Finite Group Databasebeta

← #11739849

Subgroups — #11739849

Order 896.

800 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C7×D4C211yesmaximal, characteristic, complemented
2C2×#6500C211yesmaximal, characteristic
3C2×#6492C211yesmaximal, characteristic, complemented
4C22×(C2×D7)⋊C4C211yesmaximal, characteristic, complemented
5#89992C211yesmaximal, characteristic, complemented
6#89985C211yesmaximal, characteristic, complemented
7#89982C211yesmaximal, characteristic, complemented
8#89765C211yesmaximal, characteristic, complemented
9#89764C211yesmaximal, characteristic, complemented
10#89731C211yesmaximal, characteristic, complemented
11#89731C211yesmaximal, characteristic, complemented
12#89727C211yesmaximal, characteristic, complemented
13#89714C211yesmaximal, characteristic, complemented
14#89712C211yesmaximal, characteristic, complemented
15#89712C211yesmaximal, characteristic, complemented
16C24×D7C2211yescharacteristic
17C22×C7×D4C2211yescharacteristic
18C23×C4×C7C2211yescharacteristic
19C23×C4×C7C2211yescharacteristic, complemented
20C22×C22⋊D7C2211yescharacteristic
21C22×C22⋊D7C2211yescharacteristic
22C23×Dic7C2211yescharacteristic
23C4×C7×D4—24no—
24C2×C7×C4⋊C4C2211yescharacteristic, complemented
25C2×C7×C22⋊C4C2211yescharacteristic
26C2×C7×C22⋊C4C2211yescharacteristic, complemented
27C2×C42×C7C2211yescharacteristic, complemented
28C2×C22⋊Dic7C2211yescharacteristic
29C2×C22⋊Dic7C2211yescharacteristic
30C2×C22⋊Dic7C2211yescharacteristic, complemented
31C2×C22⋊Dic7C2211yescharacteristic, complemented
32#6500—24no—
33#6492—24no—
34C2×(C2×D7)⋊C4—24no—
35C2×(C2×D7)⋊C4C2211yescharacteristic
36C2×(C2×D7)⋊C4C2211yescharacteristic
37C2×(C2×D7)⋊C4C2211yescharacteristic
38C2×(C2×D7)⋊C4C2211yescharacteristic
39C2×(C2×D7)⋊C4C2211yescharacteristic
40C2×(C2×D7)⋊C4C2211yescharacteristic
41C2×(C2×D7)⋊C4C2211yescharacteristic
42C2×(C2×D7)⋊C4C2211yescharacteristic
43C2×(C2×D7)⋊C4C2211yescharacteristic
44C2×(C2×D7)⋊C4C2211yescharacteristic
45C2×Dic7⋊C4C2211yescharacteristic, complemented
46C2×Dic7⋊C4C2211yescharacteristic, complemented
47C2×Dic7⋊C4C2211yescharacteristic, complemented
48C2×Dic7⋊C4C2211yescharacteristic, complemented
49C7⋊#95C2211yescharacteristic, complemented
50C7⋊#95C2211yescharacteristic, complemented
51C7⋊#95C2211yescharacteristic, complemented
52C7⋊#95C2211yescharacteristic, complemented
53C7⋊#95C2211yescharacteristic, complemented
54C7⋊#95C2211yescharacteristic, complemented
55#2418—71nomaximal, Sylow
56C24×C7C2311yescharacteristic
57C24×C7C2311yescharacteristic
58C23×D7—22no—
59C23×D7—22no—
60C23×D7—22no—
61C23×D7—22no—
62C23×D7—22no—
63C23×D7—41no—
64C23×D7—41no—
65C23×D7C2311yescharacteristic
66C23×D7C2311yescharacteristic
67C2×C7×D4—22no—
68C2×C7×D4—22no—
69C2×C7×D4D414yes—
70C22×C4×C7—22no—
71C22×C4×C7—22no—
72C22×C4×C7—22no—
73C22×C4×C7—22no—
74C22×C4×C7—41no—
75C22×C4×C7—41no—
76C22×C4×C7C2311yescharacteristic
77C22×C4×C7C2311yescharacteristic
78C22×C4×C7C2311yescharacteristic
79C22×C4×C7C2311yescharacteristic
80C22×C4×C7C2311yescharacteristic
81C2×C22⋊D7—22no—
82C2×C22⋊D7—22no—
83C2×C22⋊D7—22no—
84C2×C22⋊D7—22no—
85C2×C22⋊D7—41no—
86C2×C22⋊D7—41no—
87C22×Dic7—22no—
88C22×Dic7—22no—
89C22×Dic7—41no—
90C22×Dic7C2311yescharacteristic
91C22×Dic7C2311yescharacteristic
92C22×Dic7C2311yescharacteristic
93C22×Dic7C2311yescharacteristic
94C22×Dic7C2311yescharacteristic
95C22×Dic7C2311yescharacteristic
96C7×C4⋊C4—22no—
97C7×C22⋊C4—22no—
98C7×C22⋊C4—22no—
99C42×C7—22no—
100C22⋊Dic7—22no—
101C22⋊Dic7—22no—
102C22⋊Dic7—22no—
103C22⋊Dic7—41no—
104(C2×D7)⋊C4—22no—
105(C2×D7)⋊C4—22no—
106(C2×D7)⋊C4—22no—
107(C2×D7)⋊C4—22no—
108(C2×D7)⋊C4—22no—
109(C2×D7)⋊C4—22no—
110(C2×D7)⋊C4—22no—
111(C2×D7)⋊C4—41no—
112(C2×D7)⋊C4—41no—
113(C2×D7)⋊C4D414yescomplemented
114Dic7⋊C4—22no—
115Dic7⋊C4—22no—
116Dic7⋊C4—41no—
117Dic7⋊C4—41no—
118C2×#123—71no—
119C2×#120—71no—
120C2×C4×D4D711yescharacteristic, complemented
121C22×C22⋊C4—71no—
122#399—71no—
123#397—71no—
124#394—71no—
125#394—71no—
126#388—71no—
127#388—71no—
128#386—71no—
129#386—71no—
130#385—71no—
131#380—71no—
132#379—71no—
133C23×C7—21no—
134C23×C7—21no—
135C23×C7—21no—
136C23×C7—21no—
137C23×C7—21no—
138C23×C7—21no—
139C23×C7—21no—
140C23×C7—21no—
141C23×C7—21no—
142C23×C7—21no—
143C23×C7C2×D412yes—
144C23×C7C2×D412yes—
145C23×C7#4112yes—
146C23×C7#4112yes—
147C23×C7C2411yescharacteristic
148C22×D7—28no—
149C22×D7—21no—
150C22×D7—21no—
151C22×D7—21no—
152C22×D7—21no—
153C22×D7—21no—
154C22×D7—21no—
155C22×D7—21no—
156C22×D7—21no—
157C22×D7—21no—
158C22×D7—21no—
159C22×D7—21no—
160C22×D7—21no—
161C22×D7—44no—
162C22×D7—44no—
163C22×D7—44no—
164C22×D7—44no—
165C22×D7—44no—
166C22×D7—44no—
167C22×D7C2×D412yes—
168C22×D7#4112yes—
169C7×D4—28no—
170C2×C4×C7—21no—
171C2×C4×C7—21no—
172C2×C4×C7—21no—
173C2×C4×C7—21no—
174C2×C4×C7—21no—
175C2×C4×C7—21no—
176C2×C4×C7—21no—
177C2×C4×C7—21no—
178C2×C4×C7—21no—
179C2×C4×C7—21no—
180C2×C4×C7—21no—
181C2×C4×C7—21no—
182C2×C4×C7—21no—
183C2×C4×C7—44no—
184C2×C4×C7—44no—
185C2×C4×C7C2×D412yes—
186C2×C4×C7C2×D412yes—
187C22⋊D7—44no—
188C22⋊D7—44no—
189C2×Dic7—21no—
190C2×Dic7—21no—
191C2×Dic7—21no—
192C2×Dic7—21no—
193C2×Dic7—21no—
194C2×Dic7—21no—
195C2×Dic7—21no—
196C2×Dic7—21no—
197C2×Dic7—21no—
198C2×Dic7—21no—
199C2×Dic7—21no—
200C2×Dic7—21no—
201C2×Dic7—21no—
202C2×Dic7—21no—
203C2×Dic7—21no—
204C2×Dic7—21no—
205C2×Dic7—21no—
206C2×Dic7—44no—
207C2×Dic7C2×D412yes—
208C25—71no—
209C22×D4—71no—
210C22×D4—71no—
211C22×D4C2×D711yescharacteristic
212C23×C4—71no—
213C23×C4C2×D711yescharacteristic
214C23×C4C2×D711yescharacteristic, complemented
215#123—144no—
216#120—144no—
217C4×D4—24no—
218C2×C4⋊C4—71no—
219C2×C4⋊C4—71no—
220C2×C4⋊C4—71no—
221C2×C4⋊C4—71no—
222C2×C4⋊C4C2×D711yescharacteristic, complemented
223C2×C22⋊C4—71no—
224C2×C22⋊C4—71no—
225C2×C22⋊C4—71no—
226C2×C22⋊C4—71no—
227C2×C22⋊C4—71no—
228C2×C22⋊C4—71no—
229C2×C22⋊C4—71no—
230C2×C22⋊C4—71no—
231C2×C22⋊C4—71no—
232C2×C22⋊C4—71no—
233C2×C22⋊C4—71no—
234C2×C22⋊C4—71no—
235C2×C22⋊C4—71no—
236C2×C22⋊C4—71no—
237C2×C22⋊C4—144no—
238C2×C22⋊C4C2×D711yescharacteristic
239C2×C22⋊C4C2×D711yescharacteristic, complemented
240C2×C42C2×D711yescharacteristic, complemented
241#95—71no—
242#95—71no—
243#95—71no—
244#95—71no—
245#95—71no—
246#95—71no—
247C22×C7—22no—
248C22×C7—22no—
249C22×C7—22no—
250C22×C7—22no—
251C22×C7—22no—
252C22×C7—22no—
253C22×C7—22no—
254C22×C7—22no—
255C22×C7—22no—
256C22×C7—41no—
257C22×C7—41no—
258C22×C7—41no—
259C22×C7—41no—
260C22×C7#12314yescomplemented
261C22×C7C22×D411yescharacteristic
262C22×C7C22×D411yescharacteristic
263C22×C7C2×#4111yescharacteristic
264C22×C7C2×#4111yescharacteristic
265C22×C7C2×#4111yescharacteristic
266C22×C7H(5,𝔽2)11yescharacteristic
267C22×C7H(5,𝔽2)11yescharacteristic
268C2×D7—22no—
269C2×D7—22no—
270C2×D7—22no—
271C2×D7—22no—
272C2×D7—22no—
273C2×D7—22no—
274C2×D7—416no—
275C2×D7—41no—
276C2×D7—41no—
277C2×D7—41no—
278C2×D7—41no—
279C2×D7—41no—
280C2×D7—41no—
281C2×D7—41no—
282C2×D7—41no—
283C4×C7—22no—
284C4×C7—22no—
285C4×C7—41no—
286C4×C7—41no—
287C4×C7—41no—
288Dic7—22no—
289Dic7—41no—
290Dic7—41no—
291Dic7—41no—
292Dic7—41no—
293Dic7—41no—
294C24—71no—
295C24—71no—
296C24—142no—
297C24—142no—
298C24—142no—
299C24—142no—
300C24—142no—
301C24—281no—
302C24—281no—
303C24C22×D711yescharacteristic
304C24C22×D711yescharacteristic
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—142no—
308C2×D4—142no—
309C2×D4—142no—
310C2×D4—142no—
311C2×D4—281no—
312C2×D4—281no—
313C2×D4C22⋊D714yes—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—71no—
321C22×C4—71no—
322C22×C4—71no—
323C22×C4—71no—
324C22×C4—71no—
325C22×C4—71no—
326C22×C4—142no—
327C22×C4—142no—
328C22×C4—281no—
329C22×C4C22×D711yescharacteristic
330C22×C4C22×D711yescharacteristic
331C22×C4C22×D711yescharacteristic
332C22×C4C22×D711yescharacteristic
333C22×C4C22×D711yescharacteristic
334C4⋊C4—22no—
335C4⋊C4—142no—
336C4⋊C4—142no—
337C4⋊C4—281no—
338C4⋊C4—281no—
339C22⋊C4—22no—
340C22⋊C4—22no—
341C22⋊C4—74no—
342C22⋊C4—142no—
343C22⋊C4—142no—
344C22⋊C4—142no—
345C22⋊C4—142no—
346C22⋊C4—142no—
347C22⋊C4—142no—
348C22⋊C4—142no—
349C22⋊C4—142no—
350C22⋊C4—142no—
351C22⋊C4—142no—
352C22⋊C4—281no—
353C22⋊C4—281no—
354C22⋊C4—281no—
355C42—22no—
356C2×C7—24no—
357C2×C7—42no—
358C2×C7C2×#12311yescharacteristic
359C2×C7#52511yescharacteristic
360C2×C7#53811yescharacteristic
361C2×C7D4211yescharacteristic
362C2×C7#54611yescharacteristic
363C2×C7#54611yescharacteristic
364C2×C7#55111yescharacteristic
365D7—42no—
366D7—42no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—72no—
378C23—72no—
379C23—148no—
380C23—141no—
381C23—141no—
382C23—141no—
383C23—141no—
384C23—141no—
385C23—141no—
386C23—141no—
387C23—141no—
388C23—141no—
389C23—141no—
390C23—141no—
391C23—141no—
392C23—284no—
393C23—284no—
394C23—284no—
395C23—284no—
396C23—284no—
397C23—284no—
398C23#115712yes—
399C23#115712yes—
400C23C2×C22⋊D712yes—
401C23C2×C22⋊D712yes—
402C23C23×D711yescharacteristic
403D4—28no—
404D4—284no—
405D4—284no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—44no—
420C2×C4—44no—
421C2×C4—72no—
422C2×C4—141no—
423C2×C4—141no—
424C2×C4—141no—
425C2×C4—141no—
426C2×C4—141no—
427C2×C4—141no—
428C2×C4—141no—
429C2×C4—141no—
430C2×C4—141no—
431C2×C4—141no—
432C2×C4—141no—
433C2×C4—141no—
434C2×C4—141no—
435C2×C4—141no—
436C2×C4—141no—
437C2×C4—141no—
438C2×C4—141no—
439C2×C4—284no—
440C2×C4D4×D712yes—
441C2×C4C2×C22⋊D712yes—
442C7#241811yescharacteristic, complemented, Sylow
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—142no—
457C22—142no—
458C22—142no—
459C22—142no—
460C22—142no—
461C22—142no—
462C22—2816no—
463C22—281no—
464C22—281no—
465C22—281no—
466C22—281no—
467C22—281no—
468C22—281no—
469C22—281no—
470C22—281no—
471C22#649214yescomplemented
472C22C2×#115711yescharacteristic
473C22C2×#115711yescharacteristic
474C22C2×D4×D711yescharacteristic
475C22#654811yescharacteristic
476C22D7×#4111yescharacteristic
477C22#655311yescharacteristic
478C22C22×C22⋊D711yescharacteristic
479C4—22no—
480C4—22no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—142no—
485C4—281no—
486C4—281no—
487C4—281no—
488C4—281no—
489C4—281no—
490C2—24no—
491C2—42no—
492C2—282no—
493C2—282no—
494C2#9023811yescharacteristic
495C2#9024111yescharacteristic
496C2#9024711yescharacteristic
497C2#9025111yescharacteristic
498C2C2×#649211yescharacteristic
499C2D4×C22⋊D711yescharacteristic
500C2#9052011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D7
commutator, socle, cosocleC23×C7C24
FittingC2×C4×C7×D4C2
prime radicalC2×#6500C2
hypercenterC2×C4×D4D7
hypocenterC7#2418
LCSG ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C7×D4C2semidirect
3. C2×#6492C2semidirect
4. C22×(C2×D7)⋊C4C2semidirect
5. #89992C2semidirect
6. #89985C2semidirect
7. #89982C2semidirect
8. #89765C2semidirect
9. #89764C2semidirect
10. #89731C2semidirect
11. #89731C2semidirect
12. #89727C2semidirect
13. #89714C2semidirect
14. #89712C2semidirect
15. #89712C2semidirect
19. C23×C4×C7C22semidirect
24. C2×C7×C4⋊C4C22semidirect
26. C2×C7×C22⋊C4C22semidirect
27. C2×C42×C7C22semidirect
30. C2×C22⋊Dic7C22semidirect
31. C2×C22⋊Dic7C22semidirect
45. C2×Dic7⋊C4C22semidirect
46. C2×Dic7⋊C4C22semidirect
47. C2×Dic7⋊C4C22semidirect
48. C2×Dic7⋊C4C22semidirect
49. C7⋊#95C22semidirect
50. C7⋊#95C22semidirect
51. C7⋊#95C22semidirect
52. C7⋊#95C22semidirect
53. C7⋊#95C22semidirect
54. C7⋊#95C22semidirect
113. (C2×D7)⋊C4D4semidirect
120. C2×C4×D4D7semidirect
214. C23×C4C2×D7semidirect
222. C2×C4⋊C4C2×D7semidirect
239. C2×C22⋊C4C2×D7semidirect
240. C2×C42C2×D7semidirect
260. C22×C7#123semidirect
442. C7#2418semidirect
471. C22#6492semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C7×D42
C2×#65002
C2×#64922
C22×(C2×D7)⋊C42
#899922
#899852
#899822
#897652
#897642
#897312
#897272
#897142
#897122
#24187