Finite Group Databasebeta

← C2×#22601829 #32904413

Subgroups — C2×#22601829 #32904413

Order 18176.

12314 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11765866C211yesmaximal, characteristic, complemented
2C22×#41×D71C211yesmaximal, characteristic, complemented
3#22601829C2132yesmaximal, direct product factor
4C2×#17986668C211yesmaximal, characteristic, complemented
5C2×Q8×C22⋊D71C211yesmaximal, characteristic, complemented
6C2×#17986661C211yesmaximal, characteristic, complemented
7C2×#17986651C213yesmaximal, complemented
8C2×#17986645C213yesmaximal, complemented
9C2×#17986642C213yesmaximal, complemented
10C2×#17986633C213yesmaximal, complemented
11C2×#17986548C213yesmaximal, complemented
12C2×#17986512C213yesmaximal, complemented
13C2×#17986509C213yesmaximal, complemented
14C2×C4×#11765866C211yesmaximal, characteristic, complemented
15C2×C4×D4×D71C213yesmaximal, complemented
16C2×#548×C71C211yesmaximal, characteristic, complemented
17C22×#11765866—216no—
18C22×#11765866C2211yescharacteristic
19C22×#11765866C2213yescomplemented
20C22×#11765866C2211yescharacteristic, complemented
21C22×#11765866C2213yescomplemented
22C22×#11765866C22116yescomplemented
23C22×#11765865C2213yescomplemented
24C22×#11765864C2213yescomplemented
25C2×#41×D71—216no—
26C2×#41×D71C22116yescomplemented
27C22×Q8×D71C2211yescharacteristic, complemented
28C23×D284C2213yescomplemented
29C22×D4×D71C2213yes—
30C22×D4×D71C2213yescomplemented
31C23×C4×D71C2213yescomplemented
32C23×C4×D71C2213yescomplemented
33#17986668C22116yescomplemented
34Q8×C22⋊D71C22116yescomplemented
35#17986661C22116yescomplemented
36#17986651C22148yescomplemented
37#17986645C22148yescomplemented
38#17986642C22148yescomplemented
39#17986633C22148yescomplemented
40#17986548C22148yescomplemented
41C2×#14556126C2213yescomplemented
42C2×#14556124C2213yescomplemented
43C2×#14556116C2213yescomplemented
44#17986512C22148yescomplemented
45#17986509C22148yescomplemented
46C2×#14556113C2216yescomplemented
47C2×#14556110C2216yescomplemented
48C2×#14556108C2213yescomplemented
49C2×#14556107C2213yescomplemented
50C2×#14556104C2213yescomplemented
51C2×#14556103C2213yescomplemented
52C2×#14556102C2213yescomplemented
53C2×#14556101C2216yescomplemented
54C2×#14556101C2216yescomplemented
55C2×#14556099C2213yescomplemented
56C2×#14556098C2216yescomplemented
57C2×#14556096C2216yescomplemented
58C4×#11765866C22116yescomplemented
59C2×Q8×Dic71C2211yescharacteristic, complemented
60C2×C4×D284C2213yescomplemented
61C2×C4×D284C2213yescomplemented
62C2×D4×Dic71C2213yescomplemented
63C2×#14556090C2213yescomplemented
64C2×#14556090C2213yescomplemented
65C2×C4×C22⋊D71C2213yes—
66C2×C4×C22⋊D71C2213yescomplemented
67C2×(C22⋊D71)⋊C4C2211yescharacteristic
68C2×(C22⋊D71)⋊C4C2213yescomplemented
69C2×(C22⋊D71)⋊C4C2216yescomplemented
70C4×D4×D71C22148yescomplemented
71C2×#14556086C2213yescomplemented
72C2×C4⋊C4×D71C2213yescomplemented
73C2×C22⋊C4×D71C2213yescomplemented
74C2×C22⋊C4×D71C2213yescomplemented
75C2×C42×D71C2213yescomplemented
76C22×#41×C71C2211yescharacteristic, complemented
77C23×Q8×C71C2211yescharacteristic, complemented
78#548×C71C22116yescomplemented
79C2×#124×C71C2213yescomplemented
80C2×C22⋊Q8×C71C2213yescomplemented
81C2×#121×C71C2213yescomplemented
82C2×C4×Q8×C71C2211yescharacteristic, complemented
83C2×C4×D4×C71C2213yescomplemented
84C24×D71C2313yes—
85C24×D71C2313yes—
86C2×#11765866—2128no—
87C2×#11765866—224no—
88C2×#11765866—224no—
89C2×#11765866—28no—
90C2×#11765866D4116yescomplemented
91C2×#11765866C2318yes—
92C2×#11765866C23124yescomplemented
93C2×#11765866C2318yescomplemented
94C2×#11765866C23124yescomplemented
95C2×#11765865—224no—
96C2×#11765865C23124yescomplemented
97C2×#11765864—224no—
98C2×#11765864C23124yescomplemented
99#41×D71—2128no—
100C22×Dic142C2313yes—
101C2×Q8×D71—28no—
102C2×Q8×D71C2318yescomplemented
103C22×D284—224no—
104C22×D284C2313yes—
105C22×D284C2316yes—
106C22×D284C2313yes—
107C22×D284C2313yes—
108C22×D284C23124yescomplemented
109C22×C22⋊D71C2313yes—
110C22×C22⋊D71C2316yes—
111C22×C22⋊D71C2316yes—
112C22×C22⋊D71C2311yescharacteristic
113C2×D4×D71—224no—
114C2×D4×D71—224no—
115C2×D4×D71C23124yes—
116C2×D4×D71C23124yescomplemented
117C23×Dic71C2311yescharacteristic
118C23×Dic71C2313yes—
119C22×C4×D71—224no—
120C22×C4×D71—224no—
121C22×C4×D71C2311yescharacteristic
122C22×C4×D71C2313yes—
123C22×C4×D71C2313yes—
124C22×C4×D71C2313yes—
125C22×C4×D71C2313yes—
126C22×C4×D71C2313yes—
127C22×C4×D71C2313yes—
128C22×C4×D71C2313yes—
129C22×C4×D71C2313yes—
130C22×C4×D71C23124yescomplemented
131C22×C4×D71C23124yescomplemented
132#14556126C23124yescomplemented
133#14556124C23124yescomplemented
134#14556116C23124yescomplemented
135#14556113C23148yescomplemented
136#14556110C23148yescomplemented
137#14556108C23124yescomplemented
138#14556107C23124yescomplemented
139#14556104C23124yescomplemented
140#14556103C23124yescomplemented
141#14556102C23124yescomplemented
142#14556101C23148yescomplemented
143#14556101C23148yescomplemented
144#14556099C23124yescomplemented
145#14556098C23148yescomplemented
146#14556096C23148yescomplemented
147Q8×Dic71C2318yescomplemented
148C4×D284C23124yescomplemented
149C4×D284C23124yescomplemented
150D4×Dic71C23124yescomplemented
151#14556090C23124yescomplemented
152#14556090C23124yescomplemented
153C4×C22⋊D71C23124yes—
154C4×C22⋊D71C23124yescomplemented
155(C22⋊D71)⋊C4C2318yes—
156(C22⋊D71)⋊C4C23124yescomplemented
157(C22⋊D71)⋊C4C23148yescomplemented
158#14556086C23124yescomplemented
159C2×C4⋊Dic71C2313yes—
160C2×C4⋊Dic71C2313yes—
161C2×Dic71⋊C4C2311yescharacteristic
162C2×Dic71⋊C4C2313yes—
163C2×Dic71⋊C4C2316yes—
164C4⋊C4×D71C23124yescomplemented
165C2×C22⋊Dic71C2313yes—
166C2×C22⋊Dic71C2313yes—
167C2×(C2×D71)⋊C4C2311yescharacteristic
168C2×(C2×D71)⋊C4C2313yes—
169C2×(C2×D71)⋊C4C2313yes—
170C2×(C2×D71)⋊C4C2313yes—
171C2×(C2×D71)⋊C4C2316yes—
172C2×(C2×D71)⋊C4C2316yes—
173C22⋊C4×D71C23124yescomplemented
174C22⋊C4×D71C23124yescomplemented
175C2×C4×Dic71C2311yescharacteristic
176C2×C4×Dic71C2313yes—
177C2×C4×Dic71C2313yes—
178C42×D71C23124yescomplemented
179C2×#41×C71—28no—
180C2×#41×C71C2318yescomplemented
181C22×Q8×C71—28no—
182C22×Q8×C71C2313yes—
183C22×Q8×C71C2311yescharacteristic
184C22×Q8×C71C2318yescomplemented
185C22×D4×C71C2313yes—
186C22×D4×C71C2313yes—
187C23×C4×C71C2313yes—
188C23×C4×C71C2313yes—
189#124×C71C23124yescomplemented
190C22⋊Q8×C71C23124yescomplemented
191#121×C71C23124yescomplemented
192C4×Q8×C71C2318yescomplemented
193C4×D4×C71C23124yescomplemented
194C2×C4⋊C4×C71C2313yes—
195C2×C4⋊C4×C71C2313yes—
196C2×C22⋊C4×C71C2311yescharacteristic
197C2×C22⋊C4×C71C2313yes—
198C2×C22⋊C4×C71C2316yes—
199C2×C42×C71C2313yes—
200C23×D71—212no—
201C23×D71—212no—
202C23×D71—212no—
203C23×D71—212no—
204C23×D71—46no—
205C23×D71—46no—
206C23×D71C2413yes—
207C23×D71C24112yes—
208C23×D71C24112yes—
209C23×D71C2413yes—
210C23×D71C2411yescharacteristic
211#11765866—232no—
212#11765866—296no—
213#11765866—296no—
214#11765866C2×D4164yescomplemented
215#11765865—296no—
216#11765864—296no—
217C2×Dic142—212no—
218C2×Dic142C24112yes—
219Q8×D71—232no—
220C2×D284—224no—
221C2×D284—212no—
222C2×D284—212no—
223C2×D284—296no—
224C2×D284C2×D4124yescomplemented
225C2×D284C24112yes—
226C2×D284C24124yes—
227C2×D284C24112yes—
228C2×D284C24112yes—
229C2×C22⋊D71—224no—
230C2×C22⋊D71—212no—
231C2×C22⋊D71—412no—
232C2×C22⋊D71#4118yescomplemented
233C2×C22⋊D71C24112yes—
234C2×C22⋊D71C24124yes—
235C2×C22⋊D71C24124yes—
236C2×C22⋊D71C2414yes—
237D4×D71—296no—
238D4×D71—296no—
239C22×Dic71—24no—
240C22×Dic71—212no—
241C22×Dic71C2411yescharacteristic
242C22×Dic71C2413yes—
243C22×Dic71C2413yes—
244C22×Dic71C2414yes—
245C22×Dic71C24112yes—
246C22×Dic71C2411yescharacteristic
247C22×Dic71C2411yescharacteristic
248C2×C4×D71—212no—
249C2×C4×D71—212no—
250C2×C4×D71—212no—
251C2×C4×D71—212no—
252C2×C4×D71—24no—
253C2×C4×D71—212no—
254C2×C4×D71—212no—
255C2×C4×D71—296no—
256C2×C4×D71—296no—
257C2×C4×D71—46no—
258C2×C4×D71C2×D4124yescomplemented
259C2×C4×D71C2414yes—
260C2×C4×D71C24112yes—
261C2×C4×D71C24112yes—
262C2×C4×D71C24112yes—
263C2×C4×D71C24112yes—
264C2×C4×D71C24112yes—
265C2×C4×D71C24112yes—
266C2×C4×D71C24112yes—
267C2×C4×D71C24112yes—
268C4⋊Dic71C24112yes—
269C4⋊Dic71C24112yes—
270Dic71⋊C4C2414yes—
271Dic71⋊C4C24112yes—
272Dic71⋊C4C24124yes—
273C22⋊Dic71C24112yes—
274C22⋊Dic71C24112yes—
275(C2×D71)⋊C4C2414yes—
276(C2×D71)⋊C4C24112yes—
277(C2×D71)⋊C4C24112yes—
278(C2×D71)⋊C4C24112yes—
279(C2×D71)⋊C4C24124yes—
280(C2×D71)⋊C4C24124yes—
281C4×Dic71C2414yes—
282C4×Dic71C24112yes—
283C4×Dic71C24112yes—
284C24×C71C2413yes—
285C24×C71C2411yescharacteristic
286#41×C71—232no—
287C2×Q8×C71—232no—
288C2×Q8×C71—212no—
289C2×Q8×C71C2×D418yescomplemented
290C2×Q8×C71C24112yes—
291C2×Q8×C71C2414yes—
292C2×D4×C71—212no—
293C2×D4×C71—212no—
294C2×D4×C71C24112yes—
295C2×D4×C71C24112yes—
296C22×C4×C71—212no—
297C22×C4×C71—212no—
298C22×C4×C71C2411yescharacteristic
299C22×C4×C71C2411yescharacteristic
300C22×C4×C71C2413yes—
301C22×C4×C71C2413yes—
302C22×C4×C71C24112yes—
303C22×C4×C71C24112yes—
304C22×C4×C71C2413yes—
305C4⋊C4×C71C24112yes—
306C4⋊C4×C71C24112yes—
307C22⋊C4×C71C2414yes—
308C22⋊C4×C71C24112yes—
309C22⋊C4×C71C24124yes—
310C42×C71C24112yes—
311C23×C71—22no—
312C23×C71—22no—
313C23×C71—26no—
314C23×C71—26no—
315C23×C71—26no—
316C23×C71C2×#4114yescomplemented
317C23×C71C2516yes—
318C23×C71C2512yes—
319C23×C71C2511yescharacteristic
320C22×D71—22no—
321C22×D71—26no—
322C22×D71—26no—
323C22×D71—22no—
324C22×D71—26no—
325C22×D71—26no—
326C22×D71—224no—
327C22×D71—26no—
328C22×D71—224no—
329C22×D71—224no—
330C22×D71—224no—
331C22×D71—412no—
332C22×D71—412no—
333C22×D71—448no—
334C22×D71—448no—
335C22×D71C22×D4112yes—
336C22×D71C2×#4114yescomplemented
337C22×D71C2516yes—
338C22×D71C2516yes—
339C22×D71C2512yes—
340Q8×C71—224no—
341Q8×C71C22×D4116yescomplemented
342D4×C71—224no—
343D4×C71—224no—
344C2×C4×C71—22no—
345C2×C4×C71—26no—
346C2×C4×C71—26no—
347C2×C4×C71—22no—
348C2×C4×C71—224no—
349C2×C4×C71—224no—
350C2×C4×C71C22×D4112yes—
351C2×C4×C71C2512yes—
352C2×C4×C71C2516yes—
353C2×C4×C71C2516yes—
354C2×C4×C71C2512yes—
355C2×C4×C71C2516yes—
356C22⋊D71—248no—
357C22⋊D71—224no—
358C22⋊D71—424no—
359C22⋊D71C2×#41116yescomplemented
360C2×Dic71—22no—
361C2×Dic71—26no—
362C2×Dic71—26no—
363C2×Dic71—28no—
364C2×Dic71—224no—
365C2×Dic71C22×D414yes—
366C2×Dic71C2×#4114yescomplemented
367C2×Dic71C2516yes—
368C2×Dic71C2516yes—
369C2×Dic71C2512yes—
370C2×Dic71C2512yes—
371C2×Dic71C2512yes—
372D284—248no—
373D284—224no—
374D284—224no—
375D284C22×D4148yescomplemented
376C4×D71—224no—
377C4×D71—224no—
378C4×D71—224no—
379C4×D71—224no—
380C4×D71—28no—
381C4×D71—224no—
382C4×D71—224no—
383C4×D71—412no—
384C4×D71C22×D4148yescomplemented
385Dic142—224no—
386C22×C71—22no—
387C22×C71—22no—
388C22×C71—28no—
389C22×C71—26no—
390C22×C71—26no—
391C22×C71—26no—
392C22×C71—412no—
393C22×C71C23×D412yes—
394C22×C71C22×#4112yes—
395C22×C71C22×#4114yescomplemented
396C22×C71#58512yes—
397C22×C71C2611yescharacteristic
398C2×D71—22no—
399C2×D71—26no—
400C2×D71—26no—
401C2×D71—22no—
402C2×D71—28no—
403C2×D71—224no—
404C2×D71—26no—
405C2×D71—26no—
406C2×D71—26no—
407C2×D71—448no—
408C2×D71—448no—
409C2×D71—412no—
410C2×D71C23×D4112yes—
411C2×D71C22×#4114yescomplemented
412C4×C71—22no—
413C4×C71—26no—
414C4×C71—26no—
415C4×C71—22no—
416C4×C71C23×D4112yes—
417Dic71—26no—
418Dic71—22no—
419Dic71—26no—
420Dic71C23×D414yes—
421Dic71C22×#4114yescomplemented
422C2×D4×#41—711nomaximal, Sylow
423C2×C71—24no—
424C2×C71—46no—
425C2×C71D4×#4114yescomplemented
426C2×C71C24×D411yescharacteristic
427C2×C71C23×#4111yescharacteristic
428C2×C71C2×#58511yescharacteristic
429D71—24no—
430D71—212no—
431D71—46no—
432C23×#41—711no—
433C23×#41—711no—
434D4×#41—7132no—
435C2×#550—711no—
436C2×D4×Q8—711no—
437C2×#548—711no—
438C2×#548D7111yescharacteristic, complemented
439C2×#547—713no—
440C2×#546—713no—
441C2×#546—713no—
442C2×D42—713no—
443C2×#532—713no—
444C2×#525—713no—
445C2×#525—713no—
446C2×C4×#41—711no—
447C22×C4×D4—713no—
448C71C2×D4×#4111yescharacteristic, complemented, Sylow
449C22×#41—7116no—
450C22×#41—711no—
451C22×#41—713no—
452C22×#41—713no—
453C22×#41—711no—
454C22×#41—7116no—
455C22×#41—713no—
456C22×#41—713no—
457C22×#41—14216no—
458C22×#41—14216no—
459C22×#41C2×D7111yescharacteristic, complemented
460C23×Q8—711no—
461C23×Q8C2×D7111yescharacteristic, complemented
462C23×D4—713no—
463C23×D4—713no—
464C23×D4—713no—
465C24×C4—713no—
466C24×C4—713no—
467#550—7116no—
468D4×Q8—7116no—
469#548—7116no—
470#548C2×D71116yescomplemented
471#547—7148no—
472#546—7148no—
473#546—7148no—
474D42—7148no—
475#532—7148no—
476C2×C4⋊Q8—713no—
477C2×#127—713no—
478C2×#124—713no—
479C2×#124C2×D7113yescomplemented
480#525—7148no—
481#525—7148no—
482C2×#123—716no—
483C2×#123—716no—
484C2×C22⋊Q8—713no—
485C2×C22⋊Q8—713no—
486C2×C22⋊Q8—713no—
487C2×C22⋊Q8C2×D7113yescomplemented
488C2×#121—713no—
489C2×#121—713no—
490C2×#121—713no—
491C2×#121—716no—
492C2×#121—716no—
493C2×#121C2×D7113yescomplemented
494C2×#120—716no—
495C2×#120—716no—
496C4×#41—7116no—
497C2×C4×Q8—711no—
498C2×C4×Q8C2×D7111yescharacteristic, complemented
499C2×C4×D4—713no—
500C2×C4×D4—713no—
501C2×C4×D4—713no—
502C2×C4×D4—7148no—
503C2×C4×D4—713no—
504C2×C4×D4—713no—
505C2×C4×D4—711no—
506C2×C4×D4—713no—
507C2×C4×D4—716no—
508C2×C4×D4—713no—
509C2×C4×D4—713no—
510C2×C4×D4C2×D7113yescomplemented
511C2×#117—713no—
512C22×C4⋊C4—713no—
513C22×C22⋊C4—713no—
514C22×C22⋊C4—713no—
515C22×C42—713no—
516C25—713no—
517C25—713no—
518C2×#41—28no—
519C2×#41—7116no—
520C2×#41—718no—
521C2×#41—7124no—
522C2×#41—7124no—
523C2×#41—718no—
524C2×#41—7124no—
525C2×#41—7124no—
526C2×#41—14224no—
527C2×#41—14224no—
528C2×#41—14224no—
529C2×#41—14224no—
530C2×#41—142128no—
531C2×#41—142128no—
532C2×#41—1428no—
533C2×#41C22×D7118yescomplemented
534C22×Q8—28no—
535C22×Q8—718no—
536C22×Q8—713no—
537C22×Q8—1428no—
538C22×Q8C22×D7113yes—
539C22×Q8C22×D7111yescharacteristic
540C22×Q8C22×D7118yescomplemented
541C22×D4—716no—
542C22×D4—711no—
543C22×D4—713no—
544C22×D4—716no—
545C22×D4—7124no—
546C22×D4—7124no—
547C22×D4—713no—
548C22×D4—713no—
549C22×D4—716no—
550C22×D4—713no—
551C22×D4—7124no—
552C22×D4—14224no—
553C22×D4—14224no—
554C22×D4—14224no—
555C22×D4C22×D7113yes—
556C22×D4C22×D7113yes—
557C23×C4—713no—
558C23×C4—713no—
559C23×C4—711no—
560C23×C4—713no—
561C23×C4—713no—
562C23×C4—713no—
563C23×C4—713no—
564C23×C4—711no—
565C23×C4—713no—
566C23×C4—713no—
567C23×C4—713no—
568C23×C4—7124no—
569C23×C4—7124no—
570C23×C4—14224no—
571C23×C4—14224no—
572C23×C4C22×D7113yes—
573C23×C4C22×D7113yes—
574C4⋊Q8—7124no—
575#127—7124no—
576#124—7124no—
577#124C22×D71124yescomplemented
578#123—7148no—
579#123—7148no—
580C22⋊Q8—7124no—
581C22⋊Q8—7124no—
582C22⋊Q8—7124no—
583C22⋊Q8C22×D71124yescomplemented
584#121—7124no—
585#121—7124no—
586#121—7124no—
587#121—7148no—
588#121—7148no—
589#121C22×D71124yescomplemented
590#120—7148no—
591#120—7148no—
592C4×Q8—718no—
593C4×Q8C22×D7118yescomplemented
594C4×D4—7124no—
595C4×D4—7124no—
596C4×D4—7124no—
597C4×D4—7124no—
598C4×D4—7124no—
599C4×D4—718no—
600C4×D4—7124no—
601C4×D4—7148no—
602C4×D4—7124no—
603C4×D4—7124no—
604C4×D4C22×D71124yescomplemented
605#117—7124no—
606C2×C4⋊C4—711no—
607C2×C4⋊C4—713no—
608C2×C4⋊C4—713no—
609C2×C4⋊C4—713no—
610C2×C4⋊C4—716no—
611C2×C4⋊C4—7124no—
612C2×C4⋊C4C22×D7113yes—
613C2×C4⋊C4C22×D7113yes—
614C2×C22⋊C4—713no—
615C2×C22⋊C4—713no—
616C2×C22⋊C4—711no—
617C2×C22⋊C4—713no—
618C2×C22⋊C4—713no—
619C2×C22⋊C4—713no—
620C2×C22⋊C4—716no—
621C2×C22⋊C4—716no—
622C2×C22⋊C4—7124no—
623C2×C22⋊C4—7124no—
624C2×C22⋊C4C22×D7111yescharacteristic
625C2×C22⋊C4C22×D7113yes—
626C2×C22⋊C4C22×D7116yes—
627C2×C42—713no—
628C2×C42—711no—
629C2×C42—713no—
630C2×C42—7124no—
631C2×C42C22×D7113yes—
632C24—2846no—
633C24—2846no—
634C24—7112no—
635C24—7112no—
636C24—711no—
637C24—713no—
638C24—713no—
639C24—14212no—
640C24—14212no—
641C24—14212no—
642C24—14212no—
643C24C23×D7113yes—
644C24C23×D7111yescharacteristic
645#41—232no—
646#41—7164no—
647#41—14296no—
648#41—14296no—
649#41—14296no—
650#41—14296no—
651#41—14232no—
652C2×Q8—232no—
653C2×Q8—212no—
654C2×Q8—7112no—
655C2×Q8—14232no—
656C2×Q8—14212no—
657C2×Q8D4×D7118yescomplemented
658C2×Q8C23×D71112yes—
659C2×Q8C23×D7114yes—
660C2×D4—212no—
661C2×D4—212no—
662C2×D4—28412no—
663C2×D4—7124no—
664C2×D4—718no—
665C2×D4—714no—
666C2×D4—7112no—
667C2×D4—7124no—
668C2×D4—7124no—
669C2×D4—7112no—
670C2×D4—7112no—
671C2×D4—7124no—
672C2×D4—7112no—
673C2×D4—14296no—
674C2×D4—14212no—
675C2×D4—14224no—
676C2×D4—14212no—
677C2×D4—14296no—
678C2×D4—14296no—
679C2×D4—14224no—
680C2×D4—14212no—
681C2×D4C23×D71112yes—
682C2×D4C23×D71112yes—
683C22×C4—212no—
684C22×C4—212no—
685C22×C4—2846no—
686C22×C4—7112no—
687C22×C4—711no—
688C22×C4—711no—
689C22×C4—7124no—
690C22×C4—7112no—
691C22×C4—714no—
692C22×C4—7112no—
693C22×C4—713no—
694C22×C4—711no—
695C22×C4—713no—
696C22×C4—7112no—
697C22×C4—7112no—
698C22×C4—7112no—
699C22×C4—714no—
700C22×C4—7112no—
701C22×C4—7112no—
702C22×C4—7112no—
703C22×C4—1424no—
704C22×C4—14212no—
705C22×C4—14296no—
706C22×C4—14296no—
707C22×C4—14212no—
708C22×C4—14212no—
709C22×C4—14212no—
710C22×C4—1424no—
711C22×C4—14212no—
712C22×C4—14212no—
713C22×C4—14212no—
714C22×C4C23×D71112yes—
715C22×C4C23×D71112yes—
716C22×C4C23×D7111yescharacteristic
717C22×C4C23×D7113yes—
718C22×C4C23×D7111yescharacteristic
719C22×C4C23×D7113yes—
720C22×C4C23×D7113yes—
721C4⋊C4—714no—
722C4⋊C4—7112no—
723C4⋊C4—7124no—
724C4⋊C4—7112no—
725C4⋊C4—7112no—
726C4⋊C4C23×D71112yes—
727C4⋊C4C23×D71112yes—
728C22⋊C4—7112no—
729C22⋊C4—7112no—
730C22⋊C4—714no—
731C22⋊C4—7112no—
732C22⋊C4—7112no—
733C22⋊C4—7112no—
734C22⋊C4—7124no—
735C22⋊C4—7124no—
736C22⋊C4C23×D7114yes—
737C22⋊C4C23×D71112yes—
738C22⋊C4C23×D71124yes—
739C42—714no—
740C42—7112no—
741C42—7112no—
742C42C23×D71112yes—
743C23—22no—
744C23—22no—
745C23—26no—
746C23—26no—
747C23—26no—
748C23—28448no—
749C23—28412no—
750C23—28412no—
751C23—28448no—
752C23—7112no—
753C23—714no—
754C23—712no—
755C23—716no—
756C23—716no—
757C23—14224no—
758C23—14224no—
759C23—14224no—
760C23—1426no—
761C23—1426no—
762C23—14224no—
763C23—1426no—
764C23—1422no—
765C23—1426no—
766C23—1426no—
767C23—1422no—
768C23#41×D7114yescomplemented
769C23C24×D7116yes—
770C23C24×D7112yes—
771C23C24×D7111yescharacteristic
772Q8—224no—
773Q8—14224no—
774Q8C2×D4×D71116yescomplemented
775D4—224no—
776D4—224no—
777D4—28424no—
778D4—7116no—
779D4—7148no—
780D4—14248no—
781D4—14224no—
782D4—14224no—
783D4—14248no—
784D4—14224no—
785C2×C4—22no—
786C2×C4—26no—
787C2×C4—26no—
788C2×C4—22no—
789C2×C4—224no—
790C2×C4—224no—
791C2×C4—28412no—
792C2×C4—714no—
793C2×C4—714no—
794C2×C4—712no—
795C2×C4—712no—
796C2×C4—7148no—
797C2×C4—716no—
798C2×C4—712no—
799C2×C4—716no—
800C2×C4—1428no—
801C2×C4—14224no—
802C2×C4—14224no—
803C2×C4—14224no—
804C2×C4—14224no—
805C2×C4—1428no—
806C2×C4—14224no—
807C2×C4—1422no—
808C2×C4—1426no—
809C2×C4—1426no—
810C2×C4—14224no—
811C2×C4—14224no—
812C2×C4C2×D4×D71112yes—
813C2×C4C24×D7112yes—
814C2×C4C24×D7116yes—
815C2×C4C24×D7112yes—
816C2×C4C24×D7116yes—
817C2×C4C24×D7116yes—
818C22—28no—
819C22—22no—
820C22—22no—
821C22—26no—
822C22—26no—
823C22—26no—
824C22—412no—
825C22—28448no—
826C22—28448no—
827C22—28412no—
828C22—7112no—
829C22—714no—
830C22—1426no—
831C22—1426no—
832C22—1426no—
833C22—1428no—
834C22—14224no—
835C22—1422no—
836C22—1426no—
837C22—1426no—
838C22—1422no—
839C22C22×D4×D7112yes—
840C22C2×#41×D7112yes—
841C22C2×#41×D7114yescomplemented
842C22#1798683612yes—
843C22C25×D7111yescharacteristic
844C4—22no—
845C4—26no—
846C4—26no—
847C4—22no—
848C4—714no—
849C4—714no—
850C4—1422no—
851C4—1426no—
852C4—1426no—
853C4C22×D4×D71112yes—
854C2—24no—
855C2—46no—
856C2—2846no—
857C2—1424no—
858C2—14212no—
859C2#2260182914yesdirect product factor
860C2C23×D4×D7111yescharacteristic
861C2C22×#41×D7111yescharacteristic
862C2C2×#1798683611yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#548×C71C2
socleC23×C71C25
hypercenterC2×#548D71
hypocenterC71C2×D4×#41
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C23×#11765866C2semidirect
2. C22×#41×D71C2semidirect
3. #22601829C2direct (N × H)
4. C2×#17986668C2semidirect
5. C2×Q8×C22⋊D71C2semidirect
6. C2×#17986661C2semidirect
7. C2×#17986651C2semidirect
8. C2×#17986645C2semidirect
9. C2×#17986642C2semidirect
10. C2×#17986633C2semidirect
11. C2×#17986548C2semidirect
12. C2×#17986512C2semidirect
13. C2×#17986509C2semidirect
14. C2×C4×#11765866C2semidirect
15. C2×C4×D4×D71C2semidirect
16. C2×#548×C71C2semidirect
19. C22×#11765866C22semidirect
20. C22×#11765866C22semidirect
21. C22×#11765866C22semidirect
22. C22×#11765866C22semidirect
23. C22×#11765865C22semidirect
24. C22×#11765864C22semidirect
26. C2×#41×D71C22semidirect
27. C22×Q8×D71C22semidirect
28. C23×D284C22semidirect
30. C22×D4×D71C22semidirect
31. C23×C4×D71C22semidirect
32. C23×C4×D71C22semidirect
33. #17986668C22semidirect
34. Q8×C22⋊D71C22semidirect
35. #17986661C22semidirect
36. #17986651C22semidirect
37. #17986645C22semidirect
38. #17986642C22semidirect
39. #17986633C22semidirect
40. #17986548C22semidirect
41. C2×#14556126C22semidirect
42. C2×#14556124C22semidirect
43. C2×#14556116C22semidirect
44. #17986512C22semidirect
45. #17986509C22semidirect
46. C2×#14556113C22semidirect
47. C2×#14556110C22semidirect
48. C2×#14556108C22semidirect
49. C2×#14556107C22semidirect
50. C2×#14556104C22semidirect
51. C2×#14556103C22semidirect
52. C2×#14556102C22semidirect
53. C2×#14556101C22semidirect
54. C2×#14556101C22semidirect
55. C2×#14556099C22semidirect
56. C2×#14556098C22semidirect
57. C2×#14556096C22semidirect
58. C4×#11765866C22semidirect
59. C2×Q8×Dic71C22semidirect
60. C2×C4×D284C22semidirect
61. C2×C4×D284C22semidirect
62. C2×D4×Dic71C22semidirect
63. C2×#14556090C22semidirect
64. C2×#14556090C22semidirect
66. C2×C4×C22⋊D71C22semidirect
68. C2×(C22⋊D71)⋊C4C22semidirect
69. C2×(C22⋊D71)⋊C4C22semidirect
70. C4×D4×D71C22semidirect
71. C2×#14556086C22semidirect
72. C2×C4⋊C4×D71C22semidirect
73. C2×C22⋊C4×D71C22semidirect
74. C2×C22⋊C4×D71C22semidirect
75. C2×C42×D71C22semidirect
76. C22×#41×C71C22semidirect
77. C23×Q8×C71C22semidirect
78. #548×C71C22semidirect
79. C2×#124×C71C22semidirect
80. C2×C22⋊Q8×C71C22semidirect
81. C2×#121×C71C22semidirect
82. C2×C4×Q8×C71C22semidirect
83. C2×C4×D4×C71C22semidirect
90. C2×#11765866D4semidirect
92. C2×#11765866C23semidirect
93. C2×#11765866C23semidirect
94. C2×#11765866C23semidirect
96. C2×#11765865C23semidirect
98. C2×#11765864C23semidirect
102. C2×Q8×D71C23semidirect
108. C22×D284C23semidirect
116. C2×D4×D71C23semidirect
130. C22×C4×D71C23semidirect
131. C22×C4×D71C23semidirect
132. #14556126C23semidirect
133. #14556124C23semidirect
134. #14556116C23semidirect
135. #14556113C23semidirect
136. #14556110C23semidirect
137. #14556108C23semidirect
138. #14556107C23semidirect
139. #14556104C23semidirect
140. #14556103C23semidirect
141. #14556102C23semidirect
142. #14556101C23semidirect
143. #14556101C23semidirect
144. #14556099C23semidirect
145. #14556098C23semidirect
146. #14556096C23semidirect
147. Q8×Dic71C23semidirect
148. C4×D284C23semidirect
149. C4×D284C23semidirect
150. D4×Dic71C23semidirect
151. #14556090C23semidirect
152. #14556090C23semidirect
154. C4×C22⋊D71C23semidirect
156. (C22⋊D71)⋊C4C23semidirect
157. (C22⋊D71)⋊C4C23semidirect
158. #14556086C23semidirect
164. C4⋊C4×D71C23semidirect
173. C22⋊C4×D71C23semidirect
174. C22⋊C4×D71C23semidirect
178. C42×D71C23semidirect
180. C2×#41×C71C23semidirect
184. C22×Q8×C71C23semidirect
189. #124×C71C23semidirect
190. C22⋊Q8×C71C23semidirect
191. #121×C71C23semidirect
192. C4×Q8×C71C23semidirect
193. C4×D4×C71C23semidirect
214. #11765866C2×D4semidirect
224. C2×D284C2×D4semidirect
232. C2×C22⋊D71#41semidirect
258. C2×C4×D71C2×D4semidirect
289. C2×Q8×C71C2×D4semidirect
316. C23×C71C2×#41semidirect
336. C22×D71C2×#41semidirect
341. Q8×C71C22×D4semidirect
359. C22⋊D71C2×#41semidirect
366. C2×Dic71C2×#41semidirect
375. D284C22×D4semidirect
384. C4×D71C22×D4semidirect
395. C22×C71C22×#41semidirect
411. C2×D71C22×#41semidirect
421. Dic71C22×#41semidirect
425. C2×C71D4×#41semidirect
438. C2×#548D71semidirect
448. C71C2×D4×#41semidirect
459. C22×#41C2×D71semidirect
461. C23×Q8C2×D71semidirect
470. #548C2×D71semidirect
479. C2×#124C2×D71semidirect
487. C2×C22⋊Q8C2×D71semidirect
493. C2×#121C2×D71semidirect
498. C2×C4×Q8C2×D71semidirect
510. C2×C4×D4C2×D71semidirect
533. C2×#41C22×D71semidirect
540. C22×Q8C22×D71semidirect
577. #124C22×D71semidirect
583. C22⋊Q8C22×D71semidirect
589. #121C22×D71semidirect
593. C4×Q8C22×D71semidirect
604. C4×D4C22×D71semidirect
657. C2×Q8D4×D71semidirect
768. C23#41×D71semidirect
774. Q8C2×D4×D71semidirect
841. C22C2×#41×D71semidirect
859. C2#22601829direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#117658662
C22×#41×D712
#226018292
C2×#179866682
C2×Q8×C22⋊D712
C2×#179866612
C2×#179866512
C2×#179866452
C2×#179866422
C2×#179866332
C2×#179865482
C2×#179865122
C2×#179865092
C2×C4×#117658662
C2×C4×D4×D712
C2×#548×C712
C2×D4×#4171