Finite Group Databasebeta

← #13264193

Subgroups — #13264193

Order 1792.

358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 83 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#11739931C211yesmaximal, characteristic
2C4×C7×#101C211yesmaximal, characteristic
3#11729378C211yesmaximal, characteristic
4#11725302C212yesmaximal
5#11725301C212yesmaximal
6C2×C4×C7×Q8C2211yescharacteristic
7C2×#6433C411yescharacteristic
8C2×C7×#101—21no—
9C4×C7×M16—21no—
10#90001—21no—
11#89758C411yescharacteristic
12#89758C2211yescharacteristic
13#89755C411yescharacteristic
14#89755C2211yescharacteristic
15#89754—21no—
16#89709C411yescharacteristic
17#89705—21no—
18#89705—21no—
19#89697—21no—
20C7×#343C2212yes—
21#89323—21no—
22#89323C2212yes—
23#11740—71nomaximal, Sylow
24C22×C7×Q8D411yescharacteristic
25C2×C7×M16—22no—
26C4×C7×Q8—41no—
27C4×C7×Q8—41no—
28C2×C7×C4⋊C4C2×C411yescharacteristic
29C2×C7×C4⋊C4D411yescharacteristic
30C2×C7×C4⋊C4C2311yescharacteristic
31C2×C42×C7C2×C411yescharacteristic
32C2×C42×C7D411yescharacteristic
33C2×C42×C7D411yescharacteristic
34C2×C4⋊Dic7C2×C411yescharacteristic
35C2×C4⋊Dic7C2×C411yescharacteristic
36C2×Dic7⋊C4—21no—
37C2×Dic7⋊C4—21no—
38C2×Dic7⋊C4—21no—
39C2×Dic7⋊C4—21no—
40#6433—41no—
41#6433—41no—
42C7×#101—24no—
43C7×#97—41no—
44C4×C7×C8—41no—
45C7⋊#95—21no—
46C7⋊#95—21no—
47C7⋊#95—21no—
48C7⋊#95—21no—
49C7⋊#95—21no—
50C7⋊#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95C2×C411yescharacteristic
54C7⋊#95C2×C411yescharacteristic
55C22⋊(C7⋊C8)—22no—
56C4⋊(C7⋊C8)—41no—
57C4×C7⋊C8—41no—
58#2634—71no—
59C4×#101D711yescharacteristic
60#1461—71no—
61#1353—72no—
62#1346—72no—
63C2×C7×Q8—22no—
64C2×C7×Q8—22no—
65C2×C7×Q8—41no—
66C22×C4×C7C22⋊C411yescharacteristic
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—
77C7×M16—24no—
78C7×M16—42no—
79C2×C7×C8—42no—
80C7×C4⋊C4—41no—
81C7×C4⋊C4—41no—
82C7×C4⋊C4—41no—
83C42×C7—21no—
84C42×C7—21no—
85C42×C7—21no—
86C42×C7—21no—
87C42×C7—21no—
88C42×C7—21no—
89C4⋊Dic7—41no—
90C4⋊Dic7—41no—
91Dic7⋊C4—42no—
92Dic7⋊C4—41no—
93Dic7⋊C4—41no—
94Dic7⋊C4—42no—
95Dic7⋊C4—42no—
96C2×C7⋊C8—42no—
97C2×#125—71no—
98C2×C4×Q8C2×D711yescharacteristic
99#431—141no—
100C2×#101—21no—
101C4×M16—21no—
102#400—71no—
103#400—71no—
104#400—141no—
105#398—71no—
106#398—71no—
107#395—141no—
108#387—141no—
109#387—141no—
110#383—71no—
111#343C2×D712yes—
112#324—72no—
113#324—141no—
114C23×C7C2×C22⋊C411yescharacteristic
115C7×Q8—44no—
116C2×C4×C7—21no—
117C2×C4×C7—21no—
118C2×C4×C7—21no—
119C2×C4×C7—21no—
120C2×C4×C7—21no—
121C2×C4×C7—21no—
122C2×C4×C7—21no—
123C2×C4×C7—21no—
124C2×C4×C7—21no—
125C2×C4×C7—21no—
126C2×C4×C7—41no—
127C2×C4×C7—41no—
128C2×C4×C7—41no—
129C2×C4×C7—41no—
130C2×C4×C7#9911yescharacteristic
131C2×C4×C7#9911yescharacteristic
132C2×C4×C7#10412yes—
133C2×C4×C7#13512yes—
134C2×Dic7—41no—
135C2×Dic7—41no—
136C2×Dic7—41no—
137C2×Dic7—41no—
138C2×Dic7—42no—
139C2×Dic7—41no—
140C2×Dic7—41no—
141C2×Dic7—41no—
142C2×Dic7—41no—
143C2×Dic7—41no—
144C2×Dic7—41no—
145C7×C8—44no—
146C7⋊C8—82no—
147C22×Q8C22⋊D711yescharacteristic
148C2×M16—22no—
149#125—281no—
150#125—281no—
151C4×Q8—41no—
152C4×Q8—41no—
153C2×C4⋊C4—71no—
154C2×C4⋊C4—71no—
155C2×C4⋊C4—141no—
156C2×C4⋊C4—141no—
157C2×C4⋊C4—141no—
158C2×C4⋊C4—141no—
159C2×C4⋊C4C4×D711yescharacteristic
160C2×C4⋊C4D2811yescharacteristic
161C2×C4⋊C4C22×D711yescharacteristic
162C2×C42C4×D711yescharacteristic
163C2×C42D2811yescharacteristic
164C2×C42C22⋊D711yescharacteristic
165C4⋊C8—281no—
166#101—24no—
167C22⋊C8—142no—
168#97—41no—
169C4×C8—41no—
170C4×C8—281no—
171#95—71no—
172#95—71no—
173#95—141no—
174#95—141no—
175#95—141no—
176#95—141no—
177#95—141no—
178#95—141no—
179#95—141no—
180#95—141no—
181C22×C7—21no—
182C22×C7—21no—
183C22×C7C2×#9911yescharacteristic
184C22×C7#41611yescharacteristic
185C22×C7C2×#10411yescharacteristic
186C4×C7—21no—
187C4×C7—21no—
188C4×C7—22no—
189C4×C7—22no—
190C4×C7—41no—
191C4×C7—41no—
192C4×C7—41no—
193C4×C7—41no—
194Dic7—81no—
195Dic7—81no—
196Dic7—81no—
197Dic7—81no—
198C2×Q8—22no—
199C2×Q8—22no—
200C2×Q8—41no—
201C22×C4—141no—
202C22×C4—141no—
203C22×C4—141no—
204C22×C4—141no—
205C22×C4(C2×D7)⋊C411yescharacteristic
206C22×C4(C2×D7)⋊C411yescharacteristic
207C22×C4(C2×D7)⋊C411yescharacteristic
208C22×C4(C2×D7)⋊C411yescharacteristic
209C22×C4C2×C4×D711yescharacteristic
210C22×C4C2×D2811yescharacteristic
211C22×C4C2×C22⋊D711yescharacteristic
212M16—24no—
213M16—42no—
214C2×C8—42no—
215C2×C8—282no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—281no—
220C4⋊C4—281no—
221C4⋊C4—282no—
222C4⋊C4—282no—
223C4⋊C4—282no—
224C4⋊C4—281no—
225C4⋊C4—281no—
226C42—21no—
227C42—21no—
228C42—21no—
229C42—21no—
230C42—21no—
231C42—21no—
232C2×C7—21no—
233C2×C7—21no—
234C2×C7#150111yescharacteristic
235C2×C7#212311yescharacteristic
236C2×C7#213311yescharacteristic
237C23C2×(C2×D7)⋊C411yescharacteristic
238Q8—44no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—281no—
254C2×C4—281no—
255C2×C4—281no—
256C2×C4—281no—
257C2×C4—282no—
258C2×C4—281no—
259C2×C4—281no—
260C2×C4—281no—
261C2×C4—281no—
262C2×C4—281no—
263C2×C4—281no—
264C2×C4#637912yes—
265C2×C4#638011yescharacteristic
266C2×C4#638011yescharacteristic
267C2×C4#651312yes—
268C8—44no—
269C8—562no—
270C7#1174011yescharacteristic, complemented, Sylow
271C22—21no—
272C22—21no—
273C22C2×#637911yescharacteristic
274C22C2×#638011yescharacteristic
275C22#8977411yescharacteristic
276C4—21no—
277C4—21no—
278C4—22no—
279C4—22no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—561no—
285C4—561no—
286C4—561no—
287C4—561no—
288C2—21no—
289C2—21no—
290C2#1172719711yescharacteristic
291C2#1172788211yescharacteristic
292C2#1172790111yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC4×C7×#101C2
socleC22×C7C2×#99
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenterC4×#101D7
hypocenterC7#11740
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
270. C7#11740semidirect

Maximal subgroups

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

subgroupindex
#117399312
C4×C7×#1012
#117293782
#117253022
#117253012
#117407