Finite Group Databasebeta

← C2×#22601285 #32877979

Subgroups — C2×#22601285 #32877979

Order 18176.

1822 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986727C211yesmaximal, characteristic, complemented
2#22601285C2116yesmaximal, direct product factor
3C2×#17986409C211yesmaximal, characteristic, complemented
4C2×#17986405C211yesmaximal, characteristic, complemented
5C2×#17986398C211yesmaximal, characteristic, complemented
6C2×#17986303C211yesmaximal, characteristic, complemented
7C2×#17986303C211yesmaximal, characteristic, complemented
8C2×#17986281C211yesmaximal, characteristic, complemented
9C2×#17986299C211yesmaximal, characteristic
10C2×#17986299C211yesmaximal, characteristic
11C2×#17986289C211yesmaximal, characteristic
12C2×#17986130C211yesmaximal, characteristic, complemented
13C2×#17986099C211yesmaximal, characteristic
14C2×#17986099C211yesmaximal, characteristic
15C2×C4×#11765853C211yesmaximal, characteristic
16C2×#554×C71C211yesmaximal, characteristic
17C22×#11765853C2211yescharacteristic
18#17986727—24no—
19#17986727C2218yescomplemented
20C2×#14556128C2211yescharacteristic
21C2×#14556126—21no—
22C2×#14556120C2211yescharacteristic
23C2×#14556120C2211yescharacteristic
24C2×#14556118—21no—
25C2×#14556118—21no—
26C2×C4×Dic142C2211yescharacteristic
27C2×C4×Dic142C2211yescharacteristic
28C2×C4×Dic142C2211yescharacteristic
29C2×#14556093—21no—
30#17986409C2218yescomplemented
31#17986405C2218yescomplemented
32#17986398C2218yescomplemented
33#17986303C2218yescomplemented
34#17986303C2218yescomplemented
35#17986299C2218yes—
36#17986299C2218yes—
37#17986289C2218yes—
38#17986281C2218yescomplemented
39#17986130C2218yescomplemented
40#17986099C2218yes—
41#17986099C2218yes—
42C4×#11765853C2218yes—
43C2×#14556061C2211yescharacteristic
44C2×#14556061C2211yescharacteristic
45C2×#14556061C2211yescharacteristic
46C2×#14556061C2211yescharacteristic
47C2×#14556059C2211yescharacteristic
48C2×#14556059C2211yescharacteristic
49C2×#14556059C2211yescharacteristic
50C2×#14556059C2211yescharacteristic
51C2×#14556059C2211yescharacteristic
52C2×C4⋊(C71⋊C8)C2211yescharacteristic
53C2×C4⋊(C71⋊C8)C2211yescharacteristic
54C2×C4⋊(C71⋊C8)C2211yescharacteristic
55C2×#14556051C2211yescharacteristic
56C2×#14556051C2211yescharacteristic
57C2×#14556051C2211yescharacteristic
58C2×#14556049C2211yescharacteristic
59C2×#14556049C2211yescharacteristic
60C2×#14556049C2211yescharacteristic
61C2×#14556039C2211yescharacteristic
62C2×#14556039C2211yescharacteristic
63C2×C4×C71⋊C8C2211yescharacteristic
64#554×C71—24no—
65#554×C71C2218yes—
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×Dic142C2311yescharacteristic
79C2×#11765853Q818yescomplemented
80C2×#11765853C2314yes—
81C22×C71⋊C8C2311yescharacteristic
82C22×C71⋊C8C2311yescharacteristic
83C22×C71⋊C8C2311yescharacteristic
84C22×C71⋊C8C2311yescharacteristic
85#14556128—22no—
86#14556128C2314yes—
87#14556126—28no—
88#14556120—22no—
89#14556120—22no—
90#14556120C2314yes—
91#14556120C2314yes—
92#14556118—28no—
93#14556118—28no—
94C4×Dic142—22no—
95C4×Dic142—22no—
96C4×Dic142—22no—
97C4×Dic142C2314yes—
98C4×Dic142C2314yes—
99C4×Dic142C2314yes—
100#14556093—28no—
101C2×C4⋊Dic71—21no—
102C2×C4⋊Dic71C2311yescharacteristic
103C2×C4⋊Dic71C2311yescharacteristic
104C2×C4⋊Dic71C2311yescharacteristic
105C2×Dic71⋊C4—21no—
106C2×Dic71⋊C4—21no—
107C2×Dic71⋊C4—21no—
108C2×Dic71⋊C4—21no—
109C2×Dic71⋊C4—21no—
110C2×Dic71⋊C4—21no—
111C2×Dic71⋊C4—21no—
112C2×C4×Dic71—21no—
113C2×C4×Dic71—21no—
114C2×C4×Dic71—21no—
115#14556061C2314yes—
116#14556061C2314yes—
117#14556061C2314yes—
118#14556061C2314yes—
119#14556059C2314yes—
120#14556059C2314yes—
121#14556059C2314yes—
122#14556059C2314yes—
123#14556059C2314yes—
124C4⋊(C71⋊C8)C2314yes—
125C4⋊(C71⋊C8)C2314yes—
126C4⋊(C71⋊C8)C2314yes—
127#14556051C2314yes—
128#14556051C2314yes—
129#14556051C2314yes—
130#14556049C2314yes—
131#14556049C2314yes—
132#14556049C2314yes—
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
177C2×Dic142—21no—
178C2×Dic142—22no—
179C2×Dic142—24no—
180C2×Dic142—44no—
181C2×Dic142C2×Q814yes—
182C2×Dic142C2412yes—
183C22×Dic71—21no—
184C22×Dic71—21no—
185C22×Dic71—21no—
186C22×Dic71—21no—
187#11765853C2×Q8116yescomplemented
188C2×C71⋊C8—22no—
189C2×C71⋊C8—22no—
190C2×C71⋊C8—22no—
191C2×C71⋊C8C2×Q814yes—
192C2×C71⋊C8C2412yes—
193C2×C71⋊C8C2412yes—
194C2×C71⋊C8C2412yes—
195C2×C71⋊C8C2412yes—
196C4⋊Dic71—24no—
197C4⋊Dic71—21no—
198C4⋊Dic71—21no—
199C4⋊Dic71—21no—
200C4⋊Dic71C2412yes—
201C4⋊Dic71C2412yes—
202C4⋊Dic71C2412yes—
203Dic71⋊C4—24no—
204Dic71⋊C4—24no—
205Dic71⋊C4—24no—
206Dic71⋊C4—24no—
207Dic71⋊C4—24no—
208Dic71⋊C4—24no—
209Dic71⋊C4—24no—
210C4×Dic71—24no—
211C4×Dic71—24no—
212C4×Dic71—24no—
213C24×C71—21no—
214C2×Q8×C71—24no—
215C2×Q8×C71—42no—
216C2×Q8×C71—82no—
217C2×Q8×C71C2×D414yes—
218C2×D4×C71—21no—
219C2×D4×C71—22no—
220C2×D4×C71C2×Q814yes—
221C2×D4×C71C2412yes—
222C22×C4×C71—21no—
223C22×C4×C71—21no—
224C22×C4×C71—21no—
225C22×C4×C71—24no—
226C22×C4×C71—24no—
227C22×C4×C71—24no—
228C22×C4×C71—44no—
229C22×C4×C71—82no—
230C22×C4×C71—82no—
231C22×C4×C71C2×D411yescharacteristic
232C22×C4×C71C2×D411yescharacteristic
233C22×C4×C71C2×D411yescharacteristic
234C22×C4×C71C2×D411yescharacteristic
235C22×C4×C71C2×D411yescharacteristic
236C22×C4×C71C2×D411yescharacteristic
237C22×C4×C71C2411yescharacteristic
238C4⋊C4×C71—24no—
239C4⋊C4×C71—24no—
240C4⋊C4×C71—24no—
241C4⋊C4×C71—24no—
242C4⋊C4×C71—24no—
243C4⋊C4×C71—21no—
244C4⋊C4×C71—21no—
245C4⋊C4×C71—21no—
246C4⋊C4×C71C2×D414yes—
247C4⋊C4×C71C2×D414yes—
248C4⋊C4×C71C2×D414yes—
249C4⋊C4×C71C2412yes—
250C4⋊C4×C71C2412yes—
251C4⋊C4×C71C2412yes—
252C22⋊C4×C71—24no—
253C22⋊C4×C71—24no—
254C22⋊C4×C71—24no—
255C42×C71C2×D412yes—
256C42×C71C2×D412yes—
257C42×C71C2×D412yes—
258C42×C71C2412yes—
259C42×C71C2412yes—
260C42×C71C2412yes—
261C23×C71—24no—
262C23×C71—22no—
263C23×C71—42no—
264C23×C71—42no—
265C23×C71C22×D411yescharacteristic
266Q8×C71—44no—
267Q8×C71—84no—
268D4×C71—24no—
269D4×C71—22no—
270D4×C71C22×Q814yes—
271C2×C4×C71—22no—
272C2×C4×C71—22no—
273C2×C4×C71—22no—
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—48no—
281C2×C4×C71—42no—
282C2×C4×C71—42no—
283C2×C4×C71—42no—
284C2×C4×C71—84no—
285C2×C4×C71—84no—
286C2×C4×C71C22×D412yes—
287C2×C4×C71C22×D412yes—
288C2×C4×C71C22×D412yes—
289C2×C4×C71C22×D412yes—
290C2×C4×C71C22×D412yes—
291C2×C4×C71C22×D412yes—
292C2×C4×C71C22×D411yescharacteristic
293C2×C4×C71C22×Q812yes—
294C2×C4×C712−1+412yes—
295C2×C4×C71C2511yescharacteristic
296C2×Dic71—24no—
297C2×Dic71—22no—
298C2×Dic71—22no—
299C2×Dic71—22no—
300C2×Dic71—22no—
301C2×Dic71—42no—
302C2×Dic71—42no—
303C2×Dic71—42no—
304Dic142—24no—
305Dic142—22no—
306Dic142—48no—
307Dic142C22×Q814yes—
308C71⋊C8—22no—
309C71⋊C8—22no—
310C71⋊C8—22no—
311C71⋊C8C22×Q814yes—
312C22×C71—24no—
313C22×C71—48no—
314C22×C71—42no—
315C22×C71—42no—
316C22×C71D4×Q812yes—
317C22×C71#57512yes—
318C22×C71#57712yes—
319C22×C71C23×D411yescharacteristic
320C4×C71—22no—
321C4×C71—22no—
322C4×C71—22no—
323C4×C71—22no—
324C4×C71—22no—
325C4×C71—22no—
326C4×C71—42no—
327C4×C71—42no—
328C4×C71—42no—
329C4×C71D4×Q812yes—
330C4×C71C23×Q811yescharacteristic
331C4×C71C2×2−1+411yescharacteristic
332Dic71—24no—
333Dic71—42no—
334Dic71—42no—
335Dic71—42no—
336C2×#3388—711nomaximal, Sylow
337C2×C71—44no—
338C2×C71#338814yescomplemented
339C2×C71C2×D4×Q811yescharacteristic
340C2×C71C2×#57511yescharacteristic
341C2×C71C2×#57711yescharacteristic
342C2×#557—711no—
343C2×#554D7111yescharacteristic
344#3388—7116no—
345C2×#501—711no—
346C2×#501—711no—
347C2×#499—711no—
348C2×#479—711no—
349C2×#479—711no—
350C2×#475—711no—
351C2×#478—711no—
352C2×#478—711no—
353C2×#476—711no—
354C2×#446—711no—
355C2×#440—711no—
356C2×#440—711no—
357C2×C4×SD16—711no—
358C71C2×#338811yescharacteristic, complemented, Sylow
359C22×SD16—711no—
360#557—718no—
361#557—1424no—
362#554—24no—
363#554C2×D7118yes—
364C2×C4⋊Q8—711no—
365C2×C4⋊Q8—1421no—
366C2×C4⋊Q8C2×D7111yescharacteristic
367C2×#125—711no—
368C2×#125—711no—
369C2×#125—1421no—
370C2×#125—1421no—
371C2×#125C2×D7111yescharacteristic
372C2×#125C2×D7111yescharacteristic
373C2×C22⋊Q8—21no—
374C2×C22⋊Q8—21no—
375C2×C22⋊Q8—21no—
376C2×C4×Q8—711no—
377C2×C4×Q8—711no—
378C2×C4×Q8—711no—
379C2×C4×Q8—1421no—
380C2×C4×Q8C2×D7111yescharacteristic
381C2×C4×D4C2×D7111yescharacteristic
382C2×C4×D4C2×D7111yescharacteristic
383C2×C4×D4C2×D7111yescharacteristic
384C22×C4⋊C4—21no—
385#501—718no—
386#501—718no—
387#499—718no—
388#479—718no—
389#479—718no—
390#478—718no—
391#478—718no—
392#476—718no—
393#475—718no—
394#446—718no—
395#440—718no—
396#440—718no—
397C4×SD16—718no—
398C2×#107—711no—
399C2×#107—711no—
400C2×#107—711no—
401C2×#107—711no—
402C2×#106—711no—
403C2×#106—711no—
404C2×#106—711no—
405C2×#106—711no—
406C2×#106—711no—
407C2×C4⋊C8—711no—
408C2×C4⋊C8—711no—
409C2×C4⋊C8—711no—
410C2×#103—711no—
411C2×#103—711no—
412C2×#103—711no—
413C2×#102—711no—
414C2×#102—711no—
415C2×#102—711no—
416C2×#97—711no—
417C2×#97—711no—
418C2×C4×C8—711no—
419C22×Q8—21no—
420C22×Q8—711no—
421C22×Q8—1421no—
422C22×Q8C22⋊D7111yescharacteristic
423C22×D4C22×D7111yescharacteristic
424C23×C4—21no—
425C23×C4—21no—
426C23×C4—21no—
427C2×SD16—718no—
428C2×SD16—714no—
429C22×C8—711no—
430C22×C8—711no—
431C22×C8—711no—
432C22×C8—711no—
433C4⋊Q8—22no—
434C4⋊Q8—714no—
435C4⋊Q8—1428no—
436C4⋊Q8—1422no—
437C4⋊Q8C22×D7114yes—
438#125—22no—
439#125—22no—
440#125—714no—
441#125—714no—
442#125—1428no—
443#125—1428no—
444#125—1422no—
445#125—1422no—
446#125C22×D7114yes—
447#125C22×D7114yes—
448C22⋊Q8—28no—
449C22⋊Q8—28no—
450C22⋊Q8—28no—
451C4×Q8—714no—
452C4×Q8—714no—
453C4×Q8—714no—
454C4×Q8—1428no—
455C4×Q8—1422no—
456C4×Q8—1422no—
457C4×Q8—1422no—
458C4×Q8C22⋊D7114yes—
459C4×Q8C22×D7114yes—
460C4×D4—22no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4C22×D7114yes—
464C4×D4C22×D7114yes—
465C4×D4C22×D7114yes—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—28no—
472C2×C4⋊C4—711no—
473C2×C4⋊C4—711no—
474C2×C4⋊C4—711no—
475C2×C4⋊C4—1421no—
476C2×C4⋊C4—1421no—
477C2×C4⋊C4—1421no—
478C2×C4⋊C4—1421no—
479C2×C4⋊C4—1421no—
480C2×C4⋊C4—1421no—
481C2×C4⋊C4—1421no—
482C2×C4⋊C4—1421no—
483C2×C4⋊C4C22⋊D7111yescharacteristic
484C2×C4⋊C4C22⋊D7111yescharacteristic
485C2×C4⋊C4C22⋊D7111yescharacteristic
486C2×C4⋊C4C22×D7111yescharacteristic
487C2×C4⋊C4C22×D7111yescharacteristic
488C2×C4⋊C4C22×D7111yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C42—1421no—
493C2×C42—1421no—
494C2×C42—1421no—
495C2×C42C22×D7111yescharacteristic
496C2×C42C22×D7111yescharacteristic
497C2×C42C22×D7111yescharacteristic
498#107—714no—
499#107—714no—
500#107—714no—
501#107—714no—
502#106—714no—
503#106—714no—
504#106—714no—
505#106—714no—
506#106—714no—
507C4⋊C8—714no—
508C4⋊C8—714no—
509C4⋊C8—714no—
510#103—714no—
511#103—714no—
512#103—714no—
513#102—714no—
514#102—714no—
515#102—714no—
516#97—714no—
517#97—714no—
518C4×C8—714no—
519C24—21no—
520C2×Q8—24no—
521C2×Q8—42no—
522C2×Q8—82no—
523C2×Q8—2844no—
524C2×Q8—714no—
525C2×Q8—712no—
526C2×Q8—1424no—
527C2×Q8—1421no—
528C2×Q8—1422no—
529C2×Q8C2×C22⋊D7114yes—
530C2×D4—21no—
531C2×D4—22no—
532C2×D4Q8×D7114yes—
533C2×D4C23×D7112yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—44no—
541C22×C4—82no—
542C22×C4—82no—
543C22×C4—1421no—
544C22×C4—1421no—
545C22×C4—1421no—
546C22×C4—1421no—
547C22×C4C2×C22⋊D7111yescharacteristic
548C22×C4C2×C22⋊D7111yescharacteristic
549C22×C4C2×C22⋊D7111yescharacteristic
550C22×C4C2×C22⋊D7111yescharacteristic
551C22×C4C2×C22⋊D7111yescharacteristic
552C22×C4C2×C22⋊D7111yescharacteristic
553C22×C4C23×D7111yescharacteristic
554SD16—7116no—
555C2×C8—714no—
556C2×C8—712no—
557C2×C8—712no—
558C2×C8—712no—
559C2×C8—712no—
560C2×C8—1422no—
561C2×C8—1422no—
562C2×C8—1422no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—712no—
572C4⋊C4—712no—
573C4⋊C4—712no—
574C4⋊C4—1424no—
575C4⋊C4—1424no—
576C4⋊C4—1424no—
577C4⋊C4—1424no—
578C4⋊C4—1424no—
579C4⋊C4—1424no—
580C4⋊C4—1424no—
581C4⋊C4—1421no—
582C4⋊C4—1421no—
583C4⋊C4—1421no—
584C4⋊C4—1424no—
585C4⋊C4C2×C22⋊D7114yes—
586C4⋊C4C2×C22⋊D7114yes—
587C4⋊C4C2×C22⋊D7114yes—
588C4⋊C4C23×D7112yes—
589C4⋊C4C23×D7112yes—
590C4⋊C4C23×D7112yes—
591C22⋊C4—24no—
592C22⋊C4—24no—
593C22⋊C4—24no—
594C42—1424no—
595C42—1424no—
596C42—1424no—
597C42C2×C22⋊D7112yes—
598C42C2×C22⋊D7112yes—
599C42C2×C22⋊D7112yes—
600C42C23×D7112yes—
601C42C23×D7112yes—
602C42C23×D7112yes—
603C23—22no—
604C23—24no—
605C23—42no—
606C23—42no—
607C23C22×C22⋊D7111yescharacteristic
608Q8—44no—
609Q8—84no—
610Q8—2848no—
611Q8—714no—
612Q8—1422no—
613Q8—1424no—
614D4—22no—
615D4—24no—
616D4C2×Q8×D7114yes—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—48no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—84no—
631C2×C4—84no—
632C2×C4—2842no—
633C2×C4—2842no—
634C2×C4—2842no—
635C2×C4—1422no—
636C2×C4—1422no—
637C2×C4—1422no—
638C2×C4—1422no—
639C2×C4—1424no—
640C2×C4C22×C22⋊D7112yes—
641C2×C4C22×C22⋊D7112yes—
642C2×C4C22×C22⋊D7112yes—
643C2×C4C22×C22⋊D7112yes—
644C2×C4C22×C22⋊D7112yes—
645C2×C4C22×C22⋊D7112yes—
646C2×C4C22×C22⋊D7111yescharacteristic
647C2×C4C2×Q8×D7112yes—
648C2×C4#1455617612yes—
649C2×C4C24×D7111yescharacteristic
650C8—714no—
651C8—1422no—
652C8—1422no—
653C8—1422no—
654C22—24no—
655C22—48no—
656C22—42no—
657C22—42no—
658C22Q8×C22⋊D7112yes—
659C22#1798679712yes—
660C22#1798681012yes—
661C22C23×C22⋊D7111yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—22no—
666C4—22no—
667C4—22no—
668C4—42no—
669C4—42no—
670C4—42no—
671C4—2842no—
672C4—2842no—
673C4—2842no—
674C4—1424no—
675C4Q8×C22⋊D7112yes—
676C4C22×Q8×D7111yescharacteristic
677C4C2×#1455617611yescharacteristic
678C2—44no—
679C2#2260128514yesdirect product factor
680C2C2×Q8×C22⋊D7111yescharacteristic
681C2C2×#1798679711yescharacteristic
682C2C2×#1798681011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#554×C71C2
socleC23×C71C22×D4
prime radicalC22×D4×C71C23
hypercenterC2×#554D71
hypocenterC71C2×#3388
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×#17986727C2semidirect
2. #22601285C2direct (N × H)
3. C2×#17986409C2semidirect
4. C2×#17986405C2semidirect
5. C2×#17986398C2semidirect
6. C2×#17986303C2semidirect
7. C2×#17986303C2semidirect
8. C2×#17986281C2semidirect
12. C2×#17986130C2semidirect
19. #17986727C22semidirect
30. #17986409C22semidirect
31. #17986405C22semidirect
32. #17986398C22semidirect
33. #17986303C22semidirect
34. #17986303C22semidirect
38. #17986281C22semidirect
39. #17986130C22semidirect
79. C2×#11765853Q8semidirect
187. #11765853C2×Q8semidirect
338. C2×C71#3388semidirect
358. C71C2×#3388semidirect
679. C2#22601285direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867272
#226012852
C2×#179864092
C2×#179864052
C2×#179863982
C2×#179863032
C2×#179862812
C2×#179862992
C2×#179862892
C2×#179861302
C2×#179860992
C2×C4×#117658532
C2×#554×C712
C2×#338871