Finite Group Databasebeta

← #37543700

Subgroups — #37543700

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#26041859C211yesmaximal, characteristic
2#26041760C211yesmaximal, characteristic, complemented
3#26041618C211yesmaximal, characteristic, complemented
4#26041617C211yesmaximal, characteristic, complemented
5#26041613C211yesmaximal, characteristic, complemented
6#26041606C211yesmaximal, characteristic, complemented
7#26041604C211yesmaximal, characteristic, complemented
8#26041594C211yesmaximal, characteristic, complemented
9#26041592C211yesmaximal, characteristic, complemented
10#26041320C211yesmaximal, characteristic, complemented
11#107×D181C211yesmaximal, characteristic, complemented
12#26041279C211yesmaximal, characteristic, complemented
13#26041274C211yesmaximal, characteristic, complemented
14#26041244C211yesmaximal, characteristic, complemented
15#484×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668449C2211yescharacteristic
18C2×#15668432C2211yescharacteristic
19C2×C8×D181C2211yescharacteristic
20#19153794—21no—
21#19153792C2211yescharacteristic
22#19153791—21no—
23#19153791C2211yescharacteristic
24#19153790C2211yescharacteristic
25#19153789—21no—
26#19153789—21no—
27#19153781—21no—
28#19153778—21no—
29C4×C22⋊D181—21no—
30C4×C22⋊D181—21no—
31#19153775C2211yescharacteristic
32#19153774C2211yescharacteristic
33#19153774C2211yescharacteristic
34C4⋊C4×D181C2211yescharacteristic
35C4⋊C4×D181C2211yescharacteristic
36C4⋊C4×D181C2211yescharacteristic
37#19153750C2211yescharacteristic
38#19153749C2211yescharacteristic
39#19153749C2211yescharacteristic
40#19153749C2211yescharacteristic
41#19153748C2211yescharacteristic
42#19153747C2211yescharacteristic
43#19153740C2211yescharacteristic
44#19153740C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153728C2211yescharacteristic
52C22⋊Q8×C181C2211yescharacteristic
53C2×C4⋊C4×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic
55#107×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59#15668450—22no—
60#15668450—22no—
61#15668449—22no—
62#15668449—22no—
63C2×Dic362D411yescharacteristic
64C2×D724—21no—
65C2×D724—21no—
66C2×D724D411yescharacteristic
67C2×D724C2311yescharacteristic
68C2×C22⋊D181—21no—
69C2×C22⋊D181D411yescharacteristic
70C2×C22⋊D181D411yescharacteristic
71C2×C4×D181—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⋊Dic181C2311yescharacteristic
82C4⋊Dic181C2311yescharacteristic
83C4⋊Dic181C2311yescharacteristic
84#15668428—21no—
85#15668428—21no—
86#15668428—21no—
87#15668428—21no—
88C22⋊Dic181—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94C4×Dic181—21no—
95C4×Dic181—21no—
96C4×Dic181—21no—
97C2×Q8×C181C2311yescharacteristic
98C22×C4×C181—21no—
99C22×C4×C181C2311yescharacteristic
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—
108C22×D181—21no—
109C22×D181C2×D411yescharacteristic
110C22×D181C2×D411yescharacteristic
111Dic362—22no—
112D724—22no—
113D724—21no—
114D724—21no—
115D724—42no—
116D724—81no—
117C22⋊D181—22no—
118C22⋊D181—22no—
119C22⋊D181—81no—
120C2×Dic181—21no—
121C2×Dic181—21no—
122C2×Dic181—21no—
123C2×Dic181C2×D411yescharacteristic
124C2×Dic181C2×D411yescharacteristic
125C4×D181—21no—
126C4×D181—21no—
127C4×D181—42no—
128C4×D181—81no—
129C4×D181—81no—
130C4×D181—81no—
131C4×D181#4112yes—
132C4×D181#4112yes—
133#13089678—21no—
134#13089678—21no—
135C23×C181C2×D411yescharacteristic
136Q8×C181—21no—
137Q8×C181—21no—
138C2×C4×C181—21no—
139C2×C4×C181—21no—
140C2×C4×C181—21no—
141C2×C4×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181—81no—
145C2×C4×C181C2×D411yescharacteristic
146C2×C4×C181C2411yescharacteristic
147C8×C181—21no—
148C8×C181—21no—
149C22×C181—21no—
150C22×C181—21no—
151C22×C181—21no—
152C22×C181C22×D411yescharacteristic
153C2×D181—21no—
154C2×D181—21no—
155C2×D181—21no—
156C2×D181—21no—
157C2×D181—21no—
158C2×D181—41no—
159C2×D181—41no—
160C2×D181—41no—
161C2×D181#12312yes—
162C4×C181—21no—
163C4×C181—41no—
164C4×C181—41no—
165C4×C181—41no—
166C4×C181—41no—
167C4×C181C2×#4111yescharacteristic
168C4×C181C2×#4111yescharacteristic
169Dic181—21no—
170Dic181—41no—
171Dic181—41no—
172Dic181—41no—
173Dic181#12312yes—
174C2×C181—41no—
175C2×C181C2×#12311yescharacteristic
176C2×C181#57611yescharacteristic
177C2×C181#57811yescharacteristic
178D181—22no—
179D181—41no—
180D181—81no—
181C181#309811yescharacteristic, complemented, Sylow
182#3098—1811nomaximal, Sylow
183#537—1811no—
184#520—1811no—
185#485—1811no—
186#485—1811no—
187#484—1811no—
188#484D18111yescharacteristic, complemented
189#482—1811no—
190#482—1811no—
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⋊Q8C2×D18111yescharacteristic
205#121—3621no—
206#121—3621no—
207#121—3621no—
208#121—1811no—
209#121—1811no—
210C4×Q8—3621no—
211C4×D4—3621no—
212C4×D4—3621no—
213C4×D4—3621no—
214#117—1811no—
215#117—1811no—
216#117—1811no—
217C2×C4⋊C4—1811no—
218C2×C4⋊C4—1811no—
219C2×C4⋊C4—1811no—
220C2×C4⋊C4C2×D18111yescharacteristic
221#107—1811no—
222#107—1811no—
223#107—1811no—
224#107—1811no—
225#107C2×D18111yescharacteristic
226#107C2×D18111yescharacteristic
227#106—1811no—
228#106—1811no—
229#103—1811no—
230#103—1811no—
231#103C2×D18111yescharacteristic
232#103C2×D18111yescharacteristic
233#102—1811no—
234#102—1811no—
235#102—1811no—
236#102—1811no—
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×Q8C22×D18111yescharacteristic
247C2×D4—3621no—
248C2×D4—3621no—
249C2×D4—3621no—
250C2×D4—1811no—
251C2×D4—1811no—
252C2×D4—1811no—
253C2×D4—1811no—
254C22×C4—21no—
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—21no—
269C4⋊C4—21no—
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—3621no—
282C22⋊C4—3621no—
283C22⋊C4—3621no—
284C22⋊C4—3621no—
285C22⋊C4—3621no—
286C22⋊C4—3621no—
287C42—3621no—
288C42—3621no—
289C42—3621no—
290C23—3621no—
291C23—1811no—
292C23—1811no—
293C23D4×D18111yescharacteristic
294Q8—21no—
295Q8—21no—
296Q8—3622no—
297D4—3622no—
298D4—3622no—
299D4—3622no—
300D4—3621no—
301D4—3621no—
302D4—14481no—
303D4—14481no—
304D4—7242no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—3621no—
313C2×C4—3621no—
314C2×C4—3621no—
315C2×C4—3621no—
316C2×C4—3621no—
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—3621no—
335C22—3621no—
336C22—3621no—
337C22—3621no—
338C22—3621no—
339C22—1812no—
340C22—7241no—
341C22—7241no—
342C22—7241no—
343C22C2×D4×D18111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—3621no—
350C4—1812no—
351C4—7241no—
352C4—7241no—
353C4—7241no—
354C4#41×D18111yescharacteristic
355C4#41×D18111yescharacteristic
356C2—41no—
357C2—3622no—
358C2—14481no—
359C2—7241no—
360C2#123×D18111yescharacteristic
361C2#2604208311yescharacteristic
362C2#2604209211yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#484×C181C2
socleC22×C181C22×D4
prime radical#26041859C2
hypercenter#484D181
hypocenterC181#3098
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. #26041760C2semidirect
3. #26041618C2semidirect
4. #26041617C2semidirect
5. #26041613C2semidirect
6. #26041606C2semidirect
7. #26041604C2semidirect
8. #26041594C2semidirect
9. #26041592C2semidirect
10. #26041320C2semidirect
11. #107×D181C2semidirect
12. #26041279C2semidirect
13. #26041274C2semidirect
14. #26041244C2semidirect
15. #484×C181C2semidirect
181. C181#3098semidirect
188. #484D181semidirect

Maximal subgroups

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

subgroupindex
#260418592
#260417602
#260416182
#260416172
#260416132
#260416062
#260416042
#260415942
#260415922
#260413202
#107×D1812
#260412792
#260412742
#260412442
#484×C1812
#3098181