Finite Group Databasebeta

← #22616708

Subgroups — #22616708

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×#14556590C211yesmaximal, characteristic
2#17988526C211yesmaximal, characteristic
3#17988525C211yesmaximal, characteristic
4#17988520C211yesmaximal, characteristic
5#17988517C211yesmaximal, characteristic
6#17988507C211yesmaximal, characteristic
7#17988507C211yesmaximal, characteristic
8#17988493C211yesmaximal, characteristic
9#17988492C211yesmaximal, characteristic
10#17988482C211yesmaximal, characteristic
11#17988473C211yesmaximal, characteristic
12#17988471C211yesmaximal, characteristic
13#17988468C211yesmaximal, characteristic
14#17988468C211yesmaximal, characteristic
15C2×#125×C73C211yesmaximal, characteristic
16C22×Dic146C2211yescharacteristic
17C22×Dic146C2211yescharacteristic
18#14556590—24no—
19C2×C4⋊Dic73C2211yescharacteristic
20C2×C4⋊Dic73C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×C4×Dic73C2211yescharacteristic
28C2×C4×Dic73C2211yescharacteristic
29#14556498C2211yescharacteristic
30#14556498C2211yescharacteristic
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
44#14556498C2211yescharacteristic
45#125×C73—24no—
46C2×C4⋊C4×C73C2211yescharacteristic
47C2×C4⋊C4×C73C2211yescharacteristic
48C2×C4⋊C4×C73C2211yescharacteristic
49C2×C4⋊C4×C73C2211yescharacteristic
50C2×C4⋊C4×C73C2211yescharacteristic
51C2×C4⋊C4×C73C2211yescharacteristic
52C2×C42×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—41no—
69#11924007—22no—
70#11924007—22no—
71#11924007—22no—
72#11924007—41no—
73#11924007—41no—
74#11924007Q814yescomplemented
75C4×Dic73—22no—
76C4×Dic73—41no—
77C22×C4×C73C2311yescharacteristic
78C22×C4×C73C2311yescharacteristic
79C22×C4×C73C2311yescharacteristic
80C22×C4×C73C2311yescharacteristic
81C22×C4×C73C2311yescharacteristic
82C22×C4×C73C2311yescharacteristic
83C22×C4×C73C2311yescharacteristic
84C4⋊C4×C73—22no—
85C4⋊C4×C73—22no—
86C4⋊C4×C73—22no—
87C4⋊C4×C73—22no—
88C4⋊C4×C73—22no—
89C4⋊C4×C73D414yes—
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×C73—21no—
109C2×C4×C73C2×D412yes—
110C2×C4×C73C2×D412yes—
111C2×C4×C73C2×D412yes—
112C2×C4×C73C2×Q812yes—
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×Dic73C2×Q812yes—
135C2×Dic73C2×Q812yes—
136C2×Dic73#4112yes—
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—41no—
151C4×C73—41no—
152C4×C73—41no—
153Dic73—22no—
154Dic73—22no—
155Dic73—22no—
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×#125D7311yescharacteristic
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#387—731no—
185C22×Q8—731no—
186C22×Q8—731no—
187C4⋊Q8—1464no—
188#125—24no—
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⋊C4C2×D7311yescharacteristic
198C2×C4⋊C4C2×D7311yescharacteristic
199C2×C4⋊C4C2×D7311yescharacteristic
200C2×C4⋊C4C2×D7311yescharacteristic
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#95—731no—
219#95—731no—
220#95—731no—
221#95—731no—
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—22no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—2921no—
249C4⋊C4—2921no—
250C4⋊C4—2921no—
251C4⋊C4—734no—
252C4⋊C4—1462no—
253C4⋊C4—1462no—
254C4⋊C4—1462no—
255C4⋊C4—1462no—
256C4⋊C4C22⋊D7314yes—
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—21no—
280C2×C4—732no—
281C2×C4—732no—
282C2×C4—732no—
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×C4—1461no—
304C2×C4C2×C22⋊D7312yes—
305C2×C4C2×C22⋊D7312yes—
306C2×C4C2×C22⋊D7312yes—
307C2×C4Q8×D7312yes—
308C22C22×C22⋊D7311yescharacteristic
309C22C2×Q8×D7311yescharacteristic
310C22#41×D7311yescharacteristic
311C22#1455663711yescharacteristic
312C22#1455663811yescharacteristic
313C22#1455663811yescharacteristic
314C22#1455663911yescharacteristic
315C4—22no—
316C4—22no—
317C4—22no—
318C4—22no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—2921no—
323C4—2921no—
324C4—2921no—
325C4—2921no—
326C4—2921no—
327C4—1462no—
328C4—1462no—
329C4—1462no—
330C2#1798915811yescharacteristic
331C2#1798919611yescharacteristic
332C2#1798921711yescharacteristic
333C2#1798922511yescharacteristic
334C2Q8×C22⋊D7311yescharacteristic
335C2#1798931411yescharacteristic
336C2#1798934111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#125×C73C2
hypercenterC2×#125D73
hypocenterC73#2713
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
74. #11924007Q8semidirect
169. C73#2713semidirect