Finite Group Databasebeta

← #37545159

Subgroups — #37545159

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#26041885C211yesmaximal, characteristic, complemented
2#26041880C211yesmaximal, characteristic, complemented
3#26041582C211yesmaximal, characteristic, complemented
4#26041578C211yesmaximal, characteristic, complemented
5#26041576C211yesmaximal, characteristic, complemented
6#26041533C211yesmaximal, characteristic, complemented
7#26041531C211yesmaximal, characteristic, complemented
8#26041516C211yesmaximal, characteristic, complemented
9#26041514C211yesmaximal, characteristic, complemented
10#26041475C211yesmaximal, characteristic, complemented
11#26041474C211yesmaximal, characteristic, complemented
12#26041473C211yesmaximal, characteristic, complemented
13#26041473C211yesmaximal, characteristic, complemented
14#26041304C211yesmaximal, characteristic, complemented
15#478×C181C211yesmaximal, characteristic, complemented
16C2×D1448C2211yescharacteristic
17C2×D1448C2211yescharacteristic
18C2×#15668434C2211yescharacteristic
19C2×#15668434C2211yescharacteristic
20C2×#15668432C2211yescharacteristic
21C2×C8×D181C2211yescharacteristic
22#19153813C2211yescharacteristic
23#19153812C2211yescharacteristic
24#19153807C2211yescharacteristic
25#19153801—21no—
26#19153801—21no—
27#19153799—21no—
28#19153798—21no—
29#19153791—21no—
30#19153791—21no—
31#19153791C2211yescharacteristic
32#19153791C2211yescharacteristic
33#19153791C2211yescharacteristic
34#19153790—21no—
35#19153789—21no—
36#19153787C2211yescharacteristic
37C4×D724C2211yescharacteristic
38#19153778C2211yescharacteristic
39#19153778C2211yescharacteristic
40#19153773C2211yescharacteristic
41#19153749C2211yescharacteristic
42#19153747C2211yescharacteristic
43C4⋊#13089678C2211yescharacteristic
44#19153745C2211yescharacteristic
45#19153745C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153738C2211yescharacteristic
48#19153736C2211yescharacteristic
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
59C2×D724—21no—
60C2×D724—21no—
61C2×D724—21no—
62C2×D724—21no—
63C2×D724—21no—
64C2×D724C2311yescharacteristic
65C2×D724C2311yescharacteristic
66C2×D724C2311yescharacteristic
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C4×D181—21no—
71C2×C4×D181—21no—
72C2×C4×D181—21no—
73C2×C4×D181C2311yescharacteristic
74D1448—41no—
75D1448—41no—
76#15668434—41no—
77#15668434—41no—
78#15668432—41no—
79C2×#13089678C2311yescharacteristic
80C2×#13089678C2311yescharacteristic
81C8×D181—41no—
82C4⋊Dic181—21no—
83C4⋊Dic181C2311yescharacteristic
84#15668428—21no—
85#15668428D411yescharacteristic
86#15668428D411yescharacteristic
87C22⋊Dic181—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426D411yescharacteristic
95#15668426D411yescharacteristic
96C4×Dic181C2311yescharacteristic
97C2×D4×C181C2311yescharacteristic
98C22×C4×C181—21no—
99C2×C8×C181C2311yescharacteristic
100C2×C8×C181C2311yescharacteristic
101C4⋊C4×C181—21no—
102C4⋊C4×C181—21no—
103C4⋊C4×C181C2311yescharacteristic
104C4⋊C4×C181C2311yescharacteristic
105C4⋊C4×C181C2311yescharacteristic
106C22⋊C4×C181—21no—
107C42×C181C2311yescharacteristic
108C22×D181—21no—
109C22×D181—21no—
110C22×D181—21no—
111C22×D181C2×D411yescharacteristic
112D724—21no—
113D724—21no—
114D724—21no—
115D724—21no—
116D724—21no—
117D724—21no—
118D724—81no—
119D724—81no—
120D724—81no—
121D724—81no—
122D724—81no—
123C22⋊D181—81no—
124C22⋊D181—81no—
125C22⋊D181—81no—
126C2×Dic181—21no—
127C2×Dic181C2×D411yescharacteristic
128C2×Dic181C2×D411yescharacteristic
129C2×Dic181C2×D411yescharacteristic
130C4×D181—21no—
131C4×D181—21no—
132C4×D181—81no—
133C4×D181—81no—
134C4×D181—81no—
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—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×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—
162C2×D181—41no—
163C2×D181—41no—
164C2×D181—41no—
165C4×C181—21no—
166C4×C181—21no—
167C4×C181—41no—
168C4×C181—41no—
169C4×C181—41no—
170C4×C181H(5,𝔽2)11yescharacteristic
171C4×C1812−1+411yescharacteristic
172Dic181—21no—
173Dic181—21no—
174Dic181—21no—
175Dic181—41no—
176C2×C181—81no—
177C2×C181#53711yescharacteristic
178C2×C181#57611yescharacteristic
179C2×C181#57611yescharacteristic
180D181—41no—
181D181—81no—
182D181—81no—
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#478D18111yescharacteristic, complemented
192#469—1811no—
193#469—1811no—
194#466—1811no—
195#466—1811no—
196#459—1811no—
197#459—1811no—
198#459—1811no—
199#459—1811no—
200#424—1811no—
201C2×D8—1811no—
202C2×D8—1811no—
203C2×D8—1811no—
204C2×D8—1811no—
205C2×M16—1811no—
206C22×C8—1811no—
207#127—1811no—
208#127—1811no—
209#125—1811no—
210#125C2×D18111yescharacteristic
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#107C2×D18111yescharacteristic
230#106—1811no—
231#106C2×D18111yescharacteristic
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—3621no—
245C2×D4—3621no—
246C2×D4—3621no—
247C2×D4—3621no—
248C2×D4—3621no—
249C2×D4—3621no—
250C2×D4—3621no—
251C2×D4—3621no—
252C2×D4—1811no—
253C2×D4—1811no—
254C2×D4—1811no—
255C2×D4C22×D18111yescharacteristic
256C22×C4—21no—
257C22×C4—3621no—
258C22×C4—3621no—
259C22×C4—3621no—
260C22×C4—1811no—
261D8—7241no—
262D8—7241no—
263D8—7241no—
264D8—7241no—
265M16—7241no—
266C2×C8—1811no—
267C2×C8—1811no—
268C2×C8—7241no—
269C2×C8C22×D18111yescharacteristic
270C2×C8C22×D18111yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—3621no—
274C4⋊C4—3621no—
275C4⋊C4—1811no—
276C4⋊C4—1811no—
277C4⋊C4—1811no—
278C4⋊C4C22×D18111yescharacteristic
279C4⋊C4C22×D18111yescharacteristic
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—3621no—
295C23—3621no—
296C23—3621no—
297C23—1811no—
298D4—21no—
299D4—21no—
300D4—3621no—
301D4—3621no—
302D4—3621no—
303D4—3621no—
304D4—3621no—
305D4—3621no—
306D4—14481no—
307D4—14481no—
308D4—14481no—
309D4—14481no—
310D4—14481no—
311D4—14481no—
312D4—14481no—
313D4—14481no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—81no—
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—3621no—
338C22—3621no—
339C22—3621no—
340C22—7241no—
341C22—7241no—
342C22—7241no—
343C22—7241no—
344C22—7241no—
345C22—7241no—
346C22—7241no—
347C22—7241no—
348C22—7241no—
349C22C2×D4×D18111yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—3621no—
356C4—3621no—
357C4—3621no—
358C4—7241no—
359C4#1915386211yescharacteristic
360C4#1915386411yescharacteristic
361C2—81no—
362C2—14481no—
363C2—14481no—
364C2—14481no—
365C2—7241no—
366C2#2604185911yescharacteristic
367C2#2604208111yescharacteristic
368C2#2604208311yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#478×C181C2
socleC22×C181C22×D4
hypercenter#478D181
hypocenterC181#3259
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. #26041885C2semidirect
2. #26041880C2semidirect
3. #26041582C2semidirect
4. #26041578C2semidirect
5. #26041576C2semidirect
6. #26041533C2semidirect
7. #26041531C2semidirect
8. #26041516C2semidirect
9. #26041514C2semidirect
10. #26041475C2semidirect
11. #26041474C2semidirect
12. #26041473C2semidirect
13. #26041473C2semidirect
14. #26041304C2semidirect
15. #478×C181C2semidirect
184. C181#3259semidirect
191. #478D181semidirect

Maximal subgroups

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

subgroupindex
#260418852
#260418802
#260415822
#260415782
#260415762
#260415332
#260415312
#260415162
#260415142
#260414752
#260414742
#260414732
#260413042
#478×C1812
#3259181