Finite Group Databasebeta

← #32870919

Subgroups — #32870919

Order 18176.

1866 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986533C211yesmaximal, characteristic, complemented
2#22599687C214yesmaximal, complemented
3#22599508C212yesmaximal, complemented
4#22599504C212yesmaximal, complemented
5#22599305C212yesmaximal, complemented
6#22599301C212yesmaximal, complemented
7#22599112C211yesmaximal, characteristic, complemented
8#22599097C211yesmaximal, characteristic, complemented
9#22599093C211yesmaximal, characteristic, complemented
10#22599088C211yesmaximal, characteristic
11#22598904C214yesmaximal, complemented
12#22598420C212yesmaximal, complemented
13#22598416C212yesmaximal, complemented
14#22598387C212yesmaximal, complemented
15#22598383C212yesmaximal, complemented
16C2×#17986052C211yesmaximal, characteristic, complemented
17C2×#529×C71C211yesmaximal, characteristic, complemented
18#17986533—21no—
19#17986533—21no—
20#17986533—21no—
21#17986533—21no—
22#17986533C2212yes—
23#17986533C2212yes—
24#17986533C2212yescomplemented
25#17986533C2212yescomplemented
26C2×#14556122—21no—
27C2×#14556120C2211yescharacteristic, complemented
28C2×#14556116C2211yescharacteristic, complemented
29C2×#14556111—21no—
30C2×#14556107C2211yescharacteristic
31C2×#14556102C2211yescharacteristic
32C2×C4×Dic142C2211yescharacteristic, complemented
33C2×C4×D284C2211yescharacteristic, complemented
34C2×C4×C22⋊D71—21no—
35C2×#14556085—21no—
36#17986398C2214yescomplemented
37#17986381C2214yescomplemented
38#17986356C2214yescomplemented
39#17986353C2214yescomplemented
40#17986334C2212yescomplemented
41#17986332C2212yescomplemented
42#17986329C2212yescomplemented
43#17986327C2212yescomplemented
44#17986317C2212yes—
45#17986315C2212yes—
46#17986312C2212yes—
47#17986310C2212yes—
48#17986306C2214yescomplemented
49#17986303C2214yescomplemented
50#17986299C2214yescomplemented
51#17986296C2214yescomplemented
52#17986238C2214yescomplemented
53#17986233C2214yes—
54#17986230C2214yescomplemented
55#17986226C2214yescomplemented
56#17986221C2214yescomplemented
57#17986218C2214yescomplemented
58#17986214C2214yescomplemented
59#17986211C2214yescomplemented
60#17986155C2212yescomplemented
61#17986154C2212yescomplemented
62#17986150C2212yescomplemented
63#17986149C2212yescomplemented
64#17986138C2212yes—
65#17986137C2212yes—
66#17986133C2212yes—
67#17986132C2212yes—
68C4×#11765855C2214yescomplemented
69C4×#11765852C2214yescomplemented
70C4×#11765853C2214yescomplemented
71C4×#11765850C2214yescomplemented
72#17986052C2212yescomplemented
73#17986052C2212yescomplemented
74#17986052C2212yescomplemented
75#17986052C2212yescomplemented
76C2×C4⋊(C71⋊C8)C2212yescomplemented
77C2×C22⋊(C71⋊C8)C2211yescharacteristic
78C2×C22⋊(C71⋊C8)C2211yescharacteristic
79C2×C4×C71⋊C8C2212yescomplemented
80#529×C71—21no—
81#529×C71—21no—
82#529×C71—21no—
83#529×C71—21no—
84#529×C71C2212yes—
85#529×C71C2212yes—
86#529×C71C2212yescomplemented
87#529×C71C2212yescomplemented
88C2×#126×C71—21no—
89C2×#125×C71C2211yescharacteristic, complemented
90C2×#124×C71C2211yescharacteristic, complemented
91C2×#123×C71—21no—
92C2×C22⋊Q8×C71C2211yescharacteristic
93C2×#121×C71C2211yescharacteristic
94C2×C4×Q8×C71C2211yescharacteristic, complemented
95C2×C4×D4×C71—21no—
96C2×C4×D4×C71C2211yescharacteristic, complemented
97C2×#117×C71—21no—
98C22×C42×C71C2211yescharacteristic
99C22×Dic142C2311yescharacteristic
100C22×D284C2311yescharacteristic
101C22×C22⋊D71—21no—
102C22×C4×D71—21no—
103C2×#11765855C2314yes—
104C2×#11765853C2314yes—
105C2×#11765852C2314yes—
106C2×#11765850C2314yes—
107C22×C71⋊C8C2312yes—
108C22×C71⋊C8C2312yes—
109#14556122—22no—
110#14556122—22no—
111#14556122—22no—
112#14556122—22no—
113#14556120—21no—
114#14556120—21no—
115#14556120C2312yes—
116#14556120C2312yes—
117#14556116—21no—
118#14556116—21no—
119#14556116C2312yes—
120#14556116C2312yes—
121#14556111—22no—
122#14556111—22no—
123#14556111—22no—
124#14556111—22no—
125#14556107—21no—
126#14556107—21no—
127#14556107C2312yes—
128#14556107C2312yes—
129#14556102—21no—
130#14556102—21no—
131#14556102C2312yes—
132#14556102C2312yes—
133C4×Dic142—21no—
134C4×Dic142—21no—
135C4×Dic142C2312yes—
136C4×Dic142C2312yes—
137C4×D284—21no—
138C4×D284—21no—
139C4×D284C2312yes—
140C4×D284C2312yes—
141C4×C22⋊D71—22no—
142C4×C22⋊D71—22no—
143C4×C22⋊D71—22no—
144C4×C22⋊D71—22no—
145#14556085—22no—
146#14556085—22no—
147#14556085—22no—
148#14556085—22no—
149C2×C4⋊Dic71C2311yescharacteristic
150C2×C4⋊Dic71C2311yescharacteristic
151C2×Dic71⋊C4—21no—
152C2×Dic71⋊C4—21no—
153C2×Dic71⋊C4—21no—
154C2×Dic71⋊C4—21no—
155C2×C22⋊Dic71—21no—
156C2×(C2×D71)⋊C4—21no—
157C2×(C2×D71)⋊C4—21no—
158C2×(C2×D71)⋊C4—21no—
159C2×(C2×D71)⋊C4—21no—
160C2×C4×Dic71—21no—
161#14556061C2314yes—
162#14556061C2314yes—
163#14556059C2314yes—
164#14556059C2314yes—
165C4⋊(C71⋊C8)C2314yes—
166C4⋊(C71⋊C8)C2314yes—
167#14556052C2314yes—
168#14556052C2314yes—
169#14556051C2314yes—
170#14556051C2314yes—
171#14556049C2314yes—
172#14556049C2314yes—
173#14556048C2314yes—
174#14556048C2314yes—
175C22⋊(C71⋊C8)C2312yes—
176C22⋊(C71⋊C8)C2312yes—
177C22⋊(C71⋊C8)C2312yes—
178C22⋊(C71⋊C8)C2312yes—
179C4×C71⋊C8C2314yes—
180C4×C71⋊C8C2314yes—
181C22×Q8×C71C2311yescharacteristic
182C22×D4×C71—21no—
183C22×D4×C71C2311yescharacteristic
184C23×C4×C71—21no—
185C23×C4×C71D411yescharacteristic
186C23×C4×C71D411yescharacteristic
187C23×C4×C71C2311yescharacteristic
188#126×C71—22no—
189#126×C71—22no—
190#126×C71—22no—
191#126×C71—22no—
192#125×C71—21no—
193#125×C71—21no—
194#125×C71C2312yes—
195#125×C71C2312yes—
196#124×C71—21no—
197#124×C71—21no—
198#124×C71C2312yes—
199#124×C71C2312yes—
200#123×C71—22no—
201#123×C71—22no—
202#123×C71—22no—
203#123×C71—22no—
204C22⋊Q8×C71—21no—
205C22⋊Q8×C71—21no—
206C22⋊Q8×C71C2312yes—
207C22⋊Q8×C71C2312yes—
208#121×C71—21no—
209#121×C71—21no—
210#121×C71C2312yes—
211#121×C71C2312yes—
212C4×Q8×C71—21no—
213C4×Q8×C71—21no—
214C4×Q8×C71C2312yes—
215C4×Q8×C71C2312yes—
216C4×D4×C71—22no—
217C4×D4×C71—22no—
218C4×D4×C71—22no—
219C4×D4×C71—22no—
220C4×D4×C71—21no—
221C4×D4×C71—21no—
222C4×D4×C71C2312yes—
223C4×D4×C71C2312yes—
224#117×C71—22no—
225#117×C71—22no—
226#117×C71—22no—
227#117×C71—22no—
228C2×C4⋊C4×C71—21no—
229C2×C4⋊C4×C71—21no—
230C2×C4⋊C4×C71—21no—
231C2×C4⋊C4×C71—21no—
232C2×C4⋊C4×C71C2311yescharacteristic
233C2×C4⋊C4×C71C2311yescharacteristic
234C2×C22⋊C4×C71—21no—
235C2×C22⋊C4×C71—21no—
236C2×C22⋊C4×C71—21no—
237C2×C22⋊C4×C71—21no—
238C2×C22⋊C4×C71—21no—
239C2×C42×C71—21no—
240C2×C42×C71D411yescharacteristic
241C2×C42×C71D411yescharacteristic
242C2×C42×C71D411yescharacteristic
243C2×C42×C71D411yescharacteristic
244C2×C42×C71D411yescharacteristic
245C2×C42×C71D411yescharacteristic
246C2×C42×C71C2311yescharacteristic
247C2×C42×C71C2311yescharacteristic
248C2×C42×C71C2311yescharacteristic
249C2×C42×C71C2311yescharacteristic
250C2×C42×C71C2311yescharacteristic
251C2×C42×C71C2311yescharacteristic
252C23×D71—21no—
253C2×Dic142—21no—
254C2×Dic142—42no—
255C2×Dic142C2412yes—
256C2×D284—21no—
257C2×D284—42no—
258C2×D284C2412yes—
259C2×C22⋊D71—22no—
260C2×C22⋊D71—22no—
261C2×C22⋊D71—44no—
262C22×Dic71—21no—
263C22×Dic71—21no—
264C22×Dic71—21no—
265C2×C4×D71—22no—
266C2×C4×D71—22no—
267C2×C4×D71—44no—
268#11765855—44no—
269#11765853—44no—
270#11765852—44no—
271#11765850—44no—
272C2×C71⋊C8—42no—
273C2×C71⋊C8—42no—
274C2×C71⋊C8C2414yes—
275C2×C71⋊C8C2414yes—
276C4⋊Dic71—21no—
277C4⋊Dic71—21no—
278C4⋊Dic71C2412yes—
279C4⋊Dic71C2412yes—
280Dic71⋊C4—22no—
281Dic71⋊C4—22no—
282Dic71⋊C4—22no—
283Dic71⋊C4—22no—
284Dic71⋊C4—22no—
285Dic71⋊C4—22no—
286Dic71⋊C4—22no—
287Dic71⋊C4—22no—
288C22⋊Dic71—22no—
289C22⋊Dic71—22no—
290(C2×D71)⋊C4—22no—
291(C2×D71)⋊C4—22no—
292(C2×D71)⋊C4—22no—
293(C2×D71)⋊C4—22no—
294(C2×D71)⋊C4—22no—
295(C2×D71)⋊C4—22no—
296(C2×D71)⋊C4—22no—
297(C2×D71)⋊C4—22no—
298C4×Dic71—22no—
299C4×Dic71—22no—
300C24×C71—21no—
301C24×C71C2×D411yescharacteristic
302C2×Q8×C71—21no—
303C2×Q8×C71—42no—
304C2×Q8×C71C2412yes—
305C2×D4×C71—22no—
306C2×D4×C71—22no—
307C2×D4×C71—21no—
308C2×D4×C71—42no—
309C2×D4×C71—44no—
310C2×D4×C71C2412yes—
311C22×C4×C71—24no—
312C22×C4×C71—21no—
313C22×C4×C71—21no—
314C22×C4×C71—21no—
315C22×C4×C71—22no—
316C22×C4×C71—22no—
317C22×C4×C71—42no—
318C22×C4×C71—42no—
319C22×C4×C71—44no—
320C22×C4×C71C2×D411yescharacteristic
321C22×C4×C71C2×D411yescharacteristic
322C22×C4×C71C2×D411yescharacteristic
323C22×C4×C71C2×D411yescharacteristic
324C22×C4×C71C2×D411yescharacteristic
325C22×C4×C71C2×D411yescharacteristic
326C22×C4×C71C2×D411yescharacteristic
327C22×C4×C71C2×D411yescharacteristic
328C22×C4×C71C2×D411yescharacteristic
329C22×C4×C71C2×D411yescharacteristic
330C22×C4×C71C2×D411yescharacteristic
331C22×C4×C71C2×D411yescharacteristic
332C22×C4×C71C2×D411yescharacteristic
333C22×C4×C71C2×D411yescharacteristic
334C22×C4×C71C2×D411yescharacteristic
335C22×C4×C71C2411yescharacteristic
336C22×C4×C71C2411yescharacteristic
337C22×C4×C71C2411yescharacteristic
338C4⋊C4×C71—22no—
339C4⋊C4×C71—22no—
340C4⋊C4×C71—22no—
341C4⋊C4×C71—22no—
342C4⋊C4×C71—22no—
343C4⋊C4×C71—22no—
344C4⋊C4×C71—22no—
345C4⋊C4×C71—22no—
346C4⋊C4×C71—21no—
347C4⋊C4×C71—21no—
348C4⋊C4×C71C2412yes—
349C4⋊C4×C71C2412yes—
350C22⋊C4×C71—22no—
351C22⋊C4×C71—22no—
352C22⋊C4×C71—22no—
353C22⋊C4×C71—22no—
354C22⋊C4×C71—22no—
355C22⋊C4×C71—22no—
356C22⋊C4×C71—22no—
357C22⋊C4×C71—22no—
358C22⋊C4×C71—22no—
359C22⋊C4×C71—22no—
360C42×C71—22no—
361C42×C71—22no—
362C42×C71C2×D411yescharacteristic
363C42×C71C2×D411yescharacteristic
364C42×C71C2×D411yescharacteristic
365C42×C71C2×D411yescharacteristic
366C42×C71C2×D411yescharacteristic
367C42×C71C2×D411yescharacteristic
368C42×C71C2×D411yescharacteristic
369C42×C71C2×D411yescharacteristic
370C42×C71C2×D411yescharacteristic
371C42×C71C2×D411yescharacteristic
372C42×C71C2×D411yescharacteristic
373C42×C71C2×D411yescharacteristic
374C42×C71C2411yescharacteristic
375C42×C71C2411yescharacteristic
376C42×C71C2411yescharacteristic
377C42×C71C2411yescharacteristic
378C23×C71—22no—
379C23×C71—41no—
380C23×C71—41no—
381C23×C71—42no—
382C23×C71—42no—
383C23×C71—42no—
384C23×C71#13514yes—
385C23×C71C22×D411yescharacteristic
386C23×C71C22×D411yescharacteristic
387C23×C71C22×D411yescharacteristic
388C22×D71—22no—
389C22×D71—42no—
390C22×D71—42no—
391C22×D71—42no—
392Q8×C71—24no—
393Q8×C71—42no—
394D4×C71—24no—
395D4×C71—42no—
396D4×C71—44no—
397D4×C71—44no—
398C2×C4×C71—22no—
399C2×C4×C71—22no—
400C2×C4×C71—22no—
401C2×C4×C71—22no—
402C2×C4×C71—22no—
403C2×C4×C71—22no—
404C2×C4×C71—22no—
405C2×C4×C71—22no—
406C2×C4×C71—22no—
407C2×C4×C71—22no—
408C2×C4×C71—22no—
409C2×C4×C71—22no—
410C2×C4×C71—22no—
411C2×C4×C71—22no—
412C2×C4×C71—22no—
413C2×C4×C71—41no—
414C2×C4×C71—41no—
415C2×C4×C71—41no—
416C2×C4×C71—41no—
417C2×C4×C71—41no—
418C2×C4×C71—41no—
419C2×C4×C71—44no—
420C2×C4×C71—42no—
421C2×C4×C71—42no—
422C2×C4×C71—42no—
423C2×C4×C71—44no—
424C2×C4×C71C22×D411yescharacteristic
425C2×C4×C71C22×D411yescharacteristic
426C2×C4×C71C22×D411yescharacteristic
427C2×C4×C71C22×D411yescharacteristic
428C2×C4×C71C22×D411yescharacteristic
429C2×C4×C71C22×D411yescharacteristic
430C2×C4×C71C22×D411yescharacteristic
431C2×C4×C71C22×D411yescharacteristic
432C2×C4×C71C22×D411yescharacteristic
433C2×C4×C71C22×D411yescharacteristic
434C2×C4×C71C22×D411yescharacteristic
435C2×C4×C71C2511yescharacteristic
436C22⋊D71—44no—
437C22⋊D71—44no—
438C2×Dic71—22no—
439C2×Dic71—22no—
440C2×Dic71—22no—
441C2×Dic71—42no—
442C2×Dic71—42no—
443C2×Dic71—42no—
444D284—24no—
445D284—42no—
446C4×D71—44no—
447C4×D71—44no—
448Dic142—24no—
449Dic142—42no—
450C71⋊C8—24no—
451C71⋊C8—24no—
452C22×C71—21no—
453C22×C71—21no—
454C22×C71—21no—
455C22×C71—21no—
456C22×C71—21no—
457C22×C71—21no—
458C22×C71—44no—
459C22×C71—42no—
460C22×C71—42no—
461C22×C71—42no—
462C22×C71—84no—
463C22×C71C2×#13512yes—
464C22×C71C2×#13512yes—
465C22×C71C2×#13512yes—
466C22×C71C23×D411yescharacteristic
467C2×D71—42no—
468C2×D71—42no—
469C2×D71—42no—
470C2×D71—84no—
471C4×C71—21no—
472C4×C71—21no—
473C4×C71—21no—
474C4×C71—21no—
475C4×C71—21no—
476C4×C71—21no—
477C4×C71—21no—
478C4×C71—21no—
479C4×C71—21no—
480C4×C71—21no—
481C4×C71—42no—
482C4×C71—42no—
483C4×C71—42no—
484C4×C71#57512yes—
485C4×C71#58512yes—
486Dic71—42no—
487Dic71—42no—
488Dic71—42no—
489#60945—711nomaximal, Sylow
490C2×C71—22no—
491C2×C71—22no—
492C2×C71—22no—
493C2×C71—82no—
494C2×C71#344911yescharacteristic
495C2×C71C22×#13511yescharacteristic
496C2×C71C2×#57511yescharacteristic
497D71—82no—
498C2×#529—711no—
499C2×#529D7111yescharacteristic, complemented
500#3250—714no—
501#3232—712no—
502#3232—712no—
503#3211—712no—
504#3211—712no—
505#3189—711no—
506#3187—711no—
507#3187—711no—
508#3186—711no—
509#3168—714no—
510#3108—712no—
511#3108—712no—
512#3105—712no—
513#3105—712no—
514C2×#431—711no—
515C71#6094511yescharacteristic, complemented, Sylow
516#529—21no—
517#529—21no—
518#529—21no—
519#529—21no—
520#529—712no—
521#529—712no—
522#529—712no—
523#529—712no—
524#529—1421no—
525#529—1421no—
526#529—1421no—
527#529—1421no—
528#529C2×D7112yes—
529#529C2×D7112yes—
530#529C2×D7112yescomplemented
531#529C2×D7112yescomplemented
532C2×#126—21no—
533C2×#126—1421no—
534C2×#125—711no—
535C2×#125C2×D7111yescharacteristic, complemented
536C2×#124—711no—
537C2×#124C2×D7111yescharacteristic, complemented
538C2×#123—21no—
539C2×#123—1421no—
540C2×C22⋊Q8—711no—
541C2×C22⋊Q8C2×D7111yescharacteristic
542C2×#121—711no—
543C2×#121C2×D7111yescharacteristic
544C2×C4×Q8—711no—
545C2×C4×Q8C2×D7111yescharacteristic, complemented
546C2×C4×D4—21no—
547C2×C4×D4—711no—
548C2×C4×D4—1421no—
549C2×C4×D4C2×D7111yescharacteristic, complemented
550C2×#117—21no—
551C2×#117—1421no—
552C22×C42C2×D7111yescharacteristic
553#499—714no—
554#495—714no—
555#488—714no—
556#488—714no—
557#484—712no—
558#484—712no—
559#483—712no—
560#483—712no—
561#481—712no—
562#481—712no—
563#480—712no—
564#480—712no—
565#479—714no—
566#479—714no—
567#478—714no—
568#478—714no—
569#467—714no—
570#466—714no—
571#465—714no—
572#465—714no—
573#464—714no—
574#464—714no—
575#463—714no—
576#463—714no—
577#451—712no—
578#451—712no—
579#450—712no—
580#450—712no—
581#448—712no—
582#448—712no—
583#447—712no—
584#447—712no—
585C4×Q16—714no—
586C4×SD16—714no—
587C4×SD16—714no—
588C4×D8—714no—
589#431—712no—
590#431—712no—
591#431—712no—
592#431—712no—
593C2×C4⋊C8—712no—
594C2×C22⋊C8—711no—
595C2×C22⋊C8—711no—
596C2×C4×C8—712no—
597C22×Q8—711no—
598C22×Q8C22×D7111yescharacteristic
599C22×D4—21no—
600C22×D4—711no—
601C22×D4—1421no—
602C22×D4C22×D7111yescharacteristic
603C23×C4—21no—
604C23×C4—1421no—
605C23×C4C22⋊D7111yescharacteristic
606C23×C4C22⋊D7111yescharacteristic
607C23×C4C22×D7111yescharacteristic
608C2×Q16—714no—
609C2×SD16—714no—
610C2×SD16—714no—
611C2×D8—714no—
612C22×C8—712no—
613C22×C8—712no—
614#126—22no—
615#126—22no—
616#126—22no—
617#126—22no—
618#126—1422no—
619#126—1422no—
620#126—1422no—
621#126—1422no—
622#125—21no—
623#125—21no—
624#125—712no—
625#125—712no—
626#125—1421no—
627#125—1421no—
628#125C22×D7112yes—
629#125C22×D7112yes—
630#124—21no—
631#124—21no—
632#124—712no—
633#124—712no—
634#124—1421no—
635#124—1421no—
636#124C22×D7112yes—
637#124C22×D7112yes—
638#123—22no—
639#123—22no—
640#123—22no—
641#123—22no—
642#123—1422no—
643#123—1422no—
644#123—1422no—
645#123—1422no—
646C22⋊Q8—21no—
647C22⋊Q8—21no—
648C22⋊Q8—712no—
649C22⋊Q8—712no—
650C22⋊Q8—1421no—
651C22⋊Q8—1421no—
652C22⋊Q8C22×D7112yes—
653C22⋊Q8C22×D7112yes—
654#121—21no—
655#121—21no—
656#121—712no—
657#121—712no—
658#121—1421no—
659#121—1421no—
660#121C22×D7112yes—
661#121C22×D7112yes—
662C4×Q8—21no—
663C4×Q8—21no—
664C4×Q8—712no—
665C4×Q8—712no—
666C4×Q8—1421no—
667C4×Q8—1421no—
668C4×Q8C22×D7112yes—
669C4×Q8C22×D7112yes—
670C4×D4—22no—
671C4×D4—22no—
672C4×D4—22no—
673C4×D4—22no—
674C4×D4—21no—
675C4×D4—21no—
676C4×D4—712no—
677C4×D4—712no—
678C4×D4—1422no—
679C4×D4—1422no—
680C4×D4—1422no—
681C4×D4—1422no—
682C4×D4—1421no—
683C4×D4—1421no—
684C4×D4C22×D7112yes—
685C4×D4C22×D7112yes—
686#117—22no—
687#117—22no—
688#117—22no—
689#117—22no—
690#117—1422no—
691#117—1422no—
692#117—1422no—
693#117—1422no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—711no—
699C2×C4⋊C4—711no—
700C2×C4⋊C4—1421no—
701C2×C4⋊C4—1421no—
702C2×C4⋊C4—1421no—
703C2×C4⋊C4—1421no—
704C2×C4⋊C4C22×D7111yescharacteristic
705C2×C4⋊C4C22×D7111yescharacteristic
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—1421no—
712C2×C22⋊C4—1421no—
713C2×C22⋊C4—1421no—
714C2×C22⋊C4—1421no—
715C2×C22⋊C4—1421no—
716C2×C42—21no—
717C2×C42—1421no—
718C2×C42C22⋊D7111yescharacteristic
719C2×C42C22⋊D7111yescharacteristic
720C2×C42C22⋊D7111yescharacteristic
721C2×C42C22⋊D7111yescharacteristic
722C2×C42C22⋊D7111yescharacteristic
723C2×C42C22⋊D7111yescharacteristic
724C2×C42C22×D7111yescharacteristic
725C2×C42C22×D7111yescharacteristic
726C2×C42C22×D7111yescharacteristic
727C2×C42C22×D7111yescharacteristic
728C2×C42C22×D7111yescharacteristic
729C2×C42C22×D7111yescharacteristic
730#107—714no—
731#107—714no—
732#106—714no—
733#106—714no—
734C4⋊C8—714no—
735C4⋊C8—714no—
736#103—714no—
737#103—714no—
738#103—714no—
739#103—714no—
740#102—714no—
741#102—714no—
742#102—714no—
743#102—714no—
744C22⋊C8—712no—
745C22⋊C8—712no—
746C22⋊C8—712no—
747C22⋊C8—712no—
748C4×C8—714no—
749C4×C8—714no—
750C24—21no—
751C24—1421no—
752C24C2×C22⋊D7111yescharacteristic
753C2×Q8—21no—
754C2×Q8—42no—
755C2×Q8—2842no—
756C2×Q8—712no—
757C2×Q8—1421no—
758C2×Q8C23×D7112yes—
759C2×D4—22no—
760C2×D4—22no—
761C2×D4—21no—
762C2×D4—42no—
763C2×D4—44no—
764C2×D4—2842no—
765C2×D4—2844no—
766C2×D4—712no—
767C2×D4—1422no—
768C2×D4—1422no—
769C2×D4—1421no—
770C2×D4C23×D7112yes—
771C22×C4—24no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—44no—
780C22×C4—2844no—
781C22×C4—1421no—
782C22×C4—1421no—
783C22×C4—1421no—
784C22×C4—1422no—
785C22×C4—1422no—
786C22×C4C2×C22⋊D7111yescharacteristic
787C22×C4C2×C22⋊D7111yescharacteristic
788C22×C4C2×C22⋊D7111yescharacteristic
789C22×C4C2×C22⋊D7111yescharacteristic
790C22×C4C2×C22⋊D7111yescharacteristic
791C22×C4C2×C22⋊D7111yescharacteristic
792C22×C4C2×C22⋊D7111yescharacteristic
793C22×C4C2×C22⋊D7111yescharacteristic
794C22×C4C2×C22⋊D7111yescharacteristic
795C22×C4C2×C22⋊D7111yescharacteristic
796C22×C4C2×C22⋊D7111yescharacteristic
797C22×C4C2×C22⋊D7111yescharacteristic
798C22×C4C2×C22⋊D7111yescharacteristic
799C22×C4C2×C22⋊D7111yescharacteristic
800C22×C4C2×C22⋊D7111yescharacteristic
801C22×C4C23×D7111yescharacteristic
802C22×C4C23×D7111yescharacteristic
803C22×C4C23×D7111yescharacteristic
804Q16—2844no—
805SD16—2844no—
806SD16—2844no—
807D8—2844no—
808C2×C8—2842no—
809C2×C8—2842no—
810C2×C8—714no—
811C2×C8—714no—
812C4⋊C4—22no—
813C4⋊C4—22no—
814C4⋊C4—22no—
815C4⋊C4—22no—
816C4⋊C4—22no—
817C4⋊C4—22no—
818C4⋊C4—22no—
819C4⋊C4—22no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—712no—
823C4⋊C4—712no—
824C4⋊C4—1422no—
825C4⋊C4—1422no—
826C4⋊C4—1422no—
827C4⋊C4—1422no—
828C4⋊C4—1422no—
829C4⋊C4—1422no—
830C4⋊C4—1422no—
831C4⋊C4—1422no—
832C4⋊C4—1421no—
833C4⋊C4—1421no—
834C4⋊C4C23×D7112yes—
835C4⋊C4C23×D7112yes—
836C22⋊C4—22no—
837C22⋊C4—22no—
838C22⋊C4—22no—
839C22⋊C4—22no—
840C22⋊C4—22no—
841C22⋊C4—22no—
842C22⋊C4—22no—
843C22⋊C4—22no—
844C22⋊C4—22no—
845C22⋊C4—22no—
846C22⋊C4—1422no—
847C22⋊C4—1422no—
848C22⋊C4—1422no—
849C22⋊C4—1422no—
850C22⋊C4—1422no—
851C22⋊C4—1422no—
852C22⋊C4—1422no—
853C22⋊C4—1422no—
854C22⋊C4—1422no—
855C22⋊C4—1422no—
856C42—22no—
857C42—22no—
858C42—1422no—
859C42—1422no—
860C42C2×C22⋊D7111yescharacteristic
861C42C2×C22⋊D7111yescharacteristic
862C42C2×C22⋊D7111yescharacteristic
863C42C2×C22⋊D7111yescharacteristic
864C42C2×C22⋊D7111yescharacteristic
865C42C2×C22⋊D7111yescharacteristic
866C42C2×C22⋊D7111yescharacteristic
867C42C2×C22⋊D7111yescharacteristic
868C42C2×C22⋊D7111yescharacteristic
869C42C2×C22⋊D7111yescharacteristic
870C42C2×C22⋊D7111yescharacteristic
871C42C2×C22⋊D7111yescharacteristic
872C42C23×D7111yescharacteristic
873C42C23×D7111yescharacteristic
874C42C23×D7111yescharacteristic
875C42C23×D7111yescharacteristic
876C23—22no—
877C23—41no—
878C23—41no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—2842no—
883C23—2842no—
884C23—2842no—
885C23—1422no—
886C23#1455614814yes—
887C23C22×C22⋊D7111yescharacteristic
888C23C22×C22⋊D7111yescharacteristic
889C23C22×C22⋊D7111yescharacteristic
890Q8—24no—
891Q8—42no—
892Q8—2842no—
893Q8—1424no—
894D4—24no—
895D4—42no—
896D4—44no—
897D4—44no—
898D4—2842no—
899D4—2844no—
900D4—2844no—
901D4—1424no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—44no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—44no—
928C2×C4—2844no—
929C2×C4—2842no—
930C2×C4—2842no—
931C2×C4—2842no—
932C2×C4—2844no—
933C2×C4—1422no—
934C2×C4—1422no—
935C2×C4—1422no—
936C2×C4C22×C22⋊D7111yescharacteristic
937C2×C4C22×C22⋊D7111yescharacteristic
938C2×C4C22×C22⋊D7111yescharacteristic
939C2×C4C22×C22⋊D7111yescharacteristic
940C2×C4C22×C22⋊D7111yescharacteristic
941C2×C4C22×C22⋊D7111yescharacteristic
942C2×C4C22×C22⋊D7111yescharacteristic
943C2×C4C22×C22⋊D7111yescharacteristic
944C2×C4C22×C22⋊D7111yescharacteristic
945C2×C4C22×C22⋊D7111yescharacteristic
946C2×C4C22×C22⋊D7111yescharacteristic
947C2×C4C24×D7111yescharacteristic
948C8—1424no—
949C8—1424no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—44no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—84no—
961C22—2842no—
962C22—2842no—
963C22—2842no—
964C22—5684no—
965C22C2×#1455614812yes—
966C22C2×#1455614812yes—
967C22C2×#1455614812yes—
968C22C23×C22⋊D7111yescharacteristic
969C4—21no—
970C4—21no—
971C4—21no—
972C4—21no—
973C4—21no—
974C4—21no—
975C4—21no—
976C4—21no—
977C4—21no—
978C4—21no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—2842no—
983C4—2842no—
984C4—2842no—
985C4#1798679712yes—
986C4#1798683512yes—
987C2—22no—
988C2—22no—
989C2—22no—
990C2—82no—
991C2—5682no—
992C2#2260166911yescharacteristic
993C2C22×#1455614811yescharacteristic
994C2C2×#1798679711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#529×C71C2
socleC22×C71C23×D4
prime radical#22599088C2
hypercenterC2×#529D71
hypocenterC71#60945
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#17986533C2semidirect
2. #22599687C2semidirect
3. #22599508C2semidirect
4. #22599504C2semidirect
5. #22599305C2semidirect
6. #22599301C2semidirect
7. #22599112C2semidirect
8. #22599097C2semidirect
9. #22599093C2semidirect
11. #22598904C2semidirect
12. #22598420C2semidirect
13. #22598416C2semidirect
14. #22598387C2semidirect
15. #22598383C2semidirect
16. C2×#17986052C2semidirect
17. C2×#529×C71C2semidirect
24. #17986533C22semidirect
25. #17986533C22semidirect
27. C2×#14556120C22semidirect
28. C2×#14556116C22semidirect
32. C2×C4×Dic142C22semidirect
33. C2×C4×D284C22semidirect
36. #17986398C22semidirect
37. #17986381C22semidirect
38. #17986356C22semidirect
39. #17986353C22semidirect
40. #17986334C22semidirect
41. #17986332C22semidirect
42. #17986329C22semidirect
43. #17986327C22semidirect
48. #17986306C22semidirect
49. #17986303C22semidirect
50. #17986299C22semidirect
51. #17986296C22semidirect
52. #17986238C22semidirect
54. #17986230C22semidirect
55. #17986226C22semidirect
56. #17986221C22semidirect
57. #17986218C22semidirect
58. #17986214C22semidirect
59. #17986211C22semidirect
60. #17986155C22semidirect
61. #17986154C22semidirect
62. #17986150C22semidirect
63. #17986149C22semidirect
68. C4×#11765855C22semidirect
69. C4×#11765852C22semidirect
70. C4×#11765853C22semidirect
71. C4×#11765850C22semidirect
72. #17986052C22semidirect
73. #17986052C22semidirect
74. #17986052C22semidirect
75. #17986052C22semidirect
76. C2×C4⋊(C71⋊C8)C22semidirect
79. C2×C4×C71⋊C8C22semidirect
86. #529×C71C22semidirect
87. #529×C71C22semidirect
89. C2×#125×C71C22semidirect
90. C2×#124×C71C22semidirect
94. C2×C4×Q8×C71C22semidirect
96. C2×C4×D4×C71C22semidirect
499. C2×#529D71semidirect
515. C71#60945semidirect
530. #529C2×D71semidirect
531. #529C2×D71semidirect
535. C2×#125C2×D71semidirect
537. C2×#124C2×D71semidirect
545. C2×C4×Q8C2×D71semidirect
549. C2×C4×D4C2×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179865332
#225996872
#225995082
#225995042
#225993052
#225993012
#225991122
#225990972
#225990932
#225990882
#225989042
#225984202
#225984162
#225983872
#225983832
C2×#179860522
C2×#529×C712
#6094571