Finite Group Databasebeta

← #13243111

Subgroups — #13243111

Order 1792.

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

normal subgroups only

This group has 322 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#11733632C211yesmaximal, characteristic
2#11727366C211yesmaximal, characteristic
3#11726397C211yesmaximal, characteristic
4#11726397C211yesmaximal, characteristic
5C7×#1271C211yesmaximal, characteristic
6#11725284C211yesmaximal, characteristic
7#11725283C211yesmaximal, characteristic
8C7×#389C2211yescharacteristic
9#89758—21no—
10#89754—21no—
11#89753—21no—
12#89750—21no—
13#89707C2211yescharacteristic
14#89700C2211yescharacteristic
15#89700C2211yescharacteristic
16#89431—21no—
17#89427—21no—
18C7×#336C2211yescharacteristic
19C7×#336C2211yescharacteristic
20#89346—21no—
21#89346—21no—
22#89346—21no—
23#89346—21no—
24#89324—21no—
25#89324—21no—
26#89319C2211yescharacteristic
27#7832—71nomaximal, Sylow
28C22×C7×C8—21no—
29C22×C7×C8—21no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4D411yescharacteristic
32C2×C7×C4⋊C4D411yescharacteristic
33C2×C42×C7C2311yescharacteristic
34C2×C4⋊Dic7—21no—
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7—21no—
37C2×C4⋊Dic7D411yescharacteristic
38C2×C4⋊Dic7D411yescharacteristic
39C2×C4⋊Dic7D411yescharacteristic
40C2×C4⋊Dic7D411yescharacteristic
41C2×Dic7⋊C4—21no—
42C2×Dic7⋊C4—21no—
43C2×C4×Dic7—21no—
44C22×C7⋊C8—21no—
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⋊#95—21no—
54C7⋊#95—21no—
55#2810—71no—
56#2100—71no—
57#2100—71no—
58#2100—71no—
59#1271—71no—
60#1271—71no—
61#1271D711yescharacteristic
62C22×C4×C7—21no—
63C22×C4×C7—21no—
64C22×C4×C7C2×D411yescharacteristic
65C22×C4×C7C2×D411yescharacteristic
66C22×C4×C7C2×D411yescharacteristic
67C22×Dic7—21no—
68C22×Dic7—21no—
69C22×Dic7—21no—
70C22×Dic7—21no—
71C22×Dic7—41no—
72C2×C7×C8—41no—
73C2×C7×C8—41no—
74C2×C7×C8—41no—
75C2×C7×C8—41no—
76C2×C7×C8—41no—
77C2×C7×C8—41no—
78C7×C4⋊C4—21no—
79C7×C4⋊C4—21no—
80C7×C4⋊C4—41no—
81C7×C4⋊C4—41no—
82C7×C4⋊C4—41no—
83C42×C7—41no—
84C4⋊Dic7—21no—
85C4⋊Dic7—21no—
86C4⋊Dic7—21no—
87C4⋊Dic7—21no—
88C4⋊Dic7—41no—
89C4⋊Dic7—41no—
90C4⋊Dic7—42no—
91C4⋊Dic7—42no—
92C4⋊Dic7—42no—
93Dic7⋊C4—41no—
94Dic7⋊C4—41no—
95Dic7⋊C4—41no—
96Dic7⋊C4—41no—
97C4×Dic7—81no—
98C2×C7⋊C8—41no—
99C2×C7⋊C8—41no—
100C2×C7⋊C8—41no—
101#400—141no—
102#400—141no—
103#400—141no—
104#389—71no—
105#389—71no—
106#389C2×D711yescharacteristic
107#387—141no—
108#387—141no—
109#387—141no—
110#384—71no—
111#340—141no—
112#340—141no—
113#340—141no—
114#340—141no—
115#340—141no—
116#340—141no—
117#336—71no—
118#336C2×D711yescharacteristic
119#336C2×D711yescharacteristic
120C23×C7#12011yescharacteristic
121C2×C4×C7—21no—
122C2×C4×C7—21no—
123C2×C4×C7—21no—
124C2×C4×C7—21no—
125C2×C4×C7—21no—
126C2×C4×C7—21no—
127C2×C4×C7—41no—
128C2×C4×C7—41no—
129C2×C4×C7—41no—
130C2×C4×C7—41no—
131C2×C4×C7—41no—
132C2×C4×C7—41no—
133C2×C4×C7#13511yescharacteristic
134C2×C4×C7#13511yescharacteristic
135C2×C4×C7#13511yescharacteristic
136C2×C4×C7#13711yescharacteristic
137C2×C4×C7#13711yescharacteristic
138C2×C4×C7#13711yescharacteristic
139C2×Dic7—41no—
140C2×Dic7—41no—
141C2×Dic7—41no—
142C2×Dic7—41no—
143C2×Dic7—41no—
144C2×Dic7—41no—
145C2×Dic7—41no—
146C2×Dic7—41no—
147C2×Dic7—41no—
148C2×Dic7—41no—
149C2×Dic7—41no—
150C2×Dic7—41no—
151C2×Dic7—81no—
152C2×Dic7—81no—
153C2×Dic7—81no—
154C7×C8—81no—
155C7×C8—81no—
156C7⋊C8—81no—
157C22×C8—21no—
158C22×C8—21no—
159C22×C8—141no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—71no—
162C2×C4⋊C4—71no—
163C2×C4⋊C4—71no—
164C2×C4⋊C4—71no—
165C2×C4⋊C4—141no—
166C2×C4⋊C4—141no—
167C2×C4⋊C4—141no—
168C2×C4⋊C4—141no—
169C2×C4⋊C4—141no—
170C2×C4⋊C4D2811yescharacteristic
171C2×C4⋊C4D2811yescharacteristic
172C2×C42—141no—
173C2×C42C22×D711yescharacteristic
174#95—21no—
175#95—141no—
176#95—141no—
177#95—141no—
178#95—141no—
179#95—141no—
180#95—141no—
181#95—141no—
182#95—141no—
183#95—141no—
184C22×C7#45211yescharacteristic
185C22×C7#45211yescharacteristic
186C22×C7#45211yescharacteristic
187C22×C7#45411yescharacteristic
188C22×C7#45411yescharacteristic
189C22×C7#45411yescharacteristic
190C22×C7#45811yescharacteristic
191C4×C7—21no—
192C4×C7—21no—
193C4×C7—21no—
194C4×C7—21no—
195C4×C7—21no—
196C4×C7—21no—
197C4×C7—81no—
198C4×C7—81no—
199Dic7—81no—
200Dic7—81no—
201Dic7—81no—
202Dic7—81no—
203Dic7—161no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—141no—
207C22×C4—141no—
208C22×C4—141no—
209C22×C4—141no—
210C22×C4—281no—
211C22×C4C2×D2811yescharacteristic
212C22×C4D4×D711yescharacteristic
213C22×C4D4×D711yescharacteristic
214C2×C8—41no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8—41no—
220C2×C8—281no—
221C2×C8—281no—
222C2×C8—281no—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—141no—
229C4⋊C4—141no—
230C4⋊C4—141no—
231C4⋊C4—141no—
232C4⋊C4—281no—
233C4⋊C4—281no—
234C4⋊C4—282no—
235C4⋊C4—282no—
236C4⋊C4—282no—
237C4⋊C4—281no—
238C4⋊C4—281no—
239C4⋊C4—281no—
240C4⋊C4—281no—
241C42—41no—
242C42—561no—
243C2×C7#161511yescharacteristic
244C2×C7#161511yescharacteristic
245C2×C7#161511yescharacteristic
246C2×C7#163811yescharacteristic
247C2×C7#163811yescharacteristic
248C2×C7#163811yescharacteristic
249C2×C7#165811yescharacteristic
250C23#644511yescharacteristic
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—281no—
264C2×C4—281no—
265C2×C4—281no—
266C2×C4—281no—
267C2×C4—281no—
268C2×C4—281no—
269C2×C4—281no—
270C2×C4—281no—
271C2×C4—281no—
272C2×C4—281no—
273C2×C4—281no—
274C2×C4—281no—
275C2×C4—561no—
276C2×C4—561no—
277C2×C4—561no—
278C2×C4#646711yescharacteristic
279C2×C4#647211yescharacteristic
280C2×C4#647511yescharacteristic
281C2×C4#647811yescharacteristic
282C2×C4#647911yescharacteristic
283C2×C4#648111yescharacteristic
284C8—81no—
285C8—81no—
286C8—561no—
287C7#783211yescharacteristic, complemented, Sylow
288C22#8950511yescharacteristic
289C22#8951411yescharacteristic
290C22#8952511yescharacteristic
291C22#8955511yescharacteristic
292C22#8958211yescharacteristic
293C22#8959911yescharacteristic
294C22#8959911yescharacteristic
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—81no—
302C4—81no—
303C4—561no—
304C4—561no—
305C4—561no—
306C4—561no—
307C4—1121no—
308C2#1172589011yescharacteristic
309C2#1172595911yescharacteristic
310C2#1172600111yescharacteristic
311C2#1172605211yescharacteristic
312C2#1172608411yescharacteristic
313C2#1172612911yescharacteristic
314C2#1172618911yescharacteristic
subgroupG/H
centerC23#6445
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1271C2
socle, prime radicalC23×C7#120
hypercenter#1271D7
hypocenterC7#7832
LCSG ▷ C2×C42×C7 ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
287. C7#7832semidirect

Maximal subgroups

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

subgroupindex
#117336322
#117273662
#117263972
C7×#12712
#117252842
#117252832
#78327