Finite Group Databasebeta

← #21452764

Subgroups — #21452764

Order 7808.

434 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519770C211yesmaximal, characteristic
2C2×#14519768C211yesmaximal, characteristic, complemented
3#16839703C211yesmaximal, characteristic, complemented
4#16839694C211yesmaximal, characteristic, complemented
5#16839687C211yesmaximal, characteristic
6#16839685C211yesmaximal, characteristic
7#16839685C211yesmaximal, characteristic
8#16839661C211yesmaximal, characteristic, complemented
9#16839661C211yesmaximal, characteristic, complemented
10#16839657C211yesmaximal, characteristic, complemented
11#16839657C211yesmaximal, characteristic, complemented
12#16839655C211yesmaximal, characteristic
13#16839655C211yesmaximal, characteristic
14#16839643C211yesmaximal, characteristic, complemented
15C61×#396C211yesmaximal, characteristic
16#14519770—24no—
17#14519768—24no—
18C2×C4⋊Dic61C2211yescharacteristic
19C2×C4⋊Dic61C2211yescharacteristic
20C2×C4⋊Dic61C2211yescharacteristic
21C2×C4⋊Dic61C2211yescharacteristic
22C2×C4⋊Dic61C2211yescharacteristic
23C2×C4⋊Dic61C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×#11758196C2211yescharacteristic
29C2×#11758196C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic
31C2×C22⋊Dic61C2211yescharacteristic
32C2×C22⋊Dic61C2211yescharacteristic
33C2×C22⋊Dic61C2211yescharacteristic
34C2×C4×Dic61C2211yescharacteristic
35C2×C4×Dic61C2211yescharacteristic
36C2×C4×Dic61C2211yescharacteristic
37#14519684C2211yescharacteristic
38#14519684C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46C2×C4⋊C4×C61C2211yescharacteristic
47C2×C4⋊C4×C61C2211yescharacteristic
48C2×C4⋊C4×C61C2211yescharacteristic
49C2×C22⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52#95×C61C2211yescharacteristic
53C24×C61C2311yescharacteristic
54C22×C4×C61C2311yescharacteristic
55C22×C4×C61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×Dic61C2311yescharacteristic
61C22×Dic61C2311yescharacteristic
62C22×Dic61C2311yescharacteristic
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C4⋊C4×C61—22no—
69C4⋊C4×C61—22no—
70C4⋊C4×C61—22no—
71C22⋊C4×C61—22no—
72C22⋊C4×C61—22no—
73C22⋊C4×C61—22no—
74C22⋊Dic61—22no—
75C22⋊Dic61—22no—
76C22⋊Dic61—41no—
77C22⋊Dic61—41no—
78C4⋊Dic61—22no—
79C4⋊Dic61—22no—
80C4⋊Dic61—22no—
81C4⋊Dic61—22no—
82C4⋊Dic61—41no—
83C4⋊Dic61—41no—
84#11758196—22no—
85#11758196—22no—
86#11758196—22no—
87#11758196—22no—
88#11758196—41no—
89#11758196D414yes—
90C4×Dic61—22no—
91C4×Dic61—22no—
92C4×Dic61—41no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61C2411yescharacteristic
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
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×C61C2×D412yes—
117C2×C4×C61#4112yes—
118C2×C4×C61#4112yes—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
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×Dic61C2×D412yes—
142C2×Dic61C2×D412yes—
143C22×C61—41no—
144C22×C61—41no—
145C22×C61—41no—
146C22×C61—41no—
147C22×C61—41no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61C22×D411yescharacteristic
151C22×C61C2×#4111yescharacteristic
152C22×C61C2×#4111yescharacteristic
153C22×C61H(5,𝔽2)11yescharacteristic
154C22×C612−1+411yescharacteristic
155C22×C612−1+411yescharacteristic
156C22×C612−1+411yescharacteristic
157C4×C61—22no—
158C4×C61—22no—
159C4×C61—22no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—41no—
163Dic61—22no—
164Dic61—22no—
165Dic61—41no—
166Dic61—41no—
167Dic61—41no—
168Dic61—41no—
169Dic61—41no—
170Dic61—41no—
171#2725—611nomaximal, Sylow
172C2×C61—81no—
173C2×C61#53711yescharacteristic
174C2×C61#54111yescharacteristic
175C2×C61#54111yescharacteristic
176C2×C61#54711yescharacteristic
177C2×C61#54811yescharacteristic
178C2×C61#55311yescharacteristic
179C2×C61#56311yescharacteristic
180C2×#126—611no—
181C2×#125—611no—
182#400—611no—
183#398—611no—
184#397—611no—
185#396—611no—
186#396—611no—
187#396D6111yescharacteristic
188#389—611no—
189#389—611no—
190#389—611no—
191#389—611no—
192#388—611no—
193#388—611no—
194#387—611no—
195C61#272511yescharacteristic, complemented, Sylow
196#126—1224no—
197#125—1224no—
198C2×C4⋊C4—611no—
199C2×C4⋊C4—611no—
200C2×C4⋊C4—611no—
201C2×C4⋊C4—611no—
202C2×C4⋊C4—611no—
203C2×C4⋊C4—611no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—611no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4C2×D6111yescharacteristic
211C2×C4⋊C4C2×D6111yescharacteristic
212C2×C4⋊C4C2×D6111yescharacteristic
213C2×C22⋊C4—611no—
214C2×C22⋊C4—611no—
215C2×C22⋊C4—611no—
216C2×C22⋊C4—611no—
217C2×C22⋊C4C2×D6111yescharacteristic
218C2×C22⋊C4C2×D6111yescharacteristic
219C2×C22⋊C4C2×D6111yescharacteristic
220C2×C42—611no—
221C2×C42—611no—
222C2×C42—611no—
223#95—611no—
224#95—611no—
225#95—611no—
226#95—611no—
227#95—611no—
228#95—611no—
229#95—611no—
230#95—611no—
231#95—611no—
232#95C2×D6111yescharacteristic
233C24C22×D6111yescharacteristic
234C22×C4—611no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4C22×D6111yescharacteristic
243C22×C4C22×D6111yescharacteristic
244C22×C4C22×D6111yescharacteristic
245C22×C4C22×D6111yescharacteristic
246C22×C4C22×D6111yescharacteristic
247C22×C4C22×D6111yescharacteristic
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—614no—
252C4⋊C4—1222no—
253C4⋊C4—1222no—
254C4⋊C4—1222no—
255C4⋊C4—1222no—
256C4⋊C4—1222no—
257C4⋊C4—1222no—
258C4⋊C4—1222no—
259C4⋊C4—1222no—
260C4⋊C4—2441no—
261C4⋊C4—2441no—
262C4⋊C4—2441no—
263C22⋊C4—22no—
264C22⋊C4—22no—
265C22⋊C4—22no—
266C22⋊C4—1222no—
267C22⋊C4—1222no—
268C22⋊C4—2441no—
269C22⋊C4—2441no—
270C42—1222no—
271C42—1222no—
272C42—2441no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23C23×D6111yescharacteristic
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—612no—
297C2×C4—612no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4D4×D6112yes—
321C2×C4#1175822412yes—
322C2×C4#1175822412yes—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C2×D4×D6111yescharacteristic
331C22C2×#1175822411yescharacteristic
332C22C2×#1175822411yescharacteristic
333C22#1451982311yescharacteristic
334C22#1451982411yescharacteristic
335C22#1451982411yescharacteristic
336C22#1451982511yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—1222no—
344C4—1222no—
345C4—2441no—
346C4—2441no—
347C4—2441no—
348C4—2441no—
349C4—2441no—
350C4—2441no—
351C2—81no—
352C2#1684034211yescharacteristic
353C2#1684037211yescharacteristic
354C2#1684037211yescharacteristic
355C2#1684041211yescharacteristic
356C2#1684041811yescharacteristic
357C2#1684046411yescharacteristic
358C2#1684051411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#396C2
hypercenter#396D61
hypocenterC61#2725
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
2. C2×#14519768C2semidirect
3. #16839703C2semidirect
4. #16839694C2semidirect
8. #16839661C2semidirect
9. #16839661C2semidirect
10. #16839657C2semidirect
11. #16839657C2semidirect
14. #16839643C2semidirect
195. C61#2725semidirect