Finite Group Databasebeta

← #21448821

Subgroups — #21448821

Order 7808.

620 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519755C211yesmaximal, characteristic
2C2×#14519742C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×D61C211yesmaximal, characteristic
4#16839666C211yesmaximal, characteristic, complemented
5#16839659C211yesmaximal, characteristic, complemented
6#16839657C211yesmaximal, characteristic, complemented
7#16839648C211yesmaximal, characteristic, complemented
8#16839643C211yesmaximal, characteristic, complemented
9#16839633C211yesmaximal, characteristic
10#16839633C211yesmaximal, characteristic
11C4×#11758196C211yesmaximal, characteristic, complemented
12C4×#11758198C211yesmaximal, characteristic
13#16839609C211yesmaximal, characteristic
14#16839609C211yesmaximal, characteristic
15C61×#389C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic
17C22×C4×D61C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic
19C22×C4×D61C2211yescharacteristic
20#14519755C418yescomplemented
21#14519742—24no—
22C2×C4⋊Dic61C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×#11758196C2211yescharacteristic
29C4⋊C4×D61—24no—
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×C4×Dic61C2211yescharacteristic
35C2×C4×Dic61C2211yescharacteristic
36C2×C4×Dic61C2211yescharacteristic
37C2×C4×Dic61C2211yescharacteristic
38C2×C4×Dic61C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47C2×C4⋊C4×C61C2211yescharacteristic
48C2×C4⋊C4×C61C2211yescharacteristic
49C2×C4⋊C4×C61C2211yescharacteristic
50C2×C4⋊C4×C61C2211yescharacteristic
51C2×C42×C61C2211yescharacteristic
52#95×C61C2211yescharacteristic
53#95×C61C2211yescharacteristic
54C23×D61C2311yescharacteristic
55C22×C4×C61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C22×Dic61C2311yescharacteristic
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C22×Dic61C2311yescharacteristic
69C2×C4×D61—22no—
70C2×C4×D61—22no—
71C2×C4×D61—22no—
72C2×C4×D61—22no—
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—41no—
76C2×C4×D61—41no—
77C2×C4×D61C2×C414yes—
78C2×Dic122—22no—
79C2×Dic122—22no—
80C2×Dic122C2×C414yescomplemented
81C4⋊C4×C61—22no—
82C4⋊C4×C61—22no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61C2×C414yescomplemented
85C42×C61—41no—
86#11758198—22no—
87#11758198C2×C414yes—
88#11758198C2×C414yes—
89#11758198Q814yescomplemented
90C4⋊Dic61—22no—
91#11758196—22no—
92#11758196—22no—
93#11758196—41no—
94#11758196C2×C414yescomplemented
95#11758196C2×C414yescomplemented
96#11758196D414yes—
97C4×Dic61—22no—
98C4×Dic61—22no—
99C4×Dic61—22no—
100C4×Dic61—22no—
101C4×Dic61—41no—
102C23×C61C2411yescharacteristic
103C22×D61—21no—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—21no—
107C22×D61C22×C412yes—
108C22×D61C2×Q812yes—
109C22×D61#4112yes—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61C22×C412yes—
127C2×C4×C61C22×C412yes—
128C2×C4×C61C22×C412yes—
129C2×C4×C61C2×D412yes—
130C2×C4×C61C2×Q812yes—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61C22×C412yes—
146C2×Dic61C22×C412yes—
147C2×Dic61C22×C412yes—
148C2×Dic61C2×D412yes—
149C2×Dic61C2×D412yes—
150C2×Dic61C2×Q812yes—
151C2×Dic61#4112yes—
152C4×D61—28no—
153C4×D61—44no—
154C4×D61—44no—
155Dic122—28no—
156C22×C61C23×C411yescharacteristic
157C22×C61C22×D411yescharacteristic
158C22×C61C22×Q811yescharacteristic
159C22×C61C2×#4111yescharacteristic
160C22×C61C2×#4111yescharacteristic
161C22×C61H(5,𝔽2)11yescharacteristic
162C22×C612−1+411yescharacteristic
163C2×D61—22no—
164C2×D61—22no—
165C2×D61—22no—
166C2×D61—22no—
167C2×D61—22no—
168C2×D61—22no—
169C2×D61C4×Q814yescomplemented
170C4×C61—22no—
171C4×C61—22no—
172C4×C61—22no—
173C4×C61—22no—
174C4×C61—22no—
175C4×C61—41no—
176C4×C61—41no—
177Dic61—22no—
178Dic61—22no—
179Dic61—22no—
180Dic61—22no—
181Dic61—41no—
182Dic61—41no—
183Dic61C4×D414yes—
184#2360—611nomaximal, Sylow
185C2×C61C2×C4×D411yescharacteristic
186C2×C61C2×C4×Q811yescharacteristic
187C2×C61#52011yescharacteristic
188C2×C61#54611yescharacteristic
189C2×C61D4×Q811yescharacteristic
190C2×C61#55211yescharacteristic
191C2×C61#55411yescharacteristic
192D61—24no—
193C2×C22⋊Q8—611no—
194C2×C4×Q8—611no—
195C22×C4⋊C4—611no—
196#391—611no—
197#389—611no—
198#389—611no—
199#389D6111yescharacteristic, complemented
200#387—611no—
201#387—611no—
202#385—611no—
203#385—611no—
204C4×C4⋊C4—611no—
205C4×C22⋊C4—611no—
206C4×C22⋊C4—611no—
207C4×C22⋊C4—611no—
208C61#236011yescharacteristic, complemented, Sylow
209C22×Q8—611no—
210C23×C4—611no—
211C23×C4—611no—
212C23×C4—611no—
213C22⋊Q8—618no—
214C4×Q8—1224no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—611no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—1224no—
223C2×C4⋊C4C2×D6111yescharacteristic
224C2×C4⋊C4C2×D6111yescharacteristic
225C2×C4⋊C4C2×D6111yescharacteristic
226C2×C4⋊C4C2×D6111yescharacteristic
227C2×C22⋊C4—611no—
228C2×C22⋊C4—611no—
229C2×C22⋊C4—611no—
230C2×C22⋊C4—611no—
231C2×C42—611no—
232C2×C42—611no—
233C2×C42—611no—
234C2×C42—611no—
235C2×C42—611no—
236C2×C42C2×D6111yescharacteristic
237#95—611no—
238#95—611no—
239#95—611no—
240#95—611no—
241#95—611no—
242#95—611no—
243#95—611no—
244#95—611no—
245#95C2×D6111yescharacteristic
246#95C2×D6111yescharacteristic
247C24—611no—
248C2×Q8—614no—
249C2×Q8—1222no—
250C2×Q8—1222no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—614no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—1222no—
260C22×C4—1222no—
261C22×C4—1222no—
262C22×C4—1222no—
263C22×C4—1222no—
264C22×C4—1222no—
265C22×C4—2441no—
266C22×C4—2441no—
267C22×C4C22×D6111yescharacteristic
268C22×C4C22×D6111yescharacteristic
269C22×C4C22×D6111yescharacteristic
270C22×C4C22×D6111yescharacteristic
271C22×C4C22×D6111yescharacteristic
272C22×C4C22×D6111yescharacteristic
273C22×C4C22×D6111yescharacteristic
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—614no—
278C4⋊C4—614no—
279C4⋊C4—614no—
280C4⋊C4—1222no—
281C4⋊C4—1222no—
282C4⋊C4—1222no—
283C4⋊C4—2441no—
284C4⋊C4C4×D6114yescomplemented
285C22⋊C4—614no—
286C22⋊C4—614no—
287C22⋊C4—614no—
288C22⋊C4—1222no—
289C42—41no—
290C42—1222no—
291C42—1222no—
292C42—1222no—
293C42—1222no—
294C42—2441no—
295C23—612no—
296C23—612no—
297C23—612no—
298C23—1221no—
299C23—1221no—
300C23—1221no—
301C23—1221no—
302C23C23×D6111yescharacteristic
303Q8—1228no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—612no—
321C2×C4—612no—
322C2×C4—612no—
323C2×C4—612no—
324C2×C4—612no—
325C2×C4—612no—
326C2×C4—612no—
327C2×C4—1228no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—2444no—
343C2×C4—2444no—
344C2×C4C2×C4×D6112yes—
345C2×C4C2×C4×D6112yes—
346C2×C4C2×C4×D6112yes—
347C2×C4D4×D6112yes—
348C2×C4Q8×D6112yes—
349C22—614no—
350C22—1222no—
351C22—1222no—
352C22—1222no—
353C22—1222no—
354C22—1222no—
355C22—1222no—
356C22C22×C4×D6111yescharacteristic
357C22C2×D4×D6111yescharacteristic
358C22C2×Q8×D6111yescharacteristic
359C22#41×D6111yescharacteristic
360C22#41×D6111yescharacteristic
361C22#1451982211yescharacteristic
362C22#1451982511yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—22no—
367C4—22no—
368C4—41no—
369C4—41no—
370C4—614no—
371C4—1222no—
372C4—1222no—
373C4—1222no—
374C4—1222no—
375C4—2441no—
376C4—2441no—
377C2—1224no—
378C2C4×D4×D6111yescharacteristic
379C2C4×Q8×D6111yescharacteristic
380C2#1684024311yescharacteristic
381C2#1684040111yescharacteristic
382C2#1684042711yescharacteristic
383C2#1684044411yescharacteristic
384C2#1684046611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutatorC22×C61C23×C4
FittingC61×#389C2
socleC23×C61C24
hypercenter#389D61
hypocenterC61#2360
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
2. C2×#14519742C2semidirect
4. #16839666C2semidirect
5. #16839659C2semidirect
6. #16839657C2semidirect
7. #16839648C2semidirect
8. #16839643C2semidirect
11. C4×#11758196C2semidirect
15. C61×#389C2semidirect
20. #14519755C4semidirect
80. C2×Dic122C2×C4semidirect
84. C4⋊C4×C61C2×C4semidirect
89. #11758198Q8semidirect
94. #11758196C2×C4semidirect
95. #11758196C2×C4semidirect
169. C2×D61C4×Q8semidirect
199. #389D61semidirect
208. C61#2360semidirect
284. C4⋊C4C4×D61semidirect