Finite Group Databasebeta

← C2×#22600713 #32875893

Subgroups — C2×#22600713 #32875893

Order 18176.

1930 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986689C211yesmaximal, characteristic, complemented
2#22600713C2116yesmaximal, direct product factor
3C2×#17986398C211yesmaximal, characteristic, complemented
4C2×#17986334C211yesmaximal, characteristic, complemented
5C2×#17986340C211yesmaximal, characteristic, complemented
6C2×#17986320C211yesmaximal, characteristic, complemented
7C2×#17986310C211yesmaximal, characteristic, complemented
8C2×#17986303C211yesmaximal, characteristic, complemented
9C2×#17986299C211yesmaximal, characteristic, complemented
10C2×#17986226C211yesmaximal, characteristic, complemented
11C2×#17986226C211yesmaximal, characteristic, complemented
12C2×C4×#11765853C211yesmaximal, characteristic, complemented
13C2×D4×C71⋊C8C211yesmaximal, characteristic, complemented
14C2×#17986035C211yesmaximal, characteristic, complemented
15C22×#14556059C211yesmaximal, characteristic, complemented
16C2×#553×C71C211yesmaximal, characteristic
17C22×#11765853C2211yescharacteristic
18C23×C71⋊C8C2211yescharacteristic
19C23×C71⋊C8C2211yescharacteristic
20#17986689—24no—
21#17986689C2218yescomplemented
22C2×#14556121—21no—
23C2×#14556120C2211yescharacteristic
24C2×#14556118—21no—
25C2×#14556109—21no—
26C2×#14556107C2211yescharacteristic
27C2×#14556107C2211yescharacteristic
28C2×C4×Dic142C2211yescharacteristic
29C2×#14556087C2211yescharacteristic
30C2×#14556084—21no—
31C22×C4⋊Dic71C2211yescharacteristic
32#17986398C2218yescomplemented
33#17986340C2218yescomplemented
34#17986334C2218yescomplemented
35#17986320C2218yescomplemented
36#17986310C2218yescomplemented
37#17986303C2218yescomplemented
38#17986299C2218yescomplemented
39#17986226C2218yescomplemented
40#17986226C2218yescomplemented
41C4×#11765853C2218yescomplemented
42D4×C71⋊C8C2218yescomplemented
43#17986035C2218yescomplemented
44C2×#14556061C2211yescharacteristic
45C2×#14556061C2211yescharacteristic
46C2×#14556061C2211yescharacteristic
47C2×#14556061C2211yescharacteristic
48C2×#14556059C2211yescharacteristic
49C2×#14556059C2211yescharacteristic
50C2×#14556059C2211yescharacteristic
51C2×#14556059C2211yescharacteristic
52C2×#14556059C2211yescharacteristic
53C2×#14556059C2218yescomplemented
54C2×C4⋊(C71⋊C8)C2211yescharacteristic
55C2×#14556051C2211yescharacteristic
56C2×#14556051C2211yescharacteristic
57C2×#14556051C2211yescharacteristic
58C2×#14556049C2211yescharacteristic
59C2×#14556049C2211yescharacteristic
60C2×#14556049C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×C22⋊(C71⋊C8)C2211yescharacteristic
63C2×C4×C71⋊C8C2211yescharacteristic
64#553×C71—24no—
65#553×C71C2218yes—
66C2×#126×C71—21no—
67C2×#125×C71C2211yescharacteristic
68C2×#123×C71—21no—
69C2×#121×C71—21no—
70C2×#121×C71C2211yescharacteristic
71C2×#121×C71C2211yescharacteristic
72C2×C4×D4×C71—21no—
73C2×C4×D4×C71C2211yescharacteristic
74C2×C4×D4×C71C2211yescharacteristic
75C2×#117×C71C2211yescharacteristic
76C22×C4⋊C4×C71C2211yescharacteristic
77C22×Dic142C2311yescharacteristic
78C23×Dic71—21no—
79C2×#11765853—24no—
80C2×#11765853C2314yes—
81C22×C71⋊C8—24no—
82C22×C71⋊C8—24no—
83C22×C71⋊C8C2314yes—
84C22×C71⋊C8C2314yes—
85C22×C71⋊C8C2311yescharacteristic
86C22×C71⋊C8C2311yescharacteristic
87C22×C71⋊C8C2311yescharacteristic
88C22×C71⋊C8C2311yescharacteristic
89#14556121—28no—
90#14556120—22no—
91#14556120C2314yes—
92#14556118—28no—
93#14556109—28no—
94#14556107—22no—
95#14556107—22no—
96#14556107C2314yes—
97#14556107C2314yes—
98C4×Dic142—22no—
99C4×Dic142C2314yes—
100#14556087—22no—
101#14556087C2314yes—
102#14556084—28no—
103C2×C4⋊Dic71—22no—
104C2×C4⋊Dic71—21no—
105C2×C4⋊Dic71C2314yes—
106C2×C4⋊Dic71C2311yescharacteristic
107C2×C4⋊Dic71C2311yescharacteristic
108C2×C4⋊Dic71C2311yescharacteristic
109C2×Dic71⋊C4—21no—
110C2×Dic71⋊C4—21no—
111C2×Dic71⋊C4—21no—
112C2×Dic71⋊C4—21no—
113C2×Dic71⋊C4—21no—
114C2×C22⋊Dic71—21no—
115C2×C22⋊Dic71—21no—
116C2×C22⋊Dic71—21no—
117C2×C4×Dic71—21no—
118C2×C4×Dic71—21no—
119#14556061C2314yes—
120#14556061C2314yes—
121#14556061C2314yes—
122#14556061C2314yes—
123#14556059C2314yes—
124#14556059C2314yes—
125#14556059C2314yes—
126#14556059C2314yes—
127#14556059C2314yes—
128C4⋊(C71⋊C8)C2314yes—
129#14556051C2314yes—
130#14556051C2314yes—
131#14556051C2314yes—
132#14556049C2314yes—
133#14556049C2314yes—
134#14556049C2314yes—
135C22⋊(C71⋊C8)C2314yes—
136C22⋊(C71⋊C8)C2314yes—
137C4×C71⋊C8C2314yes—
138C22×D4×C71—21no—
139C22×D4×C71—21no—
140C22×D4×C71D411yescharacteristic
141C22×D4×C71C2311yescharacteristic
142C23×C4×C71—21no—
143C23×C4×C71—21no—
144C23×C4×C71C2311yescharacteristic
145C23×C4×C71C2311yescharacteristic
146#126×C71—28no—
147#125×C71—22no—
148#125×C71C2314yes—
149#123×C71—28no—
150#121×C71—28no—
151#121×C71—22no—
152#121×C71—22no—
153#121×C71C2314yes—
154#121×C71C2314yes—
155C4×D4×C71—28no—
156C4×D4×C71—22no—
157C4×D4×C71D414yes—
158C4×D4×C71C2314yes—
159C4×D4×C71C2314yes—
160#117×C71—22no—
161#117×C71C2314yes—
162C2×C4⋊C4×C71—21no—
163C2×C4⋊C4×C71—22no—
164C2×C4⋊C4×C71—21no—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71D411yescharacteristic
167C2×C4⋊C4×C71C2314yes—
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×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71D411yescharacteristic
176C2×C22⋊C4×C71D411yescharacteristic
177C2×C42×C71—21no—
178C2×C42×C71C2311yescharacteristic
179C2×Dic142—22no—
180C2×Dic142—22no—
181C2×Dic142—21no—
182C2×Dic142C2412yes—
183C22×Dic71—21no—
184C22×Dic71—21no—
185C22×Dic71—24no—
186C22×Dic71—21no—
187C22×Dic71—21no—
188C22×Dic71—44no—
189#11765853—28no—
190C2×C71⋊C8—22no—
191C2×C71⋊C8—22no—
192C2×C71⋊C8—22no—
193C2×C71⋊C8—28no—
194C2×C71⋊C8—28no—
195C2×C71⋊C8#4114yes—
196C2×C71⋊C8C2412yes—
197C2×C71⋊C8C2412yes—
198C2×C71⋊C8C2412yes—
199C2×C71⋊C8C2412yes—
200C4⋊Dic71—21no—
201C4⋊Dic71—21no—
202C4⋊Dic71—24no—
203C4⋊Dic71—21no—
204C4⋊Dic71C2412yes—
205C4⋊Dic71C2412yes—
206C4⋊Dic71C2412yes—
207Dic71⋊C4—24no—
208Dic71⋊C4—24no—
209Dic71⋊C4—24no—
210Dic71⋊C4—24no—
211Dic71⋊C4—24no—
212C22⋊Dic71—24no—
213C22⋊Dic71—24no—
214C22⋊Dic71—24no—
215C4×Dic71—24no—
216C4×Dic71—24no—
217C24×C71—21no—
218C24×C71C2×D411yescharacteristic
219C24×C71C2×D411yescharacteristic
220C2×D4×C71—24no—
221C2×D4×C71—24no—
222C2×D4×C71—24no—
223C2×D4×C71—21no—
224C2×D4×C71—22no—
225C2×D4×C71—22no—
226C2×D4×C71—44no—
227C2×D4×C71—82no—
228C2×D4×C71C2×D414yes—
229C2×D4×C71C2412yes—
230C22×C4×C71—22no—
231C22×C4×C71—22no—
232C22×C4×C71—22no—
233C22×C4×C71—22no—
234C22×C4×C71—21no—
235C22×C4×C71—21no—
236C22×C4×C71—21no—
237C22×C4×C71—24no—
238C22×C4×C71—24no—
239C22×C4×C71—82no—
240C22×C4×C71—82no—
241C22×C4×C71C2×D411yescharacteristic
242C22×C4×C71C2×D411yescharacteristic
243C22×C4×C71C2×D411yescharacteristic
244C22×C4×C71C2×D411yescharacteristic
245C22×C4×C71C2×D412yes—
246C22×C4×C71C2×D412yes—
247C22×C4×C71C2412yes—
248C22×C4×C71C2412yes—
249C22×C4×C71C2411yescharacteristic
250C4⋊C4×C71—21no—
251C4⋊C4×C71—21no—
252C4⋊C4×C71—24no—
253C4⋊C4×C71—24no—
254C4⋊C4×C71—24no—
255C4⋊C4×C71—21no—
256C4⋊C4×C71C2×D414yes—
257C4⋊C4×C71C2412yes—
258C4⋊C4×C71C2412yes—
259C4⋊C4×C71C2412yes—
260C22⋊C4×C71—24no—
261C22⋊C4×C71—24no—
262C22⋊C4×C71—24no—
263C22⋊C4×C71—24no—
264C22⋊C4×C71C2×D414yes—
265C22⋊C4×C71C2×D414yes—
266C42×C71—24no—
267C42×C71C2×D412yes—
268C42×C71C2412yes—
269C23×C71—22no—
270C23×C71—22no—
271C23×C71—22no—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71—22no—
275C23×C71—42no—
276C23×C71—42no—
277C23×C71—42no—
278C23×C71#13514yes—
279C23×C71C22×D412yes—
280C23×C71C22×D412yes—
281C23×C71C22×D411yescharacteristic
282D4×C71—28no—
283D4×C71—22no—
284D4×C71—22no—
285D4×C71—48no—
286D4×C71—42no—
287D4×C71—84no—
288C2×C4×C71—22no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—24no—
293C2×C4×C71—24no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—42no—
302C2×C4×C71—42no—
303C2×C4×C71—42no—
304C2×C4×C71—84no—
305C2×C4×C71—84no—
306C2×C4×C71C22×D412yes—
307C2×C4×C71C22×D412yes—
308C2×C4×C71C22×D412yes—
309C2×C4×C71C22×D412yes—
310C2×C4×C71C22×D411yescharacteristic
311C2×C4×C71C2×#4112yes—
312C2×C4×C712−1+412yes—
313C2×C4×C71C2511yescharacteristic
314C2×Dic71—22no—
315C2×Dic71—22no—
316C2×Dic71—22no—
317C2×Dic71—22no—
318C2×Dic71—42no—
319C2×Dic71—48no—
320C2×Dic71—42no—
321C2×Dic71—42no—
322C2×Dic71—42no—
323Dic142—22no—
324Dic142—22no—
325Dic142—42no—
326C71⋊C8—22no—
327C71⋊C8—22no—
328C71⋊C8—22no—
329C71⋊C8C2×#4114yes—
330C22×C71—28no—
331C22×C71—22no—
332C22×C71—22no—
333C22×C71—22no—
334C22×C71—22no—
335C22×C71—22no—
336C22×C71—44no—
337C22×C71—42no—
338C22×C71—42no—
339C22×C71—42no—
340C22×C71—84no—
341C22×C71#54712yes—
342C22×C71C2×#13514yes—
343C22×C71C2×#13512yes—
344C22×C71#57712yes—
345C22×C71C23×D411yescharacteristic
346C4×C71—22no—
347C4×C71—22no—
348C4×C71—22no—
349C4×C71—22no—
350C4×C71—42no—
351C4×C71—42no—
352C4×C71—42no—
353C4×C71#54712yes—
354C4×C71C22×#4111yescharacteristic
355C4×C71C2×2−1+411yescharacteristic
356Dic71—42no—
357Dic71—42no—
358Dic71—42no—
359Dic71—42no—
360C2×#3337—711nomaximal, Sylow
361C2×C71—24no—
362C2×C71—42no—
363C2×C71—82no—
364C2×C71#333714yescomplemented
365C2×C71C2×#54711yescharacteristic
366C2×C71C22×#13511yescharacteristic
367C2×C71C2×#57711yescharacteristic
368C2×#553D7111yescharacteristic
369C2×#552—711no—
370#3337—7116no—
371C2×#499—711no—
372C2×#484—711no—
373C2×#485—711no—
374C2×#482—711no—
375C2×#480—711no—
376C2×#479—711no—
377C2×#478—711no—
378C2×#465—711no—
379C2×#465—711no—
380C2×C4×SD16—711no—
381C2×C8×D4—711no—
382C2×#427—711no—
383C22×#106—711no—
384C71C2×#333711yescharacteristic, complemented, Sylow
385C22×SD16—711no—
386C23×C8—711no—
387C23×C8—711no—
388#553—24no—
389#553C2×D7118yes—
390#552—718no—
391#552—1424no—
392C2×#126—21no—
393C2×#126—1421no—
394C2×#125—711no—
395C2×#125—1421no—
396C2×#125C2×D7111yescharacteristic
397C2×#123—21no—
398C2×#123—1421no—
399C2×C22⋊Q8—711no—
400C2×C22⋊Q8—711no—
401C2×#121—21no—
402C2×#121C2×D7111yescharacteristic
403C2×#121C2×D7111yescharacteristic
404C2×C4×Q8—711no—
405C2×C4×D4—21no—
406C2×C4×D4C2×D7111yescharacteristic
407C2×C4×D4C2×D7111yescharacteristic
408C2×#117—711no—
409C2×#117—1421no—
410C2×#117C2×D7111yescharacteristic
411C22×C4⋊C4—711no—
412C22×C4⋊C4C2×D7111yescharacteristic
413#499—718no—
414#485—718no—
415#484—718no—
416#482—718no—
417#480—718no—
418#479—718no—
419#478—718no—
420#465—718no—
421#465—718no—
422C4×SD16—718no—
423C8×D4—718no—
424#427—718no—
425C2×#107—711no—
426C2×#107—711no—
427C2×#107—711no—
428C2×#107—711no—
429C2×#106—711no—
430C2×#106—711no—
431C2×#106—718no—
432C2×#106—711no—
433C2×#106—711no—
434C2×#106—711no—
435C2×C4⋊C8—711no—
436C2×#103—711no—
437C2×#103—711no—
438C2×#103—711no—
439C2×#102—711no—
440C2×#102—711no—
441C2×#102—711no—
442C2×C22⋊C8—711no—
443C2×C22⋊C8—711no—
444C2×C4×C8—711no—
445C22×Q8—711no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4C22⋊D7111yescharacteristic
449C22×D4C22×D7111yescharacteristic
450C23×C4—21no—
451C23×C4—21no—
452C23×C4—1421no—
453C23×C4C22×D7111yescharacteristic
454C23×C4C22×D7111yescharacteristic
455C2×SD16—714no—
456C2×SD16—1424no—
457C22×C8—711no—
458C22×C8—711no—
459C22×C8—711no—
460C22×C8—714no—
461C22×C8—714no—
462C22×C8—711no—
463C22×C8—1424no—
464C22×C8—1424no—
465#126—28no—
466#126—1428no—
467#125—22no—
468#125—714no—
469#125—1428no—
470#125—1422no—
471#125C22×D7114yes—
472#123—28no—
473#123—1428no—
474C22⋊Q8—714no—
475C22⋊Q8—714no—
476C22⋊Q8—1422no—
477C22⋊Q8—1422no—
478#121—28no—
479#121—22no—
480#121—22no—
481#121C22×D7114yes—
482#121C22×D7114yes—
483C4×Q8—714no—
484C4×Q8—1422no—
485C4×D4—28no—
486C4×D4—22no—
487C4×D4C22⋊D7114yes—
488C4×D4C22×D7114yes—
489C4×D4C22×D7114yes—
490#117—22no—
491#117—714no—
492#117—1422no—
493#117—1428no—
494#117C22×D7114yes—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—711no—
500C2×C4⋊C4—711no—
501C2×C4⋊C4—714no—
502C2×C4⋊C4—711no—
503C2×C4⋊C4—1421no—
504C2×C4⋊C4—1422no—
505C2×C4⋊C4—1421no—
506C2×C4⋊C4—1421no—
507C2×C4⋊C4—1421no—
508C2×C4⋊C4—1421no—
509C2×C4⋊C4—1421no—
510C2×C4⋊C4C22⋊D7111yescharacteristic
511C2×C4⋊C4C22×D7111yescharacteristic
512C2×C4⋊C4C22×D7111yescharacteristic
513C2×C4⋊C4C22×D7114yes—
514C2×C4⋊C4C22×D7111yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—1421no—
520C2×C22⋊C4—1421no—
521C2×C22⋊C4—1421no—
522C2×C22⋊C4C22⋊D7111yescharacteristic
523C2×C22⋊C4C22⋊D7111yescharacteristic
524C2×C42—21no—
525C2×C42—1421no—
526C2×C42—1421no—
527C2×C42C22×D7111yescharacteristic
528#107—714no—
529#107—714no—
530#107—714no—
531#107—714no—
532#106—714no—
533#106—714no—
534#106—714no—
535#106—714no—
536#106—714no—
537C4⋊C8—714no—
538#103—714no—
539#103—714no—
540#103—714no—
541#102—714no—
542#102—714no—
543#102—714no—
544C22⋊C8—714no—
545C22⋊C8—714no—
546C4×C8—714no—
547C24—21no—
548C24C2×C22⋊D7111yescharacteristic
549C24C2×C22⋊D7111yescharacteristic
550C2×Q8—712no—
551C2×Q8—1422no—
552C2×Q8—1422no—
553C2×Q8—1421no—
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—44no—
561C2×D4—82no—
562C2×D4C2×C22⋊D7114yes—
563C2×D4C23×D7112yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—82no—
574C22×C4—82no—
575C22×C4—2844no—
576C22×C4—1424no—
577C22×C4—1421no—
578C22×C4—1421no—
579C22×C4—1421no—
580C22×C4—1421no—
581C22×C4C2×C22⋊D7112yes—
582C22×C4C2×C22⋊D7112yes—
583C22×C4C2×C22⋊D7111yescharacteristic
584C22×C4C2×C22⋊D7111yescharacteristic
585C22×C4C2×C22⋊D7111yescharacteristic
586C22×C4C2×C22⋊D7111yescharacteristic
587C22×C4C23×D7112yes—
588C22×C4C23×D7112yes—
589C22×C4C23×D7111yescharacteristic
590SD16—1428no—
591C2×C8—714no—
592C2×C8—712no—
593C2×C8—712no—
594C2×C8—712no—
595C2×C8—712no—
596C2×C8—1428no—
597C2×C8—1428no—
598C2×C8—1422no—
599C2×C8—1422no—
600C2×C8—1422no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—712no—
608C4⋊C4—712no—
609C4⋊C4—712no—
610C4⋊C4—1424no—
611C4⋊C4—1424no—
612C4⋊C4—1424no—
613C4⋊C4—1424no—
614C4⋊C4—1424no—
615C4⋊C4—1421no—
616C4⋊C4—1421no—
617C4⋊C4—1424no—
618C4⋊C4—1421no—
619C4⋊C4C2×C22⋊D7114yes—
620C4⋊C4C23×D7112yes—
621C4⋊C4C23×D7112yes—
622C4⋊C4C23×D7112yes—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—1424no—
628C22⋊C4—1424no—
629C22⋊C4—1424no—
630C22⋊C4C2×C22⋊D7114yes—
631C22⋊C4C2×C22⋊D7114yes—
632C42—24no—
633C42—1424no—
634C42—1424no—
635C42C2×C22⋊D7112yes—
636C42C23×D7112yes—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23#1455614814yes—
647C23C22×C22⋊D7112yes—
648C23C22×C22⋊D7112yes—
649C23C22×C22⋊D7111yescharacteristic
650Q8—2842no—
651Q8—1422no—
652Q8—1422no—
653D4—28no—
654D4—22no—
655D4—22no—
656D4—48no—
657D4—42no—
658D4—84no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—84no—
676C2×C4—84no—
677C2×C4—2842no—
678C2×C4—2848no—
679C2×C4—2842no—
680C2×C4—2842no—
681C2×C4—2842no—
682C2×C4—1422no—
683C2×C4—1422no—
684C2×C4—1422no—
685C2×C4—1422no—
686C2×C4C22×C22⋊D7112yes—
687C2×C4C22×C22⋊D7112yes—
688C2×C4C22×C22⋊D7112yes—
689C2×C4C22×C22⋊D7112yes—
690C2×C4C22×C22⋊D7111yescharacteristic
691C2×C4#41×D7112yes—
692C2×C4#1455617512yes—
693C2×C4C24×D7111yescharacteristic
694C8—714no—
695C8—1422no—
696C8—1422no—
697C8—1422no—
698C22—28no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—84no—
709C22#1798664812yes—
710C22C2×#1455614814yes—
711C22C2×#1455614812yes—
712C22#1798681012yes—
713C22C23×C22⋊D7111yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—2842no—
722C4—2842no—
723C4—2842no—
724C4—2842no—
725C4#1798664812yes—
726C4C2×#41×D7111yescharacteristic
727C4C2×#1455617511yescharacteristic
728C2—24no—
729C2—42no—
730C2—82no—
731C2#2260071314yesdirect product factor
732C2C2×#1798664811yescharacteristic
733C2C22×#1455614811yescharacteristic
734C2C2×#1798681011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
Fitting, prime radicalC2×#553×C71C2
socleC23×C71C22×D4
hypercenterC2×#553D71
hypocenterC71C2×#3337
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#17986689C2semidirect
2. #22600713C2direct (N × H)
3. C2×#17986398C2semidirect
4. C2×#17986334C2semidirect
5. C2×#17986340C2semidirect
6. C2×#17986320C2semidirect
7. C2×#17986310C2semidirect
8. C2×#17986303C2semidirect
9. C2×#17986299C2semidirect
10. C2×#17986226C2semidirect
11. C2×#17986226C2semidirect
12. C2×C4×#11765853C2semidirect
13. C2×D4×C71⋊C8C2semidirect
14. C2×#17986035C2semidirect
15. C22×#14556059C2semidirect
21. #17986689C22semidirect
32. #17986398C22semidirect
33. #17986340C22semidirect
34. #17986334C22semidirect
35. #17986320C22semidirect
36. #17986310C22semidirect
37. #17986303C22semidirect
38. #17986299C22semidirect
39. #17986226C22semidirect
40. #17986226C22semidirect
41. C4×#11765853C22semidirect
42. D4×C71⋊C8C22semidirect
43. #17986035C22semidirect
53. C2×#14556059C22semidirect
364. C2×C71#3337semidirect
384. C71C2×#3337semidirect
731. C2#22600713direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866892
#226007132
C2×#179863982
C2×#179863342
C2×#179863402
C2×#179863202
C2×#179863102
C2×#179863032
C2×#179862992
C2×#179862262
C2×C4×#117658532
C2×D4×C71⋊C82
C2×#179860352
C22×#145560592
C2×#553×C712
C2×#333771