no—
659C22×C4C23×D4314yes—
660C22×C4C23×D4314yes—
661C22×C4C23×D4318yes—
662C22×C4C23×D4314yes—
663C22×C4C23×D4311yescharacteristic
664C22×C4C23×D4311yescharacteristic
665C22×C4C23×D4311yescharacteristic
666C22×C4C23×D4311yescharacteristic
667C22×C4C23×D4311yescharacteristic
668C22×C4C23×D4314yes—
669C22×C4C23×D4314yes—
670C22×C4C23×D4318yes—
671C22×C4C23×D4311yescharacteristic
672C4⋊C4—438no—
673C4⋊C4—438no—
674C4⋊C4—4316no—
675C4⋊C4—4316no—
676C4⋊C4—4316no—
677C4⋊C4—438no—
678C4⋊C4—438no—
679C4⋊C4—438no—
680C4⋊C4—4316no—
681C4⋊C4—438no—
682C4⋊C4—434no—
683C4⋊C4—434no—
684C4⋊C4C23×D4318yes—
685C4⋊C4C23×D43116yes—
686C4⋊C4C23×D4318yes—
687C4⋊C4C23×D43116yes—
688C4⋊C4C23×D43116yes—
689C4⋊C4C23×D43116yes—
690C4⋊C4C23×D4318yes—
691C4⋊C4C23×D4318yes—
692C22⋊C4—438no—
693C22⋊C4—438no—
694C22⋊C4—4316no—
695C22⋊C4—438no—
696C22⋊C4—438no—
697C22⋊C4—4316no—
698C22⋊C4—4316no—
699C22⋊C4—4316no—
700C22⋊C4—4316no—
701C22⋊C4—4316no—
702C22⋊C4—4316no—
703C22⋊C4—438no—
704C42—438no—
705C42—4316no—
706C42C23×D4314yes—
707C42C23×D4314yes—
708C42C23×D4314yes—
709C42C23×D4314yes—
710C23—22no—
711C23—22no—
712C23—434no—
713C23—438no—
714C23—864no—
715C23—868no—
716C23—864no—
717C23—868no—
718C23—868no—
719C23—864no—
720C23#1306337114yes—
721C23C24×D4312yes—
722C23C24×D4311yescharacteristic
723Q8—17216no—
724Q8—1728no—
725Q8—1724no—
726D4—8616no—
727D4—8632no—
728D4—8616no—
729D4—17216no—
730D4—1728no—
731D4—17216no—
732D4—1728no—
733D4—1724no—
734C2×C4—22no—
735C2×C4—28no—
736C2×C4—22no—
737C2×C4—28no—
738C2×C4—216no—
739C2×C4—22no—
740C2×C4—28no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—28no—
744C2×C4—48no—
745C2×C4—44no—
746C2×C4—434no—
747C2×C4—434no—
748C2×C4—434no—
749C2×C4—438no—
750C2×C4—864no—
751C2×C4—868no—
752C2×C4—864no—
753C2×C4—864no—
754C2×C4—8616no—
755C2×C4—17216no—
756C2×C4—17216no—
757C2×C4—17216no—
758C2×C4—17216no—
759C2×C4#1306337314yes—
760C2×C4C24×D4318yes—
761C2×C4C24×D4312yes—
762C2×C4C24×D4312yes—
763C2×C4C24×D4312yes—
764C2×C4C24×D4312yes—
765C2×C4C24×D4312yes—
766C2×C4C24×D4318yes—
767C2×C4C24×D4312yes—
768C22—28no—
769C22—22no—
770C22—22no—
771C22—864no—
772C22—868no—
773C22—864no—
774C22—868no—
775C22—868no—
776C22—864no—
777C22—1728no—
778C22—17216no—
779C22C2×#1306337114yes—
780C22C2×#1306337112yes—
781C22C2×#1306337312yes—
782C22#1458373512yes—
783C22C25×D4311yescharacteristic
784C4—22no—
785C4—28no—
786C4—22no—
787C4—22no—
788C4—28no—
789C4—22no—
790C4—22no—
791C4—864no—
792C4—868no—
793C4—864no—
794C4—864no—
795C4C2×#1306337314yes—
796C2—24no—
797C2—1724no—
798C2—1728no—
799C2#1914912914yesdirect product factor
800C2C22×#1306337111yescharacteristic
801C2C22×#1306337311yescharacteristic
802C2C2×#1458373511yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC22×#125×C43C2
socleC23×C43C25
hypercenterC22×#125D43
hypocenterC43C2×#3559
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
1. #19149129C2direct (N × H)
2. C2×#14583653C2semidirect
3. C2×#14583647C2semidirect
4. C2×#14583605C2semidirect
5. C2×#14583602C2semidirect
6. C2×#14583597C2semidirect
7. C2×#14583550C2semidirect
8. C2×#14583550C2semidirect
9. C2×#14583529C2semidirect
10. C2×#14583505C2semidirect
11. C2×#14583497C2semidirect
12. C2×#14583496C2semidirect
13. C2×#14583480C2semidirect
14. C2×#14583449C2semidirect
15. C2×#14583433C2semidirect
16. C22×#125×C43C2semidirect
19. #14583653C22semidirect
20. #14583647C22semidirect
21. #14583605C22semidirect
22. #14583602C22semidirect
23. #14583597C22semidirect
24. #14583550C22semidirect
25. #14583550C22semidirect
26. #14583529C22semidirect
27. #14583505C22semidirect
28. #14583497C22semidirect
29. #14583496C22semidirect
30. #14583480C22semidirect
31. #14583449C22semidirect
36. #14583433C22semidirect
85. C2×#125×C43C22semidirect
410. C22×#125D43semidirect
412. C2×C43#3559semidirect
448. C2×#125C2×D43semidirect
492. C43C2×#3559semidirect
799. C2#19149129direct (N × H)

Maximal subgroups

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

subgroupindex
#191491292
C2×#145836532
C2×#145836472
C2×#145836052
C2×#145836022
C2×#145835972
C2×#145835502
C2×#145835292
C2×#145835052
C2×#145834972
C2×#145834962
C2×#145834802
C2×#145834492
C2×#145834332
C22×#125×C432
C2×#355943