Finite Group Databasebeta

← C2×#22600513 #32874076

Subgroups — C2×#22600513 #32874076

Order 18176.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986695C211yesmaximal, characteristic
2C2×D4×Dic142C211yesmaximal, characteristic, complemented
3#22600513C2116yesmaximal, direct product factor
4C2×#17986368C211yesmaximal, characteristic, complemented
5C2×#17986335C211yesmaximal, characteristic, complemented
6C2×#17986341C211yesmaximal, characteristic, complemented
7C2×#17986307C211yesmaximal, characteristic, complemented
8C2×#17986245C211yesmaximal, characteristic, complemented
9C2×#17986228C211yesmaximal, characteristic, complemented
10C2×#17986205C211yesmaximal, characteristic, complemented
11C2×#17986140C211yesmaximal, characteristic, complemented
12C2×#17986140C211yesmaximal, characteristic, complemented
13C2×#17986101C211yesmaximal, characteristic, complemented
14C2×#17986009C211yesmaximal, characteristic, complemented
15C22×#14556053C211yesmaximal, characteristic, complemented
16C2×#435×C71C211yesmaximal, characteristic, complemented
17C23×Dic142C2211yescharacteristic
18C23×Dic142C2211yescharacteristic
19C22×#11765854C2211yescharacteristic
20C22×#11765854C2211yescharacteristic
21C22×#11765854C2211yescharacteristic
22#17986695—24no—
23#17986695C2218yes—
24D4×Dic142—24no—
25D4×Dic142C2218yescomplemented
26C2×#14556128C2211yescharacteristic
27C2×#14556127—21no—
28C2×#14556123—21no—
29C2×#14556120C2211yescharacteristic
30C2×#14556110—21no—
31C2×#14556107C2211yescharacteristic
32C2×#14556107C2211yescharacteristic
33C2×#14556105—21no—
34C2×#14556105—21no—
35C2×#14556102C2211yescharacteristic
36C2×#14556102C2211yescharacteristic
37C2×#14556100—21no—
38C2×C4×Dic142C2211yescharacteristic
39C2×C4×D284C2211yescharacteristic
40C2×D4×Dic71—21no—
41C2×(C22⋊D71)⋊C4—21no—
42C2×#14556087C2211yescharacteristic
43C22×C4⋊Dic71C2211yescharacteristic
44#17986368C2218yescomplemented
45#17986341C2218yescomplemented
46#17986335C2218yescomplemented
47#17986307C2218yescomplemented
48#17986245C2218yescomplemented
49#17986228C2218yescomplemented
50#17986205C2218yescomplemented
51#17986140C2218yescomplemented
52#17986140C2218yescomplemented
53#17986101C2218yescomplemented
54C2×#14556062C2211yescharacteristic
55C2×#14556062C2211yescharacteristic
56C2×#14556060C2211yescharacteristic
57#17986009C2218yescomplemented
58C2×#14556053C2211yescharacteristic
59C2×#14556053C2211yescharacteristic
60C2×#14556053C2211yescharacteristic
61C2×#14556053C2211yescharacteristic
62C2×#14556053C2211yescharacteristic
63C2×#14556053C2211yescharacteristic
64C2×#14556053C2211yescharacteristic
65C2×#14556053C2211yescharacteristic
66C2×#14556053C2211yescharacteristic
67C2×#14556053C2218yescomplemented
68C2×#14556050C2211yescharacteristic
69C22×M16×C71C2211yescharacteristic
70C23×C8×C71C2211yescharacteristic
71C2×C4×D4×C71C2211yescharacteristic
72#435×C71C2218yescomplemented
73C2×C4⋊C8×C71C2211yescharacteristic
74C2×C22⋊C8×C71C2211yescharacteristic
75C2×C22⋊C8×C71C2211yescharacteristic
76C2×#97×C71C2211yescharacteristic
77C22×Dic142—24no—
78C22×Dic142—24no—
79C22×Dic142—22no—
80C22×Dic142—22no—
81C22×Dic142—21no—
82C22×Dic142—21no—
83C22×Dic142—42no—
84C22×Dic142—42no—
85C22×Dic142C2311yescharacteristic
86C22×Dic142C2311yescharacteristic
87C22×Dic142C2314yes—
88C22×Dic142C2314yes—
89C22×Dic142C2311yescharacteristic
90C22×D284C2311yescharacteristic
91C22×C22⋊D71—21no—
92C22×C22⋊D71—21no—
93C23×Dic71—21no—
94C23×Dic71—21no—
95C23×Dic71—21no—
96C22×C4×D71—21no—
97C2×#11765854—24no—
98C2×#11765854—42no—
99C2×#11765854—42no—
100C2×#11765854C2314yes—
101C2×#11765854C2314yes—
102C2×#11765854C2314yes—
103#14556128—22no—
104#14556128C2314yes—
105#14556127—28no—
106#14556123—28no—
107#14556120—22no—
108#14556120C2314yes—
109#14556110—28no—
110#14556107—22no—
111#14556107—22no—
112#14556107C2314yes—
113#14556107C2314yes—
114#14556105—28no—
115#14556105—28no—
116#14556102—22no—
117#14556102—22no—
118#14556102C2314yes—
119#14556102C2314yes—
120#14556100—28no—
121C4×Dic142—22no—
122C4×Dic142C2314yes—
123C4×D284—22no—
124C4×D284C2314yes—
125D4×Dic71—28no—
126(C22⋊D71)⋊C4—28no—
127#14556087—22no—
128#14556087C2314yes—
129C2×C4⋊Dic71—22no—
130C2×C4⋊Dic71—21no—
131C2×C4⋊Dic71—21no—
132C2×C4⋊Dic71—21no—
133C2×C4⋊Dic71C2314yes—
134C2×C4⋊Dic71C2311yescharacteristic
135C2×C4⋊Dic71C2311yescharacteristic
136C2×C4⋊Dic71C2311yescharacteristic
137C2×C4⋊Dic71C2311yescharacteristic
138C2×Dic71⋊C4—21no—
139C2×Dic71⋊C4—21no—
140C2×Dic71⋊C4—21no—
141C2×Dic71⋊C4—21no—
142C2×Dic71⋊C4—21no—
143C2×C22⋊Dic71—21no—
144C2×C22⋊Dic71—21no—
145C2×C22⋊Dic71—21no—
146C2×(C2×D71)⋊C4—21no—
147C2×(C2×D71)⋊C4—21no—
148C2×(C2×D71)⋊C4—21no—
149C2×C4×Dic71—21no—
150C2×C4×Dic71—21no—
151#14556062C2314yes—
152#14556062C2314yes—
153#14556060C2314yes—
154#14556053C2314yes—
155#14556053C2314yes—
156#14556053C2314yes—
157#14556053C2314yes—
158#14556053C2314yes—
159#14556053C2314yes—
160#14556053C2314yes—
161#14556053C2314yes—
162#14556053C2314yes—
163#14556050C2314yes—
164C22×D4×C71D411yescharacteristic
165C23×C4×C71C2311yescharacteristic
166C23×C4×C71C2311yescharacteristic
167C2×M16×C71—42no—
168C2×M16×C71C2314yes—
169C22×C8×C71—42no—
170C22×C8×C71C2311yescharacteristic
171C22×C8×C71C2311yescharacteristic
172C22×C8×C71C2311yescharacteristic
173C22×C8×C71C2311yescharacteristic
174C22×C8×C71C2314yes—
175C4×D4×C71D414yes—
176C4×D4×C71C2314yes—
177C2×C4⋊C4×C71D411yescharacteristic
178C2×C22⋊C4×C71D411yescharacteristic
179C2×C22⋊C4×C71D411yescharacteristic
180C2×C42×C71C2311yescharacteristic
181C4⋊C8×C71C2314yes—
182C22⋊C8×C71C2314yes—
183C22⋊C8×C71C2314yes—
184#97×C71C2314yes—
185C23×D71—21no—
186C2×Dic142—21no—
187C2×Dic142—22no—
188C2×Dic142—22no—
189C2×Dic142—22no—
190C2×Dic142—22no—
191C2×Dic142—22no—
192C2×Dic142—28no—
193C2×Dic142—28no—
194C2×Dic142—24no—
195C2×Dic142—24no—
196C2×Dic142—21no—
197C2×Dic142—21no—
198C2×Dic142—44no—
199C2×Dic142—44no—
200C2×Dic142—48no—
201C2×Dic142—48no—
202C2×Dic142—44no—
203C2×Dic142—44no—
204C2×Dic142#4114yes—
205C2×Dic142C2412yes—
206C2×Dic142C2412yes—
207C2×Dic142C2412yes—
208C2×D284—22no—
209C2×D284—22no—
210C2×D284—21no—
211C2×D284C2412yes—
212C2×C22⋊D71—24no—
213C2×C22⋊D71—24no—
214C2×C22⋊D71—44no—
215C2×C22⋊D71—82no—
216C22×Dic71—21no—
217C22×Dic71—21no—
218C22×Dic71—21no—
219C22×Dic71—21no—
220C22×Dic71—21no—
221C22×Dic71—24no—
222C22×Dic71—24no—
223C22×Dic71—21no—
224C22×Dic71—21no—
225C22×Dic71—24no—
226C22×Dic71—44no—
227C22×Dic71—44no—
228C22×Dic71—82no—
229C2×C4×D71—24no—
230C2×C4×D71—82no—
231#11765854—28no—
232#11765854—44no—
233#11765854—44no—
234C4⋊Dic71—21no—
235C4⋊Dic71—21no—
236C4⋊Dic71—24no—
237C4⋊Dic71—24no—
238C4⋊Dic71—24no—
239C4⋊Dic71—21no—
240C4⋊Dic71—21no—
241C4⋊Dic71C2412yes—
242C4⋊Dic71C2412yes—
243C4⋊Dic71C2412yes—
244C4⋊Dic71C2412yes—
245Dic71⋊C4—24no—
246Dic71⋊C4—24no—
247Dic71⋊C4—24no—
248Dic71⋊C4—24no—
249Dic71⋊C4—24no—
250C22⋊Dic71—24no—
251C22⋊Dic71—24no—
252C22⋊Dic71—24no—
253(C2×D71)⋊C4—24no—
254(C2×D71)⋊C4—24no—
255(C2×D71)⋊C4—24no—
256C4×Dic71—24no—
257C4×Dic71—24no—
258C24×C71C2×D411yescharacteristic
259C24×C71C2×D411yescharacteristic
260C2×D4×C71—24no—
261C2×D4×C71C2×D414yes—
262C22×C4×C71—22no—
263C22×C4×C71—22no—
264C22×C4×C71—22no—
265C22×C4×C71—22no—
266C22×C4×C71C2×D411yescharacteristic
267C22×C4×C71C2×D411yescharacteristic
268C22×C4×C71C2×D411yescharacteristic
269C22×C4×C71C2×D412yes—
270C22×C4×C71C2×D412yes—
271C22×C4×C71C2×D411yescharacteristic
272C22×C4×C71C2412yes—
273C22×C4×C71C2412yes—
274C22×C4×C71C2411yescharacteristic
275M16×C71—44no—
276C2×C8×C71—22no—
277C2×C8×C71—22no—
278C2×C8×C71—22no—
279C2×C8×C71—22no—
280C2×C8×C71—44no—
281C2×C8×C71C2412yes—
282C2×C8×C71C2412yes—
283C2×C8×C71C2412yes—
284C2×C8×C71C2412yes—
285C4⋊C4×C71C2×D414yes—
286C22⋊C4×C71C2×D414yes—
287C22⋊C4×C71C2×D414yes—
288C42×C71C2×D412yes—
289C42×C71C2412yes—
290C23×C71—22no—
291C23×C71—22no—
292C23×C71—22no—
293C23×C71—22no—
294C23×C71—22no—
295C23×C71#13714yes—
296C23×C71C22×D412yes—
297C23×C71C22×D412yes—
298C23×C71C22×D411yescharacteristic
299C22×D71—22no—
300C22×D71—42no—
301C22×D71—42no—
302C22×D71—42no—
303D4×C71—28no—
304C2×C4×C71—22no—
305C2×C4×C71—22no—
306C2×C4×C71—22no—
307C2×C4×C71—22no—
308C2×C4×C71—24no—
309C2×C4×C71—24no—
310C2×C4×C71—22no—
311C2×C4×C71—22no—
312C2×C4×C71—22no—
313C2×C4×C71—22no—
314C2×C4×C71C22×D412yes—
315C2×C4×C71C22×D412yes—
316C2×C4×C71C22×D412yes—
317C2×C4×C71C22×D412yes—
318C2×C4×C71C22×D411yescharacteristic
319C2×C4×C71C2×#4112yes—
320C2×C4×C71H(5,𝔽2)12yes—
321C2×C4×C71C2511yescharacteristic
322C22⋊D71—48no—
323C22⋊D71—84no—
324C2×Dic71—24no—
325C2×Dic71—22no—
326C2×Dic71—22no—
327C2×Dic71—22no—
328C2×Dic71—22no—
329C2×Dic71—22no—
330C2×Dic71—22no—
331C2×Dic71—22no—
332C2×Dic71—48no—
333C2×Dic71—48no—
334C2×Dic71—42no—
335C2×Dic71—42no—
336C2×Dic71—42no—
337C2×Dic71—42no—
338C2×Dic71—42no—
339C2×Dic71—42no—
340C2×Dic71—84no—
341D284—22no—
342D284—22no—
343D284—42no—
344C4×D71—84no—
345Dic142—24no—
346Dic142—22no—
347Dic142—22no—
348Dic142—22no—
349Dic142—22no—
350Dic142—22no—
351Dic142—48no—
352Dic142—48no—
353Dic142—42no—
354Dic142—42no—
355Dic142C2×#4114yes—
356C8×C71—22no—
357C8×C71—22no—
358C8×C71—22no—
359C8×C71—22no—
360C22×C71—22no—
361C22×C71—28no—
362C22×C71—22no—
363C22×C71—22no—
364C22×C71—22no—
365C22×C71—22no—
366C22×C71—44no—
367C22×C71#54612yes—
368C22×C71C2×#13714yes—
369C22×C71C2×#13712yes—
370C22×C71#57712yes—
371C22×C71C23×D411yescharacteristic
372C2×D71—42no—
373C2×D71—42no—
374C2×D71—42no—
375C2×D71—84no—
376C4×C71—22no—
377C4×C71—22no—
378C4×C71—22no—
379C4×C71—22no—
380C4×C71#54612yes—
381C4×C71C22×#4111yescharacteristic
382C4×C71C2×H(5,𝔽2)11yescharacteristic
383Dic71—24no—
384Dic71—42no—
385Dic71—42no—
386Dic71—42no—
387Dic71—42no—
388Dic71—42no—
389Dic71—42no—
390C2×#3320—711nomaximal, Sylow
391C2×C71—24no—
392C2×C71—42no—
393C2×C71#332014yescomplemented
394C2×C71C2×#54611yescharacteristic
395C2×C71C22×#13711yescharacteristic
396C2×C71C2×#57711yescharacteristic
397D71—82no—
398C2×#553—711no—
399C2×D4×Q8—711no—
400#3320—7116no—
401C2×#491—711no—
402C2×#484—711no—
403C2×#485—711no—
404C2×#479—711no—
405C2×#468—711no—
406C2×#465—711no—
407C2×#461—711no—
408C2×#448—711no—
409C2×#448—711no—
410C2×#440—711no—
411C2×#435D7111yescharacteristic, complemented
412C2×#419—711no—
413C22×#103—711no—
414C71C2×#332011yescharacteristic, complemented, Sylow
415C23×Q8—711no—
416C23×Q8—711no—
417C22×SD16—711no—
418C22×SD16—711no—
419C22×SD16—711no—
420C22×M16C2×D7111yescharacteristic
421C23×C8C2×D7111yescharacteristic
422#553—718no—
423#553—1424no—
424D4×Q8—718no—
425D4×Q8—1424no—
426C2×C4⋊Q8—711no—
427C2×C4⋊Q8—1421no—
428C2×#126—1421no—
429C2×#125—711no—
430C2×#123—1421no—
431C2×C22⋊Q8—711no—
432C2×C22⋊Q8—711no—
433C2×C22⋊Q8—1421no—
434C2×C22⋊Q8—1421no—
435C2×#121—711no—
436C2×#121—711no—
437C2×#121—1421no—
438C2×C4×Q8—711no—
439C2×C4×D4—711no—
440C2×C4×D4—1421no—
441C2×C4×D4—1421no—
442C2×C4×D4C2×D7111yescharacteristic
443C2×#117—711no—
444C22×C4⋊C4—711no—
445#491—718no—
446#485—718no—
447#484—718no—
448#479—718no—
449#468—718no—
450#465—718no—
451#461—718no—
452#448—718no—
453#448—718no—
454#440—718no—
455#435C2×D7118yescomplemented
456C2×#107—711no—
457C2×#107—711no—
458C2×#106—711no—
459C2×C4⋊C8C2×D7111yescharacteristic
460#419—718no—
461C2×#103—711no—
462C2×#103—711no—
463C2×#103—711no—
464C2×#103—711no—
465C2×#103—711no—
466C2×#103—711no—
467C2×#103—711no—
468C2×#103—711no—
469C2×#103—711no—
470C2×#103—718no—
471C2×#102—711no—
472C2×C22⋊C8C2×D7111yescharacteristic
473C2×C22⋊C8C2×D7111yescharacteristic
474C2×#97C2×D7111yescharacteristic
475C22×Q8—2842no—
476C22×Q8—2842no—
477C22×Q8—714no—
478C22×Q8—714no—
479C22×Q8—711no—
480C22×Q8—711no—
481C22×Q8—711no—
482C22×Q8—1424no—
483C22×Q8—1424no—
484C22×Q8—1421no—
485C22×Q8—1421no—
486C22×Q8—1422no—
487C22×Q8—1422no—
488C22×D4—711no—
489C22×D4—1421no—
490C22×D4—1421no—
491C22×D4D28411yescharacteristic
492C23×C4—1421no—
493C23×C4—1421no—
494C23×C4—1421no—
495C23×C4—1421no—
496C23×C4C22×D7111yescharacteristic
497C23×C4C22×D7111yescharacteristic
498C2×SD16—2842no—
499C2×SD16—2842no—
500C2×SD16—714no—
501C2×SD16—714no—
502C2×SD16—714no—
503C2×SD16—1424no—
504C2×M16—42no—
505C2×M16C22×D7114yes—
506C22×C8—42no—
507C22×C8C22×D7111yescharacteristic
508C22×C8C22×D7111yescharacteristic
509C22×C8C22×D7111yescharacteristic
510C22×C8C22×D7111yescharacteristic
511C22×C8C22×D7114yes—
512C4⋊Q8—714no—
513C4⋊Q8—1428no—
514C4⋊Q8—1422no—
515#126—1428no—
516#125—714no—
517#125—1422no—
518#123—1428no—
519C22⋊Q8—714no—
520C22⋊Q8—714no—
521C22⋊Q8—1422no—
522C22⋊Q8—1422no—
523C22⋊Q8—1428no—
524C22⋊Q8—1428no—
525#121—714no—
526#121—714no—
527#121—1428no—
528#121—1422no—
529#121—1422no—
530C4×Q8—714no—
531C4×Q8—1422no—
532C4×D4—714no—
533C4×D4—1428no—
534C4×D4—1428no—
535C4×D4—1422no—
536C4×D4D28414yes—
537C4×D4C22×D7114yes—
538#117—714no—
539#117—1422no—
540C2×C4⋊C4—711no—
541C2×C4⋊C4—711no—
542C2×C4⋊C4—714no—
543C2×C4⋊C4—711no—
544C2×C4⋊C4—711no—
545C2×C4⋊C4—1421no—
546C2×C4⋊C4—1422no—
547C2×C4⋊C4—1421no—
548C2×C4⋊C4—1421no—
549C2×C4⋊C4—1421no—
550C2×C4⋊C4—1421no—
551C2×C4⋊C4—1421no—
552C2×C4⋊C4—1421no—
553C2×C4⋊C4—1421no—
554C2×C4⋊C4D28411yescharacteristic
555C2×C22⋊C4—1421no—
556C2×C22⋊C4—1421no—
557C2×C22⋊C4—1421no—
558C2×C22⋊C4—1421no—
559C2×C22⋊C4—1421no—
560C2×C22⋊C4—1421no—
561C2×C22⋊C4D28411yescharacteristic
562C2×C22⋊C4D28411yescharacteristic
563C2×C42—1421no—
564C2×C42—1421no—
565C2×C42C22×D7111yescharacteristic
566#107—714no—
567#107—714no—
568#106—714no—
569C4⋊C8C22×D7114yes—
570#103—714no—
571#103—714no—
572#103—714no—
573#103—714no—
574#103—714no—
575#103—714no—
576#103—714no—
577#103—714no—
578#103—714no—
579#102—714no—
580C22⋊C8C22×D7114yes—
581C22⋊C8C22×D7114yes—
582#97C22×D7114yes—
583C24—1421no—
584C24C2×D28411yescharacteristic
585C24C2×D28411yescharacteristic
586C2×Q8—2848no—
587C2×Q8—2848no—
588C2×Q8—2844no—
589C2×Q8—2844no—
590C2×Q8—2844no—
591C2×Q8—2844no—
592C2×Q8—714no—
593C2×Q8—712no—
594C2×Q8—712no—
595C2×Q8—712no—
596C2×Q8—1428no—
597C2×Q8—1428no—
598C2×Q8—1422no—
599C2×Q8—1422no—
600C2×Q8—1422no—
601C2×Q8—1422no—
602C2×Q8—1421no—
603C2×Q8—1421no—
604C2×Q8—1424no—
605C2×Q8—1424no—
606C2×Q8—1421no—
607C2×Q8—1422no—
608C2×D4—24no—
609C2×D4—2844no—
610C2×D4—5682no—
611C2×D4—712no—
612C2×D4—1424no—
613C2×D4—1424no—
614C2×D4—1421no—
615C2×D4—1422no—
616C2×D4—1422no—
617C2×D4C2×D28414yes—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—2844no—
623C22×C4—2844no—
624C22×C4—5682no—
625C22×C4—5682no—
626C22×C4—1424no—
627C22×C4—1424no—
628C22×C4—1421no—
629C22×C4—1421no—
630C22×C4—1421no—
631C22×C4—1421no—
632C22×C4—1421no—
633C22×C4—1421no—
634C22×C4—1424no—
635C22×C4—1424no—
636C22×C4—1421no—
637C22×C4C2×D28412yes—
638C22×C4C2×D28412yes—
639C22×C4C2×D28411yescharacteristic
640C22×C4C2×D28411yescharacteristic
641C22×C4C2×D28411yescharacteristic
642C22×C4C2×D28411yescharacteristic
643C22×C4C23×D7112yes—
644C22×C4C23×D7112yes—
645C22×C4C23×D7111yescharacteristic
646SD16—2844no—
647SD16—2844no—
648SD16—1428no—
649M16—44no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—44no—
655C2×C8C23×D7112yes—
656C2×C8C23×D7112yes—
657C2×C8C23×D7112yes—
658C2×C8C23×D7112yes—
659C4⋊C4—712no—
660C4⋊C4—712no—
661C4⋊C4—712no—
662C4⋊C4—712no—
663C4⋊C4—1424no—
664C4⋊C4—1424no—
665C4⋊C4—1424no—
666C4⋊C4—1424no—
667C4⋊C4—1424no—
668C4⋊C4—1421no—
669C4⋊C4—1421no—
670C4⋊C4—1424no—
671C4⋊C4—1421no—
672C4⋊C4—1421no—
673C4⋊C4—1424no—
674C4⋊C4—1424no—
675C4⋊C4C2×D28414yes—
676C22⋊C4—1424no—
677C22⋊C4—1424no—
678C22⋊C4—1424no—
679C22⋊C4—1424no—
680C22⋊C4—1424no—
681C22⋊C4—1424no—
682C22⋊C4C2×D28414yes—
683C22⋊C4C2×D28414yes—
684C42—1424no—
685C42—1424no—
686C42C2×D28412yes—
687C42C23×D7112yes—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—2842no—
694C23—2842no—
695C23—2842no—
696C23—1422no—
697C23#1455616114yes—
698C23C22×D28412yes—
699C23C22×D28412yes—
700C23C22×D28411yescharacteristic
701Q8—2848no—
702Q8—2848no—
703Q8—2842no—
704Q8—2842no—
705Q8—714no—
706Q8—1422no—
707Q8—1422no—
708Q8—1422no—
709Q8—1422no—
710Q8—1422no—
711Q8—1424no—
712D4—28no—
713D4—2848no—
714D4—2842no—
715D4—5684no—
716D4—1422no—
717D4—1422no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—2842no—
729C2×C4—2842no—
730C2×C4—2842no—
731C2×C4—2842no—
732C2×C4—2842no—
733C2×C4—2842no—
734C2×C4—2848no—
735C2×C4—2848no—
736C2×C4—5684no—
737C2×C4—5684no—
738C2×C4—1422no—
739C2×C4—1422no—
740C2×C4—1422no—
741C2×C4—1422no—
742C2×C4—1422no—
743C2×C4—1422no—
744C2×C4—1422no—
745C2×C4—1424no—
746C2×C4C22×D28412yes—
747C2×C4C22×D28412yes—
748C2×C4C22×D28412yes—
749C2×C4C22×D28412yes—
750C2×C4C22×D28411yescharacteristic
751C2×C4#41×D7112yes—
752C2×C4#1455617312yes—
753C2×C4C24×D7111yescharacteristic
754C8—22no—
755C8—22no—
756C8—22no—
757C8—22no—
758C22—22no—
759C22—28no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—2842no—
766C22—2842no—
767C22—2842no—
768C22—5684no—
769C22#1798664412yes—
770C22C2×#1455616114yes—
771C22C2×#1455616112yes—
772C22#1798681112yes—
773C22C23×D28411yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—2842no—
779C4—2842no—
780C4—2842no—
781C4—2842no—
782C4—2842no—
783C4—2842no—
784C4—1424no—
785C4#1798664412yes—
786C4C2×#41×D7111yescharacteristic
787C4C2×#1455617311yescharacteristic
788C2—24no—
789C2—42no—
790C2—5682no—
791C2#2260051314yesdirect product factor
792C2C2×#1798664411yescharacteristic
793C2C22×#1455616111yescharacteristic
794C2C2×#1798681111yescharacteristic
subgroupG/H
centerC23C22×D284
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#435×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986695C2
hypercenterC2×#435D71
hypocenterC71C2×#3320
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic142C2semidirect
3. #22600513C2direct (N × H)
4. C2×#17986368C2semidirect
5. C2×#17986335C2semidirect
6. C2×#17986341C2semidirect
7. C2×#17986307C2semidirect
8. C2×#17986245C2semidirect
9. C2×#17986228C2semidirect
10. C2×#17986205C2semidirect
11. C2×#17986140C2semidirect
12. C2×#17986140C2semidirect
13. C2×#17986101C2semidirect
14. C2×#17986009C2semidirect
15. C22×#14556053C2semidirect
16. C2×#435×C71C2semidirect
25. D4×Dic142C22semidirect
44. #17986368C22semidirect
45. #17986341C22semidirect
46. #17986335C22semidirect
47. #17986307C22semidirect
48. #17986245C22semidirect
49. #17986228C22semidirect
50. #17986205C22semidirect
51. #17986140C22semidirect
52. #17986140C22semidirect
53. #17986101C22semidirect
57. #17986009C22semidirect
67. C2×#14556053C22semidirect
72. #435×C71C22semidirect
393. C2×C71#3320semidirect
411. C2×#435D71semidirect
414. C71C2×#3320semidirect
455. #435C2×D71semidirect
791. C2#22600513direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866952
C2×D4×Dic1422
#226005132
C2×#179863682
C2×#179863352
C2×#179863412
C2×#179863072
C2×#179862452
C2×#179862282
C2×#179862052
C2×#179861402
C2×#179861012
C2×#179860092
C22×#145560532
C2×#435×C712
C2×#332071