Finite Group Databasebeta

← C2×#19149032 #26004208

Subgroups — C2×#19149032 #26004208

Order 11008.

7086 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149032C2132yesmaximal, direct product factor
2C2×#14583651C214yesmaximal, complemented
3C2×#14583627C211yesmaximal, characteristic, complemented
4C2×#14583619C211yesmaximal, characteristic, complemented
5C2×#14583606C212yesmaximal, complemented
6C2×#14583595C212yesmaximal, complemented
7C2×Q8×D172C211yesmaximal, characteristic, complemented
8C2×#14583562C212yesmaximal, complemented
9C2×#14583555C212yesmaximal, complemented
10C2×#14583553C211yesmaximal, characteristic, complemented
11C2×#14583527C212yesmaximal, complemented
12C2×#14583520C212yesmaximal, complemented
13C2×#14583512C212yesmaximal, complemented
14C2×#14583493C214yesmaximal, complemented
15C2×#14583469C212yesmaximal, complemented
16C22×#13063325C211yesmaximal, characteristic, complemented
17C2×#14583433C211yesmaximal, characteristic, complemented
18C2×C43×#529C211yesmaximal, characteristic, complemented
19C22×#10621900C2212yes—
20C23×Dic86C2212yes—
21C22×Q8×D43C2212yes—
22#14583651C22164yescomplemented
23#14583627C22116yescomplemented
24#14583619C22116yescomplemented
25#14583606C22132yescomplemented
26#14583595C22132yescomplemented
27Q8×D172C22116yescomplemented
28#14583562C22132yescomplemented
29#14583555C22132yescomplemented
30#14583553C22116yescomplemented
31#14583527C22132yescomplemented
32#14583520C22132yescomplemented
33#14583512C22132yescomplemented
34#14583493C22164yescomplemented
35#14583469C22132yescomplemented
36C2×#13063325C2211yescharacteristic
37C2×#13063325C2212yes—
38C2×#13063325C2211yescharacteristic
39C2×#13063325C2212yes—
40C2×#13063325C2212yes—
41C2×#13063325C2212yes—
42C2×#13063325C22116yescomplemented
43C2×#13063324C2214yes—
44C2×#13063323C2212yes—
45#14583433C22116yescomplemented
46C2×#13063320C2214yes—
47C2×#13063320C2214yes—
48C2×#13063319C2212yes—
49C2×#13063318C2214yes—
50C2×#13063317C2212yes—
51C2×#13063317C2211yescharacteristic
52C2×#13063316C2214yes—
53C2×#13063316C2214yes—
54C2×#13063315C2214yes—
55C2×#13063313C2211yescharacteristic
56C2×#13063312C2212yes—
57C2×#13063311C2214yes—
58C2×#13063309C2214yes—
59C2×#13063308C2212yes—
60C2×#13063307C2214yes—
61C2×#13063307C2214yes—
62C2×#13063305C2212yes—
63C2×#13063305C2212yes—
64C2×#13063305C2214yes—
65C2×#13063304C2211yescharacteristic
66C2×#13063304C2212yes—
67C2×#13063303C2214yes—
68C2×#13063302C2214yes—
69C2×#13063302C2214yes—
70C2×#13063302C2214yes—
71C2×#13063302C2214yes—
72C2×#13063299C2212yes—
73C2×#13063299C2211yescharacteristic
74C2×#13063297C2214yes—
75C2×C4×Dic86C2211yescharacteristic
76C2×C4×Dic86C2212yes—
77C2×#13063290C2212yes—
78C2×#13063290C2212yes—
79C2×C4×D172C2211yescharacteristic
80C2×C4×D172C2212yes—
81C2×D4×Dic43C2214yes—
82C2×C4×C22⋊D43C2212yes—
83C2×(C22⋊D43)⋊C4C2214yes—
84C2×#13063284C2212yes—
85C2×#13063282C2212yes—
86C22×C4⋊Dic43C2212yes—
87C22×C4⋊Dic43C2212yes—
88C22×C4⋊Dic43C2212yes—
89C43×#529C22116yescomplemented
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×C43C2211yescharacteristic
98C2×C4×D4×C43C2212yes—
99C2×#117×C43C2212yes—
100C22×C42×C43C2211yescharacteristic
101C2×#10621900—48no—
102C2×#10621900C23116yes—
103C22×Dic86—48no—
104C22×Dic86C2312yes—
105C22×Dic86C2312yes—
106C22×Dic86C2311yescharacteristic
107C22×Dic86C23116yes—
108C22×Dic86C2314yes—
109C22×Dic86C2314yes—
110C2×Q8×D43—48no—
111C2×Q8×D43C23116yes—
112C22×D172C2311yescharacteristic
113C22×C22⋊D43C2312yes—
114C22×C22⋊D43C2314yes—
115C23×Dic43C2314yes—
116C23×Dic43C2314yes—
117C22×C4×D43C2312yes—
118C22×C4×D43C2314yes—
119#13063325C2318yes—
120#13063325C23116yes—
121#13063325C2318yes—
122#13063325C23116yes—
123#13063325C23116yes—
124#13063325C23116yes—
125#13063324C23132yes—
126#13063323C23116yes—
127#13063320C23132yes—
128#13063320C23132yes—
129#13063319C23116yes—
130#13063318C23132yes—
131#13063317C23116yes—
132#13063317C2318yes—
133#13063316C23132yes—
134#13063316C23132yes—
135#13063315C23132yes—
136#13063313C2318yes—
137#13063312C23116yes—
138#13063311C23132yes—
139#13063309C23132yes—
140#13063308C23116yes—
141#13063307C23132yes—
142#13063307C23132yes—
143#13063305C23116yes—
144#13063305C23116yes—
145#13063305C23132yes—
146#13063304C2318yes—
147#13063304C23116yes—
148#13063303C23132yes—
149#13063302C23132yes—
150#13063302C23132yes—
151#13063302C23132yes—
152#13063302C23132yes—
153#13063299C23116yes—
154#13063299C2318yes—
155#13063297C23132yes—
156C4×Dic86C23116yes—
157C4×Dic86C2318yes—
158#13063290C23116yes—
159#13063290C23116yes—
160C4×D172C2318yes—
161C4×D172C23116yes—
162D4×Dic43C23132yes—
163C4×C22⋊D43C23116yes—
164(C22⋊D43)⋊C4C23132yes—
165#13063284C23116yes—
166#13063282C23116yes—
167C2×C4⋊Dic43C23116yes—
168C2×C4⋊Dic43C23116yes—
169C2×C4⋊Dic43C2311yescharacteristic
170C2×C4⋊Dic43C2312yes—
171C2×C4⋊Dic43C2312yes—
172C2×C4⋊Dic43C2314yes—
173C2×C4⋊Dic43C2314yes—
174C2×C4⋊Dic43C2314yes—
175C2×C4⋊Dic43C2312yes—
176C2×C4⋊Dic43C2312yes—
177C2×C4⋊Dic43C23116yes—
178C2×C4⋊Dic43C2311yescharacteristic
179C2×C4⋊Dic43C2314yes—
180C2×Dic43⋊C4C2312yes—
181C2×Dic43⋊C4C2312yes—
182C2×Dic43⋊C4C2314yes—
183C2×Dic43⋊C4C2312yes—
184C2×Dic43⋊C4C2314yes—
185C2×Dic43⋊C4C2314yes—
186C2×Dic43⋊C4C2314yes—
187C2×Dic43⋊C4C2312yes—
188C2×C22⋊Dic43C2314yes—
189C2×C22⋊Dic43C2312yes—
190C2×C22⋊Dic43C2314yes—
191C2×(C2×D43)⋊C4C2312yes—
192C2×(C2×D43)⋊C4C2312yes—
193C2×(C2×D43)⋊C4C2314yes—
194C2×(C2×D43)⋊C4C2312yes—
195C2×(C2×D43)⋊C4C2314yes—
196C2×(C2×D43)⋊C4C2312yes—
197C2×C4×Dic43C2312yes—
198C2×C4×Dic43C2314yes—
199C2×C4×Dic43C2314yes—
200C22×Q8×C43C2311yescharacteristic
201C22×D4×C43C2312yes—
202C22×D4×C43C2311yescharacteristic
203C23×C4×C43C2311yescharacteristic
204C23×C4×C43C2311yescharacteristic
205C23×C4×C43C2311yescharacteristic
206C23×C4×C43C2312yes—
207#126×C43C23116yes—
208#125×C43C2318yes—
209#124×C43C2318yes—
210#123×C43C23116yes—
211C22⋊Q8×C43C2318yes—
212#121×C43C2318yes—
213C4×Q8×C43C2318yes—
214C4×D4×C43C2318yes—
215C4×D4×C43C23116yes—
216#117×C43C23116yes—
217C2×C4⋊C4×C43C2312yes—
218C2×C4⋊C4×C43C2312yes—
219C2×C4⋊C4×C43C2311yescharacteristic
220C2×C4⋊C4×C43C2312yes—
221C2×C4⋊C4×C43C2311yescharacteristic
222C2×C4⋊C4×C43C2312yes—
223C2×C22⋊C4×C43C2312yes—
224C2×C22⋊C4×C43C2312yes—
225C2×C22⋊C4×C43C2312yes—
226C2×C22⋊C4×C43C2312yes—
227C2×C22⋊C4×C43C2312yes—
228C2×C42×C43C2311yescharacteristic
229C2×C42×C43C2311yescharacteristic
230C2×C42×C43C2311yescharacteristic
231C2×C42×C43C2311yescharacteristic
232C2×C42×C43C2318yes—
233C2×C42×C43C2312yes—
234C24×C43C2412yes—
235C24×C43C2411yescharacteristic
236C23×D43C2412yes—
237C2×Q8×C43—24no—
238C2×Q8×C43C2414yes—
239C2×D4×C43—24no—
240C2×D4×C43—28no—
241C2×D4×C43C2418yes—
242C2×D4×C43C2414yes—
243C22×C4×C43—24no—
244C22×C4×C43—24no—
245C22×C4×C43—28no—
246C22×C4×C43—24no—
247C22×C4×C43C2411yescharacteristic
248C22×C4×C43C2411yescharacteristic
249C22×C4×C43C2411yescharacteristic
250C22×C4×C43C2411yescharacteristic
251C22×C4×C43C2414yes—
252C22×C4×C43C2414yes—
253C22×C4×C43C2414yes—
254C22×C4×C43C2412yes—
255C22×C4×C43C2412yes—
256C22×C4×C43C2412yes—
257C22×C4×C43C2418yes—
258C22×C4×C43C2411yescharacteristic
259C22×C4×C43C2411yescharacteristic
260C2×C22⋊D43—28no—
261C2×C22⋊D43—48no—
262C2×C22⋊D43C2418yes—
263C2×C22⋊D43C24116yes—
264C22×Dic43—48no—
265C22×Dic43—48no—
266C22×Dic43C2412yes—
267C22×Dic43C2412yes—
268C22×Dic43C2414yes—
269C22×Dic43C2414yes—
270C22×Dic43C2412yes—
271C22×Dic43C24116yes—
272C22×Dic43C24116yes—
273Q8×D43—432no—
274#10621900—432no—
275C2×D172—24no—
276C2×D172C2414yes—
277C2×C4×D43—28no—
278C2×C4×D43—48no—
279C2×C4×D43C2418yes—
280C2×C4×D43C24116yes—
281C2×Dic86—28no—
282C2×Dic86—28no—
283C2×Dic86—24no—
284C2×Dic86—432no—
285C2×Dic86—48no—
286C2×Dic86—48no—
287C2×Dic86C2418yes—
288C2×Dic86C2418yes—
289C2×Dic86C2414yes—
290C2×Dic86C24116yes—
291C2×Dic86C24116yes—
292C4⋊C4×C43C2418yes—
293C4⋊C4×C43C2418yes—
294C4⋊C4×C43C2414yes—
295C4⋊C4×C43C2418yes—
296C4⋊C4×C43C2414yes—
297C4⋊C4×C43C2418yes—
298C22⋊C4×C43C2418yes—
299C22⋊C4×C43C2418yes—
300C22⋊C4×C43C2418yes—
301C22⋊C4×C43C2418yes—
302C22⋊C4×C43C2418yes—
303C42×C43C2414yes—
304C42×C43C2414yes—
305C42×C43C2414yes—
306C42×C43C2414yes—
307C42×C43C2418yes—
308C22⋊Dic43C24116yes—
309C22⋊Dic43C2418yes—
310C22⋊Dic43C24116yes—
311(C2×D43)⋊C4C2418yes—
312(C2×D43)⋊C4C2418yes—
313(C2×D43)⋊C4C24116yes—
314(C2×D43)⋊C4C2418yes—
315(C2×D43)⋊C4C24116yes—
316(C2×D43)⋊C4C2418yes—
317C4⋊Dic43C2414yes—
318C4⋊Dic43C2418yes—
319C4⋊Dic43C2418yes—
320C4⋊Dic43C24116yes—
321C4⋊Dic43C24116yes—
322C4⋊Dic43C24116yes—
323C4⋊Dic43C2418yes—
324C4⋊Dic43C2418yes—
325C4⋊Dic43C2414yes—
326C4⋊Dic43C24116yes—
327Dic43⋊C4C2418yes—
328Dic43⋊C4C2418yes—
329Dic43⋊C4C24116yes—
330Dic43⋊C4C2418yes—
331Dic43⋊C4C24116yes—
332Dic43⋊C4C24116yes—
333Dic43⋊C4C24116yes—
334Dic43⋊C4C2418yes—
335C4×Dic43C2418yes—
336C4×Dic43C24116yes—
337C4×Dic43C24116yes—
338C23×C43—22no—
339C23×C43—22no—
340C23×C43—24no—
341C23×C43—24no—
342C23×C43—24no—
343C23×C432−1+414yes—
344C23×C43C2514yes—
345C23×C43C2512yes—
346C23×C43C2511yescharacteristic
347C22×D43—24no—
348C22×D43—24no—
349C22×D43—24no—
350C22×D43C2514yes—
351Q8×C43—28no—
352D4×C43—216no—
353D4×C43—28no—
354C2×C4×C43—22no—
355C2×C4×C43—24no—
356C2×C4×C43—28no—
357C2×C4×C43—22no—
358C2×C4×C43—24no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—24no—
362C2×C4×C43—28no—
363C2×C4×C43—28no—
364C2×C4×C43—216no—
365C2×C4×C43H(5,𝔽2)14yes—
366C2×C4×C432−1+414yes—
367C2×C4×C43C2514yes—
368C2×C4×C43C2514yes—
369C2×C4×C43C2514yes—
370C2×C4×C43C2512yes—
371C2×C4×C43C2512yes—
372C2×C4×C43C2512yes—
373C2×C4×C43C2512yes—
374C2×C4×C43C2512yes—
375C2×C4×C43C2512yes—
376C22⋊D43—216no—
377C22⋊D43—416no—
378C2×Dic43—28no—
379C2×Dic43—28no—
380C2×Dic43—24no—
381C2×Dic43—24no—
382C2×Dic43—24no—
383C2×Dic43—416no—
384C2×Dic43—416no—
385C2×Dic43C2514yes—
386C2×Dic43C2514yes—
387C2×Dic43C2518yes—
388C2×Dic43C2518yes—
389C2×Dic43C2514yes—
390D172—28no—
391C4×D43—216no—
392C4×D43—416no—
393Dic86—216no—
394Dic86—216no—
395Dic86—28no—
396Dic86—416no—
397Dic86—416no—
398C2×#3552—431nomaximal, Sylow
399C22×C43—22no—
400C22×C43—22no—
401C22×C43—28no—
402C22×C43—24no—
403C22×C43—24no—
404C22×C43—24no—
405C22×C43—48no—
406C22×C43C2×H(5,𝔽2)12yes—
407C22×C43C2×2−1+414yes—
408C22×C43C2×2−1+412yes—
409C22×C43C2×2−1+412yes—
410C22×C43C2611yescharacteristic
411C2×D43—24no—
412C2×D43—24no—
413C2×D43—24no—
414C2×D43—48no—
415C4×C43—22no—
416C4×C43—24no—
417C4×C43—22no—
418C4×C43—22no—
419C4×C43—24no—
420C4×C43—22no—
421C4×C43—24no—
422C4×C43C2×H(5,𝔽2)14yes—
423C4×C43C2×2−1+414yes—
424Dic43—28no—
425Dic43—28no—
426Dic43—24no—
427Dic43—24no—
428Dic43—24no—
429#3552—4332no—
430C2×#563—434no—
431C2×#557—431no—
432C2×#556—431no—
433C2×#554—432no—
434C2×#553—432no—
435C2×D4×Q8—432no—
436C2×D4×Q8—431no—
437C2×#548—432no—
438C2×#547—431no—
439C2×#544—432no—
440C2×#542—432no—
441C2×#541—432no—
442C2×#539—434no—
443C2×#536—432no—
444C22×C4⋊Q8—431no—
445C2×#529—431no—
446C2×#529D4311yescharacteristic, complemented
447C2×C43—24no—
448C2×C43—44no—
449C2×C43#355214yescomplemented
450C2×C43C22×H(5,𝔽2)11yescharacteristic
451C2×C43C22×2−1+411yescharacteristic
452C2×C43C22×2−1+411yescharacteristic
453D43—44no—
454C22×#41—432no—
455C23×Q8—432no—
456C23×Q8—432no—
457#563—4364no—
458#557—4316no—
459#556—4316no—
460#554—4332no—
461#553—4332no—
462D4×Q8—4332no—
463D4×Q8—4316no—
464#548—4332no—
465#547—4316no—
466#544—4332no—
467#542—4332no—
468#541—4332no—
469#539—4364no—
470#536—4332no—
471C2×C4⋊Q8—432no—
472C2×C4⋊Q8—434no—
473C2×C4⋊Q8—432no—
474C2×C4⋊Q8—432no—
475C2×C4⋊Q8—431no—
476C2×C4⋊Q8—431no—
477C2×C4⋊Q8—432no—
478C2×C4⋊Q8—4316no—
479C2×C4⋊Q8—432no—
480#529—4316no—
481#529C2×D43116yescomplemented
482C2×#126—434no—
483C2×#126—434no—
484C2×#126—434no—
485C2×#126—432no—
486C2×#126C2×D4312yes—
487C2×#125—434no—
488C2×#125—434no—
489C2×#125—434no—
490C2×#125—431no—
491C2×#125—432no—
492C2×#125C2×D4311yescharacteristic
493C2×#124—432no—
494C2×#124—434no—
495C2×#124—431no—
496C2×#124C2×D4311yescharacteristic
497C2×#123—432no—
498C2×#123—434no—
499C2×#123—434no—
500C2×#123—434no—
501C2×#123C2×D4312yes—
502C2×C22⋊Q8—431no—
503C2×C22⋊Q8—432no—
504C2×C22⋊Q8—434no—
505C2×C22⋊Q8—434no—
506C2×C22⋊Q8—432no—
507C2×C22⋊Q8—432no—
508C2×C22⋊Q8—434no—
509C2×C22⋊Q8—434no—
510C2×C22⋊Q8—434no—
511C2×C22⋊Q8—434no—
512C2×C22⋊Q8C2×D4311yescharacteristic
513C2×#121—434no—
514C2×#121—431no—
515C2×#121—432no—
516C2×#121C2×D4311yescharacteristic
517C2×C4×Q8—432no—
518C2×C4×Q8—432no—
519C2×C4×Q8—431no—
520C2×C4×Q8—432no—
521C2×C4×Q8C2×D4311yescharacteristic
522C2×C4×D4—434no—
523C2×C4×D4—432no—
524C2×C4×D4—434no—
525C2×C4×D4—431no—
526C2×C4×D4—432no—
527C2×C4×D4C2×D4311yescharacteristic
528C2×C4×D4C2×D4312yes—
529C2×#117—432no—
530C2×#117—432no—
531C2×#117C2×D4312yes—
532C22×C4⋊C4—432no—
533C22×C4⋊C4—432no—
534C22×C4⋊C4—432no—
535C22×C42C2×D4311yescharacteristic
536C43C2×#355211yescharacteristic, complemented, Sylow
537C2×#41—4316no—
538C2×#41—1728no—
539C22×Q8—4316no—
540C22×Q8—431no—
541C22×Q8—432no—
542C22×Q8—432no—
543C22×Q8—434no—
544C22×Q8—434no—
545C22×Q8—4316no—
546C22×Q8—1728no—
547C22×Q8—1728no—
548C22×Q8C22×D4311yescharacteristic
549C22×D4—432no—
550C22×D4—434no—
551C22×D4—431no—
552C22×D4C22×D4312yes—
553C22×D4C22×D4311yescharacteristic
554C23×C4—434no—
555C23×C4—434no—
556C23×C4—432no—
557C23×C4—434no—
558C23×C4C22×D4311yescharacteristic
559C23×C4C22×D4311yescharacteristic
560C23×C4C22×D4312yes—
561C23×C4C22×D4311yescharacteristic
562C4⋊Q8—4316no—
563C4⋊Q8—4332no—
564C4⋊Q8—4316no—
565C4⋊Q8—4316no—
566C4⋊Q8—438no—
567C4⋊Q8—438no—
568C4⋊Q8—4316no—
569C4⋊Q8—4316no—
570#126—4332no—
571#126—4332no—
572#126—4332no—
573#126—4316no—
574#126C22×D43116yes—
575#125—4332no—
576#125—4332no—
577#125—4332no—
578#125—438no—
579#125—4316no—
580#125C22×D4318yes—
581#124—4316no—
582#124—4332no—
583#124—438no—
584#124C22×D4318yes—
585#123—4316no—
586#123—4332no—
587#123—4332no—
588#123—4332no—
589#123C22×D43116yes—
590C22⋊Q8—438no—
591C22⋊Q8—4316no—
592C22⋊Q8—4332no—
593C22⋊Q8—4316no—
594C22⋊Q8—4316no—
595C22⋊Q8—4332no—
596C22⋊Q8—4332no—
597C22⋊Q8—4332no—
598C22⋊Q8—4332no—
599C22⋊Q8—4332no—
600C22⋊Q8C22×D4318yes—
601#121—4332no—
602#121—438no—
603#121—4316no—
604#121C22×D4318yes—
605C4×Q8—4316no—
606C4×Q8—4316no—
607C4×Q8—438no—
608C4×Q8—4316no—
609C4×Q8C22×D4318yes—
610C4×D4—4332no—
611C4×D4—4316no—
612C4×D4—4332no—
613C4×D4—438no—
614C4×D4—4316no—
615C4×D4C22×D4318yes—
616C4×D4C22×D43116yes—
617#117—4316no—
618#117—4316no—
619#117C22×D43116yes—
620C2×C4⋊C4—431no—
621C2×C4⋊C4—432no—
622C2×C4⋊C4—432no—
623C2×C4⋊C4—434no—
624C2×C4⋊C4—432no—
625C2×C4⋊C4—434no—
626C2×C4⋊C4—434no—
627C2×C4⋊C4—432no—
628C2×C4⋊C4—4316no—
629C2×C4⋊C4—4316no—
630C2×C4⋊C4—4316no—
631C2×C4⋊C4—431no—
632C2×C4⋊C4—432no—
633C2×C4⋊C4—432no—
634C2×C4⋊C4—434no—
635C2×C4⋊C4—432no—
636C2×C4⋊C4—434no—
637C2×C4⋊C4—434no—
638C2×C4⋊C4—434no—
639C2×C4⋊C4—434no—
640C2×C4⋊C4—432no—
641C2×C4⋊C4C22×D4312yes—
642C2×C4⋊C4C22×D4312yes—
643C2×C4⋊C4C22×D4311yescharacteristic
644C2×C4⋊C4C22×D4312yes—
645C2×C4⋊C4C22×D4311yescharacteristic
646C2×C4⋊C4C22×D4312yes—
647C2×C22⋊C4—434no—
648C2×C22⋊C4—432no—
649C2×C22⋊C4—434no—
650C2×C22⋊C4—432no—
651C2×C22⋊C4—432no—
652C2×C22⋊C4—434no—
653C2×C22⋊C4—434no—
654C2×C22⋊C4—432no—
655C2×C22⋊C4—432no—
656C2×C22⋊C4C22×D4312yes—
657C2×C22⋊C4C22×D4312yes—
658C2×C22⋊C4C22×D4312yes—
659C2×C22⋊C4C22×D4312yes—
660C2×C22⋊C4C22×D4312yes—
661C2×C42—432no—
662C2×C42—434no—
663C2×C42—434no—
664C2×C42C22×D4311yescharacteristic
665C2×C42C22×D4311yescharacteristic
666C2×C42C22×D4312yes—
667C2×C42C22×D4311yescharacteristic
668C2×C42C22×D4311yescharacteristic
669C2×C42C22×D4318yes—
670C24—432no—
671C24C23×D4312yes—
672C24C23×D4311yescharacteristic
673#41—17232no—
674C2×Q8—24no—
675C2×Q8—434no—
676C2×Q8—438no—
677C2×Q8—438no—
678C2×Q8—4316no—
679C2×Q8—4316no—
680C2×Q8—868no—
681C2×Q8—868no—
682C2×Q8—864no—
683C2×Q8—1728no—
684C2×Q8—1728no—
685C2×Q8—17232no—
686C2×Q8—17232no—
687C2×Q8C23×D4314yes—
688C2×D4—28no—
689C2×D4—24no—
690C2×D4—438no—
691C2×D4—4316no—
692C2×D4—434no—
693C2×D4—868no—
694C2×D4—864no—
695C2×D4—1728no—
696C2×D4C23×D4318yes—
697C2×D4C23×D4314yes—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—28no—
702C22×C4—432no—
703C22×C4—432no—
704C22×C4—434no—
705C22×C4—434no—
706C22×C4—432no—
707C22×C4—4316no—
708C22×C4—4316no—
709C22×C4—438no—
710C22×C4—4316no—
711C22×C4—868no—
712C22×C4—1728no—
713C22×C4—1728no—
714C22×C4—1728no—
715C22×C4C23×D4314yes—
716C22×C4C23×D4314yes—
717C22×C4C23×D4314yes—
718C22×C4C23×D4318yes—
719C22×C4C23×D4312yes—
720C22×C4C23×D4312yes—
721C22×C4C23×D4311yescharacteristic
722C22×C4C23×D4311yescharacteristic
723C22×C4C23×D4311yescharacteristic
724C22×C4C23×D4311yescharacteristic
725C22×C4C23×D4312yes—
726C22×C4C23×D4311yescharacteristic
727C22×C4C23×D4311yescharacteristic
728C4⋊C4—434no—
729C4⋊C4—438no—
730C4⋊C4—438no—
731C4⋊C4—4316no—
732C4⋊C4—438no—
733C4⋊C4—4316no—
734C4⋊C4—4316no—
735C4⋊C4—438no—
736C4⋊C4—434no—
737C4⋊C4—438no—
738C4⋊C4—438no—
739C4⋊C4—4316no—
740C4⋊C4—438no—
741C4⋊C4—4316no—
742C4⋊C4—4316no—
743C4⋊C4—4316no—
744C4⋊C4—4316no—
745C4⋊C4—438no—
746C4⋊C4C23×D4318yes—
747C4⋊C4C23×D4318yes—
748C4⋊C4C23×D4314yes—
749C4⋊C4C23×D4318yes—
750C4⋊C4C23×D4314yes—
751C4⋊C4C23×D4318yes—
752C22⋊C4—4316no—
753C22⋊C4—438no—
754C22⋊C4—4316no—
755C22⋊C4—438no—
756C22⋊C4—438no—
757C22⋊C4—4316no—
758C22⋊C4—4316no—
759C22⋊C4—438no—
760C22⋊C4—438no—
761C22⋊C4C23×D4318yes—
762C22⋊C4C23×D4318yes—
763C22⋊C4C23×D4318yes—
764C22⋊C4C23×D4318yes—
765C22⋊C4C23×D4318yes—
766C42—438no—
767C42—4316no—
768C42—4316no—
769C42C23×D4314yes—
770C42C23×D4314yes—
771C42C23×D4314yes—
772C42C23×D4314yes—
773C42C23×D4318yes—
774C23—22no—
775C23—22no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—434no—
780C23—864no—
781C23—864no—
782C23—864no—
783C23#1306337214yes—
784C23C24×D4314yes—
785C23C24×D4312yes—
786C23C24×D4311yescharacteristic
787Q8—28no—
788Q8—8616no—
789Q8—8616no—
790Q8—868no—
791Q8—17216no—
792Q8—17216no—
793D4—216no—
794D4—28no—
795D4—8616no—
796D4—868no—
797D4—17216no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—28no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—24no—
804C2×C4—22no—
805C2×C4—24no—
806C2×C4—28no—
807C2×C4—28no—
808C2×C4—216no—
809C2×C4—434no—
810C2×C4—434no—
811C2×C4—438no—
812C2×C4—438no—
813C2×C4—434no—
814C2×C4—864no—
815C2×C4—868no—
816C2×C4—868no—
817C2×C4—864no—
818C2×C4—864no—
819C2×C4—8616no—
820C2×C4—17216no—
821C2×C4—17216no—
822C2×C4—17216no—
823C2×C4#1306337114yes—
824C2×C4#1306337214yes—
825C2×C4C24×D4314yes—
826C2×C4C24×D4314yes—
827C2×C4C24×D4312yes—
828C2×C4C24×D4312yes—
829C2×C4C24×D4312yes—
830C2×C4C24×D4312yes—
831C2×C4C24×D4314yes—
832C2×C4C24×D4312yes—
833C2×C4C24×D4312yes—
834C22—22no—
835C22—22no—
836C22—28no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—48no—
841C22—864no—
842C22—864no—
843C22—864no—
844C22—1728no—
845C22C2×#1306337112yes—
846C22C2×#1306337214yes—
847C22C2×#1306337212yes—
848C22C2×#1306337212yes—
849C22C25×D4311yescharacteristic
850C4—22no—
851C4—24no—
852C4—22no—
853C4—22no—
854C4—24no—
855C4—22no—
856C4—24no—
857C4—864no—
858C4—868no—
859C4—868no—
860C4—864no—
861C4—864no—
862C4C2×#1306337114yes—
863C4C2×#1306337214yes—
864C2—24no—
865C2—44no—
866C2—1724no—
867C2#1914903214yesdirect product factor
868C2C22×#1306337111yescharacteristic
869C2C22×#1306337211yescharacteristic
870C2C22×#1306337211yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#529C2
socleC23×C43C25
hypercenterC2×#529D43
hypocenterC43C2×#3552
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #19149032C2direct (N × H)
2. C2×#14583651C2semidirect
3. C2×#14583627C2semidirect
4. C2×#14583619C2semidirect
5. C2×#14583606C2semidirect
6. C2×#14583595C2semidirect
7. C2×Q8×D172C2semidirect
8. C2×#14583562C2semidirect
9. C2×#14583555C2semidirect
10. C2×#14583553C2semidirect
11. C2×#14583527C2semidirect
12. C2×#14583520C2semidirect
13. C2×#14583512C2semidirect
14. C2×#14583493C2semidirect
15. C2×#14583469C2semidirect
16. C22×#13063325C2semidirect
17. C2×#14583433C2semidirect
18. C2×C43×#529C2semidirect
22. #14583651C22semidirect
23. #14583627C22semidirect
24. #14583619C22semidirect
25. #14583606C22semidirect
26. #14583595C22semidirect
27. Q8×D172C22semidirect
28. #14583562C22semidirect
29. #14583555C22semidirect
30. #14583553C22semidirect
31. #14583527C22semidirect
32. #14583520C22semidirect
33. #14583512C22semidirect
34. #14583493C22semidirect
35. #14583469C22semidirect
42. C2×#13063325C22semidirect
45. #14583433C22semidirect
89. C43×#529C22semidirect
446. C2×#529D43semidirect
449. C2×C43#3552semidirect
481. #529C2×D43semidirect
536. C43C2×#3552semidirect
867. C2#19149032direct (N × H)

Maximal subgroups

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

subgroupindex
#191490322
C2×#145836512
C2×#145836272
C2×#145836192
C2×#145836062
C2×#145835952
C2×Q8×D1722
C2×#145835622
C2×#145835552
C2×#145835532
C2×#145835272
C2×#145835202
C2×#145835122
C2×#145834932
C2×#145834692
C22×#130633252
C2×#145834332
C2×C43×#5292
C2×#355243