Finite Group Databasebeta

← #37545082

Subgroups — #37545082

Order 23168.

392 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041826C211yesmaximal, characteristic, complemented
2#26041814C211yesmaximal, characteristic, complemented
3#26041576C211yesmaximal, characteristic, complemented
4#26041563C211yesmaximal, characteristic, complemented
5#26041558C211yesmaximal, characteristic, complemented
6#26041533C211yesmaximal, characteristic, complemented
7#26041531C211yesmaximal, characteristic, complemented
8#26041526C211yesmaximal, characteristic, complemented
9#26041524C211yesmaximal, characteristic, complemented
10#26041495C211yesmaximal, characteristic, complemented
11#26041494C211yesmaximal, characteristic, complemented
12#26041478C211yesmaximal, characteristic, complemented
13#26041473C211yesmaximal, characteristic, complemented
14#26041301C211yesmaximal, characteristic, complemented
15#478×C181C211yesmaximal, characteristic, complemented
16C2×#15668449—21no—
17C2×#15668438C2211yescharacteristic
18C2×#15668437C2211yescharacteristic
19C2×D1448C2211yescharacteristic
20C2×#15668434C2211yescharacteristic
21C2×#15668432C2211yescharacteristic
22C2×#15668432C2211yescharacteristic
23#19153815C2211yescharacteristic
24#19153812C2211yescharacteristic
25#19153811—21no—
26#19153804C2211yescharacteristic
27#19153802—21no—
28#19153801—21no—
29#19153796C2211yescharacteristic
30#19153791C2211yescharacteristic
31#19153791C2211yescharacteristic
32#19153789—21no—
33#19153787C2211yescharacteristic
34#19153781C2211yescharacteristic
35C4×D724C2211yescharacteristic
36#19153778—21no—
37#19153778C2211yescharacteristic
38C4×C22⋊D181—21no—
39#19153774—21no—
40C42×D181C2211yescharacteristic
41#19153749C2211yescharacteristic
42#19153747C2211yescharacteristic
43C4⋊#13089678C2211yescharacteristic
44#19153745C2211yescharacteristic
45#19153745C2211yescharacteristic
46#19153741C2211yescharacteristic
47#19153739C2211yescharacteristic
48#19153738C2211yescharacteristic
49#19153736C2211yescharacteristic
50#19153736C2211yescharacteristic
51#19153736C2211yescharacteristic
52#125×C181C2211yescharacteristic
53C4×D4×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic
55#106×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59#15668449—44no—
60C2×Dic362—21no—
61C2×Dic362C2311yescharacteristic
62C2×D724—21no—
63C2×D724—21no—
64C2×D724C2311yescharacteristic
65C2×D724C2311yescharacteristic
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C2×C4×D181—21no—
70C2×C4×D181—21no—
71C2×C4×D181D411yescharacteristic
72C2×C4×D181D411yescharacteristic
73C2×C4×D181C2311yescharacteristic
74#15668438—41no—
75#15668437—41no—
76D1448—41no—
77#15668434—41no—
78#15668432—41no—
79#15668432—41no—
80C2×#13089678C2311yescharacteristic
81C2×#13089678C2311yescharacteristic
82C4⋊Dic181—21no—
83C4⋊Dic181C2311yescharacteristic
84#15668428—21no—
85#15668428—21no—
86C22⋊Dic181—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94C4×Dic181—21no—
95C4×Dic181D411yescharacteristic
96C4×Dic181D411yescharacteristic
97C4×Dic181C2311yescharacteristic
98C2×D4×C181C2311yescharacteristic
99C22×C4×C181—21no—
100C2×C8×C181C2311yescharacteristic
101C2×C8×C181C2311yescharacteristic
102C4⋊C4×C181—21no—
103C4⋊C4×C181—21no—
104C4⋊C4×C181C2311yescharacteristic
105C4⋊C4×C181C2311yescharacteristic
106C4⋊C4×C181C2311yescharacteristic
107C22⋊C4×C181—21no—
108C42×C181C2311yescharacteristic
109C22×D181—21no—
110C22×D181—21no—
111C22×D181C2×D411yescharacteristic
112Dic362—21no—
113Dic362—21no—
114Dic362—42no—
115D724—21no—
116D724—21no—
117D724—21no—
118D724—21no—
119D724—42no—
120D724—42no—
121C22⋊D181—42no—
122C22⋊D181—42no—
123C22⋊D181—42no—
124C2×Dic181—21no—
125C2×Dic181—21no—
126C2×Dic181C2×D411yescharacteristic
127C2×Dic181C2×D411yescharacteristic
128C2×Dic181C2×D411yescharacteristic
129C4×D181—21no—
130C4×D181—21no—
131C4×D181—22no—
132C4×D181—41no—
133C4×D181—42no—
134C4×D181—42no—
135#13089678—21no—
136#13089678—21no—
137C23×C181—21no—
138D4×C181—21no—
139D4×C181—21no—
140C2×C4×C181—21no—
141C2×C4×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—42no—
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×C181C22×D411yescharacteristic
153C2×D181—21no—
154C2×D181—21no—
155C2×D181—21no—
156C2×D181—41no—
157C2×D181—41no—
158C2×D181—41no—
159C2×D181—41no—
160C2×D181—41no—
161C2×D181—41no—
162C4×C181—21no—
163C4×C181—21no—
164C4×C181—41no—
165C4×C181—41no—
166C4×C181—41no—
167C4×C181H(5,𝔽2)11yescharacteristic
168C4×C1812−1+411yescharacteristic
169Dic181—21no—
170Dic181—21no—
171Dic181—41no—
172Dic181—41no—
173Dic181AGL(1,ℤ/8)12yes—
174C2×C181—81no—
175C2×C181#53711yescharacteristic
176C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
177C2×C181#57511yescharacteristic
178D181—41no—
179D181—81no—
180D181—81no—
181C181#325111yescharacteristic, complemented, Sylow
182#3251—1811nomaximal, Sylow
183#532—1811no—
184#529—1811no—
185#478—1811no—
186#478D18111yescharacteristic, complemented
187#475—1811no—
188#474—1811no—
189#469—1811no—
190#469—1811no—
191#468—1811no—
192#468—1811no—
193#463—1811no—
194#463—1811no—
195#460—1811no—
196#459—1811no—
197#423—1811no—
198C2×#41—3621no—
199C2×SD16—1811no—
200C2×SD16—1811no—
201C2×D8—1811no—
202C2×D8—1811no—
203C2×M16—1811no—
204C2×M16—1811no—
205C4⋊Q8—1811no—
206#127—1811no—
207#126—3621no—
208#125C2×D18111yescharacteristic
209#124—3621no—
210#124—1811no—
211#123—3621no—
212C22⋊Q8—1811no—
213#121—3621no—
214#121—1811no—
215#121—1811no—
216#121—1811no—
217C4×Q8—1811no—
218C4×D4—3621no—
219C4×D4—3621no—
220C4×D4—1811no—
221C4×D4—1811no—
222C4×D4C2×D18111yescharacteristic
223#117—3621no—
224C2×C42—1811no—
225#107—1811no—
226#107C2×D18111yescharacteristic
227#106—1811no—
228#106C2×D18111yescharacteristic
229C4⋊C8—1811no—
230C4⋊C8—1811no—
231C4⋊C8—1811no—
232C4⋊C8C2×D18111yescharacteristic
233#103—1811no—
234#103—1811no—
235#102—1811no—
236#102—1811no—
237#102—1811no—
238#102—1811no—
239#102C2×D18111yescharacteristic
240#102C2×D18111yescharacteristic
241#41—7244no—
242C2×Q8—3621no—
243C2×Q8—1811no—
244C2×D4—3621no—
245C2×D4—3621no—
246C2×D4—3621no—
247C2×D4—3621no—
248C2×D4—3621no—
249C2×D4—1811no—
250C2×D4—1811no—
251C2×D4C22×D18111yescharacteristic
252C22×C4—21no—
253C22×C4—3621no—
254C22×C4—3621no—
255C22×C4—1811no—
256C22×C4—1811no—
257C22×C4—1811no—
258SD16—7241no—
259SD16—7241no—
260D8—7241no—
261D8—7241no—
262M16—7241no—
263M16—7241no—
264C2×C8—1811no—
265C2×C8—1811no—
266C2×C8C22×D18111yescharacteristic
267C2×C8C22×D18111yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—3621no—
271C4⋊C4—3621no—
272C4⋊C4—3621no—
273C4⋊C4—1811no—
274C4⋊C4C22×D18111yescharacteristic
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—3621no—
284C22⋊C4—3621no—
285C22⋊C4—3621no—
286C42—3621no—
287C42—1811no—
288C42—1811no—
289C42—1811no—
290C42C22×D18111yescharacteristic
291C23—21no—
292C23—3621no—
293C23—3621no—
294C23—1811no—
295Q8—3621no—
296Q8—3621no—
297Q8—7242no—
298D4—21no—
299D4—21no—
300D4—3621no—
301D4—3621no—
302D4—3621no—
303D4—3621no—
304D4—7242no—
305D4—7242no—
306D4—7242no—
307D4—7242no—
308D4—7242no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—3622no—
314C2×C4—3621no—
315C2×C4—3621no—
316C2×C4—3621no—
317C2×C4—3621no—
318C2×C4—1811no—
319C2×C4—1811no—
320C2×C4—1811no—
321C2×C4—7241no—
322C2×C4—7242no—
323C2×C4—7242no—
324C2×C4D4×D18111yescharacteristic
325C2×C4D4×D18111yescharacteristic
326C2×C4C23×D18111yescharacteristic
327C8—21no—
328C8—21no—
329C8—3621no—
330C8—3621no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—3621no—
335C22—3621no—
336C22—3621no—
337C22—7241no—
338C22—7241no—
339C22—7241no—
340C22—7241no—
341C22—7241no—
342C22—7241no—
343C22C2×D4×D18111yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—3621no—
350C4—3621no—
351C4—1812no—
352C4—7241no—
353C4—7241no—
354C4#1915386211yescharacteristic
355C4#1915386411yescharacteristic
356C2—81no—
357C2—14481no—
358C2—14481no—
359C2—7241no—
360C2#2604185911yescharacteristic
361C2AGL(1,ℤ/8)×D18111yescharacteristic
362C2#2604207611yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#478×C181C2
socleC22×C181C22×D4
hypercenter#478D181
hypocenterC181#3251
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #26041826C2semidirect
2. #26041814C2semidirect
3. #26041576C2semidirect
4. #26041563C2semidirect
5. #26041558C2semidirect
6. #26041533C2semidirect
7. #26041531C2semidirect
8. #26041526C2semidirect
9. #26041524C2semidirect
10. #26041495C2semidirect
11. #26041494C2semidirect
12. #26041478C2semidirect
13. #26041473C2semidirect
14. #26041301C2semidirect
15. #478×C181C2semidirect
181. C181#3251semidirect
186. #478D181semidirect

Maximal subgroups

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

subgroupindex
#260418262
#260418142
#260415762
#260415632
#260415582
#260415332
#260415312
#260415262
#260415242
#260414952
#260414942
#260414782
#260414732
#260413012
#478×C1812
#3251181