Finite Group Databasebeta

← C2×#19149025 #26004209

Subgroups — C2×#19149025 #26004209

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#19149025C2132yesmaximal, direct product factor
2C2×#14583651C214yesmaximal, complemented
3C2×#14583628C211yesmaximal, characteristic, complemented
4C2×#14583607C212yesmaximal, complemented
5C2×#14583593C212yesmaximal, complemented
6C2×Q8×D172C212yesmaximal, complemented
7C2×#14583564C211yesmaximal, characteristic, complemented
8C2×#14583557C212yesmaximal, complemented
9C2×#14583553C211yesmaximal, characteristic, complemented
10C2×#14583527C212yesmaximal, complemented
11C2×#14583522C212yesmaximal, complemented
12C2×#14583507C212yesmaximal, complemented
13C2×#14583490C214yesmaximal, complemented
14C2×#14583469C212yesmaximal, complemented
15C2×C4⋊Q8×D43C211yesmaximal, characteristic, complemented
16C2×#14583436C211yesmaximal, characteristic, complemented
17C2×#14583431C211yesmaximal, characteristic, complemented
18C2×C43×#556C211yesmaximal, characteristic, complemented
19C22×#10621900C2212yes—
20C22×Q8×D43C2212yes—
21C22×Q8×D43C2212yes—
22#14583651C22164yescomplemented
23#14583628C22116yescomplemented
24#14583607C22132yescomplemented
25#14583593C22132yescomplemented
26Q8×D172C22132yescomplemented
27#14583564C22116yescomplemented
28#14583557C22132yescomplemented
29#14583553C22116yescomplemented
30#14583527C22132yescomplemented
31#14583522C22132yescomplemented
32#14583507C22132yescomplemented
33#14583490C22164yescomplemented
34#14583469C22132yescomplemented
35C2×#13063325C2211yescharacteristic
36C2×#13063325C2212yes—
37C2×#13063325C2214yes—
38C2×#13063324C2212yes—
39C2×#13063324C2212yes—
40C2×#13063324C2212yes—
41C2×#13063323C2212yes—
42C4⋊Q8×D43C22116yescomplemented
43#14583436C22116yescomplemented
44#14583431C22116yescomplemented
45C2×#13063320C2212yes—
46C2×#13063320C2214yes—
47C2×#13063319C2214yes—
48C2×#13063318C2212yes—
49C2×#13063317C2214yes—
50C2×#13063316C2212yes—
51C2×#13063316C2211yescharacteristic
52C2×#13063316C2211yescharacteristic
53C2×#13063316C2214yes—
54C2×#13063315C2214yes—
55C2×#13063314C2211yescharacteristic
56C2×#13063312C2211yescharacteristic
57C2×#13063311C2214yes—
58C2×#13063310C2212yes—
59C2×#13063309C2214yes—
60C2×#13063307C2214yes—
61C2×#13063307C2212yes—
62C2×#13063307C2214yes—
63C2×#13063305C2212yes—
64C2×#13063305C2211yescharacteristic
65C2×#13063305C2214yes—
66C2×#13063305C2214yes—
67C2×#13063303C2214yes—
68C2×#13063302C2214yes—
69C2×#13063302C2214yes—
70C2×#13063302C2214yes—
71C2×#13063301C2212yes—
72C2×#13063301C2211yescharacteristic
73C2×#13063300C2211yescharacteristic
74C2×#13063299C2212yes—
75C2×#13063298C2214yes—
76C2×#13063296C2211yescharacteristic
77C2×Q8×Dic43C2212yes—
78C2×C4×Dic86C2212yes—
79C2×C4×Dic86C2211yescharacteristic
80C2×C4×D172C2211yescharacteristic
81C2×C4×D172C2212yes—
82C2×C4×D172C2214yes—
83C2×#13063287C2212yes—
84C2×C4×C22⋊D43C2212yes—
85C2×(C22⋊D43)⋊C4C2214yes—
86C2×#13063284C2212yes—
87C2×#13063282C2212yes—
88C22×C4⋊Dic43C2212yes—
89C2×C4⋊C4×D43C2212yes—
90C2×C4⋊C4×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—
101C2×#10621900—48no—
102C2×#10621900C23116yes—
103C22×Dic86C2311yescharacteristic
104C22×Dic86C2312yes—
105C22×Dic86C2314yes—
106C22×Dic86C2314yes—
107C2×Q8×D43—48no—
108C2×Q8×D43—48no—
109C2×Q8×D43C23116yes—
110C2×Q8×D43C23116yes—
111C22×D172C2311yescharacteristic
112C22×D172C2312yes—
113C22×C22⋊D43C2312yes—
114C22×C22⋊D43C2314yes—
115C23×Dic43C2314yes—
116C22×C4×D43C2311yescharacteristic
117C22×C4×D43C2311yescharacteristic
118C22×C4×D43C2311yescharacteristic
119C22×C4×D43C2312yes—
120C22×C4×D43C2314yes—
121C22×C4×D43C2314yes—
122#13063325C2318yes—
123#13063325C23116yes—
124#13063325C23132yes—
125#13063324C23116yes—
126#13063324C23116yes—
127#13063324C23116yes—
128#13063323C23116yes—
129#13063320C23116yes—
130#13063320C23132yes—
131#13063319C23132yes—
132#13063318C23116yes—
133#13063317C23132yes—
134#13063316C23116yes—
135#13063316C23132yes—
136#13063316C2318yes—
137#13063316C2318yes—
138#13063315C23132yes—
139#13063314C2318yes—
140#13063312C2318yes—
141#13063311C23132yes—
142#13063310C23116yes—
143#13063309C23132yes—
144#13063307C23132yes—
145#13063307C23116yes—
146#13063307C23132yes—
147#13063305C23116yes—
148#13063305C2318yes—
149#13063305C23132yes—
150#13063305C23132yes—
151#13063303C23132yes—
152#13063302C23132yes—
153#13063302C23132yes—
154#13063302C23132yes—
155#13063301C23116yes—
156#13063301C2318yes—
157#13063300C2318yes—
158#13063299C23116yes—
159#13063298C23132yes—
160#13063296C2318yes—
161Q8×Dic43C23116yes—
162C4×Dic86C23116yes—
163C4×Dic86C2318yes—
164C4×D172C2318yes—
165C4×D172C23116yes—
166C4×D172C23132yes—
167#13063287C23116yes—
168C4×C22⋊D43C23116yes—
169(C22⋊D43)⋊C4C23132yes—
170#13063284C23116yes—
171#13063282C23116yes—
172C2×C4⋊Dic43C23116yes—
173C2×C4⋊Dic43C2312yes—
174C2×C4⋊Dic43C2312yes—
175C2×C4⋊Dic43C2311yescharacteristic
176C2×C4⋊Dic43C2314yes—
177C2×C4⋊Dic43C2312yes—
178C2×C4⋊Dic43C2312yes—
179C2×C4⋊Dic43C2312yes—
180C2×C4⋊Dic43C2314yes—
181C2×C4⋊Dic43C2311yescharacteristic
182C2×C4⋊Dic43C2314yes—
183C2×Dic43⋊C4C2314yes—
184C2×Dic43⋊C4C2314yes—
185C2×Dic43⋊C4C2312yes—
186C2×Dic43⋊C4C2312yes—
187C2×Dic43⋊C4C2314yes—
188C2×Dic43⋊C4C2312yes—
189C2×Dic43⋊C4C2314yes—
190C2×Dic43⋊C4C2312yes—
191C4⋊C4×D43C23116yes—
192C4⋊C4×D43C23116yes—
193C2×C22⋊Dic43C2312yes—
194C2×C22⋊Dic43C2312yes—
195C2×C22⋊Dic43C2312yes—
196C2×(C2×D43)⋊C4C2312yes—
197C2×(C2×D43)⋊C4C2312yes—
198C2×(C2×D43)⋊C4C2312yes—
199C2×(C2×D43)⋊C4C2312yes—
200C2×(C2×D43)⋊C4C2314yes—
201C2×(C2×D43)⋊C4C2314yes—
202C2×(C2×D43)⋊C4C2312yes—
203C2×(C2×D43)⋊C4C2312yes—
204C2×C4×Dic43C2311yescharacteristic
205C2×C4×Dic43C2311yescharacteristic
206C2×C4×Dic43C2311yescharacteristic
207C2×C4×Dic43C2312yes—
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×C43C23116yes—
219C4×Q8×C43C2318yes—
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—28no—
238C2×Q8×C43—24no—
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×C43C2412yes—
248C22×C4×C43C2414yes—
249C22×C4×C43C2418yes—
250C22×C4×C43C2411yescharacteristic
251C22×C4×C43C2411yescharacteristic
252C2×C22⋊D43—28no—
253C2×C22⋊D43—48no—
254C2×C22⋊D43C2418yes—
255C2×C22⋊D43C24116yes—
256C22×Dic43—48no—
257C22×Dic43C2412yes—
258C22×Dic43C2411yescharacteristic
259C22×Dic43C2411yescharacteristic
260C22×Dic43C2411yescharacteristic
261C22×Dic43C2412yes—
262C22×Dic43C2414yes—
263C22×Dic43C2412yes—
264C22×Dic43C24116yes—
265Q8×D43—432no—
266Q8×D43—432no—
267#10621900—432no—
268C2×D172—24no—
269C2×D172—28no—
270C2×D172C2414yes—
271C2×D172C2418yes—
272C2×C4×D43—24no—
273C2×C4×D43—28no—
274C2×C4×D43—24no—
275C2×C4×D43—24no—
276C2×C4×D43—48no—
277C2×C4×D43—48no—
278C2×C4×D43C2414yes—
279C2×C4×D43C2414yes—
280C2×C4×D43C2414yes—
281C2×C4×D43C2418yes—
282C2×C4×D43C24116yes—
283C2×C4×D43C24116yes—
284C2×Dic86—24no—
285C2×Dic86—28no—
286C2×Dic86—48no—
287C2×Dic86—48no—
288C2×Dic86C2414yes—
289C2×Dic86C2418yes—
290C2×Dic86C24116yes—
291C2×Dic86C24116yes—
292C4⋊C4×C43C2414yes—
293C4⋊C4×C43C2418yes—
294C4⋊C4×C43C2414yes—
295C4⋊C4×C43C24116yes—
296C4⋊C4×C43C2418yes—
297C4⋊C4×C43C2418yes—
298C22⋊C4×C43C24116yes—
299C22⋊C4×C43C2418yes—
300C22⋊C4×C43C24116yes—
301C42×C43C24116yes—
302C42×C43C2414yes—
303C42×C43C2418yes—
304C22⋊Dic43C2418yes—
305C22⋊Dic43C2418yes—
306C22⋊Dic43C2418yes—
307(C2×D43)⋊C4C2418yes—
308(C2×D43)⋊C4C2418yes—
309(C2×D43)⋊C4C2418yes—
310(C2×D43)⋊C4C2418yes—
311(C2×D43)⋊C4C24116yes—
312(C2×D43)⋊C4C24116yes—
313(C2×D43)⋊C4C2418yes—
314(C2×D43)⋊C4C2418yes—
315C4⋊Dic43C2418yes—
316C4⋊Dic43C2418yes—
317C4⋊Dic43C2414yes—
318C4⋊Dic43C24116yes—
319C4⋊Dic43C2418yes—
320C4⋊Dic43C2418yes—
321C4⋊Dic43C2418yes—
322C4⋊Dic43C24116yes—
323C4⋊Dic43C2414yes—
324C4⋊Dic43C24116yes—
325Dic43⋊C4C24116yes—
326Dic43⋊C4C24116yes—
327Dic43⋊C4C2418yes—
328Dic43⋊C4C2418yes—
329Dic43⋊C4C24116yes—
330Dic43⋊C4C2418yes—
331Dic43⋊C4C24116yes—
332Dic43⋊C4C2418yes—
333C4×Dic43C2414yes—
334C4×Dic43C2414yes—
335C4×Dic43C2414yes—
336C4×Dic43C2418yes—
337C4×Dic43C24116yes—
338C23×C43—24no—
339C23×C43—24no—
340C23×C43—24no—
341C23×C43C2514yes—
342C23×C43C2511yescharacteristic
343C22×D43—22no—
344C22×D43—22no—
345C22×D43—24no—
346C22×D43—24no—
347C22×D43—24no—
348C22×D432−1+414yes—
349C22×D43C2514yes—
350C22×D43C2512yes—
351Q8×C43—216no—
352Q8×C43—28no—
353D4×C43—28no—
354C2×C4×C43—28no—
355C2×C4×C43—22no—
356C2×C4×C43—24no—
357C2×C4×C43—24no—
358C2×C4×C43—24no—
359C2×C4×C43—216no—
360C2×C4×C43H(5,𝔽2)14yes—
361C2×C4×C432−1+414yes—
362C2×C4×C43C2514yes—
363C2×C4×C43C2512yes—
364C2×C4×C43C2514yes—
365C2×C4×C43C2518yes—
366C2×C4×C43C2514yes—
367C2×C4×C43C2512yes—
368C2×C4×C43C2512yes—
369C22⋊D43—216no—
370C22⋊D43—416no—
371C2×Dic43—24no—
372C2×Dic43—28no—
373C2×Dic43—22no—
374C2×Dic43—24no—
375C2×Dic43—22no—
376C2×Dic43—22no—
377C2×Dic43—24no—
378C2×Dic43—416no—
379C2×Dic43C2514yes—
380C2×Dic43C2512yes—
381C2×Dic43C2512yes—
382C2×Dic43C2512yes—
383C2×Dic43C2518yes—
384C2×Dic43C2514yes—
385C2×Dic43C2514yes—
386D172—216no—
387D172—28no—
388C4×D43—28no—
389C4×D43—216no—
390C4×D43—28no—
391C4×D43—28no—
392C4×D43—416no—
393C4×D43—416no—
394Dic86—216no—
395Dic86—28no—
396Dic86—416no—
397Dic86—416no—
398C2×#3552—431nomaximal, Sylow
399C22×C43—24no—
400C22×C43—24no—
401C22×C43—24no—
402C22×C43—48no—
403C22×C43C2×H(5,𝔽2)12yes—
404C22×C43C2×2−1+412yes—
405C22×C43C2×2−1+412yes—
406C22×C43C2611yescharacteristic
407C2×D43—22no—
408C2×D43—22no—
409C2×D43—28no—
410C2×D43—24no—
411C2×D43—24no—
412C2×D43—24no—
413C2×D43—48no—
414C2×D43C2×2−1+414yes—
415C4×C43—28no—
416C4×C43—22no—
417C4×C43—24no—
418C4×C43—24no—
419C4×C43—24no—
420C4×C43C2×H(5,𝔽2)14yes—
421C4×C43C2×2−1+414yes—
422Dic43—24no—
423Dic43—28no—
424Dic43—22no—
425Dic43—24no—
426Dic43—22no—
427Dic43—22no—
428Dic43—24no—
429#3552—4332no—
430C2×#563—434no—
431C2×#557—431no—
432C2×#556D4311yescharacteristic, complemented
433C2×#554—432no—
434C2×#553—432no—
435C2×D4×Q8—431no—
436C2×D4×Q8—432no—
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×#529—431no—
447C2×C43—44no—
448C2×C43#355214yescomplemented
449C2×C43C22×H(5,𝔽2)11yescharacteristic
450C2×C43C22×2−1+411yescharacteristic
451C2×C43C22×2−1+411yescharacteristic
452D43—24no—
453D43—44no—
454C22×#41—432no—
455C23×Q8—432no—
456C23×Q8—432no—
457#563—4364no—
458#557—4316no—
459#556C2×D43116yescomplemented
460#554—4332no—
461#553—4332no—
462D4×Q8—4316no—
463D4×Q8—4332no—
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—4316no—
473C2×C4⋊Q8—432no—
474C2×C4⋊Q8—432no—
475C2×C4⋊Q8—432no—
476C2×C4⋊Q8—431no—
477C2×C4⋊Q8—432no—
478C2×C4⋊Q8—434no—
479C2×C4⋊Q8C2×D4311yescharacteristic
480#529—4316no—
481#529—4316no—
482C2×#126—432no—
483C2×#126—434no—
484C2×#126—432no—
485C2×#126—434no—
486C2×#126C2×D4314yes—
487C2×#125—431no—
488C2×#125—431no—
489C2×#125—434no—
490C2×#125—434no—
491C2×#125—432no—
492C2×#125—434no—
493C2×#124—431no—
494C2×#124—431no—
495C2×#124—434no—
496C2×#124C2×D4312yes—
497C2×#123—432no—
498C2×#123—432no—
499C2×#123—434no—
500C2×#123—434no—
501C2×#123—434no—
502C2×C22⋊Q8—431no—
503C2×C22⋊Q8—432no—
504C2×C22⋊Q8—434no—
505C2×C22⋊Q8—431no—
506C2×C22⋊Q8—434no—
507C2×C22⋊Q8—432no—
508C2×C22⋊Q8—434no—
509C2×C22⋊Q8—434no—
510C2×C22⋊Q8—434no—
511C2×C22⋊Q8—434no—
512C2×C22⋊Q8C2×D4312yes—
513C2×#121—431no—
514C2×#121—432no—
515C2×#121—431no—
516C2×#121—434no—
517C2×C4×Q8—432no—
518C2×C4×Q8—431no—
519C2×C4×Q8—432no—
520C2×C4×Q8C2×D4311yescharacteristic
521C2×C4×Q8C2×D4312yes—
522C2×C4×D4—432no—
523C2×C4×D4—432no—
524C2×C4×D4—434no—
525C2×C4×D4—431no—
526C2×C4×D4—432no—
527C2×C4×D4—434no—
528C2×C4×D4C2×D4311yescharacteristic
529C2×#117—432no—
530C2×#117—432no—
531C2×#117C2×D4312yes—
532C22×C4⋊C4—432no—
533C22×C4⋊C4—432no—
534C22×C4⋊C4—432no—
535C22×C42—431no—
536C43C2×#355211yescharacteristic, complemented, Sylow
537C2×#41—4316no—
538C2×#41—1728no—
539C22×Q8—4316no—
540C22×Q8—4316no—
541C22×Q8—431no—
542C22×Q8—432no—
543C22×Q8—434no—
544C22×Q8—434no—
545C22×Q8—1728no—
546C22×Q8—1728no—
547C22×Q8C22×D4311yescharacteristic
548C22×Q8C22×D4312yes—
549C22×D4—432no—
550C22×D4—434no—
551C22×D4—432no—
552C22×D4—431no—
553C22×D4C22×D4311yescharacteristic
554C23×C4—434no—
555C23×C4—431no—
556C23×C4—431no—
557C23×C4—432no—
558C23×C4—431no—
559C23×C4—434no—
560C23×C4—434no—
561C23×C4C22×D4312yes—
562C4⋊Q8—4316no—
563C4⋊Q8—4316no—
564C4⋊Q8—4316no—
565C4⋊Q8—4316no—
566C4⋊Q8—438no—
567C4⋊Q8—4316no—
568C4⋊Q8—4332no—
569C4⋊Q8C22×D4318yes—
570#126—4316no—
571#126—4332no—
572#126—4316no—
573#126—4332no—
574#126C22×D43132yes—
575#125—438no—
576#125—438no—
577#125—4332no—
578#125—4332no—
579#125—4316no—
580#125—4332no—
581#124—438no—
582#124—438no—
583#124—4332no—
584#124C22×D43116yes—
585#123—4316no—
586#123—4316no—
587#123—4332no—
588#123—4332no—
589#123—4332no—
590C22⋊Q8—438no—
591C22⋊Q8—4316no—
592C22⋊Q8—438no—
593C22⋊Q8—4332no—
594C22⋊Q8—4332no—
595C22⋊Q8—4316no—
596C22⋊Q8—4332no—
597C22⋊Q8—4332no—
598C22⋊Q8—4332no—
599C22⋊Q8—4332no—
600C22⋊Q8C22×D43116yes—
601#121—438no—
602#121—4316no—
603#121—438no—
604#121—4332no—
605C4×Q8—4316no—
606C4×Q8—438no—
607C4×Q8—4316no—
608C4×Q8C22×D4318yes—
609C4×Q8C22×D43116yes—
610C4×D4—4316no—
611C4×D4—4316no—
612C4×D4—4332no—
613C4×D4—438no—
614C4×D4—4316no—
615C4×D4—4332no—
616C4×D4C22×D4318yes—
617#117—4316no—
618#117—4316no—
619#117C22×D43116yes—
620C2×C4⋊C4—431no—
621C2×C4⋊C4—432no—
622C2×C4⋊C4—434no—
623C2×C4⋊C4—434no—
624C2×C4⋊C4—434no—
625C2×C4⋊C4—432no—
626C2×C4⋊C4—4316no—
627C2×C4⋊C4—432no—
628C2×C4⋊C4—432no—
629C2×C4⋊C4—432no—
630C2×C4⋊C4—432no—
631C2×C4⋊C4—434no—
632C2×C4⋊C4—432no—
633C2×C4⋊C4—434no—
634C2×C4⋊C4—432no—
635C2×C4⋊C4—431no—
636C2×C4⋊C4—434no—
637C2×C4⋊C4—434no—
638C2×C4⋊C4—432no—
639C2×C4⋊C4—4316no—
640C2×C4⋊C4—4316no—
641C2×C4⋊C4C22×D4312yes—
642C2×C4⋊C4C22×D4312yes—
643C2×C4⋊C4C22×D4311yescharacteristic
644C2×C4⋊C4C22×D4311yescharacteristic
645C2×C4⋊C4C22×D4314yes—
646C2×C4⋊C4C22×D4312yes—
647C2×C22⋊C4—432no—
648C2×C22⋊C4—432no—
649C2×C22⋊C4—432no—
650C2×C22⋊C4—432no—
651C2×C22⋊C4—432no—
652C2×C22⋊C4—432no—
653C2×C22⋊C4—432no—
654C2×C22⋊C4—434no—
655C2×C22⋊C4—434no—
656C2×C22⋊C4—432no—
657C2×C22⋊C4—432no—
658C2×C22⋊C4C22×D4314yes—
659C2×C22⋊C4C22×D4314yes—
660C2×C22⋊C4C22×D4312yes—
661C2×C42—431no—
662C2×C42—431no—
663C2×C42—432no—
664C2×C42—434no—
665C2×C42—431no—
666C2×C42—438no—
667C2×C42C22×D4312yes—
668C2×C42C22×D4314yes—
669C2×C42C22×D4311yescharacteristic
670C24—431no—
671C24—432no—
672C24C23×D4312yes—
673#41—17232no—
674C2×Q8—28no—
675C2×Q8—24no—
676C2×Q8—434no—
677C2×Q8—438no—
678C2×Q8—4316no—
679C2×Q8—4316no—
680C2×Q8—864no—
681C2×Q8—868no—
682C2×Q8—1728no—
683C2×Q8—1728no—
684C2×Q8—17232no—
685C2×Q8—17232no—
686C2×Q8C23×D4314yes—
687C2×Q8C23×D4318yes—
688C2×D4—24no—
689C2×D4—438no—
690C2×D4—4316no—
691C2×D4—438no—
692C2×D4—434no—
693C2×D4—868no—
694C2×D4—868no—
695C2×D4—864no—
696C2×D4—1728no—
697C2×D4C23×D4314yes—
698C22×C4—28no—
699C22×C4—432no—
700C22×C4—431no—
701C22×C4—431no—
702C22×C4—431no—
703C22×C4—432no—
704C22×C4—434no—
705C22×C4—432no—
706C22×C4—4316no—
707C22×C4—434no—
708C22×C4—434no—
709C22×C4—434no—
710C22×C4—438no—
711C22×C4—4316no—
712C22×C4—4316no—
713C22×C4—864no—
714C22×C4—864no—
715C22×C4—868no—
716C22×C4—864no—
717C22×C4—1728no—
718C22×C4—1728no—
719C22×C4—1728no—
720C22×C4C23×D4318yes—
721C22×C4C23×D4312yes—
722C22×C4C23×D4311yescharacteristic
723C22×C4C23×D4312yes—
724C22×C4C23×D4312yes—
725C22×C4C23×D4314yes—
726C22×C4C23×D4311yescharacteristic
727C22×C4C23×D4311yescharacteristic
728C4⋊C4—434no—
729C4⋊C4—438no—
730C4⋊C4—4316no—
731C4⋊C4—4316no—
732C4⋊C4—4316no—
733C4⋊C4—438no—
734C4⋊C4—438no—
735C4⋊C4—438no—
736C4⋊C4—438no—
737C4⋊C4—438no—
738C4⋊C4—4316no—
739C4⋊C4—438no—
740C4⋊C4—4316no—
741C4⋊C4—438no—
742C4⋊C4—434no—
743C4⋊C4—4316no—
744C4⋊C4—4316no—
745C4⋊C4—438no—
746C4⋊C4C23×D4318yes—
747C4⋊C4C23×D4318yes—
748C4⋊C4C23×D4314yes—
749C4⋊C4C23×D4314yes—
750C4⋊C4C23×D43116yes—
751C4⋊C4C23×D4318yes—
752C22⋊C4—438no—
753C22⋊C4—438no—
754C22⋊C4—438no—
755C22⋊C4—438no—
756C22⋊C4—438no—
757C22⋊C4—438no—
758C22⋊C4—438no—
759C22⋊C4—4316no—
760C22⋊C4—4316no—
761C22⋊C4—438no—
762C22⋊C4—438no—
763C22⋊C4C23×D43116yes—
764C22⋊C4C23×D43116yes—
765C22⋊C4C23×D4318yes—
766C42—434no—
767C42—434no—
768C42—434no—
769C42—438no—
770C42—4316no—
771C42C23×D4314yes—
772C42C23×D4318yes—
773C42C23×D43116yes—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—434no—
778C23—432no—
779C23—434no—
780C23—862no—
781C23—862no—
782C23—864no—
783C23—864no—
784C23—864no—
785C23C24×D4314yes—
786C23C24×D4311yescharacteristic
787Q8—216no—
788Q8—28no—
789Q8—868no—
790Q8—8616no—
791Q8—17216no—
792Q8—17216no—
793D4—28no—
794D4—8616no—
795D4—8616no—
796D4—868no—
797D4—17216no—
798C2×C4—28no—
799C2×C4—22no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—216no—
804C2×C4—434no—
805C2×C4—432no—
806C2×C4—432no—
807C2×C4—432no—
808C2×C4—434no—
809C2×C4—438no—
810C2×C4—434no—
811C2×C4—868no—
812C2×C4—864no—
813C2×C4—862no—
814C2×C4—868no—
815C2×C4—864no—
816C2×C4—862no—
817C2×C4—864no—
818C2×C4—862no—
819C2×C4—868no—
820C2×C4—8616no—
821C2×C4—868no—
822C2×C4—17216no—
823C2×C4—17216no—
824C2×C4—17216no—
825C2×C4#1306337114yes—
826C2×C4#1306337214yes—
827C2×C4C24×D4314yes—
828C2×C4C24×D4312yes—
829C2×C4C24×D4314yes—
830C2×C4C24×D4314yes—
831C2×C4C24×D4318yes—
832C2×C4C24×D4312yes—
833C2×C4C24×D4312yes—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—48no—
838C22—434no—
839C22—862no—
840C22—862no—
841C22—868no—
842C22—864no—
843C22—864no—
844C22—864no—
845C22—1728no—
846C22C2×#1306337112yes—
847C222−1+4×D4312yes—
848C22C2×#1306337212yes—
849C22C25×D4311yescharacteristic
850C4—28no—
851C4—22no—
852C4—24no—
853C4—24no—
854C4—24no—
855C4—864no—
856C4—862no—
857C4—868no—
858C4—864no—
859C4—862no—
860C4—864no—
861C4—862no—
862C4C2×#1306337114yes—
863C4C2×#1306337214yes—
864C2—44no—
865C2—864no—
866C2—1724no—
867C2#1914902514yesdirect product factor
868C2C22×#1306337111yescharacteristic
869C2C2×2−1+4×D4311yescharacteristic
870C2C22×#1306337211yescharacteristic
subgroupG/H
centerC23C24×D43
commutator, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC2×C43×#556C2
socleC23×C43C25
hypercenterC2×#556D43
hypocenterC43C2×#3552
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #19149025C2direct (N × H)
2. C2×#14583651C2semidirect
3. C2×#14583628C2semidirect
4. C2×#14583607C2semidirect
5. C2×#14583593C2semidirect
6. C2×Q8×D172C2semidirect
7. C2×#14583564C2semidirect
8. C2×#14583557C2semidirect
9. C2×#14583553C2semidirect
10. C2×#14583527C2semidirect
11. C2×#14583522C2semidirect
12. C2×#14583507C2semidirect
13. C2×#14583490C2semidirect
14. C2×#14583469C2semidirect
15. C2×C4⋊Q8×D43C2semidirect
16. C2×#14583436C2semidirect
17. C2×#14583431C2semidirect
18. C2×C43×#556C2semidirect
22. #14583651C22semidirect
23. #14583628C22semidirect
24. #14583607C22semidirect
25. #14583593C22semidirect
26. Q8×D172C22semidirect
27. #14583564C22semidirect
28. #14583557C22semidirect
29. #14583553C22semidirect
30. #14583527C22semidirect
31. #14583522C22semidirect
32. #14583507C22semidirect
33. #14583490C22semidirect
34. #14583469C22semidirect
42. C4⋊Q8×D43C22semidirect
43. #14583436C22semidirect
44. #14583431C22semidirect
92. C43×#556C22semidirect
432. C2×#556D43semidirect
448. C2×C43#3552semidirect
459. #556C2×D43semidirect
536. C43C2×#3552semidirect
867. C2#19149025direct (N × H)

Maximal subgroups

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

subgroupindex
#191490252
C2×#145836512
C2×#145836282
C2×#145836072
C2×#145835932
C2×Q8×D1722
C2×#145835642
C2×#145835572
C2×#145835532
C2×#145835272
C2×#145835222
C2×#145835072
C2×#145834902
C2×#145834692
C2×C4⋊Q8×D432
C2×#145834362
C2×#145834312
C2×C43×#5562
C2×#355243