Finite Group Databasebeta

← C2×#22599843 #32872426

Subgroups — C2×#22599843 #32872426

Order 18176.

2882 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556160C211yesmaximal, characteristic, complemented
2C23×#11765852C211yesmaximal, characteristic, complemented
3C2×Q8×C22⋊D71C211yesmaximal, characteristic, complemented
4C2×#17986640C211yesmaximal, characteristic
5#22599843C2116yesmaximal, direct product factor
6C2×#17986392C211yesmaximal, characteristic, complemented
7C2×#17986248C211yesmaximal, characteristic, complemented
8C2×#17986238C211yesmaximal, characteristic, complemented
9C2×#17986223C211yesmaximal, characteristic, complemented
10C2×#17986203C211yesmaximal, characteristic, complemented
11C2×#17986160C211yesmaximal, characteristic, complemented
12C2×#17986139C211yesmaximal, characteristic, complemented
13C2×#17986152C211yesmaximal, characteristic, complemented
14C2×#17986102C211yesmaximal, characteristic, complemented
15C2×#17986067C211yesmaximal, characteristic, complemented
16C2×#451×C71C211yesmaximal, characteristic, complemented
17C22×#11765866C2211yescharacteristic
18C22×Q8×D71C2211yescharacteristic, complemented
19C23×D284C2211yescharacteristic
20C2×#14556160—28no—
21C2×#14556160C2218yescomplemented
22C22×#11765855C2211yescharacteristic, complemented
23C22×#11765854C2211yescharacteristic
24C22×#11765854C2211yescharacteristic
25C22×#11765852—28no—
26C22×#11765852C2211yescharacteristic
27C22×#11765852C2211yescharacteristic
28C22×#11765852C2211yescharacteristic
29C22×#11765852C2211yescharacteristic
30C22×#11765852C2218yescomplemented
31C22×#11765848C2211yescharacteristic, complemented
32C23×C71⋊C8C2211yescharacteristic
33Q8×C22⋊D71—24no—
34Q8×C22⋊D71C2218yescomplemented
35#17986640—24no—
36#17986640C2218yes—
37C2×#14556126—21no—
38C2×#14556126C2211yescharacteristic, complemented
39C2×#14556117C2211yescharacteristic
40C2×#14556113—21no—
41C2×#14556107—21no—
42C2×#14556107C2211yescharacteristic
43C2×#14556104—21no—
44C2×#14556104C2211yescharacteristic, complemented
45C2×#14556103—21no—
46C2×#14556103C2211yescharacteristic
47C2×#14556098—21no—
48C2×Q8×Dic71C2211yescharacteristic, complemented
49C2×#14556090C2211yescharacteristic
50C2×C4×C22⋊D71—21no—
51C2×C4×C22⋊D71C2211yescharacteristic
52C2×C22⋊C4×D71—21no—
53#17986392C2218yescomplemented
54#17986248C2218yescomplemented
55#17986238C2218yescomplemented
56#17986223C2218yescomplemented
57#17986203C2218yescomplemented
58#17986160C2218yescomplemented
59#17986152C2218yescomplemented
60#17986139C2218yescomplemented
61#17986102C2218yescomplemented
62#17986067C2218yescomplemented
63C2×#14556061C2211yescharacteristic, complemented
64C2×Dic71⋊C8C2211yescharacteristic, complemented
65C2×#14556052C2211yescharacteristic, complemented
66C2×#14556051C2211yescharacteristic, complemented
67C2×#14556050C2211yescharacteristic
68C2×#14556050C2211yescharacteristic
69C2×(C2×D71)⋊C8C2211yescharacteristic, complemented
70C2×#14556038C2211yescharacteristic, complemented
71C23×Q8×C71C2211yescharacteristic
72C22×Q16×C71C2211yescharacteristic, complemented
73C22×Q16×C71C2211yescharacteristic, complemented
74C2×C22⋊Q8×C71C2211yescharacteristic
75#451×C71C2218yescomplemented
76C2×#103×C71C2211yescharacteristic, complemented
77C2×#103×C71C2211yescharacteristic, complemented
78C2×C22⋊C8×C71C2211yescharacteristic
79C24×D71—21no—
80C2×#11765866—22no—
81C2×#11765866—24no—
82C2×#11765866—42no—
83C2×#11765866C2314yes—
84C22×Dic142—21no—
85C22×Dic142C2311yescharacteristic
86C2×Q8×D71—22no—
87C2×Q8×D71—24no—
88C2×Q8×D71—42no—
89C2×Q8×D71C2314yescomplemented
90C22×D284—24no—
91C22×D284—21no—
92C22×D284—21no—
93C22×D284—22no—
94C22×D284—21no—
95C22×D284—42no—
96C22×D284C2311yescharacteristic
97C22×D284C2314yes—
98C22×D284C2311yescharacteristic
99C22×C22⋊D71D411yescharacteristic
100C22×C4×D71—21no—
101C22×C4×D71—21no—
102C22×C4×D71—21no—
103C22×C4×D71C2311yescharacteristic
104#14556160—232no—
105C2×#11765855—24no—
106C2×#11765855C2314yescomplemented
107C2×#11765854—24no—
108C2×#11765854—42no—
109C2×#11765854C2314yes—
110C2×#11765854C2314yes—
111C2×#11765852—24no—
112C2×#11765852—232no—
113C2×#11765852—24no—
114C2×#11765852—24no—
115C2×#11765852D418yescomplemented
116C2×#11765852C2314yes—
117C2×#11765852C2314yes—
118C2×#11765852C2314yes—
119C2×#11765852C2314yes—
120C2×#11765848—24no—
121C2×#11765848C2314yescomplemented
122C22×C71⋊C8—24no—
123C22×C71⋊C8C2314yes—
124C22×C71⋊C8C2311yescharacteristic
125C22×C71⋊C8C2311yescharacteristic
126#14556126—28no—
127#14556126—22no—
128#14556126C2314yescomplemented
129#14556117—22no—
130#14556117C2314yes—
131#14556113—28no—
132#14556107—28no—
133#14556107—22no—
134#14556107C2314yes—
135#14556104—22no—
136#14556104—28no—
137#14556104C2314yescomplemented
138#14556103—22no—
139#14556103—28no—
140#14556103C2314yes—
141#14556098—28no—
142Q8×Dic71—22no—
143Q8×Dic71C2314yescomplemented
144#14556090—22no—
145#14556090C2314yes—
146C4×C22⋊D71—28no—
147C4×C22⋊D71D414yes—
148C4×C22⋊D71C2314yes—
149C2×C4⋊Dic71—21no—
150C2×C4⋊Dic71C2311yescharacteristic
151C2×Dic71⋊C4—21no—
152C2×Dic71⋊C4—21no—
153C2×Dic71⋊C4—21no—
154C2×Dic71⋊C4—21no—
155C2×Dic71⋊C4D411yescharacteristic
156C2×C22⋊Dic71—21no—
157C2×C22⋊Dic71D411yescharacteristic
158C2×(C2×D71)⋊C4—21no—
159C2×(C2×D71)⋊C4—21no—
160C2×(C2×D71)⋊C4—21no—
161C2×(C2×D71)⋊C4—21no—
162C2×(C2×D71)⋊C4—21no—
163C2×(C2×D71)⋊C4D411yescharacteristic
164C22⋊C4×D71—28no—
165C2×C4×Dic71—21no—
166C2×C4×Dic71C2311yescharacteristic
167#14556061C2314yescomplemented
168Dic71⋊C8C2314yescomplemented
169#14556052C2314yescomplemented
170#14556051C2314yescomplemented
171#14556050C2314yes—
172#14556050C2314yes—
173(C2×D71)⋊C8C2314yescomplemented
174#14556038C2314yescomplemented
175C22×Q8×C71—22no—
176C22×Q8×C71—21no—
177C22×Q8×C71—24no—
178C22×Q8×C71—42no—
179C22×Q8×C71C2311yescharacteristic
180C22×Q8×C71C2311yescharacteristic
181C22×Q8×C71C2314yes—
182C22×Q8×C71C2311yescharacteristic
183C23×C4×C71—21no—
184C23×C4×C71C2311yescharacteristic
185C2×Q16×C71—24no—
186C2×Q16×C71—42no—
187C2×Q16×C71C2314yescomplemented
188C2×Q16×C71C2314yescomplemented
189C22×C8×C71C2311yescharacteristic
190C22×C8×C71C2311yescharacteristic
191C22⋊Q8×C71—22no—
192C22⋊Q8×C71C2314yes—
193C2×C4⋊C4×C71—21no—
194C2×C4⋊C4×C71C2311yescharacteristic
195C2×C22⋊C4×C71—21no—
196#103×C71C2314yescomplemented
197#103×C71C2314yescomplemented
198C22⋊C8×C71C2314yes—
199C23×D71—21no—
200C23×D71—21no—
201C23×D71—24no—
202C23×D71—44no—
203C23×D71—44no—
204C23×D71—82no—
205C23×D71C2×D411yescharacteristic
206#11765866—28no—
207#11765866—44no—
208#11765866—48no—
209C2×Dic142—22no—
210C2×Dic142—22no—
211C2×Dic142—21no—
212C2×Dic142—24no—
213C2×Dic142—44no—
214C2×Dic142C2412yes—
215Q8×D71—28no—
216Q8×D71—44no—
217Q8×D71—48no—
218C2×D284—21no—
219C2×D284—22no—
220C2×D284—22no—
221C2×D284—22no—
222C2×D284—28no—
223C2×D284—24no—
224C2×D284—24no—
225C2×D284—21no—
226C2×D284—24no—
227C2×D284—44no—
228C2×D284—48no—
229C2×D284—44no—
230C2×D284—44no—
231C2×D284—82no—
232C2×D284C2×D414yes—
233C2×D284C2412yes—
234C2×D284C2412yes—
235C2×C22⋊D71—24no—
236C2×C22⋊D71C2×D414yes—
237C22×Dic71—21no—
238C22×Dic71—21no—
239C22×Dic71C2×D411yescharacteristic
240C22×Dic71C2×D411yescharacteristic
241C22×Dic71C2×D411yescharacteristic
242C2×C4×D71—22no—
243C2×C4×D71—22no—
244C2×C4×D71—24no—
245C2×C4×D71—24no—
246C2×C4×D71—24no—
247C2×C4×D71—44no—
248C2×C4×D71—44no—
249C2×C4×D71—82no—
250C2×C4×D71C2×D412yes—
251C2×C4×D71C2412yes—
252#11765855—28no—
253#11765854—28no—
254#11765854—44no—
255#11765852—28no—
256#11765852—28no—
257#11765852—28no—
258#11765852C2×D4116yescomplemented
259#11765848—28no—
260C2×C71⋊C8—22no—
261C2×C71⋊C8—28no—
262C2×C71⋊C8C2×D414yes—
263C2×C71⋊C8C2412yes—
264C2×C71⋊C8C2412yes—
265C4⋊Dic71—21no—
266C4⋊Dic71—24no—
267C4⋊Dic71C2412yes—
268Dic71⋊C4—24no—
269Dic71⋊C4—24no—
270Dic71⋊C4—24no—
271Dic71⋊C4—24no—
272Dic71⋊C4C2×D414yes—
273C22⋊Dic71—24no—
274C22⋊Dic71C2×D414yes—
275(C2×D71)⋊C4—24no—
276(C2×D71)⋊C4—24no—
277(C2×D71)⋊C4—24no—
278(C2×D71)⋊C4—24no—
279(C2×D71)⋊C4—24no—
280(C2×D71)⋊C4C2×D414yes—
281C4×Dic71—24no—
282C4×Dic71C2×D412yes—
283C4×Dic71C2412yes—
284C24×C71C2×D411yescharacteristic
285C2×Q8×C71—21no—
286C2×Q8×C71—21no—
287C2×Q8×C71—24no—
288C2×Q8×C71—21no—
289C2×Q8×C71—22no—
290C2×Q8×C71—28no—
291C2×Q8×C71—22no—
292C2×Q8×C71—22no—
293C2×Q8×C71—22no—
294C2×Q8×C71—22no—
295C2×Q8×C71—44no—
296C2×Q8×C71—44no—
297C2×Q8×C71—48no—
298C2×Q8×C71C2×D414yes—
299C2×Q8×C71C2412yes—
300C2×Q8×C71C2412yes—
301C2×Q8×C71C2412yes—
302C22×C4×C71—21no—
303C22×C4×C71—22no—
304C22×C4×C71—22no—
305C22×C4×C71—21no—
306C22×C4×C71—21no—
307C22×C4×C71—21no—
308C22×C4×C71—24no—
309C22×C4×C71—44no—
310C22×C4×C71C2×D411yescharacteristic
311C22×C4×C71C2×D412yes—
312C22×C4×C71C2412yes—
313C22×C4×C71C2411yescharacteristic
314Q16×C71—28no—
315Q16×C71—44no—
316C2×C8×C71—22no—
317C2×C8×C71—22no—
318C2×C8×C71C2412yes—
319C2×C8×C71C2412yes—
320C4⋊C4×C71—24no—
321C4⋊C4×C71—21no—
322C4⋊C4×C71C2412yes—
323C22⋊C4×C71—24no—
324C23×C71—22no—
325C23×C71—22no—
326C23×C71#13714yescomplemented
327C23×C71C22×D412yes—
328C23×C71C22×D411yescharacteristic
329C22×D71—22no—
330C22×D71—24no—
331C22×D71—22no—
332C22×D71—22no—
333C22×D71—22no—
334C22×D71—22no—
335C22×D71—48no—
336C22×D71—42no—
337C22×D71—42no—
338C22×D71—42no—
339C22×D71—42no—
340C22×D71—48no—
341C22×D71—42no—
342C22×D71—84no—
343C22×D71—816no—
344C22×D71C22×D412yes—
345Q8×C71—24no—
346Q8×C71—22no—
347Q8×C71—22no—
348Q8×C71—22no—
349Q8×C71—22no—
350Q8×C71—22no—
351Q8×C71—48no—
352Q8×C71—42no—
353Q8×C71—42no—
354Q8×C71C22×D414yes—
355C2×C4×C71—22no—
356C2×C4×C71—24no—
357C2×C4×C71—22no—
358C2×C4×C71—24no—
359C2×C4×C71—22no—
360C2×C4×C71—22no—
361C2×C4×C71—22no—
362C2×C4×C71—22no—
363C2×C4×C71—22no—
364C2×C4×C71—48no—
365C2×C4×C71—42no—
366C2×C4×C71—42no—
367C2×C4×C71—42no—
368C2×C4×C71C22×D412yes—
369C2×C4×C71C22×D411yescharacteristic
370C2×C4×C71C22×D412yes—
371C2×C4×C71H(5,𝔽2)12yes—
372C2×C4×C71C2511yescharacteristic
373C22⋊D71—28no—
374C2×Dic71—22no—
375C2×Dic71—22no—
376C2×Dic71—22no—
377C2×Dic71—22no—
378C2×Dic71—22no—
379C2×Dic71—42no—
380C2×Dic71—42no—
381C2×Dic71C22×D412yes—
382C2×Dic71C22×D412yes—
383C2×Dic71C22×D412yes—
384D284—24no—
385D284—22no—
386D284—22no—
387D284—22no—
388D284—48no—
389D284—48no—
390D284—42no—
391D284—84no—
392D284C22×D414yes—
393C4×D71—24no—
394C4×D71—22no—
395C4×D71—22no—
396C4×D71—48no—
397C4×D71—48no—
398C4×D71—84no—
399Dic142—22no—
400Dic142—22no—
401Dic142—48no—
402Dic142—42no—
403C8×C71—22no—
404C8×C71—22no—
405C71⋊C8—22no—
406C71⋊C8C22×D414yes—
407C22×C71—22no—
408C22×C71—28no—
409C22×C71—22no—
410C22×C71D4212yes—
411C22×C71C2×#13712yes—
412C22×C71C2×#13714yescomplemented
413C22×C71#57712yes—
414C22×C71C23×D411yescharacteristic
415C2×D71—22no—
416C2×D71—24no—
417C2×D71—22no—
418C2×D71—22no—
419C2×D71—44no—
420C2×D71—48no—
421C2×D71—42no—
422C2×D71—42no—
423C2×D71—42no—
424C2×D71—42no—
425C2×D71—42no—
426C2×D71—816no—
427C2×D71—84no—
428C4×C71—24no—
429C4×C71—22no—
430C4×C71—42no—
431C4×C71—42no—
432C4×C71—42no—
433C4×C71D4212yes—
434C4×C71C23×D411yescharacteristic
435C4×C71C2×H(5,𝔽2)11yescharacteristic
436Dic71—22no—
437Dic71—22no—
438Dic71—22no—
439Dic71—42no—
440Dic71—42no—
441C2×#3266—711nomaximal, Sylow
442C2×C71—24no—
443C2×C71#326614yescomplemented
444C2×C71C2×D4211yescharacteristic
445C2×C71C22×#13711yescharacteristic
446C2×C71C2×#57711yescharacteristic
447D71—42no—
448D71—44no—
449D71—82no—
450C22×#137—711no—
451C23×SD16—711no—
452C2×D4×Q8—711no—
453C2×#546—711no—
454#3266—7116no—
455C2×#497—711no—
456C2×#468—711no—
457C2×#467—711no—
458C2×#464—711no—
459C2×#461—711no—
460C2×#452—711no—
461C2×#451D7111yescharacteristic, complemented
462C2×#448—711no—
463C2×#450—711no—
464C2×#440—711no—
465C2×#435—711no—
466C71C2×#326611yescharacteristic, complemented, Sylow
467C22×#41—711no—
468C23×Q8—711no—
469C23×Q8C2×D7111yescharacteristic
470C23×D4—711no—
471C2×#137—718no—
472C2×#137—1428no—
473C22×Q16—711no—
474C22×Q16C2×D7111yescharacteristic, complemented
475C22×Q16C2×D7111yescharacteristic, complemented
476C22×SD16—711no—
477C22×SD16—711no—
478C22×SD16—711no—
479C22×SD16—711no—
480C22×SD16—718no—
481C22×SD16—711no—
482C22×SD16—711no—
483C22×SD16—1428no—
484C22×M16—711no—
485C23×C8—711no—
486D4×Q8—718no—
487D4×Q8—1424no—
488#546—718no—
489#546—1424no—
490C2×C4⋊Q8—711no—
491C2×C4⋊Q8—1421no—
492C2×#124—711no—
493C2×#123—1421no—
494C2×C22⋊Q8—711no—
495C2×C22⋊Q8—711no—
496C2×C22⋊Q8—1421no—
497C2×C22⋊Q8—1421no—
498C2×C22⋊Q8C2×D7111yescharacteristic
499C2×#121—711no—
500C2×#121—1421no—
501C2×#120—1421no—
502C2×C4×Q8—711no—
503C2×C4×D4—711no—
504C2×C4×D4—711no—
505C2×C4×D4—1421no—
506C22×C22⋊C4—1421no—
507#497—718no—
508#468—718no—
509#467—718no—
510#464—718no—
511#461—718no—
512#452—718no—
513#451C2×D7118yescomplemented
514#450—718no—
515#448—718no—
516#440—718no—
517#435—718no—
518C2×#107—711no—
519C2×C4⋊C8—711no—
520C2×#103—711no—
521C2×#103—711no—
522C2×#103C2×D7111yescharacteristic, complemented
523C2×#103C2×D7111yescharacteristic, complemented
524C2×#102—711no—
525C2×#102—711no—
526C2×C22⋊C8—711no—
527C2×C22⋊C8C2×D7111yescharacteristic
528C2×#97—711no—
529C25—1421no—
530C2×#41—2842no—
531C2×#41—714no—
532C2×#41—1424no—
533C2×#41—1422no—
534C22×Q8—21no—
535C22×Q8—22no—
536C22×Q8—24no—
537C22×Q8—42no—
538C22×Q8—2842no—
539C22×Q8—714no—
540C22×Q8—711no—
541C22×Q8—1421no—
542C22×Q8—1424no—
543C22×Q8—1422no—
544C22×Q8C22×D7111yescharacteristic
545C22×Q8C22×D7111yescharacteristic
546C22×Q8C22×D7114yes—
547C22×Q8C22×D7111yescharacteristic
548C22×D4—2842no—
549C22×D4—711no—
550C22×D4—714no—
551C22×D4—711no—
552C22×D4—711no—
553C22×D4—1421no—
554C22×D4—1424no—
555C22×D4—1421no—
556C22×D4—1421no—
557C22×D4—1422no—
558C23×C4—21no—
559C23×C4—711no—
560C23×C4—1421no—
561C23×C4—1421no—
562C23×C4—1421no—
563C23×C4C22×D7111yescharacteristic
564#137—14232no—
565C2×Q16—24no—
566C2×Q16—42no—
567C2×Q16—714no—
568C2×Q16—1424no—
569C2×Q16C22×D7114yescomplemented
570C2×Q16C22×D7114yescomplemented
571C2×SD16—2842no—
572C2×SD16—718no—
573C2×SD16—714no—
574C2×SD16—714no—
575C2×SD16—714no—
576C2×SD16—714no—
577C2×SD16—714no—
578C2×SD16—714no—
579C2×SD16—1424no—
580C2×SD16—1424no—
581C2×SD16—14232no—
582C2×SD16—1424no—
583C2×SD16—1424no—
584C2×M16—714no—
585C2×M16—1424no—
586C22×C8—711no—
587C22×C8—711no—
588C22×C8—714no—
589C22×C8—1424no—
590C22×C8C22×D7111yescharacteristic
591C22×C8C22×D7111yescharacteristic
592C4⋊Q8—714no—
593C4⋊Q8—1422no—
594C4⋊Q8—1428no—
595#124—714no—
596#124—1422no—
597#123—1428no—
598C22⋊Q8—22no—
599C22⋊Q8—714no—
600C22⋊Q8—714no—
601C22⋊Q8—1428no—
602C22⋊Q8—1428no—
603C22⋊Q8—1422no—
604C22⋊Q8—1422no—
605C22⋊Q8C22×D7114yes—
606#121—714no—
607#121—1428no—
608#121—1422no—
609#120—1428no—
610C4×Q8—714no—
611C4×Q8—1422no—
612C4×D4—714no—
613C4×D4—714no—
614C4×D4—714no—
615C4×D4—1422no—
616C4×D4—1428no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—711no—
619C2×C4⋊C4—711no—
620C2×C4⋊C4—1421no—
621C2×C4⋊C4—1421no—
622C2×C4⋊C4—1421no—
623C2×C4⋊C4—1421no—
624C2×C4⋊C4—1421no—
625C2×C4⋊C4C22×D7111yescharacteristic
626C2×C22⋊C4—21no—
627C2×C22⋊C4—711no—
628C2×C22⋊C4—711no—
629C2×C22⋊C4—1428no—
630C2×C22⋊C4—1421no—
631C2×C22⋊C4—1421no—
632C2×C22⋊C4—1421no—
633C2×C22⋊C4—1421no—
634C2×C22⋊C4—1421no—
635C2×C22⋊C4—1421no—
636C2×C42—711no—
637C2×C42—1421no—
638#107—714no—
639C4⋊C8—714no—
640#103—714no—
641#103—714no—
642#103C22×D7114yescomplemented
643#103C22×D7114yescomplemented
644#102—714no—
645#102—714no—
646C22⋊C8—714no—
647C22⋊C8C22×D7114yes—
648#97—714no—
649C24—2844no—
650C24—2844no—
651C24—5682no—
652C24—711no—
653C24—1421no—
654C24—1424no—
655C24—1421no—
656C24D4×D7111yescharacteristic
657#41—2844no—
658#41—2848no—
659#41—1428no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—24no—
663C2×Q8—21no—
664C2×Q8—22no—
665C2×Q8—28no—
666C2×Q8—22no—
667C2×Q8—22no—
668C2×Q8—22no—
669C2×Q8—22no—
670C2×Q8—44no—
671C2×Q8—44no—
672C2×Q8—48no—
673C2×Q8—2844no—
674C2×Q8—2848no—
675C2×Q8—2844no—
676C2×Q8—712no—
677C2×Q8—1424no—
678C2×Q8—1428no—
679C2×Q8—1422no—
680C2×Q8—1422no—
681C2×Q8—1421no—
682C2×Q8D4×D7114yes—
683C2×Q8C23×D7112yes—
684C2×Q8C23×D7112yes—
685C2×Q8C23×D7112yes—
686C2×D4—2844no—
687C2×D4—2848no—
688C2×D4—2844no—
689C2×D4—2844no—
690C2×D4—5682no—
691C2×D4—714no—
692C2×D4—714no—
693C2×D4—712no—
694C2×D4—712no—
695C2×D4—1424no—
696C2×D4—1428no—
697C2×D4—1424no—
698C2×D4—1424no—
699C2×D4—1424no—
700C2×D4—1421no—
701C2×D4—1422no—
702C2×D4—1421no—
703C2×D4—1422no—
704C2×D4—1422no—
705C22×C4—21no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—24no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—44no—
713C22×C4—2844no—
714C22×C4—2844no—
715C22×C4—5682no—
716C22×C4—711no—
717C22×C4—711no—
718C22×C4—711no—
719C22×C4—712no—
720C22×C4—712no—
721C22×C4—1424no—
722C22×C4—1424no—
723C22×C4—1424no—
724C22×C4—1421no—
725C22×C4—1421no—
726C22×C4—1422no—
727C22×C4—1422no—
728C22×C4D4×D7112yes—
729C22×C4D4×D7111yescharacteristic
730C22×C4C23×D7112yes—
731C22×C4C23×D7111yescharacteristic
732Q16—28no—
733Q16—44no—
734Q16—1428no—
735SD16—2844no—
736SD16—7116no—
737SD16—1428no—
738SD16—1428no—
739SD16—1428no—
740SD16—1428no—
741M16—1428no—
742C2×C8—22no—
743C2×C8—22no—
744C2×C8—714no—
745C2×C8—712no—
746C2×C8—712no—
747C2×C8—1428no—
748C2×C8—1422no—
749C2×C8C23×D7112yes—
750C2×C8C23×D7112yes—
751C4⋊C4—24no—
752C4⋊C4—21no—
753C4⋊C4—714no—
754C4⋊C4—712no—
755C4⋊C4—1424no—
756C4⋊C4—1424no—
757C4⋊C4—1424no—
758C4⋊C4—1424no—
759C4⋊C4—1424no—
760C4⋊C4—1421no—
761C4⋊C4C23×D7112yes—
762C22⋊C4—24no—
763C22⋊C4—714no—
764C22⋊C4—714no—
765C22⋊C4—1424no—
766C22⋊C4—1424no—
767C22⋊C4—1424no—
768C22⋊C4—1424no—
769C22⋊C4—1424no—
770C22⋊C4—1424no—
771C42—712no—
772C42—712no—
773C42—1424no—
774C23—22no—
775C23—22no—
776C23—2848no—
777C23—2842no—
778C23—2842no—
779C23—2842no—
780C23—2842no—
781C23—2848no—
782C23—2842no—
783C23—5684no—
784C23—56816no—
785C23—712no—
786C23—1422no—
787C23—1422no—
788C23—1422no—
789C23—1424no—
790C23—1422no—
791C23—1422no—
792C23#1455616014yescomplemented
793C23C2×D4×D7112yes—
794C23C2×D4×D7111yescharacteristic
795Q8—22no—
796Q8—24no—
797Q8—22no—
798Q8—22no—
799Q8—22no—
800Q8—22no—
801Q8—48no—
802Q8—42no—
803Q8—42no—
804Q8—2848no—
805Q8—2842no—
806Q8—1422no—
807Q8—1422no—
808Q8C2×D4×D7114yes—
809D4—2848no—
810D4—2848no—
811D4—2842no—
812D4—5684no—
813D4—714no—
814D4—1428no—
815D4—1422no—
816D4—1422no—
817D4—1422no—
818D4—1424no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—24no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—24no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—48no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—2848no—
833C2×C4—2848no—
834C2×C4—2842no—
835C2×C4—2842no—
836C2×C4—5684no—
837C2×C4—712no—
838C2×C4—712no—
839C2×C4—712no—
840C2×C4—1422no—
841C2×C4—1422no—
842C2×C4—1422no—
843C2×C4—1422no—
844C2×C4—1422no—
845C2×C4—1422no—
846C2×C4—1422no—
847C2×C4—1424no—
848C2×C4C2×D4×D7112yes—
849C2×C4C2×D4×D7112yes—
850C2×C4C2×D4×D7111yescharacteristic
851C2×C4#1455617312yes—
852C2×C4C24×D7111yescharacteristic
853C8—22no—
854C8—22no—
855C8—714no—
856C8—1422no—
857C22—22no—
858C22—22no—
859C22—28no—
860C22—2842no—
861C22—2842no—
862C22—2848no—
863C22—2844no—
864C22—2842no—
865C22—2842no—
866C22—2842no—
867C22—56816no—
868C22—5684no—
869C22—1422no—
870C22—1424no—
871C22—1422no—
872C22—1422no—
873C22#1798663112yes—
874C22C2×#1455616012yes—
875C22C2×#1455616014yescomplemented
876C22#1798680812yes—
877C22C22×D4×D7111yescharacteristic
878C4—22no—
879C4—24no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—2842no—
884C4—2842no—
885C4—1422no—
886C4—1422no—
887C4—1422no—
888C4#1798663112yes—
889C4C22×D4×D7111yescharacteristic
890C4C2×#1455617311yescharacteristic
891C2—24no—
892C2—2844no—
893C2—2842no—
894C2—5682no—
895C2#2259984314yesdirect product factor
896C2C2×#1798663111yescharacteristic
897C2C22×#1455616011yescharacteristic
898C2C2×#1798680811yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#451×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986640C2
hypercenterC2×#451D71
hypocenterC71C2×#3266
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C22×#14556160C2semidirect
2. C23×#11765852C2semidirect
3. C2×Q8×C22⋊D71C2semidirect
5. #22599843C2direct (N × H)
6. C2×#17986392C2semidirect
7. C2×#17986248C2semidirect
8. C2×#17986238C2semidirect
9. C2×#17986223C2semidirect
10. C2×#17986203C2semidirect
11. C2×#17986160C2semidirect
12. C2×#17986139C2semidirect
13. C2×#17986152C2semidirect
14. C2×#17986102C2semidirect
15. C2×#17986067C2semidirect
16. C2×#451×C71C2semidirect
18. C22×Q8×D71C22semidirect
21. C2×#14556160C22semidirect
22. C22×#11765855C22semidirect
30. C22×#11765852C22semidirect
31. C22×#11765848C22semidirect
34. Q8×C22⋊D71C22semidirect
38. C2×#14556126C22semidirect
44. C2×#14556104C22semidirect
48. C2×Q8×Dic71C22semidirect
53. #17986392C22semidirect
54. #17986248C22semidirect
55. #17986238C22semidirect
56. #17986223C22semidirect
57. #17986203C22semidirect
58. #17986160C22semidirect
59. #17986152C22semidirect
60. #17986139C22semidirect
61. #17986102C22semidirect
62. #17986067C22semidirect
63. C2×#14556061C22semidirect
64. C2×Dic71⋊C8C22semidirect
65. C2×#14556052C22semidirect
66. C2×#14556051C22semidirect
69. C2×(C2×D71)⋊C8C22semidirect
70. C2×#14556038C22semidirect
72. C22×Q16×C71C22semidirect
73. C22×Q16×C71C22semidirect
75. #451×C71C22semidirect
76. C2×#103×C71C22semidirect
77. C2×#103×C71C22semidirect
89. C2×Q8×D71C23semidirect
106. C2×#11765855C23semidirect
115. C2×#11765852D4semidirect
121. C2×#11765848C23semidirect
128. #14556126C23semidirect
137. #14556104C23semidirect
143. Q8×Dic71C23semidirect
167. #14556061C23semidirect
168. Dic71⋊C8C23semidirect
169. #14556052C23semidirect
170. #14556051C23semidirect
173. (C2×D71)⋊C8C23semidirect
174. #14556038C23semidirect
187. C2×Q16×C71C23semidirect
188. C2×Q16×C71C23semidirect
196. #103×C71C23semidirect
197. #103×C71C23semidirect
258. #11765852C2×D4semidirect
326. C23×C71#137semidirect
412. C22×C71C2×#137semidirect
443. C2×C71#3266semidirect
461. C2×#451D71semidirect
466. C71C2×#3266semidirect
474. C22×Q16C2×D71semidirect
475. C22×Q16C2×D71semidirect
513. #451C2×D71semidirect
522. C2×#103C2×D71semidirect
523. C2×#103C2×D71semidirect
569. C2×Q16C22×D71semidirect
570. C2×Q16C22×D71semidirect
642. #103C22×D71semidirect
643. #103C22×D71semidirect
792. C23#14556160semidirect
875. C22C2×#14556160semidirect
895. C2#22599843direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561602
C23×#117658522
C2×Q8×C22⋊D712
C2×#179866402
#225998432
C2×#179863922
C2×#179862482
C2×#179862382
C2×#179862232
C2×#179862032
C2×#179861602
C2×#179861392
C2×#179861522
C2×#179861022
C2×#179860672
C2×#451×C712
C2×#326671