Finite Group Databasebeta

← #13264853

Subgroups — #13264853

Order 1792.

408 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 99 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#11739920C211yesmaximal, characteristic
2C7×#1801C211yesmaximal, characteristic
3#11729378C211yesmaximal, characteristic
4#11725301C214yesmaximal
5C2×C4×C7×Q8C2211yescharacteristic
6C2×#6507—21no—
7C2×#6432C411yescharacteristic
8C7×#423—21no—
9C2×C7×#101—21no—
10#89755C412yes—
11#89755C2212yes—
12#89746—21no—
13C4×C4⋊Dic7C411yescharacteristic
14#89700—21no—
15#89700—21no—
16#89697—21no—
17C7×#343C2212yes—
18#89323—21no—
19#89323C2212yes—
20#11883—71nomaximal, Sylow
21C22×C7×Q8D411yescharacteristic
22C22×Dic14—21no—
23C2×C7×M16—22no—
24C4×C7×Q8—41no—
25C4×C7×Q8—41no—
26C2×C7×C4⋊C4C2×C411yescharacteristic
27C2×C7×C4⋊C4D411yescharacteristic
28C2×C7×C4⋊C4C2311yescharacteristic
29C2×C42×C7C2×C411yescharacteristic
30C2×C42×C7D411yescharacteristic
31C2×C42×C7D411yescharacteristic
32#6507—42no—
33#6507—42no—
34C2×C4⋊Dic7—21no—
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7C2×C412yes—
37C2×Dic7⋊C4—22no—
38C2×Dic7⋊C4—22no—
39C2×C4×Dic7—21no—
40#6432—41no—
41#6432—41no—
42C7×C4⋊C8—41no—
43C7×C4⋊C8—41no—
44C7×#101—42no—
45C7⋊#95—22no—
46C7⋊#95—22no—
47C7⋊#95C2×C412yes—
48C22⋊(C7⋊C8)—22no—
49C4⋊(C7⋊C8)—41no—
50C4×C7⋊C8—41no—
51#2546—71no—
52#1801D711yescharacteristic
53#1461—71no—
54#1346—74no—
55C2×C7×Q8—41no—
56C2×C7×Q8—41no—
57C2×C7×Q8D812yes—
58C2×C7×Q8SD1612yes—
59C22×C4×C7C22⋊C411yescharacteristic
60C22×C4×C7C22⋊C411yescharacteristic
61C22×C4×C7C22⋊C411yescharacteristic
62C22×C4×C7C22⋊C411yescharacteristic
63C22×C4×C7C22×C411yescharacteristic
64C22×C4×C7C2×D411yescharacteristic
65C22×C4×C7C2×D411yescharacteristic
66C22×Dic7—22no—
67C22×Dic7—22no—
68C2×Dic14—42no—
69C2×Dic14—42no—
70C2×Dic14—42no—
71C7×M16—42no—
72C7×M16—42no—
73C2×C7×C8—42no—
74C7×C4⋊C4—41no—
75C7×C4⋊C4—41no—
76C7×C4⋊C4—41no—
77C42×C7—21no—
78C42×C7—21no—
79C42×C7—21no—
80C42×C7—21no—
81C42×C7—21no—
82C42×C7—21no—
83C4⋊Dic7—24no—
84C4⋊Dic7—41no—
85C4⋊Dic7—41no—
86C4⋊Dic7—42no—
87Dic7⋊C4—44no—
88Dic7⋊C4—42no—
89Dic7⋊C4—42no—
90C4×Dic7—42no—
91C2×C7⋊C8—42no—
92C2×C4⋊Q8—71no—
93C2×C4⋊Q8—141no—
94C2×C4×Q8C2×D711yescharacteristic
95#431—141no—
96#423—21no—
97C2×#101—21no—
98#398—72no—
99#398—72no—
100#391—141no—
101#389—141no—
102#389—141no—
103C4×C4⋊C4—71no—
104#343C2×D712yes—
105#324—72no—
106#324—141no—
107C23×C7C2×C22⋊C411yescharacteristic
108C7×Q8—42no—
109C7×Q8—42no—
110C2×C4×C7—21no—
111C2×C4×C7—21no—
112C2×C4×C7—21no—
113C2×C4×C7—21no—
114C2×C4×C7—21no—
115C2×C4×C7—21no—
116C2×C4×C7—22no—
117C2×C4×C7—21no—
118C2×C4×C7—21no—
119C2×C4×C7—21no—
120C2×C4×C7—41no—
121C2×C4×C7—41no—
122C2×C4×C7—41no—
123C2×C4×C7#9911yescharacteristic
124C2×C4×C7#9911yescharacteristic
125C2×C4×C7#10212yes—
126C2×C4×C7#10212yes—
127C2×C4×C7C2×D811yescharacteristic
128C2×C4×C7C2×SD1611yescharacteristic
129C2×Dic7—24no—
130C2×Dic7—42no—
131C2×Dic7—42no—
132C2×Dic7—42no—
133C2×Dic7—42no—
134C2×Dic7—42no—
135Dic14—84no—
136C7×C8—82no—
137C7⋊C8—82no—
138C22×Q8—141no—
139C22×Q8C22⋊D711yescharacteristic
140C2×M16—22no—
141C4⋊Q8—281no—
142C4⋊Q8—281no—
143C4⋊Q8—282no—
144C4⋊Q8—282no—
145C4×Q8—41no—
146C4×Q8—41no—
147C2×C4⋊C4—72no—
148C2×C4⋊C4—141no—
149C2×C4⋊C4—142no—
150C2×C4⋊C4—141no—
151C2×C4⋊C4—142no—
152C2×C4⋊C4C4×D711yescharacteristic
153C2×C4⋊C4D2811yescharacteristic
154C2×C4⋊C4C22×D711yescharacteristic
155C2×C42—141no—
156C2×C42C4×D711yescharacteristic
157C2×C42D2811yescharacteristic
158C2×C42C22⋊D711yescharacteristic
159C4⋊C8—41no—
160C4⋊C8—41no—
161C4⋊C8—281no—
162#101—42no—
163C22⋊C8—142no—
164C4×C8—281no—
165#95—72no—
166#95—142no—
167#95—142no—
168C22×C7—21no—
169C22×C7—21no—
170C22×C7C2×#9911yescharacteristic
171C22×C7C2×#10211yescharacteristic
172C22×C7#42111yescharacteristic
173C4×C7—21no—
174C4×C7—21no—
175C4×C7—22no—
176C4×C7—22no—
177C4×C7—21no—
178C4×C7—41no—
179C4×C7—41no—
180C4×C7—41no—
181C4×C7#35612yes—
182Dic7—44no—
183Dic7—82no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8—282no—
187C2×Q8—282no—
188C2×Q8—282no—
189C2×Q8#114112yes—
190C2×Q8#114312yes—
191C22×C4—142no—
192C22×C4—142no—
193C22×C4(C2×D7)⋊C411yescharacteristic
194C22×C4(C2×D7)⋊C411yescharacteristic
195C22×C4(C2×D7)⋊C411yescharacteristic
196C22×C4(C2×D7)⋊C411yescharacteristic
197C22×C4C2×C4×D711yescharacteristic
198C22×C4C2×D2811yescharacteristic
199C22×C4C2×C22⋊D711yescharacteristic
200M16—42no—
201M16—42no—
202C2×C8—42no—
203C2×C8—282no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—144no—
208C4⋊C4—282no—
209C4⋊C4—282no—
210C4⋊C4—282no—
211C4⋊C4—281no—
212C4⋊C4—281no—
213C4⋊C4—284no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—21no—
219C42—21no—
220C42—282no—
221C2×C7—21no—
222C2×C7—21no—
223C2×C7#151911yescharacteristic
224C2×C7#212311yescharacteristic
225C2×C7C2×#35611yescharacteristic
226C23C2×(C2×D7)⋊C411yescharacteristic
227Q8—42no—
228Q8—42no—
229Q8—564no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—144no—
244C2×C4—282no—
245C2×C4—282no—
246C2×C4—282no—
247C2×C4—282no—
248C2×C4—282no—
249C2×C4#638011yescharacteristic
250C2×C4#638011yescharacteristic
251C2×C4#638312yes—
252C2×C4#638312yes—
253C2×C4C2×#114111yescharacteristic
254C2×C4C2×#114311yescharacteristic
255C8—82no—
256C8—562no—
257C7#1188311yescharacteristic, complemented, Sylow
258C22—21no—
259C22—21no—
260C22C2×#638011yescharacteristic
261C22C2×#638311yescharacteristic
262C22#8977711yescharacteristic
263C4—21no—
264C4—21no—
265C4—21no—
266C4—22no—
267C4—22no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—284no—
272C4—562no—
273C4#8927312yes—
274C2—21no—
275C2—21no—
276C2#1172726311yescharacteristic
277C2C2×#8927311yescharacteristic
278C2#1172790111yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1801C2
socleC22×C7C2×#99
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1801D7
hypocenterC7#11883
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
257. C7#11883semidirect

Maximal subgroups

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

subgroupindex
#117399202
C7×#18012
#117293782
#117253012
#118837