Finite Group Databasebeta

← #21461002

Subgroups — #21461002

Order 7808.

780 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 140 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×C4⋊#6923C211yesmaximal, characteristic, complemented
2C22×C22⋊#6923C212yesmaximal
3C2×(C2×#6923)⋊C4C212yesmaximal, complemented
4C2×(C2×#6923)⋊C4C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D61C211yesmaximal, characteristic
6C23×#6923C2212yes—
7C23×#6923C2212yes—
8C2×C4⋊#6923—24no—
9C2×C4⋊#6923—22no—
10C2×C22⋊#6923—24no—
11C2×C22⋊#6923—24no—
12C2×C22⋊#6923—24no—
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—21no—
30C23×D61—21no—
31C23×D61—22no—
32C23×D61—22no—
33C23×D61C2×C411yescharacteristic
34C23×D61D412yes—
35C23×D61Q812yes—
36C23×D61C2311yescharacteristic
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×#6923—22no—
46C22×#6923—22no—
47C22×#6923—22no—
48C22×#6923—22no—
49C22×#6923D414yes—
50C22×#6923D414yes—
51C22×C4×C61C2×C411yescharacteristic
52C22×C4×C61C2×C411yescharacteristic
53C22×Dic61C2×C411yescharacteristic
54C22×Dic61C2×C411yescharacteristic
55C2×C4×D61—22no—
56C2×C4×D61—22no—
57C2×C4×D61—22no—
58C2×C4×D61—21no—
59C2×C4×D61—21no—
60C2×C4×D61—22no—
61C2×C4×D61D412yes—
62C2×C4×D61D412yes—
63C22⋊#6923—216no—
64C4⋊#6923—28no—
65C22⋊C4×C61—22no—
66C22⋊Dic61—22no—
67#11758198—22no—
68#11758198—22no—
69C23×C61—21no—
70C23×C61—21no—
71C23×C61—22no—
72C23×C61—22no—
73C23×C61C4⋊C412yescomplemented
74C23×C61C22×C411yescharacteristic
75C22×D61—21no—
76C22×D61—21no—
77C22×D61—22no—
78C22×D61—22no—
79C22×D61—24no—
80C22×D61—22no—
81C22×D61—22no—
82C22×D61—22no—
83C22×D61—22no—
84C22×D61—24no—
85C22×D61—24no—
86C22×D61—24no—
87C22×D61—41no—
88C22×D61—42no—
89C22×D61—42no—
90C22×D61—42no—
91C22×D61—41no—
92C22×D61—42no—
93C22×D61—42no—
94C22×D61—41no—
95C22×D61—42no—
96C22×D61—41no—
97C22×D61C4⋊C412yescomplemented
98C22×D61C2×D412yes—
99C22×D61C2×D411yescharacteristic
100C22×D61C2×D412yes—
101C22×D61C2×D411yescharacteristic
102C22×D61C2×D411yescharacteristic
103C22×D61C2×Q811yescharacteristic
104C22×D61#4111yescharacteristic
105C22×D61#4112yes—
106C22×D61#4111yescharacteristic
107C22×D61#4112yes—
108C2×#6923—24no—
109C2×#6923—24no—
110C2×#6923—24no—
111C2×#6923—24no—
112C2×#6923—24no—
113C2×#6923—24no—
114C2×#6923—42no—
115C2×#6923—42no—
116C2×#6923—42no—
117C2×#6923—42no—
118C2×#6923—42no—
119C2×#6923—42no—
120C2×#6923—42no—
121C2×#6923—42no—
122C2×C4×C61—22no—
123C2×C4×C61—21no—
124C2×C4×C61—22no—
125C2×C4×C61C22⋊C412yescomplemented
126C2×Dic61—22no—
127C2×Dic61—21no—
128C2×Dic61—22no—
129C2×Dic61C22⋊C412yescomplemented
130C4×D61—22no—
131C4×D61—24no—
132C4×D61—22no—
133C4×D61—42no—
134C4×D61—41no—
135C4×D61—41no—
136C22×C61—22no—
137C22×C61—24no—
138C22×C61—41no—
139C22×C61—42no—
140C22×C61—41no—
141C22×C61C2×C22⋊C411yescharacteristic
142C22×C61C2×C4⋊C411yescharacteristic
143C22×C61#11711yescharacteristic
144C22×C61C4×D412yes—
145C22×C61C4×D412yes—
146C2×D61—22no—
147C2×D61—24no—
148C2×D61—41no—
149C2×D61—42no—
150C2×D61—41no—
151C2×D61—42no—
152C2×D61—42no—
153C2×D61—44no—
154C2×D61—44no—
155C2×D61—42no—
156C2×D61—42no—
157C2×D61#12011yescharacteristic
158C2×D61#12012yes—
159C2×D61#12112yes—
160C2×D61#12111yescharacteristic
161C2×D61#12111yescharacteristic
162C2×D61#12112yes—
163C2×D61#12112yes—
164C2×D61C22⋊Q812yes—
165C2×D61C22⋊Q811yescharacteristic
166C2×D61C22⋊Q811yescharacteristic
167C2×D61C22⋊Q812yes—
168C2×D61#12312yes—
169C2×D61#12312yes—
170C2×D61#12311yescharacteristic
171C2×D61#12412yes—
172C2×D61#12411yescharacteristic
173C2×D61#12612yes—
174C2×D61#12711yescharacteristic
175#6923—44no—
176#6923—44no—
177C4×C61—22no—
178C4×C61—41no—
179Dic61—22no—
180Dic61—41no—
181#1439—611nomaximal, Sylow
182C2×C61—42no—
183C2×C61#38011yescharacteristic
184C2×C61#38512yes—
185C2×C61#38611yescharacteristic
186C2×C61#38812yes—
187C2×C61#39011yescharacteristic
188D61—42no—
189D61#39211yescharacteristic
190D61#39311yescharacteristic
191D61#39412yes—
192D61#39612yes—
193D61#39711yescharacteristic
194D61#39911yescharacteristic
195C22×C4⋊C4—611no—
196C22×C22⋊C4—611no—
197C22×C22⋊C4—612no—
198C2×#95—611no—
199C2×#95—612no—
200C61#143911yescharacteristic, complemented, Sylow
201C25—611no—
202C23×C4—611no—
203C23×C4—612no—
204C23×C4—612no—
205C23×C4—611no—
206C2×C4⋊C4—1222no—
207C2×C4⋊C4—1224no—
208C2×C22⋊C4—611no—
209C2×C22⋊C4—611no—
210C2×C22⋊C4—611no—
211C2×C22⋊C4—1222no—
212C2×C22⋊C4—1222no—
213C2×C22⋊C4—1224no—
214C2×C22⋊C4—1224no—
215C2×C22⋊C4—1224no—
216C2×C22⋊C4#692311yescharacteristic, complemented
217#95—1222no—
218#95—1224no—
219C24—611no—
220C24—612no—
221C24—612no—
222C24—611no—
223C24—1221no—
224C24—1221no—
225C24—1222no—
226C24—1222no—
227C24—1221no—
228C24—1221no—
229C24—1222no—
230C24—1222no—
231C24C2×#692311yescharacteristic
232C22×C4—611no—
233C22×C4—612no—
234C22×C4—612no—
235C22×C4—614no—
236C22×C4—614no—
237C22×C4—611no—
238C22×C4—1222no—
239C22×C4—1222no—
240C22×C4—1222no—
241C22×C4—1221no—
242C22×C4—1221no—
243C22×C4—1222no—
244C22×C4—1222no—
245C22×C4—1222no—
246C22×C4—1222no—
247C22×C4—1222no—
248C22×C4—1222no—
249C22×C4—1222no—
250C22×C4—1222no—
251C22×C4—1222no—
252C22×C4—1222no—
253C22×C4—1222no—
254C22×C4—1222no—
255C22×C4—1222no—
256C22×C4C2×#692311yescharacteristic
257C22×C4C2×#692311yescharacteristic
258C4⋊C4—1228no—
259C22⋊C4—22no—
260C22⋊C4—1222no—
261C22⋊C4—1222no—
262C22⋊C4—12216no—
263C22⋊C4—1222no—
264C23—21no—
265C23—21no—
266C23—22no—
267C23—22no—
268C23—611no—
269C23—611no—
270C23—611no—
271C23—611no—
272C23—611no—
273C23—611no—
274C23—612no—
275C23—612no—
276C23—612no—
277C23—612no—
278C23—612no—
279C23—1224no—
280C23—1222no—
281C23—1222no—
282C23—1222no—
283C23—1222no—
284C23—1224no—
285C23—1224no—
286C23—1224no—
287C23—1221no—
288C23—1221no—
289C23—1222no—
290C23—1222no—
291C23—2441no—
292C23—2442no—
293C23—2441no—
294C23—2442no—
295C23—2442no—
296C23—2442no—
297C23—2442no—
298C23—2442no—
299C23—2441no—
300C23—2441no—
301C23C4⋊#692312yescomplemented
302C23C22×#692311yescharacteristic
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—612no—
307C2×C4—1222no—
308C2×C4—1224no—
309C2×C4—1222no—
310C2×C4—1222no—
311C2×C4—1224no—
312C2×C4—1224no—
313C2×C4—1224no—
314C2×C4—1224no—
315C2×C4—1224no—
316C2×C4—1224no—
317C2×C4—1221no—
318C2×C4—1222no—
319C2×C4—2442no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2442no—
323C2×C4—2442no—
324C2×C4—2442no—
325C2×C4—2442no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4—2442no—
329C2×C4—2442no—
330C2×C4C22⋊#692312yescomplemented
331C22—22no—
332C22—24no—
333C22—41no—
334C22—42no—
335C22—41no—
336C22—611no—
337C22—611no—
338C22—611no—
339C22—611no—
340C22—612no—
341C22—612no—
342C22—612no—
343C22—612no—
344C22—611no—
345C22—612no—
346C22—611no—
347C22—612no—
348C22—612no—
349C22—612no—
350C22—612no—
351C22—612no—
352C22—611no—
353C22—611no—
354C22—1222no—
355C22—1224no—
356C22—2442no—
357C22—2444no—
358C22—2442no—
359C22—2444no—
360C22—2442no—
361C22—2442no—
362C22—2441no—
363C22—2442no—
364C22—2441no—
365C22C2×C22⋊#692311yescharacteristic
366C22C2×C4⋊#692311yescharacteristic
367C22#1451985611yescharacteristic
368C22D4×#692312yes—
369C22D4×#692312yes—
370C4—22no—
371C4—41no—
372C4—1222no—
373C4—2444no—
374C4—2444no—
375C4—2441no—
376C2—42no—
377C2—611no—
378C2—612no—
379C2—611no—
380C2—612no—
381C2—611no—
382C2—611no—
383C2—2442no—
384C2#1684070411yescharacteristic
385C2#1684070912yes—
386C2#1684071011yescharacteristic
387C2#1684071212yes—
388C2#1684071411yescharacteristic
subgroupG/H
center, FrattiniC23C22×#6923
commutator, socleC23×C61C22×C4
FittingC2×C22⋊C4×C61C4
hypercenterC2×C22⋊C4#6923
hypocenterC61#1439
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊#6923C2semidirect
3. C2×(C2×#6923)⋊C4C2semidirect
4. C2×(C2×#6923)⋊C4C2semidirect
18. C2×C22⋊Dic61C4semidirect
19. C2×#11758198C4semidirect
20. C2×#11758198C4semidirect
23. C2×C22⋊C4×C61C4semidirect
73. C23×C61C4⋊C4semidirect
97. C22×D61C4⋊C4semidirect
125. C2×C4×C61C22⋊C4semidirect
129. C2×Dic61C22⋊C4semidirect
200. C61#1439semidirect
216. C2×C22⋊C4#6923semidirect
301. C23C4⋊#6923semidirect
330. C2×C4C22⋊#6923semidirect