Finite Group Databasebeta

← C2×#22599119 #32868002

Subgroups — C2×#22599119 #32868002

Order 18176.

2374 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986506C211yesmaximal, characteristic
2C2×C22⋊Q8×D71C211yesmaximal, characteristic, complemented
3#22599119C2116yesmaximal, direct product factor
4C2×#17986341C211yesmaximal, characteristic, complemented
5C2×#17986337C211yesmaximal, characteristic, complemented
6C2×#17986328C211yesmaximal, characteristic, complemented
7C2×#17986311C211yesmaximal, characteristic, complemented
8C2×#17986239C211yesmaximal, characteristic, complemented
9C2×#17986237C211yesmaximal, characteristic, complemented
10C2×#17986227C211yesmaximal, characteristic, complemented
11C2×#17986225C211yesmaximal, characteristic, complemented
12C2×#17986161C211yesmaximal, characteristic, complemented
13C2×#17986153C211yesmaximal, characteristic, complemented
14C2×#17986136C211yesmaximal, characteristic, complemented
15C2×C22⋊C8×D71C211yesmaximal, characteristic, complemented
16C2×#452×C71C211yesmaximal, characteristic, complemented
17C22×Q8×D71C2211yescharacteristic
18C23×C4×D71C2211yescharacteristic
19C22×#11765855C2211yescharacteristic, complemented
20C22×#11765853C2211yescharacteristic, complemented
21C22×C8×D71C2211yescharacteristic
22C22×C8×D71C2211yescharacteristic
23#17986506—24no—
24#17986506C2218yes—
25C2×#14556109—21no—
26C2×#14556108C2211yescharacteristic
27C2×#14556107C2211yescharacteristic
28C2×#14556106—21no—
29C2×#14556105—21no—
30C2×#14556104C2211yescharacteristic
31C2×#14556104C2211yescharacteristic
32C2×#14556104C2211yescharacteristic
33C22⋊Q8×D71—24no—
34C22⋊Q8×D71C2218yescomplemented
35C2×#14556099C2211yescharacteristic
36C2×#14556099C2211yescharacteristic
37C2×#14556096—21no—
38C2×C4×C22⋊D71—21no—
39C2×C4×C22⋊D71—21no—
40C2×#14556087C2211yescharacteristic
41C2×C4⋊C4×D71—21no—
42C2×C4⋊C4×D71C2211yescharacteristic
43C2×C22⋊C4×D71—21no—
44#17986341C2218yescomplemented
45#17986337C2218yescomplemented
46#17986328C2218yescomplemented
47#17986311C2218yescomplemented
48#17986239C2218yescomplemented
49#17986237C2218yescomplemented
50#17986227C2218yescomplemented
51#17986225C2218yescomplemented
52#17986161C2218yescomplemented
53#17986153C2218yescomplemented
54#17986136C2218yescomplemented
55C2×#14556062C2211yescharacteristic, complemented
56C2×#14556061C2211yescharacteristic, complemented
57C2×#14556060C2211yescharacteristic, complemented
58C2×#14556059C2211yescharacteristic, complemented
59C2×#14556053C2211yescharacteristic, complemented
60C2×#14556053C2211yescharacteristic, complemented
61C2×#14556052C2211yescharacteristic, complemented
62C2×#14556052C2211yescharacteristic, complemented
63C2×#14556052C2211yescharacteristic, complemented
64C2×#14556049C2211yescharacteristic, complemented
65C2×C22⋊(C71⋊C8)C2211yescharacteristic
66C2×(C2×D71)⋊C8C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C22⋊C8×D71C2218yescomplemented
69C22×#41×C71C2211yescharacteristic
70C22×Q16×C71C2211yescharacteristic, complemented
71C22×SD16×C71C2211yescharacteristic, complemented
72C2×C22⋊Q8×C71C2211yescharacteristic
73#452×C71C2218yescomplemented
74C2×#103×C71C2211yescharacteristic, complemented
75C2×#102×C71C2211yescharacteristic, complemented
76C2×C22⋊C8×C71C2211yescharacteristic
77C24×D71D411yescharacteristic
78C22×Dic142—21no—
79C22×Dic142C2311yescharacteristic
80C2×Q8×D71—22no—
81C2×Q8×D71—42no—
82C2×Q8×D71—42no—
83C2×Q8×D71C2314yes—
84C22×C22⋊D71—21no—
85C22×C22⋊D71—21no—
86C23×Dic71D411yescharacteristic
87C22×C4×D71—21no—
88C22×C4×D71—21no—
89C22×C4×D71—42no—
90C22×C4×D71—42no—
91C22×C4×D71D411yescharacteristic
92C22×C4×D71D411yescharacteristic
93C22×C4×D71D414yes—
94C22×C4×D71C2311yescharacteristic
95C22×C4×D71C2311yescharacteristic
96C22×C4×D71C2314yes—
97C2×#11765855—42no—
98C2×#11765855C2314yescomplemented
99C2×#11765853—42no—
100C2×#11765853C2314yescomplemented
101C22×C71⋊C8C2311yescharacteristic
102C22×C71⋊C8C2311yescharacteristic
103C2×C8×D71—42no—
104C2×C8×D71—42no—
105C2×C8×D71C2314yes—
106C2×C8×D71C2314yes—
107#14556109—28no—
108#14556108—22no—
109#14556108C2314yes—
110#14556107—22no—
111#14556107C2314yes—
112#14556106—28no—
113#14556105—28no—
114#14556104—22no—
115#14556104—22no—
116#14556104—22no—
117#14556104C2314yes—
118#14556104C2314yes—
119#14556104C2314yes—
120#14556099—22no—
121#14556099—22no—
122#14556099C2314yes—
123#14556099C2314yes—
124#14556096—28no—
125C4×C22⋊D71—28no—
126C4×C22⋊D71—28no—
127#14556087—22no—
128#14556087C2314yes—
129C2×C4⋊Dic71—21no—
130C2×C4⋊Dic71C2311yescharacteristic
131C2×C4⋊Dic71C2311yescharacteristic
132C2×C4⋊Dic71C2311yescharacteristic
133C2×Dic71⋊C4—21no—
134C2×Dic71⋊C4—21no—
135C2×Dic71⋊C4—21no—
136C2×Dic71⋊C4—21no—
137C2×Dic71⋊C4—21no—
138C4⋊C4×D71—28no—
139C4⋊C4×D71—22no—
140C4⋊C4×D71C2314yes—
141C2×C22⋊Dic71—21no—
142C2×C22⋊Dic71—21no—
143C2×C22⋊Dic71—21no—
144C2×C22⋊Dic71—21no—
145C2×(C2×D71)⋊C4—21no—
146C2×(C2×D71)⋊C4—21no—
147C2×(C2×D71)⋊C4—21no—
148C2×(C2×D71)⋊C4—21no—
149C22⋊C4×D71—28no—
150C2×C4×Dic71—21no—
151#14556062C2314yescomplemented
152#14556061C2314yescomplemented
153#14556060C2314yescomplemented
154#14556059C2314yescomplemented
155#14556053C2314yescomplemented
156#14556053C2314yescomplemented
157#14556052C2314yescomplemented
158#14556052C2314yescomplemented
159#14556052C2314yescomplemented
160#14556049C2314yescomplemented
161C22⋊(C71⋊C8)C2314yes—
162(C2×D71)⋊C8C2314yes—
163(C2×D71)⋊C8C2314yes—
164C2×#41×C71—22no—
165C2×#41×C71—42no—
166C2×#41×C71—42no—
167C2×#41×C71C2314yes—
168C22×Q8×C71C2311yescharacteristic
169C22×Q8×C71C2311yescharacteristic
170C22×D4×C71—21no—
171C22×D4×C71C2311yescharacteristic
172C23×C4×C71—21no—
173C23×C4×C71C2311yescharacteristic
174C2×Q16×C71—42no—
175C2×Q16×C71C2314yescomplemented
176C2×SD16×C71—42no—
177C2×SD16×C71C2314yescomplemented
178C22×C8×C71C2311yescharacteristic
179C22×C8×C71C2311yescharacteristic
180C22⋊Q8×C71—22no—
181C22⋊Q8×C71C2314yes—
182C2×C4⋊C4×C71—21no—
183C2×C4⋊C4×C71C2311yescharacteristic
184C2×C22⋊C4×C71—21no—
185#103×C71C2314yescomplemented
186#102×C71C2314yescomplemented
187C22⋊C8×C71C2314yes—
188C23×D71—24no—
189C23×D71—24no—
190C23×D71—42no—
191C23×D71C2×D414yes—
192C23×D71C2×D411yescharacteristic
193C23×D71C2×D411yescharacteristic
194C2×Dic142—22no—
195C2×Dic142—22no—
196C2×Dic142—21no—
197C2×Dic142—24no—
198C2×Dic142—44no—
199C2×Dic142C2412yes—
200Q8×D71—44no—
201Q8×D71—44no—
202Q8×D71—48no—
203C2×C22⋊D71—24no—
204C2×C22⋊D71—24no—
205C2×C22⋊D71—44no—
206C2×C22⋊D71—44no—
207C22×Dic71—21no—
208C22×Dic71—21no—
209C22×Dic71—21no—
210C22×Dic71—21no—
211C22×Dic71—42no—
212C22×Dic71C2×D411yescharacteristic
213C22×Dic71C2×D411yescharacteristic
214C22×Dic71C2×D414yes—
215C2×C4×D71—22no—
216C2×C4×D71—22no—
217C2×C4×D71—22no—
218C2×C4×D71—22no—
219C2×C4×D71—24no—
220C2×C4×D71—24no—
221C2×C4×D71—48no—
222C2×C4×D71—44no—
223C2×C4×D71—44no—
224C2×C4×D71—42no—
225C2×C4×D71—42no—
226C2×C4×D71—44no—
227C2×C4×D71—44no—
228C2×C4×D71C2×D412yes—
229C2×C4×D71C2×D412yes—
230C2×C4×D71C2×D414yes—
231C2×C4×D71C2×D414yes—
232C2×C4×D71C2412yes—
233C2×C4×D71C2412yes—
234#11765855—44no—
235#11765853—44no—
236C2×C71⋊C8—22no—
237C2×C71⋊C8—22no—
238C2×C71⋊C8C2412yes—
239C2×C71⋊C8C2412yes—
240C8×D71—44no—
241C8×D71—44no—
242C4⋊Dic71—21no—
243C4⋊Dic71—21no—
244C4⋊Dic71—21no—
245C4⋊Dic71—24no—
246C4⋊Dic71C2412yes—
247C4⋊Dic71C2412yes—
248C4⋊Dic71C2412yes—
249Dic71⋊C4—24no—
250Dic71⋊C4—24no—
251Dic71⋊C4—24no—
252Dic71⋊C4—24no—
253Dic71⋊C4—24no—
254C22⋊Dic71—24no—
255C22⋊Dic71—24no—
256C22⋊Dic71—24no—
257C22⋊Dic71—24no—
258(C2×D71)⋊C4—24no—
259(C2×D71)⋊C4—24no—
260(C2×D71)⋊C4—24no—
261(C2×D71)⋊C4—24no—
262C4×Dic71—24no—
263C24×C71—21no—
264C24×C71C2×D411yescharacteristic
265#41×C71—44no—
266#41×C71—44no—
267#41×C71—48no—
268C2×Q8×C71—21no—
269C2×Q8×C71—21no—
270C2×Q8×C71—22no—
271C2×Q8×C71—22no—
272C2×Q8×C71—22no—
273C2×Q8×C71—22no—
274C2×Q8×C71C2412yes—
275C2×Q8×C71C2412yes—
276C2×D4×C71—24no—
277C2×D4×C71—21no—
278C2×D4×C71—22no—
279C2×D4×C71—22no—
280C2×D4×C71—44no—
281C2×D4×C71C2412yes—
282C22×C4×C71—22no—
283C22×C4×C71—22no—
284C22×C4×C71—21no—
285C22×C4×C71—21no—
286C22×C4×C71—21no—
287C22×C4×C71—24no—
288C22×C4×C71—44no—
289C22×C4×C71C2×D411yescharacteristic
290C22×C4×C71C2×D412yes—
291C22×C4×C71C2412yes—
292C22×C4×C71C2411yescharacteristic
293Q16×C71—44no—
294SD16×C71—44no—
295C2×C8×C71—22no—
296C2×C8×C71—22no—
297C2×C8×C71C2412yes—
298C2×C8×C71C2412yes—
299C4⋊C4×C71—24no—
300C4⋊C4×C71—21no—
301C4⋊C4×C71C2412yes—
302C22⋊C4×C71—24no—
303C23×C71—22no—
304C23×C71—22no—
305C23×C71—22no—
306C23×C71—22no—
307C23×C71—42no—
308C23×C71—42no—
309C23×C71—42no—
310C23×C71C22×D412yes—
311C23×C71C22×D411yescharacteristic
312C22×D71—22no—
313C22×D71—22no—
314C22×D71—22no—
315C22×D71—22no—
316C22×D71—28no—
317C22×D71—28no—
318C22×D71—44no—
319C22×D71—416no—
320C22×D71#13514yes—
321C22×D71#13714yes—
322C22×D71C22×D412yes—
323C22×D71C22×D412yes—
324Q8×C71—22no—
325Q8×C71—22no—
326Q8×C71—22no—
327Q8×C71—22no—
328Q8×C71—42no—
329Q8×C71—42no—
330D4×C71—22no—
331D4×C71—22no—
332D4×C71—48no—
333D4×C71—42no—
334C2×C4×C71—22no—
335C2×C4×C71—24no—
336C2×C4×C71—22no—
337C2×C4×C71—22no—
338C2×C4×C71—22no—
339C2×C4×C71—22no—
340C2×C4×C71—22no—
341C2×C4×C71—48no—
342C2×C4×C71—42no—
343C2×C4×C71—42no—
344C2×C4×C71—42no—
345C2×C4×C71C22×D412yes—
346C2×C4×C71C22×D411yescharacteristic
347C2×C4×C71H(5,𝔽2)12yes—
348C2×C4×C71H(5,𝔽2)12yes—
349C2×C4×C71C2511yescharacteristic
350C22⋊D71—48no—
351C22⋊D71—48no—
352C2×Dic71—22no—
353C2×Dic71—22no—
354C2×Dic71—22no—
355C2×Dic71—22no—
356C2×Dic71—22no—
357C2×Dic71—22no—
358C2×Dic71—44no—
359C2×Dic71—42no—
360C2×Dic71—42no—
361C2×Dic71—42no—
362C2×Dic71—42no—
363C2×Dic71C22×D412yes—
364C2×Dic71C22×D412yes—
365C4×D71—24no—
366C4×D71—24no—
367C4×D71—22no—
368C4×D71—22no—
369C4×D71—22no—
370C4×D71—22no—
371C4×D71—44no—
372C4×D71—44no—
373C4×D71—48no—
374C4×D71—48no—
375Dic142—22no—
376Dic142—22no—
377Dic142—48no—
378Dic142—42no—
379C8×C71—22no—
380C8×C71—22no—
381C71⋊C8—22no—
382C71⋊C8—22no—
383C22×C71—22no—
384C22×C71—22no—
385C22×C71—22no—
386C22×C71—44no—
387C22×C71—42no—
388C22×C71—42no—
389C22×C71—42no—
390C22×C71—84no—
391C22×C71#53412yes—
392C22×C71C2×#13512yes—
393C22×C71C2×#13712yes—
394C22×C71C23×D411yescharacteristic
395C2×D71—22no—
396C2×D71—22no—
397C2×D71—28no—
398C2×D71—28no—
399C2×D71—22no—
400C2×D71—22no—
401C2×D71—416no—
402C2×D71C2×#13514yes—
403C2×D71C2×#13714yes—
404C4×C71—22no—
405C4×C71—42no—
406C4×C71—42no—
407C4×C71—42no—
408C4×C71#53412yes—
409C4×C71C2×H(5,𝔽2)11yescharacteristic
410C4×C71C2×H(5,𝔽2)11yescharacteristic
411Dic71—22no—
412Dic71—22no—
413Dic71—42no—
414Dic71—42no—
415Dic71—42no—
416Dic71—42no—
417C2×#3190—711nomaximal, Sylow
418C2×C71—42no—
419C2×C71—82no—
420C2×C71#319014yescomplemented
421C2×C71C2×#53411yescharacteristic
422C2×C71C22×#13511yescharacteristic
423C2×C71C22×#13711yescharacteristic
424D71—24no—
425D71—24no—
426C2×#525—711no—
427C22×C22⋊Q8—711no—
428#3190—7116no—
429C2×#485—711no—
430C2×#485—711no—
431C2×#483—711no—
432C2×#480—711no—
433C2×#467—711no—
434C2×#467—711no—
435C2×#465—711no—
436C2×#465—711no—
437C2×#452—711no—
438C2×#452D7111yescharacteristic, complemented
439C2×#451—711no—
440C2×#448—711no—
441C22×C22⋊C8—711no—
442C71C2×#319011yescharacteristic, complemented, Sylow
443C22×#41C2×D7111yescharacteristic
444C23×Q8—711no—
445C24×C4—711no—
446C22×Q16—711no—
447C22×Q16C2×D7111yescharacteristic, complemented
448C22×SD16—711no—
449C22×SD16C2×D7111yescharacteristic, complemented
450C23×C8—711no—
451C23×C8—711no—
452#525—718no—
453#525—1424no—
454C2×#123—1421no—
455C2×C22⋊Q8—711no—
456C2×C22⋊Q8—711no—
457C2×C22⋊Q8—711no—
458C2×C22⋊Q8—711no—
459C2×C22⋊Q8—718no—
460C2×C22⋊Q8—711no—
461C2×C22⋊Q8—1421no—
462C2×C22⋊Q8—1421no—
463C2×C22⋊Q8—1424no—
464C2×C22⋊Q8C2×D7111yescharacteristic
465C2×#121—711no—
466C2×#121—711no—
467C2×#120—1421no—
468C2×C4×D4—1421no—
469C2×C4×D4—1421no—
470C2×#117—711no—
471C22×C4⋊C4—711no—
472C22×C4⋊C4—1421no—
473C22×C22⋊C4—1421no—
474#485—718no—
475#485—718no—
476#483—718no—
477#480—718no—
478#467—718no—
479#467—718no—
480#465—718no—
481#465—718no—
482#452—718no—
483#452C2×D7118yescomplemented
484#451—718no—
485#448—718no—
486C2×#107—711no—
487C2×#107—711no—
488C2×#106—711no—
489C2×#106—711no—
490C2×#103—711no—
491C2×#103—711no—
492C2×#103—711no—
493C2×#103—711no—
494C2×#103—711no—
495C2×#103C2×D7111yescharacteristic, complemented
496C2×#102—711no—
497C2×#102C2×D7111yescharacteristic, complemented
498C2×C22⋊C8—711no—
499C2×C22⋊C8—711no—
500C2×C22⋊C8—711no—
501C2×C22⋊C8—718no—
502C2×C22⋊C8C2×D7111yescharacteristic
503C25—711no—
504C2×#41—22no—
505C2×#41—42no—
506C2×#41—42no—
507C2×#41C22×D7114yes—
508C22×Q8—2842no—
509C22×Q8—2842no—
510C22×Q8—714no—
511C22×Q8—711no—
512C22×Q8—1421no—
513C22×Q8—1422no—
514C22×Q8C22×D7111yescharacteristic
515C22×Q8C22×D7111yescharacteristic
516C22×D4—21no—
517C22×D4—1421no—
518C22×D4—1421no—
519C22×D4C22×D7111yescharacteristic
520C23×C4—21no—
521C23×C4—2842no—
522C23×C4—2842no—
523C23×C4—711no—
524C23×C4—711no—
525C23×C4—711no—
526C23×C4—714no—
527C23×C4—714no—
528C23×C4—711no—
529C23×C4—711no—
530C23×C4—1421no—
531C23×C4—1421no—
532C23×C4C22×D7111yescharacteristic
533C2×Q16—42no—
534C2×Q16—2842no—
535C2×Q16—714no—
536C2×Q16C22×D7114yescomplemented
537C2×SD16—42no—
538C2×SD16—2842no—
539C2×SD16—714no—
540C2×SD16C22×D7114yescomplemented
541C22×C8—2842no—
542C22×C8—2842no—
543C22×C8—714no—
544C22×C8—714no—
545C22×C8—711no—
546C22×C8—711no—
547C22×C8C22×D7111yescharacteristic
548C22×C8C22×D7111yescharacteristic
549#123—1428no—
550C22⋊Q8—22no—
551C22⋊Q8—714no—
552C22⋊Q8—714no—
553C22⋊Q8—714no—
554C22⋊Q8—714no—
555C22⋊Q8—714no—
556C22⋊Q8—1428no—
557C22⋊Q8—1428no—
558C22⋊Q8—1422no—
559C22⋊Q8—1422no—
560C22⋊Q8—1422no—
561C22⋊Q8—1422no—
562C22⋊Q8—1422no—
563C22⋊Q8C22×D7114yes—
564#121—714no—
565#121—714no—
566#121—1422no—
567#121—1422no—
568#120—1428no—
569C4×D4—1428no—
570C4×D4—1428no—
571#117—714no—
572#117—1422no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—711no—
575C2×C4⋊C4—711no—
576C2×C4⋊C4—711no—
577C2×C4⋊C4—714no—
578C2×C4⋊C4—1422no—
579C2×C4⋊C4—1428no—
580C2×C4⋊C4—1421no—
581C2×C4⋊C4—1421no—
582C2×C4⋊C4—1421no—
583C2×C4⋊C4—1421no—
584C2×C4⋊C4—1421no—
585C2×C4⋊C4—1421no—
586C2×C4⋊C4C22×D7111yescharacteristic
587C2×C22⋊C4—21no—
588C2×C22⋊C4—1428no—
589C2×C22⋊C4—1421no—
590C2×C22⋊C4—1421no—
591C2×C22⋊C4—1421no—
592C2×C22⋊C4—1421no—
593C2×C22⋊C4—1421no—
594C2×C22⋊C4—1421no—
595C2×C22⋊C4—1421no—
596C2×C22⋊C4—1421no—
597C2×C42—1421no—
598#107—714no—
599#107—714no—
600#106—714no—
601#106—714no—
602#103—714no—
603#103—714no—
604#103—714no—
605#103—714no—
606#103—714no—
607#103C22×D7114yescomplemented
608#102—714no—
609#102C22×D7114yescomplemented
610C22⋊C8—714no—
611C22⋊C8—714no—
612C22⋊C8—714no—
613C22⋊C8C22×D7114yes—
614C24—21no—
615C24—2842no—
616C24—714no—
617C24—711no—
618C24—711no—
619C24—1424no—
620C24—1424no—
621C24D4×D7111yescharacteristic
622#41—44no—
623#41—44no—
624#41—48no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—22no—
628C2×Q8—22no—
629C2×Q8—22no—
630C2×Q8—22no—
631C2×Q8—2844no—
632C2×Q8—2844no—
633C2×Q8—2844no—
634C2×Q8—2848no—
635C2×Q8—712no—
636C2×Q8—1424no—
637C2×Q8—1422no—
638C2×Q8—1422no—
639C2×Q8—1421no—
640C2×Q8C23×D7112yes—
641C2×Q8C23×D7112yes—
642C2×D4—24no—
643C2×D4—21no—
644C2×D4—22no—
645C2×D4—22no—
646C2×D4—44no—
647C2×D4—2844no—
648C2×D4—2844no—
649C2×D4—1424no—
650C2×D4—1424no—
651C2×D4C23×D7112yes—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—24no—
658C22×C4—44no—
659C22×C4—2842no—
660C22×C4—2842no—
661C22×C4—2844no—
662C22×C4—2844no—
663C22×C4—2848no—
664C22×C4—2844no—
665C22×C4—2844no—
666C22×C4—2842no—
667C22×C4—714no—
668C22×C4—714no—
669C22×C4—714no—
670C22×C4—711no—
671C22×C4—711no—
672C22×C4—712no—
673C22×C4—712no—
674C22×C4—712no—
675C22×C4—712no—
676C22×C4—1424no—
677C22×C4—1424no—
678C22×C4—1421no—
679C22×C4—1421no—
680C22×C4—1421no—
681C22×C4—1421no—
682C22×C4—1422no—
683C22×C4—1422no—
684C22×C4—1422no—
685C22×C4—1422no—
686C22×C4D4×D7112yes—
687C22×C4D4×D7111yescharacteristic
688C22×C4C23×D7112yes—
689C22×C4C23×D7111yescharacteristic
690Q16—44no—
691Q16—2844no—
692SD16—44no—
693SD16—2844no—
694C2×C8—22no—
695C2×C8—22no—
696C2×C8—2844no—
697C2×C8—2844no—
698C2×C8—712no—
699C2×C8—712no—
700C2×C8—1422no—
701C2×C8—1422no—
702C2×C8C23×D7112yes—
703C2×C8C23×D7112yes—
704C4⋊C4—24no—
705C4⋊C4—21no—
706C4⋊C4—712no—
707C4⋊C4—712no—
708C4⋊C4—712no—
709C4⋊C4—1424no—
710C4⋊C4—1424no—
711C4⋊C4—1424no—
712C4⋊C4—1424no—
713C4⋊C4—1424no—
714C4⋊C4—1424no—
715C4⋊C4—1421no—
716C4⋊C4—1421no—
717C4⋊C4—1421no—
718C4⋊C4C23×D7112yes—
719C22⋊C4—24no—
720C22⋊C4—1424no—
721C22⋊C4—1424no—
722C22⋊C4—1424no—
723C22⋊C4—1424no—
724C22⋊C4—1424no—
725C22⋊C4—1424no—
726C22⋊C4—1424no—
727C22⋊C4—1424no—
728C42—1424no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—2844no—
737C23—28416no—
738C23—712no—
739C23—712no—
740C23—714no—
741C23—714no—
742C23—1428no—
743C23—1428no—
744C23—1422no—
745C23—1422no—
746C23—1422no—
747C23—1422no—
748C23C2×D4×D7112yes—
749C23C2×D4×D7111yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8—42no—
755Q8—42no—
756Q8—2848no—
757Q8—2842no—
758Q8—1422no—
759Q8—1422no—
760D4—22no—
761D4—22no—
762D4—48no—
763D4—42no—
764D4—2848no—
765D4—2848no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—48no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—2844no—
778C2×C4—2844no—
779C2×C4—2848no—
780C2×C4—2848no—
781C2×C4—2842no—
782C2×C4—2842no—
783C2×C4—2842no—
784C2×C4—2842no—
785C2×C4—2844no—
786C2×C4—712no—
787C2×C4—712no—
788C2×C4—1422no—
789C2×C4—1422no—
790C2×C4—1422no—
791C2×C4—1422no—
792C2×C4—1422no—
793C2×C4—1422no—
794C2×C4—1422no—
795C2×C4—1422no—
796C2×C4—1422no—
797C2×C4—1422no—
798C2×C4—1424no—
799C2×C4—1424no—
800C2×C4C2×D4×D7112yes—
801C2×C4C2×D4×D7111yescharacteristic
802C2×C4#1455617312yes—
803C2×C4#1455617312yes—
804C2×C4C24×D7111yescharacteristic
805C8—22no—
806C8—22no—
807C8—1422no—
808C8—1422no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—44no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—84no—
817C22—28416no—
818C22—714no—
819C22—714no—
820C22—1422no—
821C22—1422no—
822C22—1422no—
823C22—1422no—
824C22—1428no—
825C22—1428no—
826C22#1798655912yes—
827C22#135×D7112yes—
828C22#137×D7112yes—
829C22C22×D4×D7111yescharacteristic
830C4—22no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—2842no—
835C4—2842no—
836C4—2842no—
837C4—2842no—
838C4—1422no—
839C4—1422no—
840C4#1798655912yes—
841C4C2×#1455617311yescharacteristic
842C4C2×#1455617311yescharacteristic
843C2—42no—
844C2—82no—
845C2—1424no—
846C2—1424no—
847C2#2259911914yesdirect product factor
848C2C2×#1798655911yescharacteristic
849C2C2×#135×D7111yescharacteristic
850C2C2×#137×D7111yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#452×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986506C2
hypercenterC2×#452D71
hypocenterC71C2×#3190
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊Q8×D71C2semidirect
3. #22599119C2direct (N × H)
4. C2×#17986341C2semidirect
5. C2×#17986337C2semidirect
6. C2×#17986328C2semidirect
7. C2×#17986311C2semidirect
8. C2×#17986239C2semidirect
9. C2×#17986237C2semidirect
10. C2×#17986227C2semidirect
11. C2×#17986225C2semidirect
12. C2×#17986161C2semidirect
13. C2×#17986153C2semidirect
14. C2×#17986136C2semidirect
15. C2×C22⋊C8×D71C2semidirect
16. C2×#452×C71C2semidirect
19. C22×#11765855C22semidirect
20. C22×#11765853C22semidirect
34. C22⋊Q8×D71C22semidirect
44. #17986341C22semidirect
45. #17986337C22semidirect
46. #17986328C22semidirect
47. #17986311C22semidirect
48. #17986239C22semidirect
49. #17986237C22semidirect
50. #17986227C22semidirect
51. #17986225C22semidirect
52. #17986161C22semidirect
53. #17986153C22semidirect
54. #17986136C22semidirect
55. C2×#14556062C22semidirect
56. C2×#14556061C22semidirect
57. C2×#14556060C22semidirect
58. C2×#14556059C22semidirect
59. C2×#14556053C22semidirect
60. C2×#14556053C22semidirect
61. C2×#14556052C22semidirect
62. C2×#14556052C22semidirect
63. C2×#14556052C22semidirect
64. C2×#14556049C22semidirect
68. C22⋊C8×D71C22semidirect
70. C22×Q16×C71C22semidirect
71. C22×SD16×C71C22semidirect
73. #452×C71C22semidirect
74. C2×#103×C71C22semidirect
75. C2×#102×C71C22semidirect
98. C2×#11765855C23semidirect
100. C2×#11765853C23semidirect
151. #14556062C23semidirect
152. #14556061C23semidirect
153. #14556060C23semidirect
154. #14556059C23semidirect
155. #14556053C23semidirect
156. #14556053C23semidirect
157. #14556052C23semidirect
158. #14556052C23semidirect
159. #14556052C23semidirect
160. #14556049C23semidirect
175. C2×Q16×C71C23semidirect
177. C2×SD16×C71C23semidirect
185. #103×C71C23semidirect
186. #102×C71C23semidirect
420. C2×C71#3190semidirect
438. C2×#452D71semidirect
442. C71C2×#3190semidirect
447. C22×Q16C2×D71semidirect
449. C22×SD16C2×D71semidirect
483. #452C2×D71semidirect
495. C2×#103C2×D71semidirect
497. C2×#102C2×D71semidirect
536. C2×Q16C22×D71semidirect
540. C2×SD16C22×D71semidirect
607. #103C22×D71semidirect
609. #102C22×D71semidirect
847. C2#22599119direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179865062
C2×C22⋊Q8×D712
#225991192
C2×#179863412
C2×#179863372
C2×#179863282
C2×#179863112
C2×#179862392
C2×#179862372
C2×#179862272
C2×#179862252
C2×#179861612
C2×#179861532
C2×#179861362
C2×C22⋊C8×D712
C2×#452×C712
C2×#319071