Finite Group Databasebeta

← C2×#22602008 #32905764

Subgroups — C2×#22602008 #32905764

Order 18176.

12366 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×#14556174C211yesmaximal, characteristic, complemented
2C22×#41×D71C211yesmaximal, characteristic, complemented
3#22602008C2132yesmaximal, direct product factor
4C2×#17986668C211yesmaximal, characteristic, complemented
5C2×#17986661C211yesmaximal, characteristic, complemented
6C2×#17986656C211yesmaximal, characteristic, complemented
7C2×#17986646C213yesmaximal, complemented
8C2×#17986645C213yesmaximal, complemented
9C2×#17986634C213yesmaximal, complemented
10C2×#17986633C213yesmaximal, complemented
11C2×#17986578C213yesmaximal, complemented
12C2×#17986562C213yesmaximal, complemented
13C2×#17986508C213yesmaximal, complemented
14C2×#121×D71C213yesmaximal, complemented
15C2×#17986481C211yesmaximal, characteristic, complemented
16C2×#550×C71C211yesmaximal, characteristic, complemented
17C2×#14556174—216no—
18C2×#14556174C22116yescomplemented
19C22×#11765866C2211yescharacteristic
20C22×#11765866C2211yescharacteristic, complemented
21C22×#11765865C2213yescomplemented
22C22×#11765865C2213yescomplemented
23C22×#11765864C2213yescomplemented
24C2×#41×D71—216no—
25C2×#41×D71C22116yescomplemented
26C22×Q8×D71C2211yescharacteristic, complemented
27C23×D284C2213yescomplemented
28C22×D4×D71C2213yescomplemented
29C22×D4×D71C2213yescomplemented
30C22×D4×D71C2213yescomplemented
31C22×D4×D71C2216yescomplemented
32C23×C4×D71C2213yescomplemented
33#17986668C22116yescomplemented
34#17986661C22116yescomplemented
35#17986656C22116yescomplemented
36#17986646C22148yescomplemented
37#17986645C22148yescomplemented
38#17986634C22148yescomplemented
39#17986633C22148yescomplemented
40#17986578C22148yescomplemented
41#17986562C22148yescomplemented
42C2×#14556124C2213yescomplemented
43C2×#14556116C2213yescomplemented
44C2×#14556115C2213yescomplemented
45#17986508C22148yescomplemented
46C2×#14556113C2213yescomplemented
47C2×#14556110C2213yescomplemented
48C2×#14556108C2213yescomplemented
49C2×#14556107C2213yescomplemented
50C2×#14556106C2211yescharacteristic, complemented
51C2×#14556105C2213yescomplemented
52C2×#14556103C2213yescomplemented
53C2×#14556102C2213yescomplemented
54C2×#14556101C2216yescomplemented
55C2×#14556101C2213yescomplemented
56C2×#14556100C2216yescomplemented
57C2×#14556100C2213yescomplemented
58C2×#14556099C2216yescomplemented
59C2×#14556099C2213yescomplemented
60C2×#14556099C2213yescomplemented
61#121×D71C22148yescomplemented
62C2×#14556098C2213yescomplemented
63C2×#14556096C2216yescomplemented
64C2×#14556096C2213yescomplemented
65C2×#14556096C2216yescomplemented
66#17986481C22116yescomplemented
67C2×Q8×Dic71C2211yescharacteristic, complemented
68C2×C4×D284C2213yescomplemented
69C2×C4×D284C2213yescomplemented
70C2×#14556090C2213yescomplemented
71C2×C4×C22⋊D71C2213yescomplemented
72C2×C4×C22⋊D71C2213yescomplemented
73C2×#14556085C2213yescomplemented
74C2×C4⋊C4×D71C2213yescomplemented
75C2×C22⋊C4×D71C2216yescomplemented
76C22×#41×C71C2211yescharacteristic, complemented
77C22×#41×C71C2211yescharacteristic, complemented
78#550×C71C22116yescomplemented
79C2×#127×C71C2213yescomplemented
80C2×#121×C71C2213yescomplemented
81C2×#121×C71C2213yescomplemented
82C2×C4×Q8×C71C2211yescharacteristic, complemented
83C2×C4×D4×C71C2213yescomplemented
84C24×D71C2313yes—
85C24×D71C2316yes—
86#14556174—2128no—
87C2×#11765866—28no—
88C2×#11765866D4116yescomplemented
89C2×#11765866C2318yes—
90C2×#11765866C2318yescomplemented
91C2×#11765865—224no—
92C2×#11765865—224no—
93C2×#11765865C23124yescomplemented
94C2×#11765865C23124yescomplemented
95C2×#11765864—224no—
96C2×#11765864C23124yescomplemented
97#41×D71—2128no—
98C22×Dic142C2313yes—
99C22×Dic142C2311yescharacteristic
100C2×Q8×D71—28no—
101C2×Q8×D71C2318yescomplemented
102C22×D284—224no—
103C22×D284C2313yes—
104C22×D284C2313yes—
105C22×D284C2313yes—
106C22×D284C2313yes—
107C22×D284C23124yescomplemented
108C22×C22⋊D71C2313yes—
109C22×C22⋊D71C2313yes—
110C22×C22⋊D71C2313yes—
111C22×C22⋊D71C2316yes—
112C22×C22⋊D71C2316yes—
113C22×C22⋊D71C2313yes—
114C2×D4×D71—224no—
115C2×D4×D71—224no—
116C2×D4×D71—224no—
117C2×D4×D71—424no—
118C2×D4×D71C23124yescomplemented
119C2×D4×D71C23124yescomplemented
120C2×D4×D71C23124yescomplemented
121C2×D4×D71C23148yescomplemented
122C23×Dic71C2313yes—
123C22×C4×D71—224no—
124C22×C4×D71C2311yescharacteristic
125C22×C4×D71C2313yes—
126C22×C4×D71C2313yes—
127C22×C4×D71C2313yes—
128C22×C4×D71C2316yes—
129C22×C4×D71C2313yes—
130C22×C4×D71C23124yescomplemented
131#14556124C23124yescomplemented
132#14556116C23124yescomplemented
133#14556115C23124yescomplemented
134#14556113C23124yescomplemented
135#14556110C23124yescomplemented
136#14556108C23124yescomplemented
137#14556107C23124yescomplemented
138#14556106C2318yescomplemented
139#14556105C23124yescomplemented
140#14556103C23124yescomplemented
141#14556102C23124yescomplemented
142#14556101C23148yescomplemented
143#14556101C23124yescomplemented
144#14556100C23124yescomplemented
145#14556100C23148yescomplemented
146#14556099C23148yescomplemented
147#14556099C23124yescomplemented
148#14556099C23124yescomplemented
149#14556098C23124yescomplemented
150#14556096C23148yescomplemented
151#14556096C23148yescomplemented
152#14556096C23124yescomplemented
153Q8×Dic71C2318yescomplemented
154C4×D284C23124yescomplemented
155C4×D284C23124yescomplemented
156#14556090C23124yescomplemented
157C4×C22⋊D71C23124yescomplemented
158C4×C22⋊D71C23124yescomplemented
159#14556085C23124yescomplemented
160C2×C4⋊Dic71C2313yes—
161C2×C4⋊Dic71C2313yes—
162C2×Dic71⋊C4C2313yes—
163C2×Dic71⋊C4C2311yescharacteristic
164C2×Dic71⋊C4C2311yescharacteristic
165C2×Dic71⋊C4C2313yes—
166C4⋊C4×D71C23124yescomplemented
167C2×C22⋊Dic71C2316yes—
168C2×C22⋊Dic71C2313yes—
169C2×C22⋊Dic71C2313yes—
170C2×(C2×D71)⋊C4C2313yes—
171C2×(C2×D71)⋊C4C2316yes—
172C2×(C2×D71)⋊C4C2313yes—
173C2×(C2×D71)⋊C4C2313yes—
174C2×(C2×D71)⋊C4C2311yescharacteristic
175C2×(C2×D71)⋊C4C2311yescharacteristic
176C2×(C2×D71)⋊C4C2313yes—
177C22⋊C4×D71C23148yescomplemented
178C2×C4×Dic71C2313yes—
179C2×#41×C71—28no—
180C2×#41×C71—28no—
181C2×#41×C71C2318yescomplemented
182C2×#41×C71C2318yescomplemented
183C22×Q8×C71C2311yescharacteristic
184C22×D4×C71C2313yes—
185C22×D4×C71C2313yes—
186C22×D4×C71C2316yes—
187C22×D4×C71C2313yes—
188C23×C4×C71C2313yes—
189C23×C4×C71C2313yes—
190#127×C71C23124yescomplemented
191#121×C71C23124yescomplemented
192#121×C71C23124yescomplemented
193C4×Q8×C71C2318yescomplemented
194C4×D4×C71C23124yescomplemented
195C2×C4⋊C4×C71C2311yescharacteristic
196C2×C4⋊C4×C71C2313yes—
197C2×C22⋊C4×C71C2313yes—
198C2×C22⋊C4×C71C2313yes—
199C2×C42×C71C2313yes—
200C23×D71—212no—
201C23×D71—212no—
202C23×D71—224no—
203C23×D71—46no—
204C23×D71—412no—
205C23×D71—412no—
206C23×D71C2413yes—
207C23×D71C24112yes—
208C23×D71C2413yes—
209C23×D71C2411yescharacteristic
210C23×D71C24124yes—
211#11765866—232no—
212#11765866C2×D4164yescomplemented
213#11765865—296no—
214#11765865—296no—
215#11765864—296no—
216C2×Dic142—212no—
217C2×Dic142—24no—
218C2×Dic142C24112yes—
219C2×Dic142C2414yes—
220Q8×D71—232no—
221C2×D284—212no—
222C2×D284—212no—
223C2×D284—212no—
224C2×D284—296no—
225C2×D284C2×D4124yescomplemented
226C2×D284C24112yes—
227C2×D284C24112yes—
228C2×D284C24112yes—
229C2×D284C24112yes—
230C2×C22⋊D71—212no—
231C2×C22⋊D71—224no—
232C2×C22⋊D71—212no—
233C2×C22⋊D71—212no—
234C2×C22⋊D71—412no—
235C2×C22⋊D71—46no—
236C2×C22⋊D71C24112yes—
237C2×C22⋊D71C24112yes—
238C2×C22⋊D71C24112yes—
239C2×C22⋊D71C24124yes—
240C2×C22⋊D71C24124yes—
241C2×C22⋊D71C24112yes—
242D4×D71—296no—
243D4×D71—296no—
244D4×D71—296no—
245D4×D71—496no—
246C22×Dic71—212no—
247C22×Dic71C2411yescharacteristic
248C22×Dic71C2413yes—
249C22×Dic71C2413yes—
250C22×Dic71C24112yes—
251C22×Dic71C2411yescharacteristic
252C22×Dic71C2411yescharacteristic
253C2×C4×D71—212no—
254C2×C4×D71—212no—
255C2×C4×D71—212no—
256C2×C4×D71—24no—
257C2×C4×D71—296no—
258C2×C4×D71—412no—
259C2×C4×D71C2×D4124yescomplemented
260C2×C4×D71C2414yes—
261C2×C4×D71C24112yes—
262C2×C4×D71C24112yes—
263C2×C4×D71C24112yes—
264C2×C4×D71C24124yes—
265C2×C4×D71C24112yes—
266C4⋊Dic71C24112yes—
267C4⋊Dic71C24112yes—
268Dic71⋊C4C24112yes—
269Dic71⋊C4C2414yes—
270Dic71⋊C4C2414yes—
271Dic71⋊C4C24112yes—
272C22⋊Dic71C24124yes—
273C22⋊Dic71C24112yes—
274C22⋊Dic71C24112yes—
275(C2×D71)⋊C4C24112yes—
276(C2×D71)⋊C4C24124yes—
277(C2×D71)⋊C4C24112yes—
278(C2×D71)⋊C4C24112yes—
279(C2×D71)⋊C4C2414yes—
280(C2×D71)⋊C4C2414yes—
281(C2×D71)⋊C4C24112yes—
282C4×Dic71C24112yes—
283C24×C71C2413yes—
284C24×C71C2413yes—
285#41×C71—232no—
286#41×C71—232no—
287C2×Q8×C71C2×D418yescomplemented
288C2×Q8×C71C2414yes—
289C2×D4×C71—212no—
290C2×D4×C71—212no—
291C2×D4×C71—412no—
292C2×D4×C71—46no—
293C2×D4×C71C24112yes—
294C2×D4×C71C24112yes—
295C2×D4×C71C24124yes—
296C2×D4×C71C24112yes—
297C22×C4×C71—212no—
298C22×C4×C71—212no—
299C22×C4×C71C2411yescharacteristic
300C22×C4×C71C2413yes—
301C22×C4×C71C24112yes—
302C22×C4×C71C2411yescharacteristic
303C22×C4×C71C24112yes—
304C22×C4×C71C2411yescharacteristic
305C22×C4×C71C2413yes—
306C4⋊C4×C71C2414yes—
307C4⋊C4×C71C24112yes—
308C22⋊C4×C71C24112yes—
309C22⋊C4×C71C24112yes—
310C42×C71C24112yes—
311C23×C71—26no—
312C23×C71—26no—
313C23×C71—26no—
314C23×C71—26no—
315C23×C71—26no—
316C23×C71—26no—
317C23×C71C2516yes—
318C23×C71C2516yes—
319C23×C71C2511yescharacteristic
320C22×D71—22no—
321C22×D71—26no—
322C22×D71—22no—
323C22×D71—26no—
324C22×D71—26no—
325C22×D71—26no—
326C22×D71—26no—
327C22×D71—224no—
328C22×D71—224no—
329C22×D71—248no—
330C22×D71—412no—
331C22×D71—448no—
332C22×D71—424no—
333C22×D71—424no—
334C22×D71—848no—
335C22×D71C22×D4112yes—
336C22×D71H(5,𝔽2)14yescomplemented
337C22×D71C2516yes—
338C22×D71C2516yes—
339C22×D71C2512yes—
340Q8×C71C22×D4116yescomplemented
341D4×C71—224no—
342D4×C71—224no—
343D4×C71—412no—
344D4×C71—424no—
345C2×C4×C71—22no—
346C2×C4×C71—22no—
347C2×C4×C71—26no—
348C2×C4×C71—22no—
349C2×C4×C71—224no—
350C2×C4×C71—224no—
351C2×C4×C71C22×D4112yes—
352C2×C4×C71C2512yes—
353C2×C4×C71C2516yes—
354C2×C4×C71C2512yes—
355C2×C4×C71C2512yes—
356C2×C4×C71C2516yes—
357C22⋊D71—224no—
358C22⋊D71—248no—
359C22⋊D71—224no—
360C22⋊D71—224no—
361C22⋊D71—424no—
362C22⋊D71—412no—
363C2×Dic71—22no—
364C2×Dic71—26no—
365C2×Dic71—26no—
366C2×Dic71—22no—
367C2×Dic71—224no—
368C2×Dic71C22×D414yes—
369C2×Dic71C2512yes—
370C2×Dic71C2516yes—
371C2×Dic71C2516yes—
372C2×Dic71C2512yes—
373C2×Dic71C2512yes—
374D284—224no—
375D284—224no—
376D284—224no—
377D284C22×D4148yescomplemented
378C4×D71—224no—
379C4×D71—224no—
380C4×D71—224no—
381C4×D71—28no—
382C4×D71—424no—
383C4×D71C22×D4148yescomplemented
384Dic142—224no—
385Dic142—28no—
386C22×C71—26no—
387C22×C71—26no—
388C22×C71—26no—
389C22×C71—26no—
390C22×C71—26no—
391C22×C71—26no—
392C22×C71—412no—
393C22×C71—412no—
394C22×C71C23×D412yes—
395C22×C71C2×H(5,𝔽2)12yes—
396C22×C71#58512yes—
397C22×C71C2611yescharacteristic
398C2×D71—22no—
399C2×D71—26no—
400C2×D71—22no—
401C2×D71—26no—
402C2×D71—28no—
403C2×D71—224no—
404C2×D71—26no—
405C2×D71—26no—
406C2×D71—26no—
407C2×D71—448no—
408C2×D71—412no—
409C2×D71—848no—
410C2×D71C23×D4112yes—
411C2×D71C2×H(5,𝔽2)14yescomplemented
412C4×C71—22no—
413C4×C71—22no—
414C4×C71—26no—
415C4×C71—22no—
416C4×C71C23×D4112yes—
417Dic71—26no—
418Dic71—22no—
419Dic71—26no—
420Dic71—22no—
421Dic71C23×D414yes—
422C2×#3488—711nomaximal, Sylow
423C2×C71—46no—
424C2×C71—46no—
425C2×C71#348814yescomplemented
426C2×C71C24×D411yescharacteristic
427C2×C71C22×H(5,𝔽2)11yescharacteristic
428C2×C71C2×#58511yescharacteristic
429D71—24no—
430D71—212no—
431D71—46no—
432C22×H(5,𝔽2)—711no—
433C23×#41—711no—
434#3488—7132no—
435C2×#550—711no—
436C2×#550D7111yescharacteristic, complemented
437C2×#548—711no—
438C2×#548—711no—
439C2×#546—713no—
440C2×#546—713no—
441C2×D42—713no—
442C2×D42—713no—
443C2×#537—713no—
444C2×#535—713no—
445C2×#525—713no—
446C22×#121—713no—
447C2×#520—711no—
448C71C2×#348811yescharacteristic, complemented, Sylow
449C2×H(5,𝔽2)—7116no—
450C2×H(5,𝔽2)—14216no—
451C22×#41—7116no—
452C22×#41—711no—
453C22×#41—711no—
454C22×#41—713no—
455C22×#41—713no—
456C22×#41—713no—
457C22×#41—14216no—
458C22×#41C2×D7111yescharacteristic, complemented
459C22×#41C2×D7111yescharacteristic, complemented
460C23×Q8—711no—
461C23×D4—716no—
462C23×D4—713no—
463C23×D4—713no—
464C23×D4—713no—
465C23×D4—713no—
466C24×C4—713no—
467#550—7116no—
468#550C2×D71116yescomplemented
469#548—7116no—
470#548—7116no—
471#546—7148no—
472#546—7148no—
473D42—7148no—
474D42—7148no—
475#537—7148no—
476#535—7148no—
477C2×#127—713no—
478C2×#127C2×D7113yescomplemented
479C2×#124—713no—
480C2×#124—713no—
481#525—7148no—
482C2×#123—713no—
483C2×#123—713no—
484C2×C22⋊Q8—713no—
485C2×C22⋊Q8—711no—
486C2×C22⋊Q8—713no—
487C2×C22⋊Q8—713no—
488C2×#121—716no—
489C2×#121—713no—
490C2×#121—713no—
491C2×#121—716no—
492C2×#121—713no—
493C2×#121—713no—
494C2×#121—7148no—
495C2×#121—713no—
496C2×#121—713no—
497C2×#121—716no—
498C2×#121C2×D7113yescomplemented
499C2×#121C2×D7113yescomplemented
500C2×#120—713no—
501C2×#120—716no—
502C2×#120—716no—
503C2×#120—713no—
504#520—7116no—
505C2×C4×Q8—711no—
506C2×C4×Q8C2×D7111yescharacteristic, complemented
507C2×C4×D4—713no—
508C2×C4×D4—713no—
509C2×C4×D4—713no—
510C2×C4×D4—713no—
511C2×C4×D4—713no—
512C2×C4×D4C2×D7113yescomplemented
513C2×#117—713no—
514C22×C4⋊C4—713no—
515C22×C22⋊C4—716no—
516C25—716no—
517C25—713no—
518H(5,𝔽2)—142128no—
519C2×#41—28no—
520C2×#41—28no—
521C2×#41—7116no—
522C2×#41—718no—
523C2×#41—718no—
524C2×#41—7124no—
525C2×#41—7124no—
526C2×#41—7124no—
527C2×#41—14224no—
528C2×#41—14224no—
529C2×#41—14224no—
530C2×#41—142128no—
531C2×#41—1428no—
532C2×#41C22×D7118yescomplemented
533C2×#41C22×D7118yescomplemented
534C22×Q8—718no—
535C22×Q8—711no—
536C22×Q8—713no—
537C22×Q8—1428no—
538C22×Q8C22×D7111yescharacteristic
539C22×D4—28424no—
540C22×D4—713no—
541C22×D4—716no—
542C22×D4—7148no—
543C22×D4—713no—
544C22×D4—716no—
545C22×D4—713no—
546C22×D4—713no—
547C22×D4—7124no—
548C22×D4—7124no—
549C22×D4—7124no—
550C22×D4—713no—
551C22×D4—713no—
552C22×D4—713no—
553C22×D4—713no—
554C22×D4—7124no—
555C22×D4—14224no—
556C22×D4—14224no—
557C22×D4—14224no—
558C22×D4—14224no—
559C22×D4C22×D7113yes—
560C22×D4C22×D7113yes—
561C22×D4C22×D7113yes—
562C22×D4C22×D7116yes—
563C23×C4—716no—
564C23×C4—713no—
565C23×C4—713no—
566C23×C4—713no—
567C23×C4—713no—
568C23×C4—713no—
569C23×C4—711no—
570C23×C4—7124no—
571C23×C4—14224no—
572C23×C4C22×D7113yes—
573C23×C4C22×D7113yes—
574#127—7124no—
575#127C22×D71124yescomplemented
576#124—7124no—
577#124—7124no—
578#123—7124no—
579#123—7124no—
580C22⋊Q8—7124no—
581C22⋊Q8—718no—
582C22⋊Q8—7124no—
583C22⋊Q8—7124no—
584#121—7148no—
585#121—7124no—
586#121—7124no—
587#121—7148no—
588#121—7124no—
589#121—7124no—
590#121—7124no—
591#121—7124no—
592#121—7148no—
593#121C22×D71124yescomplemented
594#121C22×D71124yescomplemented
595#120—7124no—
596#120—7148no—
597#120—7148no—
598#120—7124no—
599C4×Q8—718no—
600C4×Q8C22×D7118yescomplemented
601C4×D4—7124no—
602C4×D4—7124no—
603C4×D4—7124no—
604C4×D4—7124no—
605C4×D4—7124no—
606C4×D4C22×D71124yescomplemented
607#117—7124no—
608C2×C4⋊C4—713no—
609C2×C4⋊C4—713no—
610C2×C4⋊C4—711no—
611C2×C4⋊C4—711no—
612C2×C4⋊C4—713no—
613C2×C4⋊C4—713no—
614C2×C4⋊C4—7124no—
615C2×C4⋊C4C22×D7113yes—
616C2×C4⋊C4C22×D7111yescharacteristic
617C2×C22⋊C4—716no—
618C2×C22⋊C4—713no—
619C2×C22⋊C4—713no—
620C2×C22⋊C4—713no—
621C2×C22⋊C4—716no—
622C2×C22⋊C4—713no—
623C2×C22⋊C4—713no—
624C2×C22⋊C4—711no—
625C2×C22⋊C4—711no—
626C2×C22⋊C4—713no—
627C2×C22⋊C4—7148no—
628C2×C22⋊C4C22×D7113yes—
629C2×C22⋊C4C22×D7113yes—
630C2×C42—713no—
631C2×C42C22×D7113yes—
632C24—2846no—
633C24—28412no—
634C24—28412no—
635C24—7124no—
636C24—7112no—
637C24—713no—
638C24—711no—
639C24—713no—
640C24—14212no—
641C24—14212no—
642C24—14224no—
643C24C23×D7113yes—
644C24C23×D7113yes—
645#41—232no—
646#41—232no—
647#41—7164no—
648#41—14296no—
649#41—14296no—
650#41—14296no—
651#41—14232no—
652C2×Q8—714no—
653C2×Q8—7112no—
654C2×Q8—1424no—
655C2×Q8—14232no—
656C2×Q8—14212no—
657C2×Q8D4×D7118yescomplemented
658C2×Q8C23×D7114yes—
659C2×D4—212no—
660C2×D4—212no—
661C2×D4—412no—
662C2×D4—46no—
663C2×D4—28496no—
664C2×D4—28412no—
665C2×D4—2846no—
666C2×D4—7112no—
667C2×D4—7124no—
668C2×D4—7112no—
669C2×D4—7124no—
670C2×D4—7112no—
671C2×D4—7112no—
672C2×D4—7124no—
673C2×D4—7112no—
674C2×D4—7112no—
675C2×D4—7112no—
676C2×D4—7112no—
677C2×D4—14296no—
678C2×D4—14212no—
679C2×D4—14212no—
680C2×D4—14296no—
681C2×D4—14212no—
682C2×D4—14296no—
683C2×D4—14296no—
684C2×D4—14212no—
685C2×D4—14212no—
686C2×D4—14224no—
687C2×D4—14212no—
688C2×D4C23×D71112yes—
689C2×D4C23×D71112yes—
690C2×D4C23×D71112yes—
691C2×D4C23×D71124yes—
692C22×C4—212no—
693C22×C4—212no—
694C22×C4—28412no—
695C22×C4—7124no—
696C22×C4—711no—
697C22×C4—7124no—
698C22×C4—7112no—
699C22×C4—7112no—
700C22×C4—711no—
701C22×C4—713no—
702C22×C4—713no—
703C22×C4—711no—
704C22×C4—7112no—
705C22×C4—7112no—
706C22×C4—7112no—
707C22×C4—714no—
708C22×C4—1424no—
709C22×C4—14296no—
710C22×C4—14212no—
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×D7111yescharacteristic
720C22×C4C23×D7113yes—
721C4⋊C4—7112no—
722C4⋊C4—714no—
723C4⋊C4—714no—
724C4⋊C4—7112no—
725C4⋊C4—7112no—
726C4⋊C4—7112no—
727C4⋊C4C23×D71112yes—
728C4⋊C4C23×D7114yes—
729C22⋊C4—7124no—
730C22⋊C4—7112no—
731C22⋊C4—7112no—
732C22⋊C4—7112no—
733C22⋊C4—7124no—
734C22⋊C4—7112no—
735C22⋊C4—7112no—
736C22⋊C4—714no—
737C22⋊C4—714no—
738C22⋊C4—7112no—
739C22⋊C4C23×D71112yes—
740C22⋊C4C23×D71112yes—
741C42—7112no—
742C42C23×D71112yes—
743C23—26no—
744C23—26no—
745C23—26no—
746C23—26no—
747C23—26no—
748C23—26no—
749C23—28412no—
750C23—28424no—
751C23—28424no—
752C23—28448no—
753C23—56848no—
754C23—7112no—
755C23—714no—
756C23—716no—
757C23—712no—
758C23—716no—
759C23—14224no—
760C23—14224no—
761C23—14248no—
762C23—1426no—
763C23—1426no—
764C23—1426no—
765C23—1422no—
766C23—1426no—
767C23—1422no—
768C23—1426no—
769C23C24×D7116yes—
770C23C24×D7116yes—
771C23C24×D7111yescharacteristic
772Q8—1428no—
773Q8—14224no—
774Q8C2×D4×D71116yescomplemented
775D4—224no—
776D4—224no—
777D4—424no—
778D4—412no—
779D4—28424no—
780D4—28412no—
781D4—7148no—
782D4—14224no—
783D4—14224no—
784D4—14224no—
785D4—14224no—
786D4—14224no—
787D4—14248no—
788D4—14224no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—26no—
792C2×C4—22no—
793C2×C4—224no—
794C2×C4—224no—
795C2×C4—28424no—
796C2×C4—714no—
797C2×C4—712no—
798C2×C4—7148no—
799C2×C4—712no—
800C2×C4—716no—
801C2×C4—716no—
802C2×C4—712no—
803C2×C4—1428no—
804C2×C4—14224no—
805C2×C4—14224no—
806C2×C4—1422no—
807C2×C4—1426no—
808C2×C4—1426no—
809C2×C4—1422no—
810C2×C4—14224no—
811C2×C4—14224no—
812C2×C4C2×D4×D71112yes—
813C2×C4C24×D7112yes—
814C2×C4C24×D7116yes—
815C2×C4C24×D7112yes—
816C2×C4C24×D7112yes—
817C2×C4C24×D7116yes—
818C22—26no—
819C22—26no—
820C22—26no—
821C22—26no—
822C22—26no—
823C22—26no—
824C22—412no—
825C22—412no—
826C22—28448no—
827C22—28412no—
828C22—56848no—
829C22—7112no—
830C22—714no—
831C22—1426no—
832C22—1426no—
833C22—1426no—
834C22—1428no—
835C22—14224no—
836C22—1422no—
837C22—1426no—
838C22—1422no—
839C22—1426no—
840C22C22×D4×D7112yes—
841C22H(5,𝔽2)×D7112yes—
842C22#1798683512yes—
843C22C25×D7111yescharacteristic
844C4—22no—
845C4—22no—
846C4—26no—
847C4—22no—
848C4—714no—
849C4—1422no—
850C4—1426no—
851C4—1426no—
852C4—1422no—
853C4C22×D4×D71112yes—
854C2—46no—
855C2—46no—
856C2—2846no—
857C2—1424no—
858C2—14212no—
859C2#2260200814yesdirect product factor
860C2C23×D4×D7111yescharacteristic
861C2C2×H(5,𝔽2)×D7111yescharacteristic
862C2C2×#1798683511yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#550×C71C2
socleC23×C71C25
hypercenterC2×#550D71
hypocenterC71C2×#3488
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C22×#14556174C2semidirect
2. C22×#41×D71C2semidirect
3. #22602008C2direct (N × H)
4. C2×#17986668C2semidirect
5. C2×#17986661C2semidirect
6. C2×#17986656C2semidirect
7. C2×#17986646C2semidirect
8. C2×#17986645C2semidirect
9. C2×#17986634C2semidirect
10. C2×#17986633C2semidirect
11. C2×#17986578C2semidirect
12. C2×#17986562C2semidirect
13. C2×#17986508C2semidirect
14. C2×#121×D71C2semidirect
15. C2×#17986481C2semidirect
16. C2×#550×C71C2semidirect
18. C2×#14556174C22semidirect
20. C22×#11765866C22semidirect
21. C22×#11765865C22semidirect
22. C22×#11765865C22semidirect
23. C22×#11765864C22semidirect
25. C2×#41×D71C22semidirect
26. C22×Q8×D71C22semidirect
27. C23×D284C22semidirect
28. C22×D4×D71C22semidirect
29. C22×D4×D71C22semidirect
30. C22×D4×D71C22semidirect
31. C22×D4×D71C22semidirect
32. C23×C4×D71C22semidirect
33. #17986668C22semidirect
34. #17986661C22semidirect
35. #17986656C22semidirect
36. #17986646C22semidirect
37. #17986645C22semidirect
38. #17986634C22semidirect
39. #17986633C22semidirect
40. #17986578C22semidirect
41. #17986562C22semidirect
42. C2×#14556124C22semidirect
43. C2×#14556116C22semidirect
44. C2×#14556115C22semidirect
45. #17986508C22semidirect
46. C2×#14556113C22semidirect
47. C2×#14556110C22semidirect
48. C2×#14556108C22semidirect
49. C2×#14556107C22semidirect
50. C2×#14556106C22semidirect
51. C2×#14556105C22semidirect
52. C2×#14556103C22semidirect
53. C2×#14556102C22semidirect
54. C2×#14556101C22semidirect
55. C2×#14556101C22semidirect
56. C2×#14556100C22semidirect
57. C2×#14556100C22semidirect
58. C2×#14556099C22semidirect
59. C2×#14556099C22semidirect
60. C2×#14556099C22semidirect
61. #121×D71C22semidirect
62. C2×#14556098C22semidirect
63. C2×#14556096C22semidirect
64. C2×#14556096C22semidirect
65. C2×#14556096C22semidirect
66. #17986481C22semidirect
67. C2×Q8×Dic71C22semidirect
68. C2×C4×D284C22semidirect
69. C2×C4×D284C22semidirect
70. C2×#14556090C22semidirect
71. C2×C4×C22⋊D71C22semidirect
72. C2×C4×C22⋊D71C22semidirect
73. C2×#14556085C22semidirect
74. C2×C4⋊C4×D71C22semidirect
75. C2×C22⋊C4×D71C22semidirect
76. C22×#41×C71C22semidirect
77. C22×#41×C71C22semidirect
78. #550×C71C22semidirect
79. C2×#127×C71C22semidirect
80. C2×#121×C71C22semidirect
81. C2×#121×C71C22semidirect
82. C2×C4×Q8×C71C22semidirect
83. C2×C4×D4×C71C22semidirect
88. C2×#11765866D4semidirect
90. C2×#11765866C23semidirect
93. C2×#11765865C23semidirect
94. C2×#11765865C23semidirect
96. C2×#11765864C23semidirect
101. C2×Q8×D71C23semidirect
107. C22×D284C23semidirect
118. C2×D4×D71C23semidirect
119. C2×D4×D71C23semidirect
120. C2×D4×D71C23semidirect
121. C2×D4×D71C23semidirect
130. C22×C4×D71C23semidirect
131. #14556124C23semidirect
132. #14556116C23semidirect
133. #14556115C23semidirect
134. #14556113C23semidirect
135. #14556110C23semidirect
136. #14556108C23semidirect
137. #14556107C23semidirect
138. #14556106C23semidirect
139. #14556105C23semidirect
140. #14556103C23semidirect
141. #14556102C23semidirect
142. #14556101C23semidirect
143. #14556101C23semidirect
144. #14556100C23semidirect
145. #14556100C23semidirect
146. #14556099C23semidirect
147. #14556099C23semidirect
148. #14556099C23semidirect
149. #14556098C23semidirect
150. #14556096C23semidirect
151. #14556096C23semidirect
152. #14556096C23semidirect
153. Q8×Dic71C23semidirect
154. C4×D284C23semidirect
155. C4×D284C23semidirect
156. #14556090C23semidirect
157. C4×C22⋊D71C23semidirect
158. C4×C22⋊D71C23semidirect
159. #14556085C23semidirect
166. C4⋊C4×D71C23semidirect
177. C22⋊C4×D71C23semidirect
181. C2×#41×C71C23semidirect
182. C2×#41×C71C23semidirect
190. #127×C71C23semidirect
191. #121×C71C23semidirect
192. #121×C71C23semidirect
193. C4×Q8×C71C23semidirect
194. C4×D4×C71C23semidirect
212. #11765866C2×D4semidirect
225. C2×D284C2×D4semidirect
259. C2×C4×D71C2×D4semidirect
287. C2×Q8×C71C2×D4semidirect
336. C22×D71H(5,𝔽2)semidirect
340. Q8×C71C22×D4semidirect
377. D284C22×D4semidirect
383. C4×D71C22×D4semidirect
411. C2×D71C2×H(5,𝔽2)semidirect
425. C2×C71#3488semidirect
436. C2×#550D71semidirect
448. C71C2×#3488semidirect
458. C22×#41C2×D71semidirect
459. C22×#41C2×D71semidirect
468. #550C2×D71semidirect
478. C2×#127C2×D71semidirect
498. C2×#121C2×D71semidirect
499. C2×#121C2×D71semidirect
506. C2×C4×Q8C2×D71semidirect
512. C2×C4×D4C2×D71semidirect
532. C2×#41C22×D71semidirect
533. C2×#41C22×D71semidirect
575. #127C22×D71semidirect
593. #121C22×D71semidirect
594. #121C22×D71semidirect
600. C4×Q8C22×D71semidirect
606. C4×D4C22×D71semidirect
657. C2×Q8D4×D71semidirect
774. Q8C2×D4×D71semidirect
859. C2#22602008direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561742
C22×#41×D712
#226020082
C2×#179866682
C2×#179866612
C2×#179866562
C2×#179866462
C2×#179866452
C2×#179866342
C2×#179866332
C2×#179865782
C2×#179865622
C2×#179865082
C2×#121×D712
C2×#179864812
C2×#550×C712
C2×#348871