Finite Group Databasebeta

← #37543696

Subgroups — #37543696

Order 23168.

398 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#26041858C211yesmaximal, characteristic
2#26041759C211yesmaximal, characteristic, complemented
3#26041623C211yesmaximal, characteristic, complemented
4#26041620C211yesmaximal, characteristic, complemented
5#26041616C211yesmaximal, characteristic, complemented
6#26041615C211yesmaximal, characteristic, complemented
7#26041601C211yesmaximal, characteristic, complemented
8#26041591C211yesmaximal, characteristic, complemented
9#26041590C211yesmaximal, characteristic, complemented
10#26041318C211yesmaximal, characteristic, complemented
11#107×D181C211yesmaximal, characteristic, complemented
12#26041277C211yesmaximal, characteristic, complemented
13#26041272C211yesmaximal, characteristic, complemented
14#26041244C211yesmaximal, characteristic, complemented
15#482×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C2×#15668448C2211yescharacteristic
18C2×#15668432C2211yescharacteristic
19C2×C8×D181C2211yescharacteristic
20#19153796C2211yescharacteristic
21#19153795C2211yescharacteristic
22#19153793—21no—
23#19153789—21no—
24#19153788—21no—
25#19153787—21no—
26#19153787C2211yescharacteristic
27C4×Dic362—21no—
28C4×D724—21no—
29#19153776—21no—
30#19153776—21no—
31#19153774C2211yescharacteristic
32#19153774C2211yescharacteristic
33C2×C4⋊Dic181C2211yescharacteristic
34C4⋊C4×D181C2211yescharacteristic
35C4⋊C4×D181C2211yescharacteristic
36C4⋊C4×D181C2211yescharacteristic
37#19153750C2211yescharacteristic
38#19153750C2211yescharacteristic
39#19153749C2211yescharacteristic
40#19153749C2211yescharacteristic
41#19153749C2211yescharacteristic
42#19153747C2211yescharacteristic
43#19153741C2211yescharacteristic
44#19153741C2211yescharacteristic
45#19153739C2211yescharacteristic
46#19153739C2211yescharacteristic
47#19153737C2211yescharacteristic
48#19153737C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153728C2211yescharacteristic
52#121×C181C2211yescharacteristic
53#117×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic
55#106×C181C2211yescharacteristic
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59#15668449—22no—
60#15668449—22no—
61#15668448—22no—
62#15668448—22no—
63C2×Dic362D411yescharacteristic
64C2×Dic362C2311yescharacteristic
65C2×D724D411yescharacteristic
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C2×C22⋊D181D411yescharacteristic
69C2×C22⋊D181D411yescharacteristic
70C22×Dic181—21no—
71C22×Dic181—21no—
72C2×C4×D181—21no—
73C2×C4×D181—21no—
74C2×C4×D181—21no—
75C2×C4×D181C2311yescharacteristic
76C2×C4×D181C2311yescharacteristic
77#15668432—22no—
78C2×#13089678C2311yescharacteristic
79C2×#13089678C2311yescharacteristic
80C8×D181—22no—
81C4⋊Dic181—21no—
82C4⋊Dic181—21no—
83C4⋊Dic181C2311yescharacteristic
84C4⋊Dic181C2311yescharacteristic
85C4⋊Dic181C2311yescharacteristic
86#15668428—21no—
87#15668428—21no—
88#15668428—21no—
89#15668428—21no—
90C22⋊Dic181—21no—
91C22⋊Dic181—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95C4×Dic181—21no—
96C4×Dic181—21no—
97C2×D4×C181—21no—
98C2×D4×C181C2311yescharacteristic
99C22×C4×C181C2311yescharacteristic
100C2×C8×C181C2311yescharacteristic
101C2×C8×C181C2311yescharacteristic
102C4⋊C4×C181C2311yescharacteristic
103C4⋊C4×C181C2311yescharacteristic
104C4⋊C4×C181C2311yescharacteristic
105C22⋊C4×C181—21no—
106C22⋊C4×C181—21no—
107C42×C181—21no—
108C22×D181C2×D411yescharacteristic
109C22×D181C2×D411yescharacteristic
110Dic362—22no—
111Dic362—21no—
112Dic362—21no—
113D724—22no—
114C22⋊D181—22no—
115C22⋊D181—22no—
116C22⋊D181—42no—
117C22⋊D181—81no—
118C2×Dic181—21no—
119C2×Dic181—21no—
120C2×Dic181—21no—
121C2×Dic181—21no—
122C2×Dic181—42no—
123C2×Dic181—81no—
124C2×Dic181C2×D411yescharacteristic
125C2×Dic181C2×D411yescharacteristic
126C4×D181—21no—
127C4×D181—21no—
128C4×D181—81no—
129C4×D181—81no—
130C4×D181—81no—
131C4×D181#4112yes—
132C4×D181#4112yes—
133#13089678—21no—
134#13089678—21no—
135C23×C181—21no—
136C23×C181C2×D411yescharacteristic
137D4×C181—21no—
138D4×C181—21no—
139D4×C181—81no—
140C2×C4×C181—21no—
141C2×C4×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181C2×D411yescharacteristic
146C2×C4×C181C2411yescharacteristic
147C8×C181—21no—
148C8×C181—21no—
149C22×C181—21no—
150C22×C181—21no—
151C22×C181—21no—
152C22×C181—41no—
153C22×C181—41no—
154C22×C181—41no—
155C22×C181C22×D411yescharacteristic
156C2×D181—21no—
157C2×D181—21no—
158C2×D181—21no—
159C2×D181—21no—
160C2×D181—21no—
161C2×D181#12312yes—
162C4×C181—21no—
163C4×C181—41no—
164C4×C181—41no—
165C4×C181—41no—
166C4×C181C2×#4111yescharacteristic
167C4×C181C2×#4111yescharacteristic
168Dic181—21no—
169Dic181—41no—
170Dic181—41no—
171Dic181—41no—
172Dic181—41no—
173Dic181#12312yes—
174C2×C181—41no—
175C2×C181—81no—
176C2×C181C2×#12311yescharacteristic
177C2×C181#57611yescharacteristic
178C2×C181#57811yescharacteristic
179D181—22no—
180D181—41no—
181C181#309811yescharacteristic, complemented, Sylow
182#3098—1811nomaximal, Sylow
183#537—1811no—
184#520—1811no—
185#485—1811no—
186#485—1811no—
187#484—1811no—
188#484—1811no—
189#482—1811no—
190#482D18111yescharacteristic, complemented
191#480—1811no—
192#480—1811no—
193#428—1811no—
194C2×#107—1811no—
195#417—1811no—
196#416—1811no—
197#408—1811no—
198C2×#41—1811no—
199C2×#41—1811no—
200C2×M16—1811no—
201C22×C8—1811no—
202C22⋊Q8—3621no—
203C22⋊Q8—1811no—
204C22⋊Q8—1811no—
205#121—3621no—
206#121—3621no—
207#121—3621no—
208#121—1811no—
209#121C2×D18111yescharacteristic
210C4×Q8—3621no—
211C4×D4—3621no—
212C4×D4—3621no—
213C4×D4—3621no—
214#117—1811no—
215#117—1811no—
216#117C2×D18111yescharacteristic
217C2×C4⋊C4—1811no—
218C2×C4⋊C4—1811no—
219C2×C4⋊C4—1811no—
220C2×C4⋊C4—1811no—
221#107—1811no—
222#107—1811no—
223#107—1811no—
224#107—1811no—
225#107—1811no—
226#107C2×D18111yescharacteristic
227#106—1811no—
228#106C2×D18111yescharacteristic
229#103—1811no—
230#103—1811no—
231#103—1811no—
232#103—1811no—
233#102—1811no—
234#102—1811no—
235#102C2×D18111yescharacteristic
236#102C2×D18111yescharacteristic
237C22⋊C8—1811no—
238C22⋊C8—1811no—
239C22⋊C8—1811no—
240C22⋊C8C2×D18111yescharacteristic
241#41—3622no—
242#41—3622no—
243#41—3622no—
244#41—3622no—
245C2×Q8—1811no—
246C2×Q8—1811no—
247C2×D4—21no—
248C2×D4—3621no—
249C2×D4—3621no—
250C2×D4—1811no—
251C2×D4—1811no—
252C2×D4—1811no—
253C2×D4C22×D18111yescharacteristic
254C22×C4—3621no—
255C22×C4—3621no—
256C22×C4—3621no—
257C22×C4—3621no—
258C22×C4—3621no—
259C22×C4—1811no—
260C22×C4—1811no—
261C22×C4C22×D18111yescharacteristic
262M16—3622no—
263C2×C8—3622no—
264C2×C8—1811no—
265C2×C8—1811no—
266C2×C8C22×D18111yescharacteristic
267C2×C8C22×D18111yescharacteristic
268C4⋊C4—3621no—
269C4⋊C4—3621no—
270C4⋊C4—3621no—
271C4⋊C4—3621no—
272C4⋊C4—3621no—
273C4⋊C4—3621no—
274C4⋊C4—1811no—
275C4⋊C4—1811no—
276C4⋊C4—1811no—
277C4⋊C4C22×D18111yescharacteristic
278C4⋊C4C22×D18111yescharacteristic
279C4⋊C4C22×D18111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—3621no—
283C22⋊C4—3621no—
284C22⋊C4—3621no—
285C22⋊C4—3621no—
286C22⋊C4—3621no—
287C42—21no—
288C42—3621no—
289C42—3621no—
290C23—21no—
291C23—1811no—
292C23—1811no—
293C23D4×D18111yescharacteristic
294Q8—3622no—
295Q8—3621no—
296Q8—3621no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—3622no—
301D4—3622no—
302D4—3622no—
303D4—14481no—
304D4—7242no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—3621no—
311C2×C4—3621no—
312C2×C4—3621no—
313C2×C4—3621no—
314C2×C4—3621no—
315C2×C4—3621no—
316C2×C4—14481no—
317C2×C4—14481no—
318C2×C4—14481no—
319C2×C4—14481no—
320C2×C4—1811no—
321C2×C4—1811no—
322C2×C4—1812no—
323C2×C4—1812no—
324C2×C4—7242no—
325C2×C4D4×D18111yescharacteristic
326C2×C4C23×D18111yescharacteristic
327C8—21no—
328C8—21no—
329C8—3621no—
330C8—3621no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—3621no—
338C22—3621no—
339C22—3621no—
340C22—3621no—
341C22—3621no—
342C22—1812no—
343C22C2×D4×D18111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—3621no—
349C4—1812no—
350C4—7241no—
351C4—7241no—
352C4—7241no—
353C4—7241no—
354C4#41×D18111yescharacteristic
355C4#41×D18111yescharacteristic
356C2—41no—
357C2—81no—
358C2—3622no—
359C2—7241no—
360C2#123×D18111yescharacteristic
361C2#2604208311yescharacteristic
362C2#2604209311yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#482×C181C2
socleC22×C181C22×D4
prime radical#26041858C2
hypercenter#482D181
hypocenterC181#3098
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #26041759C2semidirect
3. #26041623C2semidirect
4. #26041620C2semidirect
5. #26041616C2semidirect
6. #26041615C2semidirect
7. #26041601C2semidirect
8. #26041591C2semidirect
9. #26041590C2semidirect
10. #26041318C2semidirect
11. #107×D181C2semidirect
12. #26041277C2semidirect
13. #26041272C2semidirect
14. #26041244C2semidirect
15. #482×C181C2semidirect
181. C181#3098semidirect
190. #482D181semidirect

Maximal subgroups

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

subgroupindex
#260418582
#260417592
#260416232
#260416202
#260416162
#260416152
#260416012
#260415912
#260415902
#260413182
#107×D1812
#260412772
#260412722
#260412442
#482×C1812
#3098181