Finite Group Databasebeta

← C2×#22601251 #32877942

Subgroups — C2×#22601251 #32877942

Order 18176.

1854 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×Dic142C211yesmaximal, characteristic, complemented
2C2×#17986708C211yesmaximal, characteristic
3#22601251C2116yesmaximal, direct product factor
4C2×#17986408C211yesmaximal, characteristic, complemented
5C2×#17986407C211yesmaximal, characteristic, complemented
6C2×#17986403C211yesmaximal, characteristic, complemented
7C2×#17986306C211yesmaximal, characteristic, complemented
8C2×#17986304C211yesmaximal, characteristic, complemented
9C2×#17986292C211yesmaximal, characteristic, complemented
10C2×#17986287C211yesmaximal, characteristic
11C2×#17986279C211yesmaximal, characteristic
12C2×#17986277C211yesmaximal, characteristic
13C2×#17986127C211yesmaximal, characteristic, complemented
14C2×#17986100C211yesmaximal, characteristic
15C2×SD16×Dic71C211yesmaximal, characteristic
16C2×#440×C71C211yesmaximal, characteristic
17Q8×Dic142—24no—
18Q8×Dic142C2218yescomplemented
19#17986708—24no—
20#17986708C2218yes—
21C2×#14556128—21no—
22C2×#14556128C2211yescharacteristic
23C2×#14556127—21no—
24C2×#14556127—21no—
25C2×#14556127C2211yescharacteristic
26C2×#14556127C2211yescharacteristic
27C2×#14556127C2211yescharacteristic
28C2×#14556120C2211yescharacteristic
29C2×#14556119C2211yescharacteristic
30C2×#14556107—21no—
31C2×#14556105—21no—
32C2×#14556105—21no—
33C2×Q8×Dic71C2211yescharacteristic
34C2×Q8×Dic71C2211yescharacteristic
35C2×C4×Dic142—21no—
36C2×C4×Dic142C2211yescharacteristic
37C2×D4×Dic71C2211yescharacteristic
38C2×D4×Dic71C2211yescharacteristic
39C22×Dic71⋊C4—21no—
40#17986408C2218yescomplemented
41#17986407C2218yescomplemented
42#17986403C2218yescomplemented
43#17986306C2218yescomplemented
44#17986304C2218yescomplemented
45#17986292C2218yescomplemented
46#17986287C2218yes—
47#17986279C2218yes—
48#17986277C2218yes—
49#17986127C2218yescomplemented
50#17986100C2218yes—
51SD16×Dic71C2218yes—
52C2×#14556062C2211yescharacteristic
53C2×#14556062C2211yescharacteristic
54C2×#14556061C2211yescharacteristic
55C2×#14556061C2211yescharacteristic
56C2×#14556061C2211yescharacteristic
57C2×#14556060C2211yescharacteristic
58C2×#14556060C2211yescharacteristic
59C2×#14556059C2211yescharacteristic
60C2×C4⋊(C71⋊C8)C2211yescharacteristic
61C2×Dic71⋊C8C2211yescharacteristic
62C2×Dic71⋊C8C2211yescharacteristic
63C2×#14556052C2211yescharacteristic
64C2×#14556052C2211yescharacteristic
65C2×#14556049C2211yescharacteristic
66C2×#14556049C2211yescharacteristic
67C2×#14556038C2211yescharacteristic
68C2×C8×Dic71C2211yescharacteristic
69C22×SD16×C71C2211yescharacteristic
70C2×C4×Q8×C71C2211yescharacteristic
71C2×C4×D4×C71C2211yescharacteristic
72#440×C71C2218yes—
73C2×#107×C71C2211yescharacteristic
74C2×#103×C71C2211yescharacteristic
75C2×#102×C71C2211yescharacteristic
76C2×#97×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142—21no—
79C22×Dic142—21no—
80C22×Dic142—21no—
81C22×Dic142D411yescharacteristic
82C23×Dic71—21no—
83C23×Dic71—21no—
84C22×C71⋊C8C2311yescharacteristic
85C22×C71⋊C8C2311yescharacteristic
86#14556128—28no—
87#14556128—22no—
88#14556128C2314yes—
89#14556127—28no—
90#14556127—28no—
91#14556127—22no—
92#14556127—22no—
93#14556127—22no—
94#14556127C2314yes—
95#14556127C2314yes—
96#14556127C2314yes—
97#14556120—22no—
98#14556120C2314yes—
99#14556119—22no—
100#14556119C2314yes—
101#14556107—28no—
102#14556105—28no—
103#14556105—28no—
104Q8×Dic71—22no—
105Q8×Dic71—22no—
106Q8×Dic71C2314yes—
107Q8×Dic71C2314yes—
108C4×Dic142—28no—
109C4×Dic142D414yes—
110C4×Dic142C2314yes—
111D4×Dic71—22no—
112D4×Dic71—22no—
113D4×Dic71C2314yes—
114D4×Dic71C2314yes—
115C2×C4⋊Dic71—21no—
116C2×C4⋊Dic71—21no—
117C2×C4⋊Dic71—21no—
118C2×C4⋊Dic71—21no—
119C2×C4⋊Dic71D411yescharacteristic
120C2×C4⋊Dic71C2311yescharacteristic
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—28no—
129C2×Dic71⋊C4—21no—
130C2×Dic71⋊C4—21no—
131C2×Dic71⋊C4D411yescharacteristic
132C2×Dic71⋊C4D411yescharacteristic
133C2×C22⋊Dic71—21no—
134C2×C22⋊Dic71—21no—
135C2×C4×Dic71—21no—
136C2×C4×Dic71—21no—
137C2×C4×Dic71C2311yescharacteristic
138C2×C4×Dic71C2311yescharacteristic
139#14556062C2314yes—
140#14556062C2314yes—
141#14556061C2314yes—
142#14556061C2314yes—
143#14556061C2314yes—
144#14556060C2314yes—
145#14556060C2314yes—
146#14556059C2314yes—
147C4⋊(C71⋊C8)C2314yes—
148Dic71⋊C8C2314yes—
149Dic71⋊C8C2314yes—
150#14556052C2314yes—
151#14556052C2314yes—
152#14556049C2314yes—
153#14556049C2314yes—
154#14556038C2314yes—
155C8×Dic71C2314yes—
156C22×Q8×C71C2311yescharacteristic
157C22×D4×C71C2311yescharacteristic
158C23×C4×C71—21no—
159C2×SD16×C71Q818yescomplemented
160C2×SD16×C71C2314yes—
161C22×C8×C71C2311yescharacteristic
162C22×C8×C71C2311yescharacteristic
163C4×Q8×C71—22no—
164C4×Q8×C71C2314yes—
165C4×D4×C71—22no—
166C4×D4×C71C2314yes—
167C2×C4⋊C4×C71—21no—
168C2×C4⋊C4×C71C2311yescharacteristic
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C22⋊C4×C71—21no—
171C2×C42×C71—21no—
172C2×C42×C71C2311yescharacteristic
173#107×C71C2314yes—
174#103×C71C2314yes—
175#102×C71C2314yes—
176#97×C71C2314yes—
177C2×Dic142—24no—
178C2×Dic142—24no—
179C2×Dic142—24no—
180C2×Dic142—24no—
181C2×Dic142—24no—
182C2×Dic142—82no—
183C2×Dic142—82no—
184C2×Dic142—82no—
185C2×Dic142—82no—
186C2×Dic142C2×D414yes—
187C22×Dic71—21no—
188C22×Dic71—21no—
189C22×Dic71—21no—
190C22×Dic71—21no—
191C22×Dic71—24no—
192C22×Dic71—24no—
193C22×Dic71—44no—
194C22×Dic71—82no—
195C22×Dic71C2×D411yescharacteristic
196C22×Dic71C2×D411yescharacteristic
197C22×Dic71C2×D411yescharacteristic
198C22×Dic71C2×D411yescharacteristic
199C2×C71⋊C8—22no—
200C2×C71⋊C8—22no—
201C2×C71⋊C8C2412yes—
202C2×C71⋊C8C2412yes—
203C4⋊Dic71—24no—
204C4⋊Dic71—21no—
205C4⋊Dic71—21no—
206C4⋊Dic71—21no—
207C4⋊Dic71—21no—
208C4⋊Dic71—24no—
209C4⋊Dic71—24no—
210C4⋊Dic71—24no—
211C4⋊Dic71C2×D414yes—
212C4⋊Dic71C2412yes—
213C4⋊Dic71C2412yes—
214C4⋊Dic71C2412yes—
215C4⋊Dic71C2412yes—
216Dic71⋊C4—24no—
217Dic71⋊C4—24no—
218Dic71⋊C4—24no—
219Dic71⋊C4—24no—
220Dic71⋊C4—24no—
221Dic71⋊C4—24no—
222Dic71⋊C4C2×D414yes—
223Dic71⋊C4C2×D414yes—
224C22⋊Dic71—24no—
225C22⋊Dic71—24no—
226C4×Dic71—24no—
227C4×Dic71—24no—
228C4×Dic71C2×D412yes—
229C4×Dic71C2×D412yes—
230C4×Dic71C2412yes—
231C4×Dic71C2412yes—
232C24×C71—21no—
233C2×Q8×C71—21no—
234C2×Q8×C71—22no—
235C2×Q8×C71C2×Q814yes—
236C2×Q8×C71C2412yes—
237C2×D4×C71—21no—
238C2×D4×C71—22no—
239C2×D4×C71C2×Q814yes—
240C2×D4×C71C2412yes—
241C22×C4×C71—21no—
242C22×C4×C71—21no—
243C22×C4×C71—21no—
244C22×C4×C71—24no—
245C22×C4×C71—82no—
246C22×C4×C71C2×D411yescharacteristic
247C22×C4×C71C2×D411yescharacteristic
248C22×C4×C71C2411yescharacteristic
249SD16×C71C2×Q8116yescomplemented
250C2×C8×C71—22no—
251C2×C8×C71C2×Q814yes—
252C2×C8×C71C2412yes—
253C2×C8×C71C2412yes—
254C4⋊C4×C71—24no—
255C4⋊C4×C71—21no—
256C4⋊C4×C71—21no—
257C4⋊C4×C71C2412yes—
258C4⋊C4×C71C2412yes—
259C22⋊C4×C71—24no—
260C42×C71—24no—
261C42×C71C2×D412yes—
262C42×C71C2412yes—
263C23×C71—24no—
264C23×C71—22no—
265C23×C71—42no—
266C23×C71—42no—
267C23×C71C22×D411yescharacteristic
268Q8×C71—24no—
269Q8×C71—22no—
270Q8×C71C22×Q814yes—
271D4×C71—24no—
272D4×C71—22no—
273D4×C71C22×Q814yes—
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—42no—
281C2×C4×C71—42no—
282C2×C4×C71—84no—
283C2×C4×C71C22×D412yes—
284C2×C4×C71C22×D412yes—
285C2×C4×C71C22×D411yescharacteristic
286C2×C4×C71C22×Q812yes—
287C2×C4×C712−1+412yes—
288C2×C4×C71C2511yescharacteristic
289C2×Dic71—22no—
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×Dic71—42no—
299C2×Dic71—42no—
300C2×Dic71—48no—
301C2×Dic71—84no—
302C2×Dic71#13714yes—
303C2×Dic71C22×D412yes—
304C2×Dic71C22×D412yes—
305C2×Dic71C22×D412yes—
306C2×Dic71C22×D412yes—
307Dic142—28no—
308Dic142—84no—
309Dic142—84no—
310Dic142—84no—
311Dic142—84no—
312C8×C71—22no—
313C8×C71C22×Q814yes—
314C71⋊C8—22no—
315C71⋊C8—22no—
316C22×C71—24no—
317C22×C71—48no—
318C22×C71—42no—
319C22×C71—42no—
320C22×C71D4×Q812yes—
321C22×C71C2×#13712yes—
322C22×C71#57612yes—
323C22×C71C23×D411yescharacteristic
324C4×C71—24no—
325C4×C71—22no—
326C4×C71—22no—
327C4×C71—42no—
328C4×C71—42no—
329C4×C71D4×Q812yes—
330C4×C71C23×Q811yescharacteristic
331C4×C71C2×2−1+411yescharacteristic
332Dic71—22no—
333Dic71—22no—
334Dic71—22no—
335Dic71—42no—
336Dic71—42no—
337Dic71—42no—
338Dic71—42no—
339Dic71C2×#13714yes—
340C2×#3385—711nomaximal, Sylow
341C2×C71—44no—
342C2×C71#338514yescomplemented
343C2×C71C2×D4×Q811yescharacteristic
344C2×C71C22×#13711yescharacteristic
345C2×C71C2×#57611yescharacteristic
346C2×Q82—711no—
347C2×#554—711no—
348#3385—7116no—
349C2×#501—711no—
350C2×#501—711no—
351C2×#500—711no—
352C2×#479—711no—
353C2×#479—711no—
354C2×#477—711no—
355C2×#476—711no—
356C2×#474—711no—
357C2×#474—711no—
358C2×#446—711no—
359C2×#440—711no—
360C2×#440D7111yescharacteristic
361C2×C4×SD16—711no—
362C71C2×#338511yescharacteristic, complemented, Sylow
363C22×SD16C2×D7111yescharacteristic
364Q82—718no—
365Q82—1424no—
366#554—718no—
367#554—1424no—
368C2×C4⋊Q8—711no—
369C2×C4⋊Q8—711no—
370C2×C4⋊Q8—711no—
371C2×C4⋊Q8—711no—
372C2×C4⋊Q8—1421no—
373C2×C4⋊Q8—1421no—
374C2×C4⋊Q8—1421no—
375C2×#125—711no—
376C2×#125—711no—
377C2×C22⋊Q8—1421no—
378C2×C22⋊Q8—1421no—
379C2×C22⋊Q8—1421no—
380C2×C4×Q8—711no—
381C2×C4×Q8—711no—
382C2×C4×Q8—711no—
383C2×C4×Q8—1421no—
384C2×C4×Q8C2×D7111yescharacteristic
385C2×C4×D4—711no—
386C2×C4×D4—711no—
387C2×C4×D4C2×D7111yescharacteristic
388C22×C4⋊C4—1421no—
389#501—718no—
390#501—718no—
391#500—718no—
392#479—718no—
393#479—718no—
394#477—718no—
395#476—718no—
396#474—718no—
397#474—718no—
398#446—718no—
399#440—718no—
400#440C2×D7118yes—
401C4×SD16—718no—
402C2×#107—711no—
403C2×#107—711no—
404C2×#107—711no—
405C2×#107—711no—
406C2×#107—711no—
407C2×#107C2×D7111yescharacteristic
408C2×#106—711no—
409C2×#106—711no—
410C2×#106—711no—
411C2×C4⋊C8—711no—
412C2×C4⋊C8—711no—
413C2×C4⋊C8—711no—
414C2×#103—711no—
415C2×#103—711no—
416C2×#103C2×D7111yescharacteristic
417C2×#102—711no—
418C2×#102—711no—
419C2×#102C2×D7111yescharacteristic
420C2×#97—711no—
421C2×#97C2×D7111yescharacteristic
422C2×C4×C8—711no—
423C22×Q8—711no—
424C22×Q8—1421no—
425C22×Q8—1421no—
426C22×Q8—1421no—
427C22×Q8—1421no—
428C22×Q8C22×D7111yescharacteristic
429C22×D4C22×D7111yescharacteristic
430C23×C4—21no—
431C23×C4—1421no—
432C23×C4—1421no—
433C2×SD16Dic14218yescomplemented
434C2×SD16C22×D7114yes—
435C22×C8—711no—
436C22×C8—711no—
437C22×C8C22×D7111yescharacteristic
438C22×C8C22×D7111yescharacteristic
439C4⋊Q8—714no—
440C4⋊Q8—714no—
441C4⋊Q8—714no—
442C4⋊Q8—714no—
443C4⋊Q8—1428no—
444C4⋊Q8—1422no—
445C4⋊Q8—1422no—
446C4⋊Q8—1422no—
447C4⋊Q8—1428no—
448C4⋊Q8—1428no—
449C4⋊Q8—1422no—
450#125—714no—
451#125—714no—
452#125—1422no—
453#125—1422no—
454C22⋊Q8—1428no—
455C22⋊Q8—1428no—
456C22⋊Q8—1428no—
457C4×Q8—22no—
458C4×Q8—714no—
459C4×Q8—714no—
460C4×Q8—714no—
461C4×Q8—714no—
462C4×Q8—1428no—
463C4×Q8—1422no—
464C4×Q8—1422no—
465C4×Q8C22×D7114yes—
466C4×D4—22no—
467C4×D4—714no—
468C4×D4—714no—
469C4×D4—1422no—
470C4×D4—1422no—
471C4×D4C22×D7114yes—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—711no—
474C2×C4⋊C4—711no—
475C2×C4⋊C4—711no—
476C2×C4⋊C4—711no—
477C2×C4⋊C4—711no—
478C2×C4⋊C4—711no—
479C2×C4⋊C4—711no—
480C2×C4⋊C4—1428no—
481C2×C4⋊C4—1421no—
482C2×C4⋊C4—1421no—
483C2×C4⋊C4—1421no—
484C2×C4⋊C4—1421no—
485C2×C4⋊C4—1421no—
486C2×C4⋊C4—1421no—
487C2×C4⋊C4—1421no—
488C2×C4⋊C4—1421no—
489C2×C4⋊C4—1421no—
490C2×C4⋊C4—1421no—
491C2×C4⋊C4C22×D7111yescharacteristic
492C2×C4⋊C4C22×D7111yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—1421no—
495C2×C22⋊C4—1421no—
496C2×C42—21no—
497C2×C42—711no—
498C2×C42—711no—
499C2×C42—1421no—
500C2×C42—1421no—
501C2×C42C22×D7111yescharacteristic
502#107—714no—
503#107—714no—
504#107—714no—
505#107—714no—
506#107—714no—
507#107C22×D7114yes—
508#106—714no—
509#106—714no—
510#106—714no—
511C4⋊C8—714no—
512C4⋊C8—714no—
513C4⋊C8—714no—
514#103—714no—
515#103—714no—
516#103C22×D7114yes—
517#102—714no—
518#102—714no—
519#102C22×D7114yes—
520#97—714no—
521#97C22×D7114yes—
522C4×C8—714no—
523C24—21no—
524C2×Q8—21no—
525C2×Q8—22no—
526C2×Q8—5682no—
527C2×Q8—5682no—
528C2×Q8—5682no—
529C2×Q8—5682no—
530C2×Q8—714no—
531C2×Q8—1424no—
532C2×Q8—1424no—
533C2×Q8—1424no—
534C2×Q8—1424no—
535C2×Q8—1424no—
536C2×Q8C2×Dic14214yes—
537C2×Q8C23×D7112yes—
538C2×D4—21no—
539C2×D4—22no—
540C2×D4C2×Dic14214yes—
541C2×D4C23×D7112yes—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—24no—
546C22×C4—82no—
547C22×C4—2844no—
548C22×C4—5682no—
549C22×C4—711no—
550C22×C4—711no—
551C22×C4—711no—
552C22×C4—711no—
553C22×C4—1424no—
554C22×C4—1421no—
555C22×C4—1421no—
556C22×C4—1421no—
557C22×C4—1421no—
558C22×C4—1424no—
559C22×C4D4×D7111yescharacteristic
560C22×C4D4×D7111yescharacteristic
561C22×C4C23×D7111yescharacteristic
562SD16C2×Dic142116yescomplemented
563C2×C8—22no—
564C2×C8—712no—
565C2×C8—712no—
566C2×C8—1422no—
567C2×C8—1422no—
568C2×C8C2×Dic14214yes—
569C2×C8C23×D7112yes—
570C2×C8C23×D7112yes—
571C4⋊C4—24no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—714no—
575C4⋊C4—714no—
576C4⋊C4—714no—
577C4⋊C4—712no—
578C4⋊C4—712no—
579C4⋊C4—712no—
580C4⋊C4—712no—
581C4⋊C4—1424no—
582C4⋊C4—1424no—
583C4⋊C4—1424no—
584C4⋊C4—1424no—
585C4⋊C4—1424no—
586C4⋊C4—1424no—
587C4⋊C4—1424no—
588C4⋊C4—1424no—
589C4⋊C4—1424no—
590C4⋊C4—1421no—
591C4⋊C4—1421no—
592C4⋊C4—1421no—
593C4⋊C4—1421no—
594C4⋊C4—1424no—
595C4⋊C4C23×D7112yes—
596C4⋊C4C23×D7112yes—
597C22⋊C4—24no—
598C22⋊C4—1424no—
599C22⋊C4—1424no—
600C42—24no—
601C42—712no—
602C42—712no—
603C42—712no—
604C42—712no—
605C42—1424no—
606C42—1424no—
607C42D4×D7112yes—
608C42C23×D7112yes—
609C23—22no—
610C23—24no—
611C23—42no—
612C23—42no—
613C23C2×D4×D7111yescharacteristic
614Q8—22no—
615Q8—24no—
616Q8—5684no—
617Q8—5684no—
618Q8—5684no—
619Q8—5684no—
620Q8—1428no—
621Q8C22×Dic14214yes—
622D4—22no—
623D4—24no—
624D4C22×Dic14214yes—
625C2×C4—22no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—84no—
634C2×C4—2842no—
635C2×C4—2842no—
636C2×C4—2842no—
637C2×C4—2842no—
638C2×C4—2848no—
639C2×C4—5684no—
640C2×C4—712no—
641C2×C4—714no—
642C2×C4—712no—
643C2×C4—712no—
644C2×C4—712no—
645C2×C4—1422no—
646C2×C4—1422no—
647C2×C4—1422no—
648C2×C4—1422no—
649C2×C4—1422no—
650C2×C4—1422no—
651C2×C4—1422no—
652C2×C4C2×D4×D7112yes—
653C2×C4C2×D4×D7112yes—
654C2×C4C2×D4×D7111yescharacteristic
655C2×C4C22×Dic14212yes—
656C2×C4#1455617512yes—
657C2×C4C24×D7111yescharacteristic
658C8—22no—
659C8—1422no—
660C8—1422no—
661C8C22×Dic14214yes—
662C22—24no—
663C22—48no—
664C22—42no—
665C22—42no—
666C22D4×Dic14212yes—
667C22#137×D7112yes—
668C22#1798680312yes—
669C22C22×D4×D7111yescharacteristic
670C4—22no—
671C4—22no—
672C4—24no—
673C4—42no—
674C4—42no—
675C4—2842no—
676C4—2842no—
677C4—2842no—
678C4—2842no—
679C4—714no—
680C4—1422no—
681C4—1422no—
682C4—1422no—
683C4D4×Dic14212yes—
684C4C23×Dic14211yescharacteristic
685C4C2×#1455617511yescharacteristic
686C2—44no—
687C2#2260125114yesdirect product factor
688C2C2×D4×Dic14211yescharacteristic
689C2C2×#137×D7111yescharacteristic
690C2C2×#1798680311yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#440×C71C2
socleC23×C71C22×D4
prime radicalC22×D4×C71C23
hypercenterC2×#440D71
hypocenterC71C2×#3385
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic142C2semidirect
3. #22601251C2direct (N × H)
4. C2×#17986408C2semidirect
5. C2×#17986407C2semidirect
6. C2×#17986403C2semidirect
7. C2×#17986306C2semidirect
8. C2×#17986304C2semidirect
9. C2×#17986292C2semidirect
13. C2×#17986127C2semidirect
18. Q8×Dic142C22semidirect
40. #17986408C22semidirect
41. #17986407C22semidirect
42. #17986403C22semidirect
43. #17986306C22semidirect
44. #17986304C22semidirect
45. #17986292C22semidirect
49. #17986127C22semidirect
159. C2×SD16×C71Q8semidirect
249. SD16×C71C2×Q8semidirect
342. C2×C71#3385semidirect
362. C71C2×#3385semidirect
433. C2×SD16Dic142semidirect
562. SD16C2×Dic142semidirect
687. C2#22601251direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×Dic1422
C2×#179867082
#226012512
C2×#179864082
C2×#179864072
C2×#179864032
C2×#179863062
C2×#179863042
C2×#179862922
C2×#179862872
C2×#179862792
C2×#179862772
C2×#179861272
C2×#179861002
C2×SD16×Dic712
C2×#440×C712
C2×#338571