Finite Group Databasebeta

← C2×#22600445 #32874036

Subgroups — C2×#22600445 #32874036

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×#17986658C211yesmaximal, characteristic
2#22600445C2116yesmaximal, direct product factor
3C2×#17986361C211yesmaximal, characteristic, complemented
4C2×#17986317C211yesmaximal, characteristic, complemented
5C2×#17986329C211yesmaximal, characteristic, complemented
6C2×#17986281C211yesmaximal, characteristic, complemented
7C2×#17986255C211yesmaximal, characteristic, complemented
8C2×#17986230C211yesmaximal, characteristic, complemented
9C2×#17986221C211yesmaximal, characteristic, complemented
10C2×#17986159C211yesmaximal, characteristic, complemented
11C2×#17986154C211yesmaximal, characteristic, complemented
12C2×#17986104C211yesmaximal, characteristic, complemented
13C2×#17986071C211yesmaximal, characteristic, complemented
14C2×#17985998C211yesmaximal, characteristic, complemented
15C22×#14556051C211yesmaximal, characteristic, complemented
16C2×#554×C71C211yesmaximal, characteristic, complemented
17C22×#11765865C2211yescharacteristic
18C23×Dic142C2211yescharacteristic
19C22×#11765855C2211yescharacteristic
20C22×#11765855C2211yescharacteristic
21C22×#11765852C2211yescharacteristic
22C22×#11765849C2211yescharacteristic
23C23×C71⋊C8C2211yescharacteristic
24#17986658—24no—
25#17986658C2218yes—
26C2×#14556116C2211yescharacteristic
27C2×#14556114—21no—
28C2×#14556107C2211yescharacteristic
29C2×#14556106—21no—
30C2×#14556102C2211yescharacteristic
31C2×#14556100—21no—
32C2×C4×Dic142C2211yescharacteristic
33C2×(C22⋊D71)⋊C4—21no—
34#17986361C2218yescomplemented
35#17986329C2218yescomplemented
36#17986317C2218yescomplemented
37#17986281C2218yescomplemented
38#17986255C2218yescomplemented
39#17986230C2218yescomplemented
40#17986221C2218yescomplemented
41#17986159C2218yescomplemented
42#17986154C2218yescomplemented
43#17986104C2218yescomplemented
44#17986071C2218yescomplemented
45C2×#14556059C2211yescharacteristic
46C2×#14556059C2211yescharacteristic
47C2×#14556059C2211yescharacteristic
48C2×C4⋊(C71⋊C8)C2211yescharacteristic
49#17985998C2218yescomplemented
50C2×#14556052C2211yescharacteristic
51C2×#14556051C2211yescharacteristic
52C2×#14556051C2211yescharacteristic
53C2×#14556051C2211yescharacteristic
54C2×#14556051C2211yescharacteristic
55C2×#14556051C2211yescharacteristic
56C2×#14556051C2211yescharacteristic
57C2×#14556051C2218yescomplemented
58C2×#14556048C2211yescharacteristic
59C2×#14556048C2211yescharacteristic
60C2×#14556048C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×C22⋊(C71⋊C8)C2211yescharacteristic
63C2×#14556039C2211yescharacteristic
64#554×C71—24no—
65#554×C71C2218yescomplemented
66C2×C4⋊Q8×C71C2211yescharacteristic
67C2×#125×C71—21no—
68C2×C22⋊Q8×C71—21no—
69C2×C22⋊Q8×C71—21no—
70C2×C22⋊Q8×C71C2211yescharacteristic
71C2×C22⋊Q8×C71C2211yescharacteristic
72C2×C4×Q8×C71C2211yescharacteristic
73C2×C4×D4×C71—21no—
74C2×C4×D4×C71C2211yescharacteristic
75C22×C4⋊C4×C71C2211yescharacteristic
76C22×C4⋊C4×C71C2211yescharacteristic
77C2×#11765865—24no—
78C2×#11765865—22no—
79C2×#11765865—42no—
80C2×#11765865C2314yes—
81C22×Dic142—24no—
82C22×Dic142—22no—
83C22×Dic142—21no—
84C22×Dic142—42no—
85C22×Dic142C2311yescharacteristic
86C22×Dic142C2314yes—
87C22×Dic142C2311yescharacteristic
88C22×D284C2311yescharacteristic
89C22×C22⋊D71—21no—
90C22×C22⋊D71—21no—
91C23×Dic71—21no—
92C22×C4×D71—21no—
93C2×#11765855—24no—
94C2×#11765855—42no—
95C2×#11765855C2314yes—
96C2×#11765855C2314yes—
97C2×#11765852—42no—
98C2×#11765852C2314yes—
99C2×#11765849—42no—
100C2×#11765849C2314yes—
101C22×C71⋊C8—42no—
102C22×C71⋊C8C2311yescharacteristic
103C22×C71⋊C8C2311yescharacteristic
104C22×C71⋊C8C2311yescharacteristic
105C22×C71⋊C8C2311yescharacteristic
106C22×C71⋊C8C2314yes—
107#14556116—22no—
108#14556116C2314yes—
109#14556114—28no—
110#14556107—22no—
111#14556107C2314yes—
112#14556106—28no—
113#14556102—22no—
114#14556102C2314yes—
115#14556100—28no—
116C4×Dic142—22no—
117C4×Dic142C2314yes—
118(C22⋊D71)⋊C4—28no—
119C2×C4⋊Dic71C2311yescharacteristic
120C2×Dic71⋊C4—21no—
121C2×Dic71⋊C4—21no—
122C2×C22⋊Dic71—21no—
123C2×(C2×D71)⋊C4—21no—
124C2×(C2×D71)⋊C4—21no—
125C2×(C2×D71)⋊C4—21no—
126C2×C4×Dic71—21no—
127#14556059C2314yes—
128#14556059C2314yes—
129#14556059C2314yes—
130C4⋊(C71⋊C8)C2314yes—
131#14556052C2314yes—
132#14556051C2314yes—
133#14556051C2314yes—
134#14556051C2314yes—
135#14556051C2314yes—
136#14556051C2314yes—
137#14556051C2314yes—
138#14556048C2314yes—
139#14556048C2314yes—
140#14556048C2314yes—
141C22⋊(C71⋊C8)C2314yes—
142C22⋊(C71⋊C8)C2314yes—
143#14556039C2314yes—
144C22×Q8×C71—21no—
145C22×Q8×C71C2311yescharacteristic
146C22×D4×C71D411yescharacteristic
147C23×C4×C71—21no—
148C23×C4×C71—21no—
149C23×C4×C71C2311yescharacteristic
150C23×C4×C71C2311yescharacteristic
151C4⋊Q8×C71—22no—
152C4⋊Q8×C71C2314yes—
153#125×C71—28no—
154C22⋊Q8×C71—22no—
155C22⋊Q8×C71—22no—
156C22⋊Q8×C71—28no—
157C22⋊Q8×C71—28no—
158C22⋊Q8×C71C2314yes—
159C22⋊Q8×C71C2314yes—
160C4×Q8×C71—22no—
161C4×Q8×C71C2314yes—
162C4×D4×C71—28no—
163C4×D4×C71D414yes—
164C4×D4×C71C2314yes—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71—21no—
167C2×C4⋊C4×C71—22no—
168C2×C4⋊C4×C71—22no—
169C2×C4⋊C4×C71—21no—
170C2×C4⋊C4×C71—21no—
171C2×C4⋊C4×C71—21no—
172C2×C4⋊C4×C71—21no—
173C2×C4⋊C4×C71D411yescharacteristic
174C2×C4⋊C4×C71C2314yes—
175C2×C4⋊C4×C71C2314yes—
176C2×C4⋊C4×C71C2311yescharacteristic
177C2×C4⋊C4×C71C2311yescharacteristic
178C2×C4⋊C4×C71C2311yescharacteristic
179C2×C22⋊C4×C71—21no—
180C2×C22⋊C4×C71—21no—
181C2×C22⋊C4×C71D411yescharacteristic
182C2×C22⋊C4×C71D411yescharacteristic
183C2×C42×C71—21no—
184C2×C42×C71C2311yescharacteristic
185C23×D71—21no—
186#11765865—28no—
187#11765865—44no—
188#11765865—48no—
189C2×Dic142—21no—
190C2×Dic142—22no—
191C2×Dic142—22no—
192C2×Dic142—22no—
193C2×Dic142—28no—
194C2×Dic142—24no—
195C2×Dic142—21no—
196C2×Dic142—44no—
197C2×Dic142—48no—
198C2×Dic142—44no—
199C2×Dic142#4114yes—
200C2×Dic142C2412yes—
201C2×Dic142C2412yes—
202C2×D284—22no—
203C2×D284—22no—
204C2×D284—21no—
205C2×D284C2412yes—
206C2×C22⋊D71—24no—
207C2×C22⋊D71—24no—
208C2×C22⋊D71—44no—
209C2×C22⋊D71—44no—
210C22×Dic71—21no—
211C22×Dic71—21no—
212C22×Dic71—24no—
213C22×Dic71—21no—
214C22×Dic71—44no—
215C2×C4×D71—24no—
216C2×C4×D71—44no—
217#11765855—28no—
218#11765855—44no—
219#11765852—44no—
220#11765849—44no—
221C2×C71⋊C8—22no—
222C2×C71⋊C8—22no—
223C2×C71⋊C8—22no—
224C2×C71⋊C8—22no—
225C2×C71⋊C8—44no—
226C2×C71⋊C8C2412yes—
227C2×C71⋊C8C2412yes—
228C2×C71⋊C8C2412yes—
229C2×C71⋊C8C2412yes—
230C4⋊Dic71—21no—
231C4⋊Dic71C2412yes—
232Dic71⋊C4—24no—
233Dic71⋊C4—24no—
234C22⋊Dic71—24no—
235(C2×D71)⋊C4—24no—
236(C2×D71)⋊C4—24no—
237(C2×D71)⋊C4—24no—
238C4×Dic71—24no—
239C24×C71C2×D411yescharacteristic
240C24×C71C2×D411yescharacteristic
241C2×Q8×C71—21no—
242C2×Q8×C71—24no—
243C2×Q8×C71—22no—
244C2×Q8×C71—22no—
245C2×Q8×C71—82no—
246C2×Q8×C71C2412yes—
247C2×D4×C71—24no—
248C2×D4×C71C2×D414yes—
249C22×C4×C71—22no—
250C22×C4×C71—22no—
251C22×C4×C71—22no—
252C22×C4×C71—22no—
253C22×C4×C71—21no—
254C22×C4×C71—21no—
255C22×C4×C71—21no—
256C22×C4×C71—21no—
257C22×C4×C71—24no—
258C22×C4×C71—24no—
259C22×C4×C71—82no—
260C22×C4×C71—82no—
261C22×C4×C71C2×D411yescharacteristic
262C22×C4×C71C2×D411yescharacteristic
263C22×C4×C71C2×D412yes—
264C22×C4×C71C2×D412yes—
265C22×C4×C71C2×D411yescharacteristic
266C22×C4×C71C2×D411yescharacteristic
267C22×C4×C71C2412yes—
268C22×C4×C71C2412yes—
269C22×C4×C71C2411yescharacteristic
270C4⋊C4×C71—21no—
271C4⋊C4×C71—24no—
272C4⋊C4×C71—24no—
273C4⋊C4×C71—21no—
274C4⋊C4×C71—21no—
275C4⋊C4×C71—24no—
276C4⋊C4×C71—24no—
277C4⋊C4×C71—24no—
278C4⋊C4×C71—24no—
279C4⋊C4×C71C2×D414yes—
280C4⋊C4×C71C2412yes—
281C4⋊C4×C71C2412yes—
282C4⋊C4×C71C2412yes—
283C22⋊C4×C71—24no—
284C22⋊C4×C71—24no—
285C22⋊C4×C71C2×D414yes—
286C22⋊C4×C71C2×D414yes—
287C42×C71—24no—
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—
303Q8×C71—22no—
304Q8×C71—22no—
305Q8×C71—42no—
306Q8×C71—84no—
307D4×C71—28no—
308C2×C4×C71—22no—
309C2×C4×C71—22no—
310C2×C4×C71—22no—
311C2×C4×C71—22no—
312C2×C4×C71—24no—
313C2×C4×C71—24no—
314C2×C4×C71—22no—
315C2×C4×C71—22no—
316C2×C4×C71—22no—
317C2×C4×C71—22no—
318C2×C4×C71—22no—
319C2×C4×C71—22no—
320C2×C4×C71—22no—
321C2×C4×C71—22no—
322C2×C4×C71—42no—
323C2×C4×C71—42no—
324C2×C4×C71—42no—
325C2×C4×C71—42no—
326C2×C4×C71—84no—
327C2×C4×C71—84no—
328C2×C4×C71C22×D412yes—
329C2×C4×C71C22×D412yes—
330C2×C4×C71C22×D412yes—
331C2×C4×C71C22×D412yes—
332C2×C4×C71C22×D411yescharacteristic
333C2×C4×C71C2×#4112yes—
334C2×C4×C71H(5,𝔽2)12yes—
335C2×C4×C71C2511yescharacteristic
336C22⋊D71—48no—
337C22⋊D71—48no—
338C2×Dic71—24no—
339C2×Dic71—22no—
340C2×Dic71—22no—
341C2×Dic71—22no—
342C2×Dic71—48no—
343C2×Dic71—42no—
344C2×Dic71—42no—
345D284—22no—
346D284—22no—
347D284—42no—
348C4×D71—48no—
349Dic142—24no—
350Dic142—22no—
351Dic142—22no—
352Dic142—22no—
353Dic142—48no—
354Dic142—42no—
355Dic142C2×#4114yes—
356C71⋊C8—22no—
357C71⋊C8—22no—
358C71⋊C8—22no—
359C71⋊C8—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—42no—
381C4×C71—42no—
382C4×C71—42no—
383C4×C71—42no—
384C4×C71#54612yes—
385C4×C71C22×#4111yescharacteristic
386C4×C71C2×H(5,𝔽2)11yescharacteristic
387Dic71—24no—
388Dic71—42no—
389Dic71—42no—
390C2×#3316—711nomaximal, Sylow
391C2×C71—24no—
392C2×C71—42no—
393C2×C71#331614yescomplemented
394C2×C71C2×#54611yescharacteristic
395C2×C71C22×#13711yescharacteristic
396C2×C71C2×#57711yescharacteristic
397D71—82no—
398C2×#554D7111yescharacteristic, complemented
399C2×#548—711no—
400#3316—7116no—
401C2×#489—711no—
402C2×#481—711no—
403C2×#483—711no—
404C2×#475—711no—
405C2×#470—711no—
406C2×#465—711no—
407C2×#464—711no—
408C2×#452—711no—
409C2×#451—711no—
410C2×#441—711no—
411C2×#435—711no—
412C2×#417—711no—
413C22×#103—711no—
414C71C2×#331611yescharacteristic, complemented, Sylow
415C22×#41—711no—
416C23×Q8—711no—
417C22×Q16—711no—
418C22×Q16—711no—
419C22×SD16—711no—
420C22×M16—711no—
421C23×C8—711no—
422#554—24no—
423#554C2×D7118yescomplemented
424#548—718no—
425#548—1424no—
426C2×C4⋊Q8C2×D7111yescharacteristic
427C2×#125—21no—
428C2×#124—711no—
429C2×#124—1421no—
430C2×C22⋊Q8—21no—
431C2×C22⋊Q8—21no—
432C2×C22⋊Q8—711no—
433C2×C22⋊Q8—1421no—
434C2×C22⋊Q8C2×D7111yescharacteristic
435C2×C22⋊Q8C2×D7111yescharacteristic
436C2×#121—711no—
437C2×#121—1421no—
438C2×C4×Q8—711no—
439C2×C4×Q8C2×D7111yescharacteristic
440C2×C4×D4—21no—
441C2×C4×D4—1421no—
442C2×C4×D4C2×D7111yescharacteristic
443C22×C4⋊C4C2×D7111yescharacteristic
444C22×C4⋊C4C2×D7111yescharacteristic
445#489—718no—
446#483—718no—
447#481—718no—
448#475—718no—
449#470—718no—
450#465—718no—
451#464—718no—
452#452—718no—
453#451—718no—
454#441—718no—
455#435—718no—
456C2×#106—711no—
457C2×#106—711no—
458C2×#106—711no—
459C2×C4⋊C8—711no—
460#417—718no—
461C2×#103—711no—
462C2×#103—711no—
463C2×#103—711no—
464C2×#103—711no—
465C2×#103—711no—
466C2×#103—711no—
467C2×#103—711no—
468C2×#103—718no—
469C2×#102—711no—
470C2×#102—711no—
471C2×#102—711no—
472C2×C22⋊C8—711no—
473C2×C22⋊C8—711no—
474C2×#97—711no—
475C2×#41—2842no—
476C2×#41—714no—
477C2×#41—1424no—
478C2×#41—1422no—
479C22×Q8—21no—
480C22×Q8—2842no—
481C22×Q8—714no—
482C22×Q8—711no—
483C22×Q8—711no—
484C22×Q8—1424no—
485C22×Q8—1421no—
486C22×Q8—1422no—
487C22×Q8C22×D7111yescharacteristic
488C22×D4—711no—
489C22×D4—1421no—
490C22×D4—1421no—
491C22×D4C22⋊D7111yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—1421no—
495C23×C4—1421no—
496C23×C4C22×D7111yescharacteristic
497C23×C4C22×D7111yescharacteristic
498C2×Q16—2842no—
499C2×Q16—714no—
500C2×Q16—714no—
501C2×Q16—1424no—
502C2×SD16—2842no—
503C2×SD16—714no—
504C2×M16—2842no—
505C2×M16—714no—
506C22×C8—2842no—
507C22×C8—714no—
508C22×C8—711no—
509C22×C8—711no—
510C22×C8—711no—
511C22×C8—711no—
512C4⋊Q8—22no—
513C4⋊Q8C22×D7114yes—
514#125—28no—
515#124—714no—
516#124—1428no—
517#124—1422no—
518C22⋊Q8—22no—
519C22⋊Q8—22no—
520C22⋊Q8—28no—
521C22⋊Q8—28no—
522C22⋊Q8—714no—
523C22⋊Q8—1422no—
524C22⋊Q8—1428no—
525C22⋊Q8C22×D7114yes—
526C22⋊Q8C22×D7114yes—
527#121—714no—
528#121—1428no—
529#121—1422no—
530C4×Q8—22no—
531C4×Q8—714no—
532C4×Q8—1422no—
533C4×Q8C22×D7114yes—
534C4×D4—28no—
535C4×D4—1428no—
536C4×D4C22⋊D7114yes—
537C4×D4C22×D7114yes—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—711no—
547C2×C4⋊C4—1421no—
548C2×C4⋊C4—1421no—
549C2×C4⋊C4C22⋊D7111yescharacteristic
550C2×C4⋊C4C22×D7111yescharacteristic
551C2×C4⋊C4C22×D7111yescharacteristic
552C2×C4⋊C4C22×D7111yescharacteristic
553C2×C4⋊C4C22×D7114yes—
554C2×C4⋊C4C22×D7114yes—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—1421no—
558C2×C22⋊C4—1421no—
559C2×C22⋊C4—1421no—
560C2×C22⋊C4—1421no—
561C2×C22⋊C4C22⋊D7111yescharacteristic
562C2×C22⋊C4C22⋊D7111yescharacteristic
563C2×C42—21no—
564C2×C42—1421no—
565C2×C42C22×D7111yescharacteristic
566#106—714no—
567#106—714no—
568#106—714no—
569C4⋊C8—714no—
570#103—714no—
571#103—714no—
572#103—714no—
573#103—714no—
574#103—714no—
575#103—714no—
576#103—714no—
577#102—714no—
578#102—714no—
579#102—714no—
580C22⋊C8—714no—
581C22⋊C8—714no—
582#97—714no—
583C24—1421no—
584C24C2×C22⋊D7111yescharacteristic
585C24C2×C22⋊D7111yescharacteristic
586#41—2848no—
587#41—2844no—
588#41—1428no—
589C2×Q8—21no—
590C2×Q8—24no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—82no—
594C2×Q8—2848no—
595C2×Q8—2844no—
596C2×Q8—2844no—
597C2×Q8—714no—
598C2×Q8—712no—
599C2×Q8—712no—
600C2×Q8—1428no—
601C2×Q8—1422no—
602C2×Q8—1422no—
603C2×Q8—1421no—
604C2×Q8—1424no—
605C2×Q8—1421no—
606C2×Q8—1422no—
607C2×Q8C23×D7112yes—
608C2×D4—24no—
609C2×D4—2844no—
610C2×D4—2844no—
611C2×D4—712no—
612C2×D4—1424no—
613C2×D4—1424no—
614C2×D4—1421no—
615C2×D4—1422no—
616C2×D4—1422no—
617C2×D4C2×C22⋊D7114yes—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—24no—
627C22×C4—24no—
628C22×C4—82no—
629C22×C4—82no—
630C22×C4—2844no—
631C22×C4—2844no—
632C22×C4—1424no—
633C22×C4—1421no—
634C22×C4—1421no—
635C22×C4—1424no—
636C22×C4—1421no—
637C22×C4C2×C22⋊D7112yes—
638C22×C4C2×C22⋊D7112yes—
639C22×C4C2×C22⋊D7111yescharacteristic
640C22×C4C2×C22⋊D7111yescharacteristic
641C22×C4C2×C22⋊D7111yescharacteristic
642C22×C4C2×C22⋊D7111yescharacteristic
643C22×C4C23×D7112yes—
644C22×C4C23×D7112yes—
645C22×C4C23×D7111yescharacteristic
646Q16—2844no—
647Q16—1428no—
648SD16—2844no—
649M16—2844no—
650C2×C8—2844no—
651C2×C8—712no—
652C2×C8—712no—
653C2×C8—712no—
654C2×C8—712no—
655C2×C8—1422no—
656C2×C8—1422no—
657C2×C8—1422no—
658C2×C8—1422no—
659C4⋊C4—21no—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—24no—
665C4⋊C4—24no—
666C4⋊C4—24no—
667C4⋊C4—24no—
668C4⋊C4—712no—
669C4⋊C4—1424no—
670C4⋊C4—1424no—
671C4⋊C4—1421no—
672C4⋊C4C2×C22⋊D7114yes—
673C4⋊C4C23×D7112yes—
674C4⋊C4C23×D7112yes—
675C4⋊C4C23×D7112yes—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—1424no—
679C22⋊C4—1424no—
680C22⋊C4—1424no—
681C22⋊C4—1424no—
682C22⋊C4C2×C22⋊D7114yes—
683C22⋊C4C2×C22⋊D7114yes—
684C42—24no—
685C42—1424no—
686C42C2×C22⋊D7112yes—
687C42C23×D7112yes—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—2842no—
694C23—2842no—
695C23—2842no—
696C23—1422no—
697C23#1455615914yes—
698C23C22×C22⋊D7112yes—
699C23C22×C22⋊D7112yes—
700C23C22×C22⋊D7111yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—42no—
704Q8—84no—
705Q8—2848no—
706Q8—2842no—
707Q8—714no—
708Q8—1422no—
709Q8—1422no—
710Q8—1422no—
711Q8—1424no—
712D4—28no—
713D4—2848no—
714D4—2848no—
715D4—2842no—
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—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—84no—
737C2×C4—84no—
738C2×C4—2848no—
739C2×C4—2842no—
740C2×C4—2842no—
741C2×C4—2848no—
742C2×C4—1422no—
743C2×C4—1422no—
744C2×C4—1422no—
745C2×C4—1424no—
746C2×C4C22×C22⋊D7112yes—
747C2×C4C22×C22⋊D7112yes—
748C2×C4C22×C22⋊D7112yes—
749C2×C4C22×C22⋊D7112yes—
750C2×C4C22×C22⋊D7111yescharacteristic
751C2×C4#41×D7112yes—
752C2×C4#1455617412yes—
753C2×C4C24×D7111yescharacteristic
754C8—1422no—
755C8—1422no—
756C8—1422no—
757C8—1422no—
758C22—22no—
759C22—22no—
760C22—28no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—2842no—
766C22—2842no—
767C22—2842no—
768C22—5684no—
769C22#1798663712yes—
770C22C2×#1455615914yes—
771C22C2×#1455615912yes—
772C22#1798681012yes—
773C22C23×C22⋊D7111yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—2842no—
783C4—2842no—
784C4—1424no—
785C4#1798663712yes—
786C4C2×#41×D7111yescharacteristic
787C4C2×#1455617411yescharacteristic
788C2—24no—
789C2—42no—
790C2—5682no—
791C2#2260044514yesdirect product factor
792C2C2×#1798663711yescharacteristic
793C2C22×#1455615911yescharacteristic
794C2C2×#1798681011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#554×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986658C2
hypercenterC2×#554D71
hypocenterC71C2×#3316
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #22600445C2direct (N × H)
3. C2×#17986361C2semidirect
4. C2×#17986317C2semidirect
5. C2×#17986329C2semidirect
6. C2×#17986281C2semidirect
7. C2×#17986255C2semidirect
8. C2×#17986230C2semidirect
9. C2×#17986221C2semidirect
10. C2×#17986159C2semidirect
11. C2×#17986154C2semidirect
12. C2×#17986104C2semidirect
13. C2×#17986071C2semidirect
14. C2×#17985998C2semidirect
15. C22×#14556051C2semidirect
16. C2×#554×C71C2semidirect
34. #17986361C22semidirect
35. #17986329C22semidirect
36. #17986317C22semidirect
37. #17986281C22semidirect
38. #17986255C22semidirect
39. #17986230C22semidirect
40. #17986221C22semidirect
41. #17986159C22semidirect
42. #17986154C22semidirect
43. #17986104C22semidirect
44. #17986071C22semidirect
49. #17985998C22semidirect
57. C2×#14556051C22semidirect
65. #554×C71C22semidirect
393. C2×C71#3316semidirect
398. C2×#554D71semidirect
414. C71C2×#3316semidirect
423. #554C2×D71semidirect
791. C2#22600445direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866582
#226004452
C2×#179863612
C2×#179863172
C2×#179863292
C2×#179862812
C2×#179862552
C2×#179862302
C2×#179862212
C2×#179861592
C2×#179861542
C2×#179861042
C2×#179860712
C2×#179859982
C22×#145560512
C2×#554×C712
C2×#331671