Finite Group Databasebeta

← #21459436

Subgroups — #21459436

Order 7808.

1094 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840488C211yesmaximal, characteristic, complemented
2#16840484C213yesmaximal, complemented
3#16840453C213yesmaximal, complemented
4#16840447C213yesmaximal, complemented
5Q8×C22⋊D61C211yesmaximal, characteristic, complemented
6#16840424C211yesmaximal, characteristic, complemented
7#16840423C211yesmaximal, characteristic, complemented
8#16840413C213yesmaximal, complemented
9#16840316C213yesmaximal, complemented
10#16840299C213yesmaximal, complemented
11#16840296C213yesmaximal, complemented
12C4×#11758226C211yesmaximal, characteristic, complemented
13C4×#11758222C213yesmaximal, complemented
14C4×Q8×D61C211yesmaximal, characteristic, complemented
15C2×C4×Q8×C61C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×#11758222C2213yes—
18C2×Q8×D61C2211yescharacteristic
19#14519776C2213yes—
20#14519775C2213yes—
21#14519772C2216yes—
22#14519771C2216yes—
23#14519769C2213yes—
24#14519768C2213yes—
25#14519767C2216yes—
26#14519766C2213yes—
27#14519765C2213yes—
28#14519762C2216yes—
29#14519760C2216yes—
30#14519757C2213yes—
31#14519756C2213yes—
32#14519755C2216yes—
33#14519753C2213yes—
34#14519753C2213yes—
35#14519752C2213yes—
36#14519751C2213yes—
37Q8×Dic61C2211yescharacteristic
38Q8×Dic61C2211yescharacteristic
39C4×Dic122C2213yes—
40C4×Dic122C2213yes—
41C4×Dic122C2213yes—
42#14519742C2213yes—
43C4×D244C2213yes—
44C4×D244C2213yes—
45C4×D244C2213yes—
46#14519739C2213yes—
47C4×C22⋊D61C2211yescharacteristic
48C4×C22⋊D61C2213yes—
49C4×C22⋊D61C2213yes—
50C4×C22⋊D61C2213yes—
51#14519736C2213yes—
52#14519735C2213yes—
53#14519734C2213yes—
54#14519734C2213yes—
55#14519734C2216yes—
56C4⋊C4×D61C2213yes—
57C42×D61C2213yes—
58C42×D61C2213yes—
59C22×Q8×C61C2211yescharacteristic
60C4×Q8×C61C2213yes—
61C4×Q8×C61C2211yescharacteristic
62C4×Q8×C61C2211yescharacteristic
63C4×Q8×C61C2213yes—
64C2×C4⋊C4×C61C2213yes—
65C2×C42×C61C2213yes—
66C2×Q8×C61—24no—
67C2×Q8×C61C2313yes—
68C2×Q8×C61C2311yescharacteristic
69C22×C4×C61C2313yes—
70C22×C4×C61C2311yescharacteristic
71C22×C4×C61C2313yes—
72C2×C22⋊D61C2313yes—
73C2×C22⋊D61C2311yescharacteristic
74#11758226—24no—
75Q8×D61—24no—
76#11758222—212no—
77C2×D244C2313yes—
78C2×D244C2313yes—
79C2×C4×D61C2313yes—
80C2×C4×D61C2313yes—
81C2×C4×D61C2313yes—
82C2×C4×D61C2313yes—
83C2×C4×D61C2311yescharacteristic
84C2×C4×D61C2313yes—
85C2×Dic122C2313yes—
86C2×Dic122C2313yes—
87C4⋊C4×C61C2313yes—
88C4⋊C4×C61C2313yes—
89C4⋊C4×C61C2316yes—
90C42×C61C2313yes—
91C42×C61C2313yes—
92C42×C61C2313yes—
93C42×C61C2313yes—
94C22⋊Dic61C2311yescharacteristic
95C22⋊Dic61C2313yes—
96#11758198C2311yescharacteristic
97#11758198C2313yes—
98#11758198C2313yes—
99#11758198C2313yes—
100#11758198C2316yes—
101#11758198C2316yes—
102#11758198C2316yes—
103C4⋊Dic61C2313yes—
104C4⋊Dic61C2313yes—
105C4⋊Dic61C2313yes—
106C4⋊Dic61C2313yes—
107#11758196C2316yes—
108#11758196C2311yescharacteristic
109#11758196C2313yes—
110#11758196C2313yes—
111#11758196C2313yes—
112#11758196C2316yes—
113#11758196C2316yes—
114C4×Dic61C2311yescharacteristic
115C4×Dic61C2313yes—
116C4×Dic61C2313yes—
117C4×Dic61C2313yes—
118C4×Dic61C2313yes—
119C4×Dic61C2313yes—
120C23×C61C2411yescharacteristic
121C22×D61C2413yes—
122C22×D61C2411yescharacteristic
123Q8×C61—26no—
124Q8×C61#4114yescomplemented
125C2×C4×C61—26no—
126C2×C4×C61—26no—
127C2×C4×C61—22no—
128C2×C4×C61C2413yes—
129C2×C4×C61C2411yescharacteristic
130C2×C4×C61C2413yes—
131C2×C4×C61C2413yes—
132C2×C4×C61C2413yes—
133C2×C4×C61C2411yescharacteristic
134C22⋊D61—26no—
135C22⋊D61#4114yescomplemented
136C2×Dic61C2411yescharacteristic
137C2×Dic61C2411yescharacteristic
138C2×Dic61C2413yes—
139C2×Dic61C2413yes—
140C2×Dic61C2413yes—
141C2×Dic61C2411yescharacteristic
142D244—26no—
143D244—26no—
144C4×D61—26no—
145C4×D61—26no—
146C4×D61—26no—
147C4×D61—22no—
148C4×D61—26no—
149C4×D61—26no—
150Dic122—26no—
151Dic122—26no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61C2×#4112yes—
155C22×C61C2511yescharacteristic
156C2×D61—21no—
157C2×D61—21no—
158C2×D61—23no—
159C2×D61—23no—
160C2×D61—23no—
161C2×D61C2×#4112yes—
162C4×C61—23no—
163C4×C61—23no—
164C4×C61—23no—
165C4×C61—21no—
166C4×C61C2×#4116yes—
167C4×C612−1+412yes—
168Dic61—23no—
169Dic61—23no—
170Dic61—21no—
171Dic61—21no—
172Dic61—23no—
173Dic61C2×#4112yes—
174#3482—611nomaximal, Sylow
175C2×C61—22no—
176C2×C61C22×#4111yescharacteristic
177C2×C61C22×#4111yescharacteristic
178C2×C61C2×2−1+411yescharacteristic
179D61—22no—
180D61—43no—
181#557—611no—
182#556—613no—
183#552—613no—
184#552—613no—
185D4×Q8—611no—
186#548—611no—
187#548—611no—
188#547—613no—
189#533—613no—
190#529—613no—
191#529—613no—
192C4×#41—611no—
193C4×#41—613no—
194C2×C4×Q8—611no—
195C2×C4×Q8D6111yescharacteristic, complemented
196C61#348211yescharacteristic, complemented, Sylow
197C2×#41—611no—
198C2×#41—613no—
199C22×Q8—611no—
200C22×Q8C2×D6111yescharacteristic
201C4⋊Q8—613no—
202C4⋊Q8—613no—
203#126—616no—
204#126—616no—
205#125—613no—
206#125—616no—
207#125—613no—
208#124—613no—
209#124—613no—
210#123—616no—
211#123—616no—
212C22⋊Q8—613no—
213C22⋊Q8—613no—
214C22⋊Q8—613no—
215C22⋊Q8—616no—
216C22⋊Q8—613no—
217#121—613no—
218#121—613no—
219C4×Q8—611no—
220C4×Q8—611no—
221C4×Q8—613no—
222C4×Q8—613no—
223C4×Q8—613no—
224C4×Q8—613no—
225C4×Q8C2×D6111yescharacteristic
226C4×Q8C2×D6113yes—
227C4×Q8C2×D6111yescharacteristic
228C4×Q8C2×D6113yes—
229C4×D4—611no—
230C4×D4—613no—
231C4×D4—613no—
232C4×D4—613no—
233C4×D4—613no—
234C4×D4—613no—
235C4×D4—613no—
236C4×D4—613no—
237#117—613no—
238#117—613no—
239#117—613no—
240#117—613no—
241#117—616no—
242C2×C4⋊C4—613no—
243C2×C4⋊C4C2×D6113yes—
244C2×C42—613no—
245C2×C42—613no—
246C2×C42C2×D6113yes—
247#41—12212no—
248#41—1224no—
249C2×Q8—24no—
250C2×Q8—613no—
251C2×Q8—613no—
252C2×Q8—1224no—
253C2×Q8C22×D6113yes—
254C2×Q8C22×D6111yescharacteristic
255C2×D4—611no—
256C2×D4—613no—
257C2×D4—613no—
258C2×D4—613no—
259C22×C4—613no—
260C22×C4—613no—
261C22×C4—613no—
262C22×C4—613no—
263C22×C4—611no—
264C22×C4—613no—
265C22×C4C22×D6113yes—
266C22×C4C22×D6113yes—
267C22×C4C22×D6111yescharacteristic
268C4⋊C4—616no—
269C4⋊C4—613no—
270C4⋊C4—611no—
271C4⋊C4—613no—
272C4⋊C4—613no—
273C4⋊C4—613no—
274C4⋊C4—616no—
275C4⋊C4—616no—
276C4⋊C4—613no—
277C4⋊C4—613no—
278C4⋊C4—613no—
279C4⋊C4C22×D6113yes—
280C4⋊C4C22×D6113yes—
281C4⋊C4C22×D6116yes—
282C22⋊C4—611no—
283C22⋊C4—613no—
284C22⋊C4—611no—
285C22⋊C4—613no—
286C22⋊C4—616no—
287C22⋊C4—613no—
288C22⋊C4—613no—
289C22⋊C4—616no—
290C22⋊C4—616no—
291C42—613no—
292C42—613no—
293C42—613no—
294C42—613no—
295C42—611no—
296C42—613no—
297C42C22×D6113yes—
298C42C22×D6113yes—
299C42C22×D6113yes—
300C42C22×D6113yes—
301C23—611no—
302C23—613no—
303C23C23×D6111yescharacteristic
304Q8—26no—
305Q8—1226no—
306Q8—1226no—
307Q8#1175822214yescomplemented
308D4—614no—
309D4—1226no—
310D4—1226no—
311D4—1226no—
312C2×C4—26no—
313C2×C4—26no—
314C2×C4—22no—
315C2×C4—611no—
316C2×C4—611no—
317C2×C4—611no—
318C2×C4—613no—
319C2×C4—613no—
320C2×C4—613no—
321C2×C4—1226no—
322C2×C4—1226no—
323C2×C4—1226no—
324C2×C4—1226no—
325C2×C4—1222no—
326C2×C4—1226no—
327C2×C4C23×D6113yes—
328C2×C4C23×D6111yescharacteristic
329C2×C4C23×D6113yes—
330C2×C4C23×D6113yes—
331C2×C4C23×D6113yes—
332C2×C4C23×D6111yescharacteristic
333C22—21no—
334C22—21no—
335C22—612no—
336C22—1221no—
337C22—1221no—
338C22—1223no—
339C22—1223no—
340C22—1223no—
341C22#41×D6112yes—
342C22C24×D6111yescharacteristic
343C4—23no—
344C4—23no—
345C4—23no—
346C4—21no—
347C4—612no—
348C4—1223no—
349C4—1221no—
350C4—1223no—
351C4—1221no—
352C4—1223no—
353C4C2×#1175822216yes—
354C4#1451982512yes—
355C2—22no—
356C2—1222no—
357C2—2443no—
358C2C2×#41×D6111yescharacteristic
359C2C22×#1175822211yescharacteristic
360C2C2×#1451982511yescharacteristic
subgroupG/H
centerC2×C4C23×D61
commutator, socleC22×C61C25
FrattiniC22C24×D61
FittingC2×C4×Q8×C61C2
hypercenterC2×C4×Q8D61
hypocenterC61#3482
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #16840488C2semidirect
2. #16840484C2semidirect
3. #16840453C2semidirect
4. #16840447C2semidirect
5. Q8×C22⋊D61C2semidirect
6. #16840424C2semidirect
7. #16840423C2semidirect
8. #16840413C2semidirect
9. #16840316C2semidirect
10. #16840299C2semidirect
11. #16840296C2semidirect
12. C4×#11758226C2semidirect
13. C4×#11758222C2semidirect
14. C4×Q8×D61C2semidirect
15. C2×C4×Q8×C61C2semidirect
124. Q8×C61#41semidirect
135. C22⋊D61#41semidirect
195. C2×C4×Q8D61semidirect
196. C61#3482semidirect
307. Q8#11758222semidirect