Finite Group Databasebeta

← C2×#22600427 #32873984

Subgroups — C2×#22600427 #32873984

Order 18176.

2298 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986707C211yesmaximal, characteristic, complemented
2C2×#17986640C211yesmaximal, characteristic
3#22600427C2116yesmaximal, direct product factor
4C2×#17986360C211yesmaximal, characteristic, complemented
5C2×#17986332C211yesmaximal, characteristic, complemented
6C2×#17986314C211yesmaximal, characteristic, complemented
7C2×#17986278C211yesmaximal, characteristic, complemented
8C2×#17986248C211yesmaximal, characteristic, complemented
9C2×#17986223C211yesmaximal, characteristic, complemented
10C2×#17986160C211yesmaximal, characteristic, complemented
11C2×#17986149C211yesmaximal, characteristic, complemented
12C2×#17986102C211yesmaximal, characteristic, complemented
13C2×#17986070C211yesmaximal, characteristic, complemented
14C2×#17985999C211yesmaximal, characteristic, complemented
15C22×#14556050C211yesmaximal, characteristic, complemented
16C2×#467×C71C211yesmaximal, characteristic, complemented
17C22×#11765866C2211yescharacteristic
18C23×D284C2211yescharacteristic
19C22×#11765852C2211yescharacteristic
20C22×#11765852C2211yescharacteristic
21C22×#11765848C2211yescharacteristic, complemented
22#17986707—24no—
23#17986707C2218yescomplemented
24#17986640—24no—
25#17986640C2218yes—
26C2×#14556127C2211yescharacteristic, complemented
27C2×#14556118—21no—
28C2×#14556117C2211yescharacteristic
29C2×#14556113—21no—
30C2×#14556108—21no—
31C2×#14556105—21no—
32C2×#14556104C2211yescharacteristic, complemented
33C2×#14556103—21no—
34C2×#14556103C2211yescharacteristic
35C2×#14556098—21no—
36C2×Q8×Dic71C2211yescharacteristic, complemented
37C2×#14556090C2211yescharacteristic
38C2×C4×C22⋊D71C2211yescharacteristic
39C2×(C22⋊D71)⋊C4—21no—
40C22×C4⋊Dic71C2211yescharacteristic
41C2×C4⋊C4×D71C2211yescharacteristic, complemented
42C2×C22⋊C4×D71—21no—
43#17986360C2218yescomplemented
44#17986332C2218yescomplemented
45#17986314C2218yescomplemented
46#17986278C2218yescomplemented
47#17986248C2218yescomplemented
48#17986223C2218yescomplemented
49#17986160C2218yescomplemented
50#17986149C2218yescomplemented
51#17986102C2218yescomplemented
52#17986070C2218yescomplemented
53C2×#14556061C2211yescharacteristic, complemented
54C2×#14556061C2211yescharacteristic, complemented
55C2×Dic71⋊C8C2211yescharacteristic, complemented
56#17985999C2218yescomplemented
57C2×#14556052C2211yescharacteristic, complemented
58C2×#14556052C2211yescharacteristic, complemented
59C2×#14556050C2211yescharacteristic
60C2×#14556050C2211yescharacteristic
61C2×#14556050C2211yescharacteristic
62C2×#14556050C2211yescharacteristic
63C2×#14556050C2218yescomplemented
64C2×#14556048C2211yescharacteristic
65C2×#14556048C2211yescharacteristic
66C2×C22⋊(C71⋊C8)C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic, complemented
68C2×#14556038C2211yescharacteristic, complemented
69C22×Q16×C71C2211yescharacteristic, complemented
70C23×C8×C71C2211yescharacteristic
71C2×C22⋊Q8×C71C2211yescharacteristic
72C2×C22⋊Q8×C71C2211yescharacteristic
73#467×C71C2218yescomplemented
74C2×#107×C71C2211yescharacteristic, complemented
75C2×#103×C71C2211yescharacteristic, complemented
76C2×#103×C71C2211yescharacteristic, complemented
77C24×D71—21no—
78C2×#11765866—22no—
79C2×#11765866—24no—
80C2×#11765866—42no—
81C2×#11765866C2314yes—
82C22×Dic142—21no—
83C22×D284—24no—
84C22×D284—21no—
85C22×D284—21no—
86C22×D284—22no—
87C22×D284—21no—
88C22×D284—42no—
89C22×D284C2311yescharacteristic
90C22×D284C2314yes—
91C22×D284C2311yescharacteristic
92C22×C22⋊D71D411yescharacteristic
93C23×Dic71—21no—
94C22×C4×D71—21no—
95C22×C4×D71—21no—
96C22×C4×D71—21no—
97C22×C4×D71C2311yescharacteristic
98C2×#11765852—24no—
99C2×#11765852—42no—
100C2×#11765852C2314yes—
101C2×#11765852C2314yes—
102C2×#11765848—42no—
103C2×#11765848C2314yescomplemented
104C22×C71⋊C8C2311yescharacteristic
105C22×C71⋊C8C2311yescharacteristic
106#14556127—22no—
107#14556127C2314yescomplemented
108#14556118—28no—
109#14556117—22no—
110#14556117C2314yes—
111#14556113—28no—
112#14556108—28no—
113#14556105—28no—
114#14556104—22no—
115#14556104C2314yescomplemented
116#14556103—22no—
117#14556103—28no—
118#14556103C2314yes—
119#14556098—28no—
120Q8×Dic71—22no—
121Q8×Dic71C2314yescomplemented
122#14556090—22no—
123#14556090C2314yes—
124C4×C22⋊D71D414yes—
125C4×C22⋊D71C2314yes—
126(C22⋊D71)⋊C4—28no—
127C2×C4⋊Dic71—21no—
128C2×C4⋊Dic71—22no—
129C2×C4⋊Dic71—21no—
130C2×C4⋊Dic71C2314yes—
131C2×C4⋊Dic71C2311yescharacteristic
132C2×C4⋊Dic71C2311yescharacteristic
133C2×Dic71⋊C4—21no—
134C2×Dic71⋊C4—21no—
135C2×Dic71⋊C4—21no—
136C2×Dic71⋊C4D411yescharacteristic
137C4⋊C4×D71—22no—
138C4⋊C4×D71C2314yescomplemented
139C2×C22⋊Dic71D411yescharacteristic
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4—21no—
142C2×(C2×D71)⋊C4—21no—
143C2×(C2×D71)⋊C4—21no—
144C2×(C2×D71)⋊C4—21no—
145C2×(C2×D71)⋊C4D411yescharacteristic
146C22⋊C4×D71—28no—
147C2×C4×Dic71—21no—
148C2×C4×Dic71C2311yescharacteristic
149#14556061C2314yescomplemented
150#14556061C2314yescomplemented
151Dic71⋊C8C2314yescomplemented
152#14556052C2314yescomplemented
153#14556052C2314yescomplemented
154#14556050C2314yes—
155#14556050C2314yes—
156#14556050C2314yes—
157#14556050C2314yes—
158#14556048C2314yes—
159#14556048C2314yes—
160C22⋊(C71⋊C8)C2314yes—
161(C2×D71)⋊C8C2314yescomplemented
162#14556038C2314yescomplemented
163C22×Q8×C71C2311yescharacteristic
164C22×Q8×C71C2311yescharacteristic
165C23×C4×C71C2311yescharacteristic
166C2×Q16×C71—42no—
167C2×Q16×C71C2314yescomplemented
168C22×C8×C71—42no—
169C22×C8×C71C2311yescharacteristic
170C22×C8×C71C2311yescharacteristic
171C22×C8×C71C2314yes—
172C22⋊Q8×C71—22no—
173C22⋊Q8×C71—22no—
174C22⋊Q8×C71C2314yes—
175C22⋊Q8×C71C2314yes—
176C2×C4⋊C4×C71—21no—
177C2×C4⋊C4×C71—21no—
178C2×C4⋊C4×C71C2311yescharacteristic
179C2×C4⋊C4×C71C2311yescharacteristic
180C2×C22⋊C4×C71—21no—
181C2×C22⋊C4×C71—21no—
182#107×C71C2314yescomplemented
183#103×C71C2314yescomplemented
184#103×C71C2314yescomplemented
185C23×D71—21no—
186C23×D71—21no—
187C23×D71—24no—
188C23×D71—44no—
189C23×D71—44no—
190C23×D71—82no—
191C23×D71C2×D411yescharacteristic
192#11765866—28no—
193#11765866—44no—
194#11765866—48no—
195C2×Dic142—24no—
196C2×Dic142—82no—
197C2×D284—21no—
198C2×D284—22no—
199C2×D284—22no—
200C2×D284—22no—
201C2×D284—28no—
202C2×D284—24no—
203C2×D284—24no—
204C2×D284—21no—
205C2×D284—24no—
206C2×D284—44no—
207C2×D284—48no—
208C2×D284—44no—
209C2×D284—44no—
210C2×D284—82no—
211C2×D284#4114yes—
212C2×D284C2412yes—
213C2×D284C2412yes—
214C2×C22⋊D71—24no—
215C2×C22⋊D71C2×D414yes—
216C22×Dic71—21no—
217C22×Dic71—21no—
218C22×Dic71—24no—
219C22×Dic71—82no—
220C22×Dic71C2×D411yescharacteristic
221C22×Dic71C2×D411yescharacteristic
222C22×Dic71C2×D411yescharacteristic
223C2×C4×D71—22no—
224C2×C4×D71—22no—
225C2×C4×D71—24no—
226C2×C4×D71—24no—
227C2×C4×D71—24no—
228C2×C4×D71—44no—
229C2×C4×D71—82no—
230C2×C4×D71—82no—
231C2×C4×D71C2×D412yes—
232C2×C4×D71C2412yes—
233#11765852—28no—
234#11765852—44no—
235#11765848—44no—
236C2×C71⋊C8—22no—
237C2×C71⋊C8—22no—
238C2×C71⋊C8C2412yes—
239C2×C71⋊C8C2412yes—
240C4⋊Dic71—21no—
241C4⋊Dic71—21no—
242C4⋊Dic71—24no—
243C4⋊Dic71—24no—
244C4⋊Dic71C2412yes—
245C4⋊Dic71C2412yes—
246Dic71⋊C4—24no—
247Dic71⋊C4—24no—
248Dic71⋊C4—24no—
249Dic71⋊C4C2×D414yes—
250C22⋊Dic71C2×D414yes—
251(C2×D71)⋊C4—24no—
252(C2×D71)⋊C4—24no—
253(C2×D71)⋊C4—24no—
254(C2×D71)⋊C4—24no—
255(C2×D71)⋊C4—24no—
256(C2×D71)⋊C4C2×D414yes—
257C4×Dic71—24no—
258C4×Dic71C2×D412yes—
259C4×Dic71C2412yes—
260C24×C71C2×D411yescharacteristic
261C2×Q8×C71—21no—
262C2×Q8×C71—21no—
263C2×Q8×C71—22no—
264C2×Q8×C71—22no—
265C2×Q8×C71—22no—
266C2×Q8×C71—22no—
267C2×Q8×C71C2412yes—
268C2×Q8×C71C2412yes—
269C22×C4×C71—22no—
270C22×C4×C71—22no—
271C22×C4×C71—21no—
272C22×C4×C71—21no—
273C22×C4×C71—21no—
274C22×C4×C71—21no—
275C22×C4×C71C2×D411yescharacteristic
276C22×C4×C71C2×D412yes—
277C22×C4×C71C2412yes—
278C22×C4×C71C2411yescharacteristic
279Q16×C71—44no—
280C2×C8×C71—22no—
281C2×C8×C71—22no—
282C2×C8×C71—44no—
283C2×C8×C71C2412yes—
284C2×C8×C71C2412yes—
285C4⋊C4×C71—24no—
286C4⋊C4×C71—24no—
287C4⋊C4×C71—21no—
288C4⋊C4×C71—21no—
289C4⋊C4×C71C2412yes—
290C4⋊C4×C71C2412yes—
291C22⋊C4×C71—24no—
292C22⋊C4×C71—24no—
293C23×C71—22no—
294C23×C71—22no—
295C23×C71#13714yes—
296C23×C71C22×D412yes—
297C23×C71C22×D411yescharacteristic
298C22×D71—22no—
299C22×D71—24no—
300C22×D71—22no—
301C22×D71—22no—
302C22×D71—22no—
303C22×D71—22no—
304C22×D71—48no—
305C22×D71—42no—
306C22×D71—42no—
307C22×D71—42no—
308C22×D71—48no—
309C22×D71—42no—
310C22×D71—42no—
311C22×D71—84no—
312C22×D71—816no—
313C22×D71C22×D412yes—
314Q8×C71—22no—
315Q8×C71—22no—
316Q8×C71—22no—
317Q8×C71—22no—
318Q8×C71—42no—
319Q8×C71—42no—
320C2×C4×C71—22no—
321C2×C4×C71—24no—
322C2×C4×C71—22no—
323C2×C4×C71—22no—
324C2×C4×C71—22no—
325C2×C4×C71—22no—
326C2×C4×C71—22no—
327C2×C4×C71—22no—
328C2×C4×C71—42no—
329C2×C4×C71—42no—
330C2×C4×C71—42no—
331C2×C4×C71—42no—
332C2×C4×C71C22×D412yes—
333C2×C4×C71C22×D411yescharacteristic
334C2×C4×C71C2×#4112yes—
335C2×C4×C71H(5,𝔽2)12yes—
336C2×C4×C71C2511yescharacteristic
337C22⋊D71—28no—
338C2×Dic71—22no—
339C2×Dic71—22no—
340C2×Dic71—22no—
341C2×Dic71—22no—
342C2×Dic71—22no—
343C2×Dic71—42no—
344C2×Dic71—42no—
345C2×Dic71—84no—
346C2×Dic71C22×D412yes—
347C2×Dic71C22×D412yes—
348C2×Dic71C22×D412yes—
349D284—24no—
350D284—22no—
351D284—22no—
352D284—22no—
353D284—48no—
354D284—48no—
355D284—42no—
356D284—84no—
357D284C2×#4114yes—
358C4×D71—24no—
359C4×D71—22no—
360C4×D71—22no—
361C4×D71—48no—
362C4×D71—84no—
363C4×D71—84no—
364Dic142—84no—
365C8×C71—22no—
366C8×C71—22no—
367C71⋊C8—22no—
368C71⋊C8—22no—
369C22×C71—22no—
370C22×C71—28no—
371C22×C71—22no—
372C22×C71#54612yes—
373C22×C71C2×#13714yes—
374C22×C71C2×#13712yes—
375C22×C71#57612yes—
376C22×C71C23×D411yescharacteristic
377C2×D71—22no—
378C2×D71—24no—
379C2×D71—22no—
380C2×D71—22no—
381C2×D71—44no—
382C2×D71—48no—
383C2×D71—42no—
384C2×D71—42no—
385C2×D71—42no—
386C2×D71—42no—
387C2×D71—42no—
388C2×D71—816no—
389C2×D71—84no—
390C4×C71—22no—
391C4×C71—42no—
392C4×C71—42no—
393C4×C71—42no—
394C4×C71—42no—
395C4×C71#54612yes—
396C4×C71C22×#4111yescharacteristic
397C4×C71C2×H(5,𝔽2)11yescharacteristic
398Dic71—22no—
399Dic71—22no—
400Dic71—22no—
401Dic71—42no—
402Dic71—42no—
403C2×#3314—711nomaximal, Sylow
404C2×C71—24no—
405C2×C71#331414yescomplemented
406C2×C71C2×#54611yescharacteristic
407C2×C71C22×#13711yescharacteristic
408C2×C71C2×#57611yescharacteristic
409D71—42no—
410D71—44no—
411D71—82no—
412C2×#554—711no—
413C2×#546—711no—
414#3314—7116no—
415C2×#489—711no—
416C2×#484—711no—
417C2×#480—711no—
418C2×#474—711no—
419C2×#468—711no—
420C2×#467D7111yescharacteristic, complemented
421C2×#464—711no—
422C2×#452—711no—
423C2×#450—711no—
424C2×#440—711no—
425C2×#435—711no—
426C2×#417—711no—
427C22×#102—711no—
428C71C2×#331411yescharacteristic, complemented, Sylow
429C22×#41—711no—
430C23×D4—711no—
431C22×Q16C2×D7111yescharacteristic, complemented
432C22×SD16—711no—
433C22×SD16—711no—
434C22×M16—711no—
435C23×C8C2×D7111yescharacteristic
436#554—718no—
437#554—1424no—
438#546—718no—
439#546—1424no—
440C2×C4⋊Q8—711no—
441C2×#125—1421no—
442C2×#124—711no—
443C2×#123—1421no—
444C2×C22⋊Q8—711no—
445C2×C22⋊Q8—1421no—
446C2×C22⋊Q8—1421no—
447C2×C22⋊Q8C2×D7111yescharacteristic
448C2×C22⋊Q8C2×D7111yescharacteristic
449C2×#121—711no—
450C2×#121—1421no—
451C2×#120—1421no—
452C2×C4×Q8—711no—
453C2×C4×D4—711no—
454C2×C4×D4—711no—
455C2×C4×D4—1421no—
456C22×C4⋊C4—711no—
457C22×C4⋊C4—711no—
458C22×C22⋊C4—1421no—
459#489—718no—
460#484—718no—
461#480—718no—
462#474—718no—
463#468—718no—
464#467C2×D7118yescomplemented
465#464—718no—
466#452—718no—
467#450—718no—
468#440—718no—
469#435—718no—
470C2×#107—711no—
471C2×#107—711no—
472C2×#107C2×D7111yescharacteristic, complemented
473C2×C4⋊C8—711no—
474#417—718no—
475C2×#103—711no—
476C2×#103—711no—
477C2×#103C2×D7111yescharacteristic, complemented
478C2×#103C2×D7111yescharacteristic, complemented
479C2×#102—711no—
480C2×#102—711no—
481C2×#102—711no—
482C2×#102—711no—
483C2×#102—718no—
484C2×#102—711no—
485C2×#102—711no—
486C2×C22⋊C8—711no—
487C2×C22⋊C8—711no—
488C2×#97—711no—
489C25—1421no—
490C2×#41—2842no—
491C2×#41—714no—
492C2×#41—1424no—
493C2×#41—1422no—
494C22×Q8—1421no—
495C22×Q8C22×D7111yescharacteristic
496C22×Q8C22×D7111yescharacteristic
497C22×D4—2842no—
498C22×D4—711no—
499C22×D4—714no—
500C22×D4—711no—
501C22×D4—711no—
502C22×D4—1421no—
503C22×D4—1424no—
504C22×D4—1421no—
505C22×D4—1421no—
506C22×D4—1422no—
507C23×C4—711no—
508C23×C4—1421no—
509C23×C4—1421no—
510C23×C4—1421no—
511C23×C4—1421no—
512C23×C4C22×D7111yescharacteristic
513C2×Q16—42no—
514C2×Q16C22×D7114yescomplemented
515C2×SD16—2842no—
516C2×SD16—714no—
517C2×SD16—714no—
518C2×SD16—1424no—
519C2×M16—2842no—
520C2×M16—714no—
521C22×C8—42no—
522C22×C8—711no—
523C22×C8—711no—
524C22×C8C22×D7111yescharacteristic
525C22×C8C22×D7111yescharacteristic
526C22×C8C22×D7114yes—
527C4⋊Q8—714no—
528C4⋊Q8—1422no—
529#125—1428no—
530#124—714no—
531#124—1422no—
532#123—1428no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—714no—
536C22⋊Q8—1428no—
537C22⋊Q8—1428no—
538C22⋊Q8—1422no—
539C22⋊Q8C22×D7114yes—
540C22⋊Q8C22×D7114yes—
541#121—714no—
542#121—1428no—
543#121—1422no—
544#120—1428no—
545C4×Q8—714no—
546C4×Q8—1422no—
547C4×D4—714no—
548C4×D4—714no—
549C4×D4—714no—
550C4×D4—1422no—
551C4×D4—1428no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—711no—
555C2×C4⋊C4—711no—
556C2×C4⋊C4—711no—
557C2×C4⋊C4—714no—
558C2×C4⋊C4—714no—
559C2×C4⋊C4—1422no—
560C2×C4⋊C4—1421no—
561C2×C4⋊C4—1421no—
562C2×C4⋊C4—1421no—
563C2×C4⋊C4—1421no—
564C2×C4⋊C4—1421no—
565C2×C4⋊C4—1422no—
566C2×C4⋊C4C22×D7111yescharacteristic
567C2×C4⋊C4C22×D7111yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—711no—
571C2×C22⋊C4—711no—
572C2×C22⋊C4—1428no—
573C2×C22⋊C4—1421no—
574C2×C22⋊C4—1421no—
575C2×C22⋊C4—1421no—
576C2×C22⋊C4—1421no—
577C2×C22⋊C4—1421no—
578C2×C42—711no—
579C2×C42—1421no—
580#107—714no—
581#107—714no—
582#107C22×D7114yescomplemented
583C4⋊C8—714no—
584#103—714no—
585#103—714no—
586#103C22×D7114yescomplemented
587#103C22×D7114yescomplemented
588#102—714no—
589#102—714no—
590#102—714no—
591#102—714no—
592#102—714no—
593#102—714no—
594C22⋊C8—714no—
595C22⋊C8—714no—
596#97—714no—
597C24—2844no—
598C24—2844no—
599C24—5682no—
600C24—711no—
601C24—1421no—
602C24—1424no—
603C24—1421no—
604C24D4×D7111yescharacteristic
605#41—2844no—
606#41—2848no—
607#41—1428no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—22no—
613C2×Q8—22no—
614C2×Q8—5682no—
615C2×Q8—1424no—
616C2×Q8C23×D7112yes—
617C2×Q8C23×D7112yes—
618C2×D4—2844no—
619C2×D4—2848no—
620C2×D4—2844no—
621C2×D4—2844no—
622C2×D4—5682no—
623C2×D4—714no—
624C2×D4—714no—
625C2×D4—712no—
626C2×D4—712no—
627C2×D4—1424no—
628C2×D4—1428no—
629C2×D4—1424no—
630C2×D4—1424no—
631C2×D4—1424no—
632C2×D4—1421no—
633C2×D4—1421no—
634C2×D4—1422no—
635C2×D4—1422no—
636C2×D4—1422no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—2844no—
644C22×C4—5682no—
645C22×C4—5682no—
646C22×C4—5682no—
647C22×C4—711no—
648C22×C4—711no—
649C22×C4—711no—
650C22×C4—712no—
651C22×C4—712no—
652C22×C4—1424no—
653C22×C4—1424no—
654C22×C4—1424no—
655C22×C4—1421no—
656C22×C4—1421no—
657C22×C4—1424no—
658C22×C4—1422no—
659C22×C4—1422no—
660C22×C4D4×D7112yes—
661C22×C4D4×D7111yescharacteristic
662C22×C4C23×D7112yes—
663C22×C4C23×D7111yescharacteristic
664Q16—44no—
665SD16—2844no—
666SD16—1428no—
667M16—2844no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—44no—
671C2×C8—712no—
672C2×C8—712no—
673C2×C8—1422no—
674C2×C8—1422no—
675C2×C8C23×D7112yes—
676C2×C8C23×D7112yes—
677C4⋊C4—24no—
678C4⋊C4—24no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—714no—
682C4⋊C4—712no—
683C4⋊C4—712no—
684C4⋊C4—1424no—
685C4⋊C4—1424no—
686C4⋊C4—1424no—
687C4⋊C4—1424no—
688C4⋊C4—1421no—
689C4⋊C4—1424no—
690C4⋊C4—1421no—
691C4⋊C4C23×D7112yes—
692C4⋊C4C23×D7112yes—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—714no—
696C22⋊C4—714no—
697C22⋊C4—1424no—
698C22⋊C4—1424no—
699C22⋊C4—1424no—
700C22⋊C4—1424no—
701C22⋊C4—1424no—
702C42—712no—
703C42—712no—
704C42—1424no—
705C23—22no—
706C23—22no—
707C23—2848no—
708C23—2842no—
709C23—2842no—
710C23—2842no—
711C23—2848no—
712C23—2842no—
713C23—2842no—
714C23—5684no—
715C23—56816no—
716C23—712no—
717C23—1422no—
718C23—1422no—
719C23—1424no—
720C23—1422no—
721C23—1422no—
722C23—1422no—
723C23#1455616014yes—
724C23C2×D4×D7112yes—
725C23C2×D4×D7111yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—22no—
729Q8—22no—
730Q8—42no—
731Q8—42no—
732Q8—5684no—
733D4—2848no—
734D4—2848no—
735D4—2842no—
736D4—5684no—
737D4—714no—
738D4—1428no—
739D4—1422no—
740D4—1422no—
741D4—1422no—
742D4—1424no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—2848no—
756C2×C4—2842no—
757C2×C4—2842no—
758C2×C4—5684no—
759C2×C4—5684no—
760C2×C4—5684no—
761C2×C4—712no—
762C2×C4—712no—
763C2×C4—712no—
764C2×C4—1422no—
765C2×C4—1422no—
766C2×C4—1422no—
767C2×C4—1422no—
768C2×C4—1422no—
769C2×C4—1422no—
770C2×C4—1422no—
771C2×C4—1424no—
772C2×C4C2×D4×D7112yes—
773C2×C4C2×D4×D7111yescharacteristic
774C2×C4#41×D7112yes—
775C2×C4#1455617312yes—
776C2×C4C24×D7111yescharacteristic
777C8—22no—
778C8—22no—
779C8—1422no—
780C8—1422no—
781C22—22no—
782C22—22no—
783C22—28no—
784C22—2842no—
785C22—2842no—
786C22—2848no—
787C22—2844no—
788C22—2842no—
789C22—2842no—
790C22—2842no—
791C22—56816no—
792C22—5684no—
793C22—1424no—
794C22—1422no—
795C22—1422no—
796C22—1422no—
797C22#1798663812yes—
798C22C2×#1455616014yes—
799C22C2×#1455616012yes—
800C22#1798680112yes—
801C22C22×D4×D7111yescharacteristic
802C4—22no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—2842no—
808C4—2842no—
809C4—1422no—
810C4—1422no—
811C4—1422no—
812C4#1798663812yes—
813C4C2×#41×D7111yescharacteristic
814C4C2×#1455617311yescharacteristic
815C2—24no—
816C2—2844no—
817C2—2842no—
818C2—5682no—
819C2#2260042714yesdirect product factor
820C2C2×#1798663811yescharacteristic
821C2C22×#1455616011yescharacteristic
822C2C2×#1798680111yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#467×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986640C2
hypercenterC2×#467D71
hypocenterC71C2×#3314
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C2×#17986707C2semidirect
3. #22600427C2direct (N × H)
4. C2×#17986360C2semidirect
5. C2×#17986332C2semidirect
6. C2×#17986314C2semidirect
7. C2×#17986278C2semidirect
8. C2×#17986248C2semidirect
9. C2×#17986223C2semidirect
10. C2×#17986160C2semidirect
11. C2×#17986149C2semidirect
12. C2×#17986102C2semidirect
13. C2×#17986070C2semidirect
14. C2×#17985999C2semidirect
15. C22×#14556050C2semidirect
16. C2×#467×C71C2semidirect
21. C22×#11765848C22semidirect
23. #17986707C22semidirect
26. C2×#14556127C22semidirect
32. C2×#14556104C22semidirect
36. C2×Q8×Dic71C22semidirect
41. C2×C4⋊C4×D71C22semidirect
43. #17986360C22semidirect
44. #17986332C22semidirect
45. #17986314C22semidirect
46. #17986278C22semidirect
47. #17986248C22semidirect
48. #17986223C22semidirect
49. #17986160C22semidirect
50. #17986149C22semidirect
51. #17986102C22semidirect
52. #17986070C22semidirect
53. C2×#14556061C22semidirect
54. C2×#14556061C22semidirect
55. C2×Dic71⋊C8C22semidirect
56. #17985999C22semidirect
57. C2×#14556052C22semidirect
58. C2×#14556052C22semidirect
63. C2×#14556050C22semidirect
67. C2×(C2×D71)⋊C8C22semidirect
68. C2×#14556038C22semidirect
69. C22×Q16×C71C22semidirect
73. #467×C71C22semidirect
74. C2×#107×C71C22semidirect
75. C2×#103×C71C22semidirect
76. C2×#103×C71C22semidirect
103. C2×#11765848C23semidirect
107. #14556127C23semidirect
115. #14556104C23semidirect
121. Q8×Dic71C23semidirect
138. C4⋊C4×D71C23semidirect
149. #14556061C23semidirect
150. #14556061C23semidirect
151. Dic71⋊C8C23semidirect
152. #14556052C23semidirect
153. #14556052C23semidirect
161. (C2×D71)⋊C8C23semidirect
162. #14556038C23semidirect
167. C2×Q16×C71C23semidirect
182. #107×C71C23semidirect
183. #103×C71C23semidirect
184. #103×C71C23semidirect
405. C2×C71#3314semidirect
420. C2×#467D71semidirect
428. C71C2×#3314semidirect
431. C22×Q16C2×D71semidirect
464. #467C2×D71semidirect
472. C2×#107C2×D71semidirect
477. C2×#103C2×D71semidirect
478. C2×#103C2×D71semidirect
514. C2×Q16C22×D71semidirect
582. #107C22×D71semidirect
586. #103C22×D71semidirect
587. #103C22×D71semidirect
819. C2#22600427direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867072
C2×#179866402
#226004272
C2×#179863602
C2×#179863322
C2×#179863142
C2×#179862782
C2×#179862482
C2×#179862232
C2×#179861602
C2×#179861492
C2×#179861022
C2×#179860702
C2×#179859992
C22×#145560502
C2×#467×C712
C2×#331471