Finite Group Databasebeta

← #37545158

Subgroups — #37545158

Order 23168.

370 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#26041883C211yesmaximal, characteristic, complemented
2#26041880C211yesmaximal, characteristic, complemented
3#26041581C211yesmaximal, characteristic, complemented
4#26041580C211yesmaximal, characteristic, complemented
5#26041579C211yesmaximal, characteristic, complemented
6#26041577C211yesmaximal, characteristic, complemented
7#26041531C211yesmaximal, characteristic, complemented
8#26041529C211yesmaximal, characteristic, complemented
9#26041514C211yesmaximal, characteristic, complemented
10#26041512C211yesmaximal, characteristic, complemented
11#26041472C211yesmaximal, characteristic, complemented
12#26041472C211yesmaximal, characteristic, complemented
13#26041471C211yesmaximal, characteristic, complemented
14#26041304C211yesmaximal, characteristic, complemented
15#459×C181C211yesmaximal, characteristic, complemented
16C2×#15668434C2211yescharacteristic
17C2×#15668434C2211yescharacteristic
18C2×#15668432C2211yescharacteristic
19C2×C8×D181C2211yescharacteristic
20#19153812C2211yescharacteristic
21#19153808C2211yescharacteristic
22#19153807C2211yescharacteristic
23#19153799—21no—
24#19153798—21no—
25#19153797—21no—
26#19153797—21no—
27#19153791C2211yescharacteristic
28#19153790—21no—
29#19153789—21no—
30#19153788—21no—
31#19153788—21no—
32#19153787C2211yescharacteristic
33#19153787C2211yescharacteristic
34#19153787C2211yescharacteristic
35C4×D724C2211yescharacteristic
36D4×Dic181C2211yescharacteristic
37D4×Dic181C2211yescharacteristic
38#19153773C2211yescharacteristic
39#19153750C2211yescharacteristic
40#19153749C2211yescharacteristic
41#19153748C2211yescharacteristic
42#19153747C2211yescharacteristic
43C4⋊#13089678C2211yescharacteristic
44#19153745C2211yescharacteristic
45#19153745C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153738C2211yescharacteristic
48#19153737C2211yescharacteristic
49#19153737C2211yescharacteristic
50#19153737C2211yescharacteristic
51#19153737C2211yescharacteristic
52C2×D8×C181C2211yescharacteristic
53C2×D8×C181C2211yescharacteristic
54#127×C181C2211yescharacteristic
55C4×D4×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59C2×D724—21no—
60C2×D724C2311yescharacteristic
61C2×C22⋊D181—21no—
62C2×C22⋊D181—21no—
63C2×C22⋊D181—21no—
64C2×C22⋊D181—21no—
65C2×C22⋊D181—21no—
66C22×Dic181—21no—
67C22×Dic181—21no—
68C2×C4×D181—21no—
69C2×C4×D181C2311yescharacteristic
70#15668434—41no—
71#15668434—41no—
72#15668432—41no—
73C2×#13089678C2311yescharacteristic
74C2×#13089678C2311yescharacteristic
75C8×D181—41no—
76C4⋊Dic181—21no—
77C4⋊Dic181C2311yescharacteristic
78C4⋊Dic181C2311yescharacteristic
79C4⋊Dic181C2311yescharacteristic
80#15668428—21no—
81#15668428—21no—
82#15668428—21no—
83#15668428D411yescharacteristic
84#15668428D411yescharacteristic
85C22⋊Dic181—21no—
86C22⋊Dic181—21no—
87C22⋊Dic181—21no—
88C22⋊Dic181—21no—
89C22⋊Dic181—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426D411yescharacteristic
93#15668426D411yescharacteristic
94C4×Dic181C2311yescharacteristic
95C2×D4×C181—21no—
96C2×D4×C181—21no—
97C2×D4×C181C2311yescharacteristic
98C2×D4×C181C2311yescharacteristic
99C2×D4×C181C2311yescharacteristic
100C22×C4×C181—21no—
101D8×C181—41no—
102D8×C181—41no—
103C2×C8×C181C2311yescharacteristic
104C2×C8×C181C2311yescharacteristic
105C4⋊C4×C181C2311yescharacteristic
106C22⋊C4×C181—21no—
107C42×C181C2311yescharacteristic
108C22×D181—21no—
109C22×D181C2×D411yescharacteristic
110D724—21no—
111D724—21no—
112D724—81no—
113C22⋊D181—81no—
114C22⋊D181—81no—
115C22⋊D181—81no—
116C22⋊D181—81no—
117C22⋊D181—81no—
118C2×Dic181—21no—
119C2×Dic181—21no—
120C2×Dic181—21no—
121C2×Dic181—81no—
122C2×Dic181—81no—
123C2×Dic181C2×D411yescharacteristic
124C2×Dic181C2×D411yescharacteristic
125C2×Dic181C2×D411yescharacteristic
126C4×D181—21no—
127C4×D181—21no—
128C4×D181—81no—
129#13089678—21no—
130#13089678—21no—
131C23×C181—21no—
132C23×C181—21no—
133C23×C181—21no—
134D4×C181—21no—
135D4×C181—21no—
136D4×C181—21no—
137D4×C181—21no—
138D4×C181—21no—
139D4×C181—21no—
140D4×C181—81no—
141D4×C181—81no—
142C2×C4×C181—21no—
143C2×C4×C181—81no—
144C2×C4×C181C2×D411yescharacteristic
145C2×C4×C181C2×D411yescharacteristic
146C2×C4×C181C2411yescharacteristic
147C8×C181—21no—
148C8×C181—21no—
149C22×C181—41no—
150C22×C181—41no—
151C22×C181—41no—
152C22×C181—41no—
153C22×C181—41no—
154C22×C181—41no—
155C22×C181—41no—
156C22×C181—41no—
157C22×C181—41no—
158C22×C181C22×D411yescharacteristic
159C2×D181—21no—
160C2×D181—21no—
161C2×D181—21no—
162C2×D181—41no—
163C2×D181—41no—
164C2×D181—41no—
165C4×C181—21no—
166C4×C181—21no—
167C4×C181—41no—
168C4×C181H(5,𝔽2)11yescharacteristic
169C4×C1812−1+411yescharacteristic
170Dic181—21no—
171Dic181—21no—
172Dic181—21no—
173Dic181—41no—
174Dic181—41no—
175Dic181—41no—
176C2×C181—81no—
177C2×C181—81no—
178C2×C181—81no—
179C2×C181#53711yescharacteristic
180C2×C181#57611yescharacteristic
181C2×C181#57611yescharacteristic
182D181—41no—
183D181—81no—
184C181#325911yescharacteristic, complemented, Sylow
185#3259—1811nomaximal, Sylow
186#540—1811no—
187#540—1811no—
188#478—1811no—
189#478—1811no—
190#478—1811no—
191#478—1811no—
192#469—1811no—
193#469—1811no—
194#466—1811no—
195#466—1811no—
196#459—1811no—
197#459—1811no—
198#459—1811no—
199#459D18111yescharacteristic, complemented
200#424—1811no—
201C2×D8—1811no—
202C2×D8—1811no—
203C2×D8C2×D18111yescharacteristic
204C2×D8C2×D18111yescharacteristic
205C2×M16—1811no—
206C22×C8—1811no—
207#127—1811no—
208#127C2×D18111yescharacteristic
209#125—1811no—
210#125—1811no—
211#123—3621no—
212#123—3621no—
213#123—3621no—
214#123—3621no—
215#121—3621no—
216#121—3621no—
217#121—3621no—
218#121—3621no—
219#121—1811no—
220#121—1811no—
221#121—1811no—
222#121—1811no—
223C4×D4—1811no—
224C4×D4—1811no—
225C4×D4—1811no—
226C4×D4C2×D18111yescharacteristic
227#117—1811no—
228#107—1811no—
229#107—1811no—
230#106—1811no—
231#106—1811no—
232C4⋊C8—1811no—
233C4⋊C8—1811no—
234C4⋊C8—1811no—
235C4⋊C8C2×D18111yescharacteristic
236#102—1811no—
237#102—1811no—
238#102—1811no—
239#102—1811no—
240#102—1811no—
241#102—1811no—
242#102C2×D18111yescharacteristic
243#102C2×D18111yescharacteristic
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—3621no—
247C2×D4—3621no—
248C2×D4—3621no—
249C2×D4—3621no—
250C2×D4—3621no—
251C2×D4—3621no—
252C2×D4—1811no—
253C2×D4C22×D18111yescharacteristic
254C2×D4C22×D18111yescharacteristic
255C2×D4C22×D18111yescharacteristic
256C22×C4—21no—
257C22×C4—3621no—
258C22×C4—3621no—
259C22×C4—3621no—
260C22×C4—1811no—
261D8—41no—
262D8—41no—
263D8—7241no—
264D8—7241no—
265M16—7241no—
266C2×C8—1811no—
267C2×C8—1811no—
268C2×C8—7241no—
269C2×C8C22×D18111yescharacteristic
270C2×C8C22×D18111yescharacteristic
271C4⋊C4—3621no—
272C4⋊C4—3621no—
273C4⋊C4—3621no—
274C4⋊C4—3621no—
275C4⋊C4—1811no—
276C4⋊C4—1811no—
277C4⋊C4—1811no—
278C4⋊C4—1811no—
279C4⋊C4—1811no—
280C4⋊C4C22×D18111yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—3621no—
283C22⋊C4—3621no—
284C22⋊C4—3621no—
285C22⋊C4—3621no—
286C22⋊C4—3621no—
287C22⋊C4—3621no—
288C22⋊C4—3621no—
289C22⋊C4—1811no—
290C22⋊C4—1811no—
291C42—1811no—
292C42C22×D18111yescharacteristic
293C23—21no—
294C23—21no—
295C23—21no—
296C23—3621no—
297C23—1811no—
298D4—21no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—81no—
305D4—81no—
306D4—3621no—
307D4—3621no—
308D4—14481no—
309D4—14481no—
310D4—14481no—
311D4—14481no—
312D4—14481no—
313D4—14481no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—3621no—
317C2×C4—3621no—
318C2×C4—3621no—
319C2×C4—3621no—
320C2×C4—3621no—
321C2×C4—14481no—
322C2×C4—14481no—
323C2×C4—14481no—
324C2×C4—1811no—
325C2×C4—1811no—
326C2×C4—1811no—
327C2×C4D4×D18111yescharacteristic
328C2×C4D4×D18111yescharacteristic
329C2×C4C23×D18111yescharacteristic
330C8—21no—
331C8—21no—
332C8—3621no—
333C8—3621no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—3621no—
344C22—3621no—
345C22—3621no—
346C22—7241no—
347C22—7241no—
348C22—7241no—
349C22C2×D4×D18111yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—3621no—
354C4—3621no—
355C4—3621no—
356C4—7241no—
357C4—7241no—
358C4—7241no—
359C4#1915386111yescharacteristic
360C4#1915386311yescharacteristic
361C2—81no—
362C2—81no—
363C2—81no—
364C2—14481no—
365C2—7241no—
366C2#2604185811yescharacteristic
367C2#2604208011yescharacteristic
368C2#2604208311yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#459×C181C2
socleC22×C181C22×D4
hypercenter#459D181
hypocenterC181#3259
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #26041883C2semidirect
2. #26041880C2semidirect
3. #26041581C2semidirect
4. #26041580C2semidirect
5. #26041579C2semidirect
6. #26041577C2semidirect
7. #26041531C2semidirect
8. #26041529C2semidirect
9. #26041514C2semidirect
10. #26041512C2semidirect
11. #26041472C2semidirect
12. #26041472C2semidirect
13. #26041471C2semidirect
14. #26041304C2semidirect
15. #459×C181C2semidirect
184. C181#3259semidirect
199. #459D181semidirect

Maximal subgroups

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

subgroupindex
#260418832
#260418802
#260415812
#260415802
#260415792
#260415772
#260415312
#260415292
#260415142
#260415122
#260414722
#260414712
#260413042
#459×C1812
#3259181