Finite Group Databasebeta

← #37544562

Subgroups — #37544562

Order 23168.

418 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041792C211yesmaximal, characteristic, complemented
2#26041786C211yesmaximal, characteristic, complemented
3#26041619C211yesmaximal, characteristic, complemented
4#26041617C211yesmaximal, characteristic, complemented
5#26041604C211yesmaximal, characteristic, complemented
6#26041602C211yesmaximal, characteristic, complemented
7#26041534C211yesmaximal, characteristic, complemented
8#26041531C211yesmaximal, characteristic, complemented
9#26041528C211yesmaximal, characteristic, complemented
10#26041522C211yesmaximal, characteristic, complemented
11#26041440C211yesmaximal, characteristic, complemented
12#26041424C211yesmaximal, characteristic, complemented
13#26041423C211yesmaximal, characteristic, complemented
14#26041241C211yesmaximal, characteristic, complemented
15#452×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C22×C4×D181C2211yescharacteristic
18C2×#15668436C2211yescharacteristic, complemented
19C2×#15668434C2211yescharacteristic, complemented
20C2×#15668432C2211yescharacteristic
21C2×#15668432C2211yescharacteristic
22#19153801—21no—
23#19153797—21no—
24#19153792C2211yescharacteristic
25#19153792C2211yescharacteristic
26#19153792C2211yescharacteristic
27#19153791C2211yescharacteristic
28#19153790C2211yescharacteristic
29#19153787C2211yescharacteristic
30#19153787C2211yescharacteristic
31#19153786—21no—
32#19153784—21no—
33#19153778—21no—
34C4×C22⋊D181—21no—
35C4×C22⋊D181—21no—
36#19153776—21no—
37#19153775C2211yescharacteristic
38#19153774C2211yescharacteristic
39#19153750C2211yescharacteristic, complemented
40#19153749C2211yescharacteristic, complemented
41#19153748C2211yescharacteristic, complemented
42#19153747C2211yescharacteristic, complemented
43#19153740C2211yescharacteristic, complemented
44#19153740C2211yescharacteristic, complemented
45#19153740C2211yescharacteristic, complemented
46#19153738C2211yescharacteristic, complemented
47#19153738C2211yescharacteristic, complemented
48#19153737C2211yescharacteristic, complemented
49C22⋊#13089678C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153728C2211yescharacteristic
52C2×#41×C181C2211yescharacteristic
53C2×Q16×C181C2211yescharacteristic, complemented
54C2×SD16×C181C2211yescharacteristic, complemented
55C22⋊Q8×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic, complemented
57#102×C181C2211yescharacteristic, complemented
58C22⋊C8×C181C2211yescharacteristic
59C23×D181D411yescharacteristic
60#15668450—41no—
61#15668450—41no—
62C2×D724—21no—
63C2×D724—21no—
64C2×D724C2311yescharacteristic
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C22×Dic181D411yescharacteristic
69C2×C4×D181—21no—
70C2×C4×D181—41no—
71C2×C4×D181—41no—
72C2×C4×D181D411yescharacteristic
73C2×C4×D181D411yescharacteristic
74C2×C4×D181C2311yescharacteristic
75C2×C4×D181C2311yescharacteristic
76#15668436—41no—
77#15668434—41no—
78#15668432—41no—
79#15668432—41no—
80C2×#13089678C2311yescharacteristic
81C2×#13089678C2311yescharacteristic
82C4⋊Dic181C2311yescharacteristic
83C4⋊Dic181C2311yescharacteristic
84C4⋊Dic181C2311yescharacteristic
85#15668428—21no—
86#15668428—21no—
87#15668428—21no—
88C22⋊Dic181—21no—
89C22⋊Dic181—21no—
90C22⋊Dic181—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426—21no—
97C4×Dic181—21no—
98C4×Dic181—21no—
99#41×C181—41no—
100#41×C181—41no—
101C2×Q8×C181C2311yescharacteristic
102C2×Q8×C181C2311yescharacteristic
103C2×D4×C181—21no—
104C2×D4×C181C2311yescharacteristic
105C22×C4×C181—21no—
106C22×C4×C181C2311yescharacteristic
107Q16×C181—41no—
108SD16×C181—41no—
109C2×C8×C181C2311yescharacteristic
110C2×C8×C181C2311yescharacteristic
111C4⋊C4×C181—21no—
112C4⋊C4×C181C2311yescharacteristic
113C22⋊C4×C181—21no—
114C22×D181—21no—
115C22×D181—41no—
116C22×D181—41no—
117C22×D181—41no—
118C22×D181C2×D411yescharacteristic
119C22×D181C2×D411yescharacteristic
120D724—21no—
121D724—21no—
122D724—42no—
123D724—42no—
124C22⋊D181—42no—
125C22⋊D181—42no—
126C22⋊D181—42no—
127C2×Dic181—21no—
128C2×Dic181—21no—
129C2×Dic181—21no—
130C2×Dic181—41no—
131C2×Dic181C2×D411yescharacteristic
132C2×Dic181C2×D411yescharacteristic
133C4×D181—21no—
134C4×D181—21no—
135C4×D181—21no—
136C4×D181—21no—
137C4×D181—41no—
138C4×D181—41no—
139C4×D181—42no—
140#13089678—21no—
141#13089678—21no—
142C23×C181—21no—
143C23×C181C2×D411yescharacteristic
144Q8×C181—21no—
145Q8×C181—21no—
146Q8×C181—21no—
147Q8×C181—21no—
148D4×C181—21no—
149D4×C181—21no—
150D4×C181—42no—
151C2×C4×C181—21no—
152C2×C4×C181—21no—
153C2×C4×C181—21no—
154C2×C4×C181—21no—
155C2×C4×C181—21no—
156C2×C4×C181—42no—
157C2×C4×C181C2×D411yescharacteristic
158C2×C4×C181C2411yescharacteristic
159C8×C181—21no—
160C8×C181—21no—
161C22×C181—21no—
162C22×C181—21no—
163C22×C181—21no—
164C22×C181—41no—
165C22×C181—41no—
166C22×C181—41no—
167C22×C181C22×D411yescharacteristic
168C2×D181—21no—
169C2×D181—21no—
170C2×D181—21no—
171C2×D181—21no—
172C2×D181—21no—
173C2×D181—21no—
174C2×D181—44no—
175C2×D181—41no—
176C2×D181—41no—
177C2×D181—41no—
178C4×C181—21no—
179C4×C181—41no—
180C4×C181—41no—
181C4×C181—41no—
182C4×C181H(5,𝔽2)11yescharacteristic
183C4×C181H(5,𝔽2)11yescharacteristic
184Dic181—21no—
185Dic181—21no—
186Dic181—41no—
187Dic181—41no—
188Dic181—41no—
189C2×C181—41no—
190C2×C181—81no—
191C2×C181#53411yescharacteristic
192C2×C181#57511yescharacteristic
193C2×C181#57511yescharacteristic
194D181—41no—
195D181—41no—
196D181—81no—
197C181#319711yescharacteristic, complemented, Sylow
198#3197—1811nomaximal, Sylow
199#525—1811no—
200#525—1811no—
201#485—1811no—
202#485—1811no—
203#482—1811no—
204#482—1811no—
205#470—1811no—
206#469—1811no—
207#468—1811no—
208#468—1811no—
209#452—1811no—
210#452D18111yescharacteristic, complemented
211#449—1811no—
212#449—1811no—
213#407—1811no—
214C2×#41—1811no—
215C2×#41C2×D18111yescharacteristic
216C23×C4—1811no—
217C2×Q16C2×D18111yescharacteristic, complemented
218C2×SD16—1811no—
219C2×SD16C2×D18111yescharacteristic, complemented
220C2×D8—1811no—
221C2×M16—1811no—
222C2×M16—1811no—
223#123—3621no—
224#123—3621no—
225C22⋊Q8—1811no—
226C22⋊Q8—1811no—
227C22⋊Q8—1811no—
228C22⋊Q8C2×D18111yescharacteristic
229#121—1811no—
230#121—1811no—
231#121—1811no—
232#121—1811no—
233#120—3621no—
234#120—3621no—
235C4×D4—3621no—
236C4×D4—3621no—
237C4×D4—3621no—
238C4×D4—3621no—
239#117—1811no—
240#117—1811no—
241#107—1811no—
242#107—1811no—
243#106—1811no—
244#106—1811no—
245#103—1811no—
246#103—1811no—
247#103—1811no—
248#103C2×D18111yescharacteristic, complemented
249#102—1811no—
250#102—1811no—
251#102—1811no—
252#102C2×D18111yescharacteristic, complemented
253C22⋊C8—1811no—
254C22⋊C8—1811no—
255C22⋊C8—1811no—
256C22⋊C8C2×D18111yescharacteristic
257C24—1811no—
258#41—41no—
259#41—41no—
260#41—7241no—
261#41—7241no—
262C2×Q8C22×D18111yescharacteristic
263C2×Q8C22×D18111yescharacteristic
264C2×D4—21no—
265C2×D4—3621no—
266C2×D4—3621no—
267C2×D4—3621no—
268C2×D4—3621no—
269C2×D4—3621no—
270C2×D4—1811no—
271C2×D4C22×D18111yescharacteristic
272C22×C4—21no—
273C22×C4—3621no—
274C22×C4—1811no—
275C22×C4—1811no—
276C22×C4—1811no—
277C22×C4—1811no—
278C22×C4—1811no—
279C22×C4—7241no—
280C22×C4—7241no—
281C22×C4C22×D18111yescharacteristic
282Q16—41no—
283SD16—41no—
284SD16—7241no—
285D8—7241no—
286M16—7241no—
287M16—7241no—
288C2×C8—1811no—
289C2×C8—1811no—
290C2×C8C22×D18111yescharacteristic
291C2×C8C22×D18111yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—3621no—
294C4⋊C4—3621no—
295C4⋊C4—3621no—
296C4⋊C4—1811no—
297C4⋊C4—1811no—
298C4⋊C4—1811no—
299C4⋊C4C22×D18111yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—3621no—
302C22⋊C4—3621no—
303C22⋊C4—3621no—
304C22⋊C4—3621no—
305C22⋊C4—3621no—
306C22⋊C4—3621no—
307C22⋊C4—3621no—
308C22⋊C4—3621no—
309C22⋊C4—3621no—
310C42—3621no—
311C42—3621no—
312C23—21no—
313C23—3621no—
314C23—1811no—
315C23—1811no—
316C23—7241no—
317C23—7241no—
318C23—7241no—
319C23D4×D18111yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—3621no—
328D4—3621no—
329D4—7242no—
330D4—7242no—
331D4—7242no—
332D4—7242no—
333D4—7242no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—3621no—
341C2×C4—3621no—
342C2×C4—3621no—
343C2×C4—3621no—
344C2×C4—3621no—
345C2×C4—3621no—
346C2×C4—3621no—
347C2×C4—1811no—
348C2×C4—1811no—
349C2×C4—7241no—
350C2×C4—7241no—
351C2×C4—7242no—
352C2×C4—7241no—
353C2×C4D4×D18111yescharacteristic
354C2×C4C23×D18111yescharacteristic
355C8—21no—
356C8—21no—
357C8—3621no—
358C8—3621no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—3621no—
366C22—3621no—
367C22—3621no—
368C22—3621no—
369C22—3621no—
370C22—3621no—
371C22—7244no—
372C22—7241no—
373C22—7241no—
374C22—7241no—
375C22C2×D4×D18111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—3621no—
381C4—3621no—
382C4—7241no—
383C4—7241no—
384C4—7241no—
385C4#1915386111yescharacteristic
386C4#1915386111yescharacteristic
387C2—41no—
388C2—81no—
389C2—14481no—
390C2—7241no—
391C2—7241no—
392C2#2604183911yescharacteristic
393C2#2604207611yescharacteristic
394C2#2604207811yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#452×C181C2
socleC22×C181C22×D4
hypercenter#452D181
hypocenterC181#3197
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #26041792C2semidirect
2. #26041786C2semidirect
3. #26041619C2semidirect
4. #26041617C2semidirect
5. #26041604C2semidirect
6. #26041602C2semidirect
7. #26041534C2semidirect
8. #26041531C2semidirect
9. #26041528C2semidirect
10. #26041522C2semidirect
11. #26041440C2semidirect
12. #26041424C2semidirect
13. #26041423C2semidirect
14. #26041241C2semidirect
15. #452×C181C2semidirect
18. C2×#15668436C22semidirect
19. C2×#15668434C22semidirect
39. #19153750C22semidirect
40. #19153749C22semidirect
41. #19153748C22semidirect
42. #19153747C22semidirect
43. #19153740C22semidirect
44. #19153740C22semidirect
45. #19153740C22semidirect
46. #19153738C22semidirect
47. #19153738C22semidirect
48. #19153737C22semidirect
53. C2×Q16×C181C22semidirect
54. C2×SD16×C181C22semidirect
56. #103×C181C22semidirect
57. #102×C181C22semidirect
197. C181#3197semidirect
210. #452D181semidirect
217. C2×Q16C2×D181semidirect
219. C2×SD16C2×D181semidirect
248. #103C2×D181semidirect
252. #102C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260417922
#260417862
#260416192
#260416172
#260416042
#260416022
#260415342
#260415312
#260415282
#260415222
#260414402
#260414242
#260414232
#260412412
#452×C1812
#3197181