Finite Group Databasebeta

← #21461000

Subgroups — #21461000

Order 7808.

828 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 828 conjugacy classes of subgroups — too many to draw. Only its 164 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
1C22×C22⋊#6923C212yesmaximal
2C22×C4×#6923C211yesmaximal, characteristic, complemented
3C2×(C2×#6923)⋊C4C212yesmaximal, complemented
4C2×(C2×#6923)⋊C4C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D61C211yesmaximal, characteristic
6C23×#6923C2212yes—
7C23×#6923C2212yes—
8C2×C22⋊#6923—24no—
9C2×C22⋊#6923—24no—
10C2×C22⋊#6923C418yescomplemented
11C2×C4×#6923—24no—
12C2×C4×#6923—22no—
13(C2×#6923)⋊C4—24no—
14(C2×#6923)⋊C4—22no—
15C24×D61C2211yescharacteristic
16C22×C4×D61C2211yescharacteristic
17C22×C4×D61C2211yescharacteristic
18C2×C22⋊Dic61C411yescharacteristic, complemented
19C2×#11758198C411yescharacteristic, complemented
20C2×#11758198C411yescharacteristic, complemented
21C22⋊C4×D61—22no—
22C22⋊C4×D61—22no—
23C2×C22⋊C4×C61C411yescharacteristic, complemented
24C24×C61C2×C411yescharacteristic
25C23×D61—22no—
26C23×D61—22no—
27C23×D61—21no—
28C23×D61—21no—
29C23×D61—22no—
30C23×D61—22no—
31C23×D61—22no—
32C23×D61C2×C411yescharacteristic
33C23×D61C2×C414yes—
34C23×D61C2311yescharacteristic
35C22×#6923—22no—
36C22×#6923—22no—
37C22×#6923—22no—
38C22×#6923—22no—
39C22×#6923—22no—
40C22×#6923—22no—
41C22×#6923—22no—
42C22×#6923—22no—
43C22×#6923—22no—
44C22×#6923—22no—
45C22×#6923C2×C414yes—
46C22×#6923C2×C414yes—
47C22×#6923D414yes—
48C22×#6923D414yes—
49C22×C4×C61C2×C411yescharacteristic
50C22×C4×C61C2×C411yescharacteristic
51C22×Dic61C2×C411yescharacteristic
52C22×Dic61C2×C411yescharacteristic
53C2×C4×D61—22no—
54C2×C4×D61—22no—
55C2×C4×D61—22no—
56C2×C4×D61—21no—
57C2×C4×D61—21no—
58C2×C4×D61—22no—
59C2×C4×D61D412yes—
60C2×C4×D61D412yes—
61C22⋊#6923—216no—
62C4×#6923—28no—
63C22⋊C4×C61—22no—
64C22⋊Dic61—22no—
65#11758198—22no—
66#11758198—22no—
67C23×C61—21no—
68C23×C61—21no—
69C23×C61—22no—
70C23×C61—22no—
71C23×C61C4212yescomplemented
72C23×C61C22×C411yescharacteristic
73C22×D61—21no—
74C22×D61—21no—
75C22×D61—22no—
76C22×D61—22no—
77C22×D61—24no—
78C22×D61—24no—
79C22×D61—24no—
80C22×D61—24no—
81C22×D61—24no—
82C22×D61—24no—
83C22×D61—41no—
84C22×D61—42no—
85C22×D61—42no—
86C22×D61—42no—
87C22×D61—41no—
88C22×D61—42no—
89C22×D61—42no—
90C22×D61—41no—
91C22×D61—42no—
92C22×D61—41no—
93C22×D61C4212yescomplemented
94C22×D61C22×C412yes—
95C22×D61C2×D412yes—
96C22×D61C2×D412yes—
97C22×D61C2×D411yescharacteristic
98C22×D61C2×D411yescharacteristic
99C22×D61#4112yes—
100C22×D61#4112yes—
101C22×D61#4112yes—
102C2×#6923—24no—
103C2×#6923—24no—
104C2×#6923—24no—
105C2×#6923—24no—
106C2×#6923—24no—
107C2×#6923—24no—
108C2×#6923—24no—
109C2×#6923—24no—
110C2×#6923—24no—
111C2×#6923—42no—
112C2×#6923—42no—
113C2×#6923—42no—
114C2×#6923—42no—
115C2×#6923C22⋊C418yescomplemented
116C2×C4×C61—22no—
117C2×C4×C61—21no—
118C2×C4×C61—22no—
119C2×C4×C61C22⋊C412yescomplemented
120C2×Dic61—22no—
121C2×Dic61—21no—
122C2×Dic61—22no—
123C2×Dic61C22⋊C412yescomplemented
124C4×D61—22no—
125C4×D61—24no—
126C4×D61—22no—
127C4×D61—42no—
128C4×D61—41no—
129C4×D61—41no—
130C22×C61—22no—
131C22×C61—24no—
132C22×C61—41no—
133C22×C61—42no—
134C22×C61—41no—
135C22×C61C2×C4211yescharacteristic
136C22×C61C2×C22⋊C411yescharacteristic
137C22×C61#11711yescharacteristic
138C22×C61C4×D412yes—
139C22×C61C4×D412yes—
140C2×D61—22no—
141C2×D61—24no—
142C2×D61—41no—
143C2×D61—42no—
144C2×D61—41no—
145C2×D61—44no—
146C2×D61—44no—
147C2×D61—44no—
148C2×D61—44no—
149C2×D61C2×C22⋊C412yes—
150C2×D61#11712yes—
151C2×D61C4×D412yes—
152C2×D61C4×D412yes—
153C2×D61C4×D412yes—
154C2×D61C4×D412yes—
155C2×D61#12011yescharacteristic
156C2×D61#12112yes—
157C2×D61#12112yes—
158C2×D61#12112yes—
159C2×D61#12312yes—
160C2×D61#12311yescharacteristic
161C2×D61#12411yescharacteristic
162C2×D61#12412yes—
163C2×D61#12612yes—
164C2×D61#12711yescharacteristic
165#6923—28no—
166#6923—44no—
167C4×C61—22no—
168C4×C61—41no—
169Dic61—22no—
170Dic61—41no—
171#1437—611nomaximal, Sylow
172C2×C61—42no—
173C2×C61C4×C22⋊C411yescharacteristic
174C2×C61C4×C22⋊C412yes—
175C2×C61#38611yescharacteristic
176C2×C61#38812yes—
177C2×C61#39011yescharacteristic
178D61—42no—
179D61#38612yes—
180D61#38812yes—
181D61#38812yes—
182D61#39012yes—
183C22×C22⋊C4—612no—
184C22×C22⋊C4—611no—
185C22×C42—611no—
186C2×#95—612no—
187C2×#95—611no—
188C61#143711yescharacteristic, complemented, Sylow
189C25—611no—
190C23×C4—612no—
191C23×C4—611no—
192C23×C4—612no—
193C23×C4—611no—
194C2×C22⋊C4—618no—
195C2×C22⋊C4—611no—
196C2×C22⋊C4—611no—
197C2×C22⋊C4—611no—
198C2×C22⋊C4—1222no—
199C2×C22⋊C4—1222no—
200C2×C22⋊C4—1224no—
201C2×C22⋊C4—1224no—
202C2×C22⋊C4#692311yescharacteristic, complemented
203C2×C42—1224no—
204C2×C42—1222no—
205#95—1224no—
206#95—1222no—
207C24—611no—
208C24—614no—
209C24—611no—
210C24—1221no—
211C24—1221no—
212C24—1222no—
213C24—1222no—
214C24—1222no—
215C24—1222no—
216C24—1222no—
217C24C2×#692311yescharacteristic
218C22×C4—614no—
219C22×C4—614no—
220C22×C4—614no—
221C22×C4—611no—
222C22×C4—612no—
223C22×C4—612no—
224C22×C4—614no—
225C22×C4—611no—
226C22×C4—1222no—
227C22×C4—1222no—
228C22×C4—1222no—
229C22×C4—1221no—
230C22×C4—1221no—
231C22×C4—1222no—
232C22×C4—1222no—
233C22×C4—1222no—
234C22×C4—1222no—
235C22×C4—1222no—
236C22×C4—1222no—
237C22×C4—1222no—
238C22×C4—1222no—
239C22×C4—1222no—
240C22×C4—1222no—
241C22×C4—1222no—
242C22×C4C2×#692311yescharacteristic
243C22×C4C2×#692311yescharacteristic
244C22⋊C4—22no—
245C22⋊C4—1222no—
246C22⋊C4—1222no—
247C22⋊C4—12216no—
248C22⋊C4—1222no—
249C42—1228no—
250C23—21no—
251C23—21no—
252C23—22no—
253C23—22no—
254C23—612no—
255C23—611no—
256C23—611no—
257C23—612no—
258C23—612no—
259C23—612no—
260C23—612no—
261C23—612no—
262C23—612no—
263C23—1224no—
264C23—1224no—
265C23—1224no—
266C23—1224no—
267C23—1224no—
268C23—1224no—
269C23—1221no—
270C23—1221no—
271C23—1222no—
272C23—1222no—
273C23—2441no—
274C23—2442no—
275C23—2441no—
276C23—2442no—
277C23—2442no—
278C23—2442no—
279C23—2442no—
280C23—2442no—
281C23—2441no—
282C23—2441no—
283C23C4×#692312yescomplemented
284C23C22×#692311yescharacteristic
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—618no—
289C2×C4—612no—
290C2×C4—1222no—
291C2×C4—1224no—
292C2×C4—1222no—
293C2×C4—1224no—
294C2×C4—1224no—
295C2×C4—1224no—
296C2×C4—1224no—
297C2×C4—1224no—
298C2×C4—1224no—
299C2×C4—1222no—
300C2×C4—1224no—
301C2×C4—1224no—
302C2×C4—1224no—
303C2×C4—1221no—
304C2×C4—1222no—
305C2×C4—2442no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2442no—
309C2×C4—2442no—
310C2×C4—2442no—
311C2×C4—2442no—
312C2×C4C22⋊#692312yescomplemented
313C22—22no—
314C22—24no—
315C22—41no—
316C22—42no—
317C22—41no—
318C22—611no—
319C22—612no—
320C22—611no—
321C22—612no—
322C22—612no—
323C22—612no—
324C22—612no—
325C22—612no—
326C22—611no—
327C22—611no—
328C22—612no—
329C22—612no—
330C22—612no—
331C22—612no—
332C22—612no—
333C22—612no—
334C22—1222no—
335C22—1224no—
336C22—2444no—
337C22—2444no—
338C22—2444no—
339C22—2444no—
340C22—2441no—
341C22—2442no—
342C22—2441no—
343C22C2×C4×#692311yescharacteristic
344C22C2×C22⋊#692311yescharacteristic
345C22#1451985611yescharacteristic
346C22D4×#692312yes—
347C22D4×#692312yes—
348C4—22no—
349C4—41no—
350C4—1228no—
351C4—1222no—
352C4—2444no—
353C4—2441no—
354C2—42no—
355C2—612no—
356C2—612no—
357C2—612no—
358C2—612no—
359C2—2442no—
360C2C4×C22⋊#692311yescharacteristic
361C2C22⋊C4×#692312yes—
362C2#1684071011yescharacteristic
363C2#1684071212yes—
364C2#1684071411yescharacteristic
subgroupG/H
center, FrattiniC23C22×#6923
commutatorC22×C61C2×C42
FittingC2×C22⋊C4×C61C4
socleC23×C61C22×C4
hypercenterC2×C22⋊C4#6923
hypocenterC61#1437
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×#6923C2semidirect
3. C2×(C2×#6923)⋊C4C2semidirect
4. C2×(C2×#6923)⋊C4C2semidirect
10. C2×C22⋊#6923C4semidirect
18. C2×C22⋊Dic61C4semidirect
19. C2×#11758198C4semidirect
20. C2×#11758198C4semidirect
23. C2×C22⋊C4×C61C4semidirect
71. C23×C61C42semidirect
93. C22×D61C42semidirect
115. C2×#6923C22⋊C4semidirect
119. C2×C4×C61C22⋊C4semidirect
123. C2×Dic61C22⋊C4semidirect
188. C61#1437semidirect
202. C2×C22⋊C4#6923semidirect
283. C23C4×#6923semidirect
312. C2×C4C22⋊#6923semidirect