Finite Group Databasebeta

← #11737014

Subgroups — #11737014

Order 896.

362 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
1#90250C211yesmaximal, characteristic, complemented
2#90230C211yesmaximal, characteristic, complemented
3C4×C7×D8C211yesmaximal, characteristic, complemented
4#89925C211yesmaximal, characteristic, complemented
5#89922C211yesmaximal, characteristic
6#89788C211yesmaximal, characteristic, complemented
7#89781C211yesmaximal, characteristic, complemented
8#89663C211yesmaximal, characteristic, complemented
9#89647C211yesmaximal, characteristic, complemented
10#89540C211yesmaximal, characteristic, complemented
11#89532C211yesmaximal, characteristic, complemented
12#89530C211yesmaximal, characteristic, complemented
13#89528C211yesmaximal, characteristic, complemented
14#89469C211yesmaximal, characteristic, complemented
15C8×Dic14C211yesmaximal, characteristic, complemented
16C2×C7×D8C2211yescharacteristic
17C4×C7×D4C2211yescharacteristic
18C4×C7×D4C2211yescharacteristic
19#6503C2211yescharacteristic
20#6499C2211yescharacteristic
21D4×Dic7C2211yescharacteristic
22D4×Dic7C2211yescharacteristic
23C2×#1142C2211yescharacteristic
24C2×#1141C2211yescharacteristic
25#6492—21no—
26C4×C22⋊D7—21no—
27#6487—21no—
28C2×Dic7⋊C4—21no—
29#6456C2211yescharacteristic
30#6453C2211yescharacteristic
31#6451C2211yescharacteristic
32#6450C2211yescharacteristic
33#6448—21no—
34#6446—21no—
35#6441—21no—
36#6441—21no—
37#6438C2211yescharacteristic
38#6433C2211yescharacteristic
39C4×Dic14C2211yescharacteristic
40C7×#107C2211yescharacteristic
41C7×#102C2211yescharacteristic
42C7×#102C2211yescharacteristic
43C4×C7×C8C2211yescharacteristic
44#6406C2211yescharacteristic
45#6406C2211yescharacteristic
46#6395C2211yescharacteristic
47#6395C2211yescharacteristic
48#6390C2211yescharacteristic
49#6390C2211yescharacteristic
50Dic7⋊C8C2211yescharacteristic
51Dic7⋊C8C2211yescharacteristic
52C8×Dic7C2211yescharacteristic
53C8×Dic7C2211yescharacteristic
54#6384C2211yescharacteristic
55#6383C2211yescharacteristic
56#6382C2211yescharacteristic
57#6381C2211yescharacteristic
58C4⋊(C7⋊C8)C2211yescharacteristic
59#3361—71nomaximal, Sylow
60C2×C7×D4C2311yescharacteristic
61C2×C7×D4C2311yescharacteristic
62C22×C4×C7—21no—
63C22×C4×C7—21no—
64C2×C22⋊D7—21no—
65C2×C22⋊D7—21no—
66C22×Dic7—21no—
67C22×Dic7—21no—
68C2×D28C2311yescharacteristic
69C2×C4×D7—21no—
70C2×Dic14—21no—
71C2×Dic14D411yescharacteristic
72C2×Dic14C2311yescharacteristic
73C7×D8—22no—
74C2×C7×C8C2311yescharacteristic
75C2×C7×C8C2311yescharacteristic
76C7×C4⋊C4C2311yescharacteristic
77C7×C4⋊C4C2311yescharacteristic
78C7×C22⋊C4—21no—
79C7×C22⋊C4—21no—
80C42×C7C2311yescharacteristic
81C22⋊Dic7—21no—
82C22⋊Dic7—21no—
83C22⋊Dic7—21no—
84C22⋊Dic7—21no—
85#1142—22no—
86#1141—22no—
87(C2×D7)⋊C4—21no—
88(C2×D7)⋊C4—21no—
89(C2×D7)⋊C4—21no—
90C4⋊Dic7—21no—
91C4⋊Dic7D411yescharacteristic
92C4⋊Dic7C2311yescharacteristic
93C4⋊Dic7C2311yescharacteristic
94Dic7⋊C4—21no—
95Dic7⋊C4—21no—
96Dic7⋊C4—21no—
97Dic7⋊C4—21no—
98Dic7⋊C4—21no—
99Dic7⋊C4D411yescharacteristic
100Dic7⋊C4D411yescharacteristic
101C4×Dic7—21no—
102C4×Dic7C2311yescharacteristic
103C4×Dic7C2311yescharacteristic
104C2×C7⋊C8C2311yescharacteristic
105C2×C7⋊C8C2311yescharacteristic
106#559—71no—
107#554—71no—
108#488—71no—
109#488—71no—
110#486—71no—
111#478—71no—
112#478—71no—
113#477—71no—
114#463—71no—
115#463—71no—
116#459—71no—
117C8×Q8—71no—
118C4×SD16—71no—
119C4×D8—71no—
120C4×D8D711yescharacteristic, complemented
121C23×C7—21no—
122C23×C7—21no—
123C22×D7—21no—
124C7×D4—21no—
125C7×D4—21no—
126C7×D4—21no—
127C7×D4#4112yes—
128C2×C4×C7—21no—
129C2×C4×C7—21no—
130C2×C4×C7—81no—
131C2×C4×C7—81no—
132C2×C4×C7C2×D411yescharacteristic
133C2×C4×C7C2×D411yescharacteristic
134C2×C4×C7C2411yescharacteristic
135C22⋊D7—42no—
136C22⋊D7—81no—
137C2×Dic7—21no—
138C2×Dic7—21no—
139C2×Dic7—21no—
140C2×Dic7—42no—
141C2×Dic7—81no—
142C2×Dic7C2×D411yescharacteristic
143C2×Dic7C2×D411yescharacteristic
144C2×Dic7C2×D411yescharacteristic
145C2×Dic7C2×D411yescharacteristic
146D28—21no—
147D28—21no—
148C4×D7—81no—
149Dic14—22no—
150Dic14—21no—
151Dic14—21no—
152Dic14—81no—
153C7×C8—21no—
154C7×C8—21no—
155C7⋊C8—21no—
156C7⋊C8—21no—
157C2×SD16—71no—
158C2×D8—71no—
159C2×D8C2×D711yescharacteristic
160C4⋊Q8—71no—
161#127—71no—
162#125—71no—
163#125—71no—
164#124—71no—
165#124—71no—
166#124—141no—
167#123—141no—
168#123—141no—
169C22⋊Q8—141no—
170C22⋊Q8—141no—
171C22⋊Q8—141no—
172C4×Q8—71no—
173C4×Q8—71no—
174C4×D4—71no—
175C4×D4—71no—
176C4×D4—71no—
177C4×D4—141no—
178C4×D4C2×D711yescharacteristic
179C4×D4C2×D711yescharacteristic
180C2×C4⋊C4—141no—
181#107—71no—
182#107C2×D711yescharacteristic
183#106—71no—
184C4⋊C8—71no—
185C4⋊C8—71no—
186C4⋊C8—71no—
187#103—71no—
188#103—71no—
189#103—71no—
190#102—71no—
191#102—71no—
192#102—71no—
193#102—71no—
194#102—71no—
195#102C2×D711yescharacteristic
196#102C2×D711yescharacteristic
197C4×C8—71no—
198C4×C8—71no—
199C4×C8C2×D711yescharacteristic
200C22×C7—22no—
201C22×C7—41no—
202C22×C7—41no—
203C22×C7—41no—
204C22×C7—41no—
205C22×C7—41no—
206C22×C7C22×D411yescharacteristic
207C2×D7—41no—
208C2×D7—41no—
209C2×D7—41no—
210C4×C7—21no—
211C4×C7—21no—
212C4×C7—41no—
213C4×C7—41no—
214C4×C7C2×#4111yescharacteristic
215C4×C72−1+411yescharacteristic
216Dic7—21no—
217Dic7—21no—
218Dic7—21no—
219Dic7—41no—
220Dic7—41no—
221Dic7—41no—
222Dic7#13512yes—
223C2×Q8—71no—
224C2×Q8—71no—
225C2×Q8—141no—
226C2×D4—71no—
227C2×D4—141no—
228C2×D4—141no—
229C2×D4C22×D711yescharacteristic
230C2×D4C22×D711yescharacteristic
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—141no—
234C22×C4—141no—
235C22×C4—141no—
236SD16—142no—
237D8—22no—
238D8—142no—
239C2×C8—71no—
240C2×C8—71no—
241C2×C8C22×D711yescharacteristic
242C2×C8C22×D711yescharacteristic
243C4⋊C4—71no—
244C4⋊C4—71no—
245C4⋊C4—71no—
246C4⋊C4—71no—
247C4⋊C4—71no—
248C4⋊C4—141no—
249C4⋊C4—141no—
250C4⋊C4—141no—
251C4⋊C4—141no—
252C4⋊C4—141no—
253C4⋊C4—141no—
254C4⋊C4C22×D711yescharacteristic
255C4⋊C4C22×D711yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—21no—
258C22⋊C4—141no—
259C22⋊C4—141no—
260C22⋊C4—141no—
261C22⋊C4—141no—
262C22⋊C4—141no—
263C22⋊C4—141no—
264C22⋊C4—141no—
265C42—71no—
266C42—71no—
267C42—141no—
268C42C22×D711yescharacteristic
269C2×C7—42no—
270C2×C7—81no—
271C2×C7#54811yescharacteristic
272C2×C7C2×#13511yescharacteristic
273C2×C7#57611yescharacteristic
274D7—81no—
275C23—21no—
276C23—21no—
277C23—141no—
278Q8—142no—
279Q8—141no—
280Q8—141no—
281Q8—561no—
282D4—21no—
283D4—21no—
284D4—21no—
285D4—141no—
286D4—141no—
287D4—282no—
288D4—561no—
289D4#115712yes—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—71no—
293C2×C4—71no—
294C2×C4—71no—
295C2×C4—71no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—141no—
299C2×C4—141no—
300C2×C4—141no—
301C2×C4—282no—
302C2×C4—561no—
303C2×C4—561no—
304C2×C4D4×D711yescharacteristic
305C2×C4D4×D711yescharacteristic
306C2×C4C23×D711yescharacteristic
307C8—21no—
308C8—21no—
309C8—141no—
310C8—141no—
311C7#336111yescharacteristic, complemented, Sylow
312C22—22no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—281no—
319C22—281no—
320C22—281no—
321C22C2×D4×D711yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—72no—
327C4—141no—
328C4—141no—
329C4—141no—
330C4—281no—
331C4—281no—
332C4—281no—
333C4C2×#115711yescharacteristic
334C4#655411yescharacteristic
335C2—42no—
336C2—81no—
337C2—561no—
338C2#9024311yescharacteristic
339C2#9044811yescharacteristic
340C2D7×#13511yescharacteristic
subgroupG/H
centerC22C2×D4×D7
commutator, cosocleC2×C4×C7C24
FrattiniC2×C4C23×D7
FittingC4×C7×D8C2
socleC22×C7C22×D4
prime radical#89922C2
hypercenterC4×D8D7
hypocenterC7#3361
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #90250C2semidirect
2. #90230C2semidirect
3. C4×C7×D8C2semidirect
4. #89925C2semidirect
6. #89788C2semidirect
7. #89781C2semidirect
8. #89663C2semidirect
9. #89647C2semidirect
10. #89540C2semidirect
11. #89532C2semidirect
12. #89530C2semidirect
13. #89528C2semidirect
14. #89469C2semidirect
15. C8×Dic14C2semidirect
120. C4×D8D7semidirect
311. C7#3361semidirect

Maximal subgroups

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

subgroupindex
#902502
#902302
C4×C7×D82
#899252
#899222
#897882
#897812
#896632
#896472
#895402
#895322
#895302
#895282
#894692
C8×Dic142
#33617