Finite Group Databasebeta

← C2×#22598175 #32865016

Subgroups — C2×#22598175 #32865016

Order 18176.

2018 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986626C211yesmaximal, characteristic
2C2×#17986475C211yesmaximal, characteristic
3#22598175C2116yesmaximal, direct product factor
4C2×#17986309C211yesmaximal, characteristic, complemented
5C2×#17986307C211yesmaximal, characteristic, complemented
6C2×#17986306C211yesmaximal, characteristic, complemented
7C2×#17986304C211yesmaximal, characteristic, complemented
8C2×#17986292C211yesmaximal, characteristic, complemented
9C2×#17986291C211yesmaximal, characteristic, complemented
10C2×#17986283C211yesmaximal, characteristic, complemented
11C2×#17986038C211yesmaximal, characteristic
12C2×#17986034C211yesmaximal, characteristic
13C2×#17986024C211yesmaximal, characteristic
14C2×#17986006C211yesmaximal, characteristic
15C2×#103×D71C211yesmaximal, characteristic
16C2×#475×C71C211yesmaximal, characteristic, complemented
17C22×Q8×D71C2211yescharacteristic
18C22×#11765848C2211yescharacteristic
19C22×C8×D71C2211yescharacteristic
20#17986626—24no—
21#17986626C2218yes—
22C2×#14556127C2211yescharacteristic
23C2×#14556126—21no—
24C2×#14556120C2211yescharacteristic
25C2×#14556119C2211yescharacteristic
26C2×#14556118—21no—
27C2×#14556106—21no—
28C2×#14556104—21no—
29#17986475—24no—
30#17986475C2218yes—
31C2×Q8×Dic71C2211yescharacteristic
32C2×C4×Dic142—21no—
33C2×C4×Dic142C2211yescharacteristic
34C2×#14556093—21no—
35C2×#14556093C2211yescharacteristic
36C2×#14556086—21no—
37C2×#14556086C2211yescharacteristic
38C2×#14556086C2211yescharacteristic
39C2×#14556085—21no—
40C2×#14556085C2211yescharacteristic
41C2×C4⋊C4×D71C2211yescharacteristic
42#17986309C2218yescomplemented
43#17986307C2218yescomplemented
44#17986306C2218yescomplemented
45#17986304C2218yescomplemented
46#17986292C2218yescomplemented
47#17986291C2218yescomplemented
48#17986283C2218yescomplemented
49#17986038C2218yes—
50#17986034C2218yes—
51C2×#14556062C2211yescharacteristic
52C2×#14556061C2211yescharacteristic
53C2×#14556061C2211yescharacteristic
54C2×#14556061C2211yescharacteristic
55C2×#14556060C2211yescharacteristic
56C2×#14556059C2211yescharacteristic
57#17986024C2218yes—
58C2×C4⋊(C71⋊C8)C2211yescharacteristic
59C2×Dic71⋊C8C2211yescharacteristic
60C2×Dic71⋊C8C2211yescharacteristic
61#17986006C2218yes—
62C2×#14556053C2211yescharacteristic
63C2×#14556053C2211yescharacteristic
64C2×#14556052C2211yescharacteristic
65C2×#14556052C2211yescharacteristic
66C2×#14556051C2211yescharacteristic
67C2×#14556051C2211yescharacteristic
68#103×D71C2218yes—
69C2×C4⋊Q8×C71C2211yescharacteristic
70C2×C4×Q8×C71C2211yescharacteristic
71#475×C71C2218yescomplemented
72C2×#106×C71C2211yescharacteristic
73C2×#106×C71C2211yescharacteristic
74C2×C4⋊C8×C71C2211yescharacteristic
75C2×#103×C71C2211yescharacteristic
76C2×#103×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142—21no—
79C22×Dic142C2311yescharacteristic
80C2×Q8×D71—22no—
81C2×Q8×D71—24no—
82C2×Q8×D71Q818yescomplemented
83C2×Q8×D71C2314yes—
84C22×C4×D71—21no—
85C22×C4×D71—21no—
86C22×C4×D71C2311yescharacteristic
87C2×#11765848—24no—
88C2×#11765848C2314yes—
89C22×C71⋊C8C2311yescharacteristic
90C22×C71⋊C8C2311yescharacteristic
91C2×C8×D71—24no—
92C2×C8×D71C2314yes—
93#14556127—22no—
94#14556127C2314yes—
95#14556126—28no—
96#14556120—22no—
97#14556120C2314yes—
98#14556119—22no—
99#14556119C2314yes—
100#14556118—28no—
101#14556106—28no—
102#14556104—28no—
103Q8×Dic71—22no—
104Q8×Dic71C2314yes—
105C4×Dic142—28no—
106C4×Dic142—22no—
107C4×Dic142C2314yes—
108#14556093—28no—
109#14556093—22no—
110#14556093C2314yes—
111#14556086—22no—
112#14556086—22no—
113#14556086—28no—
114#14556086C2314yes—
115#14556086C2314yes—
116#14556085—28no—
117#14556085D414yes—
118#14556085C2314yes—
119C2×C4⋊Dic71—21no—
120C2×C4⋊Dic71—21no—
121C2×C4⋊Dic71C2311yescharacteristic
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×Dic71⋊C4—21no—
131C2×Dic71⋊C4D411yescharacteristic
132C2×Dic71⋊C4D411yescharacteristic
133C4⋊C4×D71—22no—
134C4⋊C4×D71C2314yes—
135C2×(C2×D71)⋊C4—21no—
136C2×(C2×D71)⋊C4—21no—
137C2×(C2×D71)⋊C4D411yescharacteristic
138C2×(C2×D71)⋊C4D411yescharacteristic
139C2×C4×Dic71—21no—
140C2×C4×Dic71—21no—
141C2×C4×Dic71—21no—
142C2×C4×Dic71—21no—
143C2×C4×Dic71—21no—
144C2×C4×Dic71C2311yescharacteristic
145#14556062C2314yes—
146#14556061C2314yes—
147#14556061C2314yes—
148#14556061C2314yes—
149#14556060C2314yes—
150#14556059C2314yes—
151C4⋊(C71⋊C8)C2314yes—
152Dic71⋊C8C2314yes—
153Dic71⋊C8C2314yes—
154#14556053C2314yes—
155#14556053C2314yes—
156#14556052C2314yes—
157#14556052C2314yes—
158#14556051C2314yes—
159#14556051C2314yes—
160C22×Q8×C71—21no—
161C22×Q8×C71C2311yescharacteristic
162C22×C8×C71C2311yescharacteristic
163C22×C8×C71C2311yescharacteristic
164C4⋊Q8×C71—22no—
165C4⋊Q8×C71C2314yes—
166C4×Q8×C71—22no—
167C4×Q8×C71C2314yes—
168C2×C4⋊C4×C71—21no—
169C2×C4⋊C4×C71—21no—
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C42×C71—21no—
174C2×C42×C71C2311yescharacteristic
175#106×C71C2314yes—
176#106×C71C2314yes—
177C4⋊C8×C71C2314yes—
178#103×C71C2314yes—
179#103×C71C2314yes—
180C23×D71C2×D411yescharacteristic
181C2×Dic142—21no—
182C2×Dic142—22no—
183C2×Dic142—28no—
184C2×Dic142—24no—
185C2×Dic142—24no—
186C2×Dic142—82no—
187C2×Dic142C2×Q814yes—
188C2×Dic142C2412yes—
189Q8×D71—216no—
190Q8×D71—28no—
191Q8×D71C2×Q8116yescomplemented
192C22×Dic71—21no—
193C22×Dic71—21no—
194C22×Dic71—21no—
195C22×Dic71—21no—
196C22×Dic71C2×D411yescharacteristic
197C22×Dic71C2×D411yescharacteristic
198C22×Dic71C2×D411yescharacteristic
199C2×C4×D71—28no—
200C2×C4×D71—24no—
201C2×C4×D71—24no—
202C2×C4×D71—82no—
203C2×C4×D71C2×D412yes—
204C2×C4×D71C2×Q814yes—
205C2×C4×D71#4114yes—
206C2×C4×D71C2412yes—
207#11765848—28no—
208C2×C71⋊C8—22no—
209C2×C71⋊C8—22no—
210C2×C71⋊C8C2412yes—
211C2×C71⋊C8C2412yes—
212C8×D71—28no—
213C4⋊Dic71—21no—
214C4⋊Dic71—21no—
215C4⋊Dic71—21no—
216C4⋊Dic71—24no—
217C4⋊Dic71—24no—
218C4⋊Dic71C2412yes—
219C4⋊Dic71C2412yes—
220C4⋊Dic71C2412yes—
221Dic71⋊C4—24no—
222Dic71⋊C4—24no—
223Dic71⋊C4—24no—
224Dic71⋊C4—24no—
225Dic71⋊C4—24no—
226Dic71⋊C4—24no—
227Dic71⋊C4—24no—
228Dic71⋊C4C2×D414yes—
229Dic71⋊C4C2×D414yes—
230(C2×D71)⋊C4—24no—
231(C2×D71)⋊C4—24no—
232(C2×D71)⋊C4C2×D414yes—
233(C2×D71)⋊C4C2×D414yes—
234C4×Dic71—24no—
235C4×Dic71—24no—
236C4×Dic71—24no—
237C4×Dic71—24no—
238C4×Dic71—24no—
239C4×Dic71C2×D412yes—
240C4×Dic71C2412yes—
241C2×Q8×C71—21no—
242C2×Q8×C71—24no—
243C2×Q8×C71—22no—
244C2×Q8×C71—82no—
245C2×Q8×C71C2×Q814yes—
246C2×Q8×C71C2412yes—
247C22×C4×C71—21no—
248C22×C4×C71—21no—
249C22×C4×C71—21no—
250C22×C4×C71—21no—
251C22×C4×C71C2×D411yescharacteristic
252C22×C4×C71C2×D411yescharacteristic
253C22×C4×C71C2411yescharacteristic
254C2×C8×C71—22no—
255C2×C8×C71—22no—
256C2×C8×C71C2412yes—
257C2×C8×C71C2412yes—
258C4⋊C4×C71—24no—
259C4⋊C4×C71—24no—
260C4⋊C4×C71—21no—
261C4⋊C4×C71—21no—
262C4⋊C4×C71—21no—
263C4⋊C4×C71C2412yes—
264C4⋊C4×C71C2412yes—
265C4⋊C4×C71C2412yes—
266C42×C71—24no—
267C42×C71C2×D412yes—
268C42×C71C2412yes—
269C23×C71C22×D411yescharacteristic
270C22×D71—22no—
271C22×D71—22no—
272C22×D71C22⋊Q814yes—
273C22×D71C22×D412yes—
274Q8×C71—24no—
275Q8×C71—22no—
276Q8×C71—84no—
277Q8×C71C22×Q814yes—
278C2×C4×C71—24no—
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—42no—
286C2×C4×C71—42no—
287C2×C4×C71—42no—
288C2×C4×C71C22×D412yes—
289C2×C4×C71C22×D412yes—
290C2×C4×C71C22×D411yescharacteristic
291C2×C4×C71C22×Q812yes—
292C2×C4×C71C2×#4112yes—
293C2×C4×C71C2511yescharacteristic
294C2×Dic71—24no—
295C2×Dic71—22no—
296C2×Dic71—22no—
297C2×Dic71—22no—
298C2×Dic71—22no—
299C2×Dic71—22no—
300C2×Dic71—22no—
301C2×Dic71—42no—
302C2×Dic71—42no—
303C2×Dic71—42no—
304C2×Dic71C22⋊Q814yes—
305C2×Dic71C22×D412yes—
306C2×Dic71C22×D412yes—
307C2×Dic71C22×D412yes—
308C4×D71—216no—
309C4×D71—84no—
310C4×D71C22⋊Q818yes—
311C4×D71C22×Q814yes—
312C4×D71C2×#4114yes—
313Dic142—24no—
314Dic142—22no—
315Dic142—216no—
316Dic142—84no—
317Dic142C22×Q814yes—
318C8×C71—22no—
319C8×C71—22no—
320C71⋊C8—22no—
321C71⋊C8—22no—
322C22×C71C2×C22⋊Q812yes—
323C22×C71#57712yes—
324C22×C71#57812yes—
325C22×C71C23×D411yescharacteristic
326C2×D71—28no—
327C2×D71—22no—
328C2×D71—22no—
329C2×D71C2×C22⋊Q814yes—
330C4×C71—24no—
331C4×C71—22no—
332C4×C71—22no—
333C4×C71—42no—
334C4×C71—42no—
335C4×C71—42no—
336C4×C71C2×C22⋊Q812yes—
337C4×C71C23×Q811yescharacteristic
338C4×C71C22×#4111yescharacteristic
339Dic71—24no—
340Dic71—22no—
341Dic71—22no—
342Dic71—42no—
343Dic71—42no—
344Dic71—42no—
345Dic71C2×C22⋊Q814yes—
346C2×#3082—711nomaximal, Sylow
347C2×C71#308214yescomplemented
348C2×C71C22×C22⋊Q811yescharacteristic
349C2×C71C2×#57711yescharacteristic
350C2×C71C2×#57811yescharacteristic
351D71—24no—
352C2×#544—711no—
353C2×#519—711no—
354#3082—7116no—
355C2×#479—711no—
356C2×#479—711no—
357C2×#479—711no—
358C2×#479—711no—
359C2×#477—711no—
360C2×#477—711no—
361C2×#475—711no—
362C2×#475D7111yescharacteristic, complemented
363C2×#428—711no—
364C2×#427—711no—
365C2×#424—711no—
366C2×#419—711no—
367C22×#103—711no—
368C71C2×#308211yescharacteristic, complemented, Sylow
369C23×Q8—711no—
370C22×M16—711no—
371C23×C8—711no—
372#544—718no—
373#544—1424no—
374C2×C4⋊Q8—711no—
375C2×C4⋊Q8—1421no—
376C2×C4⋊Q8C2×D7111yescharacteristic
377C2×#125—711no—
378C2×#125—711no—
379C2×#125—1421no—
380C2×C22⋊Q8—1421no—
381C2×C22⋊Q8—1421no—
382#519—718no—
383#519—1424no—
384C2×C4×Q8—711no—
385C2×C4×Q8—711no—
386C2×C4×Q8—711no—
387C2×C4×Q8—1421no—
388C2×C4×Q8—1421no—
389C2×C4×Q8C2×D7111yescharacteristic
390C2×#117—711no—
391C2×#117—711no—
392C2×#117—711no—
393C2×#117—1421no—
394C2×#117—1421no—
395C22×C4⋊C4—711no—
396#479—718no—
397#479—718no—
398#479—718no—
399#479—718no—
400#477—718no—
401#477—718no—
402#475—718no—
403#475C2×D7118yescomplemented
404#428—718no—
405#427—718no—
406C2×#107—711no—
407C2×#107—711no—
408C2×#107—711no—
409C2×#107—711no—
410C2×#106—711no—
411C2×#106—711no—
412C2×#106C2×D7111yescharacteristic
413C2×#106C2×D7111yescharacteristic
414#424—718no—
415C2×C4⋊C8—711no—
416C2×C4⋊C8—711no—
417C2×C4⋊C8—711no—
418C2×C4⋊C8C2×D7111yescharacteristic
419#419—718no—
420C2×#103—711no—
421C2×#103—711no—
422C2×#103—711no—
423C2×#103—711no—
424C2×#103—711no—
425C2×#103—711no—
426C2×#103—718no—
427C2×#103C2×D7111yescharacteristic
428C2×#103C2×D7111yescharacteristic
429C22×Q8—21no—
430C22×Q8—718no—
431C22×Q8—714no—
432C22×Q8—711no—
433C22×Q8—1421no—
434C22×Q8—1421no—
435C22×Q8—1422no—
436C22×Q8—1424no—
437C22×Q8C22×D7111yescharacteristic
438C23×C4—711no—
439C23×C4—1421no—
440C23×C4—1421no—
441C2×M16—714no—
442C2×M16—1424no—
443C22×C8—711no—
444C22×C8—711no—
445C22×C8—714no—
446C22×C8—1424no—
447C22×C8C22×D7111yescharacteristic
448C22×C8C22×D7111yescharacteristic
449C4⋊Q8—22no—
450C4⋊Q8—714no—
451C4⋊Q8—1422no—
452C4⋊Q8—1428no—
453C4⋊Q8C22×D7114yes—
454#125—714no—
455#125—714no—
456#125—1422no—
457#125—1428no—
458#125—1422no—
459C22⋊Q8—1428no—
460C22⋊Q8—1428no—
461C4×Q8—22no—
462C4×Q8—714no—
463C4×Q8—714no—
464C4×Q8—714no—
465C4×Q8—1428no—
466C4×Q8—1422no—
467C4×Q8—1422no—
468C4×Q8—1428no—
469C4×Q8—1422no—
470C4×Q8C22×D7114yes—
471#117—714no—
472#117—714no—
473#117—714no—
474#117—714no—
475#117—1428no—
476#117—1428no—
477#117—1422no—
478#117—1422no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—711no—
482C2×C4⋊C4—711no—
483C2×C4⋊C4—711no—
484C2×C4⋊C4—711no—
485C2×C4⋊C4—711no—
486C2×C4⋊C4—714no—
487C2×C4⋊C4—1422no—
488C2×C4⋊C4—1421no—
489C2×C4⋊C4—1421no—
490C2×C4⋊C4—1421no—
491C2×C4⋊C4—1421no—
492C2×C4⋊C4—1421no—
493C2×C4⋊C4—1421no—
494C2×C4⋊C4—1421no—
495C2×C4⋊C4—1421no—
496C2×C4⋊C4—1421no—
497C2×C4⋊C4C22×D7111yescharacteristic
498C2×C4⋊C4C22×D7111yescharacteristic
499C2×C4⋊C4C22×D7111yescharacteristic
500C2×C22⋊C4—711no—
501C2×C22⋊C4—711no—
502C2×C22⋊C4—1421no—
503C2×C22⋊C4—1421no—
504C2×C42—21no—
505C2×C42—711no—
506C2×C42—1421no—
507C2×C42—1421no—
508C2×C42—1421no—
509C2×C42—1421no—
510C2×C42—1421no—
511C2×C42C22×D7111yescharacteristic
512#107—714no—
513#107—714no—
514#107—714no—
515#107—714no—
516#106—714no—
517#106—714no—
518#106C22×D7114yes—
519#106C22×D7114yes—
520C4⋊C8—714no—
521C4⋊C8—714no—
522C4⋊C8—714no—
523C4⋊C8C22×D7114yes—
524#103—714no—
525#103—714no—
526#103—714no—
527#103—714no—
528#103—714no—
529#103—714no—
530#103C22×D7114yes—
531#103C22×D7114yes—
532C24—711no—
533C2×Q8—21no—
534C2×Q8—24no—
535C2×Q8—22no—
536C2×Q8—82no—
537C2×Q8—5682no—
538C2×Q8—7116no—
539C2×Q8—714no—
540C2×Q8—712no—
541C2×Q8—1424no—
542C2×Q8—1424no—
543C2×Q8—1428no—
544C2×Q8—1428no—
545C2×Q8—14216no—
546C2×Q8—1421no—
547C2×Q8—1422no—
548C2×Q8Q8×D7114yes—
549C2×Q8C23×D7112yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—5682no—
555C22×C4—711no—
556C22×C4—712no—
557C22×C4—714no—
558C22×C4—714no—
559C22×C4—712no—
560C22×C4—711no—
561C22×C4—711no—
562C22×C4—1424no—
563C22×C4—1424no—
564C22×C4—1428no—
565C22×C4—1421no—
566C22×C4—1421no—
567C22×C4—1421no—
568C22×C4—1421no—
569C22×C4D4×D7111yescharacteristic
570C22×C4D4×D7111yescharacteristic
571C22×C4C23×D7111yescharacteristic
572M16—1428no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—712no—
576C2×C8—712no—
577C2×C8—1428no—
578C2×C8—1422no—
579C2×C8—1422no—
580C2×C8C23×D7112yes—
581C2×C8C23×D7112yes—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—714no—
588C4⋊C4—714no—
589C4⋊C4—712no—
590C4⋊C4—712no—
591C4⋊C4—712no—
592C4⋊C4—1424no—
593C4⋊C4—1424no—
594C4⋊C4—1424no—
595C4⋊C4—1424no—
596C4⋊C4—1424no—
597C4⋊C4—1424no—
598C4⋊C4—1424no—
599C4⋊C4—1424no—
600C4⋊C4—1424no—
601C4⋊C4—1421no—
602C4⋊C4—1421no—
603C4⋊C4—1421no—
604C4⋊C4C23×D7112yes—
605C4⋊C4C23×D7112yes—
606C4⋊C4C23×D7112yes—
607C22⋊C4—714no—
608C22⋊C4—714no—
609C22⋊C4—1424no—
610C22⋊C4—1424no—
611C42—24no—
612C42—712no—
613C42—712no—
614C42—1424no—
615C42—1424no—
616C42—1424no—
617C42—1424no—
618C42—1424no—
619C42D4×D7112yes—
620C42C23×D7112yes—
621C23—712no—
622C23—714no—
623C23—1422no—
624C23—1422no—
625C23C2×D4×D7111yescharacteristic
626Q8—22no—
627Q8—24no—
628Q8—84no—
629Q8—5684no—
630Q8—714no—
631Q8—14216no—
632Q8—1422no—
633Q8—1424no—
634Q8C2×Q8×D7114yes—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—2842no—
646C2×C4—2842no—
647C2×C4—2842no—
648C2×C4—5684no—
649C2×C4—712no—
650C2×C4—714no—
651C2×C4—714no—
652C2×C4—714no—
653C2×C4—718no—
654C2×C4—712no—
655C2×C4—712no—
656C2×C4—14216no—
657C2×C4—1422no—
658C2×C4—1422no—
659C2×C4—1422no—
660C2×C4—1422no—
661C2×C4—1424no—
662C2×C4—1422no—
663C2×C4—1422no—
664C2×C4C2×D4×D7112yes—
665C2×C4C2×D4×D7112yes—
666C2×C4C2×D4×D7111yescharacteristic
667C2×C4C2×Q8×D7112yes—
668C2×C4#41×D7112yes—
669C2×C4C24×D7111yescharacteristic
670C8—22no—
671C8—22no—
672C8—1422no—
673C8—1422no—
674C22—714no—
675C22—1428no—
676C22—1422no—
677C22—1422no—
678C22C22⋊Q8×D7112yes—
679C22#1798680512yes—
680C22#1798681512yes—
681C22C22×D4×D7111yescharacteristic
682C4—22no—
683C4—24no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—2842no—
689C4—2842no—
690C4—2842no—
691C4—714no—
692C4—1422no—
693C4—1424no—
694C4—1422no—
695C4C22⋊Q8×D7112yes—
696C4C22×Q8×D7111yescharacteristic
697C4C2×#41×D7111yescharacteristic
698C2—1424no—
699C2#2259817514yesdirect product factor
700C2C2×C22⋊Q8×D7111yescharacteristic
701C2C2×#1798680511yescharacteristic
702C2C2×#1798681511yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#475×C71C2
socleC23×C71C22×D4
prime radicalC23×D71C2×D4
hypercenterC2×#475D71
hypocenterC71C2×#3082
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. #22598175C2direct (N × H)
4. C2×#17986309C2semidirect
5. C2×#17986307C2semidirect
6. C2×#17986306C2semidirect
7. C2×#17986304C2semidirect
8. C2×#17986292C2semidirect
9. C2×#17986291C2semidirect
10. C2×#17986283C2semidirect
16. C2×#475×C71C2semidirect
42. #17986309C22semidirect
43. #17986307C22semidirect
44. #17986306C22semidirect
45. #17986304C22semidirect
46. #17986292C22semidirect
47. #17986291C22semidirect
48. #17986283C22semidirect
71. #475×C71C22semidirect
82. C2×Q8×D71Q8semidirect
191. Q8×D71C2×Q8semidirect
347. C2×C71#3082semidirect
362. C2×#475D71semidirect
368. C71C2×#3082semidirect
403. #475C2×D71semidirect
699. C2#22598175direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866262
C2×#179864752
#225981752
C2×#179863092
C2×#179863072
C2×#179863062
C2×#179863042
C2×#179862922
C2×#179862912
C2×#179862832
C2×#179860382
C2×#179860342
C2×#179860242
C2×#179860062
C2×#103×D712
C2×#475×C712
C2×#308271