Finite Group Databasebeta

← C2×#22598588 #32865752

Subgroups — C2×#22598588 #32865752

Order 18176.

2210 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986609C211yesmaximal, characteristic, complemented
2C2×#17986473C211yesmaximal, characteristic
3#22598588C2116yesmaximal, direct product factor
4C2×#17986340C211yesmaximal, characteristic, complemented
5C2×#17986302C211yesmaximal, characteristic, complemented
6C2×#17986298C211yesmaximal, characteristic, complemented
7C2×#17986203C211yesmaximal, characteristic, complemented
8C2×#17986203C211yesmaximal, characteristic, complemented
9C2×#17986152C211yesmaximal, characteristic
10C2×#17986149C211yesmaximal, characteristic
11C2×#17986102C211yesmaximal, characteristic, complemented
12C2×#17986098C211yesmaximal, characteristic, complemented
13C2×#17986086C211yesmaximal, characteristic, complemented
14C2×#17986084C211yesmaximal, characteristic, complemented
15C2×#17986057C211yesmaximal, characteristic, complemented
16C2×#485×C71C211yesmaximal, characteristic, complemented
17C23×D284C2211yescharacteristic
18C22×#11765854C2211yescharacteristic
19C22×#11765854C2211yescharacteristic
20C22×#11765852C2211yescharacteristic
21C22×#11765852C2211yescharacteristic
22#17986609—24no—
23#17986609C2218yescomplemented
24C2×#14556126C2211yescharacteristic, complemented
25C2×#14556121—21no—
26C2×#14556121—21no—
27C2×#14556119—21no—
28C2×#14556119C2211yescharacteristic, complemented
29C2×#14556118—21no—
30C2×#14556107C2211yescharacteristic
31#17986473—24no—
32#17986473C2218yes—
33C2×Q8×Dic71C2211yescharacteristic, complemented
34C2×#14556093C2211yescharacteristic, complemented
35C2×C4×D284—21no—
36C2×C4×D284—21no—
37C2×#14556090C2211yescharacteristic
38C2×#14556090C2211yescharacteristic
39C2×#14556090C2211yescharacteristic
40C2×#14556090C2211yescharacteristic
41C2×#14556087C2211yescharacteristic
42C2×C22⋊C4×D71—21no—
43C2×C22⋊C4×D71—21no—
44#17986340C2218yescomplemented
45#17986302C2218yescomplemented
46#17986298C2218yescomplemented
47#17986203C2218yescomplemented
48#17986203C2218yescomplemented
49#17986152C2218yes—
50#17986149C2218yes—
51#17986102C2218yescomplemented
52#17986098C2218yescomplemented
53#17986086C2218yescomplemented
54#17986084C2218yescomplemented
55#17986057C2218yescomplemented
56C2×#14556061C2211yescharacteristic, complemented
57C2×#14556059C2211yescharacteristic, complemented
58C2×Dic71⋊C8C2211yescharacteristic, complemented
59C2×Dic71⋊C8C2211yescharacteristic, complemented
60C2×#14556051C2211yescharacteristic, complemented
61C2×#14556051C2211yescharacteristic, complemented
62C2×#14556050C2211yescharacteristic
63C2×#14556050C2211yescharacteristic
64C2×#14556048C2211yescharacteristic
65C2×#14556048C2211yescharacteristic
66C2×C22⋊(C71⋊C8)C2211yescharacteristic
67C2×#14556038C2211yescharacteristic, complemented
68C2×C8×Dic71C2211yescharacteristic, complemented
69C2×C22⋊Q8×C71C2211yescharacteristic
70C2×#117×C71C2211yescharacteristic
71#485×C71C2218yescomplemented
72C2×#107×C71C2211yescharacteristic, complemented
73C2×#106×C71C2211yescharacteristic, complemented
74C2×#103×C71C2211yescharacteristic, complemented
75C2×#103×C71C2211yescharacteristic, complemented
76C2×C22⋊C8×C71C2211yescharacteristic
77C24×D71—21no—
78C22×Dic142C2311yescharacteristic
79C22×D284—24no—
80C22×D284—24no—
81C22×D284—21no—
82C22×D284—22no—
83C22×D284C2314yes—
84C22×D284C2311yescharacteristic
85C22×D284C2311yescharacteristic
86C22×C4×D71—21no—
87C22×C4×D71—21no—
88C22×C4×D71—21no—
89C22×C4×D71—21no—
90C2×#11765854—24no—
91C2×#11765854—24no—
92C2×#11765854C2314yes—
93C2×#11765854C2314yes—
94C2×#11765852—24no—
95C2×#11765852—24no—
96C2×#11765852C2314yes—
97C2×#11765852C2314yes—
98C22×C71⋊C8C2311yescharacteristic
99C22×C71⋊C8C2311yescharacteristic
100#14556126—22no—
101#14556126C2314yescomplemented
102#14556121—28no—
103#14556121—28no—
104#14556119—28no—
105#14556119—22no—
106#14556119C2314yescomplemented
107#14556118—28no—
108#14556107—22no—
109#14556107C2314yes—
110Q8×Dic71—22no—
111Q8×Dic71C2314yescomplemented
112#14556093—22no—
113#14556093C2314yescomplemented
114C4×D284—28no—
115C4×D284—28no—
116#14556090—22no—
117#14556090—22no—
118#14556090—22no—
119#14556090—22no—
120#14556090C2314yes—
121#14556090C2314yes—
122#14556090C2314yes—
123#14556090C2314yes—
124#14556087D414yes—
125#14556087C2314yes—
126C2×C4⋊Dic71—21no—
127C2×C4⋊Dic71—21no—
128C2×C4⋊Dic71D411yescharacteristic
129C2×C4⋊Dic71D411yescharacteristic
130C2×C4⋊Dic71C2311yescharacteristic
131C2×Dic71⋊C4—21no—
132C2×Dic71⋊C4—21no—
133C2×Dic71⋊C4—21no—
134C2×Dic71⋊C4—21no—
135C2×Dic71⋊C4—21no—
136C2×C22⋊Dic71—21no—
137C2×C22⋊Dic71D411yescharacteristic
138C2×C22⋊Dic71D411yescharacteristic
139C2×(C2×D71)⋊C4—21no—
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4—21no—
142C2×(C2×D71)⋊C4—21no—
143C22⋊C4×D71—28no—
144C22⋊C4×D71—28no—
145C2×C4×Dic71—21no—
146C2×C4×Dic71—21no—
147C2×C4×Dic71C2311yescharacteristic
148C2×C4×Dic71C2311yescharacteristic
149#14556061C2314yescomplemented
150#14556059C2314yescomplemented
151Dic71⋊C8C2314yescomplemented
152Dic71⋊C8C2314yescomplemented
153#14556051C2314yescomplemented
154#14556051C2314yescomplemented
155#14556050C2314yes—
156#14556050C2314yes—
157#14556048C2314yes—
158#14556048C2314yes—
159C22⋊(C71⋊C8)C2314yes—
160#14556038C2314yescomplemented
161C8×Dic71C2314yescomplemented
162C22×Q8×C71C2311yescharacteristic
163C23×C4×C71C2311yescharacteristic
164C22×C8×C71C2311yescharacteristic
165C22×C8×C71C2311yescharacteristic
166C22⋊Q8×C71—22no—
167C22⋊Q8×C71C2314yes—
168#117×C71—22no—
169#117×C71C2314yes—
170C2×C4⋊C4×C71—21no—
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71—21no—
176C2×C42×C71—21no—
177#107×C71C2314yescomplemented
178#106×C71C2314yescomplemented
179#103×C71C2314yescomplemented
180#103×C71C2314yescomplemented
181C22⋊C8×C71C2314yes—
182C23×D71—21no—
183C23×D71—21no—
184C23×D71—28no—
185C23×D71—24no—
186C23×D71—82no—
187C23×D71—82no—
188C2×Dic142—22no—
189C2×Dic142—22no—
190C2×Dic142—21no—
191C2×Dic142C2412yes—
192C2×D284—28no—
193C2×D284—216no—
194C2×D284—21no—
195C2×D284—21no—
196C2×D284—24no—
197C2×D284—22no—
198C2×D284—22no—
199C2×D284—28no—
200C2×D284—28no—
201C2×D284#4114yes—
202C2×D284#4114yes—
203C2×D284C2412yes—
204C2×D284C2412yes—
205C22×Dic71—21no—
206C22×Dic71—21no—
207C22×Dic71C2×D411yescharacteristic
208C22×Dic71C2×D411yescharacteristic
209C22×Dic71C2×D411yescharacteristic
210C22×Dic71C2×D411yescharacteristic
211C2×C4×D71—24no—
212C2×C4×D71—24no—
213C2×C4×D71—24no—
214C2×C4×D71—24no—
215C2×C4×D71—82no—
216C2×C4×D71—82no—
217C2×C4×D71—82no—
218C2×C4×D71—82no—
219#11765854—28no—
220#11765854—28no—
221#11765852—28no—
222#11765852—28no—
223C2×C71⋊C8—22no—
224C2×C71⋊C8—22no—
225C2×C71⋊C8C2412yes—
226C2×C71⋊C8C2412yes—
227C4⋊Dic71—21no—
228C4⋊Dic71—24no—
229C4⋊Dic71—24no—
230C4⋊Dic71C2×D414yes—
231C4⋊Dic71C2×D414yes—
232C4⋊Dic71C2412yes—
233Dic71⋊C4—24no—
234Dic71⋊C4—24no—
235Dic71⋊C4—24no—
236Dic71⋊C4—24no—
237Dic71⋊C4—24no—
238C22⋊Dic71—24no—
239C22⋊Dic71C2×D414yes—
240C22⋊Dic71C2×D414yes—
241(C2×D71)⋊C4—24no—
242(C2×D71)⋊C4—24no—
243(C2×D71)⋊C4—24no—
244(C2×D71)⋊C4—24no—
245C4×Dic71—24no—
246C4×Dic71—24no—
247C4×Dic71C2×D412yes—
248C4×Dic71C2×D412yes—
249C4×Dic71C2412yes—
250C4×Dic71C2412yes—
251C24×C71C2×D411yescharacteristic
252C2×Q8×C71—21no—
253C2×Q8×C71—22no—
254C2×Q8×C71—22no—
255C2×Q8×C71C2412yes—
256C22×C4×C71—22no—
257C22×C4×C71—22no—
258C22×C4×C71—21no—
259C22×C4×C71—21no—
260C22×C4×C71—21no—
261C22×C4×C71—21no—
262C22×C4×C71C2×D411yescharacteristic
263C22×C4×C71C2×D412yes—
264C22×C4×C71C2412yes—
265C22×C4×C71C2411yescharacteristic
266C2×C8×C71—22no—
267C2×C8×C71—22no—
268C2×C8×C71C2412yes—
269C2×C8×C71C2412yes—
270C4⋊C4×C71—24no—
271C4⋊C4×C71—21no—
272C4⋊C4×C71—21no—
273C4⋊C4×C71—21no—
274C4⋊C4×C71C2412yes—
275C4⋊C4×C71C2412yes—
276C4⋊C4×C71C2412yes—
277C22⋊C4×C71—24no—
278C22⋊C4×C71—24no—
279C42×C71—24no—
280C23×C71—22no—
281C23×C71—22no—
282C23×C71—22no—
283C23×C71C22×D412yes—
284C23×C71C22×D411yescharacteristic
285C22×D71—24no—
286C22×D71—24no—
287C22×D71—22no—
288C22×D71—22no—
289C22×D71—216no—
290C22×D71—42no—
291C22×D71—42no—
292C22×D71—42no—
293C22×D71—42no—
294C22×D71—84no—
295C22×D71—84no—
296C22×D71—816no—
297Q8×C71—22no—
298Q8×C71—22no—
299Q8×C71—42no—
300C2×C4×C71—22no—
301C2×C4×C71—24no—
302C2×C4×C71—22no—
303C2×C4×C71—22no—
304C2×C4×C71—22no—
305C2×C4×C71—22no—
306C2×C4×C71—22no—
307C2×C4×C71—22no—
308C2×C4×C71—42no—
309C2×C4×C71—42no—
310C2×C4×C71—42no—
311C2×C4×C71—42no—
312C2×C4×C71C22×D412yes—
313C2×C4×C71C22×D411yescharacteristic
314C2×C4×C71C2×#4112yes—
315C2×C4×C71C2×#4112yes—
316C2×C4×C71C2511yescharacteristic
317C2×Dic71—22no—
318C2×Dic71—22no—
319C2×Dic71—22no—
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—22no—
323C2×Dic71—42no—
324C2×Dic71—42no—
325C2×Dic71C22×D412yes—
326C2×Dic71C22×D412yes—
327C2×Dic71C22×D412yes—
328C2×Dic71C22×D412yes—
329D284—216no—
330D284—24no—
331D284—24no—
332D284—22no—
333D284—22no—
334D284C2×#4114yes—
335D284C2×#4114yes—
336C4×D71—84no—
337C4×D71—84no—
338C4×D71—84no—
339C4×D71—84no—
340Dic142—22no—
341Dic142—22no—
342Dic142—42no—
343C8×C71—22no—
344C8×C71—22no—
345C71⋊C8—22no—
346C71⋊C8—22no—
347C22×C71—22no—
348C22×C71—22no—
349C22×C71—22no—
350C22×C71—44no—
351C22×C71#52512yes—
352C22×C71#57712yes—
353C22×C71#57712yes—
354C22×C71C23×D411yescharacteristic
355C2×D71—24no—
356C2×D71—24no—
357C2×D71—48no—
358C2×D71—48no—
359C2×D71—42no—
360C2×D71—42no—
361C2×D71—42no—
362C2×D71—42no—
363C2×D71—816no—
364C4×C71—22no—
365C4×C71—42no—
366C4×C71—42no—
367C4×C71—42no—
368C4×C71—42no—
369C4×C71#52512yes—
370C4×C71C22×#4111yescharacteristic
371C4×C71C22×#4111yescharacteristic
372Dic71—22no—
373Dic71—22no—
374Dic71—22no—
375Dic71—22no—
376Dic71—42no—
377Dic71—42no—
378C2×#3123—711nomaximal, Sylow
379C2×C71—42no—
380C2×C71#312314yescomplemented
381C2×C71C2×#52511yescharacteristic
382C2×C71C2×#57711yescharacteristic
383C2×C71C2×#57711yescharacteristic
384D71—44no—
385D71—44no—
386C2×#541—711no—
387C2×#518—711no—
388#3123—7116no—
389C2×#485—711no—
390C2×#485D7111yescharacteristic, complemented
391C2×#478—711no—
392C2×#478—711no—
393C2×#461—711no—
394C2×#461—711no—
395C2×#450—711no—
396C2×#450—711no—
397C2×#440—711no—
398C2×#440—711no—
399C2×C4×SD16—711no—
400C2×C4×SD16—711no—
401C2×#433—711no—
402C71C2×#312311yescharacteristic, complemented, Sylow
403C23×D4—711no—
404C22×SD16—711no—
405C22×SD16—711no—
406C22×SD16—711no—
407C22×SD16—711no—
408#541—718no—
409#541—1424no—
410C2×C4⋊Q8—711no—
411C2×#126—1421no—
412C2×#126—1421no—
413C2×#125—711no—
414C2×#125—1421no—
415C2×#125—1421no—
416C2×C22⋊Q8—711no—
417C2×C22⋊Q8C2×D7111yescharacteristic
418#518—718no—
419#518—1424no—
420C2×C4×Q8—711no—
421C2×C4×Q8—711no—
422C2×C4×D4—711no—
423C2×C4×D4—711no—
424C2×C4×D4—711no—
425C2×C4×D4—711no—
426C2×C4×D4—1421no—
427C2×C4×D4—1421no—
428C2×#117—711no—
429C2×#117C2×D7111yescharacteristic
430C22×C22⋊C4—1421no—
431C22×C22⋊C4—1421no—
432#485—718no—
433#485C2×D7118yescomplemented
434#478—718no—
435#478—718no—
436#461—718no—
437#461—718no—
438#450—718no—
439#450—718no—
440#440—718no—
441#440—718no—
442C4×SD16—718no—
443C4×SD16—718no—
444#433—718no—
445C2×#107—711no—
446C2×#107C2×D7111yescharacteristic, complemented
447C2×#106—711no—
448C2×#106C2×D7111yescharacteristic, complemented
449C2×C4⋊C8—711no—
450C2×C4⋊C8—711no—
451C2×#103—711no—
452C2×#103—711no—
453C2×#103C2×D7111yescharacteristic, complemented
454C2×#103C2×D7111yescharacteristic, complemented
455C2×#102—711no—
456C2×#102—711no—
457C2×#102—711no—
458C2×#102—711no—
459C2×C22⋊C8—711no—
460C2×C22⋊C8C2×D7111yescharacteristic
461C2×#97—711no—
462C2×C4×C8—711no—
463C25—1421no—
464C22×Q8—711no—
465C22×Q8C22×D7111yescharacteristic
466C22×D4—711no—
467C22×D4—711no—
468C22×D4—714no—
469C22×D4—1424no—
470C22×D4—1424no—
471C22×D4—1421no—
472C22×D4—1422no—
473C23×C4—1421no—
474C23×C4—1421no—
475C23×C4—1421no—
476C23×C4—1421no—
477C23×C4C22×D7111yescharacteristic
478C2×SD16—714no—
479C2×SD16—714no—
480C2×SD16—714no—
481C2×SD16—714no—
482C2×SD16—1424no—
483C2×SD16—1424no—
484C2×SD16—1424no—
485C2×SD16—1424no—
486C22×C8—711no—
487C22×C8—711no—
488C22×C8C22×D7111yescharacteristic
489C22×C8C22×D7111yescharacteristic
490C4⋊Q8—714no—
491C4⋊Q8—1422no—
492#126—1428no—
493#126—1428no—
494#125—714no—
495#125—1422no—
496#125—1428no—
497#125—1428no—
498C22⋊Q8—22no—
499C22⋊Q8—714no—
500C22⋊Q8—1422no—
501C22⋊Q8C22×D7114yes—
502C4×Q8—714no—
503C4×Q8—714no—
504C4×Q8—1422no—
505C4×Q8—1422no—
506C4×D4—714no—
507C4×D4—714no—
508C4×D4—714no—
509C4×D4—714no—
510C4×D4—1428no—
511C4×D4—1428no—
512C4×D4—1422no—
513C4×D4—1422no—
514C4×D4—1422no—
515C4×D4—1422no—
516#117—22no—
517#117—714no—
518#117—714no—
519#117C22×D7114yes—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—711no—
522C2×C4⋊C4—711no—
523C2×C4⋊C4—711no—
524C2×C4⋊C4—1421no—
525C2×C4⋊C4—1421no—
526C2×C4⋊C4—1421no—
527C2×C4⋊C4—1421no—
528C2×C4⋊C4—1421no—
529C2×C4⋊C4—1421no—
530C2×C4⋊C4—1421no—
531C2×C4⋊C4C22×D7111yescharacteristic
532C2×C4⋊C4C22×D7111yescharacteristic
533C2×C4⋊C4C22×D7111yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—711no—
537C2×C22⋊C4—711no—
538C2×C22⋊C4—1428no—
539C2×C22⋊C4—1428no—
540C2×C22⋊C4—1421no—
541C2×C22⋊C4—1421no—
542C2×C22⋊C4—1421no—
543C2×C22⋊C4—1421no—
544C2×C22⋊C4—1421no—
545C2×C42—21no—
546C2×C42—711no—
547C2×C42—711no—
548C2×C42—1421no—
549C2×C42—1421no—
550#107—714no—
551#107C22×D7114yescomplemented
552#106—714no—
553#106C22×D7114yescomplemented
554C4⋊C8—714no—
555C4⋊C8—714no—
556#103—714no—
557#103—714no—
558#103C22×D7114yescomplemented
559#103C22×D7114yescomplemented
560#102—714no—
561#102—714no—
562#102—714no—
563#102—714no—
564C22⋊C8—714no—
565C22⋊C8C22×D7114yes—
566#97—714no—
567C4×C8—714no—
568C24—5682no—
569C24—5682no—
570C24—1428no—
571C24—1421no—
572C24—1421no—
573C24—1424no—
574C24D4×D7111yescharacteristic
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—712no—
579C2×Q8—1422no—
580C2×Q8—1422no—
581C2×Q8—1421no—
582C2×Q8C23×D7112yes—
583C2×D4—714no—
584C2×D4—714no—
585C2×D4—712no—
586C2×D4—712no—
587C2×D4—1428no—
588C2×D4—1428no—
589C2×D4—1428no—
590C2×D4—14216no—
591C2×D4—1424no—
592C2×D4—1421no—
593C2×D4—1421no—
594C2×D4—1422no—
595C2×D4—1422no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—5682no—
603C22×C4—5682no—
604C22×C4—5682no—
605C22×C4—5682no—
606C22×C4—711no—
607C22×C4—711no—
608C22×C4—711no—
609C22×C4—711no—
610C22×C4—1424no—
611C22×C4—1424no—
612C22×C4—1424no—
613C22×C4—1424no—
614C22×C4—1421no—
615C22×C4—1421no—
616C22×C4D4×D7112yes—
617C22×C4D4×D7111yescharacteristic
618C22×C4C23×D7112yes—
619C22×C4C23×D7111yescharacteristic
620SD16—1428no—
621SD16—1428no—
622SD16—1428no—
623SD16—1428no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—712no—
627C2×C8—712no—
628C2×C8—1422no—
629C2×C8—1422no—
630C2×C8C23×D7112yes—
631C2×C8C23×D7112yes—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—714no—
637C4⋊C4—714no—
638C4⋊C4—712no—
639C4⋊C4—1424no—
640C4⋊C4—1424no—
641C4⋊C4—1424no—
642C4⋊C4—1424no—
643C4⋊C4—1424no—
644C4⋊C4—1424no—
645C4⋊C4—1424no—
646C4⋊C4—1421no—
647C4⋊C4C23×D7112yes—
648C4⋊C4C23×D7112yes—
649C4⋊C4C23×D7112yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—714no—
653C22⋊C4—714no—
654C22⋊C4—1424no—
655C22⋊C4—1424no—
656C22⋊C4—1424no—
657C22⋊C4—1424no—
658C22⋊C4—1424no—
659C42—24no—
660C42—712no—
661C42—712no—
662C42—712no—
663C42—712no—
664C42—1424no—
665C42—1424no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—2842no—
670C23—2842no—
671C23—2842no—
672C23—2842no—
673C23—5684no—
674C23—5684no—
675C23—56816no—
676C23—14216no—
677C23—1422no—
678C23—1422no—
679C23—1424no—
680C23—1424no—
681C23C2×D4×D7112yes—
682C23C2×D4×D7111yescharacteristic
683Q8—22no—
684Q8—22no—
685Q8—42no—
686Q8—2842no—
687Q8—1422no—
688Q8—1422no—
689D4—714no—
690D4—714no—
691D4—14216no—
692D4—1422no—
693D4—1422no—
694D4—1424no—
695D4—1424no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—2842no—
709C2×C4—2842no—
710C2×C4—5684no—
711C2×C4—5684no—
712C2×C4—5684no—
713C2×C4—5684no—
714C2×C4—712no—
715C2×C4—712no—
716C2×C4—712no—
717C2×C4—712no—
718C2×C4—1422no—
719C2×C4—1422no—
720C2×C4—1422no—
721C2×C4—1422no—
722C2×C4—1422no—
723C2×C4—1422no—
724C2×C4C2×D4×D7112yes—
725C2×C4C2×D4×D7111yescharacteristic
726C2×C4#41×D7112yes—
727C2×C4#41×D7112yes—
728C2×C4C24×D7111yescharacteristic
729C8—22no—
730C8—22no—
731C8—1422no—
732C8—1422no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—2842no—
738C22—2842no—
739C22—2842no—
740C22—2842no—
741C22—2848no—
742C22—2848no—
743C22—56816no—
744C22—1424no—
745C22—1424no—
746C22#1798650712yes—
747C22#1798680612yes—
748C22#1798680812yes—
749C22C22×D4×D7111yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—2842no—
756C4—2842no—
757C4—1422no—
758C4—1422no—
759C4—1422no—
760C4—1422no—
761C4#1798650712yes—
762C4C2×#41×D7111yescharacteristic
763C4C2×#41×D7111yescharacteristic
764C2—42no—
765C2—2844no—
766C2—2844no—
767C2#2259858814yesdirect product factor
768C2C2×#1798650711yescharacteristic
769C2C2×#1798680611yescharacteristic
770C2C2×#1798680811yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#485×C71C2
socleC23×C71C22×D4
prime radicalC23×D284C22
hypercenterC2×#485D71
hypocenterC71C2×#3123
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#17986609C2semidirect
3. #22598588C2direct (N × H)
4. C2×#17986340C2semidirect
5. C2×#17986302C2semidirect
6. C2×#17986298C2semidirect
7. C2×#17986203C2semidirect
8. C2×#17986203C2semidirect
11. C2×#17986102C2semidirect
12. C2×#17986098C2semidirect
13. C2×#17986086C2semidirect
14. C2×#17986084C2semidirect
15. C2×#17986057C2semidirect
16. C2×#485×C71C2semidirect
23. #17986609C22semidirect
24. C2×#14556126C22semidirect
28. C2×#14556119C22semidirect
33. C2×Q8×Dic71C22semidirect
34. C2×#14556093C22semidirect
44. #17986340C22semidirect
45. #17986302C22semidirect
46. #17986298C22semidirect
47. #17986203C22semidirect
48. #17986203C22semidirect
51. #17986102C22semidirect
52. #17986098C22semidirect
53. #17986086C22semidirect
54. #17986084C22semidirect
55. #17986057C22semidirect
56. C2×#14556061C22semidirect
57. C2×#14556059C22semidirect
58. C2×Dic71⋊C8C22semidirect
59. C2×Dic71⋊C8C22semidirect
60. C2×#14556051C22semidirect
61. C2×#14556051C22semidirect
67. C2×#14556038C22semidirect
68. C2×C8×Dic71C22semidirect
71. #485×C71C22semidirect
72. C2×#107×C71C22semidirect
73. C2×#106×C71C22semidirect
74. C2×#103×C71C22semidirect
75. C2×#103×C71C22semidirect
101. #14556126C23semidirect
106. #14556119C23semidirect
111. Q8×Dic71C23semidirect
113. #14556093C23semidirect
149. #14556061C23semidirect
150. #14556059C23semidirect
151. Dic71⋊C8C23semidirect
152. Dic71⋊C8C23semidirect
153. #14556051C23semidirect
154. #14556051C23semidirect
160. #14556038C23semidirect
161. C8×Dic71C23semidirect
177. #107×C71C23semidirect
178. #106×C71C23semidirect
179. #103×C71C23semidirect
180. #103×C71C23semidirect
380. C2×C71#3123semidirect
390. C2×#485D71semidirect
402. C71C2×#3123semidirect
433. #485C2×D71semidirect
446. C2×#107C2×D71semidirect
448. C2×#106C2×D71semidirect
453. C2×#103C2×D71semidirect
454. C2×#103C2×D71semidirect
551. #107C22×D71semidirect
553. #106C22×D71semidirect
558. #103C22×D71semidirect
559. #103C22×D71semidirect
767. C2#22598588direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866092
C2×#179864732
#225985882
C2×#179863402
C2×#179863022
C2×#179862982
C2×#179862032
C2×#179861522
C2×#179861492
C2×#179861022
C2×#179860982
C2×#179860862
C2×#179860842
C2×#179860572
C2×#485×C712
C2×#312371