Finite Group Databasebeta

← #22618192

Subgroups — #22618192

Order 9344.

396 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
1#17988528C211yesmaximal, characteristic, complemented
2#17988525C211yesmaximal, characteristic, complemented
3#17988523C211yesmaximal, characteristic
4#17988520C211yesmaximal, characteristic, complemented
5#17988518C211yesmaximal, characteristic, complemented
6#17988518C211yesmaximal, characteristic, complemented
7#17988517C211yesmaximal, characteristic, complemented
8#17988510C211yesmaximal, characteristic
9#17988508C211yesmaximal, characteristic, complemented
10#17988507C211yesmaximal, characteristic, complemented
11#17988499C211yesmaximal, characteristic
12#17988448C211yesmaximal, characteristic
13#17988445C211yesmaximal, characteristic
14#17988445C211yesmaximal, characteristic
15#396×C73C211yesmaximal, characteristic
16C22×Dic146C2211yescharacteristic
17C23×Dic73C2211yescharacteristic
18C2×C4⋊Dic73C2211yescharacteristic
19C2×C4⋊Dic73C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×C22⋊Dic73C2211yescharacteristic
31#14556498C2211yescharacteristic
32#14556498C2211yescharacteristic
33#14556498C2211yescharacteristic
34#14556498C2211yescharacteristic
35#14556498C2211yescharacteristic
36#14556498C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44C2×C4⋊C4×C73C2211yescharacteristic
45C2×C4⋊C4×C73C2211yescharacteristic
46C2×C4⋊C4×C73C2211yescharacteristic
47C2×C22⋊C4×C73C2211yescharacteristic
48C2×C22⋊C4×C73C2211yescharacteristic
49C2×C22⋊C4×C73C2211yescharacteristic
50#95×C73C2211yescharacteristic
51C2×Dic146—41no—
52C2×Dic146—41no—
53C2×Dic146—41no—
54C22×Dic73—41no—
55C22×Dic73—41no—
56C22×Dic73Q814yescomplemented
57C22×Dic73C2311yescharacteristic
58C22×Dic73C2311yescharacteristic
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C22×Dic73C2311yescharacteristic
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C22×Dic73C2311yescharacteristic
65C4⋊Dic73—41no—
66C4⋊Dic73—41no—
67#11924007—41no—
68#11924007—41no—
69#11924007—41no—
70#11924007—41no—
71#11924007—41no—
72#11924007—41no—
73#11924007—41no—
74#11924007—41no—
75C22⋊Dic73—41no—
76C22⋊Dic73—41no—
77C22⋊Dic73—41no—
78C24×C73C2311yescharacteristic
79C22×C4×C73C2311yescharacteristic
80C22×C4×C73C2311yescharacteristic
81C22×C4×C73C2311yescharacteristic
82C22×C4×C73C2311yescharacteristic
83C22×C4×C73C2311yescharacteristic
84C22×C4×C73C2311yescharacteristic
85C4⋊C4×C73—41no—
86C4⋊C4×C73—41no—
87C4⋊C4×C73—41no—
88C22⋊C4×C73—41no—
89C22⋊C4×C73—41no—
90C22⋊C4×C73—41no—
91C23×C73—21no—
92C23×C73—21no—
93C23×C73—21no—
94C23×C73—21no—
95C23×C73—21no—
96C23×C73—21no—
97C23×C73C2×Q812yes—
98C23×C73C2411yescharacteristic
99C2×C4×C73—21no—
100C2×C4×C73—21no—
101C2×C4×C73—21no—
102C2×C4×C73—21no—
103C2×C4×C73—21no—
104C2×C4×C73—21no—
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×Dic73—21no—
118C2×Dic73—21no—
119C2×Dic73—21no—
120C2×Dic73—21no—
121C2×Dic73—21no—
122C2×Dic73—21no—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73—44no—
140C2×Dic73C2×Q812yes—
141C2×Dic73C2×Q812yes—
142Dic146—44no—
143C22×C73—22no—
144C22×C73—22no—
145C22×C73—22no—
146C22×C73—41no—
147C22×C73—41no—
148C22×C73—41no—
149C22×C73—41no—
150C22×C73C22×Q811yescharacteristic
151C22×C73H(5,𝔽2)11yescharacteristic
152C22×C73H(5,𝔽2)11yescharacteristic
153C22×C73H(5,𝔽2)11yescharacteristic
154C22×C73H(5,𝔽2)11yescharacteristic
155C22×C732−1+411yescharacteristic
156C22×C732−1+411yescharacteristic
157C4×C73—41no—
158C4×C73—41no—
159C4×C73—41no—
160C4×C73—41no—
161C4×C73—41no—
162C4×C73—41no—
163Dic73—22no—
164Dic73—22no—
165Dic73—41no—
166Dic73—41no—
167Dic73—41no—
168Dic73—41no—
169Dic73—41no—
170Dic73—41no—
171C2×C73—42no—
172C2×C73#54311yescharacteristic
173C2×C73#54411yescharacteristic
174C2×C73#54411yescharacteristic
175C2×C73#56011yescharacteristic
176C2×C73#56211yescharacteristic
177C2×C73#56211yescharacteristic
178C2×C73#56311yescharacteristic
179#2841—731nomaximal, Sylow
180C73#284111yescharacteristic, complemented, Sylow
181#400—731no—
182#400—731no—
183#399—731no—
184#398—731no—
185#398—731no—
186#398—731no—
187#398—731no—
188#396—731no—
189#396D7311yescharacteristic
190#395—731no—
191#395—731no—
192#393—731no—
193#381—731no—
194#380—731no—
195#380—731no—
196C22×Q8—731no—
197C23×C4—731no—
198C2×C4⋊C4—731no—
199C2×C4⋊C4—731no—
200C2×C4⋊C4—731no—
201C2×C4⋊C4—731no—
202C2×C4⋊C4—731no—
203C2×C4⋊C4—731no—
204C2×C4⋊C4—731no—
205C2×C4⋊C4—731no—
206C2×C4⋊C4—731no—
207C2×C4⋊C4—731no—
208C2×C4⋊C4C2×D7311yescharacteristic
209C2×C4⋊C4C2×D7311yescharacteristic
210C2×C4⋊C4C2×D7311yescharacteristic
211C2×C22⋊C4—731no—
212C2×C22⋊C4—731no—
213C2×C22⋊C4—731no—
214C2×C22⋊C4C2×D7311yescharacteristic
215C2×C22⋊C4C2×D7311yescharacteristic
216C2×C22⋊C4C2×D7311yescharacteristic
217#95—731no—
218#95—731no—
219#95—731no—
220#95—731no—
221#95—731no—
222#95—731no—
223#95—731no—
224#95—731no—
225#95—731no—
226#95—731no—
227#95—731no—
228#95—731no—
229#95—731no—
230#95C2×D7311yescharacteristic
231C24C22×D7311yescharacteristic
232C2×Q8—2921no—
233C2×Q8—2921no—
234C2×Q8—2921no—
235C22×C4—2921no—
236C22×C4—2921no—
237C22×C4—734no—
238C22×C4—731no—
239C22×C4—731no—
240C22×C4—731no—
241C22×C4—731no—
242C22×C4—731no—
243C22×C4—731no—
244C22×C4—731no—
245C22×C4—731no—
246C22×C4C22×D7311yescharacteristic
247C22×C4C22×D7311yescharacteristic
248C22×C4C22×D7311yescharacteristic
249C22×C4C22×D7311yescharacteristic
250C22×C4C22×D7311yescharacteristic
251C22×C4C22×D7311yescharacteristic
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—2921no—
256C4⋊C4—2921no—
257C4⋊C4—2921no—
258C4⋊C4—2921no—
259C4⋊C4—2921no—
260C4⋊C4—2921no—
261C4⋊C4—2921no—
262C4⋊C4—2921no—
263C4⋊C4—2921no—
264C4⋊C4—2921no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—2921no—
269C22⋊C4—2921no—
270C22⋊C4—2921no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23Q8×D7312yes—
278C23C23×D7311yescharacteristic
279Q8—2924no—
280C2×C4—21no—
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—21no—
297C2×C4—21no—
298C2×C4—2924no—
299C2×C4—732no—
300C2×C4—732no—
301C2×C4—1461no—
302C2×C4—1461no—
303C2×C4—1461no—
304C2×C4—1461no—
305C2×C4—1461no—
306C2×C4—1461no—
307C2×C4—1461no—
308C2×C4—1461no—
309C2×C4—1461no—
310C2×C4—1461no—
311C2×C4—1461no—
312C2×C4—1461no—
313C2×C4—1461no—
314C2×C4—1461no—
315C2×C4—1461no—
316C2×C4—1461no—
317C2×C4—1461no—
318C2×C4—1461no—
319C2×C4—1461no—
320C2×C4—1461no—
321C2×C4—1461no—
322C2×C4—1461no—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C2×Q8×D7311yescharacteristic
331C22#1455663611yescharacteristic
332C22#1455663611yescharacteristic
333C22#1455663611yescharacteristic
334C22#1455663711yescharacteristic
335C22#1455663811yescharacteristic
336C22#1455663811yescharacteristic
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—2921no—
344C4—2921no—
345C4—2921no—
346C4—2921no—
347C4—2921no—
348C4—2921no—
349C4—1462no—
350C4—1462no—
351C2—42no—
352C2#1798921211yescharacteristic
353C2#1798921611yescharacteristic
354C2#1798921611yescharacteristic
355C2#1798932511yescharacteristic
356C2#1798933211yescharacteristic
357C2#1798933211yescharacteristic
358C2#1798933911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#396×C73C2
hypercenter#396D73
hypocenterC73#2841
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. #17988528C2semidirect
2. #17988525C2semidirect
4. #17988520C2semidirect
5. #17988518C2semidirect
6. #17988518C2semidirect
7. #17988517C2semidirect
9. #17988508C2semidirect
10. #17988507C2semidirect
56. C22×Dic73Q8semidirect
180. C73#2841semidirect