Finite Group Databasebeta

← #13274158

Subgroups — #13274158

Order 1792.

312 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 71 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#11740643C211yesmaximal, characteristic
2C2×C7×#356C211yesmaximal, characteristic
3C2×#89343C211yesmaximal, characteristic
4#11725357C214yesmaximal, complemented
5C2×C7×C4⋊Q8C2211yescharacteristic
6#90161C411yescharacteristic
7C2×C7×#101—21no—
8C2×#6410—21no—
9#89997—21no—
10#89997—21no—
11#89854C412yes—
12#89854C2212yes—
13#89853—21no—
14#89853—21no—
15C4×#1136C411yescharacteristic
16C7×#356—21no—
17C7×#356C2212yes—
18#89343—21no—
19#89343C2212yes—
20#13599—71nomaximal, Sylow
21C22×C7×Q8D411yescharacteristic
22C22×C7×Q8D411yescharacteristic
23C2×C7×M16—41no—
24C7×C4⋊Q8—41no—
25C7×C4⋊Q8C2×C411yescharacteristic
26C7×C4⋊Q8D411yescharacteristic
27C7×C4⋊Q8D411yescharacteristic
28C7×C4⋊Q8C2311yescharacteristic
29C2×C7×C4⋊C4—41no—
30C2×C42×C7C2×C411yescharacteristic
31#6489—21no—
32#6487—41no—
33C2×#1136—21no—
34C2×#1136—41no—
35#6433C2×C412yes—
36#6432—21no—
37C4×Dic14—41no—
38C7×#101—22no—
39C7×#101—41no—
40#6410—22no—
41#6410—41no—
42#6409—22no—
43#6409—22no—
44#6409—22no—
45#6409—22no—
46#6377C2×C412yes—
47C4×C7⋊C8—21no—
48#3139—71no—
49C2×#356—71no—
50C2×#356D711yescharacteristic
51#1413—74no—
52C2×C7×Q8—21no—
53C2×C7×Q8—21no—
54C2×C7×Q8—41no—
55C2×C7×Q8—41no—
56C2×C7×Q8—41no—
57C2×C7×Q8—41no—
58C2×C7×Q8C22⋊C411yescharacteristic
59C2×C7×Q8C22⋊C411yescharacteristic
60C2×C7×Q8C2×D411yescharacteristic
61C2×C7×Q8C2×D411yescharacteristic
62C22×C4×C7—21no—
63C22×C4×C7—21no—
64C22×C4×C7—21no—
65C22×C4×C7C22⋊C411yescharacteristic
66C2×Dic14—41no—
67C7×M16—42no—
68C7×M16—81no—
69C2×C7×C8—81no—
70C7×C4⋊C4—41no—
71C7×C4⋊C4—41no—
72C7×C4⋊C4—41no—
73C7×C4⋊C4—41no—
74C42×C7—21no—
75C42×C7C22⋊C411yescharacteristic
76C42×C7C22×C411yescharacteristic
77C22⋊Dic7—41no—
78C4⋊Dic7—22no—
79C4⋊Dic7—41no—
80Dic7⋊C4—42no—
81C4×Dic7—41no—
82#1136—41no—
83#1136—41no—
84#1136—42no—
85#1136—81no—
86C2×C7⋊C8—22no—
87C2×C7⋊C8—81no—
88#533—71no—
89C2×C4⋊Q8C2×D711yescharacteristic
90#491—72no—
91#491—72no—
92#487—141no—
93#487—141no—
94#419—141no—
95#419—141no—
96C2×#101—21no—
97C2×#101—141no—
98C4×M16—71no—
99#356—21no—
100#356—72no—
101#356—141no—
102#356C2×D712yes—
103C23×C7#9911yescharacteristic
104C7×Q8—41no—
105C7×Q8—41no—
106C7×Q8—41no—
107C7×Q8—41no—
108C7×Q8—81no—
109C7×Q8—81no—
110C2×C4×C7—21no—
111C2×C4×C7—21no—
112C2×C4×C7—21no—
113C2×C4×C7—21no—
114C2×C4×C7—21no—
115C2×C4×C7—21no—
116C2×C4×C7—21no—
117C2×C4×C7—21no—
118C2×C4×C7—42no—
119C2×C4×C7—41no—
120C2×C4×C7—41no—
121C2×C4×C7—41no—
122C2×C4×C7—41no—
123C2×C4×C7#9911yescharacteristic
124C2×C4×C7C2×C22⋊C411yescharacteristic
125C2×Dic7—42no—
126Dic14—82no—
127C7×C8—82no—
128C7⋊C8—42no—
129C7⋊C8—82no—
130C22×Q8D2811yescharacteristic
131C22×Q8C22⋊D711yescharacteristic
132C2×M16—41no—
133C2×M16—141no—
134C2×M16—281no—
135C4⋊Q8—41no—
136C4⋊Q8—141no—
137C4⋊Q8C4×D711yescharacteristic
138C4⋊Q8D2811yescharacteristic
139C4⋊Q8C22⋊D711yescharacteristic
140C4⋊Q8C22×D711yescharacteristic
141#125—72no—
142C22⋊Q8—281no—
143C4×Q8—281no—
144#117—141no—
145C2×C4⋊C4—41no—
146C2×C42C4×D711yescharacteristic
147#103—142no—
148#103—142no—
149#103—142no—
150#103—142no—
151#101—22no—
152#101—41no—
153#101—142no—
154#101—281no—
155#97—72no—
156C4×C8—141no—
157C22×C7—41no—
158C22×C7#35411yescharacteristic
159C22×C7#35411yescharacteristic
160C22×C7C2×#9911yescharacteristic
161C4×C7—22no—
162C4×C7—21no—
163C4×C7—21no—
164C4×C7—41no—
165C4×C7—41no—
166C4×C7—41no—
167C4×C7—41no—
168C4×C7—41no—
169Dic7—82no—
170C2×Q8—21no—
171C2×Q8—21no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—281no—
177C2×Q8(C2×D7)⋊C411yescharacteristic
178C2×Q8(C2×D7)⋊C411yescharacteristic
179C2×Q8C2×D2811yescharacteristic
180C2×Q8C2×C22⋊D711yescharacteristic
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4(C2×D7)⋊C411yescharacteristic
185M16—42no—
186M16—81no—
187M16—281no—
188M16—281no—
189M16—282no—
190M16—561no—
191C2×C8—81no—
192C2×C8—142no—
193C2×C8—561no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—142no—
199C4⋊C4—282no—
200C4⋊C4—281no—
201C22⋊C4—281no—
202C42—21no—
203C42—281no—
204C42(C2×D7)⋊C411yescharacteristic
205C42C2×C4×D711yescharacteristic
206C2×C7—21no—
207C2×C7—21no—
208C2×C7—21no—
209C2×C7C2×#35411yescharacteristic
210C23#638011yescharacteristic
211Q8—41no—
212Q8—41no—
213Q8—41no—
214Q8—41no—
215Q8—81no—
216Q8—81no—
217Q8—562no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—282no—
232C2×C4#638011yescharacteristic
233C2×C4C2×(C2×D7)⋊C411yescharacteristic
234C8—82no—
235C8—282no—
236C8—562no—
237C7#1359911yescharacteristic, complemented, Sylow
238C22—41no—
239C22#8926811yescharacteristic
240C22#8926811yescharacteristic
241C22C2×#638011yescharacteristic
242C4—22no—
243C4—21no—
244C4—21no—
245C4—41no—
246C4—41no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—562no—
251C2—21no—
252C2—21no—
253C2—21no—
254C2C2×#8926811yescharacteristic
subgroupG/H
centerC2C2×#89268
commutatorC42×C7C22×C4
FrattiniC4⋊Q8C22×D7
FittingC2×C7×#356C2
socleC2×C7C2×#354
prime radicalC23×C7#99
cosocleC7×C4⋊Q8C23
hypercenterC2×#356D7
hypocenterC7#13599
LCSG ▷ C42×C7 ▷ C2×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊Q8 ◁ C2×#356

Complements

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

NH ≅ G/Ntype
4. #11725357C2semidirect
237. C7#13599semidirect

Maximal subgroups

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

subgroupindex
#117406432
C2×C7×#3562
C2×#893432
#117253572
#135997