Finite Group Databasebeta

← #22622401

Subgroups — #22622401

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#17988993C211yesmaximal, characteristic, complemented
3#17988908C211yesmaximal, characteristic, complemented
4#17988905C211yesmaximal, characteristic, complemented
5#17988903C211yesmaximal, characteristic, complemented
6#17988900C211yesmaximal, characteristic, complemented
7#17988887C211yesmaximal, characteristic, complemented
8#17988874C211yesmaximal, characteristic, complemented
9#17988838C211yesmaximal, characteristic, complemented
10#17988821C211yesmaximal, characteristic, complemented
11#17988697C211yesmaximal, characteristic, complemented
12#17988659C211yesmaximal, characteristic, complemented
13#17988627C211yesmaximal, characteristic, complemented
14C2×#14556522C211yesmaximal, characteristic, complemented
15#547×C73C211yesmaximal, characteristic, complemented
16C2×#11924013C2211yescharacteristic
17C2×#11924012C2211yescharacteristic
18C22×#10596831C2211yescharacteristic
19#14556586—21no—
20#14556583C2211yescharacteristic
21#14556573—21no—
22#14556565C2211yescharacteristic
23#14556565C2211yescharacteristic
24#14556563—21no—
25C4×D292C2211yescharacteristic
26#14556551—21no—
27#14556550C2211yescharacteristic
28C2×C4⋊Dic73C2211yescharacteristic
29#14556524C2211yescharacteristic
30#14556524C2211yescharacteristic
31#14556524C2211yescharacteristic
32#14556522C2211yescharacteristic
33#14556522C2211yescharacteristic
34#14556522C2211yescharacteristic
35#14556522C2211yescharacteristic
36#14556522C2211yescharacteristic
37#14556522C2211yescharacteristic
38C4⋊#10596831C2211yescharacteristic
39#14556512C2211yescharacteristic
40#14556512C2211yescharacteristic
41#14556512C2211yescharacteristic
42#14556511C2211yescharacteristic
43#14556511C2211yescharacteristic
44#14556511C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46C22⋊#10596831C2211yescharacteristic
47#14556502C2211yescharacteristic
48C2×#41×C73—21no—
49C4⋊Q8×C73C2211yescharacteristic
50#123×C73—21no—
51#123×C73—21no—
52C22⋊Q8×C73—21no—
53#121×C73C2211yescharacteristic
54#121×C73C2211yescharacteristic
55C4×D4×C73C2211yescharacteristic
56C4×D4×C73C2211yescharacteristic
57C2×C4⋊C4×C73C2211yescharacteristic
58C2×C4⋊C4×C73C2211yescharacteristic
59C2×D292C2311yescharacteristic
60C2×C22⋊D73—21no—
61C2×C22⋊D73—21no—
62C22×Dic73—21no—
63C2×C4×D73—21no—
64#11924013—22no—
65#11924012—22no—
66C2×#10596831—22no—
67C2×#10596831C2311yescharacteristic
68C2×#10596831C2311yescharacteristic
69C2×#10596831C2311yescharacteristic
70C2×#10596831C2311yescharacteristic
71C4⋊Dic73—21no—
72C4⋊Dic73C2311yescharacteristic
73C4⋊Dic73C2311yescharacteristic
74C4⋊Dic73C2311yescharacteristic
75#11924007—21no—
76#11924007—21no—
77C22⋊Dic73—21no—
78#11924005—21no—
79#11924005—21no—
80#11924005—21no—
81C4×Dic73—21no—
82#41×C73—44no—
83C2×Q8×C73—21no—
84C2×D4×C73—21no—
85C2×D4×C73—21no—
86C2×D4×C73D411yescharacteristic
87C2×D4×C73C2311yescharacteristic
88C22×C4×C73—21no—
89C22×C4×C73—21no—
90C22×C4×C73—21no—
91C22×C4×C73C2311yescharacteristic
92C22×C4×C73C2311yescharacteristic
93C4⋊C4×C73—21no—
94C4⋊C4×C73—21no—
95C4⋊C4×C73—21no—
96C4⋊C4×C73D411yescharacteristic
97C4⋊C4×C73C2311yescharacteristic
98C4⋊C4×C73C2311yescharacteristic
99C4⋊C4×C73C2311yescharacteristic
100C22⋊C4×C73—21no—
101C22⋊C4×C73—21no—
102C22⋊C4×C73—21no—
103C22⋊C4×C73D411yescharacteristic
104C22⋊C4×C73D411yescharacteristic
105C42×C73C2311yescharacteristic
106C23×C73—21no—
107C23×C73C2×D411yescharacteristic
108C23×C73C2×D411yescharacteristic
109C22×D73—21no—
110Q8×C73—42no—
111D4×C73—22no—
112D4×C73—21no—
113D4×C73—21no—
114D4×C73—42no—
115D4×C73—42no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
123C2×C4×C73—42no—
124C2×C4×C73—42no—
125C2×C4×C73—42no—
126C2×C4×C73C2×D411yescharacteristic
127C2×C4×C73C2×D411yescharacteristic
128C2×C4×C73C2×D411yescharacteristic
129C2×C4×C73C2×D411yescharacteristic
130C2×C4×C73C2411yescharacteristic
131C22⋊D73—42no—
132C22⋊D73—81no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—81no—
137D292—21no—
138D292—21no—
139C4×D73—81no—
140#10596831—21no—
141#10596831—21no—
142#10596831—21no—
143#10596831#4112yescomplemented
144C22×C73—21no—
145C22×C73—21no—
146C22×C73—21no—
147C22×C73—21no—
148C22×C73—21no—
149C22×C73—41no—
150C22×C73—41no—
151C22×C73—41no—
152C22×C73AGL(1,ℤ/8)12yes—
153C22×C73C22×D411yescharacteristic
154C2×D73—41no—
155C2×D73—41no—
156C2×D73—41no—
157C4×C73—21no—
158C4×C73—21no—
159C4×C73—21no—
160C4×C73—21no—
161C4×C73—41no—
162C4×C73—41no—
163C4×C73—41no—
164C4×C73C2×#4111yescharacteristic
165C4×C732−1+411yescharacteristic
166Dic73—41no—
167Dic73—41no—
168Dic73—41no—
169C2×C73—22no—
170C2×C73—41no—
171C2×C73—81no—
172C2×C73#54711yescharacteristic
173C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
174C2×C73#57711yescharacteristic
175D73—81no—
176#3345—731nomaximal, Sylow
177C73#334511yescharacteristic, complemented, Sylow
178#553—731no—
179#547D7311yescharacteristic, complemented
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#435—731no—
191#428—731no—
192C2×#106—731no—
193C2×#41—21no—
194C2×D8—731no—
195C2×M16—731no—
196C22×C8—731no—
197C4⋊Q8C2×D7311yescharacteristic
198#126—1461no—
199#125—731no—
200#123—21no—
201#123—21no—
202#123—1461no—
203C22⋊Q8—21no—
204#121—731no—
205#121—731no—
206#121—1461no—
207#121C2×D7311yescharacteristic
208#121C2×D7311yescharacteristic
209C4×D4—731no—
210C4×D4—1461no—
211C4×D4C2×D7311yescharacteristic
212C4×D4C2×D7311yescharacteristic
213#117—731no—
214C2×C4⋊C4—731no—
215C2×C4⋊C4C2×D7311yescharacteristic
216C2×C4⋊C4C2×D7311yescharacteristic
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⋊C8—731no—
227#102—731no—
228#102—731no—
229#102—731no—
230#102—731no—
231#102—731no—
232#102—731no—
233C22⋊C8—731no—
234C22⋊C8—731no—
235#97—731no—
236#41—44no—
237C2×Q8—21no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—731no—
241C2×D4—1461no—
242C2×D4—1461no—
243C2×D4C22⋊D7311yescharacteristic
244C2×D4C22×D7311yescharacteristic
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—1461no—
249C22×C4—1461no—
250C22×C4C22×D7311yescharacteristic
251C22×C4C22×D7311yescharacteristic
252D8—1462no—
253M16—1462no—
254C2×C8—731no—
255C2×C8—731no—
256C2×C8—731no—
257C2×C8—731no—
258C2×C8—1462no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—731no—
263C4⋊C4—731no—
264C4⋊C4—731no—
265C4⋊C4—1461no—
266C4⋊C4—1461no—
267C4⋊C4—1461no—
268C4⋊C4C22⋊D7311yescharacteristic
269C4⋊C4C22×D7311yescharacteristic
270C4⋊C4C22×D7311yescharacteristic
271C4⋊C4C22×D7311yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—1461no—
276C22⋊C4—1461no—
277C22⋊C4—1461no—
278C22⋊C4—1461no—
279C22⋊C4C22⋊D7311yescharacteristic
280C22⋊C4C22⋊D7311yescharacteristic
281C42—1461no—
282C42C22×D7311yescharacteristic
283C23—21no—
284C23—1461no—
285C23C2×C22⋊D7311yescharacteristic
286C23C2×C22⋊D7311yescharacteristic
287Q8—42no—
288D4—22no—
289D4—21no—
290D4—21no—
291D4—42no—
292D4—42no—
293D4—2922no—
294D4—5841no—
295D4—1461no—
296D4—1461no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—5841no—
308C2×C4—5841no—
309C2×C4—1461no—
310C2×C4—1461no—
311C2×C4—1461no—
312C2×C4C2×C22⋊D7311yescharacteristic
313C2×C4C2×C22⋊D7311yescharacteristic
314C2×C4C2×C22⋊D7311yescharacteristic
315C2×C4C2×C22⋊D7311yescharacteristic
316C2×C4C23×D7311yescharacteristic
317C8—732no—
318C8—1461no—
319C8—1461no—
320C8—1461no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—2921no—
330C22—2921no—
331C22—2921no—
332C22#1455661712yes—
333C22C22×C22⋊D7311yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—2921no—
342C4—2921no—
343C4—2921no—
344C4#41×D7311yescharacteristic
345C4#1455663811yescharacteristic
346C2—22no—
347C2—41no—
348C2—81no—
349C2—5841no—
350C2#1798923611yescharacteristic
351C2C2×#1455661711yescharacteristic
352C2#1798939511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#547×C73C2
socleC22×C73C22×D4
hypercenter#547D73
hypocenterC73#3345
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #17989283C2semidirect
2. #17988993C2semidirect
3. #17988908C2semidirect
4. #17988905C2semidirect
5. #17988903C2semidirect
6. #17988900C2semidirect
7. #17988887C2semidirect
8. #17988874C2semidirect
9. #17988838C2semidirect
10. #17988821C2semidirect
11. #17988697C2semidirect
12. #17988659C2semidirect
13. #17988627C2semidirect
14. C2×#14556522C2semidirect
15. #547×C73C2semidirect
143. #10596831#41semidirect
177. C73#3345semidirect
179. #547D73semidirect