Finite Group Databasebeta

← #13263469

Subgroups — #13263469

Order 1792.

554 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 95 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×#2409C211yesmaximal, characteristic
2#11729357C211yesmaximal, characteristic
3#11729354C211yesmaximal, characteristic
4#11725442C214yesmaximal, complemented
5C23×C7×Q8C411yescharacteristic
6C2×C7×C22⋊Q8—21no—
7C2×C4×C7×D4C2211yescharacteristic
8C7×#395—21no—
9C7×#393—21no—
10C7×#391—21no—
11C7×#386C412yes—
12C7×#385C2212yes—
13C7×#380C411yescharacteristic
14C2×C22⋊(C7⋊C8)—21no—
15#89698—21no—
16#89323—21no—
17#89320—21no—
18#89320C2212yes—
19#89320C2212yes—
20#11575—71nomaximal, Sylow
21C22×C7×Q8—21no—
22C22×C7×Q8—21no—
23C22×C7×Q8—41no—
24C22×C7×Q8—41no—
25C22×C7×Q8—44no—
26C22×C7×D4C2×C411yescharacteristic
27C23×C4×C7C2×C411yescharacteristic
28C23×C4×C7C2×C412yes—
29C23×C4×C7D411yescharacteristic
30C7×C22⋊Q8—44no—
31C4×C7×D4—41no—
32C4×C7×D4—41no—
33C2×C7×C4⋊C4—21no—
34C2×C7×C4⋊C4—22no—
35C2×C7×C4⋊C4D411yescharacteristic
36C2×C7×C22⋊C4—22no—
37C2×C7×C22⋊C4C2×C412yes—
38C2×C7×C22⋊C4D411yescharacteristic
39C2×C7×C22⋊C4C2311yescharacteristic
40C2×C42×C7D411yescharacteristic
41C22×C7⋊C8—41no—
42C7×#95—21no—
43C7×#95—22no—
44C7×#95—22no—
45C22⋊(C7⋊C8)—22no—
46C22⋊(C7⋊C8)—22no—
47C22⋊(C7⋊C8)—41no—
48C4⋊(C7⋊C8)—41no—
49#6377—41no—
50#2409D711yescharacteristic
51#1466—71no—
52#1459—71no—
53#1326—74no—
54C24×C7C22⋊C411yescharacteristic
55C24×C7C22×C411yescharacteristic
56C2×C7×Q8—24no—
57C2×C7×Q8—42no—
58C2×C7×Q8—44no—
59C2×C7×Q8—42no—
60C2×C7×Q8—48no—
61C2×C7×Q8—44no—
62C2×C7×Q8—44no—
63C2×C7×Q8—41no—
64C2×C7×Q8—41no—
65C2×C7×D4—22no—
66C2×C7×D4—22no—
67C2×C7×D4—41no—
68C22×C4×C7—22no—
69C22×C4×C7—21no—
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7—21no—
73C22×C4×C7—22no—
74C22×C4×C7—42no—
75C22×C4×C7—44no—
76C22×C4×C7—42no—
77C22×C4×C7—42no—
78C22×C4×C7C22⋊C411yescharacteristic
79C22×C4×C7C22⋊C411yescharacteristic
80C22×C4×C7C22⋊C411yescharacteristic
81C22×C4×C7C2×D411yescharacteristic
82C22×C4×C7C2×D411yescharacteristic
83C7×C4⋊C4—41no—
84C7×C4⋊C4—42no—
85C7×C4⋊C4—44no—
86C7×C22⋊C4—24no—
87C7×C22⋊C4—41no—
88C7×C22⋊C4—41no—
89C7×C22⋊C4—44no—
90C42×C7—21no—
91C42×C7—21no—
92C2×C7⋊C8—42no—
93C2×C7⋊C8—42no—
94C2×C7⋊C8—82no—
95C23×Q8Dic711yescharacteristic
96C2×C22⋊Q8—21no—
97C2×C4×D4C2×D711yescharacteristic
98#432—141no—
99C2×C22⋊C8—141no—
100#395—21no—
101#393—21no—
102#391—21no—
103#386Dic712yes—
104#385C2×D712yes—
105#380Dic711yescharacteristic
106#324—141no—
107#323—72no—
108#323—72no—
109#323—141no—
110C23×C7—21no—
111C23×C7—21no—
112C23×C7—21no—
113C23×C7—21no—
114C23×C7—41no—
115C23×C7—41no—
116C23×C7—41no—
117C23×C7—41no—
118C23×C7#10112yes—
119C23×C7C2×C22⋊C411yescharacteristic
120C23×C7#13112yes—
121C7×Q8—44no—
122C7×Q8—48no—
123C7×Q8—44no—
124C7×D4—44no—
125C2×C4×C7—22no—
126C2×C4×C7—24no—
127C2×C4×C7—21no—
128C2×C4×C7—21no—
129C2×C4×C7—21no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—42no—
134C2×C4×C7—42no—
135C2×C4×C7—44no—
136C2×C4×C7—42no—
137C2×C4×C7—42no—
138C2×C4×C7—42no—
139C2×C4×C7—41no—
140C2×C4×C7—41no—
141C2×C4×C7—41no—
142C2×C4×C7—44no—
143C2×C4×C7—42no—
144C2×C4×C7—42no—
145C2×C4×C7—42no—
146C2×C4×C7—81no—
147C2×C4×C7#9911yescharacteristic
148C2×C4×C7#9911yescharacteristic
149C7⋊C8—82no—
150C7⋊C8—82no—
151C22×Q8—21no—
152C22×Q8—21no—
153C22×Q8—41no—
154C22×Q8—41no—
155C22×Q8—44no—
156C22×D4C2×Dic711yescharacteristic
157C23×C4C2×Dic711yescharacteristic
158C23×C4C2×Dic712yes—
159C23×C4C22⋊D711yescharacteristic
160C22×C8—281no—
161C22⋊Q8—44no—
162C4×D4—41no—
163C4×D4—41no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4C22⋊D711yescharacteristic
167C2×C22⋊C4—22no—
168C2×C22⋊C4C2×Dic712yes—
169C2×C22⋊C4C22⋊D711yescharacteristic
170C2×C22⋊C4C22×D711yescharacteristic
171C2×C42C22⋊D711yescharacteristic
172C4⋊C8—281no—
173C22⋊C8—142no—
174C22⋊C8—142no—
175C22⋊C8—281no—
176#97—281no—
177#95—21no—
178#95—22no—
179#95—22no—
180C22×C7—21no—
181C22×C7—21no—
182C22×C7—22no—
183C22×C7—22no—
184C22×C7—42no—
185C22×C7—42no—
186C22×C7—42no—
187C22×C7—41no—
188C22×C7—41no—
189C22×C7—41no—
190C22×C7—41no—
191C22×C7—81no—
192C22×C7#40811yescharacteristic
193C22×C7C2×#9911yescharacteristic
194C22×C7C2×#10111yescharacteristic
195C4×C7—21no—
196C4×C7—41no—
197C4×C7—44no—
198C4×C7—41no—
199C4×C7—41no—
200C4×C7—41no—
201C4×C7—82no—
202C4×C7AΣL(1,𝔽16)12yes—
203C24C22⋊Dic711yescharacteristic
204C24C22×Dic711yescharacteristic
205C2×Q8—24no—
206C2×Q8—42no—
207C2×Q8—44no—
208C2×Q8—42no—
209C2×Q8—44no—
210C2×Q8—48no—
211C2×Q8—44no—
212C2×Q8—41no—
213C2×Q8—41no—
214C2×D4—22no—
215C2×D4—22no—
216C2×D4—41no—
217C22×C4—22no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—22no—
223C22×C4—42no—
224C22×C4—44no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4C22⋊Dic711yescharacteristic
228C22×C4C22⋊Dic711yescharacteristic
229C22×C4C22⋊Dic711yescharacteristic
230C22×C4C2×C22⋊D711yescharacteristic
231C22×C4C2×C22⋊D711yescharacteristic
232C2×C8—282no—
233C2×C8—282no—
234C2×C8—562no—
235C4⋊C4—41no—
236C4⋊C4—42no—
237C4⋊C4—44no—
238C22⋊C4—24no—
239C22⋊C4—41no—
240C22⋊C4—41no—
241C22⋊C4—44no—
242C42—21no—
243C42—21no—
244C2×C7—21no—
245C2×C7—21no—
246C2×C7—42no—
247C2×C7—42no—
248C2×C7#147211yescharacteristic
249C2×C7C2×AΣL(1,𝔽16)11yescharacteristic
250C2×C7#212311yescharacteristic
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23—41no—
256C23—41no—
257C23—41no—
258C23—41no—
259C23#641012yes—
260C23#651112yes—
261C23C2×C22⋊Dic711yescharacteristic
262Q8—44no—
263Q8—48no—
264Q8—44no—
265D4—44no—
266C2×C4—22no—
267C2×C4—24no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—44no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—44no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—81no—
288C2×C4#640811yescharacteristic
289C2×C4#640811yescharacteristic
290C8—562no—
291C8—562no—
292C7#1157511yescharacteristic, complemented, Sylow
293C22—21no—
294C22—21no—
295C22—22no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—41no—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—81no—
305C22C2×#640811yescharacteristic
306C22C2×#641011yescharacteristic
307C22#9000611yescharacteristic
308C4—21no—
309C4—41no—
310C4—44no—
311C4—41no—
312C4—41no—
313C4—41no—
314C4—82no—
315C4#8933112yes—
316C2—21no—
317C2—21no—
318C2—42no—
319C2—42no—
320C2C2×#8933111yescharacteristic
321C2#1172944511yescharacteristic
322C2#1172962411yescharacteristic
subgroupG/H
centerC22C2×#6408
commutatorC24×C7C22×C4
FrattiniC2×C22⋊C4C22×D7
FittingC7×#2409C2
socleC22×C7C2×#99
prime radicalC22×C7×D4C2×C4
cosocleC2×C7×C22⋊C4C23
hypercenter#2409D7
hypocenterC7#11575
LCSG ▷ C24×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2409

Complements

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

NH ≅ G/Ntype
4. #11725442C2semidirect
292. C7#11575semidirect

Maximal subgroups

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

subgroupindex
C7×#24092
#117293572
#117293542
#117254422
#115757