Finite Group Databasebeta

← #11737101

Subgroups — #11737101

Order 896.

390 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×D7C211yesmaximal, characteristic, complemented
2#90248C211yesmaximal, characteristic
3C4×C7×SD16C211yesmaximal, characteristic, complemented
4#89942C211yesmaximal, characteristic
5#89938C211yesmaximal, characteristic, complemented
6C4×#1144C211yesmaximal, characteristic, complemented
7C4×#1142C211yesmaximal, characteristic, complemented
8#89634C211yesmaximal, characteristic, complemented
9#89629C211yesmaximal, characteristic, complemented
10#89580C211yesmaximal, characteristic, complemented
11#89568C211yesmaximal, characteristic, complemented
12#89546C211yesmaximal, characteristic
13#89539C211yesmaximal, characteristic, complemented
14C4×Dic28C211yesmaximal, characteristic, complemented
15#89457C211yesmaximal, characteristic, complemented
16C2×Q8×D7C2211yescharacteristic
17C2×C7×SD16C2211yescharacteristic
18C4×C7×Q8C2211yescharacteristic
19C4×C7×D4C2211yescharacteristic
20Q8×Dic7C2211yescharacteristic
21C2×#1144C2211yescharacteristic
22#6501C2211yescharacteristic
23#6499C2211yescharacteristic
24C2×#1142C2211yescharacteristic
25C4×C22⋊D7—21no—
26#6489—21no—
27C2×Dic28C2211yescharacteristic
28#6460C2211yescharacteristic
29D7×C4⋊C4—21no—
30D7×C4⋊C4C2211yescharacteristic
31#6453C2211yescharacteristic
32#6450—21no—
33#6450C2211yescharacteristic
34#6446—21no—
35#6442—21no—
36C42×D7—21no—
37C42×D7C2211yescharacteristic
38C4×Dic14—21no—
39C4×Dic14C2211yescharacteristic
40C4×Dic14C2211yescharacteristic
41C7×#106C2211yescharacteristic
42C7×#103C2211yescharacteristic
43C7×#102C2211yescharacteristic
44C4×C7×C8C2211yescharacteristic
45#6409C2211yescharacteristic
46#6406C2211yescharacteristic
47(C2×D7)⋊C8C2211yescharacteristic
48(C2×D7)⋊C8C2211yescharacteristic
49#6392C2211yescharacteristic
50#6390C2211yescharacteristic
51#6390C2211yescharacteristic
52Dic7⋊C8C2211yescharacteristic
53Dic7⋊C8C2211yescharacteristic
54#6384C2211yescharacteristic
55#6384C2211yescharacteristic
56#6382C2211yescharacteristic
57#6381C2211yescharacteristic
58C4×C7⋊C8C2211yescharacteristic
59#3108—71nomaximal, Sylow
60C2×C7×Q8C2311yescharacteristic
61C2×C7×D4C2311yescharacteristic
62C22×C4×C7—21no—
63C2×C22⋊D7—21no—
64Q8×D7—22no—
65Q8×D7—22no—
66C2×C4×D7—21no—
67C2×C4×D7—21no—
68C2×C4×D7D411yescharacteristic
69C2×C4×D7D411yescharacteristic
70C2×C4×D7C2311yescharacteristic
71C2×Dic14—21no—
72C2×Dic14C2311yescharacteristic
73C2×Dic14C2311yescharacteristic
74C7×SD16—22no—
75C2×C7×C8C2311yescharacteristic
76C2×C7×C8C2311yescharacteristic
77C7×C4⋊C4—21no—
78C7×C4⋊C4C2311yescharacteristic
79C7×C4⋊C4C2311yescharacteristic
80C7×C22⋊C4—21no—
81C42×C7—21no—
82C42×C7C2311yescharacteristic
83C22⋊Dic7—21no—
84C22⋊Dic7—21no—
85C22⋊Dic7—21no—
86#1144—22no—
87#1142—22no—
88(C2×D7)⋊C4—21no—
89C4⋊Dic7—21no—
90C4⋊Dic7—21no—
91C4⋊Dic7—21no—
92C4⋊Dic7C2311yescharacteristic
93C4⋊Dic7C2311yescharacteristic
94Dic7⋊C4—21no—
95Dic7⋊C4—21no—
96Dic7⋊C4—21no—
97Dic7⋊C4—21no—
98Dic7⋊C4—21no—
99C4×Dic7—21no—
100C4×Dic7—21no—
101C4×Dic7—21no—
102C4×Dic7—21no—
103C4×Dic7D411yescharacteristic
104C4×Dic7D411yescharacteristic
105C4×Dic7C2311yescharacteristic
106C2×C7⋊C8C2311yescharacteristic
107C2×C7⋊C8C2311yescharacteristic
108Dic28—22no—
109#529—71no—
110C2×C4×Q8—71no—
111#483—71no—
112#480—71no—
113#479—71no—
114#479—71no—
115#464—71no—
116#464—71no—
117#451—71no—
118#448—71no—
119C4×Q16—71no—
120C4×Q16—71no—
121C4×SD16—71no—
122C4×SD16D711yescharacteristic, complemented
123#431—71no—
124C23×C7—21no—
125C22×D7C2×D411yescharacteristic
126C7×Q8—21no—
127C7×Q8#4112yes—
128C7×D4—21no—
129C7×D4—21no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—42no—
134C2×C4×C7C2×D411yescharacteristic
135C2×C4×C7C2×D411yescharacteristic
136C2×C4×C7C2411yescharacteristic
137C22⋊D7—42no—
138C2×Dic7—21no—
139C2×Dic7—21no—
140C2×Dic7—21no—
141C2×Dic7—21no—
142C2×Dic7C2×D411yescharacteristic
143C2×Dic7C2×D411yescharacteristic
144C2×Dic7C2×D411yescharacteristic
145C4×D7—24no—
146C4×D7—22no—
147C4×D7—22no—
148C4×D7—21no—
149C4×D7—21no—
150C4×D7—42no—
151Dic14—24no—
152Dic14—21no—
153Dic14—21no—
154Dic14—21no—
155Dic14#4112yes—
156C7×C8—21no—
157C7×C8—21no—
158C7⋊C8—21no—
159C7⋊C8—21no—
160C22×Q8—71no—
161C2×Q16—71no—
162C2×Q16—71no—
163C2×SD16—71no—
164C2×SD16C2×D711yescharacteristic
165#126—141no—
166#125—71no—
167#124—71no—
168#123—141no—
169C22⋊Q8—71no—
170#121—71no—
171C4×Q8—71no—
172C4×Q8—71no—
173C4×Q8—71no—
174C4×Q8—71no—
175C4×Q8—141no—
176C4×Q8—141no—
177C4×Q8C2×D711yescharacteristic
178C4×D4—141no—
179C4×D4C2×D711yescharacteristic
180#117—141no—
181C2×C4⋊C4—71no—
182C2×C4⋊C4—141no—
183C2×C42—71no—
184C2×C42—141no—
185#107—71no—
186#107—71no—
187#106—71no—
188#106C2×D711yescharacteristic
189C4⋊C8—71no—
190C4⋊C8—71no—
191#103—71no—
192#103—71no—
193#103—71no—
194#103—71no—
195#103—71no—
196#103C2×D711yescharacteristic
197#102—71no—
198#102C2×D711yescharacteristic
199C22⋊C8—71no—
200C22⋊C8—71no—
201C4×C8—71no—
202C4×C8C2×D711yescharacteristic
203C22×C7—41no—
204C22×C7—41no—
205C22×C7—41no—
206C22×C7C22×D411yescharacteristic
207C2×D7—21no—
208C2×D7—21no—
209C2×D7#13512yes—
210C4×C7—22no—
211C4×C7—21no—
212C4×C7—41no—
213C4×C7—41no—
214C4×C7#13712yes—
215C4×C7C2×#4111yescharacteristic
216C4×C7C2×#4111yescharacteristic
217Dic7—21no—
218Dic7—22no—
219Dic7—21no—
220Dic7—21no—
221Dic7—41no—
222Dic7—41no—
223Dic7—41no—
224C2×Q8—71no—
225C2×Q8—71no—
226C2×Q8—141no—
227C2×Q8—142no—
228C2×Q8—142no—
229C2×Q8C22×D711yescharacteristic
230C2×D4—141no—
231C2×D4C22×D711yescharacteristic
232C22×C4—21no—
233C22×C4—71no—
234C22×C4—71no—
235C22×C4—71no—
236C22×C4—141no—
237C22×C4—141no—
238Q16—142no—
239Q16—142no—
240SD16—22no—
241SD16—142no—
242C2×C8—71no—
243C2×C8—71no—
244C2×C8C22×D711yescharacteristic
245C2×C8C22×D711yescharacteristic
246C4⋊C4—21no—
247C4⋊C4—71no—
248C4⋊C4—71no—
249C4⋊C4—141no—
250C4⋊C4—141no—
251C4⋊C4—141no—
252C4⋊C4—141no—
253C4⋊C4—141no—
254C4⋊C4—141no—
255C4⋊C4—141no—
256C4⋊C4—141no—
257C4⋊C4C22×D711yescharacteristic
258C4⋊C4C22×D711yescharacteristic
259C22⋊C4—21no—
260C22⋊C4—141no—
261C22⋊C4—141no—
262C22⋊C4—141no—
263C22⋊C4—141no—
264C42—21no—
265C42—71no—
266C42—71no—
267C42—71no—
268C42—141no—
269C42—141no—
270C42—141no—
271C42—141no—
272C42C22×D711yescharacteristic
273C2×C7—81no—
274C2×C7#52511yescharacteristic
275C2×C7C2×#13511yescharacteristic
276C2×C7C2×#13711yescharacteristic
277D7—22no—
278C23—21no—
279C23—71no—
280Q8—21no—
281Q8—72no—
282Q8—144no—
283Q8—141no—
284Q8—141no—
285Q8—141no—
286Q8#115712yes—
287D4—21no—
288D4—21no—
289D4—282no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—42no—
294C2×C4—71no—
295C2×C4—71no—
296C2×C4—71no—
297C2×C4—142no—
298C2×C4—144no—
299C2×C4—141no—
300C2×C4—142no—
301C2×C4—141no—
302C2×C4—141no—
303C2×C4—141no—
304C2×C4—141no—
305C2×C4—141no—
306C2×C4—282no—
307C2×C4D4×D711yescharacteristic
308C2×C4D4×D711yescharacteristic
309C2×C4C23×D711yescharacteristic
310C8—21no—
311C8—21no—
312C8—141no—
313C8—141no—
314C7#310811yescharacteristic, complemented, Sylow
315C22—41no—
316C22—41no—
317C22—41no—
318C22—72no—
319C22—141no—
320C22—141no—
321C22C2×D4×D711yescharacteristic
322C4—21no—
323C4—22no—
324C4—41no—
325C4—41no—
326C4—141no—
327C4—141no—
328C4—141no—
329C4—142no—
330C4—281no—
331C4—281no—
332C4—281no—
333C4#647812yes—
334C4C2×#115711yescharacteristic
335C4D7×#4111yescharacteristic
336C2—81no—
337C2—142no—
338C2#9023811yescharacteristic
339C2C2×#647811yescharacteristic
340C2D7×#13511yescharacteristic
subgroupG/H
centerC2×C4D4×D7
commutator, cosocleC2×C4×C7C24
FrattiniC2×C4C23×D7
FittingC4×C7×SD16C2
socleC22×C7C22×D4
prime radical#6501C22
hypercenterC4×SD16D7
hypocenterC7#3108
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. C4×Q8×D7C2semidirect
3. C4×C7×SD16C2semidirect
5. #89938C2semidirect
6. C4×#1144C2semidirect
7. C4×#1142C2semidirect
8. #89634C2semidirect
9. #89629C2semidirect
10. #89580C2semidirect
11. #89568C2semidirect
13. #89539C2semidirect
14. C4×Dic28C2semidirect
15. #89457C2semidirect
122. C4×SD16D7semidirect
314. C7#3108semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×D72
#902482
C4×C7×SD162
#899422
#899382
C4×#11442
C4×#11422
#896342
#896292
#895802
#895682
#895462
#895392
C4×Dic282
#894572
#31087