Finite Group Databasebeta

← C2×#41×C22⋊D71 #32904409

Subgroups — C2×#41×C22⋊D71 #32904409

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
1C22×#41×D71C211yesmaximal, characteristic, complemented
2#41×C22⋊D71C2132yesmaximal, direct product factor
3C2×#17986668C211yesmaximal, characteristic, complemented
4C2×Q8×C22⋊D71C211yesmaximal, characteristic, complemented
5C2×#17986660C211yesmaximal, characteristic, complemented
6C2×#17986656C211yesmaximal, characteristic, complemented
7C2×#17986648C213yesmaximal, complemented
8C2×#17986643C213yesmaximal, complemented
9C2×#17986637C213yesmaximal, complemented
10C2×D4×C22⋊D71C213yesmaximal, complemented
11C2×#17986545C213yesmaximal, complemented
12C2×#17986510C213yesmaximal, complemented
13C2×#17986506C213yesmaximal, complemented
14C2×#41×Dic71C211yesmaximal, characteristic, complemented
15C22×C4×C22⋊D71C213yesmaximal, complemented
16C23×#41×C71C211yesmaximal, characteristic, complemented
17C22×#11765866C2211yescharacteristic, complemented
18C22×#11765865C2213yescomplemented
19C22×#11765864C2213yescomplemented
20C2×#41×D71—216no—
21C2×#41×D71C22116yescomplemented
22C22×Q8×D71C2211yescharacteristic, complemented
23C23×C22⋊D71C2213yes—
24C22×D4×D71C2213yescomplemented
25C23×C4×D71C2213yescomplemented
26#17986668C22116yescomplemented
27Q8×C22⋊D71C22116yescomplemented
28#17986660C22116yescomplemented
29#17986656C22116yescomplemented
30#17986648C22148yescomplemented
31#17986643C22148yescomplemented
32#17986637C22148yescomplemented
33D4×C22⋊D71C22148yescomplemented
34#17986545C22148yescomplemented
35C2×#14556126C2213yescomplemented
36C2×#14556124C2213yescomplemented
37C2×#14556117C2213yescomplemented
38C2×#14556115C2213yescomplemented
39#17986510C22148yescomplemented
40#17986506C22148yescomplemented
41C2×#14556111C2216yescomplemented
42C2×#14556109C2216yescomplemented
43C2×#14556107C2213yescomplemented
44C2×#14556107C2213yescomplemented
45C2×#14556104C2213yescomplemented
46C2×#14556104C2213yescomplemented
47C2×#14556102C2213yescomplemented
48C2×#14556102C2213yescomplemented
49C2×#14556100C2216yescomplemented
50C2×#14556100C2216yescomplemented
51C2×#14556099C2213yescomplemented
52C2×#14556099C2213yescomplemented
53C2×#14556097C2216yescomplemented
54C2×#14556096C2216yescomplemented
55#41×Dic71C22116yescomplemented
56C2×Q8×Dic71C2211yescharacteristic, complemented
57C2×Q8×Dic71C2211yescharacteristic, complemented
58C2×D4×Dic71C2213yescomplemented
59C2×D4×Dic71C2213yescomplemented
60C2×C4×C22⋊D71C2211yescharacteristic
61C2×C4×C22⋊D71C2213yes—
62C2×C4×C22⋊D71C2213yescomplemented
63C2×C4×C22⋊D71C2213yescomplemented
64C2×C4×C22⋊D71C2213yescomplemented
65C2×C4×C22⋊D71C2213yescomplemented
66C2×C4×C22⋊D71C2213yescomplemented
67C2×C4×C22⋊D71C2213yescomplemented
68C2×C4×C22⋊D71C2216yescomplemented
69C2×C4×C22⋊D71C22148yescomplemented
70C2×#14556087C2213yescomplemented
71C22×Dic71⋊C4C2213yescomplemented
72C22×C22⋊Dic71C2213yescomplemented
73C22×(C2×D71)⋊C4C2213yescomplemented
74C22×C4×Dic71C2213yescomplemented
75C22×#41×C71—216no—
76C22×#41×C71C2211yescharacteristic
77C22×#41×C71C2213yescomplemented
78C22×#41×C71C2211yescharacteristic, complemented
79C22×#41×C71C2213yescomplemented
80C22×#41×C71C22116yescomplemented
81C23×Q8×C71C2211yescharacteristic, complemented
82C23×D4×C71C2213yescomplemented
83C24×C4×C71C2213yescomplemented
84C24×D71C2313yes—
85C2×#11765866—28no—
86C2×#11765866C2318yescomplemented
87C2×#11765865—224no—
88C2×#11765865C23124yescomplemented
89C2×#11765864—224no—
90C2×#11765864C23124yescomplemented
91#41×D71—2128no—
92C22×Dic142C2313yes—
93C2×Q8×D71—28no—
94C2×Q8×D71C2318yescomplemented
95C22×D284C2313yes—
96C22×C22⋊D71—224no—
97C22×C22⋊D71C2316yes—
98C22×C22⋊D71C23124yes—
99C22×C22⋊D71C2313yes—
100C22×C22⋊D71C2313yes—
101C22×C22⋊D71C2313yes—
102C22×C22⋊D71C2316yes—
103C22×C22⋊D71C2311yescharacteristic
104C2×D4×D71—224no—
105C2×D4×D71C23124yescomplemented
106C23×Dic71C2313yes—
107C23×Dic71C2313yes—
108C23×Dic71C2313yes—
109C22×C4×D71—224no—
110C22×C4×D71C2311yescharacteristic
111C22×C4×D71C2313yes—
112C22×C4×D71C2313yes—
113C22×C4×D71C2313yes—
114C22×C4×D71C23124yescomplemented
115#14556126C23124yescomplemented
116#14556124C23124yescomplemented
117#14556117C23124yescomplemented
118#14556115C23124yescomplemented
119#14556111C23148yescomplemented
120#14556109C23148yescomplemented
121#14556107C23124yescomplemented
122#14556107C23124yescomplemented
123#14556104C23124yescomplemented
124#14556104C23124yescomplemented
125#14556102C23124yescomplemented
126#14556102C23124yescomplemented
127#14556100C23148yescomplemented
128#14556100C23148yescomplemented
129#14556099C23124yescomplemented
130#14556099C23124yescomplemented
131#14556097C23148yescomplemented
132#14556096C23148yescomplemented
133Q8×Dic71C2318yescomplemented
134Q8×Dic71C2318yescomplemented
135D4×Dic71C23124yescomplemented
136D4×Dic71C23124yescomplemented
137C4×C22⋊D71C23124yes—
138C4×C22⋊D71C2318yes—
139C4×C22⋊D71C23124yescomplemented
140C4×C22⋊D71C23124yescomplemented
141C4×C22⋊D71C23124yescomplemented
142C4×C22⋊D71C23124yescomplemented
143C4×C22⋊D71C23124yescomplemented
144C4×C22⋊D71C23124yescomplemented
145C4×C22⋊D71C23148yescomplemented
146#14556087C23124yescomplemented
147C2×C4⋊Dic71C2313yes—
148C2×C4⋊Dic71C2313yes—
149C2×Dic71⋊C4C2311yescharacteristic
150C2×Dic71⋊C4C2313yes—
151C2×Dic71⋊C4C2313yes—
152C2×Dic71⋊C4C2313yes—
153C2×Dic71⋊C4C2316yes—
154C2×Dic71⋊C4C23124yescomplemented
155C2×C22⋊Dic71C2311yescharacteristic
156C2×C22⋊Dic71C2313yes—
157C2×C22⋊Dic71C2313yes—
158C2×C22⋊Dic71C2313yes—
159C2×C22⋊Dic71C2316yes—
160C2×C22⋊Dic71C2316yes—
161C2×C22⋊Dic71C23124yescomplemented
162C2×(C2×D71)⋊C4C2311yescharacteristic
163C2×(C2×D71)⋊C4C2313yes—
164C2×(C2×D71)⋊C4C2313yes—
165C2×(C2×D71)⋊C4C2313yes—
166C2×(C2×D71)⋊C4C2316yes—
167C2×(C2×D71)⋊C4C23124yescomplemented
168C2×C4×Dic71C2311yescharacteristic
169C2×C4×Dic71C2313yes—
170C2×C4×Dic71C2313yes—
171C2×C4×Dic71C2313yes—
172C2×C4×Dic71C23124yescomplemented
173C25×C71C2313yes—
174C2×#41×C71—2128no—
175C2×#41×C71—28no—
176C2×#41×C71—224no—
177C2×#41×C71—224no—
178C2×#41×C71D4116yescomplemented
179C2×#41×C71C2318yes—
180C2×#41×C71C23124yescomplemented
181C2×#41×C71C2318yescomplemented
182C2×#41×C71C23124yescomplemented
183C22×Q8×C71—28no—
184C22×Q8×C71C2313yes—
185C22×Q8×C71C2311yescharacteristic
186C22×Q8×C71C2318yescomplemented
187C22×D4×C71—224no—
188C22×D4×C71C2316yes—
189C22×D4×C71C2313yes—
190C22×D4×C71C2313yes—
191C22×D4×C71C23124yescomplemented
192C23×C4×C71—224no—
193C23×C4×C71C2313yes—
194C23×C4×C71C2311yescharacteristic
195C23×C4×C71C2313yes—
196C23×C4×C71C2313yes—
197C23×C4×C71C2313yes—
198C23×C4×C71C2313yes—
199C23×C4×C71C23124yescomplemented
200C23×D71—212no—
201C23×D71—212no—
202C23×D71—46no—
203C23×D71C2413yes—
204C23×D71C24112yes—
205C23×D71C2411yescharacteristic
206#11765866—232no—
207#11765865—296no—
208#11765864—296no—
209C2×Dic142—212no—
210C2×Dic142C24112yes—
211Q8×D71—232no—
212C2×D284—212no—
213C2×D284C24112yes—
214C2×C22⋊D71—224no—
215C2×C22⋊D71—212no—
216C2×C22⋊D71—212no—
217C2×C22⋊D71—296no—
218C2×C22⋊D71—212no—
219C2×C22⋊D71—412no—
220C2×C22⋊D71#4118yesdirect product factor
221C2×C22⋊D71C24124yes—
222C2×C22⋊D71C24112yes—
223C2×C22⋊D71C24112yes—
224C2×C22⋊D71C24112yes—
225C2×C22⋊D71C24124yes—
226C2×C22⋊D71C2414yes—
227D4×D71—296no—
228C22×Dic71—212no—
229C22×Dic71—212no—
230C22×Dic71—46no—
231C22×Dic71C2411yescharacteristic
232C22×Dic71C2413yes—
233C22×Dic71C24112yes—
234C22×Dic71C2411yescharacteristic
235C22×Dic71C2413yes—
236C22×Dic71C2413yes—
237C22×Dic71C24112yes—
238C22×Dic71C24112yes—
239C22×Dic71C2411yescharacteristic
240C2×C4×D71—24no—
241C2×C4×D71—212no—
242C2×C4×D71—212no—
243C2×C4×D71—212no—
244C2×C4×D71—296no—
245C2×C4×D71C2414yes—
246C2×C4×D71C24112yes—
247C2×C4×D71C24112yes—
248C2×C4×D71C24112yes—
249C4⋊Dic71C24112yes—
250C4⋊Dic71C24112yes—
251Dic71⋊C4C2414yes—
252Dic71⋊C4C24112yes—
253Dic71⋊C4C24112yes—
254Dic71⋊C4C24112yes—
255Dic71⋊C4C24124yes—
256C22⋊Dic71C2414yes—
257C22⋊Dic71C24112yes—
258C22⋊Dic71C24112yes—
259C22⋊Dic71C24112yes—
260C22⋊Dic71C24124yes—
261C22⋊Dic71C24124yes—
262(C2×D71)⋊C4C2414yes—
263(C2×D71)⋊C4C24112yes—
264(C2×D71)⋊C4C24112yes—
265(C2×D71)⋊C4C24112yes—
266(C2×D71)⋊C4C24124yes—
267C4×Dic71C2414yes—
268C4×Dic71C24112yes—
269C4×Dic71C24112yes—
270C4×Dic71C24112yes—
271C24×C71—212no—
272C24×C71—212no—
273C24×C71—46no—
274C24×C71C2413yes—
275C24×C71C24112yes—
276C24×C71C2413yes—
277C24×C71C2411yescharacteristic
278#41×C71—232no—
279#41×C71—296no—
280#41×C71—296no—
281#41×C71C2×D4164yescomplemented
282C2×Q8×C71—232no—
283C2×Q8×C71—212no—
284C2×Q8×C71C2×D418yescomplemented
285C2×Q8×C71C24112yes—
286C2×Q8×C71C2414yes—
287C2×D4×C71—224no—
288C2×D4×C71—296no—
289C2×D4×C71—212no—
290C2×D4×C71C2×D4124yescomplemented
291C2×D4×C71C24124yes—
292C2×D4×C71C24112yes—
293C2×D4×C71C24112yes—
294C22×C4×C71—212no—
295C22×C4×C71—24no—
296C22×C4×C71—212no—
297C22×C4×C71—212no—
298C22×C4×C71—212no—
299C22×C4×C71—296no—
300C22×C4×C71C2×D4124yescomplemented
301C22×C4×C71C2411yescharacteristic
302C22×C4×C71C2413yes—
303C22×C4×C71C2414yes—
304C22×C4×C71C24112yes—
305C22×C4×C71C24112yes—
306C22×C4×C71C24112yes—
307C22×C4×C71C24112yes—
308C22×C4×C71C2413yes—
309C22×C4×C71C24112yes—
310C22×C4×C71C2411yescharacteristic
311C23×C71—22no—
312C23×C71—26no—
313C23×C71—22no—
314C23×C71—26no—
315C23×C71—224no—
316C23×C71—26no—
317C23×C71—26no—
318C23×C71—224no—
319C23×C71—26no—
320C23×C71—412no—
321C23×C71—448no—
322C23×C71C22×D4112yes—
323C23×C71C2×#4114yescomplemented
324C23×C71C2516yes—
325C23×C71C2516yes—
326C23×C71C2512yes—
327C23×C71C2511yescharacteristic
328C22×D71—22no—
329C22×D71—22no—
330C22×D71—224no—
331C22×D71—26no—
332C22×D71—26no—
333C22×D71—26no—
334C22×D71—224no—
335C22×D71—412no—
336C22×D71—448no—
337C22×D71C2×#4114yescomplemented
338C22×D71C2516yes—
339C22×D71C2512yes—
340Q8×C71—224no—
341Q8×C71C22×D4116yescomplemented
342D4×C71—248no—
343D4×C71—224no—
344D4×C71C22×D4148yescomplemented
345C2×C4×C71—22no—
346C2×C4×C71—26no—
347C2×C4×C71—224no—
348C2×C4×C71—28no—
349C2×C4×C71—224no—
350C2×C4×C71—224no—
351C2×C4×C71—224no—
352C2×C4×C71C22×D414yes—
353C2×C4×C71C22×D4112yes—
354C2×C4×C71C22×D4148yescomplemented
355C2×C4×C71C2512yes—
356C2×C4×C71C2516yes—
357C2×C4×C71C2512yes—
358C2×C4×C71C2516yes—
359C22⋊D71—248no—
360C22⋊D71—224no—
361C22⋊D71—224no—
362C22⋊D71—224no—
363C22⋊D71—424no—
364C22⋊D71C2×#41116yesdirect product factor
365C2×Dic71—22no—
366C2×Dic71—26no—
367C2×Dic71—224no—
368C2×Dic71—26no—
369C2×Dic71—22no—
370C2×Dic71—26no—
371C2×Dic71—224no—
372C2×Dic71—412no—
373C2×Dic71C2×#4114yescomplemented
374C2×Dic71C2512yes—
375C2×Dic71C2516yes—
376C2×Dic71C2516yes—
377C2×Dic71C2512yes—
378C2×Dic71C2516yes—
379C2×Dic71C2512yes—
380D284—224no—
381C4×D71—28no—
382C4×D71—224no—
383C4×D71—224no—
384C4×D71—224no—
385Dic142—224no—
386C22×C71—22no—
387C22×C71—26no—
388C22×C71—26no—
389C22×C71—22no—
390C22×C71—224no—
391C22×C71—28no—
392C22×C71—26no—
393C22×C71—26no—
394C22×C71—26no—
395C22×C71—448no—
396C22×C71—412no—
397C22×C71C23×D4112yes—
398C22×C71C23×D412yes—
399C22×C71C22×#4112yes—
400C22×C71C22×#4114yescomplemented
401C22×C71#58512yes—
402C22×C71C2611yescharacteristic
403C2×D71—22no—
404C2×D71—22no—
405C2×D71—28no—
406C2×D71—26no—
407C2×D71—26no—
408C2×D71—26no—
409C2×D71—448no—
410C2×D71—412no—
411C2×D71C22×#4114yescomplemented
412C4×C71—22no—
413C4×C71—26no—
414C4×C71C23×D4112yes—
415C4×C71C23×D414yes—
416Dic71—26no—
417Dic71—22no—
418Dic71—26no—
419Dic71—22no—
420Dic71—26no—
421Dic71C22×#4114yescomplemented
422C2×D4×#41—711nomaximal, Sylow
423C2×C71—212no—
424C2×C71—24no—
425C2×C71—46no—
426C2×C71D4×#4114yescomplemented
427C2×C71C24×D411yescharacteristic
428C2×C71C23×#4111yescharacteristic
429C2×C71C2×#58511yescharacteristic
430D71—24no—
431D71—46no—
432C23×#41—711no—
433C23×#41D7111yescharacteristic, complemented
434D4×#41—7132no—
435C2×#550—711no—
436C2×D4×Q8—711no—
437C2×#548—711no—
438C2×#548—711no—
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—216no—
450C22×#41—7116no—
451C22×#41—711no—
452C22×#41—713no—
453C22×#41—713no—
454C22×#41—14216no—
455C22×#41C2×D7111yescharacteristic
456C22×#41C2×D7113yescomplemented
457C22×#41C2×D7113yescomplemented
458C22×#41C2×D7111yescharacteristic, complemented
459C22×#41C2×D71116yescomplemented
460C23×Q8—711no—
461C23×Q8C2×D7111yescharacteristic, complemented
462C23×D4—713no—
463C23×D4—713no—
464C23×D4C2×D7113yescomplemented
465C24×C4—713no—
466C24×C4C2×D7113yescomplemented
467#550—7116no—
468D4×Q8—7116no—
469#548—7116no—
470#548—7116no—
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×#124—713no—
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⋊Q8—713no—
488C2×#121—713no—
489C2×#121—713no—
490C2×#121—716no—
491C2×#121—716no—
492C2×#121—713no—
493C2×#121—713no—
494C2×#120—716no—
495C2×#120—716no—
496C4×#41—7116no—
497C2×C4×Q8—711no—
498C2×C4×Q8—711no—
499C2×C4×D4—713no—
500C2×C4×D4—713no—
501C2×C4×D4—711no—
502C2×C4×D4—713no—
503C2×C4×D4—713no—
504C2×C4×D4—713no—
505C2×C4×D4—713no—
506C2×C4×D4—713no—
507C2×C4×D4—713no—
508C2×C4×D4—713no—
509C2×C4×D4—716no—
510C2×C4×D4—7148no—
511C2×#117—713no—
512C22×C4⋊C4—713no—
513C22×C22⋊C4—713no—
514C22×C22⋊C4—713no—
515C22×C42—713no—
516C25—713no—
517C25C22×D7113yes—
518C2×#41—2128no—
519C2×#41—28no—
520C2×#41—224no—
521C2×#41—224no—
522C2×#41—718no—
523C2×#41—7124no—
524C2×#41—7124no—
525C2×#41—142128no—
526C2×#41—1428no—
527C2×#41—14224no—
528C2×#41—14224no—
529C2×#41C22⋊D71116yesdirect product factor
530C2×#41C22×D7118yes—
531C2×#41C22×D71124yescomplemented
532C2×#41C22×D71124yescomplemented
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—224no—
542C22×D4—716no—
543C22×D4—711no—
544C22×D4—713no—
545C22×D4—713no—
546C22×D4—713no—
547C22×D4—7124no—
548C22×D4—716no—
549C22×D4—7124no—
550C22×D4—713no—
551C22×D4—14224no—
552C22×D4—14224no—
553C22×D4C22×D7116yes—
554C22×D4C22×D7113yes—
555C22×D4C22×D7113yes—
556C22×D4C22×D71124yescomplemented
557C23×C4—224no—
558C23×C4—713no—
559C23×C4—713no—
560C23×C4—713no—
561C23×C4—713no—
562C23×C4—713no—
563C23×C4—7124no—
564C23×C4—711no—
565C23×C4—713no—
566C23×C4—14224no—
567C23×C4C22×D7113yes—
568C23×C4C22×D7113yes—
569C23×C4C22×D7113yes—
570C23×C4C22×D7111yescharacteristic
571C23×C4C22×D7113yes—
572C23×C4C22×D7113yes—
573C23×C4C22×D71124yescomplemented
574C4⋊Q8—7124no—
575#127—7124no—
576#124—7124no—
577#124—7124no—
578#123—7148no—
579#123—7148no—
580C22⋊Q8—7124no—
581C22⋊Q8—7124no—
582C22⋊Q8—7124no—
583C22⋊Q8—7124no—
584#121—7124no—
585#121—7124no—
586#121—7148no—
587#121—7148no—
588#121—7124no—
589#121—7124no—
590#120—7148no—
591#120—7148no—
592C4×Q8—718no—
593C4×Q8—718no—
594C4×D4—7124no—
595C4×D4—7124no—
596C4×D4—718no—
597C4×D4—7124no—
598C4×D4—7124no—
599C4×D4—7124no—
600C4×D4—7124no—
601C4×D4—7124no—
602C4×D4—7124no—
603C4×D4—7124no—
604C4×D4—7148no—
605#117—7124no—
606C2×C4⋊C4—711no—
607C2×C4⋊C4—713no—
608C2×C4⋊C4—713no—
609C2×C4⋊C4—713no—
610C2×C4⋊C4—7124no—
611C2×C4⋊C4—713no—
612C2×C4⋊C4—713no—
613C2×C4⋊C4—716no—
614C2×C22⋊C4—711no—
615C2×C22⋊C4—713no—
616C2×C22⋊C4—713no—
617C2×C22⋊C4—713no—
618C2×C22⋊C4—7124no—
619C2×C22⋊C4—716no—
620C2×C22⋊C4—716no—
621C2×C22⋊C4—711no—
622C2×C22⋊C4—713no—
623C2×C22⋊C4—713no—
624C2×C22⋊C4—713no—
625C2×C22⋊C4—7124no—
626C2×C22⋊C4—716no—
627C2×C42—713no—
628C2×C42—713no—
629C2×C42—7124no—
630C2×C42—713no—
631C2×C42—711no—
632C24—212no—
633C24—212no—
634C24—46no—
635C24—2846no—
636C24—7112no—
637C24—711no—
638C24—713no—
639C24—14212no—
640C24—14212no—
641C24C23×D7113yes—
642C24C23×D71112yes—
643C24C23×D7113yes—
644C24C23×D7111yescharacteristic
645#41—232no—
646#41—296no—
647#41—296no—
648#41—14232no—
649#41—14296no—
650#41—14296no—
651#41C2×C22⋊D71164yesdirect product factor
652C2×Q8—232no—
653C2×Q8—212no—
654C2×Q8—7112no—
655C2×Q8—14232no—
656C2×Q8—14212no—
657C2×Q8C2×C22⋊D7118yescomplemented
658C2×Q8C23×D71112yes—
659C2×Q8C23×D7114yes—
660C2×D4—224no—
661C2×D4—296no—
662C2×D4—212no—
663C2×D4—28412no—
664C2×D4—7124no—
665C2×D4—718no—
666C2×D4—714no—
667C2×D4—7112no—
668C2×D4—7112no—
669C2×D4—7112no—
670C2×D4—7124no—
671C2×D4—7112no—
672C2×D4—14212no—
673C2×D4—14296no—
674C2×D4—14212no—
675C2×D4—14224no—
676C2×D4—14212no—
677C2×D4—14296no—
678C2×D4—14212no—
679C2×D4C2×C22⋊D71124yescomplemented
680C2×D4C23×D71124yes—
681C2×D4C23×D71112yes—
682C2×D4C23×D71112yes—
683C22×C4—212no—
684C22×C4—24no—
685C22×C4—212no—
686C22×C4—212no—
687C22×C4—212no—
688C22×C4—296no—
689C22×C4—2846no—
690C22×C4—7112no—
691C22×C4—711no—
692C22×C4—711no—
693C22×C4—713no—
694C22×C4—713no—
695C22×C4—7112no—
696C22×C4—711no—
697C22×C4—713no—
698C22×C4—7112no—
699C22×C4—714no—
700C22×C4—7112no—
701C22×C4—7112no—
702C22×C4—7112no—
703C22×C4—14212no—
704C22×C4—14212no—
705C22×C4—1424no—
706C22×C4—14212no—
707C22×C4—14212no—
708C22×C4—14212no—
709C22×C4—14296no—
710C22×C4C2×C22⋊D71124yescomplemented
711C22×C4C23×D7111yescharacteristic
712C22×C4C23×D7113yes—
713C22×C4C23×D71112yes—
714C22×C4C23×D7114yes—
715C22×C4C23×D71112yes—
716C22×C4C23×D71112yes—
717C22×C4C23×D71112yes—
718C22×C4C23×D7113yes—
719C22×C4C23×D71112yes—
720C22×C4C23×D7111yescharacteristic
721C4⋊C4—714no—
722C4⋊C4—7112no—
723C4⋊C4—7112no—
724C4⋊C4—7112no—
725C4⋊C4—7124no—
726C4⋊C4—7112no—
727C4⋊C4—7112no—
728C22⋊C4—714no—
729C22⋊C4—7112no—
730C22⋊C4—7112no—
731C22⋊C4—7112no—
732C22⋊C4—7124no—
733C22⋊C4—7124no—
734C22⋊C4—714no—
735C22⋊C4—7112no—
736C22⋊C4—7112no—
737C22⋊C4—7112no—
738C22⋊C4—7124no—
739C42—714no—
740C42—7112no—
741C42—7112no—
742C42—7112no—
743C23—22no—
744C23—26no—
745C23—26no—
746C23—22no—
747C23—224no—
748C23—26no—
749C23—26no—
750C23—224no—
751C23—26no—
752C23—412no—
753C23—448no—
754C23—28448no—
755C23—28412no—
756C23—714no—
757C23—712no—
758C23—716no—
759C23—14224no—
760C23—14224no—
761C23—1426no—
762C23—1426no—
763C23—1426no—
764C23—1422no—
765C23—1422no—
766C23C22×C22⋊D71112yes—
767C23#41×D7114yescomplemented
768C23C24×D7116yes—
769C23C24×D7116yes—
770C23C24×D7112yes—
771C23C24×D7111yescharacteristic
772Q8—224no—
773Q8—14224no—
774Q8C22×C22⋊D71116yescomplemented
775D4—248no—
776D4—224no—
777D4—28424no—
778D4—7116no—
779D4—14224no—
780D4—14224no—
781D4—14248no—
782D4—14224no—
783D4—14224no—
784D4C22×C22⋊D71148yescomplemented
785C2×C4—22no—
786C2×C4—26no—
787C2×C4—224no—
788C2×C4—28no—
789C2×C4—224no—
790C2×C4—224no—
791C2×C4—224no—
792C2×C4—28412no—
793C2×C4—714no—
794C2×C4—712no—
795C2×C4—712no—
796C2×C4—716no—
797C2×C4—716no—
798C2×C4—712no—
799C2×C4—716no—
800C2×C4—14224no—
801C2×C4—1422no—
802C2×C4—1426no—
803C2×C4—14224no—
804C2×C4—1426no—
805C2×C4—1422no—
806C2×C4—1426no—
807C2×C4—1428no—
808C2×C4—14224no—
809C2×C4—14224no—
810C2×C4—14224no—
811C2×C4C22×C22⋊D7114yes—
812C2×C4C22×C22⋊D71112yes—
813C2×C4C22×C22⋊D71148yescomplemented
814C2×C4C24×D7112yes—
815C2×C4C24×D7116yes—
816C2×C4C24×D7112yes—
817C2×C4C24×D7116yes—
818C22—28no—
819C22—224no—
820C22—22no—
821C22—26no—
822C22—26no—
823C22—22no—
824C22—26no—
825C22—26no—
826C22—26no—
827C22—448no—
828C22—412no—
829C22—28448no—
830C22—28412no—
831C22—714no—
832C22—1426no—
833C22—1426no—
834C22—1426no—
835C22—1428no—
836C22—1422no—
837C22—1422no—
838C22C23×C22⋊D71112yes—
839C22C23×C22⋊D7112yes—
840C22C2×#41×D7112yes—
841C22C2×#41×D7114yescomplemented
842C22#1798683512yes—
843C22C25×D7111yescharacteristic
844C4—22no—
845C4—26no—
846C4—714no—
847C4—1422no—
848C4—1426no—
849C4—1426no—
850C4—1422no—
851C4—1426no—
852C4C23×C22⋊D7114yes—
853C4C23×C22⋊D71112yes—
854C2—24no—
855C2—212no—
856C2—46no—
857C2—2846no—
858C2—1424no—
859C2#41×C22⋊D7114yesdirect product factor
860C2C24×C22⋊D7111yescharacteristic
861C2C22×#41×D7111yescharacteristic
862C2C2×#1798683511yescharacteristic
subgroupG/H
centerC22×C4C23×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC23×#41×C71C2
socleC23×C71C25
hypercenterC23×#41D71
hypocenterC71C2×D4×#41
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C23×#41

Complements

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

NH ≅ G/Ntype
1. C22×#41×D71C2semidirect
2. #41×C22⋊D71C2direct (N × H)
3. C2×#17986668C2semidirect
4. C2×Q8×C22⋊D71C2semidirect
5. C2×#17986660C2semidirect
6. C2×#17986656C2semidirect
7. C2×#17986648C2semidirect
8. C2×#17986643C2semidirect
9. C2×#17986637C2semidirect
10. C2×D4×C22⋊D71C2semidirect
11. C2×#17986545C2semidirect
12. C2×#17986510C2semidirect
13. C2×#17986506C2semidirect
14. C2×#41×Dic71C2semidirect
15. C22×C4×C22⋊D71C2semidirect
16. C23×#41×C71C2semidirect
17. C22×#11765866C22semidirect
18. C22×#11765865C22semidirect
19. C22×#11765864C22semidirect
21. C2×#41×D71C22semidirect
22. C22×Q8×D71C22semidirect
24. C22×D4×D71C22semidirect
25. C23×C4×D71C22semidirect
26. #17986668C22semidirect
27. Q8×C22⋊D71C22semidirect
28. #17986660C22semidirect
29. #17986656C22semidirect
30. #17986648C22semidirect
31. #17986643C22semidirect
32. #17986637C22semidirect
33. D4×C22⋊D71C22semidirect
34. #17986545C22semidirect
35. C2×#14556126C22semidirect
36. C2×#14556124C22semidirect
37. C2×#14556117C22semidirect
38. C2×#14556115C22semidirect
39. #17986510C22semidirect
40. #17986506C22semidirect
41. C2×#14556111C22semidirect
42. C2×#14556109C22semidirect
43. C2×#14556107C22semidirect
44. C2×#14556107C22semidirect
45. C2×#14556104C22semidirect
46. C2×#14556104C22semidirect
47. C2×#14556102C22semidirect
48. C2×#14556102C22semidirect
49. C2×#14556100C22semidirect
50. C2×#14556100C22semidirect
51. C2×#14556099C22semidirect
52. C2×#14556099C22semidirect
53. C2×#14556097C22semidirect
54. C2×#14556096C22semidirect
55. #41×Dic71C22semidirect
56. C2×Q8×Dic71C22semidirect
57. C2×Q8×Dic71C22semidirect
58. C2×D4×Dic71C22semidirect
59. C2×D4×Dic71C22semidirect
62. C2×C4×C22⋊D71C22semidirect
63. C2×C4×C22⋊D71C22semidirect
64. C2×C4×C22⋊D71C22semidirect
65. C2×C4×C22⋊D71C22semidirect
66. C2×C4×C22⋊D71C22semidirect
67. C2×C4×C22⋊D71C22semidirect
68. C2×C4×C22⋊D71C22semidirect
69. C2×C4×C22⋊D71C22semidirect
70. C2×#14556087C22semidirect
71. C22×Dic71⋊C4C22semidirect
72. C22×C22⋊Dic71C22semidirect
73. C22×(C2×D71)⋊C4C22semidirect
74. C22×C4×Dic71C22semidirect
77. C22×#41×C71C22semidirect
78. C22×#41×C71C22semidirect
79. C22×#41×C71C22semidirect
80. C22×#41×C71C22semidirect
81. C23×Q8×C71C22semidirect
82. C23×D4×C71C22semidirect
83. C24×C4×C71C22semidirect
86. C2×#11765866C23semidirect
88. C2×#11765865C23semidirect
90. C2×#11765864C23semidirect
94. C2×Q8×D71C23semidirect
105. C2×D4×D71C23semidirect
114. C22×C4×D71C23semidirect
115. #14556126C23semidirect
116. #14556124C23semidirect
117. #14556117C23semidirect
118. #14556115C23semidirect
119. #14556111C23semidirect
120. #14556109C23semidirect
121. #14556107C23semidirect
122. #14556107C23semidirect
123. #14556104C23semidirect
124. #14556104C23semidirect
125. #14556102C23semidirect
126. #14556102C23semidirect
127. #14556100C23semidirect
128. #14556100C23semidirect
129. #14556099C23semidirect
130. #14556099C23semidirect
131. #14556097C23semidirect
132. #14556096C23semidirect
133. Q8×Dic71C23semidirect
134. Q8×Dic71C23semidirect
135. D4×Dic71C23semidirect
136. D4×Dic71C23semidirect
139. C4×C22⋊D71C23semidirect
140. C4×C22⋊D71C23semidirect
141. C4×C22⋊D71C23semidirect
142. C4×C22⋊D71C23semidirect
143. C4×C22⋊D71C23semidirect
144. C4×C22⋊D71C23semidirect
145. C4×C22⋊D71C23semidirect
146. #14556087C23semidirect
154. C2×Dic71⋊C4C23semidirect
161. C2×C22⋊Dic71C23semidirect
167. C2×(C2×D71)⋊C4C23semidirect
172. C2×C4×Dic71C23semidirect
178. C2×#41×C71D4semidirect
180. C2×#41×C71C23semidirect
181. C2×#41×C71C23semidirect
182. C2×#41×C71C23semidirect
186. C22×Q8×C71C23semidirect
191. C22×D4×C71C23semidirect
199. C23×C4×C71C23semidirect
220. C2×C22⋊D71#41direct (N × H)
281. #41×C71C2×D4semidirect
284. C2×Q8×C71C2×D4semidirect
290. C2×D4×C71C2×D4semidirect
300. C22×C4×C71C2×D4semidirect
323. C23×C71C2×#41semidirect
337. C22×D71C2×#41semidirect
341. Q8×C71C22×D4semidirect
344. D4×C71C22×D4semidirect
354. C2×C4×C71C22×D4semidirect
364. C22⋊D71C2×#41direct (N × H)
373. C2×Dic71C2×#41semidirect
400. C22×C71C22×#41semidirect
411. C2×D71C22×#41semidirect
421. Dic71C22×#41semidirect
426. C2×C71D4×#41semidirect
433. C23×#41D71semidirect
448. C71C2×D4×#41semidirect
456. C22×#41C2×D71semidirect
457. C22×#41C2×D71semidirect
458. C22×#41C2×D71semidirect
459. C22×#41C2×D71semidirect
461. C23×Q8C2×D71semidirect
464. C23×D4C2×D71semidirect
466. C24×C4C2×D71semidirect
529. C2×#41C22⋊D71direct (N × H)
531. C2×#41C22×D71semidirect
532. C2×#41C22×D71semidirect
533. C2×#41C22×D71semidirect
540. C22×Q8C22×D71semidirect
556. C22×D4C22×D71semidirect
573. C23×C4C22×D71semidirect
651. #41C2×C22⋊D71direct (N × H)
657. C2×Q8C2×C22⋊D71semidirect
679. C2×D4C2×C22⋊D71semidirect
710. C22×C4C2×C22⋊D71semidirect
767. C23#41×D71semidirect
774. Q8C22×C22⋊D71semidirect
784. D4C22×C22⋊D71semidirect
813. C2×C4C22×C22⋊D71semidirect
841. C22C2×#41×D71semidirect
859. C2#41×C22⋊D71direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41×D712
#41×C22⋊D712
C2×#179866682
C2×Q8×C22⋊D712
C2×#179866602
C2×#179866562
C2×#179866482
C2×#179866432
C2×#179866372
C2×D4×C22⋊D712
C2×#179865452
C2×#179865102
C2×#179865062
C2×#41×Dic712
C22×C4×C22⋊D712
C23×#41×C712
C2×D4×#4171