Finite Group Databasebeta

← #22622403

Subgroups — #22622403

Order 9344.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989283C211yesmaximal, characteristic, complemented
2#17989241C211yesmaximal, characteristic, complemented
3#17988996C211yesmaximal, characteristic, complemented
4#17988912C211yesmaximal, characteristic, complemented
5#17988906C211yesmaximal, characteristic, complemented
6#17988906C211yesmaximal, characteristic, complemented
7#17988901C211yesmaximal, characteristic, complemented
8#17988888C211yesmaximal, characteristic, complemented
9#17988878C211yesmaximal, characteristic, complemented
10#17988840C211yesmaximal, characteristic, complemented
11#17988823C211yesmaximal, characteristic, complemented
12#17988700C211yesmaximal, characteristic, complemented
13#17988629C211yesmaximal, characteristic, complemented
14C2×#14556523C211yesmaximal, characteristic, complemented
15#435×C73C211yesmaximal, characteristic, complemented
16C2×#11924027—21no—
17C2×D584C2211yescharacteristic
18#14556591C2211yescharacteristic
19#14556586—21no—
20#14556583C2211yescharacteristic
21#14556575—21no—
22#14556575—21no—
23#14556573—21no—
24#14556571—21no—
25#14556565C2211yescharacteristic
26#14556565C2211yescharacteristic
27#14556565C2211yescharacteristic
28#14556565C2211yescharacteristic
29#14556563—21no—
30C4×D292C2211yescharacteristic
31C4×D292C2211yescharacteristic
32#14556551—21no—
33#14556550C2211yescharacteristic
34C2×C4⋊Dic73C2211yescharacteristic
35C2×C4⋊Dic73C2211yescharacteristic
36C2×C4⋊Dic73C2211yescharacteristic
37#14556525C2211yescharacteristic
38#14556525C2211yescharacteristic
39#14556525C2211yescharacteristic
40#14556523C2211yescharacteristic
41#14556523C2211yescharacteristic
42#14556523C2211yescharacteristic
43#14556523C2211yescharacteristic
44#14556523C2211yescharacteristic
45#14556523C2211yescharacteristic
46#14556513C2211yescharacteristic
47#14556513C2211yescharacteristic
48#14556513C2211yescharacteristic
49#14556513C2211yescharacteristic
50#14556513C2211yescharacteristic
51#14556513C2211yescharacteristic
52C2×M16×C73C2211yescharacteristic
53C22×C8×C73C2211yescharacteristic
54C4×D4×C73C2211yescharacteristic
55C4⋊C8×C73C2211yescharacteristic
56C22⋊C8×C73C2211yescharacteristic
57C22⋊C8×C73C2211yescharacteristic
58#97×C73C2211yescharacteristic
59#11924027—44no—
60C2×Dic146—21no—
61C2×D292C2311yescharacteristic
62C2×D292C2311yescharacteristic
63C2×C22⋊D73—21no—
64C2×C22⋊D73—21no—
65C2×C22⋊D73—21no—
66C2×C22⋊D73—21no—
67C22×Dic73—21no—
68C22×Dic73—21no—
69C22×Dic73—21no—
70C2×C4×D73—21no—
71C2×C4×D73—21no—
72D584—22no—
73C4⋊Dic73—21no—
74C4⋊Dic73—21no—
75C4⋊Dic73—21no—
76C4⋊Dic73—21no—
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79C4⋊Dic73C2311yescharacteristic
80C4⋊Dic73C2311yescharacteristic
81C4⋊Dic73C2311yescharacteristic
82C4⋊Dic73C2311yescharacteristic
83#11924007—21no—
84#11924007—21no—
85C22⋊Dic73—21no—
86#11924005—21no—
87#11924005—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92C4×Dic73—21no—
93C2×D4×C73D411yescharacteristic
94C22×C4×C73C2311yescharacteristic
95C22×C4×C73C2311yescharacteristic
96M16×C73—22no—
97C2×C8×C73—22no—
98C2×C8×C73C2311yescharacteristic
99C2×C8×C73C2311yescharacteristic
100C2×C8×C73C2311yescharacteristic
101C2×C8×C73C2311yescharacteristic
102C4⋊C4×C73D411yescharacteristic
103C22⋊C4×C73D411yescharacteristic
104C22⋊C4×C73D411yescharacteristic
105C42×C73C2311yescharacteristic
106C23×C73C2×D411yescharacteristic
107C23×C73C2×D411yescharacteristic
108C22×D73—21no—
109C22×D73—21no—
110D4×C73—22no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73C2×D411yescharacteristic
116C2×C4×C73C2×D411yescharacteristic
117C2×C4×C73C2×D411yescharacteristic
118C2×C4×C73C2×D411yescharacteristic
119C2×C4×C73C2411yescharacteristic
120C22⋊D73—42no—
121C22⋊D73—42no—
122C22⋊D73—42no—
123C22⋊D73—81no—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—42no—
131C2×Dic73—42no—
132C2×Dic73—81no—
133D292—21no—
134D292—21no—
135D292—21no—
136D292—21no—
137C4×D73—42no—
138C4×D73—81no—
139Dic146—42no—
140C8×C73—21no—
141C8×C73—21no—
142C8×C73—21no—
143C8×C73#4112yescomplemented
144C22×C73—21no—
145C22×C73—21no—
146C22×C73—21no—
147C22×C73—21no—
148C22×C73—21no—
149C22×C73AGL(1,ℤ/8)12yes—
150C22×C73C22×D411yescharacteristic
151C2×D73—41no—
152C2×D73—41no—
153C2×D73—41no—
154C2×D73—41no—
155C2×D73—41no—
156C2×D73—41no—
157C4×C73—21no—
158C4×C73—21no—
159C4×C73—21no—
160C4×C73—21no—
161C4×C73C2×#4111yescharacteristic
162C4×C732−1+411yescharacteristic
163Dic73—41no—
164Dic73—41no—
165Dic73—41no—
166Dic73—41no—
167Dic73—41no—
168Dic73—41no—
169C2×C73—22no—
170C2×C73—41no—
171C2×C73#54711yescharacteristic
172C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C73#57711yescharacteristic
174D73—81no—
175D73—81no—
176#3345—731nomaximal, Sylow
177C73#334511yescharacteristic, complemented, Sylow
178#553—731no—
179#547—731no—
180#501—731no—
181#482—731no—
182#481—731no—
183#481—731no—
184#480—731no—
185#478—731no—
186#476—731no—
187#469—731no—
188#466—731no—
189#442—731no—
190#435D7311yescharacteristic, complemented
191#428—731no—
192C2×#106—731no—
193C2×#41—1461no—
194C2×D8—731no—
195C2×M16C2×D7311yescharacteristic
196C22×C8C2×D7311yescharacteristic
197C4⋊Q8—731no—
198#126—1461no—
199#125—731no—
200#123—1461no—
201#123—1461no—
202#123—1461no—
203C22⋊Q8—1461no—
204#121—731no—
205#121—731no—
206#121—731no—
207#121—731no—
208#121—1461no—
209C4×D4—731no—
210C4×D4—731no—
211C4×D4—1461no—
212C4×D4C2×D7311yescharacteristic
213#117—731no—
214C2×C4⋊C4—731no—
215C2×C4⋊C4—731no—
216C2×C4⋊C4—731no—
217#107—731no—
218#107—731no—
219#107—731no—
220#106—731no—
221#106—731no—
222#106—731no—
223#106—731no—
224#106—731no—
225#106—731no—
226C4⋊C8C2×D7311yescharacteristic
227#102—731no—
228#102—731no—
229#102—731no—
230#102—731no—
231#102—731no—
232#102—731no—
233C22⋊C8C2×D7311yescharacteristic
234C22⋊C8C2×D7311yescharacteristic
235#97C2×D7311yescharacteristic
236#41—2924no—
237C2×Q8—1461no—
238C2×D4—731no—
239C2×D4—731no—
240C2×D4—1461no—
241C2×D4—1461no—
242C2×D4—1461no—
243C2×D4—1461no—
244C2×D4D29211yescharacteristic
245C22×C4—1461no—
246C22×C4—1461no—
247C22×C4—1461no—
248C22×C4—1461no—
249C22×C4—1461no—
250C22×C4C22×D7311yescharacteristic
251C22×C4C22×D7311yescharacteristic
252D8—1462no—
253M16—22no—
254C2×C8—22no—
255C2×C8C22×D7311yescharacteristic
256C2×C8C22×D7311yescharacteristic
257C2×C8C22×D7311yescharacteristic
258C2×C8C22×D7311yescharacteristic
259C4⋊C4—731no—
260C4⋊C4—731no—
261C4⋊C4—731no—
262C4⋊C4—731no—
263C4⋊C4—731no—
264C4⋊C4—731no—
265C4⋊C4—1461no—
266C4⋊C4—1461no—
267C4⋊C4—1461no—
268C4⋊C4—1461no—
269C4⋊C4—1461no—
270C4⋊C4—1461no—
271C4⋊C4D29211yescharacteristic
272C22⋊C4—1461no—
273C22⋊C4—1461no—
274C22⋊C4—1461no—
275C22⋊C4—1461no—
276C22⋊C4—1461no—
277C22⋊C4—1461no—
278C22⋊C4—1461no—
279C22⋊C4D29211yescharacteristic
280C22⋊C4D29211yescharacteristic
281C42—1461no—
282C42C22×D7311yescharacteristic
283C23—1461no—
284C23—1461no—
285C23C2×D29211yescharacteristic
286C23C2×D29211yescharacteristic
287Q8—2922no—
288D4—22no—
289D4—2922no—
290D4—2922no—
291D4—2922no—
292D4—5841no—
293D4—1461no—
294D4—1461no—
295D4—1461no—
296D4—1461no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—2922no—
302C2×C4—2922no—
303C2×C4—2922no—
304C2×C4—5841no—
305C2×C4—5841no—
306C2×C4—1461no—
307C2×C4—1461no—
308C2×C4—1461no—
309C2×C4—1461no—
310C2×C4—1461no—
311C2×C4—1461no—
312C2×C4C2×D29211yescharacteristic
313C2×C4C2×D29211yescharacteristic
314C2×C4C2×D29211yescharacteristic
315C2×C4C2×D29211yescharacteristic
316C2×C4C23×D7311yescharacteristic
317C8—21no—
318C8—21no—
319C8—21no—
320C8#1192402712yescomplemented
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—2921no—
327C22—2921no—
328C22—2921no—
329C22—2921no—
330C22—2921no—
331C22—2921no—
332C22#1455661912yes—
333C22C22×D29211yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—2921no—
339C4—2921no—
340C4—2921no—
341C4—2921no—
342C4—2921no—
343C4—2921no—
344C4C2×#1192402711yescharacteristic
345C4#1455663811yescharacteristic
346C2—22no—
347C2—41no—
348C2—5841no—
349C2—5841no—
350C2#1798924111yescharacteristic
351C2C2×#1455661911yescharacteristic
352C2#1798939911yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#435×C73C2
socleC22×C73C22×D4
hypercenter#435D73
hypocenterC73#3345
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #17989283C2semidirect
2. #17989241C2semidirect
3. #17988996C2semidirect
4. #17988912C2semidirect
5. #17988906C2semidirect
6. #17988906C2semidirect
7. #17988901C2semidirect
8. #17988888C2semidirect
9. #17988878C2semidirect
10. #17988840C2semidirect
11. #17988823C2semidirect
12. #17988700C2semidirect
13. #17988629C2semidirect
14. C2×#14556523C2semidirect
15. #435×C73C2semidirect
143. C8×C73#41semidirect
177. C73#3345semidirect
190. #435D73semidirect
320. C8#11924027semidirect