Finite Group Databasebeta

← #22616885

Subgroups — #22616885

Order 9344.

416 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556583C211yesmaximal, characteristic
2C2×#14556582C211yesmaximal, characteristic
3#17988521C211yesmaximal, characteristic
4#17988521C211yesmaximal, characteristic
5#17988521C211yesmaximal, characteristic
6#17988520C211yesmaximal, characteristic
7#17988519C211yesmaximal, characteristic
8#17988519C211yesmaximal, characteristic
9#17988486C211yesmaximal, characteristic
10#17988485C211yesmaximal, characteristic
11#17988484C211yesmaximal, characteristic
12#17988484C211yesmaximal, characteristic
13#17988484C211yesmaximal, characteristic
14#17988473C211yesmaximal, characteristic
15#387×C73C211yesmaximal, characteristic
16#14556583—24no—
17#14556582—24no—
18C2×C4⋊Dic73C2211yescharacteristic
19C2×C4⋊Dic73C2211yescharacteristic
20C2×C4⋊Dic73C2211yescharacteristic
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×#11924007C2211yescharacteristic
33C2×#11924007C2211yescharacteristic
34C2×#11924007C2211yescharacteristic
35C2×#11924007C2211yescharacteristic
36C2×C4×Dic73C2211yescharacteristic
37C2×C4×Dic73C2211yescharacteristic
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
53C22×Dic73C2311yescharacteristic
54C22×Dic73C2311yescharacteristic
55C22×Dic73C2311yescharacteristic
56C22×Dic73C2311yescharacteristic
57C22×Dic73C2311yescharacteristic
58C22×Dic73C2311yescharacteristic
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C4⋊Dic73—22no—
62C4⋊Dic73—22no—
63C4⋊Dic73—22no—
64C4⋊Dic73—22no—
65C4⋊Dic73—22no—
66C4⋊Dic73—22no—
67C4⋊Dic73—41no—
68C4⋊Dic73—41no—
69#11924007—22no—
70#11924007—22no—
71#11924007—22no—
72#11924007—22no—
73#11924007—22no—
74#11924007—22no—
75#11924007—41no—
76#11924007—41no—
77#11924007—41no—
78#11924007D414yes—
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×C73Q814yes—
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×Q812yes—
111C2×C4×C73C2×Q812yes—
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×D412yes—
135C2×Dic73C2×D412yes—
136C2×Dic73#4112yes—
137C22×C73C22×D411yescharacteristic
138C22×C73C22×Q811yescharacteristic
139C22×C73C2×#4111yescharacteristic
140C22×C73H(5,𝔽2)11yescharacteristic
141C22×C732−1+411yescharacteristic
142C22×C732−1+411yescharacteristic
143C22×C732−1+411yescharacteristic
144C4×C73—22no—
145C4×C73—22no—
146C4×C73—22no—
147C4×C73—22no—
148C4×C73—41no—
149C4×C73—41no—
150C4×C73—41no—
151Dic73—22no—
152Dic73—22no—
153Dic73—22no—
154Dic73—41no—
155Dic73—41no—
156Dic73—41no—
157Dic73—41no—
158Dic73—41no—
159C2×C73#53711yescharacteristic
160C2×C73#53911yescharacteristic
161C2×C73#54411yescharacteristic
162C2×C73#54711yescharacteristic
163C2×C73D4×Q811yescharacteristic
164C2×C73#55711yescharacteristic
165C2×C73#56411yescharacteristic
166#2726—731nomaximal, Sylow
167C73#272611yescharacteristic, complemented, Sylow
168C2×#125—731no—
169C2×#125—731no—
170#398—731no—
171#398—731no—
172#398—731no—
173#398—731no—
174#398—731no—
175#398—731no—
176#389—731no—
177#389—731no—
178#389—731no—
179#389—731no—
180#389—731no—
181#387—731no—
182#387D7311yescharacteristic
183#125—1464no—
184#125—1464no—
185C2×C4⋊C4—731no—
186C2×C4⋊C4—731no—
187C2×C4⋊C4—731no—
188C2×C4⋊C4—731no—
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⋊C4—731no—
202C2×C4⋊C4—731no—
203C2×C4⋊C4C2×D7311yescharacteristic
204C2×C4⋊C4C2×D7311yescharacteristic
205C2×C42—731no—
206C2×C42—731no—
207C2×C42C2×D7311yescharacteristic
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#95C2×D7311yescharacteristic
217#95C2×D7311yescharacteristic
218#95C2×D7311yescharacteristic
219#95C2×D7311yescharacteristic
220C22×C4—731no—
221C22×C4—731no—
222C22×C4—731no—
223C22×C4—731no—
224C22×C4—731no—
225C22×C4—731no—
226C22×C4—731no—
227C22×C4—731no—
228C22×C4C22×D7311yescharacteristic
229C22×C4C22×D7311yescharacteristic
230C22×C4C22×D7311yescharacteristic
231C22×C4C22×D7311yescharacteristic
232C22×C4C22×D7311yescharacteristic
233C22×C4C22×D7311yescharacteristic
234C22×C4C22×D7311yescharacteristic
235C4⋊C4—22no—
236C4⋊C4—2921no—
237C4⋊C4—2921no—
238C4⋊C4—2921no—
239C4⋊C4—2921no—
240C4⋊C4—2921no—
241C4⋊C4—734no—
242C4⋊C4—1462no—
243C4⋊C4—1462no—
244C4⋊C4—1462no—
245C4⋊C4—1462no—
246C4⋊C4—1462no—
247C4⋊C4—1462no—
248C4⋊C4—1462no—
249C4⋊C4—1462no—
250C4⋊C4—1462no—
251C4⋊C4—1462no—
252C4⋊C4—1462no—
253C4⋊C4—1462no—
254C4⋊C4Dic14614yes—
255C42—22no—
256C42—2921no—
257C42—1462no—
258C23C23×D7311yescharacteristic
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
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—732no—
277C2×C4—732no—
278C2×C4—732no—
279C2×C4—1461no—
280C2×C4—1461no—
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×C4D4×D7312yes—
301C2×C4C2×Dic14612yes—
302C2×C4C2×Dic14612yes—
303C2×C4C2×Dic14612yes—
304C22C2×D4×D7311yescharacteristic
305C22C22×Dic14611yescharacteristic
306C22#41×D7311yescharacteristic
307C22#1455663711yescharacteristic
308C22#1455663811yescharacteristic
309C22#1455663811yescharacteristic
310C22#1455663911yescharacteristic
311C4—22no—
312C4—22no—
313C4—22no—
314C4—22no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—2921no—
319C4—2921no—
320C4—2921no—
321C4—2921no—
322C4—2921no—
323C4—1462no—
324C4—1462no—
325C4—1462no—
326C2#1798916711yescharacteristic
327C2#1798917811yescharacteristic
328C2#1798921511yescharacteristic
329C2#1798923511yescharacteristic
330C2D4×Dic14611yescharacteristic
331C2#1798931311yescharacteristic
332C2C73⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#387×C73C2
hypercenter#387D73
hypocenterC73#2726
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
167. C73#2726semidirect