Finite Group Databasebeta

← #37543996

Subgroups — #37543996

Order 23168.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041901C211yesmaximal, characteristic, complemented
2#26041761C211yesmaximal, characteristic, complemented
3#26041608C211yesmaximal, characteristic, complemented
4#26041599C211yesmaximal, characteristic, complemented
5#26041568C211yesmaximal, characteristic, complemented
6#26041562C211yesmaximal, characteristic, complemented
7#26041503C211yesmaximal, characteristic, complemented
8#26041497C211yesmaximal, characteristic, complemented
9#26041440C211yesmaximal, characteristic, complemented
10#26041427C211yesmaximal, characteristic
11#26041392C211yesmaximal, characteristic, complemented
12C4×#15668436C211yesmaximal, characteristic, complemented
13C4×#15668436C211yesmaximal, characteristic, complemented
14#26041341C211yesmaximal, characteristic, complemented
15#441×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668436C2211yescharacteristic
18C2×#15668436C2211yescharacteristic
19C2×D1448C2211yescharacteristic
20#19153815C2211yescharacteristic
21#19153810—21no—
22#19153805C2211yescharacteristic
23#19153804—21no—
24#19153801—21no—
25#19153794—21no—
26#19153792C2211yescharacteristic
27#19153791C2211yescharacteristic
28Q8×Dic181C2211yescharacteristic
29C4×D724—21no—
30C4×D724C2211yescharacteristic
31C4×D724C2211yescharacteristic
32#19153778—21no—
33#19153778C2211yescharacteristic
34#19153773—21no—
35#19153773C2211yescharacteristic
36C4⋊C4×D181—21no—
37C4⋊C4×D181C2211yescharacteristic
38#19153748C2211yescharacteristic
39#19153747C2211yescharacteristic
40#19153747C2211yescharacteristic
41#19153745C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153740C2211yescharacteristic
44#19153740C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49#19153728C2211yescharacteristic
50#19153728C2211yescharacteristic
51C4×#13089678C2211yescharacteristic
52C2×Q16×C181C2211yescharacteristic
53C4×Q8×C181C2211yescharacteristic
54C4×Q8×C181C2211yescharacteristic
55#106×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#97×C181C2211yescharacteristic
59#15668450—22no—
60#15668450—22no—
61C2×Dic362—21no—
62C2×D724—21no—
63C2×D724—21no—
64C2×D724C2311yescharacteristic
65C2×D724C2311yescharacteristic
66C2×C4×D181—21no—
67C2×C4×D181—21no—
68C2×C4×D181—21no—
69C2×C4×D181—21no—
70C2×C4×D181—21no—
71C2×C4×D181C2311yescharacteristic
72#15668436—22no—
73#15668436—22no—
74D1448—22no—
75C2×#13089678C2311yescharacteristic
76C2×#13089678C2311yescharacteristic
77C4⋊Dic181—21no—
78C4⋊Dic181C2311yescharacteristic
79C4⋊Dic181C2311yescharacteristic
80#15668428—21no—
81#15668428—21no—
82#15668428—21no—
83#15668428D411yescharacteristic
84#15668428D411yescharacteristic
85#15668426—21no—
86#15668426—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426D411yescharacteristic
93#15668426D411yescharacteristic
94C4×Dic181—21no—
95C4×Dic181C2311yescharacteristic
96C2×Q8×C181C2311yescharacteristic
97C2×Q8×C181C2311yescharacteristic
98Q16×C181—22no—
99C2×C8×C181C2311yescharacteristic
100C2×C8×C181C2311yescharacteristic
101C4⋊C4×C181—21no—
102C4⋊C4×C181—21no—
103C4⋊C4×C181C2311yescharacteristic
104C4⋊C4×C181C2311yescharacteristic
105C42×C181—21no—
106C42×C181—21no—
107C42×C181C2311yescharacteristic
108C22×D181—21no—
109C22×D181—21no—
110C22×D181C2×D411yescharacteristic
111Dic362—81no—
112D724—24no—
113D724—21no—
114D724—21no—
115D724—21no—
116D724—81no—
117D724#4112yes—
118C2×Dic181—21no—
119C2×Dic181—21no—
120C2×Dic181C2×D411yescharacteristic
121C2×Dic181C2×D411yescharacteristic
122C2×Dic181C2×D411yescharacteristic
123C4×D181—24no—
124C4×D181—21no—
125C4×D181—21no—
126C4×D181—81no—
127C4×D181—81no—
128C4×D181—81no—
129C4×D181—81no—
130#13089678—21no—
131#13089678—21no—
132Q8×C181—21no—
133Q8×C181—21no—
134Q8×C181—21no—
135Q8×C181#4112yes—
136C2×C4×C181—21no—
137C2×C4×C181—21no—
138C2×C4×C181—21no—
139C2×C4×C181—21no—
140C2×C4×C181C2×D411yescharacteristic
141C2×C4×C181C2×D411yescharacteristic
142C2×C4×C181C2411yescharacteristic
143C8×C181—21no—
144C8×C181—21no—
145C22×C181C22×D411yescharacteristic
146C2×D181—21no—
147C2×D181—22no—
148C2×D181—21no—
149C2×D181—21no—
150C2×D181—41no—
151C2×D181—41no—
152C2×D181—41no—
153C2×D181—41no—
154C2×D181—41no—
155C4×C181—22no—
156C4×C181—21no—
157C4×C181—21no—
158C4×C181—41no—
159C4×C181—41no—
160C4×C181—41no—
161C4×C181C2×#4111yescharacteristic
162C4×C181C2×#4111yescharacteristic
163Dic181—21no—
164Dic181—21no—
165Dic181—21no—
166Dic181—41no—
167Dic181—41no—
168C2×C181#52511yescharacteristic
169C2×C181#57711yescharacteristic
170C2×C181#57711yescharacteristic
171D181—41no—
172D181—42no—
173D181—81no—
174C181#312511yescharacteristic, complemented, Sylow
175#3125—1811nomaximal, Sylow
176#542—1811no—
177#520—1811no—
178#483—1811no—
179#481—1811no—
180#476—1811no—
181#475—1811no—
182#464—1811no—
183#463—1811no—
184#452—1811no—
185#449—1811no—
186#442—1811no—
187#441D18111yescharacteristic, complemented
188C4×SD16—1811no—
189C4×SD16—1811no—
190#433—1811no—
191C2×#41—1811no—
192C2×Q16C2×D18111yescharacteristic
193C2×SD16—1811no—
194C2×SD16—1811no—
195C2×D8—1811no—
196C4⋊Q8—1811no—
197#126—3621no—
198#124—3621no—
199#124—1811no—
200#123—3621no—
201C22⋊Q8—3621no—
202C22⋊Q8—1811no—
203#121—1811no—
204C4×Q8—1811no—
205C4×Q8C2×D18111yescharacteristic
206C4×Q8C2×D18111yescharacteristic
207C4×D4—3621no—
208C4×D4—3621no—
209C4×D4—1811no—
210C4×D4—1811no—
211C4×D4—1811no—
212#117—3621no—
213#117—1811no—
214C2×C4⋊C4—3621no—
215C2×C4⋊C4—1811no—
216#106—1811no—
217#106—1811no—
218#106—1811no—
219#106C2×D18111yescharacteristic
220C4⋊C8—1811no—
221C4⋊C8—1811no—
222#103—1811no—
223#103—1811no—
224#103C2×D18111yescharacteristic
225#103C2×D18111yescharacteristic
226#102—1811no—
227#102—1811no—
228#102—1811no—
229#102—1811no—
230C22⋊C8—1811no—
231C22⋊C8—1811no—
232#97C2×D18111yescharacteristic
233C4×C8—1811no—
234#41—3622no—
235#41—3622no—
236C2×Q8—3621no—
237C2×Q8C22×D18111yescharacteristic
238C2×Q8C22×D18111yescharacteristic
239C2×D4—3621no—
240C2×D4—3621no—
241C2×D4—1811no—
242C2×D4—1811no—
243C22×C4—3621no—
244C22×C4—3621no—
245C22×C4—3621no—
246C22×C4—3621no—
247C22×C4—3621no—
248C22×C4—1811no—
249Q16—22no—
250SD16—3622no—
251SD16—3622no—
252D8—3622no—
253C2×C8—1811no—
254C2×C8—1811no—
255C2×C8C22×D18111yescharacteristic
256C2×C8C22×D18111yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—3621no—
260C4⋊C4—3621no—
261C4⋊C4—3621no—
262C4⋊C4—3621no—
263C4⋊C4—1811no—
264C4⋊C4—1811no—
265C4⋊C4—1811no—
266C4⋊C4—1811no—
267C4⋊C4C22×D18111yescharacteristic
268C4⋊C4C22×D18111yescharacteristic
269C22⋊C4—3621no—
270C22⋊C4—3621no—
271C22⋊C4—3621no—
272C22⋊C4—3621no—
273C22⋊C4—3621no—
274C22⋊C4—3621no—
275C22⋊C4—3621no—
276C22⋊C4—1811no—
277C22⋊C4—1811no—
278C42—21no—
279C42—21no—
280C42—3621no—
281C42—1811no—
282C42C22×D18111yescharacteristic
283C23—3621no—
284C23—3621no—
285C23—1811no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—14481no—
290Q8#1566844912yes—
291D4—3624no—
292D4—3621no—
293D4—3621no—
294D4—3621no—
295D4—14481no—
296D4—1812no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—3624no—
302C2×C4—3621no—
303C2×C4—3621no—
304C2×C4—3621no—
305C2×C4—3621no—
306C2×C4—14481no—
307C2×C4—14481no—
308C2×C4—14481no—
309C2×C4—14481no—
310C2×C4—1811no—
311C2×C4—1811no—
312C2×C4—1811no—
313C2×C4D4×D18111yescharacteristic
314C2×C4D4×D18111yescharacteristic
315C2×C4C23×D18111yescharacteristic
316C8—21no—
317C8—21no—
318C8—3621no—
319C8—3621no—
320C22—3621no—
321C22—3622no—
322C22—3621no—
323C22—3621no—
324C22—7241no—
325C22—7241no—
326C22—7241no—
327C22—7241no—
328C22—7241no—
329C22C2×D4×D18111yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—3621no—
337C4—3621no—
338C4—3621no—
339C4—7241no—
340C4—7241no—
341C4#41×D18111yescharacteristic
342C4C2×#1566844911yescharacteristic
343C2—14481no—
344C2—7241no—
345C2—7242no—
346C2#2604178811yescharacteristic
347C2#2604208811yescharacteristic
348C2#2604208811yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#441×C181C2
socleC22×C181C22×D4
prime radical#26041427C2
hypercenter#441D181
hypocenterC181#3125
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #26041901C2semidirect
2. #26041761C2semidirect
3. #26041608C2semidirect
4. #26041599C2semidirect
5. #26041568C2semidirect
6. #26041562C2semidirect
7. #26041503C2semidirect
8. #26041497C2semidirect
9. #26041440C2semidirect
11. #26041392C2semidirect
12. C4×#15668436C2semidirect
13. C4×#15668436C2semidirect
14. #26041341C2semidirect
15. #441×C181C2semidirect
174. C181#3125semidirect
187. #441D181semidirect

Maximal subgroups

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

subgroupindex
#260419012
#260417612
#260416082
#260415992
#260415682
#260415622
#260415032
#260414972
#260414402
#260414272
#260413922
C4×#156684362
#260413412
#441×C1812
#3125181