Finite Group Databasebeta

← #13264540

Subgroups — #13264540

Order 1792.

388 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11739690C211yesmaximal, characteristic
2C7×#1464C211yesmaximal, characteristic
3#11729343C211yesmaximal, characteristic
4#11725265C212yesmaximal, complemented
5#11725263C212yesmaximal, complemented
6C2×C7×#117C2211yescharacteristic
7C2×C4×Dic14C411yescharacteristic
8C7×#432—21no—
9C4×C22⋊Dic7—21no—
10#89979—21no—
11#89758C2211yescharacteristic
12#89756—21no—
13#89751C2211yescharacteristic
14#89721C411yescharacteristic
15#89720—21no—
16#89719C411yescharacteristic
17C4×C4⋊Dic7C411yescharacteristic
18C4×Dic7⋊C4—21no—
19C7×#324C2212yes—
20C7×#323—21no—
21#89325—21no—
22#89325C2212yes—
23#11816—71nomaximal, Sylow
24C23×C4×C7D411yescharacteristic
25C22×Dic14C2×C411yescharacteristic
26C7×#117—41no—
27C7×#117—41no—
28C2×C7×C4⋊C4D411yescharacteristic
29C2×C7×C4⋊C4C2311yescharacteristic
30C2×C7×C22⋊C4C2×C411yescharacteristic
31C2×C7×C22⋊C4D411yescharacteristic
32C2×C42×C7C2×C411yescharacteristic
33C2×C42×C7D411yescharacteristic
34C2×C22⋊Dic7—21no—
35C2×C22⋊Dic7—21no—
36C2×C4⋊Dic7—21no—
37C2×C4⋊Dic7C2×C411yescharacteristic
38C2×Dic7⋊C4—21no—
39C2×Dic7⋊C4—21no—
40C2×Dic7⋊C4—21no—
41C2×C4×Dic7—21no—
42C2×C4×Dic7—21no—
43C2×#1136—22no—
44C4×Dic14—41no—
45C4×Dic14—41no—
46C7×C4⋊C8—41no—
47C7×C22⋊C8—22no—
48C7×#97—41no—
49C7⋊#95—21no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95C2×C411yescharacteristic
54C7⋊#95C2×C411yescharacteristic
55C22⋊(C7⋊C8)—41no—
56C22⋊(C7⋊C8)—41no—
57#2396—71no—
58#1822—71no—
59#1464D711yescharacteristic
60#1354—72no—
61#1353—72no—
62C24×C7C22⋊C411yescharacteristic
63C22×C4×C7—21no—
64C22×C4×C7—21no—
65C22×C4×C7—22no—
66C22×C4×C7—41no—
67C22×C4×C7C22⋊C411yescharacteristic
68C22×C4×C7C22⋊C411yescharacteristic
69C22×C4×C7C22⋊C411yescharacteristic
70C22×C4×C7C22×C411yescharacteristic
71C22×C4×C7C2×D411yescharacteristic
72C22×C4×C7C2×D411yescharacteristic
73C22×Dic7—21no—
74C22×Dic7—21no—
75C22×Dic7—21no—
76C22×Dic7—21no—
77C2×Dic14—41no—
78C2×Dic14—42no—
79C2×C7×C8—42no—
80C7×C4⋊C4—41no—
81C7×C4⋊C4—41no—
82C7×C22⋊C4—41no—
83C7×C22⋊C4—41no—
84C42×C7—21no—
85C42×C7—21no—
86C42×C7—21no—
87C42×C7—21no—
88C22⋊Dic7—42no—
89C22⋊Dic7—42no—
90C4⋊Dic7—42no—
91C4⋊Dic7—41no—
92Dic7⋊C4—42no—
93Dic7⋊C4—42no—
94Dic7⋊C4—42no—
95C4×Dic7—42no—
96C4×Dic7—41no—
97C4×Dic7—41no—
98#1136—42no—
99#1136—42no—
100C2×C7⋊C8—42no—
101C2×C4×Q8—71no—
102C2×#117C2×D711yescharacteristic
103#432—21no—
104#407—141no—
105#400—71no—
106#399—71no—
107#398—141no—
108#396—141no—
109#395—71no—
110#393—71no—
111C4×C4⋊C4—71no—
112C4×C4⋊C4—141no—
113C4×C22⋊C4—141no—
114#343—72no—
115#343—141no—
116#324C2×D712yes—
117#323—21no—
118C23×C7—21no—
119C23×C7—21no—
120C23×C7—21no—
121C23×C7—41no—
122C23×C7—41no—
123C23×C7C2×C22⋊C411yescharacteristic
124C2×C4×C7—21no—
125C2×C4×C7—21no—
126C2×C4×C7—21no—
127C2×C4×C7—21no—
128C2×C4×C7—21no—
129C2×C4×C7—21no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—42no—
133C2×C4×C7—42no—
134C2×C4×C7—41no—
135C2×C4×C7—41no—
136C2×C4×C7—41no—
137C2×C4×C7—41no—
138C2×C4×C7#9911yescharacteristic
139C2×C4×C7#9911yescharacteristic
140C2×C4×C7#13712yes—
141C2×Dic7—22no—
142C2×Dic7—22no—
143C2×Dic7—41no—
144C2×Dic7—41no—
145C2×Dic7—41no—
146C2×Dic7—41no—
147C2×Dic7—41no—
148C2×Dic7—41no—
149C2×Dic7—41no—
150C2×Dic7—41no—
151C2×Dic7—41no—
152C2×Dic7—41no—
153Dic14—42no—
154Dic14—42no—
155C7×C8—82no—
156C7⋊C8—82no—
157C22×Q8—71no—
158C23×C4D2811yescharacteristic
159C2×M16—142no—
160C4×Q8—281no—
161C4×Q8—281no—
162#117—41no—
163#117—41no—
164C2×C4⋊C4—71no—
165C2×C4⋊C4—141no—
166C2×C4⋊C4—141no—
167C2×C4⋊C4—141no—
168C2×C4⋊C4—141no—
169C2×C4⋊C4D2811yescharacteristic
170C2×C4⋊C4C22×D711yescharacteristic
171C2×C22⋊C4—141no—
172C2×C22⋊C4—141no—
173C2×C22⋊C4C4×D711yescharacteristic
174C2×C22⋊C4C22⋊D711yescharacteristic
175C2×C42—141no—
176C2×C42—141no—
177C2×C42C4×D711yescharacteristic
178C2×C42C22⋊D711yescharacteristic
179C4⋊C8—41no—
180C22⋊C8—22no—
181C22⋊C8—281no—
182C22⋊C8—281no—
183#97—41no—
184#95—71no—
185#95—71no—
186#95—141no—
187#95—141no—
188#95—141no—
189#95—141no—
190C22×C7—21no—
191C22×C7—21no—
192C22×C7—42no—
193C22×C7—41no—
194C22×C7—41no—
195C22×C7—41no—
196C22×C7—81no—
197C22×C7C2×#9911yescharacteristic
198C22×C7#41911yescharacteristic
199C22×C7#42111yescharacteristic
200C4×C7—22no—
201C4×C7—21no—
202C4×C7—21no—
203C4×C7—41no—
204C4×C7—41no—
205C4×C7—41no—
206C4×C7—41no—
207Dic7—42no—
208Dic7—42no—
209Dic7—81no—
210Dic7—81no—
211C24(C2×D7)⋊C411yescharacteristic
212C2×Q8—281no—
213C2×Q8—282no—
214C22×C4—22no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—41no—
218C22×C4—141no—
219C22×C4—141no—
220C22×C4—141no—
221C22×C4—141no—
222C22×C4(C2×D7)⋊C411yescharacteristic
223C22×C4(C2×D7)⋊C411yescharacteristic
224C22×C4(C2×D7)⋊C411yescharacteristic
225C22×C4C2×C4×D711yescharacteristic
226C22×C4C2×D2811yescharacteristic
227C22×C4C2×C22⋊D711yescharacteristic
228M16—282no—
229M16—282no—
230C2×C8—42no—
231C2×C8—282no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—281no—
235C4⋊C4—282no—
236C4⋊C4—282no—
237C4⋊C4—282no—
238C4⋊C4—282no—
239C22⋊C4—41no—
240C22⋊C4—41no—
241C22⋊C4—282no—
242C22⋊C4—282no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—282no—
248C42—281no—
249C42—281no—
250C2×C7—21no—
251C2×C7—21no—
252C2×C7—81no—
253C2×C7#151111yescharacteristic
254C2×C7#212011yescharacteristic
255C2×C7#213211yescharacteristic
256C23—21no—
257C23—21no—
258C23—21no—
259C23—41no—
260C23—41no—
261C23C2×(C2×D7)⋊C411yescharacteristic
262Q8—282no—
263Q8—282no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—142no—
279C2×C4—142no—
280C2×C4—281no—
281C2×C4—281no—
282C2×C4—281no—
283C2×C4—281no—
284C2×C4—281no—
285C2×C4—281no—
286C2×C4—281no—
287C2×C4—281no—
288C2×C4—281no—
289C2×C4—281no—
290C2×C4#638011yescharacteristic
291C2×C4#638011yescharacteristic
292C2×C4#647212yes—
293C8—82no—
294C8—562no—
295C7#1181611yescharacteristic, complemented, Sylow
296C22—21no—
297C22—21no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22C2×#638011yescharacteristic
304C22#8989211yescharacteristic
305C22#8991111yescharacteristic
306C4—22no—
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—282no—
314C4—282no—
315C4—561no—
316C4—561no—
317C2—21no—
318C2—21no—
319C2—81no—
320C2#1172773511yescharacteristic
321C2#1172781011yescharacteristic
322C2#1172790211yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1464C2
socleC22×C7C2×#99
prime radicalC24×C7C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1464D7
hypocenterC7#11816
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
4. #11725265C2semidirect
5. #11725263C2semidirect
295. C7#11816semidirect

Maximal subgroups

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

subgroupindex
#117396902
C7×#14642
#117293432
#117252652
#117252632
#118167