Finite Group Databasebeta

← #22618124

Subgroups — #22618124

Order 9344.

358 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
1#17988529C211yesmaximal, characteristic, complemented
2#17988528C211yesmaximal, characteristic, complemented
3#17988523C211yesmaximal, characteristic
4#17988521C211yesmaximal, characteristic, complemented
5#17988519C211yesmaximal, characteristic, complemented
6#17988518C211yesmaximal, characteristic, complemented
7#17988517C211yesmaximal, characteristic, complemented
8#17988515C211yesmaximal, characteristic
9#17988515C211yesmaximal, characteristic
10#17988512C211yesmaximal, characteristic
11#17988510C211yesmaximal, characteristic
12#17988510C211yesmaximal, characteristic
13#17988485C211yesmaximal, characteristic, complemented
14#17988471C211yesmaximal, characteristic, complemented
15#388×C73C211yesmaximal, characteristic
16C2×C4⋊Dic73C2211yescharacteristic
17C2×C4⋊Dic73C2211yescharacteristic
18C2×C4⋊Dic73C2211yescharacteristic
19C2×C4⋊Dic73C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2211yescharacteristic
25C2×#11924007C2211yescharacteristic
26C2×#11924007C2211yescharacteristic
27C2×#11924007C2211yescharacteristic
28C2×C22⋊Dic73C2211yescharacteristic
29C2×C22⋊Dic73C2211yescharacteristic
30C2×C22⋊Dic73C2211yescharacteristic
31C2×C22⋊Dic73C2211yescharacteristic
32#14556498C2211yescharacteristic
33#14556498C2211yescharacteristic
34#14556498C2211yescharacteristic
35#14556498C2211yescharacteristic
36#14556498C2211yescharacteristic
37#14556498C2211yescharacteristic
38#14556498C2211yescharacteristic
39#14556498C2211yescharacteristic
40#14556498C2211yescharacteristic
41#14556498C2211yescharacteristic
42#14556498C2211yescharacteristic
43#14556498C2211yescharacteristic
44C2×C4⋊C4×C73C2211yescharacteristic
45C2×C22⋊C4×C73C2211yescharacteristic
46C2×C22⋊C4×C73C2211yescharacteristic
47C2×C22⋊C4×C73C2211yescharacteristic
48C2×C42×C73C2211yescharacteristic
49#95×C73C2211yescharacteristic
50#95×C73C2211yescharacteristic
51C22×Dic73C2311yescharacteristic
52C22×Dic73C2311yescharacteristic
53C22×Dic73C2311yescharacteristic
54C22×Dic73C2311yescharacteristic
55C22×Dic73C2311yescharacteristic
56C22×Dic73C2311yescharacteristic
57C22×Dic73C2311yescharacteristic
58C22×Dic73C2311yescharacteristic
59C4⋊Dic73—22no—
60C4⋊Dic73—41no—
61C4⋊Dic73—41no—
62C4⋊Dic73—41no—
63#11924007—22no—
64#11924007—41no—
65#11924007—41no—
66#11924007—41no—
67#11924007—41no—
68#11924007—41no—
69#11924007—41no—
70#11924007—41no—
71C22⋊Dic73—41no—
72C22⋊Dic73—41no—
73C22⋊Dic73—41no—
74C22⋊Dic73—41no—
75C24×C73C2311yescharacteristic
76C22×C4×C73C2311yescharacteristic
77C22×C4×C73C2311yescharacteristic
78C22×C4×C73C2311yescharacteristic
79C22×C4×C73C2311yescharacteristic
80C22×C4×C73C2311yescharacteristic
81C22×C4×C73C2311yescharacteristic
82C4⋊C4×C73—41no—
83C22⋊C4×C73—22no—
84C22⋊C4×C73—41no—
85C22⋊C4×C73—41no—
86C42×C73—41no—
87C23×C73—21no—
88C23×C73—21no—
89C23×C73—21no—
90C23×C73—21no—
91C23×C73—21no—
92C23×C73—21no—
93C23×C73—21no—
94C23×C73C2411yescharacteristic
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×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
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×Dic73—21no—
136C2×Dic73—21no—
137C22×C73—41no—
138C22×C73—41no—
139C22×C73—41no—
140C22×C73—41no—
141C22×C73—41no—
142C22×C73—41no—
143C22×C73—41no—
144C22×C73C2×#4111yescharacteristic
145C22×C73H(5,𝔽2)11yescharacteristic
146C22×C73H(5,𝔽2)11yescharacteristic
147C22×C73H(5,𝔽2)11yescharacteristic
148C22×C732−1+411yescharacteristic
149C22×C732−1+411yescharacteristic
150C22×C732−1+411yescharacteristic
151C4×C73—22no—
152C4×C73—41no—
153C4×C73—41no—
154C4×C73—41no—
155C4×C73—41no—
156C4×C73—41no—
157Dic73—41no—
158Dic73—41no—
159Dic73—41no—
160Dic73—41no—
161Dic73—41no—
162Dic73—41no—
163Dic73—41no—
164Dic73—41no—
165C2×C73—81no—
166C2×C73#53911yescharacteristic
167C2×C73#54011yescharacteristic
168C2×C73#54111yescharacteristic
169C2×C73#56211yescharacteristic
170C2×C73#56211yescharacteristic
171C2×C73#56311yescharacteristic
172C2×C73#56311yescharacteristic
173#2836—731nomaximal, Sylow
174C73#283611yescharacteristic, complemented, Sylow
175#400—731no—
176#400—731no—
177#399—731no—
178#398—731no—
179#398—731no—
180#398—731no—
181#398—731no—
182#397—731no—
183#397—731no—
184#397—731no—
185#396—731no—
186#396—731no—
187#389—731no—
188#388D7311yescharacteristic
189#387—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⋊C4C2×D7311yescharacteristic
203C2×C22⋊C4—731no—
204C2×C22⋊C4—731no—
205C2×C22⋊C4—731no—
206C2×C22⋊C4—731no—
207C2×C22⋊C4C2×D7311yescharacteristic
208C2×C22⋊C4C2×D7311yescharacteristic
209C2×C22⋊C4C2×D7311yescharacteristic
210C2×C42C2×D7311yescharacteristic
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—
222#95—731no—
223#95C2×D7311yescharacteristic
224#95C2×D7311yescharacteristic
225C24C22×D7311yescharacteristic
226C22×C4—731no—
227C22×C4—731no—
228C22×C4—731no—
229C22×C4—731no—
230C22×C4—731no—
231C22×C4—731no—
232C22×C4—731no—
233C22×C4—731no—
234C22×C4C22×D7311yescharacteristic
235C22×C4C22×D7311yescharacteristic
236C22×C4C22×D7311yescharacteristic
237C22×C4C22×D7311yescharacteristic
238C22×C4C22×D7311yescharacteristic
239C22×C4C22×D7311yescharacteristic
240C4⋊C4—41no—
241C4⋊C4—2921no—
242C4⋊C4—2921no—
243C4⋊C4—2921no—
244C4⋊C4—2921no—
245C4⋊C4—2921no—
246C4⋊C4—2921no—
247C4⋊C4—2921no—
248C4⋊C4—2921no—
249C4⋊C4—2921no—
250C4⋊C4—2921no—
251C4⋊C4—1462no—
252C4⋊C4—1462no—
253C22⋊C4—22no—
254C22⋊C4—41no—
255C22⋊C4—41no—
256C22⋊C4—2921no—
257C22⋊C4—2921no—
258C22⋊C4—2921no—
259C22⋊C4—2921no—
260C42—41no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23C23×D7311yescharacteristic
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—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
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×C4—1461no—
305C2×C4—1461no—
306C2×C4—1461no—
307C2×C4—1461no—
308C2×C4—1461no—
309C2×C4—1461no—
310C2×C4#1192402812yes—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22C2×#1192402811yescharacteristic
319C22#1455663611yescharacteristic
320C22#1455663611yescharacteristic
321C22#1455663711yescharacteristic
322C22#1455663811yescharacteristic
323C22#1455663811yescharacteristic
324C22#1455663811yescharacteristic
325C4—22no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—2921no—
332C4—2921no—
333C4—2921no—
334C4—2921no—
335C4—2921no—
336C4—2921no—
337C4—2921no—
338C4—2921no—
339C2—81no—
340C2#1798917911yescharacteristic
341C2#1798918811yescharacteristic
342C2#1798919911yescharacteristic
343C2#1798933211yescharacteristic
344C2#1798933411yescharacteristic
345C2#1798933711yescharacteristic
346C2#1798933911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#388×C73C2
hypercenter#388D73
hypocenterC73#2836
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. #17988529C2semidirect
2. #17988528C2semidirect
4. #17988521C2semidirect
5. #17988519C2semidirect
6. #17988518C2semidirect
7. #17988517C2semidirect
13. #17988485C2semidirect
14. #17988471C2semidirect
174. C73#2836semidirect