Finite Group Databasebeta

← #37544832

Subgroups — #37544832

Order 23168.

376 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#26041900C211yesmaximal, characteristic, complemented
2#26041855C211yesmaximal, characteristic, complemented
3#26041673C211yesmaximal, characteristic, complemented
4#26041663C211yesmaximal, characteristic, complemented
5#26041639C211yesmaximal, characteristic, complemented
6#26041630C211yesmaximal, characteristic, complemented
7#26041502C211yesmaximal, characteristic, complemented
8#26041495C211yesmaximal, characteristic, complemented
9#26041490C211yesmaximal, characteristic, complemented
10#26041485C211yesmaximal, characteristic, complemented
11#26041443C211yesmaximal, characteristic, complemented
12#26041437C211yesmaximal, characteristic, complemented
13#26041426C211yesmaximal, characteristic
14#26041420C211yesmaximal, characteristic, complemented
15#433×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C22×Dic362C2211yescharacteristic
18C2×Dic724C2211yescharacteristic
19C2×Dic724C2211yescharacteristic
20C2×Dic724C2211yescharacteristic
21C2×#15668438C2211yescharacteristic
22C2×#15668438C2211yescharacteristic
23C2×#15668438C2211yescharacteristic
24C2×#15668438C2211yescharacteristic
25C2×D1448C2211yescharacteristic
26#19153816C2211yescharacteristic
27#19153816C2211yescharacteristic
28#19153816C2211yescharacteristic
29#19153811—21no—
30#19153804C2211yescharacteristic
31#19153804C2211yescharacteristic
32#19153804C2211yescharacteristic
33#19153802—21no—
34#19153800—21no—
35#19153800—21no—
36#19153798—21no—
37#19153796—21no—
38#19153796—21no—
39#19153795C2211yescharacteristic
40#19153794—21no—
41#19153790C2211yescharacteristic
42C4×Dic362C2211yescharacteristic
43C4×D724C2211yescharacteristic
44#19153741C2211yescharacteristic
45#19153741C2211yescharacteristic
46#19153741C2211yescharacteristic
47#19153741C2211yescharacteristic
48#19153741C2211yescharacteristic
49#19153741C2211yescharacteristic
50#19153738C2211yescharacteristic
51#19153738C2211yescharacteristic
52#117×C181C2211yescharacteristic
53C4⋊C8×C181C2211yescharacteristic
54C4⋊C8×C181C2211yescharacteristic
55C22⋊C8×C181C2211yescharacteristic
56C22⋊C8×C181C2211yescharacteristic
57#97×C181C2211yescharacteristic
58C4×C8×C181C2211yescharacteristic
59#15668449—41no—
60#15668449—41no—
61C2×Dic362—21no—
62C2×Dic362—21no—
63C2×Dic362—41no—
64C2×Dic362—41no—
65C2×Dic362C2311yescharacteristic
66C2×Dic362C2311yescharacteristic
67C2×Dic362C2311yescharacteristic
68C2×Dic362C2311yescharacteristic
69C2×D724C2311yescharacteristic
70C2×D724C2311yescharacteristic
71C2×C22⋊D181—21no—
72C2×C22⋊D181—21no—
73C22×Dic181—21no—
74C2×C4×D181—21no—
75C2×C4×D181—21no—
76Dic724—41no—
77Dic724—41no—
78Dic724—41no—
79#15668438—41no—
80#15668438—41no—
81#15668438—41no—
82#15668438—41no—
83D1448—41no—
84C4⋊Dic181—21no—
85C4⋊Dic181—21no—
86C4⋊Dic181—21no—
87C4⋊Dic181—21no—
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—
116Dic362—21no—
117Dic362—21no—
118Dic362—21no—
119Dic362—21no—
120Dic362—21no—
121Dic362—21no—
122Dic362—21no—
123Dic362—21no—
124Dic362—42no—
125Dic362—81no—
126D724—21no—
127D724—21no—
128D724—21no—
129D724—21no—
130C22⋊D181—42no—
131C22⋊D181—81no—
132C2×Dic181—21no—
133C2×Dic181—21no—
134C2×Dic181—21no—
135C2×Dic181—21no—
136C2×Dic181—21no—
137C2×Dic181—21no—
138C2×Dic181—42no—
139C4×D181—42no—
140C4×D181—81no—
141C23×C181C2×D411yescharacteristic
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181C2×D411yescharacteristic
145C2×C4×C181C2×D411yescharacteristic
146C2×C4×C181C2×D411yescharacteristic
147C2×C4×C181C2×D411yescharacteristic
148C2×C4×C181C2×D411yescharacteristic
149C2×C4×C181C2411yescharacteristic
150C8×C181—21no—
151C8×C181—21no—
152C8×C181—21no—
153C8×C181—21no—
154C22×C181—21no—
155C22×C181—21no—
156C22×C181—21no—
157C22×C181C22×D411yescharacteristic
158C2×D181—41no—
159C2×D181—41no—
160C2×D181—41no—
161C2×D181—41no—
162C2×D181—41no—
163C2×D181—41no—
164C4×C181—21no—
165C4×C181—21no—
166C4×C181—21no—
167C4×C181—21no—
168C4×C181—21no—
169C4×C181H(5,𝔽2)11yescharacteristic
170C4×C181H(5,𝔽2)11yescharacteristic
171Dic181—41no—
172Dic181—41no—
173Dic181—41no—
174Dic181—41no—
175Dic181—41no—
176Dic181—41no—
177C2×C181—41no—
178C2×C181#53511yescharacteristic
179C2×C181#57711yescharacteristic
180C2×C181#57811yescharacteristic
181D181—81no—
182D181—81no—
183C181#322511yescharacteristic, complemented, Sylow
184#3225—1811nomaximal, Sylow
185#542—1811no—
186#536—1811no—
187#497—1811no—
188#495—1811no—
189#489—1811no—
190#487—1811no—
191#464—1811no—
192#463—1811no—
193#462—1811no—
194#461—1811no—
195#452—1811no—
196#451—1811no—
197#449—1811no—
198#448—1811no—
199#433D18111yescharacteristic, complemented
200C2×#41—1811no—
201C22×Q8—1811no—
202C2×Q16—1811no—
203C2×Q16—1811no—
204C2×Q16—1811no—
205C2×SD16—1811no—
206C2×SD16—1811no—
207C2×SD16—1811no—
208C2×SD16—1811no—
209C2×D8—1811no—
210C4⋊Q8—1811no—
211C4⋊Q8—1811no—
212C4⋊Q8—1811no—
213#126—3621no—
214#124—3621no—
215#124—1811no—
216#124—1811no—
217#124—1811no—
218#123—3621no—
219#123—3621no—
220#123—3621no—
221C22⋊Q8—3621no—
222C22⋊Q8—3621no—
223C22⋊Q8—3621no—
224C22⋊Q8—1811no—
225#121—1811no—
226C4×Q8—1811no—
227C4×D4—1811no—
228#117C2×D18111yescharacteristic
229C4⋊C8C2×D18111yescharacteristic
230C4⋊C8C2×D18111yescharacteristic
231#103—1811no—
232#103—1811no—
233#103—1811no—
234#103—1811no—
235#103—1811no—
236#103—1811no—
237#102—1811no—
238#102—1811no—
239C22⋊C8C2×D18111yescharacteristic
240C22⋊C8C2×D18111yescharacteristic
241#97C2×D18111yescharacteristic
242C4×C8C2×D18111yescharacteristic
243#41—7241no—
244#41—7241no—
245C2×Q8—3621no—
246C2×Q8—3621no—
247C2×Q8—1811no—
248C2×Q8—1811no—
249C2×Q8—1811no—
250C2×Q8—1811no—
251C2×Q8—7241no—
252C2×Q8—7241no—
253C2×D4—3621no—
254C2×D4—3621no—
255C2×D4—1811no—
256C2×D4—1811no—
257C22×C4—3621no—
258C22×C4—3621no—
259C22×C4—3621no—
260C22×C4C22×D18111yescharacteristic
261Q16—7241no—
262Q16—7241no—
263Q16—7241no—
264SD16—7241no—
265SD16—7241no—
266SD16—7241no—
267SD16—7241no—
268D8—7241no—
269C2×C8C22×D18111yescharacteristic
270C2×C8C22×D18111yescharacteristic
271C2×C8C22×D18111yescharacteristic
272C2×C8C22×D18111yescharacteristic
273C4⋊C4—3621no—
274C4⋊C4—3621no—
275C4⋊C4—3621no—
276C4⋊C4—3621no—
277C4⋊C4—3621no—
278C4⋊C4—3621no—
279C4⋊C4—3621no—
280C4⋊C4—1811no—
281C4⋊C4—1811no—
282C4⋊C4D72411yescharacteristic
283C4⋊C4D72411yescharacteristic
284C22⋊C4—3621no—
285C22⋊C4—3621no—
286C22⋊C4—3621no—
287C22⋊C4—3621no—
288C22⋊C4—3621no—
289C22⋊C4—3621no—
290C22⋊C4—3621no—
291C22⋊C4—3621no—
292C22⋊C4—3621no—
293C22⋊C4D72411yescharacteristic
294C22⋊C4D72411yescharacteristic
295C42—3621no—
296C42C22×D18111yescharacteristic
297C42C22×D18111yescharacteristic
298C23—3621no—
299C23—3621no—
300C23C2×D72411yescharacteristic
301Q8—3621no—
302Q8—3621no—
303Q8—3621no—
304Q8—3621no—
305Q8—3621no—
306Q8—3621no—
307Q8—3621no—
308Q8—3621no—
309Q8—14481no—
310Q8—7242no—
311D4—3621no—
312D4—3621no—
313D4—3621no—
314D4—3621no—
315D4—14481no—
316D4—7242no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—3621no—
320C2×C4—3621no—
321C2×C4—3621no—
322C2×C4—3621no—
323C2×C4—3621no—
324C2×C4—3621no—
325C2×C4—14481no—
326C2×C4—7242no—
327C2×C4—7242no—
328C2×C4C2×D72411yescharacteristic
329C2×C4C2×D72411yescharacteristic
330C2×C4C2×D72411yescharacteristic
331C2×C4C2×D72411yescharacteristic
332C2×C4C2×D72411yescharacteristic
333C2×C4C23×D18111yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—7241no—
342C22—7241no—
343C22—7241no—
344C22—7241no—
345C22—7241no—
346C22—7241no—
347C22C22×D72411yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—7241no—
354C4—7241no—
355C4—7241no—
356C4—7241no—
357C4—7241no—
358C4—7241no—
359C4#1915386211yescharacteristic
360C4#1915386211yescharacteristic
361C2—41no—
362C2—14481no—
363C2—14481no—
364C2#2604184811yescharacteristic
365C2#2604209111yescharacteristic
366C2#2604209611yescharacteristic
subgroupG/H
centerC22C22×D724
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#433×C181C2
socleC22×C181C22×D4
prime radical#26041426C2
hypercenter#433D181
hypocenterC181#3225
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. #26041855C2semidirect
3. #26041673C2semidirect
4. #26041663C2semidirect
5. #26041639C2semidirect
6. #26041630C2semidirect
7. #26041502C2semidirect
8. #26041495C2semidirect
9. #26041490C2semidirect
10. #26041485C2semidirect
11. #26041443C2semidirect
12. #26041437C2semidirect
14. #26041420C2semidirect
15. #433×C181C2semidirect
183. C181#3225semidirect
199. #433D181semidirect

Maximal subgroups

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

subgroupindex
#260419002
#260418552
#260416732
#260416632
#260416392
#260416302
#260415022
#260414952
#260414902
#260414852
#260414432
#260414372
#260414262
#260414202
#433×C1812
#3225181