Finite Group Databasebeta

← #37544817

Subgroups — #37544817

Order 23168.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041900C211yesmaximal, characteristic, complemented
2#26041848C211yesmaximal, characteristic, complemented
3#26041668C211yesmaximal, characteristic, complemented
4#26041663C211yesmaximal, characteristic, complemented
5#26041639C211yesmaximal, characteristic, complemented
6#26041626C211yesmaximal, characteristic, complemented
7#26041502C211yesmaximal, characteristic, complemented
8#26041495C211yesmaximal, characteristic, complemented
9#26041480C211yesmaximal, characteristic, complemented
10#26041475C211yesmaximal, characteristic, complemented
11#26041443C211yesmaximal, characteristic, complemented
12#26041432C211yesmaximal, characteristic, complemented
13#26041426C211yesmaximal, characteristic, complemented
14#26041415C211yesmaximal, characteristic, complemented
15#433×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C22×D724C2211yescharacteristic
18C2×Dic724C2211yescharacteristic, complemented
19C2×#15668438C2211yescharacteristic
20C2×#15668438C2211yescharacteristic
21C2×#15668438C2211yescharacteristic, complemented
22C2×#15668438C2211yescharacteristic, complemented
23C2×D1448C2211yescharacteristic
24C2×D1448C2211yescharacteristic
25C2×D1448C2211yescharacteristic, complemented
26#19153816C2211yescharacteristic, complemented
27#19153813C2211yescharacteristic
28#19153813C2211yescharacteristic
29#19153811—21no—
30#19153804C2211yescharacteristic
31#19153804C2211yescharacteristic
32#19153804C2211yescharacteristic, complemented
33#19153802—21no—
34#19153798—21no—
35#19153795C2211yescharacteristic
36#19153794—21no—
37#19153791—21no—
38#19153791—21no—
39#19153790C2211yescharacteristic
40#19153786—21no—
41#19153786—21no—
42C4×Dic362C2211yescharacteristic, complemented
43C4×D724C2211yescharacteristic, complemented
44#19153741C2211yescharacteristic, complemented
45#19153741C2211yescharacteristic, complemented
46#19153738C2211yescharacteristic
47#19153738C2211yescharacteristic
48#19153738C2211yescharacteristic
49#19153738C2211yescharacteristic
50#19153738C2211yescharacteristic, complemented
51#19153738C2211yescharacteristic, complemented
52#117×C181C2211yescharacteristic
53C4⋊C8×C181C2211yescharacteristic, complemented
54C4⋊C8×C181C2211yescharacteristic, complemented
55C22⋊C8×C181C2211yescharacteristic
56C22⋊C8×C181C2211yescharacteristic
57#97×C181C2211yescharacteristic, complemented
58C4×C8×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60#15668449—41no—
61#15668449—41no—
62C2×Dic362—21no—
63C2×Dic362C2311yescharacteristic
64C2×Dic362C2311yescharacteristic
65C2×D724—21no—
66C2×D724—21no—
67C2×D724—21no—
68C2×D724—21no—
69C2×D724—21no—
70C2×D724—41no—
71C2×D724—41no—
72C2×D724C2311yescharacteristic
73C2×D724C2311yescharacteristic
74C2×D724C2311yescharacteristic
75C2×D724C2311yescharacteristic
76C2×C22⋊D181—21no—
77C2×C22⋊D181—21no—
78C2×C4×D181—21no—
79C2×C4×D181—21no—
80Dic724—41no—
81#15668438—41no—
82#15668438—41no—
83#15668438—41no—
84#15668438—41no—
85D1448—41no—
86D1448—41no—
87D1448—41no—
88C4⋊Dic181—21no—
89C4⋊Dic181C2311yescharacteristic
90C4⋊Dic181C2311yescharacteristic
91#15668428—21no—
92#15668428—21no—
93C22⋊Dic181—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426—21no—
97#15668426—21no—
98#15668426—21no—
99#15668426—21no—
100#15668426—21no—
101#15668426—21no—
102C4×Dic181—21no—
103C22×C4×C181C2311yescharacteristic
104C2×C8×C181C2311yescharacteristic
105C2×C8×C181C2311yescharacteristic
106C2×C8×C181C2311yescharacteristic
107C2×C8×C181C2311yescharacteristic
108C4⋊C4×C181D411yescharacteristic
109C4⋊C4×C181D411yescharacteristic
110C22⋊C4×C181D411yescharacteristic
111C22⋊C4×C181D411yescharacteristic
112C42×C181C2311yescharacteristic
113C42×C181C2311yescharacteristic
114C22×D181—21no—
115C22×D181—21no—
116C22×D181—21no—
117C22×D181—21no—
118C22×D181—42no—
119C22×D181—81no—
120C22×D181—81no—
121Dic362—21no—
122Dic362—21no—
123Dic362—21no—
124Dic362—21no—
125Dic362—81no—
126D724—21no—
127D724—21no—
128D724—21no—
129D724—21no—
130D724—21no—
131D724—21no—
132D724—21no—
133D724—21no—
134D724—42no—
135D724—81no—
136D724—81no—
137D724—81no—
138D724—81no—
139C22⋊D181—42no—
140C22⋊D181—81no—
141C2×Dic181—21no—
142C2×Dic181—21no—
143C2×Dic181—21no—
144C2×Dic181—21no—
145C4×D181—42no—
146C4×D181—81no—
147C23×C181C2×D411yescharacteristic
148C2×C4×C181—21no—
149C2×C4×C181—21no—
150C2×C4×C181C2×D411yescharacteristic
151C2×C4×C181C2×D411yescharacteristic
152C2×C4×C181C2×D411yescharacteristic
153C2×C4×C181C2×D411yescharacteristic
154C2×C4×C181C2×D411yescharacteristic
155C2×C4×C181C2411yescharacteristic
156C8×C181—21no—
157C8×C181—21no—
158C8×C181—21no—
159C8×C181—21no—
160C22×C181—21no—
161C22×C181—21no—
162C22×C181—21no—
163C22×C181C22×D411yescharacteristic
164C2×D181—41no—
165C2×D181—41no—
166C2×D181—41no—
167C2×D181—41no—
168C2×D181—41no—
169C2×D181—41no—
170C2×D181—41no—
171C2×D181—41no—
172C2×D181—41no—
173C2×D181—41no—
174C2×D181—41no—
175C2×D181—41no—
176C2×D181—84no—
177C4×C181—21no—
178C4×C181—21no—
179C4×C181—21no—
180C4×C181—21no—
181C4×C181—21no—
182C4×C181H(5,𝔽2)11yescharacteristic
183C4×C181H(5,𝔽2)11yescharacteristic
184Dic181—41no—
185Dic181—41no—
186Dic181—41no—
187Dic181—41no—
188C2×C181—41no—
189C2×C181#53511yescharacteristic
190C2×C181#57611yescharacteristic
191C2×C181#57711yescharacteristic
192D181—81no—
193D181—81no—
194D181—81no—
195D181—81no—
196C181#322411yescharacteristic, complemented, Sylow
197#3224—1811nomaximal, Sylow
198#542—1811no—
199#535—1811no—
200#496—1811no—
201#495—1811no—
202#489—1811no—
203#486—1811no—
204#464—1811no—
205#463—1811no—
206#460—1811no—
207#459—1811no—
208#452—1811no—
209#450—1811no—
210#449—1811no—
211#447—1811no—
212#433D18111yescharacteristic, complemented
213C2×#41—1811no—
214C22×D4—1811no—
215C2×Q16—1811no—
216C2×SD16—1811no—
217C2×SD16—1811no—
218C2×SD16—1811no—
219C2×SD16—1811no—
220C2×D8—1811no—
221C2×D8—1811no—
222C2×D8—1811no—
223C4⋊Q8—1811no—
224#127—1811no—
225#127—1811no—
226#126—3621no—
227#124—3621no—
228#124—1811no—
229#124—1811no—
230#124—1811no—
231#123—3621no—
232C22⋊Q8—3621no—
233C22⋊Q8—1811no—
234#121—3621no—
235#121—3621no—
236#121—1811no—
237#120—3621no—
238#120—3621no—
239C4×Q8—1811no—
240C4×D4—1811no—
241#117C2×D18111yescharacteristic
242C4⋊C8C2×D18111yescharacteristic, complemented
243C4⋊C8C2×D18111yescharacteristic, complemented
244#103—1811no—
245#103—1811no—
246#102—1811no—
247#102—1811no—
248#102—1811no—
249#102—1811no—
250#102—1811no—
251#102—1811no—
252C22⋊C8C2×D18111yescharacteristic
253C22⋊C8C2×D18111yescharacteristic
254#97C2×D18111yescharacteristic, complemented
255C4×C8C2×D18111yescharacteristic, complemented
256C24—3621no—
257#41—7241no—
258#41—7241no—
259C2×Q8—3621no—
260C2×Q8—1811no—
261C2×Q8—1811no—
262C2×D4—3621no—
263C2×D4—3621no—
264C2×D4—3621no—
265C2×D4—3621no—
266C2×D4—3621no—
267C2×D4—3621no—
268C2×D4—3621no—
269C2×D4—1811no—
270C2×D4—1811no—
271C2×D4—1811no—
272C2×D4—1811no—
273C2×D4—7241no—
274C2×D4—7241no—
275C22×C4—3621no—
276C22×C4—3621no—
277C22×C4C22×D18111yescharacteristic
278Q16—7241no—
279SD16—7241no—
280SD16—7241no—
281SD16—7241no—
282SD16—7241no—
283D8—7241no—
284D8—7241no—
285D8—7241no—
286C2×C8C22×D18111yescharacteristic
287C2×C8C22×D18111yescharacteristic
288C2×C8C22×D18111yescharacteristic
289C2×C8C22×D18111yescharacteristic
290C4⋊C4—3621no—
291C4⋊C4—3621no—
292C4⋊C4—3621no—
293C4⋊C4—1811no—
294C4⋊C4—1811no—
295C4⋊C4D72411yescharacteristic
296C4⋊C4D72411yescharacteristic
297C22⋊C4—3621no—
298C22⋊C4—3621no—
299C22⋊C4—3621no—
300C22⋊C4—3621no—
301C22⋊C4—3621no—
302C22⋊C4—3621no—
303C22⋊C4—3621no—
304C22⋊C4—3621no—
305C22⋊C4—3621no—
306C22⋊C4D72411yescharacteristic
307C22⋊C4D72411yescharacteristic
308C42—3621no—
309C42C22×D18111yescharacteristic
310C42C22×D18111yescharacteristic
311C23—3621no—
312C23—3621no—
313C23—3621no—
314C23—3621no—
315C23—14481no—
316C23—14481no—
317C23—7242no—
318C23C2×D72411yescharacteristic
319Q8—3621no—
320Q8—3621no—
321Q8—3621no—
322Q8—3621no—
323Q8—14481no—
324D4—3621no—
325D4—3621no—
326D4—3621no—
327D4—3621no—
328D4—3621no—
329D4—3621no—
330D4—3621no—
331D4—3621no—
332D4—14481no—
333D4—14481no—
334D4—14481no—
335D4—14481no—
336D4—14481no—
337D4—7242no—
338D4—7242no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—3621no—
342C2×C4—3621no—
343C2×C4—3621no—
344C2×C4—3621no—
345C2×C4—14481no—
346C2×C4—7242no—
347C2×C4C2×D72411yescharacteristic
348C2×C4C2×D72411yescharacteristic
349C2×C4C2×D72411yescharacteristic
350C2×C4C2×D72411yescharacteristic
351C2×C4C2×D72411yescharacteristic
352C2×C4C23×D18111yescharacteristic
353C8—21no—
354C8—21no—
355C8—21no—
356C8—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—14484no—
361C22—7241no—
362C22—7241no—
363C22—7241no—
364C22—7241no—
365C22—7241no—
366C22—7241no—
367C22—7241no—
368C22—7241no—
369C22—7241no—
370C22—7241no—
371C22—7241no—
372C22—7241no—
373C22C22×D72411yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—7241no—
380C4—7241no—
381C4—7241no—
382C4—7241no—
383C4#1915386211yescharacteristic
384C4#1915386211yescharacteristic
385C2—41no—
386C2—14481no—
387C2—14481no—
388C2—14481no—
389C2—14481no—
390C2#2604184811yescharacteristic
391C2#2604208411yescharacteristic
392C2#2604209111yescharacteristic
subgroupG/H
centerC22C22×D724
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#433×C181C2
socleC22×C181C22×D4
hypercenter#433D181
hypocenterC181#3224
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #26041900C2semidirect
2. #26041848C2semidirect
3. #26041668C2semidirect
4. #26041663C2semidirect
5. #26041639C2semidirect
6. #26041626C2semidirect
7. #26041502C2semidirect
8. #26041495C2semidirect
9. #26041480C2semidirect
10. #26041475C2semidirect
11. #26041443C2semidirect
12. #26041432C2semidirect
13. #26041426C2semidirect
14. #26041415C2semidirect
15. #433×C181C2semidirect
18. C2×Dic724C22semidirect
21. C2×#15668438C22semidirect
22. C2×#15668438C22semidirect
25. C2×D1448C22semidirect
26. #19153816C22semidirect
32. #19153804C22semidirect
42. C4×Dic362C22semidirect
43. C4×D724C22semidirect
44. #19153741C22semidirect
45. #19153741C22semidirect
50. #19153738C22semidirect
51. #19153738C22semidirect
53. C4⋊C8×C181C22semidirect
54. C4⋊C8×C181C22semidirect
57. #97×C181C22semidirect
58. C4×C8×C181C22semidirect
196. C181#3224semidirect
212. #433D181semidirect
242. C4⋊C8C2×D181semidirect
243. C4⋊C8C2×D181semidirect
254. #97C2×D181semidirect
255. C4×C8C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419002
#260418482
#260416682
#260416632
#260416392
#260416262
#260415022
#260414952
#260414802
#260414752
#260414432
#260414322
#260414262
#260414152
#433×C1812
#3224181