Finite Group Databasebeta

← #22616713

Subgroups — #22616713

Order 9344.

432 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556591C211yesmaximal, characteristic
2C2×#14556582C211yesmaximal, characteristic
3#17988529C211yesmaximal, characteristic
4#17988526C211yesmaximal, characteristic
5#17988519C211yesmaximal, characteristic
6#17988519C211yesmaximal, characteristic
7#17988508C211yesmaximal, characteristic
8#17988508C211yesmaximal, characteristic
9#17988491C211yesmaximal, characteristic
10#17988491C211yesmaximal, characteristic
11#17988486C211yesmaximal, characteristic
12#17988473C211yesmaximal, characteristic
13#17988471C211yesmaximal, characteristic
14#17988470C211yesmaximal, characteristic
15#387×C73C211yesmaximal, characteristic
16C22×Dic146C2211yescharacteristic
17C22×Dic146C2211yescharacteristic
18#14556591—24no—
19#14556582—24no—
20C2×C4⋊Dic73C2211yescharacteristic
21C2×C4⋊Dic73C2211yescharacteristic
22C2×C4⋊Dic73C2211yescharacteristic
23C2×C4⋊Dic73C2211yescharacteristic
24C2×C4⋊Dic73C2211yescharacteristic
25C2×C4⋊Dic73C2211yescharacteristic
26C2×C4⋊Dic73C2211yescharacteristic
27C2×C4⋊Dic73C2211yescharacteristic
28C2×#11924007C2211yescharacteristic
29C2×#11924007C2211yescharacteristic
30C2×#11924007C2211yescharacteristic
31C2×#11924007C2211yescharacteristic
32C2×C4×Dic73C2211yescharacteristic
33C2×C4×Dic73C2211yescharacteristic
34#14556498C2211yescharacteristic
35#14556498C2211yescharacteristic
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—41no—
58C2×Dic146—41no—
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C22×Dic73C2311yescharacteristic
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C22×Dic73C2311yescharacteristic
65C22×Dic73C2311yescharacteristic
66C22×Dic73C2311yescharacteristic
67C4⋊Dic73—22no—
68C4⋊Dic73—22no—
69C4⋊Dic73—22no—
70C4⋊Dic73—22no—
71C4⋊Dic73—22no—
72C4⋊Dic73—41no—
73C4⋊Dic73—41no—
74C4⋊Dic73D414yes—
75#11924007—22no—
76#11924007—22no—
77#11924007—22no—
78#11924007—41no—
79C4×Dic73—22no—
80C4×Dic73—41no—
81C22×C4×C73C2311yescharacteristic
82C22×C4×C73C2311yescharacteristic
83C22×C4×C73C2311yescharacteristic
84C22×C4×C73C2311yescharacteristic
85C22×C4×C73C2311yescharacteristic
86C22×C4×C73C2311yescharacteristic
87C22×C4×C73C2311yescharacteristic
88C4⋊C4×C73—22no—
89C4⋊C4×C73Q814yescomplemented
90C42×C73—22no—
91C23×C73C2411yescharacteristic
92C2×C4×C73—21no—
93C2×C4×C73—21no—
94C2×C4×C73—21no—
95C2×C4×C73—21no—
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×C73C2×D412yes—
109C2×C4×C73C2×Q812yes—
110C2×C4×C73C2×Q812yes—
111C2×C4×C73C2×Q812yes—
112C2×C4×C73#4112yes—
113C2×Dic73—21no—
114C2×Dic73—21no—
115C2×Dic73—21no—
116C2×Dic73—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×Dic73C2×D412yes—
136C2×Dic73C2×D412yes—
137Dic146—44no—
138Dic146—44no—
139C22×C73C22×D411yescharacteristic
140C22×C73C22×Q811yescharacteristic
141C22×C73C2×#4111yescharacteristic
142C22×C73H(5,𝔽2)11yescharacteristic
143C22×C732−1+411yescharacteristic
144C22×C732−1+411yescharacteristic
145C22×C732−1+411yescharacteristic
146C4×C73—22no—
147C4×C73—22no—
148C4×C73—22no—
149C4×C73—22no—
150C4×C73—22no—
151C4×C73—41no—
152C4×C73—41no—
153Dic73—22no—
154Dic73—22no—
155Dic73—41no—
156Dic73—41no—
157Dic73—41no—
158Dic73—41no—
159Dic73—41no—
160Dic73—41no—
161C2×C73#53611yescharacteristic
162C2×C73#54111yescharacteristic
163C2×C73#54411yescharacteristic
164C2×C73#54611yescharacteristic
165C2×C73D4×Q811yescharacteristic
166C2×C73#55711yescharacteristic
167C2×C73#56311yescharacteristic
168#2713—731nomaximal, Sylow
169C73#271311yescharacteristic, complemented, Sylow
170C2×C4⋊Q8—731no—
171C2×#125—731no—
172#400—731no—
173#400—731no—
174#398—731no—
175#398—731no—
176#395—731no—
177#395—731no—
178#391—731no—
179#391—731no—
180#389—731no—
181#387—731no—
182#387—731no—
183#387—731no—
184#387D7311yescharacteristic
185C22×Q8—731no—
186C22×Q8—731no—
187C4⋊Q8—1464no—
188#125—1464no—
189C2×C4⋊C4—731no—
190C2×C4⋊C4—731no—
191C2×C4⋊C4—731no—
192C2×C4⋊C4—731no—
193C2×C4⋊C4—731no—
194C2×C4⋊C4—731no—
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⋊C4C2×D7311yescharacteristic
202C2×C4⋊C4C2×D7311yescharacteristic
203C2×C42—731no—
204C2×C42—731no—
205C2×C42C2×D7311yescharacteristic
206#95—731no—
207#95—731no—
208#95—731no—
209#95—731no—
210#95—731no—
211#95—731no—
212#95—731no—
213#95—731no—
214#95—731no—
215#95—731no—
216#95—731no—
217#95—731no—
218#95C2×D7311yescharacteristic
219#95C2×D7311yescharacteristic
220#95C2×D7311yescharacteristic
221#95C2×D7311yescharacteristic
222C2×Q8—2921no—
223C2×Q8—2921no—
224C2×Q8—1462no—
225C2×Q8—1462no—
226C2×Q8—1462no—
227C2×Q8—1462no—
228C22×C4—731no—
229C22×C4—731no—
230C22×C4—731no—
231C22×C4—731no—
232C22×C4—731no—
233C22×C4—731no—
234C22×C4—731no—
235C22×C4—731no—
236C22×C4C22×D7311yescharacteristic
237C22×C4C22×D7311yescharacteristic
238C22×C4C22×D7311yescharacteristic
239C22×C4C22×D7311yescharacteristic
240C22×C4C22×D7311yescharacteristic
241C22×C4C22×D7311yescharacteristic
242C22×C4C22×D7311yescharacteristic
243C4⋊C4—22no—
244C4⋊C4—2921no—
245C4⋊C4—2921no—
246C4⋊C4—2921no—
247C4⋊C4—734no—
248C4⋊C4—1462no—
249C4⋊C4—1462no—
250C4⋊C4—1462no—
251C4⋊C4—1462no—
252C4⋊C4—1462no—
253C4⋊C4—1462no—
254C4⋊C4—1462no—
255C4⋊C4—1462no—
256C4⋊C4Dic14614yescomplemented
257C42—22no—
258C42—2921no—
259C42—1462no—
260C23C23×D7311yescharacteristic
261Q8—2924no—
262Q8—2924no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—732no—
280C2×C4—732no—
281C2×C4—1461no—
282C2×C4—1461no—
283C2×C4—1461no—
284C2×C4—1461no—
285C2×C4—1461no—
286C2×C4—1461no—
287C2×C4—1461no—
288C2×C4—1461no—
289C2×C4—1461no—
290C2×C4—1461no—
291C2×C4—1461no—
292C2×C4—1461no—
293C2×C4—1461no—
294C2×C4—1461no—
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×C4D4×D7312yes—
304C2×C4C2×Dic14612yes—
305C2×C4C2×Dic14612yes—
306C2×C4C2×Dic14612yes—
307C2×C4#1192402912yes—
308C22C2×D4×D7311yescharacteristic
309C22C22×Dic14611yescharacteristic
310C22C2×#1192402911yescharacteristic
311C22#1455663711yescharacteristic
312C22#1455663811yescharacteristic
313C22#1455663811yescharacteristic
314C22#1455663811yescharacteristic
315C4—22no—
316C4—22no—
317C4—22no—
318C4—22no—
319C4—22no—
320C4—41no—
321C4—41no—
322C4—2921no—
323C4—2921no—
324C4—2921no—
325C4—2921no—
326C4—2921no—
327C4—2921no—
328C4—1462no—
329C4—1462no—
330C2#1798915911yescharacteristic
331C2#1798920011yescharacteristic
332C2#1798921511yescharacteristic
333C2#1798922811yescharacteristic
334C2D4×Dic14611yescharacteristic
335C2#1798931611yescharacteristic
336C2#1798933911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#387×C73C2
hypercenter#387D73
hypocenterC73#2713
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
89. C4⋊C4×C73Q8semidirect
169. C73#2713semidirect
256. C4⋊C4Dic146semidirect