Finite Group Databasebeta

← #13264114

Subgroups — #13264114

Order 1792.

432 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 107 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#11739709C211yesmaximal, characteristic
2C7×#1742C211yesmaximal, characteristic
3#11729325C211yesmaximal, characteristic
4#11725300C214yesmaximal, complemented
5C22×C7×M16—21no—
6C2×C7×#117C2211yescharacteristic
7C2×#6432C411yescharacteristic
8#89984—21no—
9#89758—21no—
10#89751C2212yes—
11#89721—21no—
12#89719C412yes—
13#89708C411yescharacteristic
14#89700—21no—
15#89697—21no—
16C7×#343—21no—
17C7×#343C2212yes—
18#89323C2212yes—
19#89320—21no—
20#11724—71nomaximal, Sylow
21C23×C4×C7D411yescharacteristic
22C22×Dic14C2×C412yes—
23C2×C7×M16—24no—
24C2×C7×M16—22no—
25C2×C7×M16—41no—
26C2×C7×M16—42no—
27C22×C7×C8—41no—
28C7×#117—41no—
29C7×#117—41no—
30C2×C7×C4⋊C4D411yescharacteristic
31C2×C7×C4⋊C4C2311yescharacteristic
32C2×C7×C22⋊C4C2×C411yescharacteristic
33C2×C7×C22⋊C4D411yescharacteristic
34C2×C42×C7C2×C411yescharacteristic
35C2×C42×C7D411yescharacteristic
36C2×C22⋊Dic7—22no—
37C2×C4⋊Dic7—21no—
38C2×C4⋊Dic7—21no—
39C2×C4⋊Dic7—21no—
40C2×Dic7⋊C4—22no—
41#6432—41no—
42#6432—41no—
43C7⋊#95—22no—
44C7⋊#95—21no—
45C7⋊#95—22no—
46C7⋊#95C2×C412yes—
47C22⋊(C7⋊C8)—22no—
48C4⋊(C7⋊C8)—41no—
49C4×C7⋊C8—41no—
50#2628—71no—
51#1742D711yescharacteristic
52#1458—71no—
53#1354—74no—
54C24×C7C22⋊C411yescharacteristic
55C22×C4×C7—21no—
56C22×C4×C7—21no—
57C22×C4×C7—22no—
58C22×C4×C7C22⋊C411yescharacteristic
59C22×C4×C7C22⋊C411yescharacteristic
60C22×C4×C7C22⋊C411yescharacteristic
61C22×C4×C7SD1612yes—
62C22×C4×C7Q1612yes—
63C22×C4×C7C22×C411yescharacteristic
64C22×C4×C7C2×D411yescharacteristic
65C22×C4×C7C2×D411yescharacteristic
66C22×Dic7—22no—
67C22×Dic7—22no—
68C2×Dic14—42no—
69C2×Dic14—82no—
70C7×M16—24no—
71C7×M16—44no—
72C7×M16—42no—
73C2×C7×C8—42no—
74C2×C7×C8—44no—
75C7×C4⋊C4—41no—
76C7×C4⋊C4—41no—
77C7×C22⋊C4—41no—
78C7×C22⋊C4—41no—
79C42×C7—21no—
80C42×C7—21no—
81C42×C7—21no—
82C42×C7—21no—
83C22⋊Dic7—82no—
84C4⋊Dic7—42no—
85C4⋊Dic7—41no—
86C4⋊Dic7—41no—
87C4⋊Dic7—42no—
88Dic7⋊C4—82no—
89C2×C7⋊C8—42no—
90C22×M16—21no—
91C2×C4⋊Q8—71no—
92C2×#117C2×D711yescharacteristic
93#431—141no—
94#400—141no—
95#399—141no—
96#395—72no—
97#393—72no—
98#389—141no—
99#382—71no—
100#380—141no—
101#343—21no—
102#343C2×D712yes—
103#324—72no—
104#323—141no—
105C23×C7—21no—
106C23×C7—21no—
107C23×C7—41no—
108C23×C7—41no—
109C23×C7#10312yes—
110C23×C7C2×C22⋊C411yescharacteristic
111C2×C4×C7—21no—
112C2×C4×C7—21no—
113C2×C4×C7—22no—
114C2×C4×C7—22no—
115C2×C4×C7—22no—
116C2×C4×C7—22no—
117C2×C4×C7—21no—
118C2×C4×C7—21no—
119C2×C4×C7—21no—
120C2×C4×C7—21no—
121C2×C4×C7—41no—
122C2×C4×C7—41no—
123C2×C4×C7—41no—
124C2×C4×C7—41no—
125C2×C4×C7#9911yescharacteristic
126C2×C4×C7#9911yescharacteristic
127C2×C4×C7#10312yes—
128C2×C4×C7#10412yes—
129C2×C4×C7C2×SD1611yescharacteristic
130C2×C4×C7C2×Q1611yescharacteristic
131C2×Dic7—42no—
132C2×Dic7—42no—
133C2×Dic7—42no—
134C2×Dic7—42no—
135C2×Dic7—42no—
136C2×Dic7—42no—
137Dic14—84no—
138C7×C8—44no—
139C7⋊C8—82no—
140C22×Q8—72no—
141C23×C4C22⋊D711yescharacteristic
142C2×M16—24no—
143C2×M16—22no—
144C2×M16—41no—
145C2×M16—42no—
146C22×C8—41no—
147C4⋊Q8—281no—
148C4⋊Q8—281no—
149#117—41no—
150#117—41no—
151C2×C4⋊C4—141no—
152C2×C4⋊C4—141no—
153C2×C4⋊C4—141no—
154C2×C4⋊C4—142no—
155C2×C4⋊C4C22⋊D711yescharacteristic
156C2×C4⋊C4C22×D711yescharacteristic
157C2×C22⋊C4—142no—
158C2×C22⋊C4C4×D711yescharacteristic
159C2×C22⋊C4D2811yescharacteristic
160C2×C42C4×D711yescharacteristic
161C2×C42D2811yescharacteristic
162C4⋊C8—281no—
163C22⋊C8—142no—
164C4×C8—281no—
165#95—72no—
166#95—141no—
167#95—142no—
168#95—142no—
169C22×C7—21no—
170C22×C7—21no—
171C22×C7—22no—
172C22×C7—42no—
173C22×C7—41no—
174C22×C7—41no—
175C22×C7—81no—
176C22×C7C2×#9911yescharacteristic
177C22×C7C2×#10311yescharacteristic
178C22×C7C2×#10411yescharacteristic
179C4×C7—21no—
180C4×C7—21no—
181C4×C7—41no—
182C4×C7—41no—
183C4×C7—41no—
184C4×C7—41no—
185C4×C7#32812yes—
186C4×C7#32812yes—
187Dic7—82no—
188Dic7—82no—
189C24(C2×D7)⋊C411yescharacteristic
190C2×Q8—282no—
191C2×Q8—562no—
192C22×C4—22no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—142no—
196C22×C4—142no—
197C22×C4(C2×D7)⋊C411yescharacteristic
198C22×C4(C2×D7)⋊C411yescharacteristic
199C22×C4(C2×D7)⋊C411yescharacteristic
200C22×C4#114212yes—
201C22×C4#114412yes—
202C22×C4C2×C4×D711yescharacteristic
203C22×C4C2×D2811yescharacteristic
204C22×C4C2×C22⋊D711yescharacteristic
205M16—24no—
206M16—44no—
207M16—42no—
208C2×C8—42no—
209C2×C8—44no—
210C2×C8—282no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—282no—
214C4⋊C4—282no—
215C4⋊C4—281no—
216C4⋊C4—281no—
217C4⋊C4—562no—
218C22⋊C4—41no—
219C22⋊C4—41no—
220C22⋊C4—562no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C2×C7—21no—
226C2×C7—21no—
227C2×C7—42no—
228C2×C7C2×#32811yescharacteristic
229C2×C7#212211yescharacteristic
230C2×C7#213511yescharacteristic
231C23—21no—
232C23—21no—
233C23—41no—
234C23—41no—
235C23#638412yes—
236C23C2×(C2×D7)⋊C411yescharacteristic
237Q8—564no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—282no—
253C2×C4—282no—
254C2×C4—282no—
255C2×C4—282no—
256C2×C4—282no—
257C2×C4—282no—
258C2×C4#637912yes—
259C2×C4#638011yescharacteristic
260C2×C4#638011yescharacteristic
261C2×C4#638412yes—
262C2×C4C2×#114211yescharacteristic
263C2×C4C2×#114411yescharacteristic
264C8—44no—
265C8—562no—
266C7#1172411yescharacteristic, complemented, Sylow
267C22—21no—
268C22—21no—
269C22—22no—
270C22—42no—
271C22—41no—
272C22—41no—
273C22—81no—
274C22C2×#637911yescharacteristic
275C22C2×#638011yescharacteristic
276C22C2×#638411yescharacteristic
277C4—21no—
278C4—21no—
279C4—41no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—562no—
284C4—562no—
285C4#8924712yes—
286C4#8924712yes—
287C2—21no—
288C2—21no—
289C2—42no—
290C2C2×#8924711yescharacteristic
291C2#1172790011yescharacteristic
292C2#1172790411yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1742C2
socleC22×C7C2×#99
prime radicalC24×C7C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1742D7
hypocenterC7#11724
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1742

Complements

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

NH ≅ G/Ntype
4. #11725300C2semidirect
266. C7#11724semidirect

Maximal subgroups

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

subgroupindex
#117397092
C7×#17422
#117293252
#117253002
#117247