Finite Group Databasebeta

← C2×#22601294 #32877989

Subgroups — C2×#22601294 #32877989

Order 18176.

1898 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986709C211yesmaximal, characteristic, complemented
2#22601294C2116yesmaximal, direct product factor
3C2×#17986409C211yesmaximal, characteristic, complemented
4C2×#17986405C211yesmaximal, characteristic, complemented
5C2×#17986398C211yesmaximal, characteristic, complemented
6C2×#17986299C211yesmaximal, characteristic, complemented
7C2×#17986299C211yesmaximal, characteristic, complemented
8C2×#17986296C211yesmaximal, characteristic, complemented
9C2×#17986296C211yesmaximal, characteristic, complemented
10C2×#17986279C211yesmaximal, characteristic, complemented
11C2×#17986276C211yesmaximal, characteristic, complemented
12C2×#17986130C211yesmaximal, characteristic, complemented
13C2×#17986109C211yesmaximal, characteristic
14C2×#17986109C211yesmaximal, characteristic
15C2×C4×#11765850C211yesmaximal, characteristic
16C2×#554×C71C211yesmaximal, characteristic, complemented
17C22×#11765850C2211yescharacteristic
18#17986709—24no—
19#17986709C2218yescomplemented
20C2×#14556128C2211yescharacteristic
21C2×#14556120C2211yescharacteristic
22C2×#14556120C2211yescharacteristic
23C2×#14556106—21no—
24C2×#14556106—21no—
25C2×#14556104—21no—
26C2×C4×D284C2211yescharacteristic
27C2×C4×D284C2211yescharacteristic
28C2×C4×D284C2211yescharacteristic
29C2×C4⋊C4×D71—21no—
30#17986409C2218yescomplemented
31#17986405C2218yescomplemented
32#17986398C2218yescomplemented
33#17986299C2218yescomplemented
34#17986299C2218yescomplemented
35#17986296C2218yescomplemented
36#17986296C2218yescomplemented
37#17986279C2218yescomplemented
38#17986276C2218yescomplemented
39#17986130C2218yescomplemented
40#17986109C2218yes—
41#17986109C2218yes—
42C4×#11765850C2218yes—
43C2×#14556061C2211yescharacteristic
44C2×#14556061C2211yescharacteristic
45C2×#14556061C2211yescharacteristic
46C2×#14556061C2211yescharacteristic
47C2×#14556061C2211yescharacteristic
48C2×#14556059C2211yescharacteristic
49C2×#14556059C2211yescharacteristic
50C2×#14556059C2211yescharacteristic
51C2×#14556059C2211yescharacteristic
52C2×C4⋊(C71⋊C8)C2211yescharacteristic
53C2×C4⋊(C71⋊C8)C2211yescharacteristic
54C2×C4⋊(C71⋊C8)C2211yescharacteristic
55C2×#14556049C2211yescharacteristic
56C2×#14556049C2211yescharacteristic
57C2×#14556049C2211yescharacteristic
58C2×#14556048C2211yescharacteristic
59C2×#14556048C2211yescharacteristic
60C2×#14556048C2211yescharacteristic
61C2×#14556039C2211yescharacteristic
62C2×#14556039C2211yescharacteristic
63C2×C4×C71⋊C8C2211yescharacteristic
64#554×C71—24no—
65#554×C71C2218yescomplemented
66C2×C4⋊Q8×C71C2211yescharacteristic
67C2×#125×C71C2211yescharacteristic
68C2×#125×C71C2211yescharacteristic
69C2×C22⋊Q8×C71—21no—
70C2×C22⋊Q8×C71—21no—
71C2×C22⋊Q8×C71—21no—
72C2×C4×Q8×C71C2211yescharacteristic
73C2×C4×D4×C71C2211yescharacteristic
74C2×C4×D4×C71C2211yescharacteristic
75C2×C4×D4×C71C2211yescharacteristic
76C22×C4⋊C4×C71—21no—
77C22×Dic142—21no—
78C22×D284C2311yescharacteristic
79C22×C4×D71—21no—
80C22×C4×D71—21no—
81C22×C4×D71—21no—
82C2×#11765850Q818yescomplemented
83C2×#11765850C2314yes—
84C22×C71⋊C8C2311yescharacteristic
85C22×C71⋊C8C2311yescharacteristic
86C22×C71⋊C8C2311yescharacteristic
87C22×C71⋊C8C2311yescharacteristic
88#14556128—22no—
89#14556128C2314yes—
90#14556120—22no—
91#14556120—22no—
92#14556120C2314yes—
93#14556120C2314yes—
94#14556106—28no—
95#14556106—28no—
96#14556104—28no—
97C4×D284—22no—
98C4×D284—22no—
99C4×D284—22no—
100C4×D284C2314yes—
101C4×D284C2314yes—
102C4×D284C2314yes—
103C2×C4⋊Dic71—21no—
104C2×C4⋊Dic71C2311yescharacteristic
105C2×C4⋊Dic71C2311yescharacteristic
106C2×C4⋊Dic71C2311yescharacteristic
107C2×Dic71⋊C4—21no—
108C2×Dic71⋊C4—21no—
109C2×Dic71⋊C4—21no—
110C2×Dic71⋊C4—21no—
111C4⋊C4×D71—28no—
112C2×(C2×D71)⋊C4—21no—
113C2×(C2×D71)⋊C4—21no—
114C2×(C2×D71)⋊C4—21no—
115#14556061C2314yes—
116#14556061C2314yes—
117#14556061C2314yes—
118#14556061C2314yes—
119#14556061C2314yes—
120#14556059C2314yes—
121#14556059C2314yes—
122#14556059C2314yes—
123#14556059C2314yes—
124C4⋊(C71⋊C8)C2314yes—
125C4⋊(C71⋊C8)C2314yes—
126C4⋊(C71⋊C8)C2314yes—
127#14556049C2314yes—
128#14556049C2314yes—
129#14556049C2314yes—
130#14556048C2314yes—
131#14556048C2314yes—
132#14556048C2314yes—
133#14556039C2314yes—
134#14556039C2314yes—
135C4×C71⋊C8C2314yes—
136C22×Q8×C71—21no—
137C22×Q8×C71D411yescharacteristic
138C22×D4×C71C2311yescharacteristic
139C23×C4×C71—21no—
140C23×C4×C71—21no—
141C23×C4×C71—21no—
142C4⋊Q8×C71—22no—
143C4⋊Q8×C71C2314yes—
144#125×C71—22no—
145#125×C71—22no—
146#125×C71C2314yes—
147#125×C71C2314yes—
148C22⋊Q8×C71—28no—
149C22⋊Q8×C71—28no—
150C22⋊Q8×C71—28no—
151C4×Q8×C71D414yes—
152C4×Q8×C71C2314yes—
153C4×D4×C71—22no—
154C4×D4×C71—22no—
155C4×D4×C71—22no—
156C4×D4×C71C2314yes—
157C4×D4×C71C2314yes—
158C4×D4×C71C2314yes—
159C2×C4⋊C4×C71—21no—
160C2×C4⋊C4×C71—21no—
161C2×C4⋊C4×C71—21no—
162C2×C4⋊C4×C71—21no—
163C2×C4⋊C4×C71—21no—
164C2×C4⋊C4×C71—28no—
165C2×C4⋊C4×C71D411yescharacteristic
166C2×C4⋊C4×C71D411yescharacteristic
167C2×C4⋊C4×C71D411yescharacteristic
168C2×C4⋊C4×C71C2311yescharacteristic
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C22⋊C4×C71—21no—
172C2×C22⋊C4×C71—21no—
173C2×C22⋊C4×C71—21no—
174C2×C42×C71C2311yescharacteristic
175C2×C42×C71C2311yescharacteristic
176C2×C42×C71C2311yescharacteristic
177C23×D71—21no—
178C2×Dic142—24no—
179C2×Dic142—82no—
180C2×D284—21no—
181C2×D284—22no—
182C2×D284C2×Q814yes—
183C2×D284C2412yes—
184C22×Dic71—21no—
185C22×Dic71—21no—
186C22×Dic71—21no—
187C2×C4×D71—24no—
188C2×C4×D71—24no—
189C2×C4×D71—24no—
190C2×C4×D71—44no—
191C2×C4×D71—82no—
192C2×C4×D71—82no—
193#11765850C2×Q8116yescomplemented
194C2×C71⋊C8—22no—
195C2×C71⋊C8—22no—
196C2×C71⋊C8—22no—
197C2×C71⋊C8C2×Q814yes—
198C2×C71⋊C8C2412yes—
199C2×C71⋊C8C2412yes—
200C2×C71⋊C8C2412yes—
201C2×C71⋊C8C2412yes—
202C4⋊Dic71—24no—
203C4⋊Dic71—21no—
204C4⋊Dic71—21no—
205C4⋊Dic71—21no—
206C4⋊Dic71C2412yes—
207C4⋊Dic71C2412yes—
208C4⋊Dic71C2412yes—
209Dic71⋊C4—24no—
210Dic71⋊C4—24no—
211Dic71⋊C4—24no—
212Dic71⋊C4—24no—
213(C2×D71)⋊C4—24no—
214(C2×D71)⋊C4—24no—
215(C2×D71)⋊C4—24no—
216C24×C71—21no—
217C2×Q8×C71—24no—
218C2×Q8×C71—42no—
219C2×Q8×C71—82no—
220C2×Q8×C71C2×D414yes—
221C2×D4×C71—21no—
222C2×D4×C71—22no—
223C2×D4×C71C2×Q814yes—
224C2×D4×C71C2412yes—
225C22×C4×C71—21no—
226C22×C4×C71—21no—
227C22×C4×C71—21no—
228C22×C4×C71—24no—
229C22×C4×C71—24no—
230C22×C4×C71—24no—
231C22×C4×C71—44no—
232C22×C4×C71—82no—
233C22×C4×C71—82no—
234C22×C4×C71C2×D411yescharacteristic
235C22×C4×C71C2×D411yescharacteristic
236C22×C4×C71C2×D411yescharacteristic
237C22×C4×C71C2×D411yescharacteristic
238C22×C4×C71C2×D411yescharacteristic
239C22×C4×C71C2×D411yescharacteristic
240C22×C4×C71C2411yescharacteristic
241C4⋊C4×C71—24no—
242C4⋊C4×C71—24no—
243C4⋊C4×C71—24no—
244C4⋊C4×C71—24no—
245C4⋊C4×C71—24no—
246C4⋊C4×C71—21no—
247C4⋊C4×C71—21no—
248C4⋊C4×C71—21no—
249C4⋊C4×C71C2×D414yes—
250C4⋊C4×C71C2×D414yes—
251C4⋊C4×C71C2×D414yes—
252C4⋊C4×C71C2412yes—
253C4⋊C4×C71C2412yes—
254C4⋊C4×C71C2412yes—
255C22⋊C4×C71—24no—
256C22⋊C4×C71—24no—
257C22⋊C4×C71—24no—
258C42×C71C2×D412yes—
259C42×C71C2×D412yes—
260C42×C71C2×D412yes—
261C42×C71C2412yes—
262C42×C71C2412yes—
263C42×C71C2412yes—
264C23×C71—24no—
265C23×C71—22no—
266C23×C71—42no—
267C23×C71—42no—
268C23×C71C22×D411yescharacteristic
269C22×D71—24no—
270C22×D71—22no—
271C22×D71—42no—
272C22×D71—42no—
273Q8×C71—44no—
274Q8×C71—84no—
275D4×C71—24no—
276D4×C71—22no—
277D4×C71C22×Q814yes—
278C2×C4×C71—22no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—22no—
282C2×C4×C71—22no—
283C2×C4×C71—22no—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—48no—
288C2×C4×C71—42no—
289C2×C4×C71—42no—
290C2×C4×C71—42no—
291C2×C4×C71—84no—
292C2×C4×C71—84no—
293C2×C4×C71C22×D412yes—
294C2×C4×C71C22×D412yes—
295C2×C4×C71C22×D412yes—
296C2×C4×C71C22×D412yes—
297C2×C4×C71C22×D412yes—
298C2×C4×C71C22×D412yes—
299C2×C4×C71C22×D411yescharacteristic
300C2×C4×C71C22×Q812yes—
301C2×C4×C712−1+412yes—
302C2×C4×C71C2511yescharacteristic
303C2×Dic71—22no—
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—42no—
307C2×Dic71—42no—
308C2×Dic71—42no—
309D284—24no—
310D284—22no—
311D284C22×Q814yes—
312C4×D71—48no—
313C4×D71—84no—
314C4×D71—84no—
315Dic142—84no—
316C71⋊C8—22no—
317C71⋊C8—22no—
318C71⋊C8—22no—
319C71⋊C8C22×Q814yes—
320C22×C71—24no—
321C22×C71—48no—
322C22×C71—42no—
323C22×C71—42no—
324C22×C71D4×Q812yes—
325C22×C71#57512yes—
326C22×C71#57612yes—
327C22×C71C23×D411yescharacteristic
328C2×D71—24no—
329C2×D71—48no—
330C2×D71—42no—
331C2×D71—42no—
332C4×C71—22no—
333C4×C71—22no—
334C4×C71—22no—
335C4×C71—22no—
336C4×C71—22no—
337C4×C71—22no—
338C4×C71—42no—
339C4×C71—42no—
340C4×C71—42no—
341C4×C71D4×Q812yes—
342C4×C71C23×Q811yescharacteristic
343C4×C71C2×2−1+411yescharacteristic
344Dic71—42no—
345Dic71—42no—
346Dic71—42no—
347C2×#3389—711nomaximal, Sylow
348C2×C71—44no—
349C2×C71#338914yescomplemented
350C2×C71C2×D4×Q811yescharacteristic
351C2×C71C2×#57511yescharacteristic
352C2×C71C2×#57611yescharacteristic
353D71—44no—
354C2×#554—711no—
355C2×#554D7111yescharacteristic, complemented
356#3389—7116no—
357C2×#501—711no—
358C2×#501—711no—
359C2×#499—711no—
360C2×#478—711no—
361C2×#478—711no—
362C2×#478—711no—
363C2×#478—711no—
364C2×#474—711no—
365C2×#474—711no—
366C2×#446—711no—
367C2×#442—711no—
368C2×#442—711no—
369C2×C4×D8—711no—
370C71C2×#338911yescharacteristic, complemented, Sylow
371C22×D8—711no—
372#554—24no—
373#554—718no—
374#554—1424no—
375#554C2×D7118yescomplemented
376C2×C4⋊Q8—711no—
377C2×C4⋊Q8C2×D7111yescharacteristic
378C2×#125—711no—
379C2×#125—711no—
380C2×#125C2×D7111yescharacteristic
381C2×#125C2×D7111yescharacteristic
382C2×C22⋊Q8—21no—
383C2×C22⋊Q8—21no—
384C2×C22⋊Q8—21no—
385C2×C22⋊Q8—1421no—
386C2×C22⋊Q8—1421no—
387C2×C22⋊Q8—1421no—
388C2×C4×Q8C2×D7111yescharacteristic
389C2×C4×D4—711no—
390C2×C4×D4—711no—
391C2×C4×D4—711no—
392C2×C4×D4C2×D7111yescharacteristic
393C2×C4×D4C2×D7111yescharacteristic
394C2×C4×D4C2×D7111yescharacteristic
395C22×C4⋊C4—21no—
396C22×C4⋊C4—1421no—
397#501—718no—
398#501—718no—
399#499—718no—
400#478—718no—
401#478—718no—
402#478—718no—
403#478—718no—
404#474—718no—
405#474—718no—
406#446—718no—
407#442—718no—
408#442—718no—
409C4×D8—718no—
410C2×#107—711no—
411C2×#107—711no—
412C2×#107—711no—
413C2×#107—711no—
414C2×#107—711no—
415C2×#106—711no—
416C2×#106—711no—
417C2×#106—711no—
418C2×#106—711no—
419C2×C4⋊C8—711no—
420C2×C4⋊C8—711no—
421C2×C4⋊C8—711no—
422C2×#102—711no—
423C2×#102—711no—
424C2×#102—711no—
425C2×#102—711no—
426C2×#102—711no—
427C2×#102—711no—
428C2×#97—711no—
429C2×#97—711no—
430C2×C4×C8—711no—
431C22×Q8—21no—
432C22×Q8—1421no—
433C22×Q8C22⋊D7111yescharacteristic
434C22×D4—711no—
435C22×D4C22×D7111yescharacteristic
436C23×C4—21no—
437C23×C4—21no—
438C23×C4—21no—
439C23×C4—1421no—
440C23×C4—1421no—
441C23×C4—1421no—
442C2×D8—718no—
443C2×D8—714no—
444C22×C8—711no—
445C22×C8—711no—
446C22×C8—711no—
447C22×C8—711no—
448C4⋊Q8—22no—
449C4⋊Q8—714no—
450C4⋊Q8—1422no—
451C4⋊Q8C22×D7114yes—
452#125—22no—
453#125—22no—
454#125—714no—
455#125—714no—
456#125—1422no—
457#125—1422no—
458#125C22×D7114yes—
459#125C22×D7114yes—
460C22⋊Q8—28no—
461C22⋊Q8—28no—
462C22⋊Q8—28no—
463C22⋊Q8—1428no—
464C22⋊Q8—1428no—
465C22⋊Q8—1428no—
466C4×Q8C22⋊D7114yes—
467C4×Q8C22×D7114yes—
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—714no—
472C4×D4—714no—
473C4×D4—714no—
474C4×D4—1422no—
475C4×D4—1422no—
476C4×D4—1422no—
477C4×D4C22×D7114yes—
478C4×D4C22×D7114yes—
479C4×D4C22×D7114yes—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—28no—
486C2×C4⋊C4—711no—
487C2×C4⋊C4—711no—
488C2×C4⋊C4—711no—
489C2×C4⋊C4—1421no—
490C2×C4⋊C4—1421no—
491C2×C4⋊C4—1421no—
492C2×C4⋊C4—1421no—
493C2×C4⋊C4—1421no—
494C2×C4⋊C4—1428no—
495C2×C4⋊C4C22⋊D7111yescharacteristic
496C2×C4⋊C4C22⋊D7111yescharacteristic
497C2×C4⋊C4C22⋊D7111yescharacteristic
498C2×C4⋊C4C22×D7111yescharacteristic
499C2×C4⋊C4C22×D7111yescharacteristic
500C2×C4⋊C4C22×D7111yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—1421no—
505C2×C22⋊C4—1421no—
506C2×C22⋊C4—1421no—
507C2×C42C22×D7111yescharacteristic
508C2×C42C22×D7111yescharacteristic
509C2×C42C22×D7111yescharacteristic
510#107—714no—
511#107—714no—
512#107—714no—
513#107—714no—
514#107—714no—
515#106—714no—
516#106—714no—
517#106—714no—
518#106—714no—
519C4⋊C8—714no—
520C4⋊C8—714no—
521C4⋊C8—714no—
522#102—714no—
523#102—714no—
524#102—714no—
525#102—714no—
526#102—714no—
527#102—714no—
528#97—714no—
529#97—714no—
530C4×C8—714no—
531C24—21no—
532C24—1421no—
533C2×Q8—24no—
534C2×Q8—42no—
535C2×Q8—82no—
536C2×Q8—5682no—
537C2×Q8—1424no—
538C2×Q8C2×C22⋊D7114yes—
539C2×D4—21no—
540C2×D4—22no—
541C2×D4—714no—
542C2×D4—712no—
543C2×D4—1421no—
544C2×D4—1422no—
545C2×D4Q8×D7114yes—
546C2×D4C23×D7112yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—44no—
554C22×C4—82no—
555C22×C4—82no—
556C22×C4—2844no—
557C22×C4—5682no—
558C22×C4—5682no—
559C22×C4—1421no—
560C22×C4—1421no—
561C22×C4—1421no—
562C22×C4—1424no—
563C22×C4—1424no—
564C22×C4—1424no—
565C22×C4C2×C22⋊D7111yescharacteristic
566C22×C4C2×C22⋊D7111yescharacteristic
567C22×C4C2×C22⋊D7111yescharacteristic
568C22×C4C2×C22⋊D7111yescharacteristic
569C22×C4C2×C22⋊D7111yescharacteristic
570C22×C4C2×C22⋊D7111yescharacteristic
571C22×C4C23×D7111yescharacteristic
572D8—7116no—
573C2×C8—714no—
574C2×C8—712no—
575C2×C8—712no—
576C2×C8—712no—
577C2×C8—712no—
578C2×C8—1422no—
579C2×C8—1422no—
580C2×C8—1422no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—712no—
590C4⋊C4—712no—
591C4⋊C4—712no—
592C4⋊C4—1424no—
593C4⋊C4—1424no—
594C4⋊C4—1424no—
595C4⋊C4—1424no—
596C4⋊C4—1421no—
597C4⋊C4—1421no—
598C4⋊C4—1421no—
599C4⋊C4—1424no—
600C4⋊C4C2×C22⋊D7114yes—
601C4⋊C4C2×C22⋊D7114yes—
602C4⋊C4C2×C22⋊D7114yes—
603C4⋊C4C23×D7112yes—
604C4⋊C4C23×D7112yes—
605C4⋊C4C23×D7112yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—1424no—
610C22⋊C4—1424no—
611C22⋊C4—1424no—
612C42C2×C22⋊D7112yes—
613C42C2×C22⋊D7112yes—
614C42C2×C22⋊D7112yes—
615C42C23×D7112yes—
616C42C23×D7112yes—
617C42C23×D7112yes—
618C23—22no—
619C23—24no—
620C23—42no—
621C23—42no—
622C23—2842no—
623C23—2842no—
624C23—1422no—
625C23—1424no—
626C23C22×C22⋊D7111yescharacteristic
627Q8—44no—
628Q8—84no—
629Q8—5684no—
630D4—22no—
631D4—24no—
632D4—714no—
633D4—1422no—
634D4—1424no—
635D4C2×Q8×D7114yes—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—48no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4—2848no—
652C2×C4—2842no—
653C2×C4—2842no—
654C2×C4—2842no—
655C2×C4—5684no—
656C2×C4—5684no—
657C2×C4—1422no—
658C2×C4—1422no—
659C2×C4—1422no—
660C2×C4C22×C22⋊D7112yes—
661C2×C4C22×C22⋊D7112yes—
662C2×C4C22×C22⋊D7112yes—
663C2×C4C22×C22⋊D7112yes—
664C2×C4C22×C22⋊D7112yes—
665C2×C4C22×C22⋊D7112yes—
666C2×C4C22×C22⋊D7111yescharacteristic
667C2×C4C2×Q8×D7112yes—
668C2×C4#1455617612yes—
669C2×C4C24×D7111yescharacteristic
670C8—714no—
671C8—1422no—
672C8—1422no—
673C8—1422no—
674C22—24no—
675C22—42no—
676C22—48no—
677C22—42no—
678C22—2842no—
679C22—2848no—
680C22—2842no—
681C22—1424no—
682C22Q8×C22⋊D7112yes—
683C22#1798679712yes—
684C22#1798680212yes—
685C22C23×C22⋊D7111yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—22no—
691C4—22no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—2842no—
696C4—2842no—
697C4—2842no—
698C4Q8×C22⋊D7112yes—
699C4C22×Q8×D7111yescharacteristic
700C4C2×#1455617611yescharacteristic
701C2—44no—
702C2—2844no—
703C2#2260129414yesdirect product factor
704C2C2×Q8×C22⋊D7111yescharacteristic
705C2C2×#1798679711yescharacteristic
706C2C2×#1798680211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#554×C71C2
socleC23×C71C22×D4
prime radicalC22×#11765850C22
hypercenterC2×#554D71
hypocenterC71C2×#3389
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#17986709C2semidirect
2. #22601294C2direct (N × H)
3. C2×#17986409C2semidirect
4. C2×#17986405C2semidirect
5. C2×#17986398C2semidirect
6. C2×#17986299C2semidirect
7. C2×#17986299C2semidirect
8. C2×#17986296C2semidirect
9. C2×#17986296C2semidirect
10. C2×#17986279C2semidirect
11. C2×#17986276C2semidirect
12. C2×#17986130C2semidirect
16. C2×#554×C71C2semidirect
19. #17986709C22semidirect
30. #17986409C22semidirect
31. #17986405C22semidirect
32. #17986398C22semidirect
33. #17986299C22semidirect
34. #17986299C22semidirect
35. #17986296C22semidirect
36. #17986296C22semidirect
37. #17986279C22semidirect
38. #17986276C22semidirect
39. #17986130C22semidirect
65. #554×C71C22semidirect
82. C2×#11765850Q8semidirect
193. #11765850C2×Q8semidirect
349. C2×C71#3389semidirect
355. C2×#554D71semidirect
370. C71C2×#3389semidirect
375. #554C2×D71semidirect
703. C2#22601294direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867092
#226012942
C2×#179864092
C2×#179864052
C2×#179863982
C2×#179862992
C2×#179862962
C2×#179862792
C2×#179862762
C2×#179861302
C2×#179861092
C2×C4×#117658502
C2×#554×C712
C2×#338971