Finite Group Databasebeta

← #22620077

Subgroups — #22620077

Order 9344.

430 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989132C211yesmaximal, characteristic, complemented
2#17989055C211yesmaximal, characteristic, complemented
3#17988911C211yesmaximal, characteristic, complemented
4#17988871C211yesmaximal, characteristic, complemented
5#17988866C211yesmaximal, characteristic, complemented
6#17988786C211yesmaximal, characteristic, complemented
7#17988781C211yesmaximal, characteristic, complemented
8#17988734C211yesmaximal, characteristic, complemented
9#17988730C211yesmaximal, characteristic, complemented
10#17988698C211yesmaximal, characteristic, complemented
11#17988696C211yesmaximal, characteristic, complemented
12#17988686C211yesmaximal, characteristic, complemented
13#17988684C211yesmaximal, characteristic, complemented
14#17988641C211yesmaximal, characteristic, complemented
15#482×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C2×#11924027—21no—
18C2×#11924017C2211yescharacteristic
19C2×#11924016C2211yescharacteristic
20C2×D584C2211yescharacteristic
21C2×#11924013C2211yescharacteristic
22#14556590C2211yescharacteristic
23#14556587C2211yescharacteristic
24#14556577—21no—
25#14556565C2211yescharacteristic
26#14556563—21no—
27#14556556C2211yescharacteristic
28#14556556C2211yescharacteristic
29D4×Dic73C2211yescharacteristic
30#14556553C2211yescharacteristic
31#14556553C2211yescharacteristic
32#14556553C2211yescharacteristic
33#14556551—21no—
34#14556551—21no—
35#14556551—21no—
36#14556548—21no—
37C2×C4×Dic73C2211yescharacteristic
38C42×D73—21no—
39#14556524C2211yescharacteristic
40#14556522C2211yescharacteristic
41#14556520C2211yescharacteristic
42#14556520C2211yescharacteristic
43#14556516C2211yescharacteristic
44#14556514C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556511C2211yescharacteristic
47#14556511C2211yescharacteristic
48#14556511C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556501C2211yescharacteristic
51#14556501C2211yescharacteristic
52#121×C73C2211yescharacteristic
53#117×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic
55#106×C73C2211yescharacteristic
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic
59#11924028—22no—
60#11924028—22no—
61#11924027—44no—
62C2×Dic146—21no—
63C2×Dic146C2311yescharacteristic
64C2×D292C2311yescharacteristic
65C2×D292C2311yescharacteristic
66C2×C22⋊D73—21no—
67C2×C22⋊D73—21no—
68C2×C22⋊D73—21no—
69C2×C22⋊D73—21no—
70C22×Dic73—21no—
71C22×Dic73D411yescharacteristic
72C22×Dic73D411yescharacteristic
73C2×C4×D73—21no—
74C2×C4×D73—21no—
75C2×C4×D73—21no—
76C2×C4×D73—21no—
77#11924017—22no—
78#11924016—22no—
79D584—22no—
80#11924013—22no—
81C2×#10596831C2311yescharacteristic
82C2×#10596831C2311yescharacteristic
83C4⋊Dic73C2311yescharacteristic
84#11924007—21no—
85#11924007—21no—
86#11924007—21no—
87C22⋊Dic73—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92C4×Dic73—21no—
93C4×Dic73—21no—
94C4×Dic73D411yescharacteristic
95C4×Dic73D411yescharacteristic
96C4×Dic73C2311yescharacteristic
97C4×Dic73C2311yescharacteristic
98C2×D4×C73—21no—
99C2×D4×C73C2311yescharacteristic
100C22×C4×C73C2311yescharacteristic
101C2×C8×C73C2311yescharacteristic
102C2×C8×C73C2311yescharacteristic
103C4⋊C4×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C4⋊C4×C73C2311yescharacteristic
106C22⋊C4×C73—21no—
107C22⋊C4×C73—21no—
108C42×C73—21no—
109C23×C73—21no—
110C23×C73C2×D411yescharacteristic
111C22×D73—21no—
112C22×D73—21no—
113D4×C73—21no—
114D4×C73—21no—
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×C73C2×D411yescharacteristic
122C2×C4×C73C2411yescharacteristic
123C22⋊D73—24no—
124C22⋊D73—42no—
125C22⋊D73—42no—
126C22⋊D73—42no—
127C2×Dic73—21no—
128C2×Dic73—22no—
129C2×Dic73—21no—
130C2×Dic73—41no—
131C2×Dic73—42no—
132C2×Dic73C2×D411yescharacteristic
133C2×Dic73C2×D411yescharacteristic
134C2×Dic73C2×D411yescharacteristic
135C2×Dic73C2×D411yescharacteristic
136D292—21no—
137D292—21no—
138D292—21no—
139D292#4112yescomplemented
140C4×D73—24no—
141C4×D73—42no—
142C4×D73—42no—
143C4×D73—42no—
144Dic146—21no—
145Dic146—42no—
146Dic146#4112yescomplemented
147C8×C73—21no—
148C8×C73—21no—
149#10596831—21no—
150#10596831—21no—
151C22×C73—21no—
152C22×C73—21no—
153C22×C73—21no—
154C22×C73—41no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73C22×D411yescharacteristic
158C2×D73—22no—
159C2×D73—41no—
160C2×D73—41no—
161C2×D73—41no—
162C2×D73—41no—
163C2×D73—41no—
164C4×C73—21no—
165C4×C73—41no—
166C4×C73—41no—
167C4×C73—41no—
168C4×C73C2×#4111yescharacteristic
169C4×C73C2×#4111yescharacteristic
170Dic73—22no—
171Dic73—21no—
172Dic73—21no—
173Dic73—21no—
174Dic73—41no—
175Dic73AGL(1,ℤ/8)12yes—
176C2×C73—41no—
177C2×C73—81no—
178C2×C73#52511yescharacteristic
179C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
180C2×C73#57511yescharacteristic
181D73—42no—
182D73—81no—
183#3115—731nomaximal, Sylow
184C73#311511yescharacteristic, complemented, Sylow
185#532—731no—
186C4×#41—731no—
187#482—731no—
188#482D7311yescharacteristic, complemented
189#475—731no—
190#474—731no—
191#460—731no—
192#459—731no—
193#449—731no—
194#449—731no—
195#442—731no—
196#442—731no—
197#440—731no—
198#440—731no—
199#432—731no—
200C2×#41—731no—
201C2×#41—1461no—
202C2×SD16—731no—
203C2×SD16—731no—
204C2×D8—731no—
205C2×D8—731no—
206C4⋊Q8—731no—
207#127—731no—
208#124—1461no—
209#121—731no—
210#121—1461no—
211#121C2×D7311yescharacteristic
212C4×Q8—731no—
213C4×Q8—731no—
214C4×D4—731no—
215C4×D4—731no—
216C4×D4—731no—
217C4×D4—731no—
218C4×D4—1461no—
219C4×D4—1461no—
220C4×D4—1461no—
221#117—1461no—
222#117C2×D7311yescharacteristic
223C2×C42—731no—
224C2×C42—1461no—
225#107—731no—
226#107C2×D7311yescharacteristic
227#106—731no—
228#106C2×D7311yescharacteristic
229C4⋊C8—731no—
230C4⋊C8—731no—
231#103—731no—
232#103—731no—
233#102—731no—
234#102—731no—
235#102—731no—
236#102—731no—
237#102C2×D7311yescharacteristic
238#102C2×D7311yescharacteristic
239C22⋊C8—731no—
240C22⋊C8C2×D7311yescharacteristic
241#97—731no—
242#97—731no—
243#41—2924no—
244#41—1462no—
245#41—1462no—
246C2×Q8—731no—
247C2×Q8—1461no—
248C2×D4—21no—
249C2×D4—731no—
250C2×D4—731no—
251C2×D4—1461no—
252C2×D4—1461no—
253C2×D4—1461no—
254C2×D4—1461no—
255C2×D4C22×D7311yescharacteristic
256C22×C4—731no—
257C22×C4—731no—
258C22×C4—1461no—
259C22×C4—1461no—
260C22×C4—1461no—
261C22×C4—1461no—
262C22×C4—1461no—
263C22×C4C22×D7311yescharacteristic
264SD16—1462no—
265SD16—1462no—
266D8—1462no—
267D8—1462no—
268C2×C8—731no—
269C2×C8—731no—
270C2×C8C22×D7311yescharacteristic
271C2×C8C22×D7311yescharacteristic
272C4⋊C4—731no—
273C4⋊C4—1461no—
274C4⋊C4—1461no—
275C4⋊C4—1461no—
276C4⋊C4C22×D7311yescharacteristic
277C4⋊C4C22×D7311yescharacteristic
278C4⋊C4C22×D7311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—1461no—
282C22⋊C4—1461no—
283C22⋊C4—1461no—
284C22⋊C4—1461no—
285C22⋊C4—1461no—
286C42—21no—
287C42—731no—
288C42—731no—
289C42—731no—
290C42—731no—
291C42—1461no—
292C42—1461no—
293C23—21no—
294C23—1461no—
295C23—1461no—
296C23D4×D7311yescharacteristic
297Q8—2922no—
298Q8—732no—
299Q8—1461no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—2922no—
304D4—2922no—
305D4—2922no—
306D4—732no—
307D4—1464no—
308D4—1461no—
309D4—1461no—
310D4—1461no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—2922no—
317C2×C4—2922no—
318C2×C4—2922no—
319C2×C4—2922no—
320C2×C4—2921no—
321C2×C4—731no—
322C2×C4—731no—
323C2×C4—731no—
324C2×C4—731no—
325C2×C4—1464no—
326C2×C4—1461no—
327C2×C4—1462no—
328C2×C4—1461no—
329C2×C4D4×D7311yescharacteristic
330C2×C4C23×D7311yescharacteristic
331C8—21no—
332C8—21no—
333C8—1461no—
334C8—1461no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—2921no—
342C22—2921no—
343C22—2921no—
344C22—2921no—
345C22—2921no—
346C22—1462no—
347C22C2×D4×D7311yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—2921no—
353C4—732no—
354C4—1461no—
355C4—1461no—
356C4—1462no—
357C4—1461no—
358C4#41×D7311yescharacteristic
359C4#41×D7311yescharacteristic
360C2—41no—
361C2—81no—
362C2—2922no—
363C2—5841no—
364C2#1798909511yescharacteristic
365C2AGL(1,ℤ/8)×D7311yescharacteristic
366C2#1798938411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#482×C73C2
socleC22×C73C22×D4
hypercenter#482D73
hypocenterC73#3115
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #17989132C2semidirect
2. #17989055C2semidirect
3. #17988911C2semidirect
4. #17988871C2semidirect
5. #17988866C2semidirect
6. #17988786C2semidirect
7. #17988781C2semidirect
8. #17988734C2semidirect
9. #17988730C2semidirect
10. #17988698C2semidirect
11. #17988696C2semidirect
12. #17988686C2semidirect
13. #17988684C2semidirect
14. #17988641C2semidirect
15. #482×C73C2semidirect
139. D292#41semidirect
146. Dic146#41semidirect
184. C73#3115semidirect
188. #482D73semidirect