Finite Group Databasebeta

← #22613769

Subgroups — #22613769

Order 9344.

484 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556590C211yesmaximal, characteristic
2C2×C4×Dic146C211yesmaximal, characteristic
3#17988520C211yesmaximal, characteristic
4#17988519C211yesmaximal, characteristic
5#17988508C211yesmaximal, characteristic
6#17988508C211yesmaximal, characteristic
7#17988493C211yesmaximal, characteristic
8#17988491C211yesmaximal, characteristic
9#17988491C211yesmaximal, characteristic
10#17988491C211yesmaximal, characteristic
11#17988484C211yesmaximal, characteristic
12#17988484C211yesmaximal, characteristic
13#17988473C211yesmaximal, characteristic
14C4⋊C4×Dic73C211yesmaximal, characteristic
15#387×C73C211yesmaximal, characteristic
16C22×Dic146C2211yescharacteristic
17C22×Dic146C2211yescharacteristic
18C22×Dic146C2211yescharacteristic
19#14556590—24no—
20C4×Dic146—24no—
21C2×C4⋊Dic73C2211yescharacteristic
22C2×C4⋊Dic73C2211yescharacteristic
23C2×C4⋊Dic73C2211yescharacteristic
24C2×C4⋊Dic73C2211yescharacteristic
25C2×C4⋊Dic73C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×#11924007C2211yescharacteristic
29C2×#11924007C2211yescharacteristic
30C2×#11924007C2211yescharacteristic
31C2×#11924007C2211yescharacteristic
32C2×C4×Dic73C2211yescharacteristic
33C2×C4×Dic73C2211yescharacteristic
34C2×C4×Dic73C2211yescharacteristic
35C2×C4×Dic73C2211yescharacteristic
36#14556498C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46C2×C4⋊C4×C73C2211yescharacteristic
47C2×C4⋊C4×C73C2211yescharacteristic
48C2×C42×C73C2211yescharacteristic
49#95×C73C2211yescharacteristic
50#95×C73C2211yescharacteristic
51#95×C73C2211yescharacteristic
52#95×C73C2211yescharacteristic
53C2×Dic146—22no—
54C2×Dic146—22no—
55C2×Dic146—22no—
56C2×Dic146—22no—
57C2×Dic146—22no—
58C2×Dic146—22no—
59C2×Dic146—41no—
60C2×Dic146—41no—
61C2×Dic146Q814yescomplemented
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C22×Dic73C2311yescharacteristic
65C22×Dic73C2311yescharacteristic
66C22×Dic73C2311yescharacteristic
67C22×Dic73C2311yescharacteristic
68C22×Dic73C2311yescharacteristic
69C22×Dic73C2311yescharacteristic
70C4⋊Dic73—22no—
71C4⋊Dic73—22no—
72C4⋊Dic73—22no—
73C4⋊Dic73—41no—
74C4⋊Dic73—41no—
75#11924007—22no—
76#11924007—22no—
77#11924007—22no—
78#11924007—41no—
79#11924007—41no—
80#11924007D414yes—
81C4×Dic73—22no—
82C4×Dic73—22no—
83C4×Dic73—22no—
84C4×Dic73—22no—
85C22×C4×C73C2311yescharacteristic
86C22×C4×C73C2311yescharacteristic
87C22×C4×C73C2311yescharacteristic
88C22×C4×C73C2311yescharacteristic
89C22×C4×C73C2311yescharacteristic
90C22×C4×C73C2311yescharacteristic
91C22×C4×C73C2311yescharacteristic
92C4⋊C4×C73—22no—
93C4⋊C4×C73Q814yescomplemented
94C42×C73—22no—
95C23×C73C2411yescharacteristic
96C2×C4×C73—21no—
97C2×C4×C73—21no—
98C2×C4×C73—21no—
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×C73C2×D412yes—
113C2×C4×C73C2×Q812yes—
114C2×C4×C73C2×Q812yes—
115C2×C4×C73C2×Q812yes—
116C2×C4×C73C2×Q812yes—
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×Dic73C2×D412yes—
136C2×Dic73C2×D412yes—
137C2×Dic73C2×Q812yes—
138C2×Dic73C2×Q812yes—
139C2×Dic73#4112yes—
140C2×Dic73#4112yes—
141Dic146—28no—
142Dic146—44no—
143Dic146—44no—
144C22×C73C22×D411yescharacteristic
145C22×C73C22×Q811yescharacteristic
146C22×C73C22×Q811yescharacteristic
147C22×C73C2×#4111yescharacteristic
148C22×C73C2×#4111yescharacteristic
149C22×C73H(5,𝔽2)11yescharacteristic
150C22×C732−1+411yescharacteristic
151C4×C73—22no—
152C4×C73—22no—
153C4×C73—22no—
154C4×C73—22no—
155C4×C73—22no—
156C4×C73—41no—
157C4×C73—41no—
158Dic73—22no—
159Dic73—22no—
160Dic73—22no—
161Dic73—41no—
162Dic73—41no—
163Dic73—41no—
164Dic73—41no—
165Dic73C22⋊Q814yes—
166C2×C73C2×C22⋊Q811yescharacteristic
167C2×C73#53311yescharacteristic
168C2×C73#54211yescharacteristic
169C2×C73#54611yescharacteristic
170C2×C73D4×Q811yescharacteristic
171C2×C73#55711yescharacteristic
172C2×C73Q8211yescharacteristic
173#2451—731nomaximal, Sylow
174C73#245111yescharacteristic, complemented, Sylow
175C2×C4⋊Q8—731no—
176C2×C4×Q8—731no—
177#398—731no—
178#398—731no—
179#395—731no—
180#395—731no—
181#391—731no—
182#391—731no—
183#391—731no—
184#391—731no—
185#389—731no—
186#389—731no—
187#387—731no—
188#387D7311yescharacteristic
189C4×C4⋊C4—731no—
190C22×Q8—731no—
191C22×Q8—731no—
192C22×Q8—731no—
193C4⋊Q8—1464no—
194C4×Q8—1464no—
195C2×C4⋊C4—731no—
196C2×C4⋊C4—731no—
197C2×C4⋊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⋊C4C2×D7311yescharacteristic
207C2×C4⋊C4C2×D7311yescharacteristic
208C2×C42—731no—
209C2×C42—731no—
210C2×C42—731no—
211C2×C42—731no—
212C2×C42C2×D7311yescharacteristic
213#95—731no—
214#95—731no—
215#95—731no—
216#95—731no—
217#95—731no—
218#95—731no—
219#95—731no—
220#95—731no—
221#95—731no—
222#95—731no—
223#95C2×D7311yescharacteristic
224#95C2×D7311yescharacteristic
225#95C2×D7311yescharacteristic
226#95C2×D7311yescharacteristic
227C2×Q8—2921no—
228C2×Q8—2921no—
229C2×Q8—734no—
230C2×Q8—1462no—
231C2×Q8—1462no—
232C2×Q8—1462no—
233C2×Q8—1462no—
234C2×Q8—1462no—
235C2×Q8—1462no—
236C22×C4—731no—
237C22×C4—731no—
238C22×C4—731no—
239C22×C4—731no—
240C22×C4—731no—
241C22×C4—731no—
242C22×C4—731no—
243C22×C4—731no—
244C22×C4C22×D7311yescharacteristic
245C22×C4C22×D7311yescharacteristic
246C22×C4C22×D7311yescharacteristic
247C22×C4C22×D7311yescharacteristic
248C22×C4C22×D7311yescharacteristic
249C22×C4C22×D7311yescharacteristic
250C22×C4C22×D7311yescharacteristic
251C4⋊C4—22no—
252C4⋊C4—2921no—
253C4⋊C4—2921no—
254C4⋊C4—2921no—
255C4⋊C4—2921no—
256C4⋊C4—734no—
257C4⋊C4—1462no—
258C4⋊C4—1462no—
259C4⋊C4—1462no—
260C4⋊C4—1462no—
261C4⋊C4—1462no—
262C4⋊C4—1462no—
263C4⋊C4Dic14614yescomplemented
264C42—22no—
265C42—1462no—
266C42—1462no—
267C42—1462no—
268C42—1462no—
269C23C23×D7311yescharacteristic
270Q8—2924no—
271Q8—2924no—
272Q8—1468no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
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—732no—
290C2×C4—732no—
291C2×C4—732no—
292C2×C4—732no—
293C2×C4—732no—
294C2×C4—732no—
295C2×C4—1461no—
296C2×C4—1461no—
297C2×C4—1461no—
298C2×C4—1461no—
299C2×C4—1461no—
300C2×C4—1461no—
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×C4D4×D7312yes—
314C2×C4Q8×D7312yes—
315C2×C4C2×Dic14612yes—
316C2×C4C2×Dic14612yes—
317C2×C4C2×Dic14612yes—
318C22C2×D4×D7311yescharacteristic
319C22C2×Q8×D7311yescharacteristic
320C22C22×Dic14611yescharacteristic
321C22#41×D7311yescharacteristic
322C22#41×D7311yescharacteristic
323C22#1455663711yescharacteristic
324C22#1455663811yescharacteristic
325C4—22no—
326C4—22no—
327C4—22no—
328C4—22no—
329C4—22no—
330C4—41no—
331C4—41no—
332C4—2921no—
333C4—2921no—
334C4—2921no—
335C4—2921no—
336C4—734no—
337C4—1462no—
338C4—1462no—
339C4—1462no—
340C2C22⋊Q8×D7311yescharacteristic
341C2#1798914011yescharacteristic
342C2#1798920311yescharacteristic
343C2#1798922911yescharacteristic
344C2D4×Dic14611yescharacteristic
345C2#1798931411yescharacteristic
346C2Q8×Dic14611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#387×C73C2
hypercenter#387D73
hypocenterC73#2451
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
61. C2×Dic146Q8semidirect
93. C4⋊C4×C73Q8semidirect
174. C73#2451semidirect
263. C4⋊C4Dic146semidirect