Finite Group Databasebeta

← #13264549

Subgroups — #13264549

Order 1792.

368 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 79 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×#1464C211yesmaximal, characteristic
3#11729343C211yesmaximal, characteristic
4#11725265C214yesmaximal, complemented
5C2×C7×#117C2211yescharacteristic
6C2×#6432C411yescharacteristic
7C7×#432—21no—
8#89984—21no—
9#89979—21no—
10#89758C2212yes—
11#89751—21no—
12#89721C412yes—
13#89719—21no—
14#89708C411yescharacteristic
15#89700—21no—
16C7×#324C2212yes—
17C7×#323—21no—
18#89325—21no—
19#89325C2212yes—
20#11818—71nomaximal, Sylow
21C23×C4×C7D411yescharacteristic
22C22×Dic14—21no—
23C7×#117—41no—
24C7×#117—41no—
25C2×C7×C4⋊C4D411yescharacteristic
26C2×C7×C4⋊C4C2311yescharacteristic
27C2×C7×C22⋊C4C2×C411yescharacteristic
28C2×C7×C22⋊C4D411yescharacteristic
29C2×C42×C7C2×C411yescharacteristic
30C2×C42×C7D411yescharacteristic
31C2×C22⋊Dic7—22no—
32C2×C4⋊Dic7—21no—
33C2×C4⋊Dic7—21no—
34C2×C4⋊Dic7C2×C412yes—
35C2×Dic7⋊C4—22no—
36C2×#1136—22no—
37#6432—41no—
38#6432—41no—
39C7×C4⋊C8—41no—
40C7×C22⋊C8—22no—
41C7×#97—41no—
42C7⋊#95—21no—
43C7⋊#95—22no—
44C7⋊#95—22no—
45C7⋊#95C2×C412yes—
46C22⋊(C7⋊C8)—41no—
47C22⋊(C7⋊C8)—41no—
48#2628—71no—
49#1822—71no—
50#1464D711yescharacteristic
51#1353—74no—
52C24×C7C22⋊C411yescharacteristic
53C22×C4×C7—21no—
54C22×C4×C7—21no—
55C22×C4×C7—22no—
56C22×C4×C7—41no—
57C22×C4×C7C22⋊C411yescharacteristic
58C22×C4×C7C22⋊C411yescharacteristic
59C22×C4×C7C22⋊C411yescharacteristic
60C22×C4×C7C22×C411yescharacteristic
61C22×C4×C7C2×D411yescharacteristic
62C22×C4×C7C2×D411yescharacteristic
63C22×Dic7—22no—
64C22×Dic7—22no—
65C2×Dic14—42no—
66C2×Dic14—82no—
67C2×C7×C8—42no—
68C7×C4⋊C4—41no—
69C7×C4⋊C4—41no—
70C7×C22⋊C4—41no—
71C7×C22⋊C4—41no—
72C42×C7—21no—
73C42×C7—21no—
74C42×C7—21no—
75C42×C7—21no—
76C22⋊Dic7—82no—
77C4⋊Dic7—42no—
78C4⋊Dic7—41no—
79C4⋊Dic7—41no—
80C4⋊Dic7—42no—
81Dic7⋊C4—82no—
82#1136—42no—
83#1136—42no—
84C2×C7⋊C8—42no—
85C2×C4⋊Q8—71no—
86C2×#117C2×D711yescharacteristic
87#432—21no—
88#407—141no—
89#400—72no—
90#399—72no—
91#395—141no—
92#393—141no—
93#389—141no—
94#382—71no—
95#380—141no—
96#343—72no—
97#343—141no—
98#324C2×D712yes—
99#323—21no—
100C23×C7—21no—
101C23×C7—21no—
102C23×C7—21no—
103C23×C7—41no—
104C23×C7—41no—
105C23×C7C2×C22⋊C411yescharacteristic
106C2×C4×C7—21no—
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—42no—
115C2×C4×C7—42no—
116C2×C4×C7—41no—
117C2×C4×C7—41no—
118C2×C4×C7—41no—
119C2×C4×C7—41no—
120C2×C4×C7#9911yescharacteristic
121C2×C4×C7#9911yescharacteristic
122C2×C4×C7#13712yes—
123C2×Dic7—42no—
124C2×Dic7—42no—
125C2×Dic7—42no—
126C2×Dic7—42no—
127C2×Dic7—42no—
128C2×Dic7—42no—
129Dic14—84no—
130C7×C8—82no—
131C7⋊C8—82no—
132C22×Q8—141no—
133C23×C4D2811yescharacteristic
134C2×M16—142no—
135C4⋊Q8—281no—
136C4⋊Q8—281no—
137#117—41no—
138#117—41no—
139C2×C4⋊C4—72no—
140C2×C4⋊C4—141no—
141C2×C4⋊C4—141no—
142C2×C4⋊C4—142no—
143C2×C4⋊C4D2811yescharacteristic
144C2×C4⋊C4C22×D711yescharacteristic
145C2×C22⋊C4—142no—
146C2×C22⋊C4C4×D711yescharacteristic
147C2×C22⋊C4C22⋊D711yescharacteristic
148C2×C42C4×D711yescharacteristic
149C2×C42C22⋊D711yescharacteristic
150C4⋊C8—41no—
151C22⋊C8—22no—
152C22⋊C8—281no—
153C22⋊C8—281no—
154#97—41no—
155#95—72no—
156#95—141no—
157#95—142no—
158#95—142no—
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—
176Dic7—82no—
177Dic7—82no—
178C24(C2×D7)⋊C411yescharacteristic
179C2×Q8—282no—
180C2×Q8—562no—
181C22×C4—22no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—41no—
185C22×C4—142no—
186C22×C4—142no—
187C22×C4(C2×D7)⋊C411yescharacteristic
188C22×C4(C2×D7)⋊C411yescharacteristic
189C22×C4(C2×D7)⋊C411yescharacteristic
190C22×C4C2×C4×D711yescharacteristic
191C22×C4C2×D2811yescharacteristic
192C22×C4C2×C22⋊D711yescharacteristic
193M16—282no—
194M16—282no—
195C2×C8—42no—
196C2×C8—282no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—282no—
200C4⋊C4—282no—
201C4⋊C4—281no—
202C4⋊C4—281no—
203C4⋊C4—562no—
204C22⋊C4—41no—
205C22⋊C4—41no—
206C22⋊C4—562no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C2×C7—21no—
212C2×C7—21no—
213C2×C7—81no—
214C2×C7#151111yescharacteristic
215C2×C7#212311yescharacteristic
216C2×C7#213411yescharacteristic
217C23—21no—
218C23—21no—
219C23—21no—
220C23—41no—
221C23—41no—
222C23C2×(C2×D7)⋊C411yescharacteristic
223Q8—564no—
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—282no—
239C2×C4—282no—
240C2×C4—282no—
241C2×C4—282no—
242C2×C4—282no—
243C2×C4—282no—
244C2×C4#638011yescharacteristic
245C2×C4#638011yescharacteristic
246C2×C4#647212yes—
247C8—82no—
248C8—562no—
249C7#1181811yescharacteristic, complemented, Sylow
250C22—21no—
251C22—21no—
252C22—42no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—81no—
257C22C2×#638011yescharacteristic
258C22#8989211yescharacteristic
259C22#8991111yescharacteristic
260C4—22no—
261C4—21no—
262C4—21no—
263C4—41no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—562no—
268C4—562no—
269C2—21no—
270C2—21no—
271C2—81no—
272C2#1172773511yescharacteristic
273C2#1172781211yescharacteristic
274C2#1172790311yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1464C2
socleC22×C7C2×#99
prime radicalC24×C7C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1464D7
hypocenterC7#11818
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
4. #11725265C2semidirect
249. C7#11818semidirect

Maximal subgroups

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

subgroupindex
#117397092
C7×#14642
#117293432
#117252652
#118187