Finite Group Databasebeta

← #11736918

Subgroups — #11736918

Order 896.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#90256C211yesmaximal, characteristic, complemented
2#90254C211yesmaximal, characteristic, complemented
3C7×#435C211yesmaximal, characteristic, complemented
4#89907C211yesmaximal, characteristic, complemented
5#89893C211yesmaximal, characteristic, complemented
6#89887C211yesmaximal, characteristic, complemented
7#89878C211yesmaximal, characteristic, complemented
8#89619C211yesmaximal, characteristic, complemented
9#89618C211yesmaximal, characteristic, complemented
10#89509C211yesmaximal, characteristic, complemented
11#89509C211yesmaximal, characteristic, complemented
12#89509C211yesmaximal, characteristic, complemented
13#89508C211yesmaximal, characteristic, complemented
14#89483C211yesmaximal, characteristic, complemented
15#89474C211yesmaximal, characteristic, complemented
16C2×C7×M16C2211yescharacteristic
17C22×C7×C8C2211yescharacteristic
18C4×C7×D4C2211yescharacteristic
19#6502—21no—
20#6501—21no—
21#6493C2211yescharacteristic
22#6493C2211yescharacteristic
23#6493C2211yescharacteristic
24#6493C2211yescharacteristic
25#6489C2211yescharacteristic
26#6489C2211yescharacteristic
27#6489C2211yescharacteristic
28C2×C4⋊Dic7C2211yescharacteristic
29C2×D56C2211yescharacteristic
30#6461—21no—
31#6455—21no—
32#6448—21no—
33#6448—21no—
34#6446—21no—
35(C22⋊D7)⋊C4—21no—
36C4×D28C2211yescharacteristic
37C4×D28C2211yescharacteristic
38#6433C2211yescharacteristic
39#6432C2211yescharacteristic
40C7×C4⋊C8C2211yescharacteristic
41C7×C22⋊C8C2211yescharacteristic
42C7×C22⋊C8C2211yescharacteristic
43C7×#97C2211yescharacteristic
44#6395C2211yescharacteristic
45#6395C2211yescharacteristic
46#6395C2211yescharacteristic
47#6395C2211yescharacteristic
48#6395C2211yescharacteristic
49#6395C2211yescharacteristic
50#6392C2211yescharacteristic
51#6392C2211yescharacteristic
52#6392C2211yescharacteristic
53#6392C2211yescharacteristic
54#6392C2211yescharacteristic
55#6391C2211yescharacteristic
56#6391C2211yescharacteristic
57#6391C2211yescharacteristic
58#6391C2211yescharacteristic
59#3347—71nomaximal, Sylow
60C2×C7×D4D411yescharacteristic
61C22×C4×C7C2311yescharacteristic
62C22×C4×C7C2311yescharacteristic
63C2×C22⋊D7—21no—
64C2×C22⋊D7—21no—
65C2×C22⋊D7—21no—
66C2×C22⋊D7—21no—
67C22×Dic7—21no—
68C2×D28C2311yescharacteristic
69C2×D28C2311yescharacteristic
70C2×C4×D7—21no—
71C2×C4×D7—21no—
72C2×Dic14—21no—
73C7×M16—22no—
74C2×C7×C8—22no—
75C2×C7×C8C2311yescharacteristic
76C2×C7×C8C2311yescharacteristic
77C2×C7×C8C2311yescharacteristic
78C2×C7×C8C2311yescharacteristic
79C7×C4⋊C4D411yescharacteristic
80C7×C22⋊C4D411yescharacteristic
81C7×C22⋊C4D411yescharacteristic
82C42×C7C2311yescharacteristic
83C22⋊Dic7—21no—
84C22⋊Dic7—21no—
85C22⋊Dic7—21no—
86(C2×D7)⋊C4—21no—
87(C2×D7)⋊C4—21no—
88(C2×D7)⋊C4—21no—
89(C2×D7)⋊C4—21no—
90(C2×D7)⋊C4—21no—
91(C2×D7)⋊C4—21no—
92C4⋊Dic7—21no—
93C4⋊Dic7—21no—
94C4⋊Dic7C2311yescharacteristic
95C4⋊Dic7C2311yescharacteristic
96C4⋊Dic7C2311yescharacteristic
97C4⋊Dic7C2311yescharacteristic
98C4⋊Dic7C2311yescharacteristic
99C4⋊Dic7C2311yescharacteristic
100Dic7⋊C4—21no—
101Dic7⋊C4—21no—
102C4×Dic7—21no—
103C4×Dic7—21no—
104C4×Dic7—21no—
105D56—22no—
106#555—71no—
107#553—71no—
108#501—71no—
109#482—71no—
110#482—71no—
111#482—71no—
112#480—71no—
113#478—71no—
114#474—71no—
115#469—71no—
116#466—71no—
117#442—71no—
118#435D711yescharacteristic, complemented
119#428—71no—
120#427—71no—
121C23×C7C2×D411yescharacteristic
122C23×C7C2×D411yescharacteristic
123C22×D7—21no—
124C22×D7—21no—
125C7×D4—41no—
126C2×C4×C7—21no—
127C2×C4×C7—21no—
128C2×C4×C7—21no—
129C2×C4×C7—21no—
130C2×C4×C7C2×D411yescharacteristic
131C2×C4×C7C2×D411yescharacteristic
132C2×C4×C7C2×D411yescharacteristic
133C2×C4×C7C2×D411yescharacteristic
134C2×C4×C7C2411yescharacteristic
135C22⋊D7—42no—
136C22⋊D7—81no—
137C22⋊D7—81no—
138C22⋊D7—81no—
139C2×Dic7—21no—
140C2×Dic7—21no—
141C2×Dic7—21no—
142C2×Dic7—21no—
143C2×Dic7—21no—
144C2×Dic7—21no—
145C2×Dic7—81no—
146D28—21no—
147D28—21no—
148D28—21no—
149D28—21no—
150C4×D7—42no—
151C4×D7—81no—
152Dic14—81no—
153C7×C8—21no—
154C7×C8—21no—
155C7×C8—21no—
156C7×C8#4112yes—
157C2×D8—71no—
158C2×M16C2×D711yescharacteristic
159C22×C8C2×D711yescharacteristic
160C4⋊Q8—71no—
161#126—141no—
162#125—71no—
163#124—141no—
164#124—141no—
165#123—141no—
166#121—71no—
167#121—71no—
168#121—71no—
169#121—71no—
170#121—141no—
171#121—141no—
172C4×D4—71no—
173C4×D4—71no—
174C4×D4—141no—
175C4×D4C2×D711yescharacteristic
176#117—71no—
177#117—71no—
178#117—71no—
179#117—141no—
180C2×C4⋊C4—71no—
181#107—71no—
182#107—71no—
183#107—71no—
184#107—71no—
185#107—71no—
186#106—71no—
187#106—71no—
188#106—71no—
189#106—71no—
190C4⋊C8C2×D711yescharacteristic
191#102—71no—
192#102—71no—
193#102—71no—
194#102—71no—
195#102—71no—
196#102—71no—
197C22⋊C8C2×D711yescharacteristic
198C22⋊C8C2×D711yescharacteristic
199#97C2×D711yescharacteristic
200C22×C7—21no—
201C22×C7—21no—
202C22×C7—21no—
203C22×C7—21no—
204C22×C7—21no—
205C22×C7—21no—
206C22×C7C22×D411yescharacteristic
207C2×D7—41no—
208C2×D7—41no—
209C2×D7—41no—
210C2×D7—41no—
211C2×D7—41no—
212C2×D7—41no—
213C4×C7—21no—
214C4×C7—21no—
215C4×C7—21no—
216C4×C7—21no—
217C4×C7C2×#4111yescharacteristic
218C4×C72−1+411yescharacteristic
219Dic7—41no—
220Dic7—41no—
221Dic7—41no—
222Dic7—41no—
223Dic7—41no—
224Dic7—41no—
225C2×Q8—141no—
226C2×D4—71no—
227C2×D4—71no—
228C2×D4—141no—
229C2×D4—141no—
230C2×D4—141no—
231C2×D4—141no—
232C2×D4D2811yescharacteristic
233C22×C4—141no—
234C22×C4—141no—
235C22×C4—141no—
236C22×C4C22×D711yescharacteristic
237C22×C4C22×D711yescharacteristic
238D8—142no—
239M16—22no—
240C2×C8—22no—
241C2×C8C22×D711yescharacteristic
242C2×C8C22×D711yescharacteristic
243C2×C8C22×D711yescharacteristic
244C2×C8C22×D711yescharacteristic
245C4⋊C4—71no—
246C4⋊C4—71no—
247C4⋊C4—71no—
248C4⋊C4—71no—
249C4⋊C4—71no—
250C4⋊C4—71no—
251C4⋊C4—141no—
252C4⋊C4—141no—
253C4⋊C4—141no—
254C4⋊C4—141no—
255C4⋊C4D2811yescharacteristic
256C22⋊C4—141no—
257C22⋊C4—141no—
258C22⋊C4—141no—
259C22⋊C4—141no—
260C22⋊C4—141no—
261C22⋊C4—141no—
262C22⋊C4—141no—
263C22⋊C4—141no—
264C22⋊C4—141no—
265C22⋊C4D2811yescharacteristic
266C22⋊C4D2811yescharacteristic
267C42—141no—
268C42—141no—
269C42—141no—
270C42C22×D711yescharacteristic
271C2×C7—41no—
272C2×C7—41no—
273C2×C7#54711yescharacteristic
274C2×C7#57511yescharacteristic
275C2×C7#57611yescharacteristic
276D7—81no—
277D7—81no—
278C23—141no—
279C23—141no—
280C23C2×D2811yescharacteristic
281C23C2×D2811yescharacteristic
282Q8—561no—
283D4—41no—
284D4—141no—
285D4—141no—
286D4—141no—
287D4—141no—
288D4—282no—
289D4—561no—
290D4—561no—
291D4—561no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—141no—
297C2×C4—141no—
298C2×C4—141no—
299C2×C4—141no—
300C2×C4—141no—
301C2×C4—141no—
302C2×C4—282no—
303C2×C4—561no—
304C2×C4—561no—
305C2×C4C2×D2811yescharacteristic
306C2×C4C2×D2811yescharacteristic
307C2×C4C2×D2811yescharacteristic
308C2×C4C2×D2811yescharacteristic
309C2×C4C23×D711yescharacteristic
310C8—21no—
311C8—21no—
312C8—21no—
313C8#115912yes—
314C7#334711yescharacteristic, complemented, Sylow
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—281no—
322C22—281no—
323C22—281no—
324C22—281no—
325C22—281no—
326C22—281no—
327C22C22×D2811yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—281no—
333C4—281no—
334C4—281no—
335C4—281no—
336C4—281no—
337C4—281no—
338C4C2×#115911yescharacteristic
339C4#655411yescharacteristic
340C2—41no—
341C2—41no—
342C2—561no—
343C2—561no—
344C2#9024611yescharacteristic
345C2#9043911yescharacteristic
346C2#9044311yescharacteristic
subgroupG/H
centerC22C22×D28
commutator, cosocleC2×C4×C7C24
FrattiniC2×C4C23×D7
FittingC7×#435C2
socleC22×C7C22×D4
hypercenter#435D7
hypocenterC7#3347
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #90256C2semidirect
2. #90254C2semidirect
3. C7×#435C2semidirect
4. #89907C2semidirect
5. #89893C2semidirect
6. #89887C2semidirect
7. #89878C2semidirect
8. #89619C2semidirect
9. #89618C2semidirect
10. #89509C2semidirect
11. #89509C2semidirect
12. #89509C2semidirect
13. #89508C2semidirect
14. #89483C2semidirect
15. #89474C2semidirect
118. #435D7semidirect
314. C7#3347semidirect

Maximal subgroups

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

subgroupindex
#902562
#902542
C7×#4352
#899072
#898932
#898872
#898782
#896192
#896182
#895092
#895082
#894832
#894742
#33477