Finite Group Databasebeta

← #37545824

Subgroups — #37545824

Order 23168.

382 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041970C211yesmaximal, characteristic, complemented
2#26041932C211yesmaximal, characteristic
3#26041647C211yesmaximal, characteristic, complemented
4#26041618C211yesmaximal, characteristic, complemented
5#26041613C211yesmaximal, characteristic, complemented
6#26041580C211yesmaximal, characteristic, complemented
7#26041534C211yesmaximal, characteristic, complemented
8#26041517C211yesmaximal, characteristic, complemented
9#26041440C211yesmaximal, characteristic, complemented
10#26041440C211yesmaximal, characteristic, complemented
11#26041377C211yesmaximal, characteristic, complemented
12#26041349C211yesmaximal, characteristic, complemented
13#26041279C211yesmaximal, characteristic, complemented
14#26041274C211yesmaximal, characteristic, complemented
15#462×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668450C2211yescharacteristic
18C2×#15668436C2211yescharacteristic
19C2×#15668432C2211yescharacteristic
20C2×C8×D181C2211yescharacteristic
21#19153810—21no—
22#19153808C2211yescharacteristic
23#19153806—21no—
24#19153801—21no—
25#19153801—21no—
26#19153801—21no—
27#19153792C2211yescharacteristic
28#19153792C2211yescharacteristic
29#19153792C2211yescharacteristic
30#19153792C2211yescharacteristic
31#19153791—21no—
32C4×D724C2211yescharacteristic
33C4×D724C2211yescharacteristic
34#19153774C2211yescharacteristic
35#19153773—21no—
36C4⋊C4×D181—21no—
37C4⋊C4×D181C2211yescharacteristic
38#19153750C2211yescharacteristic
39#19153749C2211yescharacteristic
40#19153748C2211yescharacteristic
41#19153740C2211yescharacteristic
42#19153740C2211yescharacteristic
43#19153740C2211yescharacteristic
44#19153740C2211yescharacteristic
45#19153740C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153738C2211yescharacteristic
48#19153736C2211yescharacteristic
49#19153728C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153727C2211yescharacteristic
52C2×Q16×C181C2211yescharacteristic
53C2×Q16×C181C2211yescharacteristic
54C4⋊Q8×C181C2211yescharacteristic
55C4×Q8×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#103×C181C2211yescharacteristic
59#15668450—22no—
60#15668450—22no—
61#15668450—41no—
62#15668450—41no—
63C2×D724—21no—
64C2×D724—21no—
65C2×D724D411yescharacteristic
66C2×D724C2311yescharacteristic
67C2×C4×D181—21no—
68C2×C4×D181—21no—
69C2×C4×D181—21no—
70C2×C4×D181—21no—
71C2×C4×D181C2311yescharacteristic
72C2×C4×D181C2311yescharacteristic
73#15668436—22no—
74#15668432—41no—
75C2×#13089678C2311yescharacteristic
76C2×#13089678C2311yescharacteristic
77C8×D181—41no—
78C4⋊Dic181D411yescharacteristic
79C4⋊Dic181C2311yescharacteristic
80C4⋊Dic181C2311yescharacteristic
81C4⋊Dic181C2311yescharacteristic
82#15668428—21no—
83#15668428—21no—
84#15668428—21no—
85#15668428—21no—
86#15668428—21no—
87#15668428—21no—
88#15668428—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426D411yescharacteristic
96#15668426D411yescharacteristic
97C4×Dic181—21no—
98C2×Q8×C181C2311yescharacteristic
99C2×Q8×C181C2311yescharacteristic
100C2×Q8×C181C2311yescharacteristic
101Q16×C181—41no—
102Q16×C181—41no—
103C2×C8×C181C2311yescharacteristic
104C2×C8×C181C2311yescharacteristic
105C4⋊C4×C181—21no—
106C4⋊C4×C181—21no—
107C4⋊C4×C181—21no—
108C4⋊C4×C181C2311yescharacteristic
109C42×C181—21no—
110C42×C181C2311yescharacteristic
111C22×D181—21no—
112C22×D181C2×D411yescharacteristic
113C22×D181C2×D411yescharacteristic
114D724—21no—
115D724—41no—
116D724—42no—
117D724—42no—
118D724#4112yes—
119C2×Dic181—21no—
120C2×Dic181—21no—
121C2×Dic181—21no—
122C2×Dic181C2×D411yescharacteristic
123C2×Dic181C2×D411yescharacteristic
124C4×D181—21no—
125C4×D181—21no—
126C4×D181—21no—
127C4×D181—21no—
128C4×D181—42no—
129C4×D181—42no—
130C4×D181—42no—
131C4×D181—42no—
132#13089678—21no—
133#13089678—21no—
134Q8×C181—21no—
135Q8×C181—21no—
136Q8×C181—21no—
137Q8×C181—21no—
138Q8×C181—21no—
139Q8×C181—21no—
140C2×C4×C181—21no—
141C2×C4×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181C2×D411yescharacteristic
145C2×C4×C181C2×D411yescharacteristic
146C2×C4×C181C2411yescharacteristic
147C8×C181—21no—
148C8×C181—21no—
149C22×C181C22×D411yescharacteristic
150C2×D181—21no—
151C2×D181—21no—
152C2×D181—22no—
153C2×D181—21no—
154C2×D181—21no—
155C2×D181—21no—
156C2×D181—21no—
157C2×D181—41no—
158C2×D181—41no—
159C4×C181—21no—
160C4×C181—21no—
161C4×C181—41no—
162C4×C181—41no—
163C4×C181—41no—
164C4×C181—41no—
165C4×C181C2×#4111yescharacteristic
166C4×C181H(5,𝔽2)11yescharacteristic
167Dic181—21no—
168Dic181—21no—
169Dic181—41no—
170Dic181—41no—
171Dic181—41no—
172C2×C181#54611yescharacteristic
173C2×C181#57511yescharacteristic
174C2×C181#57811yescharacteristic
175D181—41no—
176D181—41no—
177D181—42no—
178C181#331511yescharacteristic, complemented, Sylow
179#3315—1811nomaximal, Sylow
180#552—1811no—
181#547—1811no—
182#491—1811no—
183#485—1811no—
184#484—1811no—
185#478—1811no—
186#470—1811no—
187#467—1811no—
188#462D18111yescharacteristic, complemented
189#452—1811no—
190#452—1811no—
191#440—1811no—
192#435—1811no—
193#417—1811no—
194#416—1811no—
195C2×#41—1811no—
196C2×#41—1811no—
197C2×Q16C2×D18111yescharacteristic
198C2×Q16C2×D18111yescharacteristic
199C2×SD16—1811no—
200C2×M16—1811no—
201C22×C8—1811no—
202C4⋊Q8C2×D18111yescharacteristic
203#126—3621no—
204#125—3621no—
205#125—1811no—
206#123—3621no—
207#123—3621no—
208#123—3621no—
209C22⋊Q8—1811no—
210C22⋊Q8—1811no—
211C22⋊Q8—1811no—
212C22⋊Q8—1811no—
213#121—3621no—
214C4×Q8C2×D18111yescharacteristic
215C4×D4—1811no—
216C4×D4—1811no—
217#117—3621no—
218#117—1811no—
219C2×C4⋊C4—3621no—
220C2×C4⋊C4—1811no—
221#107—1811no—
222#107—1811no—
223#106—1811no—
224C4⋊C8C2×D18111yescharacteristic
225#103—1811no—
226#103—1811no—
227#103—1811no—
228#103—1811no—
229#103—1811no—
230#103C2×D18111yescharacteristic
231#103C2×D18111yescharacteristic
232#102—1811no—
233#102—1811no—
234#102—1811no—
235C22⋊C8—1811no—
236C22⋊C8—1811no—
237#97—1811no—
238#41—3622no—
239#41—3622no—
240#41—7241no—
241#41—7241no—
242C2×Q8C22×D18111yescharacteristic
243C2×Q8C22×D18111yescharacteristic
244C2×Q8C22×D18111yescharacteristic
245C2×D4—3621no—
246C2×D4—3621no—
247C2×D4—1811no—
248C2×D4—1811no—
249C22×C4—3621no—
250C22×C4—3621no—
251C22×C4—3621no—
252C22×C4—3621no—
253C22×C4—1811no—
254C22×C4—1811no—
255Q16—41no—
256Q16—41no—
257SD16—3622no—
258M16—7241no—
259C2×C8—1811no—
260C2×C8—1811no—
261C2×C8—7241no—
262C2×C8C22×D18111yescharacteristic
263C2×C8C22×D18111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
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⋊C4—1811no—
278C4⋊C4C22×D18111yescharacteristic
279C22⋊C4—3621no—
280C22⋊C4—3621no—
281C22⋊C4—3621no—
282C22⋊C4—3621no—
283C22⋊C4—3621no—
284C22⋊C4—3621no—
285C22⋊C4—1811no—
286C22⋊C4—1811no—
287C42—21no—
288C42—3621no—
289C42C22×D18111yescharacteristic
290C23—3621no—
291C23—1811no—
292C23—1811no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299D4—3621no—
300D4—1812no—
301D4—7241no—
302D4—7242no—
303D4—7242no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—3621no—
309C2×C4—3621no—
310C2×C4—3621no—
311C2×C4—3621no—
312C2×C4—3621no—
313C2×C4—3621no—
314C2×C4—3621no—
315C2×C4—1811no—
316C2×C4—1811no—
317C2×C4—7242no—
318C2×C4—7242no—
319C2×C4—7242no—
320C2×C4—7242no—
321C2×C4D4×D18111yescharacteristic
322C2×C4D4×D18111yescharacteristic
323C2×C4C23×D18111yescharacteristic
324C8—21no—
325C8—21no—
326C8—3621no—
327C8—3621no—
328C22—3621no—
329C22—3621no—
330C22—3622no—
331C22—3621no—
332C22—3621no—
333C22—3621no—
334C22—3621no—
335C22—7241no—
336C22—7241no—
337C22C2×D4×D18111yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—3621no—
345C4—3621no—
346C4—7241no—
347C4—7241no—
348C4—7241no—
349C4#41×D18111yescharacteristic
350C4#1915386111yescharacteristic
351C2—7241no—
352C2—7241no—
353C2—7242no—
354C2#2604192611yescharacteristic
355C2#2604207811yescharacteristic
356C2#2604209211yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#462×C181C2
socleC22×C181C22×D4
prime radical#26041932C2
hypercenter#462D181
hypocenterC181#3315
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. #26041970C2semidirect
3. #26041647C2semidirect
4. #26041618C2semidirect
5. #26041613C2semidirect
6. #26041580C2semidirect
7. #26041534C2semidirect
8. #26041517C2semidirect
9. #26041440C2semidirect
10. #26041440C2semidirect
11. #26041377C2semidirect
12. #26041349C2semidirect
13. #26041279C2semidirect
14. #26041274C2semidirect
15. #462×C181C2semidirect
178. C181#3315semidirect
188. #462D181semidirect

Maximal subgroups

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

subgroupindex
#260419702
#260419322
#260416472
#260416182
#260416132
#260415802
#260415342
#260415172
#260414402
#260413772
#260413492
#260412792
#260412742
#462×C1812
#3315181