Finite Group Databasebeta

← C2×#22598164 #32865004

Subgroups — C2×#22598164 #32865004

Order 18176.

2234 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986626C211yesmaximal, characteristic, complemented
2C2×#17986471C211yesmaximal, characteristic
3#22598164C2116yesmaximal, direct product factor
4C2×#17986302C211yesmaximal, characteristic, complemented
5C2×#17986300C211yesmaximal, characteristic, complemented
6C2×#17986299C211yesmaximal, characteristic, complemented
7C2×#17986297C211yesmaximal, characteristic, complemented
8C2×#17986287C211yesmaximal, characteristic, complemented
9C2×#17986286C211yesmaximal, characteristic, complemented
10C2×#17986278C211yesmaximal, characteristic, complemented
11C2×#17986040C211yesmaximal, characteristic, complemented
12C2×#17986036C211yesmaximal, characteristic, complemented
13C2×#17986024C211yesmaximal, characteristic, complemented
14C2×#17986002C211yesmaximal, characteristic
15C2×#102×D71C211yesmaximal, characteristic
16C2×#474×C71C211yesmaximal, characteristic, complemented
17C22×D4×D71C2211yescharacteristic
18C22×#11765848C2211yescharacteristic
19C22×C8×D71C2211yescharacteristic
20#17986626—24no—
21#17986626C2218yescomplemented
22C2×#14556127C2211yescharacteristic, complemented
23C2×#14556126—21no—
24C2×#14556120C2211yescharacteristic, complemented
25C2×#14556119C2211yescharacteristic, complemented
26C2×#14556118—21no—
27C2×#14556106—21no—
28C2×#14556104—21no—
29#17986471—24no—
30#17986471C2218yes—
31C2×C4×D284C2211yescharacteristic
32C2×D4×Dic71C2211yescharacteristic
33C2×#14556090C2211yescharacteristic
34C2×C4×C22⋊D71—21no—
35C2×(C22⋊D71)⋊C4—21no—
36C2×#14556086C2211yescharacteristic
37C2×#14556086C2211yescharacteristic
38C2×#14556085C2211yescharacteristic
39C2×C4⋊C4×D71C2211yescharacteristic
40C22×(C2×D71)⋊C4—21no—
41C2×C22⋊C4×D71—21no—
42#17986302C2218yescomplemented
43#17986300C2218yescomplemented
44#17986299C2218yescomplemented
45#17986297C2218yescomplemented
46#17986287C2218yescomplemented
47#17986286C2218yescomplemented
48#17986278C2218yescomplemented
49#17986040C2218yescomplemented
50#17986036C2218yescomplemented
51C2×#14556062C2211yescharacteristic, complemented
52C2×#14556061C2211yescharacteristic, complemented
53C2×#14556060C2211yescharacteristic, complemented
54C2×#14556059C2211yescharacteristic, complemented
55C2×#14556059C2211yescharacteristic, complemented
56C2×#14556059C2211yescharacteristic, complemented
57#17986024C2218yescomplemented
58C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
59C2×Dic71⋊C8C2211yescharacteristic, complemented
60C2×Dic71⋊C8C2211yescharacteristic, complemented
61#17986002C2218yes—
62C2×#14556050C2211yescharacteristic
63C2×#14556050C2211yescharacteristic
64C2×#14556049C2211yescharacteristic
65C2×#14556049C2211yescharacteristic
66C2×#14556048C2211yescharacteristic
67C2×#14556048C2211yescharacteristic
68#102×D71C2218yes—
69C2×C4⋊Q8×C71C2211yescharacteristic, complemented
70C2×C4×D4×C71C2211yescharacteristic
71#474×C71C2218yescomplemented
72C2×#107×C71C2211yescharacteristic, complemented
73C2×#107×C71C2211yescharacteristic, complemented
74C2×C4⋊C8×C71C2211yescharacteristic, complemented
75C2×#102×C71C2211yescharacteristic
76C2×#102×C71C2211yescharacteristic
77C24×D71—21no—
78C22×Dic142—21no—
79C22×D284C2311yescharacteristic
80C22×C22⋊D71—21no—
81C2×D4×D71—22no—
82C2×D4×D71—24no—
83C2×D4×D71Q818yescomplemented
84C2×D4×D71C2314yes—
85C23×Dic71—21no—
86C22×C4×D71—21no—
87C22×C4×D71—21no—
88C22×C4×D71—21no—
89C22×C4×D71C2311yescharacteristic
90C2×#11765848—24no—
91C2×#11765848C2314yes—
92C22×C71⋊C8C2311yescharacteristic
93C22×C71⋊C8C2311yescharacteristic
94C2×C8×D71—24no—
95C2×C8×D71C2314yes—
96#14556127—22no—
97#14556127C2314yescomplemented
98#14556126—28no—
99#14556120—22no—
100#14556120C2314yescomplemented
101#14556119—22no—
102#14556119C2314yescomplemented
103#14556118—28no—
104#14556106—28no—
105#14556104—28no—
106C4×D284—22no—
107C4×D284C2314yes—
108D4×Dic71—22no—
109D4×Dic71C2314yes—
110#14556090—22no—
111#14556090C2314yes—
112C4×C22⋊D71—28no—
113(C22⋊D71)⋊C4—28no—
114#14556086—22no—
115#14556086—22no—
116#14556086C2314yes—
117#14556086C2314yes—
118#14556085D414yes—
119#14556085C2314yes—
120C2×C4⋊Dic71—21no—
121C2×C4⋊Dic71C2311yescharacteristic
122C2×C4⋊Dic71C2311yescharacteristic
123C2×C4⋊Dic71C2311yescharacteristic
124C2×Dic71⋊C4—21no—
125C2×Dic71⋊C4—21no—
126C2×Dic71⋊C4—21no—
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C2×Dic71⋊C4D411yescharacteristic
130C2×Dic71⋊C4D411yescharacteristic
131C4⋊C4×D71—22no—
132C4⋊C4×D71C2314yes—
133C2×C22⋊Dic71—21no—
134C2×(C2×D71)⋊C4—21no—
135C2×(C2×D71)⋊C4—21no—
136C2×(C2×D71)⋊C4—21no—
137C2×(C2×D71)⋊C4—28no—
138C2×(C2×D71)⋊C4—21no—
139C2×(C2×D71)⋊C4D411yescharacteristic
140C2×(C2×D71)⋊C4D411yescharacteristic
141C22⋊C4×D71—28no—
142C2×C4×Dic71—21no—
143C2×C4×Dic71—21no—
144C2×C4×Dic71C2311yescharacteristic
145#14556062C2314yescomplemented
146#14556061C2314yescomplemented
147#14556060C2314yescomplemented
148#14556059C2314yescomplemented
149#14556059C2314yescomplemented
150#14556059C2314yescomplemented
151C4⋊(C71⋊C8)C2314yescomplemented
152Dic71⋊C8C2314yescomplemented
153Dic71⋊C8C2314yescomplemented
154#14556050C2314yes—
155#14556050C2314yes—
156#14556049C2314yes—
157#14556049C2314yes—
158#14556048C2314yes—
159#14556048C2314yes—
160C22×Q8×C71—21no—
161C22×D4×C71C2311yescharacteristic
162C23×C4×C71—21no—
163C22×C8×C71C2311yescharacteristic
164C22×C8×C71C2311yescharacteristic
165C4⋊Q8×C71—22no—
166C4⋊Q8×C71C2314yescomplemented
167C4×D4×C71—22no—
168C4×D4×C71C2314yes—
169C2×C4⋊C4×C71—21no—
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C22⋊C4×C71—21no—
174C2×C42×C71C2311yescharacteristic
175#107×C71C2314yescomplemented
176#107×C71C2314yescomplemented
177C4⋊C8×C71C2314yescomplemented
178#102×C71C2314yes—
179#102×C71C2314yes—
180C23×D71—21no—
181C23×D71—28no—
182C23×D71—24no—
183C23×D71—82no—
184C23×D71—82no—
185C23×D71C2×D411yescharacteristic
186C2×Dic142—24no—
187C2×Dic142—82no—
188C2×D284—21no—
189C2×D284—22no—
190C2×D284C2×Q814yes—
191C2×D284C2412yes—
192C2×C22⋊D71—28no—
193C2×C22⋊D71—24no—
194D4×D71—216no—
195D4×D71—28no—
196D4×D71C2×Q8116yescomplemented
197C22×Dic71—21no—
198C22×Dic71—21no—
199C22×Dic71—21no—
200C22×Dic71—24no—
201C22×Dic71—82no—
202C22×Dic71C2×D411yescharacteristic
203C22×Dic71C2×D411yescharacteristic
204C22×Dic71C2×D411yescharacteristic
205C2×C4×D71—24no—
206C2×C4×D71—24no—
207C2×C4×D71—24no—
208C2×C4×D71—82no—
209C2×C4×D71—82no—
210C2×C4×D71—82no—
211C2×C4×D71C2×D412yes—
212C2×C4×D71C2×Q814yes—
213C2×C4×D71#4114yes—
214C2×C4×D71C2412yes—
215#11765848—28no—
216C2×C71⋊C8—22no—
217C2×C71⋊C8—22no—
218C2×C71⋊C8C2412yes—
219C2×C71⋊C8C2412yes—
220C8×D71—28no—
221C4⋊Dic71—21no—
222C4⋊Dic71—21no—
223C4⋊Dic71—21no—
224C4⋊Dic71—24no—
225C4⋊Dic71C2412yes—
226C4⋊Dic71C2412yes—
227C4⋊Dic71C2412yes—
228Dic71⋊C4—24no—
229Dic71⋊C4—24no—
230Dic71⋊C4—24no—
231Dic71⋊C4—24no—
232Dic71⋊C4—24no—
233Dic71⋊C4C2×D414yes—
234Dic71⋊C4C2×D414yes—
235C22⋊Dic71—24no—
236(C2×D71)⋊C4—24no—
237(C2×D71)⋊C4—24no—
238(C2×D71)⋊C4—24no—
239(C2×D71)⋊C4—24no—
240(C2×D71)⋊C4C2×D414yes—
241(C2×D71)⋊C4C2×D414yes—
242C4×Dic71—24no—
243C4×Dic71—24no—
244C4×Dic71C2×D412yes—
245C4×Dic71C2412yes—
246C24×C71—21no—
247C2×Q8×C71—24no—
248C2×Q8×C71—82no—
249C2×D4×C71—21no—
250C2×D4×C71—22no—
251C2×D4×C71C2×Q814yes—
252C2×D4×C71C2412yes—
253C22×C4×C71—21no—
254C22×C4×C71—21no—
255C22×C4×C71—21no—
256C22×C4×C71—24no—
257C22×C4×C71—82no—
258C22×C4×C71C2×D411yescharacteristic
259C22×C4×C71C2×D411yescharacteristic
260C22×C4×C71C2411yescharacteristic
261C2×C8×C71—22no—
262C2×C8×C71—22no—
263C2×C8×C71C2412yes—
264C2×C8×C71C2412yes—
265C4⋊C4×C71—24no—
266C4⋊C4×C71—21no—
267C4⋊C4×C71—21no—
268C4⋊C4×C71—21no—
269C4⋊C4×C71C2412yes—
270C4⋊C4×C71C2412yes—
271C4⋊C4×C71C2412yes—
272C22⋊C4×C71—24no—
273C42×C71C2×D412yes—
274C42×C71C2412yes—
275C23×C71—24no—
276C23×C71—22no—
277C23×C71—42no—
278C23×C71—42no—
279C23×C71C22×D411yescharacteristic
280C22×D71—22no—
281C22×D71—22no—
282C22×D71—24no—
283C22×D71—22no—
284C22×D71—216no—
285C22×D71—42no—
286C22×D71—42no—
287C22×D71—816no—
288C22×D71—84no—
289C22×D71—84no—
290C22×D71C22⋊Q814yes—
291C22×D71C22×D412yes—
292Q8×C71—84no—
293D4×C71—24no—
294D4×C71—22no—
295D4×C71C22×Q814yes—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—42no—
302C2×C4×C71—42no—
303C2×C4×C71—42no—
304C2×C4×C71—84no—
305C2×C4×C71C22×D412yes—
306C2×C4×C71C22×D412yes—
307C2×C4×C71C22×D411yescharacteristic
308C2×C4×C71C22×Q812yes—
309C2×C4×C71C2×#4112yes—
310C2×C4×C71C2511yescharacteristic
311C22⋊D71—216no—
312C2×Dic71—22no—
313C2×Dic71—22no—
314C2×Dic71—22no—
315C2×Dic71—22no—
316C2×Dic71—22no—
317C2×Dic71—42no—
318C2×Dic71—42no—
319C2×Dic71—42no—
320C2×Dic71—84no—
321C2×Dic71C22⋊Q814yes—
322C2×Dic71C22×D412yes—
323C2×Dic71C22×D412yes—
324C2×Dic71C22×D412yes—
325D284—24no—
326D284—22no—
327D284C22×Q814yes—
328C4×D71—84no—
329C4×D71—84no—
330C4×D71—84no—
331C4×D71C22⋊Q818yes—
332C4×D71C22×Q814yes—
333C4×D71C2×#4114yes—
334Dic142—84no—
335C8×C71—22no—
336C8×C71—22no—
337C71⋊C8—22no—
338C71⋊C8—22no—
339C22×C71—24no—
340C22×C71—48no—
341C22×C71—42no—
342C22×C71—42no—
343C22×C71C2×C22⋊Q812yes—
344C22×C71#57612yes—
345C22×C71#57712yes—
346C22×C71C23×D411yescharacteristic
347C2×D71—28no—
348C2×D71—22no—
349C2×D71—22no—
350C2×D71—24no—
351C2×D71—48no—
352C2×D71—42no—
353C2×D71—42no—
354C2×D71—816no—
355C2×D71C2×C22⋊Q814yes—
356C4×C71—22no—
357C4×C71—22no—
358C4×C71—42no—
359C4×C71—42no—
360C4×C71—42no—
361C4×C71C2×C22⋊Q812yes—
362C4×C71C23×Q811yescharacteristic
363C4×C71C22×#4111yescharacteristic
364Dic71—22no—
365Dic71—22no—
366Dic71—42no—
367Dic71—42no—
368Dic71—42no—
369Dic71C2×C22⋊Q814yes—
370C2×#3081—711nomaximal, Sylow
371C2×C71—44no—
372C2×C71#308114yescomplemented
373C2×C71C22×C22⋊Q811yescharacteristic
374C2×C71C2×#57611yescharacteristic
375C2×C71C2×#57711yescharacteristic
376D71—24no—
377D71—44no—
378C2×#544—711no—
379C2×#518—711no—
380#3081—7116no—
381C2×#478—711no—
382C2×#478—711no—
383C2×#478—711no—
384C2×#478—711no—
385C2×#476—711no—
386C2×#476—711no—
387C2×#474—711no—
388C2×#474D7111yescharacteristic, complemented
389C2×#428—711no—
390C2×#427—711no—
391C2×#424—711no—
392C2×#418—711no—
393C22×#102—711no—
394C71C2×#308111yescharacteristic, complemented, Sylow
395C23×D4—711no—
396C22×M16—711no—
397C23×C8—711no—
398#544—718no—
399#544—1424no—
400C2×C4⋊Q8—711no—
401C2×C4⋊Q8—1421no—
402C2×C4⋊Q8C2×D7111yescharacteristic, complemented
403C2×#125—711no—
404C2×#125—711no—
405C2×#125—1421no—
406C2×C22⋊Q8—1421no—
407C2×C22⋊Q8—1421no—
408#518—718no—
409#518—1424no—
410C2×C4×D4—711no—
411C2×C4×D4—711no—
412C2×C4×D4—711no—
413C2×C4×D4—1421no—
414C2×C4×D4—1421no—
415C2×C4×D4C2×D7111yescharacteristic
416C2×#117—711no—
417C2×#117—711no—
418C2×#117—711no—
419C22×C4⋊C4—711no—
420C22×C22⋊C4—1421no—
421C22×C22⋊C4—1421no—
422#478—718no—
423#478—718no—
424#478—718no—
425#478—718no—
426#476—718no—
427#476—718no—
428#474—718no—
429#474C2×D7118yescomplemented
430#428—718no—
431#427—718no—
432C2×#107—711no—
433C2×#107—711no—
434C2×#107C2×D7111yescharacteristic, complemented
435C2×#107C2×D7111yescharacteristic, complemented
436C2×#106—711no—
437C2×#106—711no—
438C2×#106—711no—
439C2×#106—711no—
440#424—718no—
441C2×C4⋊C8—711no—
442C2×C4⋊C8—711no—
443C2×C4⋊C8—711no—
444C2×C4⋊C8C2×D7111yescharacteristic, complemented
445#418—718no—
446C2×#102—711no—
447C2×#102—711no—
448C2×#102—711no—
449C2×#102—711no—
450C2×#102—711no—
451C2×#102—711no—
452C2×#102—718no—
453C2×#102C2×D7111yescharacteristic
454C2×#102C2×D7111yescharacteristic
455C25—1421no—
456C22×Q8—21no—
457C22×Q8—1421no—
458C22×D4—718no—
459C22×D4—714no—
460C22×D4—711no—
461C22×D4—1422no—
462C22×D4—1424no—
463C22×D4—1421no—
464C22×D4C22×D7111yescharacteristic
465C23×C4—21no—
466C23×C4—711no—
467C23×C4—1421no—
468C23×C4—1421no—
469C23×C4—1421no—
470C23×C4—1421no—
471C2×M16—714no—
472C2×M16—1424no—
473C22×C8—711no—
474C22×C8—711no—
475C22×C8—714no—
476C22×C8—1424no—
477C22×C8C22×D7111yescharacteristic
478C22×C8C22×D7111yescharacteristic
479C4⋊Q8—22no—
480C4⋊Q8—714no—
481C4⋊Q8—1422no—
482C4⋊Q8—1428no—
483C4⋊Q8C22×D7114yescomplemented
484#125—714no—
485#125—714no—
486#125—1422no—
487#125—1428no—
488#125—1422no—
489C22⋊Q8—1428no—
490C22⋊Q8—1428no—
491C4×D4—22no—
492C4×D4—714no—
493C4×D4—714no—
494C4×D4—714no—
495C4×D4—1422no—
496C4×D4—1422no—
497C4×D4—1428no—
498C4×D4—1428no—
499C4×D4—1422no—
500C4×D4C22×D7114yes—
501#117—714no—
502#117—714no—
503#117—714no—
504#117—714no—
505#117—1422no—
506#117—1422no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—711no—
509C2×C4⋊C4—711no—
510C2×C4⋊C4—711no—
511C2×C4⋊C4—711no—
512C2×C4⋊C4—711no—
513C2×C4⋊C4—714no—
514C2×C4⋊C4—1422no—
515C2×C4⋊C4—1421no—
516C2×C4⋊C4—1421no—
517C2×C4⋊C4—1421no—
518C2×C4⋊C4—1421no—
519C2×C4⋊C4—1421no—
520C2×C4⋊C4—1421no—
521C2×C4⋊C4C22×D7111yescharacteristic
522C2×C4⋊C4C22×D7111yescharacteristic
523C2×C4⋊C4C22×D7111yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—711no—
526C2×C22⋊C4—711no—
527C2×C22⋊C4—1428no—
528C2×C22⋊C4—1428no—
529C2×C22⋊C4—1421no—
530C2×C22⋊C4—1421no—
531C2×C22⋊C4—1421no—
532C2×C22⋊C4—1421no—
533C2×C22⋊C4—1421no—
534C2×C42—711no—
535C2×C42—1421no—
536C2×C42—1421no—
537C2×C42C22×D7111yescharacteristic
538#107—714no—
539#107—714no—
540#107C22×D7114yescomplemented
541#107C22×D7114yescomplemented
542#106—714no—
543#106—714no—
544#106—714no—
545#106—714no—
546C4⋊C8—714no—
547C4⋊C8—714no—
548C4⋊C8—714no—
549C4⋊C8C22×D7114yescomplemented
550#102—714no—
551#102—714no—
552#102—714no—
553#102—714no—
554#102—714no—
555#102—714no—
556#102C22×D7114yes—
557#102C22×D7114yes—
558C24—21no—
559C24—5682no—
560C24—5682no—
561C24—711no—
562C24—1424no—
563C24—1428no—
564C24—1421no—
565C2×Q8—24no—
566C2×Q8—82no—
567C2×Q8—5682no—
568C2×Q8—1424no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—7116no—
572C2×D4—714no—
573C2×D4—712no—
574C2×D4—1428no—
575C2×D4—14216no—
576C2×D4—1424no—
577C2×D4—1428no—
578C2×D4—1421no—
579C2×D4—1422no—
580C2×D4Q8×D7114yes—
581C2×D4C23×D7112yes—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—82no—
587C22×C4—5682no—
588C22×C4—5682no—
589C22×C4—5682no—
590C22×C4—5682no—
591C22×C4—711no—
592C22×C4—712no—
593C22×C4—714no—
594C22×C4—714no—
595C22×C4—712no—
596C22×C4—711no—
597C22×C4—711no—
598C22×C4—1424no—
599C22×C4—1424no—
600C22×C4—1421no—
601C22×C4—1421no—
602C22×C4—1421no—
603C22×C4—1424no—
604C22×C4—1424no—
605C22×C4D4×D7111yescharacteristic
606C22×C4D4×D7111yescharacteristic
607C22×C4C23×D7111yescharacteristic
608M16—1428no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—712no—
612C2×C8—712no—
613C2×C8—1428no—
614C2×C8—1422no—
615C2×C8—1422no—
616C2×C8C23×D7112yes—
617C2×C8C23×D7112yes—
618C4⋊C4—24no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—714no—
623C4⋊C4—714no—
624C4⋊C4—712no—
625C4⋊C4—712no—
626C4⋊C4—712no—
627C4⋊C4—1424no—
628C4⋊C4—1424no—
629C4⋊C4—1424no—
630C4⋊C4—1424no—
631C4⋊C4—1424no—
632C4⋊C4—1424no—
633C4⋊C4—1421no—
634C4⋊C4—1421no—
635C4⋊C4—1421no—
636C4⋊C4C23×D7112yes—
637C4⋊C4C23×D7112yes—
638C4⋊C4C23×D7112yes—
639C22⋊C4—24no—
640C22⋊C4—714no—
641C22⋊C4—714no—
642C22⋊C4—1424no—
643C22⋊C4—1424no—
644C22⋊C4—1424no—
645C22⋊C4—1424no—
646C22⋊C4—1424no—
647C42—712no—
648C42—712no—
649C42—1424no—
650C42—1424no—
651C42D4×D7112yes—
652C42C23×D7112yes—
653C23—22no—
654C23—24no—
655C23—42no—
656C23—42no—
657C23—2842no—
658C23—2842no—
659C23—56816no—
660C23—5684no—
661C23—5684no—
662C23—712no—
663C23—714no—
664C23—14216no—
665C23—1422no—
666C23—1424no—
667C23—1422no—
668C23—1422no—
669C23C2×D4×D7111yescharacteristic
670Q8—84no—
671Q8—5684no—
672D4—22no—
673D4—24no—
674D4—714no—
675D4—14216no—
676D4—1422no—
677D4—1424no—
678D4C2×Q8×D7114yes—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—84no—
688C2×C4—2842no—
689C2×C4—2842no—
690C2×C4—2842no—
691C2×C4—5684no—
692C2×C4—5684no—
693C2×C4—5684no—
694C2×C4—5684no—
695C2×C4—712no—
696C2×C4—714no—
697C2×C4—714no—
698C2×C4—714no—
699C2×C4—718no—
700C2×C4—712no—
701C2×C4—712no—
702C2×C4—1422no—
703C2×C4—1422no—
704C2×C4—1422no—
705C2×C4—1422no—
706C2×C4—1422no—
707C2×C4C2×D4×D7112yes—
708C2×C4C2×D4×D7112yes—
709C2×C4C2×D4×D7111yescharacteristic
710C2×C4C2×Q8×D7112yes—
711C2×C4#41×D7112yes—
712C2×C4C24×D7111yescharacteristic
713C8—22no—
714C8—22no—
715C8—1422no—
716C8—1422no—
717C22—24no—
718C22—48no—
719C22—42no—
720C22—42no—
721C22—2848no—
722C22—2842no—
723C22—2842no—
724C22—56816no—
725C22—714no—
726C22—1424no—
727C22—1428no—
728C22—1422no—
729C22—1422no—
730C22C22⋊Q8×D7112yes—
731C22#1798680012yes—
732C22#1798680812yes—
733C22C22×D4×D7111yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—2842no—
740C4—2842no—
741C4—2842no—
742C4—714no—
743C4—1422no—
744C4—1422no—
745C4C22⋊Q8×D7112yes—
746C4C22×Q8×D7111yescharacteristic
747C4C2×#41×D7111yescharacteristic
748C2—44no—
749C2—2844no—
750C2—1424no—
751C2#2259816414yesdirect product factor
752C2C2×C22⋊Q8×D7111yescharacteristic
753C2C2×#1798680011yescharacteristic
754C2C2×#1798680811yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#474×C71C2
socleC23×C71C22×D4
prime radicalC22×D4×D71C22
hypercenterC2×#474D71
hypocenterC71C2×#3081
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#17986626C2semidirect
3. #22598164C2direct (N × H)
4. C2×#17986302C2semidirect
5. C2×#17986300C2semidirect
6. C2×#17986299C2semidirect
7. C2×#17986297C2semidirect
8. C2×#17986287C2semidirect
9. C2×#17986286C2semidirect
10. C2×#17986278C2semidirect
11. C2×#17986040C2semidirect
12. C2×#17986036C2semidirect
13. C2×#17986024C2semidirect
16. C2×#474×C71C2semidirect
21. #17986626C22semidirect
22. C2×#14556127C22semidirect
24. C2×#14556120C22semidirect
25. C2×#14556119C22semidirect
42. #17986302C22semidirect
43. #17986300C22semidirect
44. #17986299C22semidirect
45. #17986297C22semidirect
46. #17986287C22semidirect
47. #17986286C22semidirect
48. #17986278C22semidirect
49. #17986040C22semidirect
50. #17986036C22semidirect
51. C2×#14556062C22semidirect
52. C2×#14556061C22semidirect
53. C2×#14556060C22semidirect
54. C2×#14556059C22semidirect
55. C2×#14556059C22semidirect
56. C2×#14556059C22semidirect
57. #17986024C22semidirect
58. C2×C4⋊(C71⋊C8)C22semidirect
59. C2×Dic71⋊C8C22semidirect
60. C2×Dic71⋊C8C22semidirect
69. C2×C4⋊Q8×C71C22semidirect
71. #474×C71C22semidirect
72. C2×#107×C71C22semidirect
73. C2×#107×C71C22semidirect
74. C2×C4⋊C8×C71C22semidirect
83. C2×D4×D71Q8semidirect
97. #14556127C23semidirect
100. #14556120C23semidirect
102. #14556119C23semidirect
145. #14556062C23semidirect
146. #14556061C23semidirect
147. #14556060C23semidirect
148. #14556059C23semidirect
149. #14556059C23semidirect
150. #14556059C23semidirect
151. C4⋊(C71⋊C8)C23semidirect
152. Dic71⋊C8C23semidirect
153. Dic71⋊C8C23semidirect
166. C4⋊Q8×C71C23semidirect
175. #107×C71C23semidirect
176. #107×C71C23semidirect
177. C4⋊C8×C71C23semidirect
196. D4×D71C2×Q8semidirect
372. C2×C71#3081semidirect
388. C2×#474D71semidirect
394. C71C2×#3081semidirect
402. C2×C4⋊Q8C2×D71semidirect
429. #474C2×D71semidirect
434. C2×#107C2×D71semidirect
435. C2×#107C2×D71semidirect
444. C2×C4⋊C8C2×D71semidirect
483. C4⋊Q8C22×D71semidirect
540. #107C22×D71semidirect
541. #107C22×D71semidirect
549. C4⋊C8C22×D71semidirect
751. C2#22598164direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866262
C2×#179864712
#225981642
C2×#179863022
C2×#179863002
C2×#179862992
C2×#179862972
C2×#179862872
C2×#179862862
C2×#179862782
C2×#179860402
C2×#179860362
C2×#179860242
C2×#179860022
C2×#102×D712
C2×#474×C712
C2×#308171