Finite Group Databasebeta

← C2×#22598126 #32864951

Subgroups — C2×#22598126 #32864951

Order 18176.

2162 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986552C211yesmaximal, characteristic, complemented
2C2×#17986467C211yesmaximal, characteristic
3#22598126C2116yesmaximal, direct product factor
4C2×#17986309C211yesmaximal, characteristic, complemented
5C2×#17986305C211yesmaximal, characteristic, complemented
6C2×#17986293C211yesmaximal, characteristic, complemented
7C2×#17986283C211yesmaximal, characteristic, complemented
8C2×#17986302C211yesmaximal, characteristic, complemented
9C2×#17986298C211yesmaximal, characteristic, complemented
10C2×#17986288C211yesmaximal, characteristic, complemented
11C2×#17986278C211yesmaximal, characteristic, complemented
12C2×#17986035C211yesmaximal, characteristic, complemented
13C22×Dic71⋊C8C211yesmaximal, characteristic, complemented
14C2×#17985996C211yesmaximal, characteristic
15C2×#17985993C211yesmaximal, characteristic
16C2×#427×C71C211yesmaximal, characteristic, complemented
17C22×#11765865C2211yescharacteristic
18C23×C71⋊C8C2211yescharacteristic
19#17986552—24no—
20#17986552C2218yescomplemented
21C2×#14556127C2211yescharacteristic
22C2×#14556127C2211yescharacteristic
23C2×#14556119C2211yescharacteristic
24C2×#14556119C2211yescharacteristic
25C2×#14556105—21no—
26C2×#14556105—21no—
27#17986467—24no—
28#17986467C2218yes—
29C2×C4×Dic142—21no—
30C2×C4×Dic142—21no—
31C2×#14556093C2211yescharacteristic
32C2×#14556093C2211yescharacteristic
33C2×#14556090C2211yescharacteristic
34C2×#14556090C2211yescharacteristic
35C2×(C22⋊D71)⋊C4—21no—
36C2×(C22⋊D71)⋊C4—21no—
37C2×#14556087C2211yescharacteristic
38C2×#14556085—21no—
39C22×C4×Dic71C2211yescharacteristic
40C2×C42×D71—21no—
41#17986309C2218yescomplemented
42#17986305C2218yescomplemented
43#17986302C2218yescomplemented
44#17986298C2218yescomplemented
45#17986293C2218yescomplemented
46#17986288C2218yescomplemented
47#17986283C2218yescomplemented
48#17986278C2218yescomplemented
49#17986035C2218yescomplemented
50C2×#14556061C2211yescharacteristic
51C2×#14556061C2211yescharacteristic
52C2×#14556059C2211yescharacteristic
53C2×#14556059C2211yescharacteristic
54C2×Dic71⋊C8C2211yescharacteristic
55C2×Dic71⋊C8C2211yescharacteristic
56C2×Dic71⋊C8C2211yescharacteristic
57C2×Dic71⋊C8C2211yescharacteristic
58C2×Dic71⋊C8C2218yescomplemented
59#17985996C2218yes—
60#17985993C2218yes—
61C2×#14556053C2211yescharacteristic
62C2×#14556053C2211yescharacteristic
63C2×#14556051C2211yescharacteristic
64C2×#14556051C2211yescharacteristic
65C2×#14556050C2211yescharacteristic
66C2×#14556050C2211yescharacteristic
67C2×#14556048C2211yescharacteristic
68C2×#14556048C2211yescharacteristic
69C23×C8×C71C2211yescharacteristic
70C2×#117×C71C2211yescharacteristic
71C2×#117×C71C2211yescharacteristic
72#427×C71C2218yescomplemented
73C2×#107×C71C2211yescharacteristic
74C2×#107×C71C2211yescharacteristic
75C2×#106×C71C2211yescharacteristic
76C2×#106×C71C2211yescharacteristic
77C2×#11765865—22no—
78C2×#11765865—24no—
79C2×#11765865Q818yescomplemented
80C2×#11765865C2314yes—
81C22×Dic142—21no—
82C22×Dic142—21no—
83C22×Dic142C2311yescharacteristic
84C22×D284C2311yescharacteristic
85C22×C22⋊D71—21no—
86C23×Dic71D411yescharacteristic
87C23×Dic71D411yescharacteristic
88C22×C4×D71—21no—
89C22×C4×D71—21no—
90C22×C4×D71—21no—
91C22×C71⋊C8—24no—
92C22×C71⋊C8C2311yescharacteristic
93C22×C71⋊C8C2311yescharacteristic
94C22×C71⋊C8C2314yes—
95#14556127—22no—
96#14556127—22no—
97#14556127C2314yes—
98#14556127C2314yes—
99#14556119—22no—
100#14556119—22no—
101#14556119C2314yes—
102#14556119C2314yes—
103#14556105—28no—
104#14556105—28no—
105C4×Dic142—28no—
106C4×Dic142—28no—
107#14556093—22no—
108#14556093—22no—
109#14556093C2314yes—
110#14556093C2314yes—
111#14556090—22no—
112#14556090—22no—
113#14556090C2314yes—
114#14556090C2314yes—
115(C22⋊D71)⋊C4—28no—
116(C22⋊D71)⋊C4—28no—
117#14556087—22no—
118#14556087C2314yes—
119#14556085—28no—
120C2×C4⋊Dic71—21no—
121C2×C4⋊Dic71—21no—
122C2×C4⋊Dic71C2311yescharacteristic
123C2×C4⋊Dic71C2311yescharacteristic
124C2×Dic71⋊C4—21no—
125C2×Dic71⋊C4—21no—
126C2×Dic71⋊C4—21no—
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C2×Dic71⋊C4—21no—
130C2×C22⋊Dic71—21no—
131C2×(C2×D71)⋊C4—21no—
132C2×(C2×D71)⋊C4—21no—
133C2×C4×Dic71—21no—
134C2×C4×Dic71—21no—
135C2×C4×Dic71—21no—
136C2×C4×Dic71D411yescharacteristic
137C2×C4×Dic71D411yescharacteristic
138C2×C4×Dic71D414yes—
139C2×C4×Dic71C2311yescharacteristic
140C2×C4×Dic71C2311yescharacteristic
141C2×C4×Dic71C2314yes—
142C42×D71—28no—
143#14556061C2314yes—
144#14556061C2314yes—
145#14556059C2314yes—
146#14556059C2314yes—
147Dic71⋊C8C2314yes—
148Dic71⋊C8C2314yes—
149Dic71⋊C8C2314yes—
150Dic71⋊C8C2314yes—
151#14556053C2314yes—
152#14556053C2314yes—
153#14556051C2314yes—
154#14556051C2314yes—
155#14556050C2314yes—
156#14556050C2314yes—
157#14556048C2314yes—
158#14556048C2314yes—
159C23×C4×C71C2311yescharacteristic
160C22×C8×C71—24no—
161C22×C8×C71C2311yescharacteristic
162C22×C8×C71C2311yescharacteristic
163C22×C8×C71C2314yes—
164#117×C71—22no—
165#117×C71—22no—
166#117×C71C2314yes—
167#117×C71C2314yes—
168C2×C4⋊C4×C71C2311yescharacteristic
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C22⋊C4×C71—21no—
173C2×C22⋊C4×C71—21no—
174C2×C42×C71—21no—
175C2×C42×C71—21no—
176#107×C71C2314yes—
177#107×C71C2314yes—
178#106×C71C2314yes—
179#106×C71C2314yes—
180C23×D71—21no—
181#11765865—216no—
182#11765865—28no—
183#11765865C2×Q8116yescomplemented
184C2×Dic142—21no—
185C2×Dic142—22no—
186C2×Dic142—24no—
187C2×Dic142—24no—
188C2×Dic142—44no—
189C2×Dic142—44no—
190C2×Dic142C2×Q814yes—
191C2×Dic142C2412yes—
192C2×D284—21no—
193C2×D284—22no—
194C2×D284C2×Q814yes—
195C2×D284C2412yes—
196C2×C22⋊D71—28no—
197C2×C22⋊D71—24no—
198C22×Dic71—21no—
199C22×Dic71—24no—
200C22×Dic71—21no—
201C22×Dic71—21no—
202C22×Dic71—42no—
203C22×Dic71C2×D411yescharacteristic
204C22×Dic71C2×D411yescharacteristic
205C22×Dic71C2×D411yescharacteristic
206C22×Dic71C2×D414yes—
207C22×Dic71C2×D414yes—
208C22×Dic71C2×D411yescharacteristic
209C2×C4×D71—28no—
210C2×C4×D71—24no—
211C2×C4×D71—24no—
212C2×C4×D71—24no—
213C2×C4×D71—44no—
214C2×C4×D71—44no—
215C2×C71⋊C8—22no—
216C2×C71⋊C8—22no—
217C2×C71⋊C8—28no—
218C2×C71⋊C8C2412yes—
219C2×C71⋊C8C2412yes—
220C4⋊Dic71—21no—
221C4⋊Dic71—21no—
222C4⋊Dic71—24no—
223C4⋊Dic71—24no—
224C4⋊Dic71C2412yes—
225C4⋊Dic71C2412yes—
226Dic71⋊C4—24no—
227Dic71⋊C4—24no—
228Dic71⋊C4—24no—
229Dic71⋊C4—24no—
230Dic71⋊C4—24no—
231Dic71⋊C4—24no—
232C22⋊Dic71—24no—
233(C2×D71)⋊C4—24no—
234(C2×D71)⋊C4—24no—
235C4×Dic71—24no—
236C4×Dic71—24no—
237C4×Dic71—24no—
238C4×Dic71C2×D414yes—
239C4×Dic71C2×D414yes—
240C4×Dic71C2×D412yes—
241C4×Dic71C2×D412yes—
242C4×Dic71C2412yes—
243C4×Dic71C2412yes—
244C24×C71C2×D411yescharacteristic
245C22×C4×C71—21no—
246C22×C4×C71—21no—
247C22×C4×C71—21no—
248C22×C4×C71—21no—
249C22×C4×C71C2×D412yes—
250C22×C4×C71C2×D411yescharacteristic
251C22×C4×C71C2×Q814yes—
252C22×C4×C71#4114yes—
253C22×C4×C71C2411yescharacteristic
254C22×C4×C71C2412yes—
255C2×C8×C71—22no—
256C2×C8×C71—22no—
257C2×C8×C71—28no—
258C2×C8×C71C2412yes—
259C2×C8×C71C2412yes—
260C4⋊C4×C71—21no—
261C4⋊C4×C71—21no—
262C4⋊C4×C71—21no—
263C4⋊C4×C71—21no—
264C4⋊C4×C71C2412yes—
265C4⋊C4×C71C2412yes—
266C4⋊C4×C71C2412yes—
267C4⋊C4×C71C2412yes—
268C22⋊C4×C71—24no—
269C22⋊C4×C71—24no—
270C42×C71—24no—
271C42×C71—24no—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71C22⋊Q814yes—
275C23×C71C22×D412yes—
276C23×C71C22×D411yescharacteristic
277C22×D71—24no—
278C22×D71—22no—
279C22×D71—42no—
280C22×D71—42no—
281C2×C4×C71—22no—
282C2×C4×C71—22no—
283C2×C4×C71—22no—
284C2×C4×C71—22no—
285C2×C4×C71—42no—
286C2×C4×C71—42no—
287C2×C4×C71—42no—
288C2×C4×C71—42no—
289C2×C4×C71C22⋊Q814yes—
290C2×C4×C71C22⋊Q818yes—
291C2×C4×C71C22×D412yes—
292C2×C4×C71C22×D411yescharacteristic
293C2×C4×C71C22×Q812yes—
294C2×C4×C71C22×Q814yes—
295C2×C4×C71C2×#4112yes—
296C2×C4×C71C2×#4114yes—
297C2×C4×C71C2511yescharacteristic
298C22⋊D71—216no—
299C2×Dic71—24no—
300C2×Dic71—22no—
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—28no—
305C2×Dic71—22no—
306C2×Dic71—22no—
307C2×Dic71—44no—
308C2×Dic71—42no—
309C2×Dic71—42no—
310C2×Dic71#13514yes—
311C2×Dic71C22×D412yes—
312C2×Dic71C22×D412yes—
313C2×Dic71C22×D412yes—
314C2×Dic71C22×D412yes—
315D284—24no—
316D284—22no—
317D284C22×Q814yes—
318C4×D71—216no—
319C4×D71—48no—
320C4×D71—48no—
321Dic142—24no—
322Dic142—22no—
323Dic142—48no—
324Dic142—48no—
325Dic142C22×Q814yes—
326C8×C71—22no—
327C8×C71—22no—
328C71⋊C8—22no—
329C71⋊C8—22no—
330C22×C71—28no—
331C22×C71—22no—
332C22×C71—22no—
333C22×C71C2×C22⋊Q814yes—
334C22×C71C2×C22⋊Q812yes—
335C22×C71C2×#13512yes—
336C22×C71#57512yes—
337C22×C71C23×D411yescharacteristic
338C2×D71—24no—
339C2×D71—48no—
340C2×D71—42no—
341C2×D71—42no—
342C4×C71—42no—
343C4×C71—42no—
344C4×C71—42no—
345C4×C71—42no—
346C4×C71C2×C22⋊Q812yes—
347C4×C71C2×C22⋊Q814yes—
348C4×C71C23×Q811yescharacteristic
349C4×C71C22×#4111yescharacteristic
350Dic71—24no—
351Dic71—22no—
352Dic71—22no—
353Dic71—22no—
354Dic71—42no—
355Dic71—42no—
356Dic71C2×#13514yes—
357C2×#3076—711nomaximal, Sylow
358C2×C71—24no—
359C2×C71#307614yescomplemented
360C2×C71C22×C22⋊Q811yescharacteristic
361C2×C71C22×#13511yescharacteristic
362C2×C71C2×#57511yescharacteristic
363D71—44no—
364C2×#533—711no—
365C2×C4×#41—711no—
366#3076—7116no—
367C2×#479—711no—
368C2×#479—711no—
369C2×#477—711no—
370C2×#475—711no—
371C2×#478—711no—
372C2×#478—711no—
373C2×#476—711no—
374C2×#474—711no—
375C2×#427—711no—
376C2×#427D7111yescharacteristic, complemented
377C22×C4⋊C8—711no—
378C2×#416—711no—
379C2×#416—711no—
380C71C2×#307611yescharacteristic, complemented, Sylow
381C22×#41—711no—
382C23×C8—711no—
383C23×C8C2×D7111yescharacteristic
384#533—718no—
385#533—1424no—
386C2×C4⋊Q8—711no—
387C2×C4⋊Q8—711no—
388C2×#125—711no—
389C2×#125—711no—
390C2×C22⋊Q8—1421no—
391C2×C22⋊Q8—1421no—
392C4×#41—718no—
393C4×#41—1424no—
394C2×C4×Q8—711no—
395C2×C4×Q8—711no—
396C2×C4×Q8—1421no—
397C2×C4×Q8—1421no—
398C2×C4×D4—711no—
399C2×C4×D4—711no—
400C2×C4×D4—1421no—
401C2×C4×D4—1421no—
402C2×#117—711no—
403C2×#117—1421no—
404C2×#117C2×D7111yescharacteristic
405C2×#117C2×D7111yescharacteristic
406C22×C42—711no—
407C22×C42—1421no—
408#479—718no—
409#479—718no—
410#478—718no—
411#478—718no—
412#477—718no—
413#476—718no—
414#475—718no—
415#474—718no—
416#427—718no—
417#427C2×D7118yescomplemented
418C2×#107—711no—
419C2×#107—711no—
420C2×#107C2×D7111yescharacteristic
421C2×#107C2×D7111yescharacteristic
422C2×#106—711no—
423C2×#106—711no—
424C2×#106C2×D7111yescharacteristic
425C2×#106C2×D7111yescharacteristic
426C2×C4⋊C8—711no—
427C2×C4⋊C8—711no—
428C2×C4⋊C8—711no—
429C2×C4⋊C8—711no—
430C2×C4⋊C8—718no—
431#416—718no—
432#416—718no—
433C2×#103—711no—
434C2×#103—711no—
435C2×#103—711no—
436C2×#103—711no—
437C2×#102—711no—
438C2×#102—711no—
439C2×#102—711no—
440C2×#102—711no—
441C2×#41—718no—
442C2×#41—714no—
443C2×#41—1422no—
444C2×#41—1424no—
445C22×Q8—711no—
446C22×Q8—1421no—
447C22×Q8—1421no—
448C22×D4—711no—
449C22×D4—1421no—
450C23×C4—711no—
451C23×C4—711no—
452C23×C4—1421no—
453C23×C4—1421no—
454C23×C4—1421no—
455C23×C4C22×D7111yescharacteristic
456C22×C8—24no—
457C22×C8—711no—
458C22×C8—711no—
459C22×C8—714no—
460C22×C8—1424no—
461C22×C8C22×D7111yescharacteristic
462C22×C8C22×D7111yescharacteristic
463C22×C8C22×D7114yes—
464C4⋊Q8—714no—
465C4⋊Q8—714no—
466C4⋊Q8—1422no—
467C4⋊Q8—1422no—
468#125—714no—
469#125—714no—
470#125—1422no—
471#125—1422no—
472C22⋊Q8—1428no—
473C22⋊Q8—1428no—
474C4×Q8—714no—
475C4×Q8—714no—
476C4×Q8—1428no—
477C4×Q8—1428no—
478C4×Q8—1422no—
479C4×Q8—1422no—
480C4×D4—714no—
481C4×D4—714no—
482C4×D4—1422no—
483C4×D4—1422no—
484C4×D4—1428no—
485C4×D4—1428no—
486#117—22no—
487#117—22no—
488#117—714no—
489#117—1428no—
490#117—1422no—
491#117C22×D7114yes—
492#117C22×D7114yes—
493C2×C4⋊C4—711no—
494C2×C4⋊C4—711no—
495C2×C4⋊C4—1421no—
496C2×C4⋊C4—1421no—
497C2×C4⋊C4—1421no—
498C2×C4⋊C4—1421no—
499C2×C4⋊C4—1421no—
500C2×C4⋊C4—1421no—
501C2×C4⋊C4—1421no—
502C2×C4⋊C4—1421no—
503C2×C4⋊C4C22×D7111yescharacteristic
504C2×C4⋊C4C22×D7111yescharacteristic
505C2×C4⋊C4C22×D7111yescharacteristic
506C2×C4⋊C4C22×D7111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—1421no—
510C2×C22⋊C4—1421no—
511C2×C22⋊C4—1421no—
512C2×C42—21no—
513C2×C42—21no—
514C2×C42—714no—
515C2×C42—711no—
516C2×C42—711no—
517C2×C42—711no—
518C2×C42—711no—
519C2×C42—714no—
520C2×C42—1428no—
521C2×C42—1421no—
522C2×C42—1421no—
523C2×C42—1421no—
524#107—714no—
525#107—714no—
526#107C22×D7114yes—
527#107C22×D7114yes—
528#106—714no—
529#106—714no—
530#106C22×D7114yes—
531#106C22×D7114yes—
532C4⋊C8—714no—
533C4⋊C8—714no—
534C4⋊C8—714no—
535C4⋊C8—714no—
536#103—714no—
537#103—714no—
538#103—714no—
539#103—714no—
540#102—714no—
541#102—714no—
542#102—714no—
543#102—714no—
544C24—1421no—
545C24D4×D7111yescharacteristic
546#41—7116no—
547#41—1428no—
548#41—14216no—
549C2×Q8—2844no—
550C2×Q8—2844no—
551C2×Q8—714no—
552C2×Q8—712no—
553C2×Q8—1424no—
554C2×Q8—1424no—
555C2×Q8—1421no—
556C2×Q8—1422no—
557C2×D4—714no—
558C2×D4—712no—
559C2×D4—1424no—
560C2×D4—1428no—
561C2×D4—1421no—
562C2×D4—1422no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—2844no—
568C22×C4—2844no—
569C22×C4—2842no—
570C22×C4—714no—
571C22×C4—711no—
572C22×C4—711no—
573C22×C4—711no—
574C22×C4—711no—
575C22×C4—714no—
576C22×C4—1424no—
577C22×C4—1424no—
578C22×C4—1421no—
579C22×C4—1421no—
580C22×C4—1424no—
581C22×C4—1421no—
582C22×C4—1424no—
583C22×C4—1428no—
584C22×C4D4×D7112yes—
585C22×C4D4×D7111yescharacteristic
586C22×C4Q8×D7114yes—
587C22×C4#1176586514yes—
588C22×C4C23×D7111yescharacteristic
589C22×C4C23×D7112yes—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—28no—
593C2×C8—712no—
594C2×C8—712no—
595C2×C8—1422no—
596C2×C8—1422no—
597C2×C8—1428no—
598C2×C8C23×D7112yes—
599C2×C8C23×D7112yes—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—712no—
605C4⋊C4—712no—
606C4⋊C4—1424no—
607C4⋊C4—1424no—
608C4⋊C4—1424no—
609C4⋊C4—1424no—
610C4⋊C4—1424no—
611C4⋊C4—1424no—
612C4⋊C4—1424no—
613C4⋊C4—1424no—
614C4⋊C4—1421no—
615C4⋊C4—1421no—
616C4⋊C4C23×D7112yes—
617C4⋊C4C23×D7112yes—
618C4⋊C4C23×D7112yes—
619C4⋊C4C23×D7112yes—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4—1424no—
623C22⋊C4—1424no—
624C22⋊C4—1424no—
625C42—24no—
626C42—24no—
627C42—714no—
628C42—714no—
629C42—712no—
630C42—712no—
631C42—712no—
632C42—712no—
633C42—1424no—
634C42—1424no—
635C42—1424no—
636C23—22no—
637C23—22no—
638C23—2842no—
639C23—2842no—
640C23—1422no—
641C23—1424no—
642C23#1455610614yes—
643C23C2×D4×D7112yes—
644C23C2×D4×D7111yescharacteristic
645Q8—2848no—
646Q8—2848no—
647Q8—714no—
648Q8—1422no—
649Q8—1424no—
650D4—714no—
651D4—14216no—
652D4—1422no—
653D4—1424no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—2848no—
663C2×C4—2848no—
664C2×C4—2842no—
665C2×C4—2842no—
666C2×C4—2844no—
667C2×C4—712no—
668C2×C4—714no—
669C2×C4—712no—
670C2×C4—712no—
671C2×C4—712no—
672C2×C4—1422no—
673C2×C4—1422no—
674C2×C4—1428no—
675C2×C4—1422no—
676C2×C4—1424no—
677C2×C4—1422no—
678C2×C4—1422no—
679C2×C4—1422no—
680C2×C4—14216no—
681C2×C4#1455610614yes—
682C2×C4#1455610618yes—
683C2×C4C2×D4×D7112yes—
684C2×C4C2×D4×D7111yescharacteristic
685C2×C4C2×Q8×D7112yes—
686C2×C4C2×Q8×D7114yes—
687C2×C4C2×#1176586512yes—
688C2×C4C2×#1176586514yes—
689C2×C4C24×D7111yescharacteristic
690C8—22no—
691C8—22no—
692C8—1422no—
693C8—1422no—
694C22—22no—
695C22—22no—
696C22—28no—
697C22—2842no—
698C22—2842no—
699C22—2848no—
700C22—1424no—
701C22C2×#1455610614yes—
702C22C2×#1455610612yes—
703C22#135×D7112yes—
704C22#1798679612yes—
705C22C22×D4×D7111yescharacteristic
706C4—42no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—2842no—
711C4—2842no—
712C4—714no—
713C4—1422no—
714C4—1422no—
715C4—1422no—
716C4—1424no—
717C4C2×#1455610614yes—
718C4C2×#1455610612yes—
719C4C22×Q8×D7111yescharacteristic
720C4C22×#1176586511yescharacteristic
721C2—24no—
722C2—2844no—
723C2#2259812614yesdirect product factor
724C2C22×#1455610611yescharacteristic
725C2C2×#135×D7111yescharacteristic
726C2C2×#1798679611yescharacteristic
subgroupG/H
centerC22×C4D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#427×C71C2
socleC23×C71C22×D4
prime radicalC22×#11765865C22
hypercenterC2×#427D71
hypocenterC71C2×#3076
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
1. C2×#17986552C2semidirect
3. #22598126C2direct (N × H)
4. C2×#17986309C2semidirect
5. C2×#17986305C2semidirect
6. C2×#17986293C2semidirect
7. C2×#17986283C2semidirect
8. C2×#17986302C2semidirect
9. C2×#17986298C2semidirect
10. C2×#17986288C2semidirect
11. C2×#17986278C2semidirect
12. C2×#17986035C2semidirect
13. C22×Dic71⋊C8C2semidirect
16. C2×#427×C71C2semidirect
20. #17986552C22semidirect
41. #17986309C22semidirect
42. #17986305C22semidirect
43. #17986302C22semidirect
44. #17986298C22semidirect
45. #17986293C22semidirect
46. #17986288C22semidirect
47. #17986283C22semidirect
48. #17986278C22semidirect
49. #17986035C22semidirect
58. C2×Dic71⋊C8C22semidirect
72. #427×C71C22semidirect
79. C2×#11765865Q8semidirect
183. #11765865C2×Q8semidirect
359. C2×C71#3076semidirect
376. C2×#427D71semidirect
380. C71C2×#3076semidirect
417. #427C2×D71semidirect
723. C2#22598126direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179865522
C2×#179864672
#225981262
C2×#179863092
C2×#179863052
C2×#179862932
C2×#179862832
C2×#179863022
C2×#179862982
C2×#179862882
C2×#179862782
C2×#179860352
C22×Dic71⋊C82
C2×#179859962
C2×#179859932
C2×#427×C712
C2×#307671