Finite Group Databasebeta

← #13243129

Subgroups — #13243129

Order 1792.

350 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 81 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#11733626C211yesmaximal, characteristic
2#11727366C211yesmaximal, characteristic
3#11726445C211yesmaximal, characteristic
4#11726397C211yesmaximal, characteristic
5C7×#1271C211yesmaximal, characteristic
6#11725286C211yesmaximal, characteristic
7#11725283C211yesmaximal, characteristic
8C7×#389C2211yescharacteristic
9C2×#6392—21no—
10C2×#6390—21no—
11#89754—21no—
12#89753—21no—
13#89751—21no—
14#89744—21no—
15#89707C2211yescharacteristic
16#89701C2211yescharacteristic
17#89700C2211yescharacteristic
18#89432—21no—
19#89425—21no—
20C7×#336C2211yescharacteristic
21C7×#336C2211yescharacteristic
22#89346—21no—
23#89346—21no—
24#89324—21no—
25#89324—21no—
26#89319C2211yescharacteristic
27#7835—71nomaximal, Sylow
28C22×Dic14D411yescharacteristic
29C22×C7×C8—21no—
30C22×C7×C8—21no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4D411yescharacteristic
33C2×C7×C4⋊C4D411yescharacteristic
34C2×C42×C7C2311yescharacteristic
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7—21no—
37C2×C4⋊Dic7—21no—
38C2×C4⋊Dic7D411yescharacteristic
39C2×C4⋊Dic7D411yescharacteristic
40C2×C4⋊Dic7D411yescharacteristic
41C2×Dic7⋊C4—21no—
42C2×Dic7⋊C4—21no—
43C2×Dic7⋊C4—21no—
44C2×C4×Dic7—21no—
45C22×C7⋊C8—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#6392—42no—
56#6390—42no—
57#2805—71no—
58#2100—71no—
59#2100—71no—
60#2095—71no—
61#1272—71no—
62#1271—71no—
63#1271D711yescharacteristic
64C22×C4×C7—21no—
65C22×C4×C7—21no—
66C22×C4×C7C2×D411yescharacteristic
67C22×C4×C7C2×D411yescharacteristic
68C22×C4×C7C2×D411yescharacteristic
69C22×Dic7—21no—
70C22×Dic7—21no—
71C22×Dic7—21no—
72C22×Dic7—21no—
73C22×Dic7—41no—
74C2×Dic14—21no—
75C2×Dic14—21no—
76C2×Dic14—41no—
77C2×Dic14—41no—
78C2×C7×C8—22no—
79C2×C7×C8—41no—
80C2×C7×C8—41no—
81C2×C7×C8—41no—
82C2×C7×C8—41no—
83C2×C7×C8—41no—
84C7×C4⋊C4—21no—
85C7×C4⋊C4—21no—
86C7×C4⋊C4—41no—
87C7×C4⋊C4—41no—
88C7×C4⋊C4—41no—
89C42×C7—41no—
90C4⋊Dic7—21no—
91C4⋊Dic7—41no—
92C4⋊Dic7—41no—
93C4⋊Dic7—42no—
94C4⋊Dic7—42no—
95C4⋊Dic7—41no—
96C4⋊Dic7—41no—
97C4⋊Dic7Q1612yes—
98Dic7⋊C4—41no—
99Dic7⋊C4—41no—
100Dic7⋊C4—81no—
101Dic7⋊C4—81no—
102C4×Dic7—81no—
103C2×C7⋊C8—41no—
104C2×C7⋊C8—41no—
105C2×C7⋊C8—41no—
106C2×#107—141no—
107C2×#103—141no—
108#400—141no—
109#400—141no—
110#395—141no—
111#391—71no—
112#389—71no—
113#389—141no—
114#389C2×D711yescharacteristic
115#387—141no—
116#387—141no—
117#384—71no—
118#340—141no—
119#340—141no—
120#340—141no—
121#340—141no—
122#336—71no—
123#336C2×D711yescharacteristic
124#336C2×D711yescharacteristic
125C23×C7#12011yescharacteristic
126C2×C4×C7—21no—
127C2×C4×C7—21no—
128C2×C4×C7—21no—
129C2×C4×C7—21no—
130C2×C4×C7—21no—
131C2×C4×C7—21no—
132C2×C4×C7—41no—
133C2×C4×C7—41no—
134C2×C4×C7—41no—
135C2×C4×C7—41no—
136C2×C4×C7—41no—
137C2×C4×C7—41no—
138C2×C4×C7C2×Q1611yescharacteristic
139C2×C4×C7#13511yescharacteristic
140C2×C4×C7#13511yescharacteristic
141C2×C4×C7#13711yescharacteristic
142C2×C4×C7#13711yescharacteristic
143C2×C4×C7#13711yescharacteristic
144C2×Dic7—22no—
145C2×Dic7—41no—
146C2×Dic7—41no—
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—81no—
157C2×Dic7—81no—
158C2×Dic7—81no—
159Dic14—42no—
160Dic14—81no—
161C7×C8—42no—
162C7×C8—81no—
163C7⋊C8—81no—
164C22×Q8—71no—
165C22×C8—21no—
166C22×C8—21no—
167C22×C8—141no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—71no—
170C2×C4⋊C4—71no—
171C2×C4⋊C4—71no—
172C2×C4⋊C4—141no—
173C2×C4⋊C4—141no—
174C2×C4⋊C4—141no—
175C2×C4⋊C4—141no—
176C2×C4⋊C4—141no—
177C2×C4⋊C4—141no—
178C2×C4⋊C4D2811yescharacteristic
179C2×C4⋊C4D2811yescharacteristic
180C2×C42—141no—
181C2×C42C22×D711yescharacteristic
182#107—282no—
183#103—282no—
184#95—21no—
185#95—141no—
186#95—141no—
187#95—141no—
188#95—141no—
189#95—141no—
190#95—141no—
191#95—141no—
192#95—141no—
193C22×C7#45111yescharacteristic
194C22×C7#45211yescharacteristic
195C22×C7#45211yescharacteristic
196C22×C7#45311yescharacteristic
197C22×C7#45411yescharacteristic
198C22×C7#45411yescharacteristic
199C22×C7#45811yescharacteristic
200C4×C7—21no—
201C4×C7—21no—
202C4×C7—21no—
203C4×C7—21no—
204C4×C7—21no—
205C4×C7—21no—
206C4×C7—81no—
207C4×C7—81no—
208Dic7—42no—
209Dic7—81no—
210Dic7—81no—
211Dic7—81no—
212Dic7—161no—
213C2×Q8—141no—
214C2×Q8—141no—
215C2×Q8—281no—
216C2×Q8—281no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—141no—
220C22×C4—141no—
221C22×C4—141no—
222C22×C4—141no—
223C22×C4—281no—
224C22×C4C2×D2811yescharacteristic
225C22×C4D4×D711yescharacteristic
226C22×C4D4×D711yescharacteristic
227C2×C8—22no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—281no—
234C2×C8—281no—
235C2×C8—281no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—72no—
242C4⋊C4—141no—
243C4⋊C4—281no—
244C4⋊C4—281no—
245C4⋊C4—281no—
246C4⋊C4—281no—
247C4⋊C4—282no—
248C4⋊C4—282no—
249C4⋊C4—281no—
250C4⋊C4—281no—
251C4⋊C4—561no—
252C4⋊C4—561no—
253C42—41no—
254C42—561no—
255C2×C7#161511yescharacteristic
256C2×C7#161711yescharacteristic
257C2×C7#161811yescharacteristic
258C2×C7#163211yescharacteristic
259C2×C7#163611yescharacteristic
260C2×C7#163811yescharacteristic
261C2×C7#165711yescharacteristic
262C23#644511yescharacteristic
263Q8—282no—
264Q8—561no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—142no—
278C2×C4—281no—
279C2×C4—281no—
280C2×C4—281no—
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—561no—
290C2×C4—561no—
291C2×C4—561no—
292C2×C4#646711yescharacteristic
293C2×C4#647211yescharacteristic
294C2×C4#647511yescharacteristic
295C2×C4#647811yescharacteristic
296C2×C4#647811yescharacteristic
297C2×C4D7×Q1611yescharacteristic
298C8—42no—
299C8—81no—
300C8—561no—
301C7#783511yescharacteristic, complemented, Sylow
302C22#8950511yescharacteristic
303C22#8951411yescharacteristic
304C22#8952511yescharacteristic
305C22#8955511yescharacteristic
306C22#8958011yescharacteristic
307C22#8959411yescharacteristic
308C22#8959911yescharacteristic
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—81no—
316C4—81no—
317C4—282no—
318C4—561no—
319C4—561no—
320C4—561no—
321C4—1121no—
322C2#1172589011yescharacteristic
323C2#1172595911yescharacteristic
324C2#1172600011yescharacteristic
325C2#1172604511yescharacteristic
326C2#1172608511yescharacteristic
327C2#1172612511yescharacteristic
328C2#1172621211yescharacteristic
subgroupG/H
centerC23#6445
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1271C2
socle, prime radicalC23×C7#120
hypercenter#1271D7
hypocenterC7#7835
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
301. C7#7835semidirect

Maximal subgroups

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

subgroupindex
#117336262
#117273662
#117264452
#117263972
C7×#12712
#117252862
#117252832
#78357