Finite Group Databasebeta

← #13263291

Subgroups — #13263291

Order 1792.

376 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 75 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#11731597C211yesmaximal, characteristic
2#11725881C212yesmaximal
3C7×#1324C211yesmaximal, characteristic
4#11725438C211yesmaximal, characteristic
5#11725261C212yesmaximal
6C2×#6450C411yescharacteristic
7C2×#6450C2211yescharacteristic
8C2×#6432C411yescharacteristic
9C7×#382C2211yescharacteristic
10#89746C411yescharacteristic
11#89746C2211yescharacteristic
12#89704C411yescharacteristic
13#89491—22no—
14#89426—22no—
15#89426—22no—
16C7×#324C2212yes—
17#89323C2212yes—
18#89264—22no—
19#11536—71nomaximal, Sylow
20C22×Dic14C2×C411yescharacteristic
21C22×Dic14C2×C411yescharacteristic
22C2×C7×C4⋊C4C2×C411yescharacteristic
23C2×C7×C4⋊C4C2311yescharacteristic
24C2×C42×C7C2×C411yescharacteristic
25C2×C4⋊Dic7—22no—
26C2×Dic7⋊C4—21no—
27C2×Dic7⋊C4D412yes—
28C2×C4×Dic7—21no—
29C2×C4×Dic7C2×C411yescharacteristic
30C2×C4×Dic7C2×C411yescharacteristic
31C2×C4×Dic7D412yes—
32#6450—42no—
33#6450—42no—
34#6432—22no—
35#6432—22no—
36C7×C22⋊C8—22no—
37C7×#95—22no—
38C7⋊#95—22no—
39C7⋊#95—21no—
40C7⋊#95—21no—
41C7⋊#95—22no—
42C22⋊(C7⋊C8)—22no—
43#6389—42no—
44Dic7⋊C8—42no—
45#2327—71no—
46#1467—72no—
47#1324—71no—
48#1324D711yescharacteristic
49#1319—72no—
50C22×C4×C7—21no—
51C22×C4×C7—21no—
52C22×C4×C7C22×C411yescharacteristic
53C22×C4×C7C2×D412yes—
54C22×Dic7—21no—
55C22×Dic7—21no—
56C22×Dic7C22⋊C412yes—
57C22×Dic7C22⋊C411yescharacteristic
58C22×Dic7C22⋊C411yescharacteristic
59C2×Dic14—21no—
60C2×Dic14—21no—
61C2×Dic14—21no—
62C2×Dic14—41no—
63C2×Dic14—41no—
64C2×Dic14—41no—
65C2×Dic14—41no—
66C2×Dic14M1612yes—
67C2×C7×C8—42no—
68C7×C4⋊C4—41no—
69C7×C4⋊C4—41no—
70C42×C7—21no—
71C42×C7M1612yes—
72C4⋊Dic7—28no—
73Dic7⋊C4—42no—
74Dic7⋊C4—42no—
75C4×Dic7—22no—
76C4×Dic7—22no—
77C4×Dic7—22no—
78C4×Dic7—42no—
79C4×Dic7—41no—
80C2×C7⋊C8—42no—
81C2×C4⋊Q8—71no—
82C2×C4×Q8—71no—
83C2×C4×Q8—71no—
84#432—142no—
85#391—71no—
86#391—71no—
87#387—142no—
88#387—142no—
89#382C2×D711yescharacteristic
90#376—71no—
91#324—72no—
92#324—142no—
93#324C2×D712yes—
94C23×C7C2×C22⋊C411yescharacteristic
95C2×C4×C7—21no—
96C2×C4×C7—21no—
97C2×C4×C7—22no—
98C2×C4×C7—22no—
99C2×C4×C7—41no—
100C2×C4×C7—41no—
101C2×C4×C7—42no—
102C2×C4×C7—42no—
103C2×C4×C7—41no—
104C2×C4×C7C2×M1611yescharacteristic
105C2×C4×C7C2×M1611yescharacteristic
106C2×Dic7—22no—
107C2×Dic7—22no—
108C2×Dic7—21no—
109C2×Dic7—22no—
110C2×Dic7—22no—
111C2×Dic7—41no—
112C2×Dic7—41no—
113C2×Dic7—41no—
114C2×Dic7—41no—
115C2×Dic7—41no—
116C2×Dic7—41no—
117C2×Dic7—41no—
118C2×Dic7#9912yes—
119Dic14—42no—
120Dic14—42no—
121Dic14—42no—
122Dic14—42no—
123C7×C8—82no—
124C7⋊C8—82no—
125C22×Q8—71no—
126C22×Q8—71no—
127C4⋊Q8—142no—
128C4⋊Q8—142no—
129C4×Q8—282no—
130C4×Q8—282no—
131C2×C4⋊C4—72no—
132C2×C4⋊C4—142no—
133C2×C4⋊C4—141no—
134C2×C4⋊C4C4×D711yescharacteristic
135C2×C4⋊C4C22×D711yescharacteristic
136C2×C42—71no—
137C2×C42—72no—
138C2×C42—71no—
139C2×C42—141no—
140C2×C42C4×D711yescharacteristic
141C4⋊C8—282no—
142C22⋊C8—22no—
143C22⋊C8—142no—
144#97—282no—
145#95—22no—
146#95—141no—
147#95—141no—
148#95—142no—
149#95—142no—
150C22×C7—21no—
151C22×C7—21no—
152C22×C7#40711yescharacteristic
153C22×C7C2×#9911yescharacteristic
154C22×C7#41311yescharacteristic
155C4×C7—21no—
156C4×C7—21no—
157C4×C7—42no—
158C4×C7—42no—
159C4×C7—81no—
160Dic7—22no—
161Dic7—41no—
162Dic7—42no—
163Dic7—42no—
164Dic7—81no—
165C2×Q8—72no—
166C2×Q8—141no—
167C2×Q8—141no—
168C2×Q8—141no—
169C2×Q8—281no—
170C2×Q8—281no—
171C2×Q8—281no—
172C2×Q8—281no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—71no—
176C22×C4—72no—
177C22×C4—71no—
178C22×C4—141no—
179C22×C4—141no—
180C22×C4C2×C4×D711yescharacteristic
181C22×C4D4×D712yes—
182C2×C8—42no—
183C2×C8—282no—
184C4⋊C4—41no—
185C4⋊C4—41no—
186C4⋊C4—148no—
187C4⋊C4—282no—
188C4⋊C4—282no—
189C42—21no—
190C42—142no—
191C42—142no—
192C42—142no—
193C42—281no—
194C42—282no—
195C42#113112yes—
196C2×C7—21no—
197C2×C7—21no—
198C2×C7#146511yescharacteristic
199C2×C7#212911yescharacteristic
200C2×C7#213311yescharacteristic
201C23D7×C22⋊C411yescharacteristic
202Q8—282no—
203Q8—282no—
204Q8—282no—
205Q8—282no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—72no—
216C2×C4—142no—
217C2×C4—142no—
218C2×C4—141no—
219C2×C4—142no—
220C2×C4—142no—
221C2×C4—281no—
222C2×C4—281no—
223C2×C4—281no—
224C2×C4—281no—
225C2×C4—281no—
226C2×C4—281no—
227C2×C4—281no—
228C2×C4C2×#113111yescharacteristic
229C2×C4D7×M1611yescharacteristic
230C8—82no—
231C8—562no—
232C7#1153611yescharacteristic, complemented, Sylow
233C22—21no—
234C22—21no—
235C22#8949811yescharacteristic
236C22D7×#9911yescharacteristic
237C22#8952311yescharacteristic
238C4—21no—
239C4—21no—
240C4—42no—
241C4—42no—
242C4—81no—
243C4—142no—
244C4—281no—
245C4—282no—
246C4—282no—
247C4—561no—
248C2—21no—
249C2—21no—
250C2#1172589911yescharacteristic
251C2#1172691311yescharacteristic
252C2#1172691811yescharacteristic
subgroupG/H
centerC22D7×#99
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1324C2
socleC22×C7C2×#99
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1324D7
hypocenterC7#11536
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
232. C7#11536semidirect

Maximal subgroups

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

subgroupindex
#117315972
#117258812
C7×#13242
#117254382
#117252612
#115367