Finite Group Databasebeta

← C2×#22598257 #32865223

Subgroups — C2×#22598257 #32865223

Order 18176.

2378 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986511C211yesmaximal, characteristic
2C2×#117×D71C211yesmaximal, characteristic, complemented
3#22598257C2116yesmaximal, direct product factor
4C2×#17986336C211yesmaximal, characteristic, complemented
5C2×#17986319C211yesmaximal, characteristic, complemented
6C2×#17986343C211yesmaximal, characteristic, complemented
7C2×#17986342C211yesmaximal, characteristic, complemented
8C2×#17986326C211yesmaximal, characteristic, complemented
9C2×#17986325C211yesmaximal, characteristic, complemented
10C2×#17986331C211yesmaximal, characteristic, complemented
11C2×#17986314C211yesmaximal, characteristic, complemented
12C2×#17986035C211yesmaximal, characteristic, complemented
13C2×#17985996C211yesmaximal, characteristic, complemented
14C2×#17985993C211yesmaximal, characteristic, complemented
15C22×(C2×D71)⋊C8C211yesmaximal, characteristic, complemented
16C2×#427×C71C211yesmaximal, characteristic, complemented
17C22×#11765865C2211yescharacteristic
18C23×C4×D71C2211yescharacteristic
19C23×C71⋊C8C2211yescharacteristic
20#17986511—24no—
21#17986511C2218yes—
22C2×#14556112—21no—
23C2×#14556108C2211yescharacteristic
24C2×#14556108C2211yescharacteristic
25C2×#14556103C2211yescharacteristic
26C2×#14556103C2211yescharacteristic
27C2×#14556098—21no—
28C2×C4×D284—21no—
29C2×C4×D284—21no—
30C2×#14556087C2211yescharacteristic
31C2×#14556086C2211yescharacteristic
32C2×#14556086C2211yescharacteristic
33C2×#14556085—21no—
34C2×#14556084—21no—
35#117×D71—24no—
36#117×D71C2218yescomplemented
37C2×C4⋊C4×D71C2211yescharacteristic
38C2×C4⋊C4×D71C2211yescharacteristic
39C2×C22⋊C4×D71—21no—
40C2×C42×D71—21no—
41#17986343C2218yescomplemented
42#17986342C2218yescomplemented
43#17986336C2218yescomplemented
44#17986331C2218yescomplemented
45#17986326C2218yescomplemented
46#17986325C2218yescomplemented
47#17986319C2218yescomplemented
48#17986314C2218yescomplemented
49#17986035C2218yescomplemented
50C2×#14556061C2211yescharacteristic, complemented
51C2×#14556061C2211yescharacteristic, complemented
52C2×#14556059C2211yescharacteristic, complemented
53C2×#14556059C2211yescharacteristic, complemented
54#17985996C2218yescomplemented
55#17985993C2218yescomplemented
56C2×#14556053C2211yescharacteristic, complemented
57C2×#14556053C2211yescharacteristic, complemented
58C2×#14556051C2211yescharacteristic, complemented
59C2×#14556051C2211yescharacteristic, complemented
60C2×#14556050C2211yescharacteristic, complemented
61C2×#14556050C2211yescharacteristic, complemented
62C2×#14556048C2211yescharacteristic, complemented
63C2×#14556048C2211yescharacteristic, complemented
64C2×(C2×D71)⋊C8C2211yescharacteristic
65C2×(C2×D71)⋊C8C2211yescharacteristic
66C2×(C2×D71)⋊C8C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×(C2×D71)⋊C8C2218yescomplemented
69C23×C8×C71C2211yescharacteristic
70C2×#117×C71C2211yescharacteristic
71C2×#117×C71C2211yescharacteristic
72#427×C71C2218yescomplemented
73C2×#107×C71C2211yescharacteristic, complemented
74C2×#107×C71C2211yescharacteristic, complemented
75C2×#106×C71C2211yescharacteristic, complemented
76C2×#106×C71C2211yescharacteristic, complemented
77C24×D71D411yescharacteristic
78C2×#11765865—22no—
79C2×#11765865—24no—
80C2×#11765865—24no—
81C2×#11765865C2314yes—
82C22×Dic142C2311yescharacteristic
83C22×D284—21no—
84C22×D284—21no—
85C22×D284C2311yescharacteristic
86C22×C22⋊D71—21no—
87C23×Dic71D411yescharacteristic
88C22×C4×D71—21no—
89C22×C4×D71—21no—
90C22×C4×D71—21no—
91C22×C4×D71—24no—
92C22×C4×D71—24no—
93C22×C4×D71D411yescharacteristic
94C22×C4×D71D414yes—
95C22×C4×D71D411yescharacteristic
96C22×C4×D71C2311yescharacteristic
97C22×C4×D71C2314yes—
98C22×C4×D71C2311yescharacteristic
99C22×C71⋊C8—24no—
100C22×C71⋊C8C2311yescharacteristic
101C22×C71⋊C8C2311yescharacteristic
102C22×C71⋊C8C2314yes—
103#14556112—28no—
104#14556108—22no—
105#14556108—22no—
106#14556108C2314yes—
107#14556108C2314yes—
108#14556103—22no—
109#14556103—22no—
110#14556103C2314yes—
111#14556103C2314yes—
112#14556098—28no—
113C4×D284—28no—
114C4×D284—28no—
115#14556087—22no—
116#14556087C2314yes—
117#14556086—22no—
118#14556086—22no—
119#14556086C2314yes—
120#14556086C2314yes—
121#14556085—28no—
122#14556084—28no—
123C2×C4⋊Dic71—21no—
124C2×C4⋊Dic71—21no—
125C2×C4⋊Dic71C2311yescharacteristic
126C2×C4⋊Dic71C2311yescharacteristic
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C4⋊C4×D71—22no—
130C4⋊C4×D71—22no—
131C4⋊C4×D71C2314yes—
132C4⋊C4×D71C2314yes—
133C2×C22⋊Dic71—21no—
134C2×(C2×D71)⋊C4—21no—
135C2×(C2×D71)⋊C4—21no—
136C2×(C2×D71)⋊C4—21no—
137C2×(C2×D71)⋊C4—21no—
138C2×(C2×D71)⋊C4—21no—
139C2×(C2×D71)⋊C4—21no—
140C22⋊C4×D71—28no—
141C2×C4×Dic71—21no—
142C2×C4×Dic71—21no—
143C2×C4×Dic71—21no—
144C42×D71—28no—
145#14556061C2314yescomplemented
146#14556061C2314yescomplemented
147#14556059C2314yescomplemented
148#14556059C2314yescomplemented
149#14556053C2314yescomplemented
150#14556053C2314yescomplemented
151#14556051C2314yescomplemented
152#14556051C2314yescomplemented
153#14556050C2314yescomplemented
154#14556050C2314yescomplemented
155#14556048C2314yescomplemented
156#14556048C2314yescomplemented
157(C2×D71)⋊C8C2314yes—
158(C2×D71)⋊C8C2314yes—
159(C2×D71)⋊C8C2314yes—
160(C2×D71)⋊C8C2314yes—
161C23×C4×C71C2311yescharacteristic
162C22×C8×C71—24no—
163C22×C8×C71C2311yescharacteristic
164C22×C8×C71C2311yescharacteristic
165C22×C8×C71C2314yes—
166#117×C71—22no—
167#117×C71—22no—
168#117×C71C2314yes—
169#117×C71C2314yes—
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71—21no—
176C2×C42×C71—21no—
177C2×C42×C71—21no—
178#107×C71C2314yescomplemented
179#107×C71C2314yescomplemented
180#106×C71C2314yescomplemented
181#106×C71C2314yescomplemented
182C23×D71—24no—
183C23×D71—24no—
184C23×D71—21no—
185C23×D71—42no—
186C23×D71C2×D411yescharacteristic
187C23×D71C2×D414yes—
188C23×D71C2×D411yescharacteristic
189#11765865—28no—
190#11765865—28no—
191#11765865—48no—
192C2×Dic142—22no—
193C2×Dic142—22no—
194C2×Dic142—21no—
195C2×Dic142C2412yes—
196C2×D284—22no—
197C2×D284—22no—
198C2×D284—24no—
199C2×D284—24no—
200C2×D284—21no—
201C2×D284—44no—
202C2×D284—44no—
203C2×D284C2412yes—
204C2×C22⋊D71—24no—
205C2×C22⋊D71—44no—
206C22×Dic71—24no—
207C22×Dic71—21no—
208C22×Dic71—21no—
209C22×Dic71—21no—
210C22×Dic71C2×D411yescharacteristic
211C22×Dic71C2×D411yescharacteristic
212C22×Dic71C2×D414yes—
213C2×C4×D71—24no—
214C2×C4×D71—24no—
215C2×C4×D71—216no—
216C2×C4×D71—22no—
217C2×C4×D71—22no—
218C2×C4×D71—28no—
219C2×C4×D71—22no—
220C2×C4×D71—22no—
221C2×C4×D71—28no—
222C2×C4×D71—24no—
223C2×C4×D71—24no—
224C2×C4×D71—24no—
225C2×C4×D71—44no—
226C2×C4×D71—44no—
227C2×C4×D71—44no—
228C2×C4×D71C2×D414yes—
229C2×C4×D71C2×D412yes—
230C2×C4×D71C2×D414yes—
231C2×C4×D71C2×D412yes—
232C2×C4×D71C2412yes—
233C2×C4×D71C2412yes—
234C2×C71⋊C8—22no—
235C2×C71⋊C8—22no—
236C2×C71⋊C8—28no—
237C2×C71⋊C8C2412yes—
238C2×C71⋊C8C2412yes—
239C4⋊Dic71—21no—
240C4⋊Dic71—21no—
241C4⋊Dic71—24no—
242C4⋊Dic71—24no—
243C4⋊Dic71C2412yes—
244C4⋊Dic71C2412yes—
245Dic71⋊C4—24no—
246Dic71⋊C4—24no—
247C22⋊Dic71—24no—
248(C2×D71)⋊C4—24no—
249(C2×D71)⋊C4—24no—
250(C2×D71)⋊C4—24no—
251(C2×D71)⋊C4—24no—
252(C2×D71)⋊C4—24no—
253(C2×D71)⋊C4—24no—
254C4×Dic71—24no—
255C4×Dic71—24no—
256C4×Dic71—24no—
257C24×C71C2×D411yescharacteristic
258C22×C4×C71—21no—
259C22×C4×C71—21no—
260C22×C4×C71—21no—
261C22×C4×C71—21no—
262C22×C4×C71C2×D412yes—
263C22×C4×C71C2×D411yescharacteristic
264C22×C4×C71#4114yes—
265C22×C4×C71#4114yes—
266C22×C4×C71C2411yescharacteristic
267C22×C4×C71C2412yes—
268C2×C8×C71—22no—
269C2×C8×C71—22no—
270C2×C8×C71—28no—
271C2×C8×C71C2412yes—
272C2×C8×C71C2412yes—
273C4⋊C4×C71—21no—
274C4⋊C4×C71—21no—
275C4⋊C4×C71—21no—
276C4⋊C4×C71—21no—
277C4⋊C4×C71C2412yes—
278C4⋊C4×C71C2412yes—
279C4⋊C4×C71C2412yes—
280C4⋊C4×C71C2412yes—
281C22⋊C4×C71—24no—
282C22⋊C4×C71—24no—
283C42×C71—24no—
284C42×C71—24no—
285C23×C71—22no—
286C23×C71—22no—
287C23×C71#12314yes—
288C23×C71C22×D412yes—
289C23×C71C22×D411yescharacteristic
290C22×D71—22no—
291C22×D71—22no—
292C22×D71—28no—
293C22×D71—22no—
294C22×D71—22no—
295C22×D71—22no—
296C22×D71—28no—
297C22×D71—22no—
298C22×D71—44no—
299C22×D71—416no—
300C22×D71—42no—
301C22×D71—42no—
302C22×D71—42no—
303C22×D71#13514yes—
304C22×D71C22×D412yes—
305C22×D71C22×D412yes—
306C2×C4×C71—22no—
307C2×C4×C71—22no—
308C2×C4×C71—22no—
309C2×C4×C71—22no—
310C2×C4×C71—42no—
311C2×C4×C71—42no—
312C2×C4×C71—42no—
313C2×C4×C71—42no—
314C2×C4×C71#12314yes—
315C2×C4×C71#12318yes—
316C2×C4×C71C22×D412yes—
317C2×C4×C71C22×D411yescharacteristic
318C2×C4×C71C2×#4112yes—
319C2×C4×C71C2×#4114yes—
320C2×C4×C71C2×#4112yes—
321C2×C4×C71C2×#4114yes—
322C2×C4×C71C2511yescharacteristic
323C22⋊D71—48no—
324C2×Dic71—28no—
325C2×Dic71—22no—
326C2×Dic71—22no—
327C2×Dic71—22no—
328C2×Dic71—22no—
329C2×Dic71—22no—
330C2×Dic71—42no—
331C2×Dic71—42no—
332C2×Dic71—42no—
333C2×Dic71C22×D412yes—
334C2×Dic71C22×D412yes—
335D284—22no—
336D284—22no—
337D284—48no—
338D284—48no—
339D284—42no—
340C4×D71—24no—
341C4×D71—24no—
342C4×D71—28no—
343C4×D71—28no—
344C4×D71—22no—
345C4×D71—22no—
346C4×D71—22no—
347C4×D71—22no—
348C4×D71—48no—
349C4×D71—48no—
350C4×D71—48no—
351Dic142—22no—
352Dic142—22no—
353Dic142—42no—
354C8×C71—22no—
355C8×C71—22no—
356C71⋊C8—22no—
357C71⋊C8—22no—
358C22×C71—28no—
359C22×C71—22no—
360C22×C71—22no—
361C22×C71C2×#12314yes—
362C22×C71C2×#12312yes—
363C22×C71C2×#13512yes—
364C22×C71#57512yes—
365C22×C71C23×D411yescharacteristic
366C2×D71—28no—
367C2×D71—22no—
368C2×D71—22no—
369C2×D71—22no—
370C2×D71—22no—
371C2×D71—22no—
372C2×D71—416no—
373C2×D71—44no—
374C2×D71—42no—
375C2×D71—42no—
376C2×D71—42no—
377C2×D71—84no—
378C2×D71C2×#13514yes—
379C4×C71—42no—
380C4×C71—42no—
381C4×C71—42no—
382C4×C71—42no—
383C4×C71C2×#12312yes—
384C4×C71C2×#12314yes—
385C4×C71C22×#4111yescharacteristic
386C4×C71C22×#4111yescharacteristic
387Dic71—22no—
388Dic71—22no—
389Dic71—42no—
390Dic71—42no—
391Dic71—42no—
392C2×#3091—711nomaximal, Sylow
393C2×C71—24no—
394C2×C71#309114yescomplemented
395C2×C71C22×#12311yescharacteristic
396C2×C71C22×#13511yescharacteristic
397C2×C71C2×#57511yescharacteristic
398D71—24no—
399D71—42no—
400D71—82no—
401C2×#525—711no—
402C22×#117—711no—
403#3091—7116no—
404C2×#484—711no—
405C2×#481—711no—
406C2×#485—711no—
407C2×#485—711no—
408C2×#482—711no—
409C2×#482—711no—
410C2×#483—711no—
411C2×#480—711no—
412C2×#427—711no—
413C2×#427D7111yescharacteristic, complemented
414C2×#416—711no—
415C2×#416—711no—
416C22×C22⋊C8—711no—
417C71C2×#309111yescharacteristic, complemented, Sylow
418C22×#41—711no—
419C24×C4—711no—
420C23×C8—711no—
421C23×C8C2×D7111yescharacteristic
422#525—718no—
423#525—1424no—
424C2×#123—1421no—
425C2×C22⋊Q8—711no—
426C2×C22⋊Q8—711no—
427C2×#121—711no—
428C2×#121—711no—
429C2×#120—1421no—
430C2×C4×D4—1421no—
431C2×C4×D4—1421no—
432C2×#117—711no—
433C2×#117—718no—
434C2×#117—711no—
435C2×#117—711no—
436C2×#117—1421no—
437C2×#117—1421no—
438C2×#117—1424no—
439C2×#117C2×D7111yescharacteristic
440C2×#117C2×D7111yescharacteristic
441C22×C4⋊C4—711no—
442C22×C4⋊C4—711no—
443C22×C22⋊C4—1421no—
444C22×C42—1421no—
445#485—718no—
446#485—718no—
447#484—718no—
448#483—718no—
449#482—718no—
450#482—718no—
451#481—718no—
452#480—718no—
453#427—718no—
454#427C2×D7118yescomplemented
455C2×#107—711no—
456C2×#107—711no—
457C2×#107C2×D7111yescharacteristic, complemented
458C2×#107C2×D7111yescharacteristic, complemented
459C2×#106—711no—
460C2×#106—711no—
461C2×#106C2×D7111yescharacteristic, complemented
462C2×#106C2×D7111yescharacteristic, complemented
463#416—718no—
464#416—718no—
465C2×#103—711no—
466C2×#103—711no—
467C2×#103—711no—
468C2×#103—711no—
469C2×#102—711no—
470C2×#102—711no—
471C2×#102—711no—
472C2×#102—711no—
473C2×C22⋊C8—711no—
474C2×C22⋊C8—711no—
475C2×C22⋊C8—711no—
476C2×C22⋊C8—711no—
477C2×C22⋊C8—718no—
478C25—711no—
479C2×#41—714no—
480C2×#41—1424no—
481C2×#41—1424no—
482C2×#41—1422no—
483C22×Q8—711no—
484C22×D4—711no—
485C22×D4—1421no—
486C22×D4—1421no—
487C22×D4—1421no—
488C23×C4—711no—
489C23×C4—714no—
490C23×C4—711no—
491C23×C4—711no—
492C23×C4—711no—
493C23×C4—711no—
494C23×C4—714no—
495C23×C4—1421no—
496C23×C4—1421no—
497C23×C4—1421no—
498C23×C4—1424no—
499C23×C4—1424no—
500C23×C4C22×D7111yescharacteristic
501C22×C8—24no—
502C22×C8—711no—
503C22×C8—711no—
504C22×C8—714no—
505C22×C8—1424no—
506C22×C8C22×D7111yescharacteristic
507C22×C8C22×D7111yescharacteristic
508C22×C8C22×D7114yes—
509#123—1428no—
510C22⋊Q8—714no—
511C22⋊Q8—714no—
512C22⋊Q8—1422no—
513C22⋊Q8—1422no—
514#121—714no—
515#121—714no—
516#121—1422no—
517#121—1422no—
518#120—1428no—
519C4×D4—1428no—
520C4×D4—1428no—
521#117—22no—
522#117—22no—
523#117—714no—
524#117—714no—
525#117—714no—
526#117—1428no—
527#117—1428no—
528#117—1422no—
529#117—1422no—
530#117—1422no—
531#117C22×D7114yes—
532#117C22×D7114yes—
533C2×C4⋊C4—711no—
534C2×C4⋊C4—711no—
535C2×C4⋊C4—714no—
536C2×C4⋊C4—714no—
537C2×C4⋊C4—1422no—
538C2×C4⋊C4—1422no—
539C2×C4⋊C4—1421no—
540C2×C4⋊C4—1421no—
541C2×C4⋊C4—1421no—
542C2×C4⋊C4—1421no—
543C2×C4⋊C4C22×D7111yescharacteristic
544C2×C4⋊C4C22×D7111yescharacteristic
545C2×C4⋊C4C22×D7111yescharacteristic
546C2×C4⋊C4C22×D7111yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—1428no—
550C2×C22⋊C4—1421no—
551C2×C22⋊C4—1421no—
552C2×C22⋊C4—1421no—
553C2×C22⋊C4—1421no—
554C2×C22⋊C4—1421no—
555C2×C22⋊C4—1421no—
556C2×C22⋊C4—1421no—
557C2×C42—21no—
558C2×C42—21no—
559C2×C42—1428no—
560C2×C42—1421no—
561C2×C42—1421no—
562C2×C42—1421no—
563#107—714no—
564#107—714no—
565#107C22×D7114yescomplemented
566#107C22×D7114yescomplemented
567#106—714no—
568#106—714no—
569#106C22×D7114yescomplemented
570#106C22×D7114yescomplemented
571#103—714no—
572#103—714no—
573#103—714no—
574#103—714no—
575#102—714no—
576#102—714no—
577#102—714no—
578#102—714no—
579C22⋊C8—714no—
580C22⋊C8—714no—
581C22⋊C8—714no—
582C22⋊C8—714no—
583C24—2842no—
584C24—714no—
585C24—711no—
586C24—711no—
587C24—1424no—
588C24—1421no—
589C24—1424no—
590C24D4×D7111yescharacteristic
591#41—2848no—
592#41—1428no—
593#41—1428no—
594C2×Q8—712no—
595C2×Q8—1422no—
596C2×Q8—1422no—
597C2×Q8—1421no—
598C2×D4—2844no—
599C2×D4—2844no—
600C2×D4—2844no—
601C2×D4—712no—
602C2×D4—1424no—
603C2×D4—1424no—
604C2×D4—1424no—
605C2×D4—1421no—
606C2×D4—1422no—
607C2×D4—1422no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—2844no—
613C22×C4—2844no—
614C22×C4—2844no—
615C22×C4—711no—
616C22×C4—711no—
617C22×C4—714no—
618C22×C4—714no—
619C22×C4—712no—
620C22×C4—714no—
621C22×C4—712no—
622C22×C4—712no—
623C22×C4—712no—
624C22×C4—1424no—
625C22×C4—1424no—
626C22×C4—1421no—
627C22×C4—1421no—
628C22×C4—1421no—
629C22×C4—1424no—
630C22×C4—1424no—
631C22×C4—1422no—
632C22×C4—1422no—
633C22×C4—1428no—
634C22×C4—1422no—
635C22×C4—1422no—
636C22×C4—1428no—
637C22×C4—1424no—
638C22×C4—1424no—
639C22×C4—14216no—
640C22×C4D4×D7112yes—
641C22×C4D4×D7111yescharacteristic
642C22×C4#1176586514yes—
643C22×C4#1176586614yes—
644C22×C4C23×D7111yescharacteristic
645C22×C4C23×D7112yes—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—28no—
649C2×C8—712no—
650C2×C8—712no—
651C2×C8—1422no—
652C2×C8—1422no—
653C2×C8—1428no—
654C2×C8C23×D7112yes—
655C2×C8C23×D7112yes—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—712no—
661C4⋊C4—712no—
662C4⋊C4—1424no—
663C4⋊C4—1424no—
664C4⋊C4—1424no—
665C4⋊C4—1424no—
666C4⋊C4—1421no—
667C4⋊C4—1421no—
668C4⋊C4C23×D7112yes—
669C4⋊C4C23×D7112yes—
670C4⋊C4C23×D7112yes—
671C4⋊C4C23×D7112yes—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—1424no—
675C22⋊C4—1424no—
676C22⋊C4—1424no—
677C22⋊C4—1424no—
678C22⋊C4—1424no—
679C22⋊C4—1424no—
680C22⋊C4—1424no—
681C42—24no—
682C42—24no—
683C42—1424no—
684C42—1424no—
685C42—1424no—
686C23—22no—
687C23—22no—
688C23—28416no—
689C23—2844no—
690C23—2842no—
691C23—2842no—
692C23—2842no—
693C23—712no—
694C23—714no—
695C23—712no—
696C23—1428no—
697C23—1422no—
698C23—1428no—
699C23—1422no—
700C23—1422no—
701C23—1422no—
702C23—1422no—
703C23—1422no—
704C23#1455611314yes—
705C23C2×D4×D7112yes—
706C23C2×D4×D7111yescharacteristic
707Q8—2842no—
708Q8—1422no—
709Q8—1422no—
710D4—2848no—
711D4—2848no—
712D4—2848no—
713D4—2842no—
714D4—1422no—
715D4—1422no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—2848no—
725C2×C4—2848no—
726C2×C4—2842no—
727C2×C4—2842no—
728C2×C4—2842no—
729C2×C4—2848no—
730C2×C4—712no—
731C2×C4—712no—
732C2×C4—1422no—
733C2×C4—1422no—
734C2×C4—1422no—
735C2×C4—1428no—
736C2×C4—1422no—
737C2×C4—1422no—
738C2×C4—1422no—
739C2×C4—1422no—
740C2×C4—1422no—
741C2×C4—1422no—
742C2×C4—1428no—
743C2×C4—1428no—
744C2×C4—1424no—
745C2×C4—1424no—
746C2×C4#1455611314yes—
747C2×C4#1455611318yes—
748C2×C4C2×D4×D7112yes—
749C2×C4C2×D4×D7111yescharacteristic
750C2×C4C2×#1176586512yes—
751C2×C4C2×#1176586514yes—
752C2×C4C2×#1176586612yes—
753C2×C4C2×#1176586614yes—
754C2×C4C24×D7111yescharacteristic
755C8—22no—
756C8—22no—
757C8—1422no—
758C8—1422no—
759C22—22no—
760C22—22no—
761C22—28no—
762C22—28416no—
763C22—2844no—
764C22—2842no—
765C22—2842no—
766C22—2842no—
767C22—5684no—
768C22—714no—
769C22—1422no—
770C22—1422no—
771C22—1422no—
772C22—1422no—
773C22—1422no—
774C22—1428no—
775C22C2×#1455611314yes—
776C22C2×#1455611312yes—
777C22#135×D7112yes—
778C22#1798679612yes—
779C22C22×D4×D7111yescharacteristic
780C4—42no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—2842no—
785C4—2842no—
786C4—2842no—
787C4—1422no—
788C4—1422no—
789C4C2×#1455611314yes—
790C4C2×#1455611312yes—
791C4C22×#1176586511yescharacteristic
792C4C22×#1176586611yescharacteristic
793C2—24no—
794C2—2842no—
795C2—5682no—
796C2—1424no—
797C2#2259825714yesdirect product factor
798C2C22×#1455611311yescharacteristic
799C2C2×#135×D7111yescharacteristic
800C2C2×#1798679611yescharacteristic
subgroupG/H
centerC22×C4D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#427×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986511C2
hypercenterC2×#427D71
hypocenterC71C2×#3091
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. C2×#117×D71C2semidirect
3. #22598257C2direct (N × H)
4. C2×#17986336C2semidirect
5. C2×#17986319C2semidirect
6. C2×#17986343C2semidirect
7. C2×#17986342C2semidirect
8. C2×#17986326C2semidirect
9. C2×#17986325C2semidirect
10. C2×#17986331C2semidirect
11. C2×#17986314C2semidirect
12. C2×#17986035C2semidirect
13. C2×#17985996C2semidirect
14. C2×#17985993C2semidirect
15. C22×(C2×D71)⋊C8C2semidirect
16. C2×#427×C71C2semidirect
36. #117×D71C22semidirect
41. #17986343C22semidirect
42. #17986342C22semidirect
43. #17986336C22semidirect
44. #17986331C22semidirect
45. #17986326C22semidirect
46. #17986325C22semidirect
47. #17986319C22semidirect
48. #17986314C22semidirect
49. #17986035C22semidirect
50. C2×#14556061C22semidirect
51. C2×#14556061C22semidirect
52. C2×#14556059C22semidirect
53. C2×#14556059C22semidirect
54. #17985996C22semidirect
55. #17985993C22semidirect
56. C2×#14556053C22semidirect
57. C2×#14556053C22semidirect
58. C2×#14556051C22semidirect
59. C2×#14556051C22semidirect
60. C2×#14556050C22semidirect
61. C2×#14556050C22semidirect
62. C2×#14556048C22semidirect
63. C2×#14556048C22semidirect
68. C2×(C2×D71)⋊C8C22semidirect
72. #427×C71C22semidirect
73. C2×#107×C71C22semidirect
74. C2×#107×C71C22semidirect
75. C2×#106×C71C22semidirect
76. C2×#106×C71C22semidirect
145. #14556061C23semidirect
146. #14556061C23semidirect
147. #14556059C23semidirect
148. #14556059C23semidirect
149. #14556053C23semidirect
150. #14556053C23semidirect
151. #14556051C23semidirect
152. #14556051C23semidirect
153. #14556050C23semidirect
154. #14556050C23semidirect
155. #14556048C23semidirect
156. #14556048C23semidirect
178. #107×C71C23semidirect
179. #107×C71C23semidirect
180. #106×C71C23semidirect
181. #106×C71C23semidirect
394. C2×C71#3091semidirect
413. C2×#427D71semidirect
417. C71C2×#3091semidirect
454. #427C2×D71semidirect
457. C2×#107C2×D71semidirect
458. C2×#107C2×D71semidirect
461. C2×#106C2×D71semidirect
462. C2×#106C2×D71semidirect
565. #107C22×D71semidirect
566. #107C22×D71semidirect
569. #106C22×D71semidirect
570. #106C22×D71semidirect
797. C2#22598257direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179865112
C2×#117×D712
#225982572
C2×#179863362
C2×#179863192
C2×#179863432
C2×#179863422
C2×#179863262
C2×#179863252
C2×#179863312
C2×#179863142
C2×#179860352
C2×#179859962
C2×#179859932
C22×(C2×D71)⋊C82
C2×#427×C712
C2×#309171