Finite Group Databasebeta

← C2×#22599805 #32870422

Subgroups — C2×#22599805 #32870422

Order 18176.

1882 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986620C211yesmaximal, characteristic, complemented
2#22599805C2116yesmaximal, direct product factor
3C2×#17986284C211yesmaximal, characteristic, complemented
4C2×#17986281C211yesmaximal, characteristic, complemented
5C2×#17986289C211yesmaximal, characteristic, complemented
6C2×#17986286C211yesmaximal, characteristic, complemented
7C2×#17986255C211yesmaximal, characteristic, complemented
8C2×#17986250C211yesmaximal, characteristic
9C2×#17986230C211yesmaximal, characteristic, complemented
10C2×#17986226C211yesmaximal, characteristic, complemented
11C2×#17986221C211yesmaximal, characteristic, complemented
12C2×#17986218C211yesmaximal, characteristic, complemented
13C2×#17986214C211yesmaximal, characteristic, complemented
14C2×#17986211C211yesmaximal, characteristic, complemented
15C2×#17986026C211yesmaximal, characteristic, complemented
16C2×#542×C71C211yesmaximal, characteristic, complemented
17C22×#11765855C2211yescharacteristic
18C22×#11765853C2211yescharacteristic
19C22×#11765852C2211yescharacteristic
20C22×#11765850C2211yescharacteristic
21C22×#11765849C2211yescharacteristic
22C23×C71⋊C8C2211yescharacteristic
23#17986620—24no—
24#17986620C2218yescomplemented
25C2×#14556128C2211yescharacteristic
26C2×#14556123—21no—
27C2×#14556116C2211yescharacteristic
28C2×#14556114—21no—
29C2×#14556110—21no—
30C2×#14556107C2211yescharacteristic
31C2×#14556106—21no—
32C2×#14556102C2211yescharacteristic
33C2×C4×Dic142C2211yescharacteristic
34C2×C4×D284C2211yescharacteristic
35#17986289C2218yescomplemented
36#17986286C2218yescomplemented
37#17986284C2218yescomplemented
38#17986281C2218yescomplemented
39#17986255C2218yescomplemented
40#17986250C2218yes—
41#17986230C2218yescomplemented
42#17986226C2218yescomplemented
43#17986221C2218yescomplemented
44#17986218C2218yescomplemented
45#17986214C2218yescomplemented
46#17986211C2218yescomplemented
47C2×#14556059C2211yescharacteristic
48C2×#14556059C2211yescharacteristic
49C2×#14556059C2211yescharacteristic
50C2×#14556059C2211yescharacteristic
51#17986026C2218yescomplemented
52C2×C4⋊(C71⋊C8)C2211yescharacteristic
53C2×C4⋊(C71⋊C8)C2211yescharacteristic
54C2×C4⋊(C71⋊C8)C2211yescharacteristic
55C2×C4⋊(C71⋊C8)C2211yescharacteristic
56C2×#14556052C2211yescharacteristic
57C2×#14556052C2211yescharacteristic
58C2×#14556051C2211yescharacteristic
59C2×#14556051C2211yescharacteristic
60C2×#14556049C2211yescharacteristic
61C2×#14556049C2211yescharacteristic
62C2×#14556048C2211yescharacteristic
63C2×#14556048C2211yescharacteristic
64#542×C71—24no—
65#542×C71C2218yescomplemented
66C2×C4⋊Q8×C71C2211yescharacteristic
67C2×#126×C71—21no—
68C2×#124×C71—21no—
69C2×#124×C71C2211yescharacteristic
70C2×#123×C71—21no—
71C2×C22⋊Q8×C71—21no—
72C2×C22⋊Q8×C71C2211yescharacteristic
73C2×#121×C71C2211yescharacteristic
74C2×C4×Q8×C71C2211yescharacteristic
75C2×C4×D4×C71C2211yescharacteristic
76C2×#117×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142C2311yescharacteristic
79C22×D284C2311yescharacteristic
80C22×C22⋊D71—21no—
81C22×C4×D71—21no—
82C2×#11765855—42no—
83C2×#11765855C2314yes—
84C2×#11765853—42no—
85C2×#11765853C2314yes—
86C2×#11765852—42no—
87C2×#11765852C2314yes—
88C2×#11765850—42no—
89C2×#11765850C2314yes—
90C2×#11765849—42no—
91C2×#11765849C2314yes—
92C22×C71⋊C8—42no—
93C22×C71⋊C8C2311yescharacteristic
94C22×C71⋊C8C2311yescharacteristic
95C22×C71⋊C8C2311yescharacteristic
96C22×C71⋊C8C2311yescharacteristic
97C22×C71⋊C8C2314yes—
98#14556128—22no—
99#14556128C2314yes—
100#14556123—28no—
101#14556116—22no—
102#14556116C2314yes—
103#14556114—28no—
104#14556110—28no—
105#14556107—22no—
106#14556107C2314yes—
107#14556106—28no—
108#14556102—22no—
109#14556102C2314yes—
110C4×Dic142—22no—
111C4×Dic142C2314yes—
112C4×D284—22no—
113C4×D284C2314yes—
114C2×C4⋊Dic71—21no—
115C2×C4⋊Dic71C2311yescharacteristic
116C2×C4⋊Dic71C2311yescharacteristic
117C2×Dic71⋊C4—21no—
118C2×Dic71⋊C4—21no—
119C2×C22⋊Dic71—21no—
120C2×(C2×D71)⋊C4—21no—
121C2×(C2×D71)⋊C4—21no—
122C2×(C2×D71)⋊C4—21no—
123C2×(C2×D71)⋊C4—21no—
124C2×C4×Dic71—21no—
125#14556059C2314yes—
126#14556059C2314yes—
127#14556059C2314yes—
128#14556059C2314yes—
129C4⋊(C71⋊C8)C2314yes—
130C4⋊(C71⋊C8)C2314yes—
131C4⋊(C71⋊C8)C2314yes—
132C4⋊(C71⋊C8)C2314yes—
133#14556052C2314yes—
134#14556052C2314yes—
135#14556051C2314yes—
136#14556051C2314yes—
137#14556049C2314yes—
138#14556049C2314yes—
139#14556048C2314yes—
140#14556048C2314yes—
141C22×Q8×C71—21no—
142C22×Q8×C71C2311yescharacteristic
143C22×D4×C71—21no—
144C22×D4×C71C2311yescharacteristic
145C23×C4×C71—21no—
146C23×C4×C71C2311yescharacteristic
147C4⋊Q8×C71—22no—
148C4⋊Q8×C71C2314yes—
149#126×C71—28no—
150#124×C71—28no—
151#124×C71—22no—
152#124×C71C2314yes—
153#123×C71—28no—
154C22⋊Q8×C71—22no—
155C22⋊Q8×C71—28no—
156C22⋊Q8×C71C2314yes—
157#121×C71—22no—
158#121×C71C2314yes—
159C4×Q8×C71—22no—
160C4×Q8×C71C2314yes—
161C4×D4×C71—22no—
162C4×D4×C71C2314yes—
163#117×C71D414yes—
164#117×C71C2314yes—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71—21no—
167C2×C4⋊C4×C71—21no—
168C2×C4⋊C4×C71D411yescharacteristic
169C2×C4⋊C4×C71D411yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C22⋊C4×C71—21no—
173C2×C22⋊C4×C71—21no—
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71—21no—
176C2×C22⋊C4×C71—21no—
177C2×C22⋊C4×C71D411yescharacteristic
178C2×C22⋊C4×C71D411yescharacteristic
179C2×C42×C71—21no—
180C2×C42×C71C2311yescharacteristic
181C2×C42×C71C2311yescharacteristic
182C23×D71—21no—
183C2×Dic142—22no—
184C2×Dic142—22no—
185C2×Dic142—21no—
186C2×Dic142—24no—
187C2×Dic142—82no—
188C2×Dic142C2412yes—
189C2×D284—22no—
190C2×D284—22no—
191C2×D284—21no—
192C2×D284C2412yes—
193C2×C22⋊D71—24no—
194C2×C22⋊D71—82no—
195C22×Dic71—21no—
196C22×Dic71—21no—
197C22×Dic71—21no—
198C2×C4×D71—24no—
199C2×C4×D71—82no—
200#11765855—44no—
201#11765853—44no—
202#11765852—44no—
203#11765850—44no—
204#11765849—44no—
205C2×C71⋊C8—22no—
206C2×C71⋊C8—22no—
207C2×C71⋊C8—22no—
208C2×C71⋊C8—22no—
209C2×C71⋊C8—44no—
210C2×C71⋊C8C2412yes—
211C2×C71⋊C8C2412yes—
212C2×C71⋊C8C2412yes—
213C2×C71⋊C8C2412yes—
214C4⋊Dic71—24no—
215C4⋊Dic71—21no—
216C4⋊Dic71—21no—
217C4⋊Dic71C2412yes—
218C4⋊Dic71C2412yes—
219Dic71⋊C4—24no—
220Dic71⋊C4—24no—
221C22⋊Dic71—24no—
222(C2×D71)⋊C4—24no—
223(C2×D71)⋊C4—24no—
224(C2×D71)⋊C4—24no—
225(C2×D71)⋊C4—24no—
226C4×Dic71—24no—
227C24×C71—21no—
228C24×C71C2×D411yescharacteristic
229C2×Q8×C71—21no—
230C2×Q8×C71—24no—
231C2×Q8×C71—22no—
232C2×Q8×C71—22no—
233C2×Q8×C71—82no—
234C2×Q8×C71C2412yes—
235C2×D4×C71—24no—
236C2×D4×C71—21no—
237C2×D4×C71—22no—
238C2×D4×C71—22no—
239C2×D4×C71—82no—
240C2×D4×C71C2412yes—
241C22×C4×C71—22no—
242C22×C4×C71—22no—
243C22×C4×C71—21no—
244C22×C4×C71—21no—
245C22×C4×C71—21no—
246C22×C4×C71—24no—
247C22×C4×C71—82no—
248C22×C4×C71C2×D411yescharacteristic
249C22×C4×C71C2×D411yescharacteristic
250C22×C4×C71C2×D411yescharacteristic
251C22×C4×C71C2×D411yescharacteristic
252C22×C4×C71C2×D411yescharacteristic
253C22×C4×C71C2×D412yes—
254C22×C4×C71C2412yes—
255C22×C4×C71C2411yescharacteristic
256C4⋊C4×C71—24no—
257C4⋊C4×C71—24no—
258C4⋊C4×C71—24no—
259C4⋊C4×C71—21no—
260C4⋊C4×C71—21no—
261C4⋊C4×C71C2×D414yes—
262C4⋊C4×C71C2×D414yes—
263C4⋊C4×C71C2412yes—
264C4⋊C4×C71C2412yes—
265C22⋊C4×C71—24no—
266C22⋊C4×C71—24no—
267C22⋊C4×C71—24no—
268C22⋊C4×C71—24no—
269C22⋊C4×C71—24no—
270C22⋊C4×C71C2×D414yes—
271C22⋊C4×C71C2×D414yes—
272C42×C71—24no—
273C42×C71C2×D412yes—
274C42×C71C2×D412yes—
275C42×C71C2412yes—
276C42×C71C2412yes—
277C23×C71—22no—
278C23×C71—22no—
279C23×C71—22no—
280C23×C71—22no—
281C23×C71—42no—
282C23×C71—42no—
283C23×C71—42no—
284C23×C71C22×D412yes—
285C23×C71C22×D411yescharacteristic
286C22×D71—22no—
287C22×D71—42no—
288C22×D71—42no—
289C22×D71—42no—
290Q8×C71—22no—
291Q8×C71—22no—
292Q8×C71—42no—
293Q8×C71—84no—
294D4×C71—22no—
295D4×C71—22no—
296D4×C71—42no—
297D4×C71—84no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—22no—
302C2×C4×C71—22no—
303C2×C4×C71—24no—
304C2×C4×C71—22no—
305C2×C4×C71—22no—
306C2×C4×C71—22no—
307C2×C4×C71—22no—
308C2×C4×C71—22no—
309C2×C4×C71—42no—
310C2×C4×C71—42no—
311C2×C4×C71—42no—
312C2×C4×C71—84no—
313C2×C4×C71C22×D412yes—
314C2×C4×C71C22×D412yes—
315C2×C4×C71C22×D412yes—
316C2×C4×C71C22×D412yes—
317C2×C4×C71C22×D412yes—
318C2×C4×C71C22×D411yescharacteristic
319C2×C4×C71H(5,𝔽2)12yes—
320C2×C4×C712−1+412yes—
321C2×C4×C71C2511yescharacteristic
322C22⋊D71—84no—
323C2×Dic71—22no—
324C2×Dic71—22no—
325C2×Dic71—22no—
326C2×Dic71—42no—
327C2×Dic71—42no—
328C2×Dic71—42no—
329D284—22no—
330D284—22no—
331D284—42no—
332C4×D71—84no—
333Dic142—22no—
334Dic142—22no—
335Dic142—42no—
336Dic142—84no—
337C71⋊C8—22no—
338C71⋊C8—22no—
339C71⋊C8—22no—
340C71⋊C8—22no—
341C22×C71—22no—
342C22×C71—22no—
343C22×C71—22no—
344C22×C71—44no—
345C22×C71—42no—
346C22×C71—42no—
347C22×C71—42no—
348C22×C71—84no—
349C22×C71#53712yes—
350C22×C71#57712yes—
351C22×C71#57712yes—
352C22×C71C23×D411yescharacteristic
353C2×D71—42no—
354C2×D71—42no—
355C2×D71—42no—
356C2×D71—84no—
357C4×C71—22no—
358C4×C71—22no—
359C4×C71—22no—
360C4×C71—22no—
361C4×C71—22no—
362C4×C71—42no—
363C4×C71—42no—
364C4×C71—42no—
365C4×C71#53712yes—
366C4×C71C2×H(5,𝔽2)11yescharacteristic
367C4×C71C2×2−1+411yescharacteristic
368Dic71—42no—
369Dic71—42no—
370Dic71—42no—
371C2×#3263—711nomaximal, Sylow
372C2×C71—42no—
373C2×C71—82no—
374C2×C71#326314yescomplemented
375C2×C71C2×#53711yescharacteristic
376C2×C71C2×#57711yescharacteristic
377C2×C71C2×#57711yescharacteristic
378D71—82no—
379C2×#542—711no—
380C2×#542D7111yescharacteristic, complemented
381#3263—7116no—
382C2×#475—711no—
383C2×#475—711no—
384C2×#476—711no—
385C2×#476—711no—
386C2×#470—711no—
387C2×#469—711no—
388C2×#465—711no—
389C2×#465—711no—
390C2×#464—711no—
391C2×#464—711no—
392C2×#463—711no—
393C2×#463—711no—
394C2×#424—711no—
395C71C2×#326311yescharacteristic, complemented, Sylow
396C22×Q16—711no—
397C22×SD16—711no—
398C22×SD16—711no—
399C22×D8—711no—
400C22×M16—711no—
401C23×C8—711no—
402#542—24no—
403#542—718no—
404#542—1424no—
405#542C2×D7118yescomplemented
406C2×C4⋊Q8—711no—
407C2×C4⋊Q8C2×D7111yescharacteristic
408C2×#126—21no—
409C2×#126—1421no—
410C2×#124—21no—
411C2×#124—711no—
412C2×#124—1421no—
413C2×#124C2×D7111yescharacteristic
414C2×#123—21no—
415C2×#123—1421no—
416C2×C22⋊Q8—21no—
417C2×C22⋊Q8—711no—
418C2×C22⋊Q8—1421no—
419C2×C22⋊Q8C2×D7111yescharacteristic
420C2×#121—711no—
421C2×#121C2×D7111yescharacteristic
422C2×C4×Q8—711no—
423C2×C4×Q8C2×D7111yescharacteristic
424C2×C4×D4—711no—
425C2×C4×D4C2×D7111yescharacteristic
426C2×#117C2×D7111yescharacteristic
427#476—718no—
428#476—718no—
429#475—718no—
430#475—718no—
431#470—718no—
432#469—718no—
433#465—718no—
434#465—718no—
435#464—718no—
436#464—718no—
437#463—718no—
438#463—718no—
439C2×#106—711no—
440C2×#106—711no—
441C2×#106—711no—
442C2×#106—711no—
443#424—718no—
444C2×C4⋊C8—711no—
445C2×C4⋊C8—711no—
446C2×C4⋊C8—711no—
447C2×C4⋊C8—711no—
448C2×#103—711no—
449C2×#103—711no—
450C2×#103—711no—
451C2×#103—711no—
452C2×#102—711no—
453C2×#102—711no—
454C2×#102—711no—
455C2×#102—711no—
456C22×Q8—21no—
457C22×Q8—711no—
458C22×Q8—1421no—
459C22×Q8C22×D7111yescharacteristic
460C22×D4—21no—
461C22×D4—711no—
462C22×D4—1421no—
463C22×D4C22×D7111yescharacteristic
464C23×C4—21no—
465C23×C4—1421no—
466C23×C4C22×D7111yescharacteristic
467C2×Q16—2842no—
468C2×Q16—714no—
469C2×SD16—2842no—
470C2×SD16—2842no—
471C2×SD16—714no—
472C2×SD16—714no—
473C2×D8—2842no—
474C2×D8—714no—
475C2×M16—2842no—
476C2×M16—714no—
477C22×C8—2842no—
478C22×C8—714no—
479C22×C8—711no—
480C22×C8—711no—
481C22×C8—711no—
482C22×C8—711no—
483C4⋊Q8—22no—
484C4⋊Q8—714no—
485C4⋊Q8—1422no—
486C4⋊Q8C22×D7114yes—
487#126—28no—
488#126—1428no—
489#124—28no—
490#124—22no—
491#124—714no—
492#124—1428no—
493#124—1422no—
494#124C22×D7114yes—
495#123—28no—
496#123—1428no—
497C22⋊Q8—22no—
498C22⋊Q8—28no—
499C22⋊Q8—714no—
500C22⋊Q8—1422no—
501C22⋊Q8—1428no—
502C22⋊Q8C22×D7114yes—
503#121—22no—
504#121—714no—
505#121—1422no—
506#121C22×D7114yes—
507C4×Q8—22no—
508C4×Q8—714no—
509C4×Q8—1422no—
510C4×Q8C22×D7114yes—
511C4×D4—22no—
512C4×D4—714no—
513C4×D4—1422no—
514C4×D4C22×D7114yes—
515#117C22⋊D7114yes—
516#117C22×D7114yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—711no—
521C2×C4⋊C4—711no—
522C2×C4⋊C4—1421no—
523C2×C4⋊C4—1421no—
524C2×C4⋊C4—1421no—
525C2×C4⋊C4C22⋊D7111yescharacteristic
526C2×C4⋊C4C22⋊D7111yescharacteristic
527C2×C4⋊C4C22×D7111yescharacteristic
528C2×C4⋊C4C22×D7111yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—1421no—
535C2×C22⋊C4—1421no—
536C2×C22⋊C4—1421no—
537C2×C22⋊C4—1421no—
538C2×C22⋊C4—1421no—
539C2×C22⋊C4C22⋊D7111yescharacteristic
540C2×C22⋊C4C22⋊D7111yescharacteristic
541C2×C42—21no—
542C2×C42—1421no—
543C2×C42C22×D7111yescharacteristic
544C2×C42C22×D7111yescharacteristic
545#106—714no—
546#106—714no—
547#106—714no—
548#106—714no—
549C4⋊C8—714no—
550C4⋊C8—714no—
551C4⋊C8—714no—
552C4⋊C8—714no—
553#103—714no—
554#103—714no—
555#103—714no—
556#103—714no—
557#102—714no—
558#102—714no—
559#102—714no—
560#102—714no—
561C24—21no—
562C24—1421no—
563C24C2×C22⋊D7111yescharacteristic
564C2×Q8—21no—
565C2×Q8—24no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—82no—
569C2×Q8—5682no—
570C2×Q8—712no—
571C2×Q8—1422no—
572C2×Q8—1422no—
573C2×Q8—1421no—
574C2×Q8—1424no—
575C2×Q8C23×D7112yes—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—82no—
581C2×D4—5682no—
582C2×D4—712no—
583C2×D4—1424no—
584C2×D4—1421no—
585C2×D4—1422no—
586C2×D4—1422no—
587C2×D4C23×D7112yes—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—24no—
594C22×C4—82no—
595C22×C4—5682no—
596C22×C4—1421no—
597C22×C4—1421no—
598C22×C4—1421no—
599C22×C4—1424no—
600C22×C4C2×C22⋊D7112yes—
601C22×C4C2×C22⋊D7111yescharacteristic
602C22×C4C2×C22⋊D7111yescharacteristic
603C22×C4C2×C22⋊D7111yescharacteristic
604C22×C4C2×C22⋊D7111yescharacteristic
605C22×C4C2×C22⋊D7111yescharacteristic
606C22×C4C23×D7112yes—
607C22×C4C23×D7111yescharacteristic
608Q16—2844no—
609SD16—2844no—
610SD16—2844no—
611D8—2844no—
612M16—2844no—
613C2×C8—2844no—
614C2×C8—712no—
615C2×C8—712no—
616C2×C8—712no—
617C2×C8—712no—
618C2×C8—1422no—
619C2×C8—1422no—
620C2×C8—1422no—
621C2×C8—1422no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—712no—
628C4⋊C4—712no—
629C4⋊C4—1424no—
630C4⋊C4—1424no—
631C4⋊C4—1421no—
632C4⋊C4—1421no—
633C4⋊C4—1424no—
634C4⋊C4C2×C22⋊D7114yes—
635C4⋊C4C2×C22⋊D7114yes—
636C4⋊C4C23×D7112yes—
637C4⋊C4C23×D7112yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—1424no—
644C22⋊C4—1424no—
645C22⋊C4—1424no—
646C22⋊C4—1424no—
647C22⋊C4—1424no—
648C22⋊C4C2×C22⋊D7114yes—
649C22⋊C4C2×C22⋊D7114yes—
650C42—24no—
651C42—1424no—
652C42C2×C22⋊D7112yes—
653C42C2×C22⋊D7112yes—
654C42C23×D7112yes—
655C42C23×D7112yes—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—2842no—
664C23—2842no—
665C23—2842no—
666C23—1422no—
667C23C22×C22⋊D7112yes—
668C23C22×C22⋊D7111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—84no—
673Q8—2842no—
674Q8—5684no—
675Q8—1422no—
676Q8—1422no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—84no—
681D4—2842no—
682D4—5684no—
683D4—1422no—
684D4—1422no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—84no—
700C2×C4—2842no—
701C2×C4—2842no—
702C2×C4—2842no—
703C2×C4—5684no—
704C2×C4—1422no—
705C2×C4—1422no—
706C2×C4—1422no—
707C2×C4C22×C22⋊D7112yes—
708C2×C4C22×C22⋊D7112yes—
709C2×C4C22×C22⋊D7112yes—
710C2×C4C22×C22⋊D7112yes—
711C2×C4C22×C22⋊D7112yes—
712C2×C4C22×C22⋊D7111yescharacteristic
713C2×C4#1455617412yes—
714C2×C4#1455617512yes—
715C2×C4C24×D7111yescharacteristic
716C8—1422no—
717C8—1422no—
718C8—1422no—
719C8—1422no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—2842no—
729C22—2842no—
730C22—2842no—
731C22—5684no—
732C22#1798657712yes—
733C22#1798680712yes—
734C22#1798681012yes—
735C22C23×C22⋊D7111yescharacteristic
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—22no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—2842no—
745C4—2842no—
746C4—2842no—
747C4#1798657712yes—
748C4C2×#1455617411yescharacteristic
749C4C2×#1455617511yescharacteristic
750C2—42no—
751C2—82no—
752C2—5682no—
753C2#2259980514yesdirect product factor
754C2C2×#1798657711yescharacteristic
755C2C2×#1798680711yescharacteristic
756C2C2×#1798681011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#542×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986250C2
hypercenterC2×#542D71
hypocenterC71C2×#3263
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#17986620C2semidirect
2. #22599805C2direct (N × H)
3. C2×#17986284C2semidirect
4. C2×#17986281C2semidirect
5. C2×#17986289C2semidirect
6. C2×#17986286C2semidirect
7. C2×#17986255C2semidirect
9. C2×#17986230C2semidirect
10. C2×#17986226C2semidirect
11. C2×#17986221C2semidirect
12. C2×#17986218C2semidirect
13. C2×#17986214C2semidirect
14. C2×#17986211C2semidirect
15. C2×#17986026C2semidirect
16. C2×#542×C71C2semidirect
24. #17986620C22semidirect
35. #17986289C22semidirect
36. #17986286C22semidirect
37. #17986284C22semidirect
38. #17986281C22semidirect
39. #17986255C22semidirect
41. #17986230C22semidirect
42. #17986226C22semidirect
43. #17986221C22semidirect
44. #17986218C22semidirect
45. #17986214C22semidirect
46. #17986211C22semidirect
51. #17986026C22semidirect
65. #542×C71C22semidirect
374. C2×C71#3263semidirect
380. C2×#542D71semidirect
395. C71C2×#3263semidirect
405. #542C2×D71semidirect
753. C2#22599805direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866202
#225998052
C2×#179862842
C2×#179862812
C2×#179862892
C2×#179862862
C2×#179862552
C2×#179862502
C2×#179862302
C2×#179862262
C2×#179862212
C2×#179862182
C2×#179862142
C2×#179862112
C2×#179860262
C2×#542×C712
C2×#326371