Finite Group Databasebeta

← #13264552

Subgroups — #13264552

Order 1792.

368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C7×#2628C211yesmaximal, characteristic
2#11729343C211yesmaximal, characteristic
3#11729326C211yesmaximal, characteristic
4#11725454C214yesmaximal, complemented
5C2×C7×C4⋊Q8C411yescharacteristic
6C2×C7×#117C2211yescharacteristic
7C7×#400—21no—
8C7×#399—21no—
9C7×#395C2212yes—
10C7×#393C412yes—
11C7×#389—21no—
12C7×#382C411yescharacteristic
13C7×#380—21no—
14#89979—21no—
15#89698—21no—
16#89325—21no—
17#89325C2212yes—
18#89323C2212yes—
19#89320—21no—
20#11819—71nomaximal, Sylow
21C22×C7×Q8C2×C412yes—
22C23×C4×C7D411yescharacteristic
23C7×C4⋊Q8—41no—
24C7×C4⋊Q8—41no—
25C7×#117—41no—
26C7×#117—41no—
27C2×C7×C4⋊C4—21no—
28C2×C7×C4⋊C4—21no—
29C2×C7×C4⋊C4—21no—
30C2×C7×C4⋊C4—22no—
31C2×C7×C4⋊C4D411yescharacteristic
32C2×C7×C4⋊C4C2311yescharacteristic
33C2×C7×C22⋊C4—22no—
34C2×C7×C22⋊C4C2×C411yescharacteristic
35C2×C7×C22⋊C4D411yescharacteristic
36C2×C42×C7C2×C411yescharacteristic
37C2×C42×C7D411yescharacteristic
38C2×#1136—22no—
39C7×#95—21no—
40C7×#95—22no—
41C7×#95—22no—
42C7×#95C2×C412yes—
43C22⋊(C7⋊C8)—22no—
44C22⋊(C7⋊C8)—41no—
45C22⋊(C7⋊C8)—41no—
46C4⋊(C7⋊C8)—41no—
47#6377—41no—
48#2628D711yescharacteristic
49#1822—71no—
50#1464—71no—
51#1354—74no—
52C24×C7C22⋊C411yescharacteristic
53C2×C7×Q8—42no—
54C2×C7×Q8—82no—
55C22×C4×C7—21no—
56C22×C4×C7—21no—
57C22×C4×C7—22no—
58C22×C4×C7—22no—
59C22×C4×C7—22no—
60C22×C4×C7—41no—
61C22×C4×C7C22⋊C411yescharacteristic
62C22×C4×C7C22⋊C411yescharacteristic
63C22×C4×C7C22⋊C411yescharacteristic
64C22×C4×C7C22×C411yescharacteristic
65C22×C4×C7C2×D411yescharacteristic
66C22×C4×C7C2×D411yescharacteristic
67C7×C4⋊C4—41no—
68C7×C4⋊C4—41no—
69C7×C4⋊C4—42no—
70C7×C4⋊C4—42no—
71C7×C4⋊C4—41no—
72C7×C4⋊C4—41no—
73C7×C4⋊C4—82no—
74C7×C22⋊C4—41no—
75C7×C22⋊C4—41no—
76C7×C22⋊C4—82no—
77C42×C7—21no—
78C42×C7—21no—
79C42×C7—21no—
80C42×C7—21no—
81#1136—42no—
82#1136—42no—
83C2×C7⋊C8—42no—
84C2×C7⋊C8—42no—
85C2×C4⋊Q8Dic711yescharacteristic
86C2×#117C2×D711yescharacteristic
87#432—141no—
88#407—141no—
89#400—21no—
90#399—21no—
91#395C2×D712yes—
92#393Dic712yes—
93#389—21no—
94#382Dic711yescharacteristic
95#380—21no—
96#343—72no—
97#343—141no—
98#324—72no—
99#323—141no—
100C23×C7—21no—
101C23×C7—21no—
102C23×C7—21no—
103C23×C7—41no—
104C23×C7—41no—
105C23×C7C2×C22⋊C411yescharacteristic
106C7×Q8—84no—
107C2×C4×C7—21no—
108C2×C4×C7—21no—
109C2×C4×C7—21no—
110C2×C4×C7—21no—
111C2×C4×C7—21no—
112C2×C4×C7—21no—
113C2×C4×C7—21no—
114C2×C4×C7—21no—
115C2×C4×C7—42no—
116C2×C4×C7—42no—
117C2×C4×C7—41no—
118C2×C4×C7—41no—
119C2×C4×C7—41no—
120C2×C4×C7—41no—
121C2×C4×C7—42no—
122C2×C4×C7—42no—
123C2×C4×C7—42no—
124C2×C4×C7—42no—
125C2×C4×C7—42no—
126C2×C4×C7—42no—
127C2×C4×C7#9911yescharacteristic
128C2×C4×C7#9911yescharacteristic
129C2×C4×C7#13712yes—
130C7⋊C8—82no—
131C7⋊C8—82no—
132C22×Q8C2×Dic712yes—
133C23×C4C22⋊D711yescharacteristic
134C2×M16—142no—
135C4⋊Q8—41no—
136C4⋊Q8—41no—
137#117—41no—
138#117—41no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—21no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4C22⋊D711yescharacteristic
144C2×C4⋊C4C22×D711yescharacteristic
145C2×C22⋊C4—22no—
146C2×C22⋊C4C2×Dic711yescharacteristic
147C2×C22⋊C4C22⋊D711yescharacteristic
148C2×C42C2×Dic711yescharacteristic
149C2×C42C22⋊D711yescharacteristic
150C4⋊C8—281no—
151C22⋊C8—142no—
152C22⋊C8—281no—
153C22⋊C8—281no—
154#97—281no—
155#95—21no—
156#95—22no—
157#95—22no—
158#95C2×Dic712yes—
159C22×C7—21no—
160C22×C7—21no—
161C22×C7—42no—
162C22×C7—41no—
163C22×C7—41no—
164C22×C7—41no—
165C22×C7—81no—
166C22×C7C2×#9911yescharacteristic
167C22×C7#41911yescharacteristic
168C22×C7#42111yescharacteristic
169C4×C7—22no—
170C4×C7—21no—
171C4×C7—21no—
172C4×C7—41no—
173C4×C7—41no—
174C4×C7—41no—
175C4×C7—41no—
176C4×C7—82no—
177C4×C7—82no—
178C24C22⋊Dic711yescharacteristic
179C2×Q8—42no—
180C2×Q8—82no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—41no—
187C22×C4C22⋊Dic711yescharacteristic
188C22×C4C22⋊Dic711yescharacteristic
189C22×C4C22⋊Dic711yescharacteristic
190C22×C4C22×Dic711yescharacteristic
191C22×C4C2×C22⋊D711yescharacteristic
192C22×C4C2×C22⋊D711yescharacteristic
193M16—282no—
194M16—282no—
195C2×C8—282no—
196C2×C8—282no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—82no—
204C22⋊C4—41no—
205C22⋊C4—41no—
206C22⋊C4—82no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C2×C7—21no—
212C2×C7—21no—
213C2×C7—81no—
214C2×C7#151111yescharacteristic
215C2×C7#212211yescharacteristic
216C2×C7#213511yescharacteristic
217C23—21no—
218C23—21no—
219C23—21no—
220C23—41no—
221C23—41no—
222C23C2×C22⋊Dic711yescharacteristic
223Q8—84no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4#640811yescharacteristic
245C2×C4#640811yescharacteristic
246C2×C4#650512yes—
247C8—562no—
248C8—562no—
249C7#1181911yescharacteristic, complemented, Sylow
250C22—21no—
251C22—21no—
252C22—42no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—81no—
257C22C2×#640811yescharacteristic
258C22#8999711yescharacteristic
259C22#9000811yescharacteristic
260C4—22no—
261C4—21no—
262C4—21no—
263C4—41no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—82no—
268C4—82no—
269C2—21no—
270C2—21no—
271C2—81no—
272C2#1172944311yescharacteristic
273C2#1172961311yescharacteristic
274C2#1172962711yescharacteristic
subgroupG/H
centerC22C2×#6408
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#2628C2
socleC22×C7C2×#99
prime radicalC24×C7C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#2628D7
hypocenterC7#11819
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2628

Complements

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

NH ≅ G/Ntype
4. #11725454C2semidirect
249. C7#11819semidirect

Maximal subgroups

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

subgroupindex
C7×#26282
#117293432
#117293262
#117254542
#118197