Finite Group Databasebeta

← #37544614

Subgroups — #37544614

Order 23168.

378 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041853C211yesmaximal, characteristic
2#26041852C211yesmaximal, characteristic
3#26041621C211yesmaximal, characteristic, complemented
4#26041619C211yesmaximal, characteristic, complemented
5#26041618C211yesmaximal, characteristic, complemented
6#26041617C211yesmaximal, characteristic, complemented
7#26041536C211yesmaximal, characteristic, complemented
8#26041534C211yesmaximal, characteristic, complemented
9#26041519C211yesmaximal, characteristic, complemented
10#26041517C211yesmaximal, characteristic, complemented
11#26041435C211yesmaximal, characteristic, complemented
12#26041433C211yesmaximal, characteristic, complemented
13#26041433C211yesmaximal, characteristic, complemented
14#26041244C211yesmaximal, characteristic
15#451×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C2×Q8×D181C2211yescharacteristic
18C2×#15668439C2211yescharacteristic
19C2×#15668439C2211yescharacteristic
20C2×#15668432C2211yescharacteristic
21C2×C8×D181C2211yescharacteristic
22#19153815—21no—
23#19153814—21no—
24#19153805—21no—
25#19153802—21no—
26#19153801—21no—
27#19153799—21no—
28#19153799—21no—
29#19153798—21no—
30#19153796C2211yescharacteristic
31#19153795C2211yescharacteristic
32#19153792C2211yescharacteristic
33#19153792C2211yescharacteristic
34#19153792C2211yescharacteristic
35#19153792C2211yescharacteristic
36#19153792C2211yescharacteristic
37#19153775C2211yescharacteristic
38#19153774C2211yescharacteristic
39#19153750C2211yescharacteristic
40#19153749C2211yescharacteristic
41#19153748C2211yescharacteristic
42#19153747C2211yescharacteristic
43#19153741C2211yescharacteristic
44#19153741C2211yescharacteristic
45#19153740C2211yescharacteristic
46#19153740C2211yescharacteristic
47#19153740C2211yescharacteristic
48#19153740C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153728C2211yescharacteristic
52C22×Q8×C181C2211yescharacteristic
53C2×Q16×C181C2211yescharacteristic
54C2×Q16×C181C2211yescharacteristic
55C22⋊Q8×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59#15668449—41no—
60#15668449—41no—
61C2×Dic362—21no—
62C2×Dic362D411yescharacteristic
63C2×Dic362C2311yescharacteristic
64Q8×D181—41no—
65Q8×D181—41no—
66C2×D724D411yescharacteristic
67C2×C22⋊D181D411yescharacteristic
68C2×C22⋊D181D411yescharacteristic
69C2×C4×D181—21no—
70C2×C4×D181C2311yescharacteristic
71C2×C4×D181C2311yescharacteristic
72#15668439—41no—
73#15668439—41no—
74#15668432—41no—
75C2×#13089678C2311yescharacteristic
76C2×#13089678C2311yescharacteristic
77C8×D181—41no—
78C4⋊Dic181—21no—
79C4⋊Dic181C2311yescharacteristic
80C4⋊Dic181C2311yescharacteristic
81C4⋊Dic181C2311yescharacteristic
82#15668428—21no—
83#15668428—21no—
84#15668428—21no—
85#15668428—21no—
86#15668428—21no—
87#15668428—21no—
88C22⋊Dic181—21no—
89C22⋊Dic181—21no—
90#15668426—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—
99C2×Q8×C181—21no—
100C2×Q8×C181—41no—
101C2×Q8×C181—41no—
102C2×Q8×C181C2311yescharacteristic
103C2×Q8×C181C2311yescharacteristic
104C2×Q8×C181C2311yescharacteristic
105C22×C4×C181—21no—
106C22×C4×C181C2311yescharacteristic
107Q16×C181—41no—
108Q16×C181—41no—
109C2×C8×C181C2311yescharacteristic
110C2×C8×C181C2311yescharacteristic
111C4⋊C4×C181—21no—
112C4⋊C4×C181C2311yescharacteristic
113C22⋊C4×C181—21no—
114C22×D181C2×D411yescharacteristic
115C22×D181C2×D411yescharacteristic
116Dic362—21no—
117Dic362—21no—
118Dic362—41no—
119Dic362—42no—
120D724—41no—
121C22⋊D181—41no—
122C22⋊D181—41no—
123C2×Dic181—21no—
124C2×Dic181—21no—
125C2×Dic181—21no—
126C2×Dic181—21no—
127C2×Dic181C2×D411yescharacteristic
128C2×Dic181C2×D411yescharacteristic
129C4×D181—21no—
130C4×D181—21no—
131C4×D181—21no—
132C4×D181—21no—
133C4×D181—42no—
134#13089678—21no—
135#13089678—21no—
136C23×C181C2×D411yescharacteristic
137Q8×C181—21no—
138Q8×C181—21no—
139Q8×C181—21no—
140Q8×C181—21no—
141Q8×C181—21no—
142Q8×C181—21no—
143Q8×C181—42no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—21no—
147C2×C4×C181—21no—
148C2×C4×C181—21no—
149C2×C4×C181—21no—
150C2×C4×C181—42no—
151C2×C4×C181C2×D411yescharacteristic
152C2×C4×C181C2411yescharacteristic
153C8×C181—21no—
154C8×C181—21no—
155C22×C181—21no—
156C22×C181—21no—
157C22×C181—21no—
158C22×C181C22×D411yescharacteristic
159C2×D181—21no—
160C2×D181—21no—
161C2×D181—21no—
162C2×D181—21no—
163C2×D181—21no—
164C2×D181—21no—
165C4×C181—21no—
166C4×C181—41no—
167C4×C181—41no—
168C4×C181—41no—
169C4×C181—41no—
170C4×C181H(5,𝔽2)11yescharacteristic
171C4×C181H(5,𝔽2)11yescharacteristic
172Dic181—21no—
173Dic181—21no—
174Dic181—41no—
175Dic181—41no—
176Dic181—41no—
177Dic181—41no—
178C2×C181—41no—
179C2×C181#53411yescharacteristic
180C2×C181#57811yescharacteristic
181C2×C181#57811yescharacteristic
182D181—41no—
183D181—41no—
184C181#320211yescharacteristic, complemented, Sylow
185#3202—1811nomaximal, Sylow
186#536—1811no—
187#536—1811no—
188#485—1811no—
189#485—1811no—
190#485—1811no—
191#485—1811no—
192#470—1811no—
193#470—1811no—
194#467—1811no—
195#467—1811no—
196#451—1811no—
197#451—1811no—
198#451—1811no—
199#451D18111yescharacteristic, complemented
200#408—1811no—
201C2×#41—1811no—
202C22×Q8—1811no—
203C22×Q8C2×D18111yescharacteristic
204C2×Q16—1811no—
205C2×Q16—1811no—
206C2×Q16C2×D18111yescharacteristic
207C2×Q16C2×D18111yescharacteristic
208C2×M16—1811no—
209C22×C8—1811no—
210C4⋊Q8—3621no—
211C4⋊Q8—3621no—
212#124—3621no—
213#124—3621no—
214#123—3621no—
215#123—3621no—
216#123—3621no—
217#123—3621no—
218C22⋊Q8—1811no—
219C22⋊Q8—1811no—
220C22⋊Q8—1811no—
221C22⋊Q8—1811no—
222C22⋊Q8—1811no—
223C22⋊Q8—1811no—
224C22⋊Q8—1811no—
225C22⋊Q8C2×D18111yescharacteristic
226#117—1811no—
227#117—1811no—
228#107—1811no—
229#107—1811no—
230#106—1811no—
231#106—1811no—
232#103—1811no—
233#103—1811no—
234#103—1811no—
235#103—1811no—
236#103—1811no—
237#103—1811no—
238#103C2×D18111yescharacteristic
239#103C2×D18111yescharacteristic
240C22⋊C8—1811no—
241C22⋊C8—1811no—
242C22⋊C8—1811no—
243C22⋊C8C2×D18111yescharacteristic
244#41—7241no—
245#41—7241no—
246C2×Q8—21no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—3621no—
250C2×Q8—1811no—
251C2×Q8—1811no—
252C2×Q8—7241no—
253C2×Q8—7241no—
254C2×Q8C22×D18111yescharacteristic
255C2×Q8C22×D18111yescharacteristic
256C2×Q8C22×D18111yescharacteristic
257C2×D4—1811no—
258C2×D4—1811no—
259C2×D4—1811no—
260C22×C4—21no—
261C22×C4—3621no—
262C22×C4—1811no—
263C22×C4—1811no—
264C22×C4C22×D18111yescharacteristic
265Q16—41no—
266Q16—41no—
267Q16—7241no—
268Q16—7241no—
269M16—7241no—
270C2×C8—1811no—
271C2×C8—1811no—
272C2×C8—7241no—
273C2×C8C22×D18111yescharacteristic
274C2×C8C22×D18111yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—3621no—
277C4⋊C4—3621no—
278C4⋊C4—3621no—
279C4⋊C4—3621no—
280C4⋊C4—3621no—
281C4⋊C4—3621no—
282C4⋊C4—3621no—
283C4⋊C4—1811no—
284C4⋊C4—1811no—
285C4⋊C4—1811no—
286C4⋊C4C22×D18111yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—3621no—
289C22⋊C4—3621no—
290C22⋊C4—3621no—
291C22⋊C4—3621no—
292C22⋊C4—3621no—
293C22⋊C4—3621no—
294C22⋊C4—3621no—
295C22⋊C4—3621no—
296C22⋊C4—3621no—
297C42—3621no—
298C42—3621no—
299C23—1811no—
300C23—1811no—
301C23D4×D18111yescharacteristic
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308Q8—42no—
309Q8—3621no—
310Q8—3621no—
311Q8—7241no—
312Q8—7242no—
313D4—7241no—
314D4—7241no—
315D4—7241no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—3621no—
324C2×C4—3621no—
325C2×C4—3621no—
326C2×C4—3621no—
327C2×C4—3621no—
328C2×C4—3621no—
329C2×C4—3621no—
330C2×C4—3621no—
331C2×C4—1811no—
332C2×C4—1811no—
333C2×C4—7242no—
334C2×C4D4×D18111yescharacteristic
335C2×C4C23×D18111yescharacteristic
336C8—21no—
337C8—21no—
338C8—3621no—
339C8—3621no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—3621no—
344C22—3621no—
345C22—3621no—
346C22—3621no—
347C22—3621no—
348C22—3621no—
349C22C2×D4×D18111yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—3621no—
356C4—3621no—
357C4—7241no—
358C4—7241no—
359C4—7241no—
360C4—7241no—
361C4#1915386111yescharacteristic
362C4#1915386111yescharacteristic
363C2—41no—
364C2—7241no—
365C2—7241no—
366C2#2604183911yescharacteristic
367C2#2604209211yescharacteristic
368C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#451×C181C2
socleC22×C181C22×D4
prime radicalC2×#15668449C22
hypercenter#451D181
hypocenterC181#3202
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #26041621C2semidirect
4. #26041619C2semidirect
5. #26041618C2semidirect
6. #26041617C2semidirect
7. #26041536C2semidirect
8. #26041534C2semidirect
9. #26041519C2semidirect
10. #26041517C2semidirect
11. #26041435C2semidirect
12. #26041433C2semidirect
13. #26041433C2semidirect
15. #451×C181C2semidirect
184. C181#3202semidirect
199. #451D181semidirect

Maximal subgroups

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

subgroupindex
#260418532
#260418522
#260416212
#260416192
#260416182
#260416172
#260415362
#260415342
#260415192
#260415172
#260414352
#260414332
#260412442
#451×C1812
#3202181