Finite Group Databasebeta

← #37543926

Subgroups — #37543926

Order 23168.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041880C211yesmaximal, characteristic, complemented
2#26041761C211yesmaximal, characteristic, complemented
3#26041599C211yesmaximal, characteristic, complemented
4#26041591C211yesmaximal, characteristic, complemented
5#26041588C211yesmaximal, characteristic, complemented
6#26041578C211yesmaximal, characteristic, complemented
7#26041477C211yesmaximal, characteristic, complemented
8#26041473C211yesmaximal, characteristic, complemented
9#26041427C211yesmaximal, characteristic, complemented
10#26041423C211yesmaximal, characteristic, complemented
11#26041389C211yesmaximal, characteristic, complemented
12#26041377C211yesmaximal, characteristic, complemented
13C4×D1448C211yesmaximal, characteristic, complemented
14#26041338C211yesmaximal, characteristic, complemented
15C4×SD16×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668436C2211yescharacteristic
18C2×D1448C2211yescharacteristic
19C2×#15668434C2211yescharacteristic
20#19153812C2211yescharacteristic
21#19153807C2211yescharacteristic
22#19153799—21no—
23#19153798—21no—
24#19153791C2211yescharacteristic
25#19153790—21no—
26#19153789—21no—
27#19153787C2211yescharacteristic
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#19153750C2211yescharacteristic
39#19153749C2211yescharacteristic
40#19153747C2211yescharacteristic
41#19153745C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153740C2211yescharacteristic
44#19153738C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153737C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49#19153728C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153727C2211yescharacteristic
52C2×SD16×C181C2211yescharacteristic
53C4×Q8×C181C2211yescharacteristic
54C4×D4×C181C2211yescharacteristic
55#106×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C4×C8×C181C2211yescharacteristic
59#15668450—22no—
60#15668450—22no—
61C2×D724—21no—
62C2×D724—21no—
63C2×D724C2311yescharacteristic
64C2×D724C2311yescharacteristic
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C2×C4×D181—21no—
69C2×C4×D181—21no—
70C2×C4×D181—21no—
71C2×C4×D181—21no—
72C2×C4×D181—21no—
73C2×C4×D181C2311yescharacteristic
74#15668436—22no—
75D1448—22no—
76#15668434—22no—
77C2×#13089678C2311yescharacteristic
78C2×#13089678C2311yescharacteristic
79C4⋊Dic181—21no—
80C4⋊Dic181—21no—
81C4⋊Dic181C2311yescharacteristic
82C4⋊Dic181C2311yescharacteristic
83#15668428—21no—
84#15668428—21no—
85#15668428D411yescharacteristic
86#15668428D411yescharacteristic
87C22⋊Dic181—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×D4×C181C2311yescharacteristic
98C22×C4×C181—21no—
99SD16×C181—22no—
100C2×C8×C181C2311yescharacteristic
101C2×C8×C181C2311yescharacteristic
102C4⋊C4×C181—21no—
103C4⋊C4×C181C2311yescharacteristic
104C4⋊C4×C181C2311yescharacteristic
105C22⋊C4×C181—21no—
106C42×C181—21no—
107C42×C181C2311yescharacteristic
108C22×D181—21no—
109C22×D181—21no—
110C22×D181C2×D411yescharacteristic
111D724—24no—
112D724—21no—
113D724—21no—
114D724—21no—
115D724—81no—
116D724#4112yes—
117C22⋊D181—81no—
118C22⋊D181—81no—
119C22⋊D181—81no—
120C2×Dic181—21no—
121C2×Dic181—21no—
122C2×Dic181C2×D411yescharacteristic
123C2×Dic181C2×D411yescharacteristic
124C2×Dic181C2×D411yescharacteristic
125C4×D181—24no—
126C4×D181—21no—
127C4×D181—21no—
128C4×D181—81no—
129C4×D181—81no—
130C4×D181—81no—
131C4×D181—81no—
132#13089678—21no—
133#13089678—21no—
134C23×C181—21no—
135Q8×C181—21no—
136Q8×C181#4112yes—
137D4×C181—21no—
138D4×C181—21no—
139C2×C4×C181—21no—
140C2×C4×C181—21no—
141C2×C4×C181—21no—
142C2×C4×C181—81no—
143C2×C4×C181C2×D411yescharacteristic
144C2×C4×C181C2×D411yescharacteristic
145C2×C4×C181C2411yescharacteristic
146C8×C181—21no—
147C8×C181—21no—
148C22×C181—41no—
149C22×C181—41no—
150C22×C181—41no—
151C22×C181C22×D411yescharacteristic
152C2×D181—21no—
153C2×D181—22no—
154C2×D181—21no—
155C2×D181—21no—
156C2×D181—41no—
157C2×D181—41no—
158C2×D181—41no—
159C2×D181—41no—
160C2×D181—41no—
161C4×C181—22no—
162C4×C181—21no—
163C4×C181—21no—
164C4×C181—41no—
165C4×C181—41no—
166C4×C181C2×#4111yescharacteristic
167C4×C181C2×#4111yescharacteristic
168Dic181—21no—
169Dic181—21no—
170Dic181—21no—
171Dic181—41no—
172Dic181—41no—
173C2×C181—81no—
174C2×C181#52511yescharacteristic
175C2×C181#57611yescharacteristic
176C2×C181#57711yescharacteristic
177D181—41no—
178D181—42no—
179D181—81no—
180C181#311911yescharacteristic, complemented, Sylow
181#3119—1811nomaximal, Sylow
182#540—1811no—
183#520—1811no—
184#481—1811no—
185#480—1811no—
186#479—1811no—
187#478—1811no—
188#460—1811no—
189#459—1811no—
190#449—1811no—
191#449—1811no—
192#442—1811no—
193#440—1811no—
194C4×SD16D18111yescharacteristic, complemented
195C4×D8—1811no—
196#433—1811no—
197C2×#41—1811no—
198C2×SD16—1811no—
199C2×SD16C2×D18111yescharacteristic
200C2×D8—1811no—
201C2×D8—1811no—
202#127—1811no—
203#125—1811no—
204#123—3621no—
205#123—3621no—
206#121—3621no—
207#121—3621no—
208#121—1811no—
209#121—1811no—
210C4×Q8—1811no—
211C4×Q8C2×D18111yescharacteristic
212C4×D4—3621no—
213C4×D4—3621no—
214C4×D4—1811no—
215C4×D4—1811no—
216C4×D4—1811no—
217C4×D4C2×D18111yescharacteristic
218#117—3621no—
219#117—1811no—
220C2×C4⋊C4—3621no—
221C2×C4⋊C4—1811no—
222#107—1811no—
223#107—1811no—
224#106—1811no—
225#106C2×D18111yescharacteristic
226C4⋊C8—1811no—
227C4⋊C8—1811no—
228#103—1811no—
229#103C2×D18111yescharacteristic
230#102—1811no—
231#102—1811no—
232#102—1811no—
233#102—1811no—
234#102—1811no—
235#102C2×D18111yescharacteristic
236C22⋊C8—1811no—
237C22⋊C8—1811no—
238#97—1811no—
239C4×C8C2×D18111yescharacteristic
240#41—3622no—
241#41—3622no—
242C2×Q8C22×D18111yescharacteristic
243C2×D4—3621no—
244C2×D4—3621no—
245C2×D4—3621no—
246C2×D4—3621no—
247C2×D4—3621no—
248C2×D4—1811no—
249C2×D4—1811no—
250C2×D4C22×D18111yescharacteristic
251C22×C4—21no—
252C22×C4—3621no—
253C22×C4—3621no—
254C22×C4—3621no—
255C22×C4—3621no—
256C22×C4—3621no—
257C22×C4—1811no—
258SD16—22no—
259SD16—3622no—
260D8—3622no—
261D8—3622no—
262C2×C8—1811no—
263C2×C8—1811no—
264C2×C8C22×D18111yescharacteristic
265C2×C8C22×D18111yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—3621no—
268C4⋊C4—3621no—
269C4⋊C4—3621no—
270C4⋊C4—3621no—
271C4⋊C4—1811no—
272C4⋊C4—1811no—
273C4⋊C4—1811no—
274C4⋊C4—1811no—
275C4⋊C4C22×D18111yescharacteristic
276C4⋊C4C22×D18111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—3621no—
279C22⋊C4—3621no—
280C22⋊C4—3621no—
281C22⋊C4—3621no—
282C22⋊C4—3621no—
283C22⋊C4—1811no—
284C22⋊C4—1811no—
285C42—21no—
286C42—3621no—
287C42—1811no—
288C42C22×D18111yescharacteristic
289C23—21no—
290C23—3621no—
291C23—3621no—
292C23—1811no—
293Q8—21no—
294Q8#1566844912yes—
295D4—21no—
296D4—21no—
297D4—3624no—
298D4—3621no—
299D4—3621no—
300D4—3621no—
301D4—14481no—
302D4—14481no—
303D4—14481no—
304D4—14481no—
305D4—1812no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—3624no—
311C2×C4—3621no—
312C2×C4—3621no—
313C2×C4—3621no—
314C2×C4—3621no—
315C2×C4—14481no—
316C2×C4—14481no—
317C2×C4—14481no—
318C2×C4—14481no—
319C2×C4—1811no—
320C2×C4—1811no—
321C2×C4—1811no—
322C2×C4D4×D18111yescharacteristic
323C2×C4D4×D18111yescharacteristic
324C2×C4C23×D18111yescharacteristic
325C8—21no—
326C8—21no—
327C8—3621no—
328C8—3621no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—3621no—
333C22—3622no—
334C22—3621no—
335C22—3621no—
336C22—7241no—
337C22—7241no—
338C22—7241no—
339C22—7241no—
340C22—7241no—
341C22C2×D4×D18111yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—3621no—
348C4—3621no—
349C4—3621no—
350C4—7241no—
351C4—7241no—
352C4#41×D18111yescharacteristic
353C4C2×#1566844911yescharacteristic
354C2—81no—
355C2—14481no—
356C2—7241no—
357C2—7242no—
358C2#2604178811yescharacteristic
359C2#2604208111yescharacteristic
360C2#2604208511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
FittingC4×SD16×C181C2
socleC22×C181C22×D4
hypercenterC4×SD16D181
hypocenterC181#3119
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #26041880C2semidirect
2. #26041761C2semidirect
3. #26041599C2semidirect
4. #26041591C2semidirect
5. #26041588C2semidirect
6. #26041578C2semidirect
7. #26041477C2semidirect
8. #26041473C2semidirect
9. #26041427C2semidirect
10. #26041423C2semidirect
11. #26041389C2semidirect
12. #26041377C2semidirect
13. C4×D1448C2semidirect
14. #26041338C2semidirect
15. C4×SD16×C181C2semidirect
180. C181#3119semidirect
194. C4×SD16D181semidirect

Maximal subgroups

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

subgroupindex
#260418802
#260417612
#260415992
#260415912
#260415882
#260415782
#260414772
#260414732
#260414272
#260414232
#260413892
#260413772
C4×D14482
#260413382
C4×SD16×C1812
#3119181