Finite Group Databasebeta

← #22621066

Subgroups — #22621066

Order 9344.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989143C211yesmaximal, characteristic, complemented
2#17989134C211yesmaximal, characteristic
3#17988991C211yesmaximal, characteristic, complemented
4#17988984C211yesmaximal, characteristic, complemented
5#17988932C211yesmaximal, characteristic, complemented
6#17988932C211yesmaximal, characteristic, complemented
7#17988914C211yesmaximal, characteristic, complemented
8#17988913C211yesmaximal, characteristic, complemented
9#17988910C211yesmaximal, characteristic, complemented
10#17988909C211yesmaximal, characteristic, complemented
11#17988888C211yesmaximal, characteristic, complemented
12#17988887C211yesmaximal, characteristic, complemented
13#17988884C211yesmaximal, characteristic, complemented
14#17988639C211yesmaximal, characteristic, complemented
15#478×C73C211yesmaximal, characteristic, complemented
16C2×#11924028—21no—
17#14556590C2211yescharacteristic
18#14556590C2211yescharacteristic
19#14556590C2211yescharacteristic
20#14556587C2211yescharacteristic
21#14556583C2211yescharacteristic
22#14556577—21no—
23#14556569—21no—
24#14556569—21no—
25#14556566C2211yescharacteristic
26#14556564—21no—
27#14556562C2211yescharacteristic
28#14556556—21no—
29#14556556—21no—
30C4×D292C2211yescharacteristic
31C4×C22⋊D73—21no—
32#14556549C2211yescharacteristic
33#14556549C2211yescharacteristic
34C42×D73C2211yescharacteristic
35#14556525C2211yescharacteristic
36#14556524C2211yescharacteristic
37#14556524C2211yescharacteristic
38#14556523C2211yescharacteristic
39#14556522C2211yescharacteristic
40#14556522C2211yescharacteristic
41C4⋊#10596831C2211yescharacteristic
42#14556513C2211yescharacteristic
43#14556513C2211yescharacteristic
44#14556512C2211yescharacteristic
45#14556512C2211yescharacteristic
46#14556511C2211yescharacteristic
47#14556511C2211yescharacteristic
48#14556503C2211yescharacteristic
49#14556503C2211yescharacteristic
50C8×Dic73C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52#125×C73C2211yescharacteristic
53C4×D4×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic
55#106×C73C2211yescharacteristic
56C4⋊C8×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59#11924028—44no—
60C2×Dic146—21no—
61C2×Dic146—21no—
62C2×Dic146—21no—
63C2×D292—21no—
64C2×D292C2311yescharacteristic
65C2×C22⋊D73—21no—
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C2×C4×D73—21no—
69C2×C4×D73D411yescharacteristic
70C2×C4×D73D411yescharacteristic
71C2×C4×D73C2311yescharacteristic
72C2×#10596831C2311yescharacteristic
73C2×#10596831C2311yescharacteristic
74C4⋊Dic73C2311yescharacteristic
75C4⋊Dic73C2311yescharacteristic
76C4⋊Dic73C2311yescharacteristic
77#11924007—21no—
78#11924007—21no—
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82C22⋊Dic73—21no—
83#11924005—21no—
84#11924005—21no—
85#11924005—21no—
86#11924005—21no—
87C4×Dic73—21no—
88C4×Dic73—21no—
89C4×Dic73D411yescharacteristic
90C4×Dic73D411yescharacteristic
91C4×Dic73C2311yescharacteristic
92C2×D4×C73C2311yescharacteristic
93C22×C4×C73—21no—
94C2×C8×C73C2311yescharacteristic
95C2×C8×C73C2311yescharacteristic
96C4⋊C4×C73—21no—
97C4⋊C4×C73—21no—
98C4⋊C4×C73C2311yescharacteristic
99C4⋊C4×C73C2311yescharacteristic
100C4⋊C4×C73C2311yescharacteristic
101C22⋊C4×C73—21no—
102C42×C73C2311yescharacteristic
103C23×C73—21no—
104C22×D73—21no—
105C22×D73C2×D411yescharacteristic
106D4×C73—21no—
107D4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—42no—
112C2×C4×C73C2×D411yescharacteristic
113C2×C4×C73C2×D411yescharacteristic
114C2×C4×C73C2411yescharacteristic
115C22⋊D73—42no—
116C22⋊D73—42no—
117C22⋊D73—42no—
118C2×Dic73—21no—
119C2×Dic73—21no—
120C2×Dic73—21no—
121C2×Dic73C2×D411yescharacteristic
122C2×Dic73C2×D411yescharacteristic
123C2×Dic73C2×D411yescharacteristic
124D292—21no—
125D292—21no—
126D292—42no—
127C4×D73—21no—
128C4×D73—21no—
129C4×D73—22no—
130C4×D73—22no—
131C4×D73—42no—
132Dic146—42no—
133Dic146—42no—
134Dic146—42no—
135C8×C73—21no—
136C8×C73—21no—
137#10596831—21no—
138#10596831—21no—
139C22×C73—41no—
140C22×C73—41no—
141C22×C73—41no—
142C22×C73C22×D411yescharacteristic
143C2×D73—21no—
144C2×D73—21no—
145C2×D73—21no—
146C2×D73—41no—
147C2×D73—41no—
148C2×D73—41no—
149C4×C73—21no—
150C4×C73—21no—
151C4×C73—41no—
152C4×C73—41no—
153C4×C73—41no—
154C4×C732−1+411yescharacteristic
155C4×C732−1+411yescharacteristic
156Dic73—21no—
157Dic73—41no—
158Dic73—41no—
159Dic73—41no—
160Dic73#13512yes—
161Dic73AGL(1,ℤ/8)12yes—
162C2×C73—81no—
163C2×C73#53611yescharacteristic
164C2×C73C2×#13511yescharacteristic
165C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
166D73—41no—
167D73—81no—
168#3228—731nomaximal, Sylow
169C73#322811yescharacteristic, complemented, Sylow
170#533—731no—
171#532—731no—
172#500—731no—
173#498—731no—
174#486—731no—
175#486—731no—
176#482—731no—
177#482—731no—
178#482—731no—
179#482—731no—
180#478—731no—
181#478—731no—
182#478—731no—
183#478D7311yescharacteristic, complemented
184#431—731no—
185C2×#41—1461no—
186C4⋊Q8—731no—
187C4⋊Q8—731no—
188C4⋊Q8—731no—
189#127—731no—
190#125—731no—
191#125C2×D7311yescharacteristic
192#124—1461no—
193C22⋊Q8—1461no—
194C22⋊Q8—1461no—
195#121—731no—
196#121—731no—
197#121—1461no—
198C4×Q8—1461no—
199C4×Q8—1461no—
200C4×D4—731no—
201C4×D4—1461no—
202C4×D4C2×D7311yescharacteristic
203#117—731no—
204#117—731no—
205C2×C42—731no—
206#107—731no—
207#107—731no—
208#107—731no—
209#107C2×D7311yescharacteristic
210#106—731no—
211#106—731no—
212#106—731no—
213#106C2×D7311yescharacteristic
214C4⋊C8—731no—
215C4⋊C8C2×D7311yescharacteristic
216#102—731no—
217#102—731no—
218#102—731no—
219#102—731no—
220#102—731no—
221#102—731no—
222#102C2×D7311yescharacteristic
223#102C2×D7311yescharacteristic
224C22⋊C8—731no—
225C22⋊C8—731no—
226C4×C8—731no—
227C4×C8—731no—
228#41—2924no—
229C2×Q8—1461no—
230C2×Q8—1461no—
231C2×Q8—1461no—
232C2×D4—731no—
233C2×D4—1461no—
234C2×D4—1461no—
235C2×D4—1461no—
236C2×D4—1461no—
237C2×D4C22×D7311yescharacteristic
238C22×C4—21no—
239C22×C4—731no—
240C22×C4—731no—
241C22×C4—731no—
242C22×C4—1461no—
243C2×C8—731no—
244C2×C8—731no—
245C2×C8C22×D7311yescharacteristic
246C2×C8C22×D7311yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—731no—
250C4⋊C4—731no—
251C4⋊C4—731no—
252C4⋊C4—1461no—
253C4⋊C4—1461no—
254C4⋊C4—1461no—
255C4⋊C4—1461no—
256C4⋊C4—1461no—
257C4⋊C4C22×D7311yescharacteristic
258C4⋊C4C22×D7311yescharacteristic
259C4⋊C4C22×D7311yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—1461no—
262C22⋊C4—1461no—
263C22⋊C4—1461no—
264C22⋊C4—1461no—
265C22⋊C4—1461no—
266C42—731no—
267C42—731no—
268C42—731no—
269C42—1461no—
270C42—1461no—
271C42C22×D7311yescharacteristic
272C23—21no—
273C23—731no—
274C23—1461no—
275Q8—2922no—
276Q8—2922no—
277Q8—2922no—
278D4—21no—
279D4—21no—
280D4—2922no—
281D4—2922no—
282D4—2922no—
283D4—2922no—
284D4—1461no—
285D4—1461no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—42no—
290C2×C4—2922no—
291C2×C4—731no—
292C2×C4—731no—
293C2×C4—731no—
294C2×C4—1462no—
295C2×C4—1462no—
296C2×C4—1461no—
297C2×C4—1461no—
298C2×C4—1461no—
299C2×C4—1461no—
300C2×C4—1461no—
301C2×C4D4×D7311yescharacteristic
302C2×C4D4×D7311yescharacteristic
303C2×C4C23×D7311yescharacteristic
304C8—21no—
305C8—21no—
306C8—1461no—
307C8—1461no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22—2921no—
312C22—2921no—
313C22—2921no—
314C22—1461no—
315C22—1461no—
316C22—1461no—
317C22C2×D4×D7311yescharacteristic
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—2921no—
324C4—2921no—
325C4—2921no—
326C4—732no—
327C4—732no—
328C4—1461no—
329C4#1455663811yescharacteristic
330C4#1455663911yescharacteristic
331C2—81no—
332C2—2921no—
333C2—5841no—
334C2#1798916011yescharacteristic
335C2#135×D7311yescharacteristic
336C2AGL(1,ℤ/8)×D7311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#478×C73C2
socleC22×C73C22×D4
hypercenter#478D73
hypocenterC73#3228
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #17989143C2semidirect
3. #17988991C2semidirect
4. #17988984C2semidirect
5. #17988932C2semidirect
6. #17988932C2semidirect
7. #17988914C2semidirect
8. #17988913C2semidirect
9. #17988910C2semidirect
10. #17988909C2semidirect
11. #17988888C2semidirect
12. #17988887C2semidirect
13. #17988884C2semidirect
14. #17988639C2semidirect
15. #478×C73C2semidirect
169. C73#3228semidirect
183. #478D73semidirect