Finite Group Databasebeta

← #13263188

Subgroups — #13263188

Order 1792.

510 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 77 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#11734055C211yesmaximal, characteristic
2#11725880C212yesmaximal
3C7×#1319C211yesmaximal, characteristic, complemented
4#11725449C211yesmaximal, characteristic, complemented
5#11725261C212yesmaximal, complemented
6C22×Q8×D7C411yescharacteristic
7C2×#6455C2211yescharacteristic
8C2×#6435C411yescharacteristic
9C7×#391C2211yescharacteristic
10#90002C411yescharacteristic
11#89746C2211yescharacteristic
12#89701C411yescharacteristic
13#89491—22no—
14#89436—22no—
15#89418—22no—
16C7×#324C2212yes—
17#89323C2212yes—
18#89263—22no—
19#11510—71nomaximal, Sylow
20C22×C7×Q8C2×C411yescharacteristic
21C2×Q8×D7—22no—
22C2×Q8×D7—22no—
23C2×Q8×D7—42no—
24C2×Q8×D7—42no—
25C22×C4×D7—21no—
26C22×C4×D7C2×C411yescharacteristic
27C22×Dic14—21no—
28C22×Dic14C2×C411yescharacteristic
29C2×C7×C4⋊C4C2311yescharacteristic
30C2×C42×C7C2×C411yescharacteristic
31C2×(C2×D7)⋊C4—21no—
32C2×(C2×D7)⋊C4D412yes—
33C2×C4⋊Dic7C2×C411yescharacteristic
34C2×Dic7⋊C4—21no—
35C2×C4×Dic7C2×C411yescharacteristic
36C2×C4×Dic7D412yes—
37#6455—42no—
38#6435—42no—
39C7×C22⋊C8—22no—
40C7×#95—22no—
41C7⋊#95—22no—
42C7⋊#95—22no—
43C7⋊#95—22no—
44C22⋊(C7⋊C8)—22no—
45#6389—42no—
46Dic7⋊C8—42no—
47#2310—71no—
48#1464—72no—
49#1319—71no—
50#1319—72no—
51#1319D711yescharacteristic, complemented
52C23×D7C22⋊C411yescharacteristic
53C2×C7×Q8—21no—
54C2×C7×Q8—41no—
55C2×C7×Q8—41no—
56C2×C7×Q8M1612yes—
57C22×C4×C7—21no—
58C22×C4×C7—21no—
59C22×C4×C7C22×C411yescharacteristic
60C22×C4×C7C2×D412yes—
61C22×Dic7—21no—
62C22×Dic7—21no—
63C22×Dic7C22⋊C411yescharacteristic
64C22×Dic7C22⋊C412yes—
65Q8×D7—48no—
66Q8×D7—48no—
67C2×C4×D7—22no—
68C2×C4×D7—21no—
69C2×C4×D7—21no—
70C2×C4×D7—22no—
71C2×C4×D7—24no—
72C2×C4×D7—42no—
73C2×C4×D7—42no—
74C2×Dic14—24no—
75C2×Dic14—21no—
76C2×Dic14—42no—
77C2×Dic14—42no—
78C2×Dic14—41no—
79C2×Dic14—41no—
80C2×Dic14M1612yes—
81C2×C7×C8—42no—
82C7×C4⋊C4—41no—
83C42×C7—41no—
84(C2×D7)⋊C4—42no—
85(C2×D7)⋊C4—42no—
86C4⋊Dic7—41no—
87Dic7⋊C4—42no—
88C4×Dic7—22no—
89C4×Dic7—22no—
90C4×Dic7—41no—
91C2×C7⋊C8—42no—
92C23×Q8—71no—
93C2×#117—71no—
94C2×#117—71no—
95#432—142no—
96#391—71no—
97#391—71no—
98#391—71no—
99#391—142no—
100#391C2×D711yescharacteristic
101#381—142no—
102#324—72no—
103#324C2×D712yes—
104#323—142no—
105C23×C7C2×C22⋊C411yescharacteristic
106C22×D7—21no—
107C22×D7—21no—
108C22×D7—41no—
109C22×D7—41no—
110C22×D7#10012yes—
111C7×Q8—42no—
112C7×Q8—42no—
113C2×C4×C7—21no—
114C2×C4×C7—21no—
115C2×C4×C7—22no—
116C2×C4×C7—22no—
117C2×C4×C7—41no—
118C2×C4×C7—41no—
119C2×C4×C7—42no—
120C2×C4×C7—41no—
121C2×C4×C7—41no—
122C2×C4×C7—41no—
123C2×C4×C7C2×M1611yescharacteristic
124C2×C4×C7C2×M1611yescharacteristic
125C2×Dic7—21no—
126C2×Dic7—21no—
127C2×Dic7—22no—
128C2×Dic7—22no—
129C2×Dic7—41no—
130C2×Dic7—41no—
131C2×Dic7—42no—
132C2×Dic7—41no—
133C2×Dic7—41no—
134C2×Dic7—41no—
135C2×Dic7#9912yes—
136C4×D7—24no—
137C4×D7—24no—
138C4×D7—48no—
139Dic14—48no—
140Dic14—42no—
141Dic14—42no—
142C7×C8—82no—
143C7⋊C8—82no—
144C22×Q8—71no—
145C22×Q8—141no—
146C22×Q8—142no—
147C22×Q8—142no—
148C22×Q8—282no—
149C22×Q8—282no—
150C22×Q8C4×D711yescharacteristic
151C23×C4—71no—
152C23×C4—141no—
153#117—282no—
154#117—282no—
155C2×C4⋊C4—71no—
156C2×C4⋊C4—141no—
157C2×C4⋊C4C22×D711yescharacteristic
158C2×C22⋊C4—72no—
159C2×C22⋊C4—141no—
160C2×C42—72no—
161C2×C42—71no—
162C2×C42C4×D711yescharacteristic
163C4⋊C8—282no—
164C22⋊C8—22no—
165C22⋊C8—142no—
166#97—282no—
167#95—22no—
168#95—142no—
169#95—142no—
170#95—142no—
171C22×C7—21no—
172C22×C7—21no—
173C22×C7#40711yescharacteristic
174C22×C7C2×#9911yescharacteristic
175C22×C7C2×#10011yescharacteristic
176C2×D7—22no—
177C2×D7—42no—
178C2×D7—41no—
179C2×D7—41no—
180C2×D7—42no—
181C4×C7—21no—
182C4×C7—21no—
183C4×C7—42no—
184C4×C7—42no—
185C4×C7—81no—
186Dic7—22no—
187Dic7—42no—
188Dic7—42no—
189Dic7—81no—
190C24—71no—
191C2×Q8—21no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8—72no—
195C2×Q8—144no—
196C2×Q8—141no—
197C2×Q8—281no—
198C2×Q8—281no—
199C2×Q8—282no—
200C2×Q8—282no—
201C2×Q8—288no—
202C2×Q8—288no—
203C2×Q8#113112yes—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—71no—
207C22×C4—72no—
208C22×C4—142no—
209C22×C4—142no—
210C22×C4—144no—
211C22×C4—141no—
212C22×C4—141no—
213C22×C4—141no—
214C22×C4—141no—
215C22×C4—282no—
216C22×C4—282no—
217C22×C4C2×C4×D711yescharacteristic
218C22×C4D4×D712yes—
219C2×C8—42no—
220C2×C8—282no—
221C4⋊C4—41no—
222C4⋊C4—281no—
223C4⋊C4—282no—
224C22⋊C4—282no—
225C22⋊C4—282no—
226C42—41no—
227C42—142no—
228C42—142no—
229C42—281no—
230C2×C7—21no—
231C2×C7—21no—
232C2×C7#146211yescharacteristic
233C2×C7#212911yescharacteristic
234C2×C7#213511yescharacteristic
235D7—42no—
236C23—72no—
237C23—141no—
238C23—141no—
239C23—281no—
240C23—281no—
241C23D7×C22⋊C411yescharacteristic
242Q8—42no—
243Q8—42no—
244Q8—282no—
245Q8—282no—
246Q8—288no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—72no—
258C2×C4—144no—
259C2×C4—144no—
260C2×C4—141no—
261C2×C4—141no—
262C2×C4—142no—
263C2×C4—142no—
264C2×C4—288no—
265C2×C4—281no—
266C2×C4—281no—
267C2×C4—282no—
268C2×C4—281no—
269C2×C4—281no—
270C2×C4—281no—
271C2×C4C2×#113111yescharacteristic
272C2×C4D7×M1611yescharacteristic
273C8—82no—
274C8—562no—
275C7#1151011yescharacteristic, complemented, Sylow
276C22—21no—
277C22—21no—
278C22—142no—
279C22—282no—
280C22—282no—
281C22—281no—
282C22—281no—
283C22#8949811yescharacteristic
284C22D7×#9911yescharacteristic
285C22D7×#10011yescharacteristic
286C4—21no—
287C4—21no—
288C4—42no—
289C4—42no—
290C4—81no—
291C4—142no—
292C4—282no—
293C4—282no—
294C4—561no—
295C2—21no—
296C2—21no—
297C2—282no—
298C2#1172587411yescharacteristic
299C2#1172691311yescharacteristic
300C2#1172692711yescharacteristic
subgroupG/H
centerC22D7×#99
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1319C2
socleC22×C7C2×#99
prime radicalC23×D7C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1319D7
hypocenterC7#11510
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
3. C7×#1319C2semidirect
4. #11725449C2semidirect
5. #11725261C2semidirect
51. #1319D7semidirect
275. C7#11510semidirect

Maximal subgroups

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

subgroupindex
#117340552
#117258802
C7×#13192
#117254492
#117252612
#115107