Finite Group Databasebeta

← #37544571

Subgroups — #37544571

Order 23168.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041858C211yesmaximal, characteristic, complemented
2#26041848C211yesmaximal, characteristic, complemented
3#26041620C211yesmaximal, characteristic, complemented
4#26041599C211yesmaximal, characteristic, complemented
5#26041594C211yesmaximal, characteristic, complemented
6#26041531C211yesmaximal, characteristic, complemented
7#26041526C211yesmaximal, characteristic, complemented
8#26041514C211yesmaximal, characteristic, complemented
9#26041509C211yesmaximal, characteristic, complemented
10#26041432C211yesmaximal, characteristic, complemented
11#26041425C211yesmaximal, characteristic, complemented
12#26041425C211yesmaximal, characteristic, complemented
13#26041412C211yesmaximal, characteristic, complemented
14#26041244C211yesmaximal, characteristic, complemented
15#482×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C2×#15668448C2211yescharacteristic, complemented
18C22×D724C2211yescharacteristic
19C2×#15668438C2211yescharacteristic
20C2×#15668438C2211yescharacteristic
21C2×#15668434C2211yescharacteristic
22C2×#15668434C2211yescharacteristic
23C2×#15668432C2211yescharacteristic, complemented
24C2×C8×D181C2211yescharacteristic, complemented
25#19153813—21no—
26#19153804—21no—
27#19153796C2211yescharacteristic, complemented
28#19153795C2211yescharacteristic
29#19153793—21no—
30#19153791C2211yescharacteristic
31#19153791C2211yescharacteristic
32#19153791C2211yescharacteristic
33#19153791C2211yescharacteristic
34#19153789—21no—
35#19153788—21no—
36#19153787—21no—
37#19153787C2211yescharacteristic, complemented
38#19153786—21no—
39#19153786—21no—
40C4⋊C4×D181C2211yescharacteristic, complemented
41#19153749C2211yescharacteristic, complemented
42#19153747C2211yescharacteristic, complemented
43#19153739C2211yescharacteristic, complemented
44#19153739C2211yescharacteristic, complemented
45#19153738C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153728C2211yescharacteristic, complemented
51#19153728C2211yescharacteristic, complemented
52#121×C181C2211yescharacteristic
53#117×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic, complemented
55#106×C181C2211yescharacteristic, complemented
56#102×C181C2211yescharacteristic, complemented
57#102×C181C2211yescharacteristic, complemented
58C22⋊C8×C181C2211yescharacteristic
59C23×D181—21no—
60#15668449—41no—
61#15668449—41no—
62#15668448—41no—
63#15668448—41no—
64C2×Dic362D411yescharacteristic
65C2×Dic362C2311yescharacteristic
66C2×D724—21no—
67C2×D724—21no—
68C2×D724—21no—
69C2×D724—21no—
70C2×D724—21no—
71C2×D724—41no—
72C2×D724—41no—
73C2×D724D411yescharacteristic
74C2×D724C2311yescharacteristic
75C2×D724C2311yescharacteristic
76C2×C22⋊D181—21no—
77C2×C22⋊D181—21no—
78C2×C22⋊D181D411yescharacteristic
79C2×C22⋊D181D411yescharacteristic
80C22×Dic181—21no—
81C2×C4×D181—21no—
82C2×C4×D181C2311yescharacteristic
83C2×C4×D181C2311yescharacteristic
84#15668438—41no—
85#15668438—41no—
86#15668434—41no—
87#15668434—41no—
88#15668432—41no—
89C2×#13089678C2311yescharacteristic
90C2×#13089678C2311yescharacteristic
91C8×D181—41no—
92C4⋊Dic181—21no—
93C4⋊Dic181C2311yescharacteristic
94#15668428—21no—
95#15668428—21no—
96C22⋊Dic181—21no—
97C22⋊Dic181—21no—
98#15668426—21no—
99#15668426—21no—
100#15668426—21no—
101#15668426—21no—
102#15668426—21no—
103C2×D4×C181—21no—
104C2×D4×C181C2311yescharacteristic
105C22×C4×C181C2311yescharacteristic
106C2×C8×C181C2311yescharacteristic
107C2×C8×C181C2311yescharacteristic
108C4⋊C4×C181C2311yescharacteristic
109C4⋊C4×C181C2311yescharacteristic
110C4⋊C4×C181C2311yescharacteristic
111C22⋊C4×C181—21no—
112C22⋊C4×C181—21no—
113C42×C181—21no—
114C22×D181—21no—
115C22×D181—21no—
116C22×D181—42no—
117C22×D181—81no—
118C22×D181—81no—
119C22×D181C2×D411yescharacteristic
120C22×D181C2×D411yescharacteristic
121Dic362—21no—
122Dic362—21no—
123Dic362—41no—
124D724—21no—
125D724—21no—
126D724—21no—
127D724—21no—
128D724—41no—
129D724—42no—
130D724—81no—
131D724—81no—
132D724—81no—
133D724—81no—
134C22⋊D181—41no—
135C22⋊D181—41no—
136C22⋊D181—42no—
137C22⋊D181—81no—
138C2×Dic181—21no—
139C2×Dic181—21no—
140C2×Dic181—42no—
141C2×Dic181C2×D411yescharacteristic
142C2×Dic181C2×D411yescharacteristic
143C4×D181—21no—
144C4×D181—21no—
145C4×D181—21no—
146C4×D181—21no—
147C4×D181—81no—
148#13089678—21no—
149#13089678—21no—
150C23×C181—21no—
151C23×C181C2×D411yescharacteristic
152D4×C181—21no—
153D4×C181—21no—
154D4×C181—81no—
155C2×C4×C181—21no—
156C2×C4×C181—21no—
157C2×C4×C181—21no—
158C2×C4×C181—21no—
159C2×C4×C181—21no—
160C2×C4×C181C2×D411yescharacteristic
161C2×C4×C181C2411yescharacteristic
162C8×C181—21no—
163C8×C181—21no—
164C22×C181—21no—
165C22×C181—21no—
166C22×C181—21no—
167C22×C181—41no—
168C22×C181—41no—
169C22×C181—41no—
170C22×C181C22×D411yescharacteristic
171C2×D181—21no—
172C2×D181—21no—
173C2×D181—21no—
174C2×D181—21no—
175C2×D181—21no—
176C2×D181—21no—
177C2×D181—41no—
178C2×D181—41no—
179C2×D181—41no—
180C2×D181—41no—
181C2×D181—41no—
182C2×D181—41no—
183C2×D181—84no—
184C4×C181—21no—
185C4×C181—41no—
186C4×C181—41no—
187C4×C181—41no—
188C4×C181H(5,𝔽2)11yescharacteristic
189C4×C181H(5,𝔽2)11yescharacteristic
190Dic181—21no—
191Dic181—21no—
192Dic181—41no—
193Dic181—41no—
194C2×C181—41no—
195C2×C181—81no—
196C2×C181#53411yescharacteristic
197C2×C181#57611yescharacteristic
198C2×C181#57711yescharacteristic
199D181—41no—
200D181—41no—
201D181—81no—
202D181—81no—
203C181#319811yescharacteristic, complemented, Sylow
204#3198—1811nomaximal, Sylow
205#537—1811no—
206#535—1811no—
207#485—1811no—
208#482D18111yescharacteristic, complemented
209#481—1811no—
210#480—1811no—
211#469—1811no—
212#468—1811no—
213#466—1811no—
214#465—1811no—
215#450—1811no—
216#449—1811no—
217#449—1811no—
218#447—1811no—
219#408—1811no—
220C2×#41—1811no—
221C2×#41—1811no—
222C22×D4—1811no—
223C2×SD16—1811no—
224C2×SD16—1811no—
225C2×D8—1811no—
226C2×D8—1811no—
227C2×M16—1811no—
228C22×C8—1811no—
229#127—3621no—
230#124—3621no—
231C22⋊Q8—3621no—
232C22⋊Q8—1811no—
233C22⋊Q8—1811no—
234#121—3621no—
235#121—3621no—
236#121—3621no—
237#121—1811no—
238#121—1811no—
239#121—1811no—
240#121—1811no—
241#121—1811no—
242#121C2×D18111yescharacteristic
243#120—3621no—
244#120—3621no—
245#117C2×D18111yescharacteristic
246C2×C4⋊C4—1811no—
247#107—1811no—
248#107C2×D18111yescharacteristic, complemented
249#106—1811no—
250#106C2×D18111yescharacteristic, complemented
251#103—1811no—
252#103—1811no—
253#102—1811no—
254#102—1811no—
255#102—1811no—
256#102—1811no—
257#102C2×D18111yescharacteristic, complemented
258#102C2×D18111yescharacteristic, complemented
259C22⋊C8—1811no—
260C22⋊C8—1811no—
261C22⋊C8—1811no—
262C22⋊C8C2×D18111yescharacteristic
263C24—3621no—
264#41—7241no—
265#41—7241no—
266#41—7241no—
267#41—7241no—
268C2×Q8—1811no—
269C2×Q8—1811no—
270C2×D4—21no—
271C2×D4—3621no—
272C2×D4—3621no—
273C2×D4—3621no—
274C2×D4—3621no—
275C2×D4—3621no—
276C2×D4—3621no—
277C2×D4—3621no—
278C2×D4—1811no—
279C2×D4—1811no—
280C2×D4—1811no—
281C2×D4—1811no—
282C2×D4—1811no—
283C2×D4—7241no—
284C2×D4—7241no—
285C2×D4C22×D18111yescharacteristic
286C22×C4—3621no—
287C22×C4—3621no—
288C22×C4—1811no—
289C22×C4—1811no—
290C22×C4C22×D18111yescharacteristic
291SD16—7241no—
292SD16—7241no—
293D8—7241no—
294D8—7241no—
295M16—7241no—
296C2×C8—1811no—
297C2×C8—1811no—
298C2×C8—7241no—
299C2×C8C22×D18111yescharacteristic
300C2×C8C22×D18111yescharacteristic
301C4⋊C4—3621no—
302C4⋊C4—3621no—
303C4⋊C4—3621no—
304C4⋊C4—1811no—
305C4⋊C4C22×D18111yescharacteristic
306C4⋊C4C22×D18111yescharacteristic
307C4⋊C4C22×D18111yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—3621no—
311C22⋊C4—3621no—
312C22⋊C4—3621no—
313C22⋊C4—3621no—
314C22⋊C4—3621no—
315C22⋊C4—3621no—
316C22⋊C4—3621no—
317C42—21no—
318C23—21no—
319C23—3621no—
320C23—3621no—
321C23—14481no—
322C23—14481no—
323C23—1811no—
324C23—1811no—
325C23—7242no—
326C23D4×D18111yescharacteristic
327Q8—3621no—
328Q8—3621no—
329Q8—7241no—
330D4—21no—
331D4—21no—
332D4—81no—
333D4—3621no—
334D4—3621no—
335D4—3621no—
336D4—3621no—
337D4—14481no—
338D4—14481no—
339D4—14481no—
340D4—14481no—
341D4—14481no—
342D4—7241no—
343D4—7242no—
344D4—7241no—
345D4—7241no—
346D4—7242no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—3621no—
353C2×C4—3621no—
354C2×C4—3621no—
355C2×C4—3621no—
356C2×C4—3621no—
357C2×C4—3621no—
358C2×C4—14481no—
359C2×C4—1811no—
360C2×C4—1811no—
361C2×C4—7242no—
362C2×C4D4×D18111yescharacteristic
363C2×C4C23×D18111yescharacteristic
364C8—21no—
365C8—21no—
366C8—3621no—
367C8—3621no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—3621no—
375C22—3621no—
376C22—3621no—
377C22—3621no—
378C22—3621no—
379C22—3621no—
380C22—14484no—
381C22—7241no—
382C22—7241no—
383C22—7241no—
384C22—7241no—
385C22—7241no—
386C22—7241no—
387C22C2×D4×D18111yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—3621no—
393C4—3621no—
394C4—7241no—
395C4—7241no—
396C4#1915386211yescharacteristic
397C4#1915386211yescharacteristic
398C2—41no—
399C2—81no—
400C2—14481no—
401C2—14481no—
402C2—7241no—
403C2—7241no—
404C2#2604184011yescharacteristic
405C2#2604208311yescharacteristic
406C2#2604208611yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#482×C181C2
socleC22×C181C22×D4
hypercenter#482D181
hypocenterC181#3198
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #26041858C2semidirect
2. #26041848C2semidirect
3. #26041620C2semidirect
4. #26041599C2semidirect
5. #26041594C2semidirect
6. #26041531C2semidirect
7. #26041526C2semidirect
8. #26041514C2semidirect
9. #26041509C2semidirect
10. #26041432C2semidirect
11. #26041425C2semidirect
12. #26041425C2semidirect
13. #26041412C2semidirect
14. #26041244C2semidirect
15. #482×C181C2semidirect
17. C2×#15668448C22semidirect
23. C2×#15668432C22semidirect
24. C2×C8×D181C22semidirect
27. #19153796C22semidirect
37. #19153787C22semidirect
40. C4⋊C4×D181C22semidirect
41. #19153749C22semidirect
42. #19153747C22semidirect
43. #19153739C22semidirect
44. #19153739C22semidirect
50. #19153728C22semidirect
51. #19153728C22semidirect
54. #107×C181C22semidirect
55. #106×C181C22semidirect
56. #102×C181C22semidirect
57. #102×C181C22semidirect
203. C181#3198semidirect
208. #482D181semidirect
248. #107C2×D181semidirect
250. #106C2×D181semidirect
257. #102C2×D181semidirect
258. #102C2×D181semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#260418582
#260418482
#260416202
#260415992
#260415942
#260415312
#260415262
#260415142
#260415092
#260414322
#260414252
#260414122
#260412442
#482×C1812
#3198181