Finite Group Databasebeta

← #13264412

Subgroups — #13264412

Order 1792.

460 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 87 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#11739829C211yesmaximal, characteristic
2C4×C7×#99C211yesmaximal, characteristic
3#11729356C211yesmaximal, characteristic
4#11725296C214yesmaximal, complemented
5C2×C4×C7×D4C2211yescharacteristic
6C2×#6432C411yescharacteristic, complemented
7C2×C7×#99—21no—
8C4×C7×C22⋊C4—21no—
9#89993—21no—
10#89984—21no—
11#89984—21no—
12#89979—21no—
13#89749—21no—
14#89719C412yescomplemented
15#89719C2212yes—
16C4×C4⋊Dic7C411yescharacteristic, complemented
17C7×#342C2212yes—
18#89323—21no—
19#89320C2212yes—
20#11787—71nomaximal, Sylow
21C22×C7×D4D411yescharacteristic
22C23×C4×C7D411yescharacteristic
23C23×C4×C7D411yescharacteristic
24C22×Dic14C2×C412yes—
25C4×C7×D4—41no—
26C4×C7×D4—41no—
27C2×C7×C4⋊C4D411yescharacteristic
28C2×C7×C22⋊C4—22no—
29C2×C7×C22⋊C4C2×C411yescharacteristic
30C2×C7×C22⋊C4C2311yescharacteristic
31C2×C42×C7—41no—
32C2×C42×C7C2×C411yescharacteristic
33C2×C22⋊Dic7—22no—
34C2×C22⋊Dic7—22no—
35C2×C4⋊Dic7—21no—
36C2×C4⋊Dic7—21no—
37C2×C4⋊Dic7—21no—
38C2×C4×Dic7—21no—
39C2×#1136—41no—
40#6432—41no—
41#6432—41no—
42C7×#99—24no—
43C7×#95—41no—
44C7⋊#95—22no—
45C7⋊#95—22no—
46C7⋊#95C2×C412yes—
47C22⋊(C7⋊C8)—22no—
48C22⋊(C7⋊C8)—41no—
49#2563—71no—
50C4×#99D711yescharacteristic
51#1465—71no—
52#1351—74no—
53C24×C7C22⋊C411yescharacteristic
54C24×C7C2×D411yescharacteristic
55C2×C7×D4—22no—
56C2×C7×D4—22no—
57C2×C7×D4—41no—
58C22×C4×C7—21no—
59C22×C4×C7—21no—
60C22×C4×C7—21no—
61C22×C4×C7—21no—
62C22×C4×C7—42no—
63C22×C4×C7—42no—
64C22×C4×C7—42no—
65C22×C4×C7C22⋊C411yescharacteristic
66C22×C4×C7C22⋊C411yescharacteristic
67C22×C4×C7C22⋊C411yescharacteristic
68C22×C4×C7C22×C411yescharacteristic
69C22×C4×C7C2×D411yescharacteristic
70C22×Dic7—22no—
71C22×Dic7—22no—
72C2×Dic14—42no—
73C2×Dic14—82no—
74C7×C4⋊C4—41no—
75C7×C22⋊C4—24no—
76C7×C22⋊C4—41no—
77C7×C22⋊C4—41no—
78C7×C22⋊C4—42no—
79C42×C7—21no—
80C42×C7—21no—
81C42×C7—82no—
82C22⋊Dic7—82no—
83C22⋊Dic7—82no—
84C4⋊Dic7—42no—
85C4⋊Dic7—42no—
86C4⋊Dic7—41no—
87C4⋊Dic7—41no—
88C4×Dic7—42no—
89#1136—82no—
90C2×C7⋊C8—42no—
91C2×C4⋊Q8—71no—
92C2×C4×D4C2×D711yescharacteristic
93C2×#99—21no—
94#407—141no—
95#393—72no—
96#393—72no—
97#390—141no—
98#382—141no—
99#380—141no—
100#380—141no—
101C4×C4⋊C4—71no—
102C4×C22⋊C4—21no—
103#342C2×D712yes—
104#324—141no—
105#323—72no—
106C23×C7—21no—
107C23×C7—21no—
108C23×C7—21no—
109C23×C7—21no—
110C23×C7—21no—
111C23×C7—41no—
112C23×C7—41no—
113C23×C7—41no—
114C23×C7—41no—
115C23×C7C2×C22⋊C411yescharacteristic
116C23×C7#13712yes—
117C7×D4—44no—
118C2×C4×C7—21no—
119C2×C4×C7—21no—
120C2×C4×C7—22no—
121C2×C4×C7—21no—
122C2×C4×C7—21no—
123C2×C4×C7—21no—
124C2×C4×C7—42no—
125C2×C4×C7—42no—
126C2×C4×C7—41no—
127C2×C4×C7—41no—
128C2×C4×C7—41no—
129C2×C4×C7—44no—
130C2×C4×C7—81no—
131C2×C4×C7—81no—
132C2×C4×C7—82no—
133C2×C4×C7—82no—
134C2×C4×C7#9911yescharacteristic
135C2×C4×C7#9911yescharacteristic
136C2×C4×C7#10412yes—
137C2×Dic7—42no—
138C2×Dic7—42no—
139C2×Dic7—42no—
140C2×Dic7—42no—
141C2×Dic7—42no—
142C2×Dic7—42no—
143Dic14—84no—
144C7⋊C8—82no—
145C22×Q8—72no—
146C22×D4C22⋊D711yescharacteristic
147C23×C4D2811yescharacteristic
148C23×C4C22⋊D711yescharacteristic
149C2×M16—281no—
150C4⋊Q8—281no—
151C4⋊Q8—281no—
152C4×D4—41no—
153C4×D4—41no—
154C2×C4⋊C4—141no—
155C2×C4⋊C4—141no—
156C2×C4⋊C4—141no—
157C2×C4⋊C4D2811yescharacteristic
158C2×C22⋊C4—22no—
159C2×C22⋊C4—142no—
160C2×C22⋊C4—142no—
161C2×C22⋊C4C4×D711yescharacteristic
162C2×C22⋊C4C22×D711yescharacteristic
163C2×C42—41no—
164C2×C42—141no—
165C2×C42C4×D711yescharacteristic
166#99—24no—
167C22⋊C8—142no—
168C22⋊C8—281no—
169#95—41no—
170#95—72no—
171#95—142no—
172#95—142no—
173C22×C7—21no—
174C22×C7—21no—
175C22×C7—22no—
176C22×C7—42no—
177C22×C7—42no—
178C22×C7—41no—
179C22×C7—41no—
180C22×C7—41no—
181C22×C7—41no—
182C22×C7—41no—
183C22×C7—81no—
184C22×C7—81no—
185C22×C7C2×#9911yescharacteristic
186C22×C7#41911yescharacteristic
187C22×C7C2×#10411yescharacteristic
188C4×C7—21no—
189C4×C7—22no—
190C4×C7—41no—
191C4×C7—41no—
192C4×C7—41no—
193C4×C7—84no—
194C4×C7#35412yes—
195Dic7—82no—
196Dic7—82no—
197C24(C2×D7)⋊C411yescharacteristic
198C24C2×C22⋊D711yescharacteristic
199C2×Q8—282no—
200C2×Q8—562no—
201C2×D4—22no—
202C2×D4—22no—
203C2×D4—41no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—142no—
212C22×C4—142no—
213C22×C4(C2×D7)⋊C411yescharacteristic
214C22×C4(C2×D7)⋊C411yescharacteristic
215C22×C4(C2×D7)⋊C411yescharacteristic
216C22×C4C2×C4×D711yescharacteristic
217C22×C4C2×D2811yescharacteristic
218M16—562no—
219C2×C8—282no—
220C4⋊C4—41no—
221C4⋊C4—282no—
222C4⋊C4—282no—
223C4⋊C4—281no—
224C4⋊C4—281no—
225C22⋊C4—24no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C22⋊C4—42no—
229C22⋊C4—562no—
230C22⋊C4—562no—
231C42—21no—
232C42—21no—
233C42—82no—
234C42—282no—
235C2×C7—21no—
236C2×C7—21no—
237C2×C7—42no—
238C2×C7—81no—
239C2×C7#150811yescharacteristic
240C2×C7#212211yescharacteristic
241C2×C7C2×#35411yescharacteristic
242C23—21no—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—41no—
248C23—41no—
249C23—41no—
250C23—41no—
251C23C2×(C2×D7)⋊C411yescharacteristic
252C23#651412yes—
253Q8—564no—
254D4—44no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—44no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—82no—
270C2×C4—82no—
271C2×C4—282no—
272C2×C4—282no—
273C2×C4—282no—
274C2×C4—282no—
275C2×C4—282no—
276C2×C4—282no—
277C2×C4#637912yes—
278C2×C4#638011yescharacteristic
279C2×C4#638011yescharacteristic
280C8—562no—
281C7#1178711yescharacteristic, complemented, Sylow
282C22—21no—
283C22—21no—
284C22—22no—
285C22—42no—
286C22—42no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—81no—
293C22—81no—
294C22C2×#637911yescharacteristic
295C22C2×#638011yescharacteristic
296C22#8977611yescharacteristic
297C4—22no—
298C4—21no—
299C4—41no—
300C4—41no—
301C4—41no—
302C4—84no—
303C4—562no—
304C4—562no—
305C4#8926812yes—
306C2—21no—
307C2—21no—
308C2—42no—
309C2—81no—
310C2#1172719911yescharacteristic
311C2C2×#8926811yescharacteristic
312C2#1172781111yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C22⋊C4C22×D7
FittingC4×C7×#99C2
socleC22×C7C2×#99
prime radicalC22×C7×D4D4
cosocleC2×C7×C22⋊C4C23
hypercenterC4×#99D7
hypocenterC7#11787
LCSG ▷ C22×C4×C7 ▷ C23×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
4. #11725296C2semidirect
6. C2×#6432C4semidirect
14. #89719C4semidirect
16. C4×C4⋊Dic7C4semidirect
281. C7#11787semidirect

Maximal subgroups

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

subgroupindex
#117398292
C4×C7×#992
#117293562
#117252962
#117877