Finite Group Databasebeta

← C2×#22601295 #32877990

Subgroups — C2×#22601295 #32877990

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×#17986710C211yesmaximal, characteristic, complemented
2C2×#17986705C211yesmaximal, characteristic, complemented
3#22601295C2116yesmaximal, direct product factor
4C2×#17986407C211yesmaximal, characteristic, complemented
5C2×#17986399C211yesmaximal, characteristic, complemented
6C2×#17986302C211yesmaximal, characteristic, complemented
7C2×#17986298C211yesmaximal, characteristic, complemented
8C2×#17986298C211yesmaximal, characteristic, complemented
9C2×#17986296C211yesmaximal, characteristic, complemented
10C2×#17986278C211yesmaximal, characteristic, complemented
11C2×#17986276C211yesmaximal, characteristic, complemented
12C2×#17986127C211yesmaximal, characteristic, complemented
13C2×#17986112C211yesmaximal, characteristic
14C2×#17986110C211yesmaximal, characteristic
15C2×#17986081C211yesmaximal, characteristic
16C2×#501×C71C211yesmaximal, characteristic, complemented
17C22×D568C2211yescharacteristic
18#17986710—24no—
19#17986710C2218yescomplemented
20#17986705—24no—
21#17986705C2218yescomplemented
22C2×#14556127C2211yescharacteristic
23C2×#14556119C2211yescharacteristic
24C2×#14556119C2211yescharacteristic
25C2×#14556119C2211yescharacteristic
26C2×#14556108—21no—
27C2×#14556108—21no—
28C2×#14556106—21no—
29C2×#14556106—21no—
30C2×#14556104—21no—
31C2×#14556104—21no—
32C2×C4×Dic142C2211yescharacteristic
33C2×C4×D284C2211yescharacteristic
34C2×C4×D284C2211yescharacteristic
35C2×#14556090C2211yescharacteristic
36C2×#14556090C2211yescharacteristic
37C2×#14556090C2211yescharacteristic
38C2×#14556090C2211yescharacteristic
39C2×C4⋊C4×D71—21no—
40C2×C4⋊C4×D71—21no—
41#17986407C2218yescomplemented
42#17986399C2218yescomplemented
43#17986302C2218yescomplemented
44#17986298C2218yescomplemented
45#17986298C2218yescomplemented
46#17986296C2218yescomplemented
47#17986278C2218yescomplemented
48#17986276C2218yescomplemented
49#17986127C2218yescomplemented
50#17986112C2218yes—
51#17986110C2218yes—
52#17986081C2218yes—
53C2×#14556061C2211yescharacteristic
54C2×#14556061C2211yescharacteristic
55C2×#14556061C2211yescharacteristic
56C2×#14556060C2211yescharacteristic
57C2×#14556059C2211yescharacteristic
58C2×C4⋊(C71⋊C8)C2211yescharacteristic
59C2×Dic71⋊C8C2211yescharacteristic
60C2×Dic71⋊C8C2211yescharacteristic
61C2×#14556050C2211yescharacteristic
62C2×#14556050C2211yescharacteristic
63C2×#14556048C2211yescharacteristic
64C2×#14556048C2211yescharacteristic
65C2×#14556048C2211yescharacteristic
66C2×#14556048C2211yescharacteristic
67C2×#14556038C2211yescharacteristic
68C2×C8×Dic71C2211yescharacteristic
69C2×C4⋊Q8×C71C2211yescharacteristic
70C2×#125×C71C2211yescharacteristic
71#501×C71C2218yescomplemented
72C2×#107×C71C2211yescharacteristic
73C2×#107×C71C2211yescharacteristic
74C2×#106×C71C2211yescharacteristic
75C2×#106×C71C2211yescharacteristic
76C2×#97×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142D411yescharacteristic
79C22×D284C2311yescharacteristic
80C22×D284C2311yescharacteristic
81C22×C4×D71—21no—
82C22×C4×D71—21no—
83C22×C4×D71—21no—
84C22×C4×D71—21no—
85C22×C4×D71—21no—
86C22×C4×D71—21no—
87C2×D568Q818yescomplemented
88C2×D568C2314yes—
89C22×C71⋊C8C2311yescharacteristic
90C22×C71⋊C8C2311yescharacteristic
91#14556127—22no—
92#14556127C2314yes—
93#14556119—22no—
94#14556119—22no—
95#14556119—22no—
96#14556119C2314yes—
97#14556119C2314yes—
98#14556119C2314yes—
99#14556108—28no—
100#14556108—28no—
101#14556106—28no—
102#14556106—28no—
103#14556104—28no—
104#14556104—28no—
105C4×Dic142D414yes—
106C4×Dic142C2314yes—
107C4×D284—22no—
108C4×D284—22no—
109C4×D284C2314yes—
110C4×D284C2314yes—
111#14556090—22no—
112#14556090—22no—
113#14556090—22no—
114#14556090—22no—
115#14556090C2314yes—
116#14556090C2314yes—
117#14556090C2314yes—
118#14556090C2314yes—
119C2×C4⋊Dic71—21no—
120C2×C4⋊Dic71—21no—
121C2×C4⋊Dic71—21no—
122C2×C4⋊Dic71D411yescharacteristic
123C2×C4⋊Dic71C2311yescharacteristic
124C2×C4⋊Dic71C2311yescharacteristic
125C2×Dic71⋊C4—21no—
126C2×Dic71⋊C4—21no—
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C2×Dic71⋊C4D411yescharacteristic
130C2×Dic71⋊C4D411yescharacteristic
131C4⋊C4×D71—28no—
132C4⋊C4×D71—28no—
133C2×(C2×D71)⋊C4—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×C4×Dic71C2311yescharacteristic
140C2×C4×Dic71C2311yescharacteristic
141#14556061C2314yes—
142#14556061C2314yes—
143#14556061C2314yes—
144#14556060C2314yes—
145#14556059C2314yes—
146C4⋊(C71⋊C8)C2314yes—
147Dic71⋊C8C2314yes—
148Dic71⋊C8C2314yes—
149#14556050C2314yes—
150#14556050C2314yes—
151#14556048C2314yes—
152#14556048C2314yes—
153#14556048C2314yes—
154#14556048C2314yes—
155#14556038C2314yes—
156C8×Dic71C2314yes—
157C22×Q8×C71—21no—
158C22×C8×C71C2311yescharacteristic
159C22×C8×C71C2311yescharacteristic
160C4⋊Q8×C71—22no—
161C4⋊Q8×C71C2314yes—
162#125×C71—22no—
163#125×C71C2314yes—
164C2×C4⋊C4×C71—21no—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71—21no—
167C2×C4⋊C4×C71C2311yescharacteristic
168C2×C4⋊C4×C71C2311yescharacteristic
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C42×C71C2311yescharacteristic
172#107×C71C2314yes—
173#107×C71C2314yes—
174#106×C71C2314yes—
175#106×C71C2314yes—
176#97×C71C2314yes—
177C23×D71—21no—
178C23×D71—21no—
179C2×Dic142—24no—
180C2×Dic142—42no—
181C2×Dic142—82no—
182C2×Dic142C2×D414yes—
183C2×D284—21no—
184C2×D284—21no—
185C2×D284—22no—
186C2×D284—22no—
187C2×D284C2×Q814yes—
188C2×D284C2×Q814yes—
189C2×D284C2412yes—
190C2×D284C2412yes—
191C22×Dic71—21no—
192C22×Dic71—21no—
193C22×Dic71C2×D411yescharacteristic
194C22×Dic71C2×D411yescharacteristic
195C22×Dic71C2×D411yescharacteristic
196C22×Dic71C2×D411yescharacteristic
197C2×C4×D71—24no—
198C2×C4×D71—24no—
199C2×C4×D71—24no—
200C2×C4×D71—24no—
201C2×C4×D71—24no—
202C2×C4×D71—24no—
203C2×C4×D71—44no—
204C2×C4×D71—44no—
205C2×C4×D71—82no—
206C2×C4×D71—82no—
207C2×C4×D71—82no—
208C2×C4×D71—82no—
209D568C2×Q8116yescomplemented
210C2×C71⋊C8—22no—
211C2×C71⋊C8—22no—
212C2×C71⋊C8C2412yes—
213C2×C71⋊C8C2412yes—
214C4⋊Dic71—21no—
215C4⋊Dic71—21no—
216C4⋊Dic71—24no—
217C4⋊Dic71—24no—
218C4⋊Dic71—24no—
219C4⋊Dic71C2×D414yes—
220C4⋊Dic71C2412yes—
221C4⋊Dic71C2412yes—
222Dic71⋊C4—24no—
223Dic71⋊C4—24no—
224Dic71⋊C4—24no—
225Dic71⋊C4—24no—
226Dic71⋊C4C2×D414yes—
227Dic71⋊C4C2×D414yes—
228(C2×D71)⋊C4—24no—
229(C2×D71)⋊C4—24no—
230(C2×D71)⋊C4—24no—
231(C2×D71)⋊C4—24no—
232(C2×D71)⋊C4—24no—
233(C2×D71)⋊C4—24no—
234C4×Dic71C2×D412yes—
235C4×Dic71C2×D412yes—
236C4×Dic71C2412yes—
237C4×Dic71C2412yes—
238C2×Q8×C71—24no—
239C2×Q8×C71—82no—
240C22×C4×C71—21no—
241C22×C4×C71—21no—
242C22×C4×C71—21no—
243C22×C4×C71—21no—
244C22×C4×C71C2×D411yescharacteristic
245C22×C4×C71C2×D411yescharacteristic
246C22×C4×C71C2411yescharacteristic
247C2×C8×C71—22no—
248C2×C8×C71C2×Q814yes—
249C2×C8×C71C2412yes—
250C2×C8×C71C2412yes—
251C4⋊C4×C71—24no—
252C4⋊C4×C71—24no—
253C4⋊C4×C71—24no—
254C4⋊C4×C71—21no—
255C4⋊C4×C71—21no—
256C4⋊C4×C71—21no—
257C4⋊C4×C71—21no—
258C4⋊C4×C71C2412yes—
259C4⋊C4×C71C2412yes—
260C4⋊C4×C71C2412yes—
261C4⋊C4×C71C2412yes—
262C42×C71C2×D412yes—
263C42×C71C2412yes—
264C23×C71C22×D411yescharacteristic
265C22×D71—24no—
266C22×D71—24no—
267C22×D71—22no—
268C22×D71—22no—
269C22×D71—42no—
270C22×D71—42no—
271C22×D71—42no—
272C22×D71—42no—
273Q8×C71—84no—
274C2×C4×C71—22no—
275C2×C4×C71—22no—
276C2×C4×C71—22no—
277C2×C4×C71—22no—
278C2×C4×C71—22no—
279C2×C4×C71—22no—
280C2×C4×C71—42no—
281C2×C4×C71—42no—
282C2×C4×C71—42no—
283C2×C4×C71—42no—
284C2×C4×C71C22×D412yes—
285C2×C4×C71C22×D412yes—
286C2×C4×C71C22×D411yescharacteristic
287C2×C4×C71C22×Q812yes—
288C2×C4×C712−1+412yes—
289C2×C4×C71C2511yescharacteristic
290C2×Dic71—22no—
291C2×Dic71—22no—
292C2×Dic71—22no—
293C2×Dic71—22no—
294C2×Dic71—22no—
295C2×Dic71—22no—
296C2×Dic71—42no—
297C2×Dic71—42no—
298C2×Dic71C22×D412yes—
299C2×Dic71C22×D412yes—
300C2×Dic71C22×D412yes—
301C2×Dic71C22×D412yes—
302D284—24no—
303D284—24no—
304D284—22no—
305D284—22no—
306D284C22×Q814yes—
307D284C22×Q814yes—
308C4×D71—48no—
309C4×D71—48no—
310C4×D71—84no—
311C4×D71—84no—
312C4×D71—84no—
313C4×D71—84no—
314Dic142—44no—
315Dic142—84no—
316C8×C71—22no—
317C8×C71C22×Q814yes—
318C71⋊C8—22no—
319C71⋊C8—22no—
320C22×C71D4×Q812yes—
321C22×C71#57512yes—
322C22×C71#57612yes—
323C22×C71C23×D411yescharacteristic
324C2×D71—24no—
325C2×D71—24no—
326C2×D71—48no—
327C2×D71—48no—
328C2×D71—42no—
329C2×D71—42no—
330C2×D71—42no—
331C2×D71—42no—
332C4×C71—22no—
333C4×C71—22no—
334C4×C71—42no—
335C4×C71—42no—
336C4×C71—42no—
337C4×C71—42no—
338C4×C71D4×Q812yes—
339C4×C71C23×Q811yescharacteristic
340C4×C71C2×2−1+411yescharacteristic
341Dic71—22no—
342Dic71—22no—
343Dic71—22no—
344Dic71—22no—
345Dic71—42no—
346Dic71—42no—
347C2×#3389—711nomaximal, Sylow
348C2×C71#338914yescomplemented
349C2×C71C2×D4×Q811yescharacteristic
350C2×C71C2×#57511yescharacteristic
351C2×C71C2×#57611yescharacteristic
352D71—44no—
353D71—44no—
354C2×#554—711no—
355C2×#554—711no—
356#3389—7116no—
357C2×#501—711no—
358C2×#501D7111yescharacteristic, complemented
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—718no—
373#554—718no—
374#554—1424no—
375#554—1424no—
376C2×C4⋊Q8—711no—
377C2×C4⋊Q8C2×D7111yescharacteristic
378C2×#125—711no—
379C2×#125—711no—
380C2×#125—711no—
381C2×#125C2×D7111yescharacteristic
382C2×C22⋊Q8—1421no—
383C2×C22⋊Q8—1421no—
384C2×C22⋊Q8—1421no—
385C2×C22⋊Q8—1421no—
386C2×C22⋊Q8—1421no—
387C2×C22⋊Q8—1421no—
388C2×C4×Q8—711no—
389C2×C4×D4—711no—
390C2×C4×D4—711no—
391C2×C4×D4—711no—
392C2×C4×D4—711no—
393C2×C4×D4—711no—
394C2×C4×D4—711no—
395C22×C4⋊C4—1421no—
396C22×C4⋊C4—1421no—
397#501—718no—
398#501C2×D7118yescomplemented
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×#107C2×D7111yescharacteristic
414C2×#107C2×D7111yescharacteristic
415C2×#106—711no—
416C2×#106—711no—
417C2×#106C2×D7111yescharacteristic
418C2×#106C2×D7111yescharacteristic
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×#97C2×D7111yescharacteristic
430C2×C4×C8—711no—
431C22×Q8—21no—
432C22×Q8—711no—
433C22×Q8—1421no—
434C22×D4—711no—
435C22×D4—711no—
436C23×C4—1421no—
437C23×C4—1421no—
438C23×C4—1421no—
439C23×C4—1421no—
440C23×C4—1421no—
441C23×C4—1421no—
442C2×D8—718no—
443C2×D8—714no—
444C22×C8—711no—
445C22×C8—711no—
446C22×C8C22×D7111yescharacteristic
447C22×C8C22×D7111yescharacteristic
448C4⋊Q8—22no—
449C4⋊Q8—714no—
450C4⋊Q8—1422no—
451C4⋊Q8C22×D7114yes—
452#125—22no—
453#125—714no—
454#125—714no—
455#125—714no—
456#125—1422no—
457#125—1422no—
458#125—1422no—
459#125C22×D7114yes—
460C22⋊Q8—1428no—
461C22⋊Q8—1428no—
462C22⋊Q8—1428no—
463C22⋊Q8—1428no—
464C22⋊Q8—1428no—
465C22⋊Q8—1428no—
466C4×Q8—714no—
467C4×Q8—714no—
468C4×D4—714no—
469C4×D4—714no—
470C4×D4—714no—
471C4×D4—714no—
472C4×D4—714no—
473C4×D4—714no—
474C4×D4—1422no—
475C4×D4—1422no—
476C4×D4—1422no—
477C4×D4—1422no—
478C4×D4—1422no—
479C4×D4—1422no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—711no—
484C2×C4⋊C4—711no—
485C2×C4⋊C4—711no—
486C2×C4⋊C4—711no—
487C2×C4⋊C4—711no—
488C2×C4⋊C4—1428no—
489C2×C4⋊C4—1428no—
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×C4⋊C4C22×D7111yescharacteristic
501C2×C22⋊C4—1421no—
502C2×C22⋊C4—1421no—
503C2×C22⋊C4—1421no—
504C2×C22⋊C4—1421no—
505C2×C22⋊C4—1421no—
506C2×C22⋊C4—1421no—
507C2×C42—711no—
508C2×C42—711no—
509C2×C42C22×D7111yescharacteristic
510#107—714no—
511#107—714no—
512#107—714no—
513#107C22×D7114yes—
514#107C22×D7114yes—
515#106—714no—
516#106—714no—
517#106C22×D7114yes—
518#106C22×D7114yes—
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#97C22×D7114yes—
530C4×C8—714no—
531C24—1421no—
532C24—1421no—
533C2×Q8—24no—
534C2×Q8—82no—
535C2×Q8—2842no—
536C2×Q8—5682no—
537C2×Q8—714no—
538C2×Q8—1424no—
539C2×D4—714no—
540C2×D4—714no—
541C2×D4—712no—
542C2×D4—712no—
543C2×D4—1421no—
544C2×D4—1421no—
545C2×D4—1422no—
546C2×D4—1422no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—2844no—
552C22×C4—2844no—
553C22×C4—5682no—
554C22×C4—5682no—
555C22×C4—5682no—
556C22×C4—5682no—
557C22×C4—711no—
558C22×C4—711no—
559C22×C4—711no—
560C22×C4—711no—
561C22×C4—1424no—
562C22×C4—1424no—
563C22×C4—1424no—
564C22×C4—1424no—
565C22×C4—1421no—
566C22×C4—1421no—
567C22×C4—1424no—
568C22×C4—1424no—
569C22×C4D4×D7111yescharacteristic
570C22×C4D4×D7111yescharacteristic
571C22×C4C23×D7111yescharacteristic
572D8—7116no—
573C2×C8—22no—
574C2×C8—712no—
575C2×C8—712no—
576C2×C8—1422no—
577C2×C8—1422no—
578C2×C8Q8×D7114yes—
579C2×C8C23×D7112yes—
580C2×C8C23×D7112yes—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—714no—
589C4⋊C4—714no—
590C4⋊C4—714no—
591C4⋊C4—712no—
592C4⋊C4—712no—
593C4⋊C4—1424no—
594C4⋊C4—1424no—
595C4⋊C4—1424no—
596C4⋊C4—1424no—
597C4⋊C4—1424no—
598C4⋊C4—1424no—
599C4⋊C4—1424no—
600C4⋊C4—1421no—
601C4⋊C4—1421no—
602C4⋊C4C23×D7112yes—
603C4⋊C4C23×D7112yes—
604C4⋊C4C23×D7112yes—
605C4⋊C4C23×D7112yes—
606C22⋊C4—1424no—
607C22⋊C4—1424no—
608C22⋊C4—1424no—
609C22⋊C4—1424no—
610C22⋊C4—1424no—
611C22⋊C4—1424no—
612C42—712no—
613C42—712no—
614C42—712no—
615C42—712no—
616C42D4×D7112yes—
617C42C23×D7112yes—
618C23—2842no—
619C23—2842no—
620C23—2842no—
621C23—2842no—
622C23—1422no—
623C23—1422no—
624C23—1424no—
625C23—1424no—
626C23C2×D4×D7111yescharacteristic
627Q8—84no—
628Q8—2844no—
629Q8—5684no—
630D4—714no—
631D4—714no—
632D4—1422no—
633D4—1422no—
634D4—1424no—
635D4—1424no—
636C2×C4—22no—
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—42no—
646C2×C4—2848no—
647C2×C4—2848no—
648C2×C4—2842no—
649C2×C4—2842no—
650C2×C4—5684no—
651C2×C4—5684no—
652C2×C4—5684no—
653C2×C4—5684no—
654C2×C4—712no—
655C2×C4—712no—
656C2×C4—712no—
657C2×C4—712no—
658C2×C4—1422no—
659C2×C4—1422no—
660C2×C4—1422no—
661C2×C4—1422no—
662C2×C4—1422no—
663C2×C4—1422no—
664C2×C4C2×D4×D7112yes—
665C2×C4C2×D4×D7112yes—
666C2×C4C2×D4×D7111yescharacteristic
667C2×C4C2×Q8×D7112yes—
668C2×C4#1455617612yes—
669C2×C4C24×D7111yescharacteristic
670C8—22no—
671C8—1422no—
672C8—1422no—
673C8C2×Q8×D7114yes—
674C22—2842no—
675C22—2842no—
676C22—2848no—
677C22—2848no—
678C22—2842no—
679C22—2842no—
680C22—1424no—
681C22—1424no—
682C22#1798666412yes—
683C22#1798679812yes—
684C22#1798680312yes—
685C22C22×D4×D7111yescharacteristic
686C4—22no—
687C4—22no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4—42no—
692C4—2842no—
693C4—2842no—
694C4—1422no—
695C4—1422no—
696C4—1422no—
697C4—1422no—
698C4#1798666412yes—
699C4C22×Q8×D7111yescharacteristic
700C4C2×#1455617611yescharacteristic
701C2—2844no—
702C2—2844no—
703C2#2260129514yesdirect product factor
704C2C2×#1798666411yescharacteristic
705C2C2×#1798679811yescharacteristic
706C2C2×#1798680311yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#501×C71C2
socleC23×C71C22×D4
prime radicalC22×D568C22
hypercenterC2×#501D71
hypocenterC71C2×#3389
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×#17986710C2semidirect
2. C2×#17986705C2semidirect
3. #22601295C2direct (N × H)
4. C2×#17986407C2semidirect
5. C2×#17986399C2semidirect
6. C2×#17986302C2semidirect
7. C2×#17986298C2semidirect
8. C2×#17986298C2semidirect
9. C2×#17986296C2semidirect
10. C2×#17986278C2semidirect
11. C2×#17986276C2semidirect
12. C2×#17986127C2semidirect
16. C2×#501×C71C2semidirect
19. #17986710C22semidirect
21. #17986705C22semidirect
41. #17986407C22semidirect
42. #17986399C22semidirect
43. #17986302C22semidirect
44. #17986298C22semidirect
45. #17986298C22semidirect
46. #17986296C22semidirect
47. #17986278C22semidirect
48. #17986276C22semidirect
49. #17986127C22semidirect
71. #501×C71C22semidirect
87. C2×D568Q8semidirect
209. D568C2×Q8semidirect
348. C2×C71#3389semidirect
358. C2×#501D71semidirect
370. C71C2×#3389semidirect
398. #501C2×D71semidirect
703. C2#22601295direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867102
C2×#179867052
#226012952
C2×#179864072
C2×#179863992
C2×#179863022
C2×#179862982
C2×#179862962
C2×#179862782
C2×#179862762
C2×#179861272
C2×#179861122
C2×#179861102
C2×#179860812
C2×#501×C712
C2×#338971