Finite Group Databasebeta

← C2×#22598695 #32866689

Subgroups — C2×#22598695 #32866689

Order 18176.

2262 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986629C211yesmaximal, characteristic, complemented
2C2×#17986562C211yesmaximal, characteristic
3#22598695C2116yesmaximal, direct product factor
4C2×#17986362C211yesmaximal, characteristic, complemented
5C2×#17986359C211yesmaximal, characteristic, complemented
6C2×#17986357C211yesmaximal, characteristic, complemented
7C2×#17986356C211yesmaximal, characteristic, complemented
8C2×#17986352C211yesmaximal, characteristic, complemented
9C2×#17986345C211yesmaximal, characteristic, complemented
10C2×#17986344C211yesmaximal, characteristic, complemented
11C2×#17985997C211yesmaximal, characteristic, complemented
12C2×#17986002C211yesmaximal, characteristic, complemented
13C2×#17985992C211yesmaximal, characteristic, complemented
14C2×#102×D71C211yesmaximal, characteristic, complemented
15C2×#17985956C211yesmaximal, characteristic, complemented
16C2×#490×C71C211yesmaximal, characteristic, complemented
17C22×#11765864C2211yescharacteristic
18C22×D4×D71C2211yescharacteristic
19C22×#11765848C2211yescharacteristic
20C22×C8×D71C2211yescharacteristic
21#17986629—24no—
22#17986629C2218yescomplemented
23#17986562—24no—
24#17986562C2218yes—
25C2×#14556128C2211yescharacteristic, complemented
26C2×#14556127—21no—
27C2×#14556127C2211yescharacteristic, complemented
28C2×#14556124C2211yescharacteristic
29C2×#14556119C2211yescharacteristic, complemented
30C2×#14556118—21no—
31C2×#14556116C2211yescharacteristic
32C2×#14556115C2211yescharacteristic
33C2×#14556108—21no—
34C2×#14556106—21no—
35C2×#14556100—21no—
36C2×#14556100—21no—
37C2×#14556096—21no—
38C2×#14556096—21no—
39C2×#14556086C2211yescharacteristic
40C2×#14556085C2211yescharacteristic
41C2×C4⋊C4×D71C2211yescharacteristic
42#17986362C2218yescomplemented
43#17986359C2218yescomplemented
44#17986357C2218yescomplemented
45#17986356C2218yescomplemented
46#17986352C2218yescomplemented
47#17986345C2218yescomplemented
48#17986344C2218yescomplemented
49#17986002C2218yescomplemented
50#17985997C2218yescomplemented
51#17985992C2218yescomplemented
52C2×#14556053C2211yescharacteristic, complemented
53C2×#14556053C2211yescharacteristic, complemented
54C2×#14556051C2211yescharacteristic, complemented
55C2×#14556051C2211yescharacteristic, complemented
56C2×#14556050C2211yescharacteristic
57C2×#14556050C2211yescharacteristic
58C2×#14556049C2211yescharacteristic
59C2×#14556049C2211yescharacteristic
60C2×#14556049C2211yescharacteristic, complemented
61C2×#14556049C2211yescharacteristic, complemented
62C2×#14556048C2211yescharacteristic
63C2×#14556048C2211yescharacteristic
64#102×D71C2218yescomplemented
65#17985956C2218yescomplemented
66C2×#14556038C2211yescharacteristic, complemented
67C2×C4×C71⋊C8C2211yescharacteristic, complemented
68C2×C8×Dic71C2211yescharacteristic, complemented
69C2×#127×C71C2211yescharacteristic
70C2×#125×C71C2211yescharacteristic, complemented
71#490×C71C2218yescomplemented
72C2×#102×C71C2211yescharacteristic
73C2×#102×C71C2211yescharacteristic
74C2×#102×C71C2211yescharacteristic, complemented
75C2×#102×C71C2211yescharacteristic, complemented
76C2×#97×C71C2211yescharacteristic, complemented
77C24×D71—21no—
78C2×#11765864—22no—
79C2×#11765864—24no—
80C2×#11765864—24no—
81C2×#11765864C2314yes—
82C22×Dic142—21no—
83C22×Dic142—21no—
84C22×Dic142C2311yescharacteristic
85C22×D284C2311yescharacteristic
86C22×C22⋊D71—21no—
87C22×C22⋊D71—21no—
88C22×C22⋊D71—21no—
89C22×C22⋊D71—21no—
90C2×D4×D71—22no—
91C2×D4×D71—24no—
92C2×D4×D71—24no—
93C2×D4×D71C2314yes—
94C23×Dic71—21no—
95C22×C4×D71—21no—
96C22×C4×D71C2311yescharacteristic
97C2×#11765848—24no—
98C2×#11765848C2314yes—
99C22×C71⋊C8C2311yescharacteristic
100C22×C71⋊C8C2311yescharacteristic
101C2×C8×D71—24no—
102C2×C8×D71C2314yes—
103#14556128—22no—
104#14556128C2314yescomplemented
105#14556127—28no—
106#14556127—22no—
107#14556127C2314yescomplemented
108#14556124—22no—
109#14556124C2314yes—
110#14556119—22no—
111#14556119C2314yescomplemented
112#14556118—28no—
113#14556116—22no—
114#14556116C2314yes—
115#14556115—22no—
116#14556115C2314yes—
117#14556108—28no—
118#14556106—28no—
119#14556100—28no—
120#14556100—28no—
121#14556096—28no—
122#14556096—28no—
123#14556086—22no—
124#14556086C2314yes—
125#14556085D414yes—
126#14556085C2314yes—
127C2×C4⋊Dic71—21no—
128C2×C4⋊Dic71—21no—
129C2×C4⋊Dic71C2311yescharacteristic
130C2×C4⋊Dic71C2311yescharacteristic
131C2×Dic71⋊C4—21no—
132C2×Dic71⋊C4—21no—
133C2×Dic71⋊C4—21no—
134C2×Dic71⋊C4D411yescharacteristic
135C2×Dic71⋊C4D411yescharacteristic
136C4⋊C4×D71—22no—
137C4⋊C4×D71C2314yes—
138C2×C22⋊Dic71—21no—
139C2×C22⋊Dic71—21no—
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4—21no—
142C2×(C2×D71)⋊C4—21no—
143C2×(C2×D71)⋊C4D411yescharacteristic
144C2×(C2×D71)⋊C4D411yescharacteristic
145C2×C4×Dic71—21no—
146C2×C4×Dic71C2311yescharacteristic
147#14556053C2314yescomplemented
148#14556053C2314yescomplemented
149#14556051C2314yescomplemented
150#14556051C2314yescomplemented
151#14556050C2314yes—
152#14556050C2314yes—
153#14556049C2314yes—
154#14556049C2314yes—
155#14556049C2314yescomplemented
156#14556049C2314yescomplemented
157#14556048C2314yes—
158#14556048C2314yes—
159#14556038C2314yescomplemented
160C4×C71⋊C8C2314yescomplemented
161C8×Dic71C2314yescomplemented
162C22×D4×C71—21no—
163C22×D4×C71—21no—
164C22×D4×C71C2311yescharacteristic
165C22×D4×C71C2311yescharacteristic
166C22×C8×C71C2311yescharacteristic
167C22×C8×C71C2311yescharacteristic
168#127×C71—22no—
169#127×C71C2314yes—
170#125×C71—22no—
171#125×C71C2314yescomplemented
172C2×C4⋊C4×C71—21no—
173C2×C4⋊C4×C71—21no—
174C2×C4⋊C4×C71C2311yescharacteristic
175C2×C4⋊C4×C71C2311yescharacteristic
176C2×C42×C71C2311yescharacteristic
177#102×C71C2314yes—
178#102×C71C2314yes—
179#102×C71C2314yescomplemented
180#102×C71C2314yescomplemented
181#97×C71C2314yescomplemented
182C23×D71—21no—
183C23×D71—24no—
184C23×D71—44no—
185C23×D71—82no—
186C23×D71—82no—
187C23×D71C2×D411yescharacteristic
188#11765864—28no—
189#11765864—28no—
190#11765864—48no—
191C2×Dic142—22no—
192C2×Dic142—22no—
193C2×Dic142—21no—
194C2×Dic142—24no—
195C2×Dic142—24no—
196C2×Dic142—82no—
197C2×Dic142—82no—
198C2×Dic142C2412yes—
199C2×D284—22no—
200C2×D284—22no—
201C2×D284—21no—
202C2×D284C2412yes—
203C2×C22⋊D71—24no—
204C2×C22⋊D71—24no—
205C2×C22⋊D71—24no—
206C2×C22⋊D71—24no—
207C2×C22⋊D71—44no—
208C2×C22⋊D71—44no—
209C2×C22⋊D71—82no—
210C2×C22⋊D71—82no—
211D4×D71—28no—
212D4×D71—28no—
213D4×D71—48no—
214C22×Dic71—21no—
215C22×Dic71—21no—
216C22×Dic71—21no—
217C22×Dic71—24no—
218C22×Dic71—44no—
219C22×Dic71C2×D411yescharacteristic
220C22×Dic71C2×D411yescharacteristic
221C22×Dic71C2×D411yescharacteristic
222C2×C4×D71—24no—
223C2×C4×D71—82no—
224C2×C4×D71C2×D412yes—
225C2×C4×D71#4114yes—
226C2×C4×D71#4114yes—
227C2×C4×D71C2412yes—
228#11765848—28no—
229C2×C71⋊C8—22no—
230C2×C71⋊C8—22no—
231C2×C71⋊C8C2412yes—
232C2×C71⋊C8C2412yes—
233C8×D71—28no—
234C4⋊Dic71—21no—
235C4⋊Dic71—24no—
236C4⋊Dic71—21no—
237C4⋊Dic71—24no—
238C4⋊Dic71C2412yes—
239C4⋊Dic71C2412yes—
240Dic71⋊C4—24no—
241Dic71⋊C4—24no—
242Dic71⋊C4—24no—
243Dic71⋊C4C2×D414yes—
244Dic71⋊C4C2×D414yes—
245C22⋊Dic71—24no—
246C22⋊Dic71—24no—
247(C2×D71)⋊C4—24no—
248(C2×D71)⋊C4—24no—
249(C2×D71)⋊C4—24no—
250(C2×D71)⋊C4C2×D414yes—
251(C2×D71)⋊C4C2×D414yes—
252C4×Dic71—24no—
253C4×Dic71C2×D412yes—
254C4×Dic71C2412yes—
255C24×C71—21no—
256C24×C71—21no—
257C2×D4×C71—21no—
258C2×D4×C71—21no—
259C2×D4×C71—24no—
260C2×D4×C71—24no—
261C2×D4×C71—22no—
262C2×D4×C71—22no—
263C2×D4×C71—22no—
264C2×D4×C71—22no—
265C2×D4×C71—82no—
266C2×D4×C71—82no—
267C2×D4×C71C2412yes—
268C2×D4×C71C2412yes—
269C22×C4×C71—21no—
270C22×C4×C71—21no—
271C22×C4×C71C2×D411yescharacteristic
272C22×C4×C71C2×D411yescharacteristic
273C22×C4×C71C2411yescharacteristic
274C2×C8×C71—22no—
275C2×C8×C71—22no—
276C2×C8×C71C2412yes—
277C2×C8×C71C2412yes—
278C4⋊C4×C71—24no—
279C4⋊C4×C71—24no—
280C4⋊C4×C71—21no—
281C4⋊C4×C71—21no—
282C4⋊C4×C71C2412yes—
283C4⋊C4×C71C2412yes—
284C42×C71C2×D412yes—
285C42×C71C2412yes—
286C23×C71—22no—
287C23×C71—22no—
288C23×C71—42no—
289C23×C71—42no—
290C23×C71—42no—
291C23×C71—42no—
292C23×C71—42no—
293C23×C71—42no—
294C23×C71C22×D411yescharacteristic
295C22×D71—22no—
296C22×D71—22no—
297C22×D71—22no—
298C22×D71—42no—
299C22×D71—42no—
300C22×D71—42no—
301C22×D71—48no—
302C22×D71—84no—
303C22×D71—84no—
304C22×D71—816no—
305C22×D71#12414yes—
306C22×D71C22×D412yes—
307D4×C71—22no—
308D4×C71—22no—
309D4×C71—22no—
310D4×C71—22no—
311D4×C71—42no—
312D4×C71—42no—
313D4×C71—84no—
314D4×C71—84no—
315C2×C4×C71—22no—
316C2×C4×C71—22no—
317C2×C4×C71—22no—
318C2×C4×C71—22no—
319C2×C4×C71—42no—
320C2×C4×C71—42no—
321C2×C4×C71C22×D412yes—
322C2×C4×C71C22×D412yes—
323C2×C4×C71C22×D411yescharacteristic
324C2×C4×C71C2×#4112yes—
325C2×C4×C71C2×#4112yes—
326C2×C4×C71C2511yescharacteristic
327C22⋊D71—48no—
328C22⋊D71—48no—
329C22⋊D71—84no—
330C22⋊D71—84no—
331C2×Dic71—22no—
332C2×Dic71—22no—
333C2×Dic71—22no—
334C2×Dic71—22no—
335C2×Dic71—22no—
336C2×Dic71—42no—
337C2×Dic71—42no—
338C2×Dic71—42no—
339C2×Dic71—48no—
340C2×Dic71#12414yes—
341C2×Dic71C22×D412yes—
342C2×Dic71C22×D412yes—
343C2×Dic71C22×D412yes—
344D284—22no—
345D284—22no—
346D284—42no—
347C4×D71—84no—
348C4×D71#12418yes—
349C4×D71C2×#4114yes—
350C4×D71C2×#4114yes—
351Dic142—22no—
352Dic142—22no—
353Dic142—42no—
354Dic142—84no—
355Dic142—84no—
356C8×C71—22no—
357C8×C71—22no—
358C71⋊C8—22no—
359C71⋊C8—22no—
360C22×C71—42no—
361C22×C71—42no—
362C22×C71—42no—
363C22×C71—42no—
364C22×C71—42no—
365C22×C71—42no—
366C22×C71—84no—
367C22×C71—84no—
368C22×C71C2×#12412yes—
369C22×C71#57612yes—
370C22×C71#57712yes—
371C22×C71C23×D411yescharacteristic
372C2×D71—28no—
373C2×D71—22no—
374C2×D71—22no—
375C2×D71—42no—
376C2×D71—42no—
377C2×D71—42no—
378C2×D71—816no—
379C2×D71—84no—
380C2×D71C2×#12414yes—
381C4×C71—22no—
382C4×C71—22no—
383C4×C71—42no—
384C4×C71—42no—
385C4×C71C2×#12412yes—
386C4×C71C22×#4111yescharacteristic
387C4×C71C22×#4111yescharacteristic
388Dic71—22no—
389Dic71—22no—
390Dic71—42no—
391Dic71—42no—
392Dic71—42no—
393Dic71C2×#12414yes—
394C2×#3136—711nomaximal, Sylow
395C2×C71—82no—
396C2×C71—82no—
397C2×C71#313614yescomplemented
398C2×C71C22×#12411yescharacteristic
399C2×C71C2×#57611yescharacteristic
400C2×C71C2×#57711yescharacteristic
401D71—24no—
402D71—82no—
403C2×#544—711no—
404C2×#535—711no—
405#3136—7116no—
406C2×#490—711no—
407C2×#490D7111yescharacteristic, complemented
408C2×#489—711no—
409C2×#489—711no—
410C2×#488—711no—
411C2×#488—711no—
412C2×#486—711no—
413C2×#486—711no—
414C2×#417—711no—
415C2×#418—711no—
416C2×#416—711no—
417C22×#102—711no—
418C2×#405—711no—
419C71C2×#313611yescharacteristic, complemented, Sylow
420C22×#41—711no—
421C23×D4—711no—
422C22×M16—711no—
423C23×C8—711no—
424#544—718no—
425#544—1424no—
426#535—718no—
427#535—1424no—
428C2×C4⋊Q8—711no—
429C2×C4⋊Q8—711no—
430C2×C4⋊Q8—1421no—
431C2×#127—711no—
432C2×#127C2×D7111yescharacteristic
433C2×#125—711no—
434C2×#125—1421no—
435C2×#125C2×D7111yescharacteristic, complemented
436C2×#124—711no—
437C2×#124—711no—
438C2×C22⋊Q8—1421no—
439C2×C22⋊Q8—1421no—
440C2×#121—1421no—
441C2×#121—1421no—
442C2×#120—1421no—
443C2×#120—1421no—
444C2×#117—711no—
445C2×#117—711no—
446C22×C4⋊C4—711no—
447#490—718no—
448#490C2×D7118yescomplemented
449#489—718no—
450#489—718no—
451#488—718no—
452#488—718no—
453#486—718no—
454#486—718no—
455#418—718no—
456#417—718no—
457#416—718no—
458C2×#103—711no—
459C2×#103—711no—
460C2×#103—711no—
461C2×#103—711no—
462C2×#102—711no—
463C2×#102—711no—
464C2×#102—711no—
465C2×#102—711no—
466C2×#102—711no—
467C2×#102—711no—
468C2×#102—711no—
469C2×#102—711no—
470C2×#102—718no—
471C2×#102C2×D7111yescharacteristic
472C2×#102C2×D7111yescharacteristic
473C2×#102C2×D7111yescharacteristic, complemented
474C2×#102C2×D7111yescharacteristic, complemented
475#405—718no—
476C2×#97—711no—
477C2×#97C2×D7111yescharacteristic, complemented
478C2×C4×C8—711no—
479C2×C4×C8—711no—
480C25—1421no—
481C2×#41—714no—
482C2×#41—1424no—
483C2×#41—1424no—
484C2×#41—1422no—
485C22×Q8—711no—
486C22×Q8—1421no—
487C22×Q8—1421no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—714no—
491C22×D4—711no—
492C22×D4—1422no—
493C22×D4—1424no—
494C22×D4—1424no—
495C22×D4—1421no—
496C22×D4—1421no—
497C22×D4—1421no—
498C22×D4—1421no—
499C22×D4C22×D7111yescharacteristic
500C22×D4C22×D7111yescharacteristic
501C23×C4—711no—
502C23×C4—1421no—
503C23×C4—1421no—
504C2×M16—714no—
505C2×M16—1424no—
506C22×C8—711no—
507C22×C8—711no—
508C22×C8—714no—
509C22×C8—1424no—
510C22×C8C22×D7111yescharacteristic
511C22×C8C22×D7111yescharacteristic
512C4⋊Q8—714no—
513C4⋊Q8—714no—
514C4⋊Q8—1422no—
515C4⋊Q8—1428no—
516C4⋊Q8—1422no—
517#127—22no—
518#127—714no—
519#127—1422no—
520#127C22×D7114yes—
521#125—22no—
522#125—714no—
523#125—1422no—
524#125—1428no—
525#125C22×D7114yescomplemented
526#124—714no—
527#124—714no—
528#124—1422no—
529#124—1422no—
530C22⋊Q8—1428no—
531C22⋊Q8—1428no—
532#121—1428no—
533#121—1428no—
534#120—1428no—
535#120—1428no—
536#117—714no—
537#117—714no—
538#117—714no—
539#117—1422no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—711no—
543C2×C4⋊C4—711no—
544C2×C4⋊C4—711no—
545C2×C4⋊C4—711no—
546C2×C4⋊C4—714no—
547C2×C4⋊C4—1422no—
548C2×C4⋊C4—1421no—
549C2×C4⋊C4—1421no—
550C2×C4⋊C4—1421no—
551C2×C4⋊C4—1421no—
552C2×C4⋊C4—1421no—
553C2×C4⋊C4C22×D7111yescharacteristic
554C2×C4⋊C4C22×D7111yescharacteristic
555C2×C22⋊C4—711no—
556C2×C22⋊C4—711no—
557C2×C22⋊C4—1421no—
558C2×C22⋊C4—1421no—
559C2×C22⋊C4—1421no—
560C2×C22⋊C4—1421no—
561C2×C22⋊C4—1421no—
562C2×C42—711no—
563C2×C42—1421no—
564C2×C42C22×D7111yescharacteristic
565#103—714no—
566#103—714no—
567#103—714no—
568#103—714no—
569#102—714no—
570#102—714no—
571#102—714no—
572#102—714no—
573#102—714no—
574#102—714no—
575#102—714no—
576#102—714no—
577#102C22×D7114yes—
578#102C22×D7114yes—
579#102C22×D7114yescomplemented
580#102C22×D7114yescomplemented
581#97—714no—
582#97C22×D7114yescomplemented
583C4×C8—714no—
584C4×C8—714no—
585C24—21no—
586C24—21no—
587C24—2844no—
588C24—5682no—
589C24—5682no—
590C24—711no—
591C24—1424no—
592C24—1421no—
593#41—2848no—
594#41—1428no—
595#41—1428no—
596C2×Q8—5682no—
597C2×Q8—5682no—
598C2×Q8—712no—
599C2×Q8—1424no—
600C2×Q8—1422no—
601C2×Q8—1422no—
602C2×Q8—1421no—
603C2×Q8—1424no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—24no—
607C2×D4—24no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—82no—
613C2×D4—82no—
614C2×D4—2844no—
615C2×D4—2848no—
616C2×D4—2844no—
617C2×D4—5682no—
618C2×D4—5682no—
619C2×D4—712no—
620C2×D4—1428no—
621C2×D4—1428no—
622C2×D4—1424no—
623C2×D4—1424no—
624C2×D4—1424no—
625C2×D4—1424no—
626C2×D4—1421no—
627C2×D4—1422no—
628C2×D4—1422no—
629C2×D4C23×D7112yes—
630C2×D4C23×D7112yes—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—2844no—
634C22×C4—5682no—
635C22×C4—711no—
636C22×C4—712no—
637C22×C4—714no—
638C22×C4—714no—
639C22×C4—712no—
640C22×C4—711no—
641C22×C4—711no—
642C22×C4—1424no—
643C22×C4—1424no—
644C22×C4—1421no—
645C22×C4—1421no—
646C22×C4—1421no—
647C22×C4D4×D7111yescharacteristic
648C22×C4D4×D7111yescharacteristic
649C22×C4C23×D7111yescharacteristic
650M16—1428no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—712no—
654C2×C8—712no—
655C2×C8—1428no—
656C2×C8—1422no—
657C2×C8—1422no—
658C2×C8C23×D7112yes—
659C2×C8C23×D7112yes—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—714no—
665C4⋊C4—714no—
666C4⋊C4—712no—
667C4⋊C4—712no—
668C4⋊C4—1424no—
669C4⋊C4—1424no—
670C4⋊C4—1424no—
671C4⋊C4—1424no—
672C4⋊C4—1421no—
673C4⋊C4—1421no—
674C4⋊C4—1424no—
675C4⋊C4C23×D7112yes—
676C4⋊C4C23×D7112yes—
677C22⋊C4—714no—
678C22⋊C4—714no—
679C22⋊C4—1424no—
680C22⋊C4—1424no—
681C22⋊C4—1424no—
682C22⋊C4—1424no—
683C22⋊C4—1424no—
684C42—712no—
685C42—712no—
686C42—1424no—
687C42D4×D7112yes—
688C42C23×D7112yes—
689C23—22no—
690C23—22no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—2848no—
698C23—2842no—
699C23—2842no—
700C23—2842no—
701C23—5684no—
702C23—5684no—
703C23—56816no—
704C23—712no—
705C23—714no—
706C23—1422no—
707C23—1422no—
708C23—1422no—
709C23C2×D4×D7111yescharacteristic
710Q8—2842no—
711Q8—5684no—
712Q8—5684no—
713Q8—1422no—
714Q8—1422no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—42no—
720D4—42no—
721D4—84no—
722D4—84no—
723D4—2848no—
724D4—2848no—
725D4—2842no—
726D4—5684no—
727D4—5684no—
728D4—1422no—
729D4—1422no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—2842no—
737C2×C4—2842no—
738C2×C4—2842no—
739C2×C4—2848no—
740C2×C4—5684no—
741C2×C4—712no—
742C2×C4—714no—
743C2×C4—714no—
744C2×C4—714no—
745C2×C4—718no—
746C2×C4—712no—
747C2×C4—712no—
748C2×C4—1422no—
749C2×C4—1422no—
750C2×C4—1422no—
751C2×C4—1422no—
752C2×C4—1422no—
753C2×C4C2×D4×D7112yes—
754C2×C4C2×D4×D7112yes—
755C2×C4C2×D4×D7111yescharacteristic
756C2×C4#41×D7112yes—
757C2×C4#41×D7112yes—
758C2×C4C24×D7111yescharacteristic
759C8—22no—
760C8—22no—
761C8—1422no—
762C8—1422no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—84no—
770C22—84no—
771C22—2842no—
772C22—2842no—
773C22—2842no—
774C22—56816no—
775C22—5684no—
776C22—714no—
777C22—1428no—
778C22—1422no—
779C22—1422no—
780C22#124×D7112yes—
781C22#1798680312yes—
782C22#1798680912yes—
783C22C22×D4×D7111yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—2842no—
789C4—2842no—
790C4—2842no—
791C4—714no—
792C4—1422no—
793C4—1422no—
794C4#124×D7112yes—
795C4C2×#41×D7111yescharacteristic
796C4C2×#41×D7111yescharacteristic
797C2—82no—
798C2—82no—
799C2—5682no—
800C2—1424no—
801C2#2259869514yesdirect product factor
802C2C2×#124×D7111yescharacteristic
803C2C2×#1798680311yescharacteristic
804C2C2×#1798680911yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#490×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986562C2
hypercenterC2×#490D71
hypocenterC71C2×#3136
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. C2×#17986629C2semidirect
3. #22598695C2direct (N × H)
4. C2×#17986362C2semidirect
5. C2×#17986359C2semidirect
6. C2×#17986357C2semidirect
7. C2×#17986356C2semidirect
8. C2×#17986352C2semidirect
9. C2×#17986345C2semidirect
10. C2×#17986344C2semidirect
11. C2×#17985997C2semidirect
12. C2×#17986002C2semidirect
13. C2×#17985992C2semidirect
14. C2×#102×D71C2semidirect
15. C2×#17985956C2semidirect
16. C2×#490×C71C2semidirect
22. #17986629C22semidirect
25. C2×#14556128C22semidirect
27. C2×#14556127C22semidirect
29. C2×#14556119C22semidirect
42. #17986362C22semidirect
43. #17986359C22semidirect
44. #17986357C22semidirect
45. #17986356C22semidirect
46. #17986352C22semidirect
47. #17986345C22semidirect
48. #17986344C22semidirect
49. #17986002C22semidirect
50. #17985997C22semidirect
51. #17985992C22semidirect
52. C2×#14556053C22semidirect
53. C2×#14556053C22semidirect
54. C2×#14556051C22semidirect
55. C2×#14556051C22semidirect
60. C2×#14556049C22semidirect
61. C2×#14556049C22semidirect
64. #102×D71C22semidirect
65. #17985956C22semidirect
66. C2×#14556038C22semidirect
67. C2×C4×C71⋊C8C22semidirect
68. C2×C8×Dic71C22semidirect
70. C2×#125×C71C22semidirect
71. #490×C71C22semidirect
74. C2×#102×C71C22semidirect
75. C2×#102×C71C22semidirect
76. C2×#97×C71C22semidirect
104. #14556128C23semidirect
107. #14556127C23semidirect
111. #14556119C23semidirect
147. #14556053C23semidirect
148. #14556053C23semidirect
149. #14556051C23semidirect
150. #14556051C23semidirect
155. #14556049C23semidirect
156. #14556049C23semidirect
159. #14556038C23semidirect
160. C4×C71⋊C8C23semidirect
161. C8×Dic71C23semidirect
171. #125×C71C23semidirect
179. #102×C71C23semidirect
180. #102×C71C23semidirect
181. #97×C71C23semidirect
397. C2×C71#3136semidirect
407. C2×#490D71semidirect
419. C71C2×#3136semidirect
435. C2×#125C2×D71semidirect
448. #490C2×D71semidirect
473. C2×#102C2×D71semidirect
474. C2×#102C2×D71semidirect
477. C2×#97C2×D71semidirect
525. #125C22×D71semidirect
579. #102C22×D71semidirect
580. #102C22×D71semidirect
582. #97C22×D71semidirect
801. C2#22598695direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866292
C2×#179865622
#225986952
C2×#179863622
C2×#179863592
C2×#179863572
C2×#179863562
C2×#179863522
C2×#179863452
C2×#179863442
C2×#179859972
C2×#179860022
C2×#179859922
C2×#102×D712
C2×#179859562
C2×#490×C712
C2×#313671