Finite Group Databasebeta

← C2×#22599602 #32869651

Subgroups — C2×#22599602 #32869651

Order 18176.

1678 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986627C211yesmaximal, characteristic
2#22599602C2116yesmaximal, direct product factor
3C2×#17986409C211yesmaximal, characteristic, complemented
4C2×#17986398C211yesmaximal, characteristic, complemented
5C2×#17986367C211yesmaximal, characteristic, complemented
6C2×#17986349C211yesmaximal, characteristic, complemented
7C2×#17986332C211yesmaximal, characteristic
8C2×#17986337C211yesmaximal, characteristic
9C2×#17986337C211yesmaximal, characteristic
10C2×#17986327C211yesmaximal, characteristic
11C2×#17986306C211yesmaximal, characteristic, complemented
12C2×#17986306C211yesmaximal, characteristic, complemented
13C2×#17986294C211yesmaximal, characteristic, complemented
14C2×#17986284C211yesmaximal, characteristic, complemented
15C2×#17986060C211yesmaximal, characteristic
16C2×#541×C71C211yesmaximal, characteristic
17#17986627—24no—
18#17986627C2218yes—
19C2×#14556128C2211yescharacteristic
20C2×#14556128C2211yescharacteristic
21C2×#14556127—21no—
22C2×#14556120C2211yescharacteristic
23C2×#14556120C2211yescharacteristic
24C2×#14556119—21no—
25C2×#14556105—21no—
26C2×#14556105—21no—
27C2×#14556087C2211yescharacteristic
28C22×C4⋊Dic71C2211yescharacteristic
29#17986409C2218yescomplemented
30#17986398C2218yescomplemented
31#17986367C2218yescomplemented
32#17986349C2218yescomplemented
33#17986337C2218yes—
34#17986337C2218yes—
35#17986332C2218yes—
36#17986327C2218yes—
37#17986306C2218yescomplemented
38#17986306C2218yescomplemented
39#17986294C2218yescomplemented
40#17986284C2218yescomplemented
41#17986060C2218yes—
42C2×#14556061C2211yescharacteristic
43C2×#14556061C2211yescharacteristic
44C2×#14556061C2211yescharacteristic
45C2×#14556061C2211yescharacteristic
46C2×#14556059C2211yescharacteristic
47C2×#14556059C2211yescharacteristic
48C2×#14556059C2211yescharacteristic
49C2×#14556059C2211yescharacteristic
50C2×C4⋊(C71⋊C8)C2211yescharacteristic
51C2×C4⋊(C71⋊C8)C2211yescharacteristic
52C2×#14556052C2211yescharacteristic
53C2×#14556052C2211yescharacteristic
54C2×#14556052C2211yescharacteristic
55C2×#14556052C2211yescharacteristic
56C2×#14556052C2211yescharacteristic
57C2×#14556052C2211yescharacteristic
58C2×#14556052C2211yescharacteristic
59C2×#14556052C2211yescharacteristic
60C2×C22⋊(C71⋊C8)C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×#14556039C2211yescharacteristic
63C2×C4×C71⋊C8C2211yescharacteristic
64#541×C71—24no—
65#541×C71C2218yes—
66C2×C4⋊Q8×C71C2211yescharacteristic
67C2×#126×C71—21no—
68C2×#126×C71—21no—
69C2×#125×C71—21no—
70C2×#125×C71—21no—
71C2×#125×C71C2211yescharacteristic
72C2×C22⋊Q8×C71C2211yescharacteristic
73C2×C22⋊Q8×C71C2211yescharacteristic
74C2×C4×Q8×C71C2211yescharacteristic
75C2×C4×Q8×C71C2211yescharacteristic
76C2×#117×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142—21no—
79C23×Dic71—21no—
80C22×C71⋊C8C2311yescharacteristic
81C22×C71⋊C8C2311yescharacteristic
82C22×C71⋊C8C2311yescharacteristic
83C22×C71⋊C8C2311yescharacteristic
84#14556128—22no—
85#14556128—22no—
86#14556128C2314yes—
87#14556128C2314yes—
88#14556127—28no—
89#14556120—22no—
90#14556120—22no—
91#14556120C2314yes—
92#14556120C2314yes—
93#14556119—28no—
94#14556105—28no—
95#14556105—28no—
96#14556087—22no—
97#14556087C2314yes—
98C2×C4⋊Dic71—22no—
99C2×C4⋊Dic71—21no—
100C2×C4⋊Dic71—21no—
101C2×C4⋊Dic71—21no—
102C2×C4⋊Dic71C2314yes—
103C2×C4⋊Dic71C2311yescharacteristic
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—
111C2×C22⋊Dic71—21no—
112C2×C4×Dic71—21no—
113#14556061C2314yes—
114#14556061C2314yes—
115#14556061C2314yes—
116#14556061C2314yes—
117#14556059C2314yes—
118#14556059C2314yes—
119#14556059C2314yes—
120#14556059C2314yes—
121C4⋊(C71⋊C8)C2314yes—
122C4⋊(C71⋊C8)C2314yes—
123#14556052C2314yes—
124#14556052C2314yes—
125#14556052C2314yes—
126#14556052C2314yes—
127#14556052C2314yes—
128#14556052C2314yes—
129#14556052C2314yes—
130#14556052C2314yes—
131C22⋊(C71⋊C8)C2314yes—
132C22⋊(C71⋊C8)C2314yes—
133#14556039C2314yes—
134C4×C71⋊C8C2314yes—
135C22×Q8×C71C2311yescharacteristic
136C22×Q8×C71C2311yescharacteristic
137C23×C4×C71C2311yescharacteristic
138C4⋊Q8×C71—22no—
139C4⋊Q8×C71C2314yes—
140#126×C71—28no—
141#126×C71—28no—
142#125×C71—28no—
143#125×C71—28no—
144#125×C71—22no—
145#125×C71C2314yes—
146C22⋊Q8×C71—22no—
147C22⋊Q8×C71—22no—
148C22⋊Q8×C71C2314yes—
149C22⋊Q8×C71C2314yes—
150C4×Q8×C71—22no—
151C4×Q8×C71—22no—
152C4×Q8×C71C2314yes—
153C4×Q8×C71C2314yes—
154#117×C71D414yes—
155#117×C71C2314yes—
156C2×C4⋊C4×C71—21no—
157C2×C4⋊C4×C71—21no—
158C2×C4⋊C4×C71—21no—
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×C71D411yescharacteristic
165C2×C4⋊C4×C71D411yescharacteristic
166C2×C4⋊C4×C71C2311yescharacteristic
167C2×C4⋊C4×C71C2311yescharacteristic
168C2×C22⋊C4×C71—21no—
169C2×C22⋊C4×C71—21no—
170C2×C22⋊C4×C71D411yescharacteristic
171C2×C22⋊C4×C71D411yescharacteristic
172C2×C42×C71—21no—
173C2×C42×C71—21no—
174C2×C42×C71C2311yescharacteristic
175C2×C42×C71C2311yescharacteristic
176C2×Dic142—24no—
177C2×Dic142—24no—
178C2×Dic142—82no—
179C2×Dic142—82no—
180C22×Dic71—21no—
181C22×Dic71—21no—
182C22×Dic71—21no—
183C22×Dic71—21no—
184C22×Dic71—24no—
185C22×Dic71—82no—
186C2×C71⋊C8—22no—
187C2×C71⋊C8—22no—
188C2×C71⋊C8—22no—
189C2×C71⋊C8—22no—
190C2×C71⋊C8C2412yes—
191C2×C71⋊C8C2412yes—
192C2×C71⋊C8C2412yes—
193C2×C71⋊C8C2412yes—
194C4⋊Dic71—24no—
195C4⋊Dic71—21no—
196C4⋊Dic71—21no—
197C4⋊Dic71—24no—
198C4⋊Dic71—24no—
199C4⋊Dic71—21no—
200C4⋊Dic71—21no—
201C4⋊Dic71C2412yes—
202C4⋊Dic71C2412yes—
203C4⋊Dic71C2412yes—
204C4⋊Dic71C2412yes—
205Dic71⋊C4—24no—
206Dic71⋊C4—24no—
207Dic71⋊C4—24no—
208Dic71⋊C4—24no—
209C22⋊Dic71—24no—
210C4×Dic71—24no—
211C24×C71C2×D411yescharacteristic
212C2×Q8×C71—21no—
213C2×Q8×C71—21no—
214C2×Q8×C71—22no—
215C2×Q8×C71—22no—
216C2×Q8×C71—22no—
217C2×Q8×C71—22no—
218C2×Q8×C71C2412yes—
219C2×Q8×C71C2412yes—
220C22×C4×C71—22no—
221C22×C4×C71—22no—
222C22×C4×C71—21no—
223C22×C4×C71—21no—
224C22×C4×C71—21no—
225C22×C4×C71—21no—
226C22×C4×C71C2×D411yescharacteristic
227C22×C4×C71C2×D411yescharacteristic
228C22×C4×C71C2×D411yescharacteristic
229C22×C4×C71C2×D411yescharacteristic
230C22×C4×C71C2×D411yescharacteristic
231C22×C4×C71C2×D412yes—
232C22×C4×C71C2412yes—
233C22×C4×C71C2411yescharacteristic
234C4⋊C4×C71—24no—
235C4⋊C4×C71—24no—
236C4⋊C4×C71—24no—
237C4⋊C4×C71—24no—
238C4⋊C4×C71—24no—
239C4⋊C4×C71—24no—
240C4⋊C4×C71—24no—
241C4⋊C4×C71—24no—
242C4⋊C4×C71—21no—
243C4⋊C4×C71—21no—
244C4⋊C4×C71C2×D414yes—
245C4⋊C4×C71C2×D414yes—
246C4⋊C4×C71C2412yes—
247C4⋊C4×C71C2412yes—
248C22⋊C4×C71—24no—
249C22⋊C4×C71—24no—
250C22⋊C4×C71C2×D414yes—
251C22⋊C4×C71C2×D414yes—
252C42×C71—24no—
253C42×C71—24no—
254C42×C71C2×D412yes—
255C42×C71C2×D412yes—
256C42×C71C2412yes—
257C42×C71C2412yes—
258C23×C71—22no—
259C23×C71—22no—
260C23×C71—22no—
261C23×C71C22×D412yes—
262C23×C71C22×D411yescharacteristic
263Q8×C71—22no—
264Q8×C71—22no—
265Q8×C71—22no—
266Q8×C71—22no—
267Q8×C71—42no—
268Q8×C71—42no—
269C2×C4×C71—22no—
270C2×C4×C71—22no—
271C2×C4×C71—22no—
272C2×C4×C71—22no—
273C2×C4×C71—22no—
274C2×C4×C71—24no—
275C2×C4×C71—22no—
276C2×C4×C71—22no—
277C2×C4×C71—22no—
278C2×C4×C71—22no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—42no—
282C2×C4×C71—42no—
283C2×C4×C71—42no—
284C2×C4×C71—42no—
285C2×C4×C71C22×D412yes—
286C2×C4×C71C22×D412yes—
287C2×C4×C71C22×D412yes—
288C2×C4×C71C22×D412yes—
289C2×C4×C71C22×D412yes—
290C2×C4×C71C22×D411yescharacteristic
291C2×C4×C712−1+412yes—
292C2×C4×C712−1+412yes—
293C2×C4×C71C2511yescharacteristic
294C2×Dic71—22no—
295C2×Dic71—22no—
296C2×Dic71—22no—
297C2×Dic71—22no—
298C2×Dic71—42no—
299C2×Dic71—42no—
300C2×Dic71—42no—
301C2×Dic71—42no—
302C2×Dic71—84no—
303Dic142—84no—
304Dic142—84no—
305C71⋊C8—22no—
306C71⋊C8—22no—
307C71⋊C8—22no—
308C71⋊C8—22no—
309C22×C71—22no—
310C22×C71—22no—
311C22×C71—22no—
312C22×C71—44no—
313C22×C71#53612yes—
314C22×C71#57712yes—
315C22×C71#57812yes—
316C22×C71C23×D411yescharacteristic
317C4×C71—22no—
318C4×C71—22no—
319C4×C71—22no—
320C4×C71—22no—
321C4×C71—22no—
322C4×C71—42no—
323C4×C71—42no—
324C4×C71—42no—
325C4×C71—42no—
326C4×C71#53612yes—
327C4×C71C2×2−1+411yescharacteristic
328C4×C71C2×2−1+411yescharacteristic
329Dic71—42no—
330Dic71—42no—
331Dic71—42no—
332Dic71—42no—
333C2×#3242—711nomaximal, Sylow
334C2×C71—42no—
335C2×C71#324214yescomplemented
336C2×C71C2×#53611yescharacteristic
337C2×C71C2×#57711yescharacteristic
338C2×C71C2×#57811yescharacteristic
339C2×#544—711no—
340C2×#541D7111yescharacteristic
341#3242—7116no—
342C2×#501—711no—
343C2×#499—711no—
344C2×#491—711no—
345C2×#487—711no—
346C2×#484—711no—
347C2×#485—711no—
348C2×#485—711no—
349C2×#483—711no—
350C2×#479—711no—
351C2×#479—711no—
352C2×#477—711no—
353C2×#475—711no—
354C2×#433—711no—
355C71C2×#324211yescharacteristic, complemented, Sylow
356#544—718no—
357#544—1424no—
358#541—24no—
359#541C2×D7118yes—
360C2×C4⋊Q8—711no—
361C2×C4⋊Q8—711no—
362C2×C4⋊Q8—1421no—
363C2×C4⋊Q8C2×D7111yescharacteristic
364C2×#126—21no—
365C2×#126—21no—
366C2×#125—21no—
367C2×#125—21no—
368C2×#125—711no—
369C2×#125—711no—
370C2×#125—1421no—
371C2×#125C2×D7111yescharacteristic
372C2×C22⋊Q8—1421no—
373C2×C22⋊Q8—1421no—
374C2×C22⋊Q8C2×D7111yescharacteristic
375C2×C22⋊Q8C2×D7111yescharacteristic
376C2×C4×Q8C2×D7111yescharacteristic
377C2×C4×Q8C2×D7111yescharacteristic
378C2×#117—711no—
379C2×#117C2×D7111yescharacteristic
380C22×C4⋊C4—711no—
381#501—718no—
382#499—718no—
383#491—718no—
384#487—718no—
385#485—718no—
386#485—718no—
387#484—718no—
388#483—718no—
389#479—718no—
390#479—718no—
391#477—718no—
392#475—718no—
393#433—718no—
394C2×#107—711no—
395C2×#107—711no—
396C2×#107—711no—
397C2×#107—711no—
398C2×#106—711no—
399C2×#106—711no—
400C2×#106—711no—
401C2×#106—711no—
402C2×C4⋊C8—711no—
403C2×C4⋊C8—711no—
404C2×#103—711no—
405C2×#103—711no—
406C2×#103—711no—
407C2×#103—711no—
408C2×#103—711no—
409C2×#103—711no—
410C2×#103—711no—
411C2×#103—711no—
412C2×C22⋊C8—711no—
413C2×C22⋊C8—711no—
414C2×#97—711no—
415C2×C4×C8—711no—
416C22×Q8—1421no—
417C22×Q8—1421no—
418C22×Q8C22×D7111yescharacteristic
419C22×Q8C22×D7111yescharacteristic
420C23×C4—1421no—
421C23×C4C22×D7111yescharacteristic
422C22×C8—711no—
423C22×C8—711no—
424C22×C8—711no—
425C22×C8—711no—
426C4⋊Q8—22no—
427C4⋊Q8—714no—
428C4⋊Q8—714no—
429C4⋊Q8—1428no—
430C4⋊Q8—1422no—
431C4⋊Q8—1422no—
432C4⋊Q8C22×D7114yes—
433#126—28no—
434#126—28no—
435#125—28no—
436#125—28no—
437#125—22no—
438#125—714no—
439#125—714no—
440#125—1428no—
441#125—1422no—
442#125—1422no—
443#125C22×D7114yes—
444C22⋊Q8—22no—
445C22⋊Q8—22no—
446C22⋊Q8—1428no—
447C22⋊Q8—1428no—
448C22⋊Q8C22×D7114yes—
449C22⋊Q8C22×D7114yes—
450C4×Q8—22no—
451C4×Q8—22no—
452C4×Q8C22×D7114yes—
453C4×Q8C22×D7114yes—
454#117—714no—
455#117—1422no—
456#117C22⋊D7114yes—
457#117C22×D7114yes—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—711no—
467C2×C4⋊C4—711no—
468C2×C4⋊C4—714no—
469C2×C4⋊C4—711no—
470C2×C4⋊C4—711no—
471C2×C4⋊C4—1421no—
472C2×C4⋊C4—1422no—
473C2×C4⋊C4—1421no—
474C2×C4⋊C4—1421no—
475C2×C4⋊C4—1421no—
476C2×C4⋊C4—1421no—
477C2×C4⋊C4—1421no—
478C2×C4⋊C4—1421no—
479C2×C4⋊C4C22⋊D7111yescharacteristic
480C2×C4⋊C4C22⋊D7111yescharacteristic
481C2×C4⋊C4C22×D7111yescharacteristic
482C2×C4⋊C4C22×D7111yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—1421no—
486C2×C22⋊C4C22⋊D7111yescharacteristic
487C2×C22⋊C4C22⋊D7111yescharacteristic
488C2×C42—21no—
489C2×C42—21no—
490C2×C42—1421no—
491C2×C42C22×D7111yescharacteristic
492C2×C42C22×D7111yescharacteristic
493#107—714no—
494#107—714no—
495#107—714no—
496#107—714no—
497#106—714no—
498#106—714no—
499#106—714no—
500#106—714no—
501C4⋊C8—714no—
502C4⋊C8—714no—
503#103—714no—
504#103—714no—
505#103—714no—
506#103—714no—
507#103—714no—
508#103—714no—
509#103—714no—
510#103—714no—
511C22⋊C8—714no—
512C22⋊C8—714no—
513#97—714no—
514C4×C8—714no—
515C24C2×C22⋊D7111yescharacteristic
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—5682no—
523C2×Q8—5682no—
524C2×Q8—1424no—
525C2×Q8—1424no—
526C2×Q8C23×D7112yes—
527C2×Q8C23×D7112yes—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—5682no—
535C22×C4—1421no—
536C22×C4—1421no—
537C22×C4—1421no—
538C22×C4—1421no—
539C22×C4—1424no—
540C22×C4C2×C22⋊D7112yes—
541C22×C4C2×C22⋊D7111yescharacteristic
542C22×C4C2×C22⋊D7111yescharacteristic
543C22×C4C2×C22⋊D7111yescharacteristic
544C22×C4C2×C22⋊D7111yescharacteristic
545C22×C4C2×C22⋊D7111yescharacteristic
546C22×C4C23×D7112yes—
547C22×C4C23×D7111yescharacteristic
548C2×C8—712no—
549C2×C8—712no—
550C2×C8—712no—
551C2×C8—712no—
552C2×C8—1422no—
553C2×C8—1422no—
554C2×C8—1422no—
555C2×C8—1422no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—712no—
567C4⋊C4—712no—
568C4⋊C4—712no—
569C4⋊C4—712no—
570C4⋊C4—1424no—
571C4⋊C4—1424no—
572C4⋊C4—1424no—
573C4⋊C4—1424no—
574C4⋊C4—1424no—
575C4⋊C4—1421no—
576C4⋊C4—1421no—
577C4⋊C4—1421no—
578C4⋊C4—1421no—
579C4⋊C4—1424no—
580C4⋊C4—1424no—
581C4⋊C4C2×C22⋊D7114yes—
582C4⋊C4C2×C22⋊D7114yes—
583C4⋊C4C23×D7112yes—
584C4⋊C4C23×D7112yes—
585C22⋊C4—24no—
586C22⋊C4—24no—
587C22⋊C4—1424no—
588C22⋊C4C2×C22⋊D7114yes—
589C22⋊C4C2×C22⋊D7114yes—
590C42—24no—
591C42—24no—
592C42—1424no—
593C42C2×C22⋊D7112yes—
594C42C2×C22⋊D7112yes—
595C42C23×D7112yes—
596C42C23×D7112yes—
597C23—22no—
598C23—22no—
599C23—22no—
600C23C22×C22⋊D7112yes—
601C23C22×C22⋊D7111yescharacteristic
602Q8—22no—
603Q8—22no—
604Q8—22no—
605Q8—22no—
606Q8—42no—
607Q8—42no—
608Q8—5684no—
609Q8—5684no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—2842no—
627C2×C4—2842no—
628C2×C4—2842no—
629C2×C4—2842no—
630C2×C4—5684no—
631C2×C4—1422no—
632C2×C4—1422no—
633C2×C4—1422no—
634C2×C4—1422no—
635C2×C4C22×C22⋊D7112yes—
636C2×C4C22×C22⋊D7112yes—
637C2×C4C22×C22⋊D7112yes—
638C2×C4C22×C22⋊D7112yes—
639C2×C4C22×C22⋊D7112yes—
640C2×C4C22×C22⋊D7111yescharacteristic
641C2×C4#1455617512yes—
642C2×C4#1455617512yes—
643C2×C4C24×D7111yescharacteristic
644C8—1422no—
645C8—1422no—
646C8—1422no—
647C8—1422no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—44no—
652C22#1798657012yes—
653C22#1798680712yes—
654C22#1798681412yes—
655C22C23×C22⋊D7111yescharacteristic
656C4—22no—
657C4—22no—
658C4—22no—
659C4—22no—
660C4—22no—
661C4—42no—
662C4—42no—
663C4—42no—
664C4—42no—
665C4—2842no—
666C4—2842no—
667C4—2842no—
668C4—2842no—
669C4#1798657012yes—
670C4C2×#1455617511yescharacteristic
671C4C2×#1455617511yescharacteristic
672C2—42no—
673C2#2259960214yesdirect product factor
674C2C2×#1798657011yescharacteristic
675C2C2×#1798680711yescharacteristic
676C2C2×#1798681411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#541×C71C2
socleC23×C71C22×D4
prime radicalC24×C71C2×D4
hypercenterC2×#541D71
hypocenterC71C2×#3242
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
2. #22599602C2direct (N × H)
3. C2×#17986409C2semidirect
4. C2×#17986398C2semidirect
5. C2×#17986367C2semidirect
6. C2×#17986349C2semidirect
11. C2×#17986306C2semidirect
12. C2×#17986306C2semidirect
13. C2×#17986294C2semidirect
14. C2×#17986284C2semidirect
29. #17986409C22semidirect
30. #17986398C22semidirect
31. #17986367C22semidirect
32. #17986349C22semidirect
37. #17986306C22semidirect
38. #17986306C22semidirect
39. #17986294C22semidirect
40. #17986284C22semidirect
335. C2×C71#3242semidirect
355. C71C2×#3242semidirect
673. C2#22599602direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866272
#225996022
C2×#179864092
C2×#179863982
C2×#179863672
C2×#179863492
C2×#179863322
C2×#179863372
C2×#179863272
C2×#179863062
C2×#179862942
C2×#179862842
C2×#179860602
C2×#541×C712
C2×#324271