Finite Group Databasebeta

← #37544802

Subgroups — #37544802

Order 23168.

364 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041889C211yesmaximal, characteristic, complemented
2#26041850C211yesmaximal, characteristic
3#26041670C211yesmaximal, characteristic, complemented
4#26041657C211yesmaximal, characteristic, complemented
5#26041646C211yesmaximal, characteristic, complemented
6#26041632C211yesmaximal, characteristic, complemented
7#26041500C211yesmaximal, characteristic, complemented
8#26041499C211yesmaximal, characteristic, complemented
9#26041488C211yesmaximal, characteristic, complemented
10#26041487C211yesmaximal, characteristic, complemented
11#26041441C211yesmaximal, characteristic
12#26041437C211yesmaximal, characteristic, complemented
13#26041434C211yesmaximal, characteristic, complemented
14#26041337C211yesmaximal, characteristic, complemented
15#452×C181C211yesmaximal, characteristic
16C22×Dic362C2211yescharacteristic
17C2×Dic724C2211yescharacteristic
18C2×Dic724C2211yescharacteristic
19C2×#15668439C2211yescharacteristic
20C2×#15668439C2211yescharacteristic
21C2×#15668439C2211yescharacteristic
22C2×#15668437C2211yescharacteristic
23#19153814C2211yescharacteristic
24#19153814C2211yescharacteristic
25#19153814C2211yescharacteristic
26#19153809—21no—
27#19153809—21no—
28#19153807—21no—
29#19153807C2211yescharacteristic
30#19153806—21no—
31#19153803C2211yescharacteristic
32#19153803C2211yescharacteristic
33#19153797—21no—
34#19153797—21no—
35#19153795—21no—
36#19153795—21no—
37#19153795C2211yescharacteristic
38Q8×Dic181C2211yescharacteristic
39#19153781C2211yescharacteristic
40#19153775C2211yescharacteristic
41#19153745C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153741C2211yescharacteristic
44#19153741C2211yescharacteristic
45#19153740C2211yescharacteristic
46#19153739C2211yescharacteristic
47#19153739C2211yescharacteristic
48#19153737C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153726C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C2×#41×C181C2211yescharacteristic
53C2×Q16×C181C2211yescharacteristic
54C2×SD16×C181C2211yescharacteristic
55C22⋊Q8×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362—41no—
61C2×Dic362—41no—
62C2×Dic362C2311yescharacteristic
63C2×Dic362C2311yescharacteristic
64C2×Dic362C2311yescharacteristic
65C22×Dic181—21no—
66Dic724—41no—
67Dic724—41no—
68#15668439—41no—
69#15668439—41no—
70#15668439—41no—
71#15668437—41no—
72C2×#13089678C2311yescharacteristic
73C2×#13089678C2311yescharacteristic
74C4⋊Dic181—21no—
75C4⋊Dic181—21no—
76C4⋊Dic181D411yescharacteristic
77C4⋊Dic181D411yescharacteristic
78C4⋊Dic181C2311yescharacteristic
79#15668428—21no—
80#15668428—21no—
81#15668428—21no—
82#15668428—21no—
83#15668428—21no—
84#15668428—21no—
85#15668428—21no—
86#15668428—21no—
87#15668428—21no—
88C22⋊Dic181—21no—
89C22⋊Dic181—21no—
90C22⋊Dic181—21no—
91C22⋊Dic181—21no—
92C22⋊Dic181—21no—
93C22⋊Dic181D411yescharacteristic
94C22⋊Dic181D411yescharacteristic
95C4×Dic181—21no—
96C4×Dic181—21no—
97C4×Dic181C2311yescharacteristic
98C4×Dic181C2311yescharacteristic
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—
114Dic362—21no—
115Dic362—21no—
116Dic362—21no—
117Dic362—21no—
118Dic362—21no—
119Dic362—21no—
120Dic362—42no—
121C2×Dic181—21no—
122C2×Dic181—21no—
123C2×Dic181—21no—
124C2×Dic181—21no—
125C2×Dic181—42no—
126C2×Dic181C2×D411yescharacteristic
127C2×Dic181C2×D411yescharacteristic
128C2×Dic181C2×D411yescharacteristic
129C2×Dic181C2×D411yescharacteristic
130#13089678—21no—
131#13089678—21no—
132C23×C181—21no—
133C23×C181C2×D411yescharacteristic
134Q8×C181—21no—
135Q8×C181—21no—
136Q8×C181—21no—
137Q8×C181—21no—
138D4×C181—21no—
139D4×C181—21no—
140D4×C181—42no—
141C2×C4×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—42no—
147C2×C4×C181C2×D411yescharacteristic
148C2×C4×C181C2411yescharacteristic
149C8×C181—21no—
150C8×C181—21no—
151C22×C181—21no—
152C22×C181—21no—
153C22×C181—21no—
154C22×C181—41no—
155C22×C181—41no—
156C22×C181—41no—
157C22×C181C22×D411yescharacteristic
158C4×C181—21no—
159C4×C181—41no—
160C4×C181—41no—
161C4×C181—41no—
162C4×C181H(5,𝔽2)11yescharacteristic
163C4×C181H(5,𝔽2)11yescharacteristic
164Dic181—21no—
165Dic181—21no—
166Dic181—21no—
167Dic181—21no—
168Dic181—41no—
169Dic181—41no—
170Dic181—41no—
171Dic181—41no—
172C2×C181—41no—
173C2×C181—81no—
174C2×C181#53511yescharacteristic
175C2×C181#57811yescharacteristic
176C2×C181#57811yescharacteristic
177C181#322311yescharacteristic, complemented, Sylow
178#3223—1811nomaximal, Sylow
179#541—1811no—
180#536—1811no—
181#497—1811no—
182#494—1811no—
183#491—1811no—
184#488—1811no—
185#464—1811no—
186#464—1811no—
187#462—1811no—
188#462—1811no—
189#452—1811no—
190#452D18111yescharacteristic
191#451—1811no—
192#451—1811no—
193#433—1811no—
194C2×#41C2×D18111yescharacteristic
195C22×Q8—1811no—
196C2×Q16—1811no—
197C2×Q16—1811no—
198C2×Q16—1811no—
199C2×Q16—1811no—
200C2×Q16—1811no—
201C2×Q16C2×D18111yescharacteristic
202C2×SD16—1811no—
203C2×SD16C2×D18111yescharacteristic
204C4⋊Q8—1811no—
205C4⋊Q8—1811no—
206C4⋊Q8—1811no—
207#126—3621no—
208#126—3621no—
209#125—3621no—
210#125—3621no—
211#125—1811no—
212#124—1811no—
213#124—1811no—
214#123—3621no—
215#123—3621no—
216C22⋊Q8—3621no—
217C22⋊Q8—3621no—
218C22⋊Q8—1811no—
219C22⋊Q8C2×D18111yescharacteristic
220C4×Q8—1811no—
221C4×Q8—1811no—
222#117—1811no—
223C4⋊C8—1811no—
224C4⋊C8—1811no—
225#103—1811no—
226#103—1811no—
227#103—1811no—
228#103—1811no—
229#103—1811no—
230#103C2×D18111yescharacteristic
231#102—1811no—
232#102C2×D18111yescharacteristic
233C22⋊C8—1811no—
234C22⋊C8C2×D18111yescharacteristic
235#97—1811no—
236C4×C8—1811no—
237#41—41no—
238#41—41no—
239C2×Q8—3621no—
240C2×Q8—1811no—
241C2×Q8—1811no—
242C2×Q8—1811no—
243C2×Q8—7241no—
244C2×Q8—7241no—
245C2×Q8C22×D18111yescharacteristic
246C2×Q8C22×D18111yescharacteristic
247C2×D4—21no—
248C2×D4C22×D18111yescharacteristic
249C22×C4—21no—
250C22×C4—3621no—
251C22×C4C22×D18111yescharacteristic
252Q16—41no—
253Q16—7241no—
254Q16—7241no—
255Q16—7241no—
256Q16—7241no—
257Q16—7241no—
258SD16—41no—
259SD16—7241no—
260C2×C8—1811no—
261C2×C8—1811no—
262C2×C8C22×D18111yescharacteristic
263C2×C8C22×D18111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—3621no—
266C4⋊C4—3621no—
267C4⋊C4—3621no—
268C4⋊C4—3621no—
269C4⋊C4—3621no—
270C4⋊C4—3621no—
271C4⋊C4—3621no—
272C4⋊C4—3621no—
273C4⋊C4—3621no—
274C4⋊C4—3621no—
275C4⋊C4—3621no—
276C4⋊C4—1811no—
277C4⋊C4—1811no—
278C4⋊C4—1811no—
279C4⋊C4C22×D18111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—3621no—
282C22⋊C4—3621no—
283C22⋊C4—3621no—
284C22⋊C4—3621no—
285C22⋊C4—3621no—
286C22⋊C4—1811no—
287C22⋊C4—1811no—
288C42—3621no—
289C42—3621no—
290C42—1811no—
291C42—1811no—
292C23—21no—
293C23D4×D18111yescharacteristic
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—3621no—
299Q8—3621no—
300Q8—3621no—
301Q8—3621no—
302Q8—3621no—
303Q8—3621no—
304Q8—7242no—
305D4—21no—
306D4—21no—
307D4—42no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—3621no—
315C2×C4—3621no—
316C2×C4—3621no—
317C2×C4—3621no—
318C2×C4—1811no—
319C2×C4—1811no—
320C2×C4—1811no—
321C2×C4—1811no—
322C2×C4—7242no—
323C2×C4D4×D18111yescharacteristic
324C2×C4C23×D18111yescharacteristic
325C8—21no—
326C8—21no—
327C8—3621no—
328C8—3621no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22C2×D4×D18111yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—3621no—
341C4—3621no—
342C4—3621no—
343C4—3621no—
344C4—7241no—
345C4—7241no—
346C4—7241no—
347C4—7241no—
348C4#1915386111yescharacteristic
349C4#1915386111yescharacteristic
350C2—41no—
351C2—81no—
352C2#2604184411yescharacteristic
353C2#2604209311yescharacteristic
354C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#452×C181C2
socleC22×C181C22×D4
prime radicalC2×#41×C181C22
hypercenter#452D181
hypocenterC181#3223
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. #26041889C2semidirect
3. #26041670C2semidirect
4. #26041657C2semidirect
5. #26041646C2semidirect
6. #26041632C2semidirect
7. #26041500C2semidirect
8. #26041499C2semidirect
9. #26041488C2semidirect
10. #26041487C2semidirect
12. #26041437C2semidirect
13. #26041434C2semidirect
14. #26041337C2semidirect
177. C181#3223semidirect

Maximal subgroups

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

subgroupindex
#260418892
#260418502
#260416702
#260416572
#260416462
#260416322
#260415002
#260414992
#260414882
#260414872
#260414412
#260414372
#260414342
#260413372
#452×C1812
#3223181