Finite Group Databasebeta

← #13258299

Subgroups — #13258299

Order 1792.

374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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#11731663C211yesmaximal, characteristic
2#11727570C211yesmaximal, characteristic
3#11727569C211yesmaximal, characteristic
4#11727302C211yesmaximal, characteristic
5C7×#1295C211yesmaximal, characteristic
6#11725465C211yesmaximal, characteristic
7#11725465C211yesmaximal, characteristic
8C2×C7×#97C2211yescharacteristic
9C2×C7×#97C2211yescharacteristic
10C7×#382C2211yescharacteristic
11C2×#6392—21no—
12C2×#6391—21no—
13#89758—21no—
14#89751—21no—
15#89708C2211yescharacteristic
16#89708C2211yescharacteristic
17#89707C2211yescharacteristic
18C2×#6377C2211yescharacteristic
19#89432—21no—
20#89432—21no—
21#89428—21no—
22#89428—21no—
23#89346—21no—
24#89346—21no—
25#89324—21no—
26#89324—21no—
27#10584—71nomaximal, Sylow
28C22×Dic14—21no—
29C22×C7×C8—21no—
30C22×C7×C8—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⋊Dic7—21no—
38C2×C4⋊Dic7D411yescharacteristic
39C2×C4⋊Dic7D411yescharacteristic
40C2×C4⋊Dic7D411yescharacteristic
41C2×C4⋊Dic7D411yescharacteristic
42C2×Dic7⋊C4—21no—
43C2×Dic7⋊C4—21no—
44C22×C7⋊C8—21no—
45C7×#97—21no—
46C7×#97—21no—
47C7×#97Q812yescomplemented
48C7×#97Q812yescomplemented
49C7×#95—21no—
50C7×#95—21no—
51C7⋊#95—21no—
52C7⋊#95—21no—
53C7⋊#95—21no—
54C7⋊#95—21no—
55C7⋊#95—21no—
56C7⋊#95—21no—
57C7⋊#95—21no—
58C7⋊#95—21no—
59#6392—42no—
60#6391—42no—
61#6377—21no—
62#6377Q812yescomplemented
63#2844—71no—
64#1847—71no—
65#1836—71no—
66#1836—71no—
67#1295—71no—
68#1295—71no—
69#1295D711yescharacteristic
70C22×C4×C7—21no—
71C22×C4×C7—21no—
72C22×C4×C7C2×D411yescharacteristic
73C22×C4×C7C2×D411yescharacteristic
74C22×C4×C7C2×D411yescharacteristic
75C22×Dic7—21no—
76C22×Dic7—21no—
77C22×Dic7—21no—
78C22×Dic7—21no—
79C22×Dic7—41no—
80C2×Dic14—81no—
81C2×Dic14—81no—
82C2×Dic14—81no—
83C2×C7×C8—22no—
84C2×C7×C8—22no—
85C2×C7×C8—22no—
86C2×C7×C8—22no—
87C2×C7×C8—41no—
88C2×C7×C8—41no—
89C7×C4⋊C4—41no—
90C7×C4⋊C4—41no—
91C42×C7C2×Q811yescharacteristic
92C42×C7C2×Q811yescharacteristic
93C42×C7C2×Q811yescharacteristic
94C42×C7#4111yescharacteristic
95C4⋊Dic7—41no—
96C4⋊Dic7—41no—
97C4⋊Dic7—41no—
98C4⋊Dic7—41no—
99C4⋊Dic7—42no—
100C4⋊Dic7—42no—
101C4⋊Dic7—41no—
102C4⋊Dic7—41no—
103C4⋊Dic7—81no—
104Dic7⋊C4—81no—
105Dic7⋊C4—81no—
106C2×C7⋊C8—22no—
107C2×C7⋊C8—41no—
108C2×C7⋊C8—41no—
109C2×#107—141no—
110C2×#106—141no—
111C2×#97—71no—
112C2×#97C2×D711yescharacteristic
113C2×#97C2×D711yescharacteristic
114#400—141no—
115#400—141no—
116#400—141no—
117#395—141no—
118#395—141no—
119#395—141no—
120#384—71no—
121#382—71no—
122#382—71no—
123#382C2×D711yescharacteristic
124#340—141no—
125#340—141no—
126#340—141no—
127#340—141no—
128C23×C7#12011yescharacteristic
129C2×C4×C7—21no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—21no—
133C2×C4×C7—21no—
134C2×C4×C7—21no—
135C2×C4×C7—41no—
136C2×C4×C7—41no—
137C2×C4×C7—41no—
138C2×C4×C7—41no—
139C2×C4×C7—41no—
140C2×C4×C7—41no—
141C2×C4×C7C22⋊Q811yescharacteristic
142C2×C4×C7C22⋊Q811yescharacteristic
143C2×C4×C7C22⋊Q811yescharacteristic
144C2×C4×C7C4⋊Q811yescharacteristic
145C2×C4×C7C4⋊Q811yescharacteristic
146C2×C4×C7C4⋊Q811yescharacteristic
147C2×Dic7—41no—
148C2×Dic7—41no—
149C2×Dic7—41no—
150C2×Dic7—41no—
151C2×Dic7—41no—
152C2×Dic7—41no—
153C2×Dic7—41no—
154C2×Dic7—41no—
155C2×Dic7—41no—
156C2×Dic7—41no—
157C2×Dic7—41no—
158C2×Dic7—41no—
159C2×Dic7—81no—
160C2×Dic7—81no—
161C2×Dic7—81no—
162Dic14—84no—
163C7×C8—24no—
164C7×C8—42no—
165C7⋊C8—42no—
166C22×Q8—141no—
167C22×C8—21no—
168C22×C8—21no—
169C22×C8—141no—
170C2×C4⋊C4—71no—
171C2×C4⋊C4—71no—
172C2×C4⋊C4—71no—
173C2×C4⋊C4—71no—
174C2×C4⋊C4—141no—
175C2×C4⋊C4—141no—
176C2×C4⋊C4—141no—
177C2×C4⋊C4—141no—
178C2×C4⋊C4—141no—
179C2×C4⋊C4—141no—
180C2×C4⋊C4D2811yescharacteristic
181C2×C4⋊C4D2811yescharacteristic
182C2×C42C22×D711yescharacteristic
183#107—282no—
184#106—282no—
185#97—21no—
186#97—21no—
187#97—72no—
188#97—141no—
189#97Dic1412yescomplemented
190#97Dic1412yescomplemented
191#95—21no—
192#95—21no—
193#95—141no—
194#95—141no—
195#95—141no—
196#95—141no—
197#95—141no—
198#95—141no—
199#95—141no—
200#95—141no—
201C22×C7#39511yescharacteristic
202C22×C7#45311yescharacteristic
203C22×C7#45411yescharacteristic
204C22×C7#45411yescharacteristic
205C22×C7#45511yescharacteristic
206C22×C7#45511yescharacteristic
207C22×C7#45611yescharacteristic
208C4×C7—21no—
209C4×C7—21no—
210C4×C7—21no—
211C4×C7—21no—
212C4×C7—21no—
213C4×C7—21no—
214C4×C7—81no—
215C4×C7—81no—
216Dic7—81no—
217Dic7—81no—
218Dic7—81no—
219Dic7—81no—
220Dic7—161no—
221C2×Q8—561no—
222C2×Q8—561no—
223C2×Q8—561no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—141no—
227C22×C4—141no—
228C22×C4—141no—
229C22×C4—141no—
230C22×C4—281no—
231C22×C4C2×D2811yescharacteristic
232C22×C4D4×D711yescharacteristic
233C22×C4D4×D711yescharacteristic
234C2×C8—22no—
235C2×C8—22no—
236C2×C8—22no—
237C2×C8—22no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—142no—
241C2×C8—281no—
242C2×C8—281no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—281no—
246C4⋊C4—281no—
247C4⋊C4—281no—
248C4⋊C4—281no—
249C4⋊C4—281no—
250C4⋊C4—281no—
251C4⋊C4—282no—
252C4⋊C4—282no—
253C4⋊C4—561no—
254C4⋊C4—561no—
255C4⋊C4—561no—
256C42C2×Dic1411yescharacteristic
257C42C2×Dic1411yescharacteristic
258C42#115911yescharacteristic
259C42Q8×D711yescharacteristic
260C2×C7#165711yescharacteristic
261C2×C7#165911yescharacteristic
262C2×C7#166411yescharacteristic
263C2×C7#166411yescharacteristic
264C2×C7#206011yescharacteristic
265C2×C7#206111yescharacteristic
266C2×C7#206111yescharacteristic
267C23#644511yescharacteristic
268Q8—564no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—281no—
282C2×C4—281no—
283C2×C4—281no—
284C2×C4—281no—
285C2×C4—281no—
286C2×C4—281no—
287C2×C4—281no—
288C2×C4—281no—
289C2×C4—281no—
290C2×C4—281no—
291C2×C4—281no—
292C2×C4—281no—
293C2×C4—561no—
294C2×C4—561no—
295C2×C4—561no—
296C2×C4#643211yescharacteristic
297C2×C4#644111yescharacteristic
298C2×C4#644111yescharacteristic
299C2×C4#645111yescharacteristic
300C2×C4#645111yescharacteristic
301C2×C4#646011yescharacteristic
302C8—24no—
303C8—42no—
304C8—282no—
305C7#1058411yescharacteristic, complemented, Sylow
306C22#8942811yescharacteristic
307C22#8951811yescharacteristic
308C22#8952511yescharacteristic
309C22#8959411yescharacteristic
310C22#8959711yescharacteristic
311C22#8959811yescharacteristic
312C22#8959911yescharacteristic
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—81no—
320C4—81no—
321C4—561no—
322C4—561no—
323C4—561no—
324C4—561no—
325C4—1121no—
326C2#1172610611yescharacteristic
327C2#1172611311yescharacteristic
328C2#1172612511yescharacteristic
329C2#1172613311yescharacteristic
330C2#1172648911yescharacteristic
331C2#1172649011yescharacteristic
332C2#1172673311yescharacteristic
subgroupG/H
centerC23#6445
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1295C2
socle, prime radicalC23×C7#120
hypercenter#1295D7
hypocenterC7#10584
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
47. C7×#97Q8semidirect
48. C7×#97Q8semidirect
62. #6377Q8semidirect
189. #97Dic14semidirect
190. #97Dic14semidirect
305. C7#10584semidirect

Maximal subgroups

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

subgroupindex
#117316632
#117275702
#117275692
#117273022
C7×#12952
#117254652
#105847