Finite Group Databasebeta

← #37545593

Subgroups — #37545593

Order 23168.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041984C211yesmaximal, characteristic
2Q8×C22⋊D181C211yesmaximal, characteristic
3#26041628C211yesmaximal, characteristic, complemented
4#26041614C211yesmaximal, characteristic, complemented
5#26041613C211yesmaximal, characteristic, complemented
6#26041572C211yesmaximal, characteristic, complemented
7#26041520C211yesmaximal, characteristic, complemented
8#26041519C211yesmaximal, characteristic, complemented
9#26041488C211yesmaximal, characteristic, complemented
10#26041436C211yesmaximal, characteristic, complemented
11#26041435C211yesmaximal, characteristic, complemented
12#26041371C211yesmaximal, characteristic, complemented
13C8×C22⋊D181C211yesmaximal, characteristic
14#103×D181C211yesmaximal, characteristic, complemented
15C2×#103×C181C211yesmaximal, characteristic, complemented
16C2×Q8×D181C2211yescharacteristic
17C2×Dic724C2211yescharacteristic
18C2×#15668439C2211yescharacteristic
19C2×#15668439C2211yescharacteristic
20C2×C8×D181C2211yescharacteristic
21#19153815C2211yescharacteristic
22#19153814—21no—
23#19153814C2211yescharacteristic
24#19153806—21no—
25#19153796C2211yescharacteristic
26#19153795—21no—
27#19153795—21no—
28#19153795C2211yescharacteristic
29#19153795C2211yescharacteristic
30#19153794—21no—
31#19153792—21no—
32#19153792C2211yescharacteristic
33Q8×Dic181C2211yescharacteristic
34#19153781C2211yescharacteristic
35C4×C22⋊D181—21no—
36C4×C22⋊D181—21no—
37C4×C22⋊D181C2211yescharacteristic
38C4⋊C4×D181C2211yescharacteristic
39#19153750C2211yescharacteristic
40#19153749C2211yescharacteristic
41#19153749C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153741C2211yescharacteristic
44#19153741C2211yescharacteristic
45#19153740C2211yescharacteristic
46#19153740C2211yescharacteristic
47#19153739C2211yescharacteristic
48#19153739C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153728C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C22×Q8×C181C2211yescharacteristic
53C22×C8×C181C2211yescharacteristic
54C2×C4⋊C4×C181C2211yescharacteristic
55#103×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#103×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362—21no—
61C2×Dic362C2311yescharacteristic
62C2×Dic362C2311yescharacteristic
63Q8×D181—22no—
64Q8×D181—41no—
65C2×C22⋊D181D411yescharacteristic
66C2×C4×D181—21no—
67C2×C4×D181—21no—
68C2×C4×D181C2311yescharacteristic
69Dic724—41no—
70#15668439—22no—
71#15668439—41no—
72C2×#13089678C2311yescharacteristic
73C2×#13089678C2311yescharacteristic
74C8×D181—41no—
75C4⋊Dic181—21no—
76C4⋊Dic181—21no—
77C4⋊Dic181C2311yescharacteristic
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#15668428D411yescharacteristic
88C22⋊Dic181—21no—
89C22⋊Dic181—21no—
90C22⋊Dic181D411yescharacteristic
91#15668426—21no—
92#15668426—21no—
93#15668426D411yescharacteristic
94C4×Dic181—21no—
95C4×Dic181—21no—
96C4×Dic181C2311yescharacteristic
97C2×Q8×C181—21no—
98C2×Q8×C181—22no—
99C2×Q8×C181—41no—
100C2×Q8×C181C2311yescharacteristic
101C2×Q8×C181C2311yescharacteristic
102C22×C4×C181—21no—
103C22×C4×C181—21no—
104C22×C4×C181C2311yescharacteristic
105C2×C8×C181—41no—
106C2×C8×C181C2311yescharacteristic
107C2×C8×C181C2311yescharacteristic
108C4⋊C4×C181—21no—
109C4⋊C4×C181C2311yescharacteristic
110C4⋊C4×C181C2311yescharacteristic
111C22×D181C2×D411yescharacteristic
112Dic362—21no—
113Dic362—21no—
114Dic362—21no—
115Dic362—21no—
116Dic362—42no—
117Dic362—81no—
118C22⋊D181Q1614yescomplemented
119C2×Dic181—21no—
120C2×Dic181—21no—
121C2×Dic181—21no—
122C2×Dic181—21no—
123C2×Dic181C2×D411yescharacteristic
124C2×Dic181C2×D411yescharacteristic
125C2×Dic181C2×D411yescharacteristic
126C4×D181—21no—
127C4×D181—21no—
128C4×D181—42no—
129C4×D181—81no—
130#13089678—21no—
131#13089678—21no—
132C23×C181C2×D411yescharacteristic
133Q8×C181—21no—
134Q8×C181—21no—
135Q8×C181—21no—
136Q8×C181—42no—
137Q8×C181#4112yes—
138C2×C4×C181—21no—
139C2×C4×C181—21no—
140C2×C4×C181—21no—
141C2×C4×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181—42no—
145C2×C4×C181—81no—
146C2×C4×C181C2×D411yescharacteristic
147C2×C4×C181C2411yescharacteristic
148C8×C181—21no—
149C8×C181—21no—
150C22×C181—21no—
151C22×C181—21no—
152C22×C181C2×Q1612yes—
153C22×C181C22×D411yescharacteristic
154C2×D181—21no—
155C2×D181—21no—
156C2×D181C2×Q1612yes—
157C4×C181—21no—
158C4×C181—22no—
159C4×C181—41no—
160C4×C181—41no—
161C4×C181—41no—
162C4×C181C2×#4111yescharacteristic
163C4×C181H(5,𝔽2)11yescharacteristic
164Dic181—21no—
165Dic181—21no—
166Dic181—41no—
167Dic181—41no—
168Dic181—41no—
169Dic181—41no—
170Dic181C2×Q1612yes—
171C2×C181—22no—
172C2×C181#54611yescharacteristic
173C2×C181C22×Q1611yescharacteristic
174C2×C181#57711yescharacteristic
175D181—22no—
176C181#329911yescharacteristic, complemented, Sylow
177#3299—1811nomaximal, Sylow
178#554—1811no—
179D4×Q8—1811no—
180#487—1811no—
181#484—1811no—
182#484—1811no—
183#477—1811no—
184#467—1811no—
185#467—1811no—
186#462—1811no—
187#451—1811no—
188#451—1811no—
189C4×Q16—1811no—
190C8×D4—1811no—
191C2×#103—1811no—
192C2×#103D18111yescharacteristic, complemented
193C22×Q8—1811no—
194C22×Q8C2×D18111yescharacteristic
195C2×Q16—1811no—
196C2×Q16—1811no—
197C2×Q16—1811no—
198C22×C8—1811no—
199C22×C8C2×D18111yescharacteristic
200C4⋊Q8—3621no—
201C4⋊Q8—1811no—
202C4⋊Q8—1811no—
203#125—3621no—
204C22⋊Q8—3621no—
205C22⋊Q8—3621no—
206C22⋊Q8—3621no—
207C22⋊Q8—3621no—
208C22⋊Q8—1811no—
209C22⋊Q8—1811no—
210C22⋊Q8—1811no—
211C22⋊Q8—1811no—
212C4×Q8—1811no—
213C4×Q8—1811no—
214C4×D4—3621no—
215C4×D4—3621no—
216C4×D4—1811no—
217C2×C4⋊C4—1811no—
218C2×C4⋊C4C2×D18111yescharacteristic
219#107—1811no—
220#107—1811no—
221#107—1811no—
222C4⋊C8—1811no—
223#103—1811no—
224#103—1811no—
225#103—1811no—
226#103—1811no—
227#103—1811no—
228#103—1811no—
229#103C2×D18111yescharacteristic
230#103C2×D18111yescharacteristic
231#103C2×D18111yescharacteristic
232#103C2×D18111yescharacteristic
233C22⋊C8—1811no—
234C22⋊C8—1811no—
235C4×C8—1811no—
236C2×Q8—21no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—3621no—
240C2×Q8—3621no—
241C2×Q8—3622no—
242C2×Q8—1811no—
243C2×Q8—1811no—
244C2×Q8—7241no—
245C2×Q8C22×D18111yescharacteristic
246C2×Q8C22×D18111yescharacteristic
247C2×D4—1811no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—3621no—
251C22×C4—3621no—
252C22×C4—1811no—
253C22×C4C22×D18111yescharacteristic
254Q16—3622no—
255Q16—7241no—
256Q16—7241no—
257C2×C8—41no—
258C2×C8—1811no—
259C2×C8—1811no—
260C2×C8—7241no—
261C2×C8C22×D18111yescharacteristic
262C2×C8C22×D18111yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—3621no—
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—1811no—
275C4⋊C4—1811no—
276C4⋊C4—1811no—
277C4⋊C4C22×D18111yescharacteristic
278C4⋊C4C22×D18111yescharacteristic
279C22⋊C4—3621no—
280C22⋊C4—3621no—
281C22⋊C4—3621no—
282C22⋊C4—3621no—
283C22⋊C4—1811no—
284C22⋊C4—1811no—
285C42—3621no—
286C42—3621no—
287C42—1811no—
288C23—1811no—
289C23D4×D18111yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—42no—
294Q8—3621no—
295Q8—3621no—
296Q8—3621no—
297Q8—3621no—
298Q8—14481no—
299Q8—7242no—
300Q8#1566844912yes—
301D4—1814no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—81no—
310C2×C4—3621no—
311C2×C4—3621no—
312C2×C4—3621no—
313C2×C4—3621no—
314C2×C4—3621no—
315C2×C4—3621no—
316C2×C4—14481no—
317C2×C4—1811no—
318C2×C4—1811no—
319C2×C4—1811no—
320C2×C4—7242no—
321C2×C4D4×D18111yescharacteristic
322C2×C4C23×D18111yescharacteristic
323C8—21no—
324C8—21no—
325C8—3621no—
326C8—3621no—
327C22—21no—
328C22—21no—
329C22—3621no—
330C22—3621no—
331C22—1812no—
332C22Q16×D18112yes—
333C22C2×D4×D18111yescharacteristic
334C4—21no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—3621no—
340C4—3621no—
341C4—1812no—
342C4—7241no—
343C4—7241no—
344C4—7241no—
345C4—7241no—
346C4C2×#1566844911yescharacteristic
347C4#1915386111yescharacteristic
348C2—22no—
349C2—3622no—
350C2#2604191911yescharacteristic
351C2C2×Q16×D18111yescharacteristic
352C2#2604208511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
FittingC2×#103×C181C2
socleC22×C181C22×D4
prime radicalC2×C22⋊D181D4
hypercenterC2×#103D181
hypocenterC181#3299
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. #26041628C2semidirect
4. #26041614C2semidirect
5. #26041613C2semidirect
6. #26041572C2semidirect
7. #26041520C2semidirect
8. #26041519C2semidirect
9. #26041488C2semidirect
10. #26041436C2semidirect
11. #26041435C2semidirect
12. #26041371C2semidirect
14. #103×D181C2semidirect
15. C2×#103×C181C2semidirect
118. C22⋊D181Q16semidirect
176. C181#3299semidirect
192. C2×#103D181semidirect

Maximal subgroups

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

subgroupindex
#260419842
Q8×C22⋊D1812
#260416282
#260416142
#260416132
#260415722
#260415202
#260415192
#260414882
#260414362
#260414352
#260413712
C8×C22⋊D1812
#103×D1812
C2×#103×C1812
#3299181