Finite Group Databasebeta

← #22614949

Subgroups — #22614949

Order 9344.

468 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556589C211yesmaximal, characteristic
2C2×#14556581C211yesmaximal, characteristic
3#17988521C211yesmaximal, characteristic
4#17988518C211yesmaximal, characteristic
5#17988508C211yesmaximal, characteristic
6#17988506C211yesmaximal, characteristic
7#17988491C211yesmaximal, characteristic
8#17988485C211yesmaximal, characteristic
9#17988484C211yesmaximal, characteristic
10#17988484C211yesmaximal, characteristic
11#17988484C211yesmaximal, characteristic
12#17988451C211yesmaximal, characteristic
13C4×#11924007C211yesmaximal, characteristic
14#17988438C211yesmaximal, characteristic
15#391×C73C211yesmaximal, characteristic
16C22×Dic146C2211yescharacteristic
17#14556589—24no—
18#14556581—24no—
19C2×C4⋊Dic73C2211yescharacteristic
20C2×C4⋊Dic73C2211yescharacteristic
21C2×C4⋊Dic73C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×#11924007C2211yescharacteristic
29C2×#11924007C2211yescharacteristic
30C2×#11924007C2211yescharacteristic
31C2×#11924007C2211yescharacteristic
32C2×#11924007C2211yescharacteristic
33C2×#11924007C2211yescharacteristic
34C2×C4×Dic73C2211yescharacteristic
35C2×C4×Dic73C2211yescharacteristic
36C2×C4×Dic73C2211yescharacteristic
37C2×C4×Dic73C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44#14556498C2211yescharacteristic
45#14556498C2211yescharacteristic
46C22×Q8×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—41no—
56C22×Dic73C2311yescharacteristic
57C22×Dic73C2311yescharacteristic
58C22×Dic73C2311yescharacteristic
59C22×Dic73C2311yescharacteristic
60C22×Dic73C2311yescharacteristic
61C22×Dic73C2311yescharacteristic
62C22×Dic73C2311yescharacteristic
63C22×Dic73C2311yescharacteristic
64C4⋊Dic73—22no—
65C4⋊Dic73—22no—
66C4⋊Dic73—41no—
67#11924007—22no—
68#11924007—22no—
69#11924007—22no—
70#11924007—22no—
71#11924007—22no—
72#11924007—22no—
73#11924007—22no—
74#11924007—22no—
75#11924007—22no—
76#11924007—41no—
77#11924007D414yes—
78#11924007Q814yescomplemented
79C4×Dic73—22no—
80C4×Dic73—22no—
81C4×Dic73—41no—
82C4×Dic73Q814yescomplemented
83C2×Q8×C73—22no—
84C2×Q8×C73—22no—
85C2×Q8×C73—41no—
86C22×C4×C73C2311yescharacteristic
87C22×C4×C73C2311yescharacteristic
88C22×C4×C73C2311yescharacteristic
89C22×C4×C73C2311yescharacteristic
90C22×C4×C73C2311yescharacteristic
91C22×C4×C73C2311yescharacteristic
92C22×C4×C73C2311yescharacteristic
93C4⋊C4×C73—22no—
94C42×C73—41no—
95C23×C73C2411yescharacteristic
96Q8×C73—44no—
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×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73C2×D412yes—
115C2×C4×C73C2×Q812yes—
116C2×C4×C73C2×Q812yes—
117C2×C4×C73#4112yes—
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×Dic73C2×Q812yes—
140C2×Dic73C2×Q812yes—
141C2×Dic73#4112yes—
142Dic146—44no—
143C22×C73C22×D411yescharacteristic
144C22×C73C22×Q811yescharacteristic
145C22×C73C22×Q811yescharacteristic
146C22×C73C2×#4111yescharacteristic
147C22×C73C2×#4111yescharacteristic
148C22×C73H(5,𝔽2)11yescharacteristic
149C22×C732−1+411yescharacteristic
150C4×C73—22no—
151C4×C73—22no—
152C4×C73—22no—
153C4×C73—22no—
154C4×C73—41no—
155C4×C73—41no—
156C4×C73—41no—
157Dic73—22no—
158Dic73—22no—
159Dic73—22no—
160Dic73—22no—
161Dic73—41no—
162Dic73—41no—
163Dic73—41no—
164Dic73C4⋊Q814yes—
165C2×C73C2×C4⋊Q811yescharacteristic
166C2×C73#53311yescharacteristic
167C2×C73#54411yescharacteristic
168C2×C73#54611yescharacteristic
169C2×C73#54811yescharacteristic
170C2×C73#55411yescharacteristic
171C2×C73#55711yescharacteristic
172#2550—731nomaximal, Sylow
173C73#255011yescharacteristic, complemented, Sylow
174C2×C4⋊Q8—731no—
175C2×#125—731no—
176#398—731no—
177#398—731no—
178#395—731no—
179#395—731no—
180#391—731no—
181#391D7311yescharacteristic
182#389—731no—
183#389—731no—
184#389—731no—
185#389—731no—
186#382—731no—
187C4×C4⋊C4—731no—
188C4×C4⋊C4—731no—
189C22×Q8—731no—
190C22×Q8C2×D7311yescharacteristic
191C4⋊Q8—1464no—
192#125—1464no—
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⋊C4—731no—
204C2×C4⋊C4—731no—
205C2×C4⋊C4—731no—
206C2×C4⋊C4—731no—
207C2×C4⋊C4—731no—
208C2×C4⋊C4C2×D7311yescharacteristic
209C2×C42—731no—
210C2×C42—731no—
211C2×C42—731no—
212C2×C42—731no—
213C2×C42C2×D7311yescharacteristic
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#95C2×D7311yescharacteristic
223#95C2×D7311yescharacteristic
224#95C2×D7311yescharacteristic
225#95C2×D7311yescharacteristic
226C2×Q8—22no—
227C2×Q8—22no—
228C2×Q8—41no—
229C2×Q8—2921no—
230C2×Q8—1462no—
231C2×Q8—1462no—
232C22×C4—731no—
233C22×C4—731no—
234C22×C4—731no—
235C22×C4—731no—
236C22×C4—731no—
237C22×C4—731no—
238C22×C4—731no—
239C22×C4—731no—
240C22×C4C22×D7311yescharacteristic
241C22×C4C22×D7311yescharacteristic
242C22×C4C22×D7311yescharacteristic
243C22×C4C22×D7311yescharacteristic
244C22×C4C22×D7311yescharacteristic
245C22×C4C22×D7311yescharacteristic
246C22×C4C22×D7311yescharacteristic
247C4⋊C4—22no—
248C4⋊C4—2921no—
249C4⋊C4—2921no—
250C4⋊C4—734no—
251C4⋊C4—734no—
252C4⋊C4—1462no—
253C4⋊C4—1462no—
254C4⋊C4—1462no—
255C4⋊C4—1462no—
256C4⋊C4—1462no—
257C4⋊C4—1462no—
258C4⋊C4—1462no—
259C4⋊C4—1462no—
260C4⋊C4—1462no—
261C4⋊C4—1462no—
262C4⋊C4—1462no—
263C42—41no—
264C42—2921no—
265C42—734no—
266C42—1462no—
267C42—1462no—
268C23C23×D7311yescharacteristic
269Q8—44no—
270Q8—2924no—
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—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—732no—
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×C4D4×D7312yes—
313C2×C4Q8×D7312yes—
314C2×C4Q8×D7312yes—
315C2×C4#1192402812yes—
316C22C2×D4×D7311yescharacteristic
317C22C2×Q8×D7311yescharacteristic
318C22C2×Q8×D7311yescharacteristic
319C22#41×D7311yescharacteristic
320C22C2×#1192402811yescharacteristic
321C22#1455663611yescharacteristic
322C22#1455663811yescharacteristic
323C4—22no—
324C4—22no—
325C4—22no—
326C4—22no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—2921no—
331C4—2921no—
332C4—2921no—
333C4—734no—
334C4—1462no—
335C4—1462no—
336C4—1462no—
337C4—1462no—
338C2C4⋊Q8×D7311yescharacteristic
339C2#1798914111yescharacteristic
340C2#1798921611yescharacteristic
341C2#1798922711yescharacteristic
342C2#1798924511yescharacteristic
343C2#1798929111yescharacteristic
344C2#1798931511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#391×C73C2
hypercenter#391D73
hypocenterC73#2550
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
78. #11924007Q8semidirect
82. C4×Dic73Q8semidirect
173. C73#2550semidirect