Finite Group Databasebeta

← #37544605

Subgroups — #37544605

Order 23168.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041857C211yesmaximal, characteristic
2#26041850C211yesmaximal, characteristic, complemented
3#26041621C211yesmaximal, characteristic, complemented
4#26041615C211yesmaximal, characteristic, complemented
5#26041610C211yesmaximal, characteristic, complemented
6#26041604C211yesmaximal, characteristic, complemented
7#26041537C211yesmaximal, characteristic, complemented
8#26041525C211yesmaximal, characteristic, complemented
9#26041520C211yesmaximal, characteristic, complemented
10#26041508C211yesmaximal, characteristic, complemented
11#26041443C211yesmaximal, characteristic, complemented
12#26041443C211yesmaximal, characteristic, complemented
13#26041437C211yesmaximal, characteristic, complemented
14#26041420C211yesmaximal, characteristic, complemented
15#408×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C22×Dic362C2211yescharacteristic
18C2×Dic724C2211yescharacteristic
19C2×Dic724C2211yescharacteristic
20C2×#15668438C2211yescharacteristic
21C2×#15668438C2211yescharacteristic
22#19153814—21no—
23#19153803—21no—
24#19153797—21no—
25#19153797—21no—
26#19153795C2211yescharacteristic
27#19153795C2211yescharacteristic
28#19153795C2211yescharacteristic
29#19153795C2211yescharacteristic
30#19153795C2211yescharacteristic
31#19153795C2211yescharacteristic
32#19153792—21no—
33#19153790C2211yescharacteristic
34#19153790C2211yescharacteristic
35#19153788—21no—
36#19153788—21no—
37#19153787—21no—
38#19153775C2211yescharacteristic
39C2×C4⋊Dic181C2211yescharacteristic
40#19153750C2211yescharacteristic
41#19153750C2211yescharacteristic
42#19153748C2211yescharacteristic
43#19153748C2211yescharacteristic
44#19153741C2211yescharacteristic
45#19153741C2211yescharacteristic
46#19153741C2211yescharacteristic
47#19153741C2211yescharacteristic
48#19153741C2211yescharacteristic
49#19153741C2211yescharacteristic
50#19153738C2211yescharacteristic
51#19153738C2211yescharacteristic
52C2×#41×C181C2211yescharacteristic
53C2×M16×C181C2211yescharacteristic
54C22×C8×C181C2211yescharacteristic
55C22⋊C8×C181C2211yescharacteristic
56C22⋊C8×C181C2211yescharacteristic
57C22⋊C8×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59#15668449—41no—
60#15668449—41no—
61C2×Dic362—21no—
62C2×Dic362—41no—
63C2×Dic362—41no—
64C2×Dic362C2311yescharacteristic
65C2×Dic362C2311yescharacteristic
66C2×Dic362C2311yescharacteristic
67C2×D724C2311yescharacteristic
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C22⋊D181—21no—
71C22×Dic181—21no—
72C22×Dic181—21no—
73C2×C4×D181—21no—
74Dic724—41no—
75Dic724—41no—
76#15668438—41no—
77#15668438—41no—
78C4⋊Dic181—21no—
79C4⋊Dic181C2311yescharacteristic
80C4⋊Dic181C2311yescharacteristic
81C4⋊Dic181C2311yescharacteristic
82C4⋊Dic181C2311yescharacteristic
83#15668428—21no—
84#15668428—21no—
85#15668428—21no—
86#15668428—21no—
87#15668428—21no—
88#15668428—21no—
89C22⋊Dic181—21no—
90C22⋊Dic181—21no—
91C22⋊Dic181—21no—
92C22⋊Dic181—21no—
93C22⋊Dic181—21no—
94C22⋊Dic181—21no—
95C22⋊Dic181—21no—
96#15668426—21no—
97#15668426—21no—
98C4×Dic181—21no—
99#41×C181—41no—
100#41×C181—41no—
101C2×Q8×C181D411yescharacteristic
102C2×D4×C181D411yescharacteristic
103C2×D4×C181D411yescharacteristic
104C2×D4×C181D411yescharacteristic
105C22×C4×C181C2311yescharacteristic
106C22×C4×C181C2311yescharacteristic
107C22×C4×C181C2311yescharacteristic
108M16×C181—41no—
109C2×C8×C181—41no—
110C2×C8×C181C2311yescharacteristic
111C2×C8×C181C2311yescharacteristic
112C2×C8×C181C2311yescharacteristic
113C2×C8×C181C2311yescharacteristic
114C22×D181—21no—
115Dic362—21no—
116Dic362—21no—
117Dic362—21no—
118Dic362—21no—
119Dic362—21no—
120Dic362—21no—
121Dic362—42no—
122D724—21no—
123D724—21no—
124C22⋊D181—42no—
125C22⋊D181—81no—
126C22⋊D181—81no—
127C2×Dic181—21no—
128C2×Dic181—21no—
129C2×Dic181—21no—
130C2×Dic181—21no—
131C2×Dic181—21no—
132C2×Dic181—21no—
133C2×Dic181—21no—
134C2×Dic181—42no—
135C2×Dic181—81no—
136C4×D181—42no—
137C23×C181C2×D411yescharacteristic
138C23×C181C2×D411yescharacteristic
139C23×C181C2×D411yescharacteristic
140Q8×C181—41no—
141D4×C181—41no—
142D4×C181—41no—
143D4×C181—41no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—21no—
147C2×C4×C181—21no—
148C2×C4×C181—21no—
149C2×C4×C181—21no—
150C2×C4×C181C2×D411yescharacteristic
151C2×C4×C181C2×D411yescharacteristic
152C2×C4×C181C2×D411yescharacteristic
153C2×C4×C181C2411yescharacteristic
154C8×C181—21no—
155C8×C181—21no—
156C8×C181—21no—
157C8×C181—21no—
158C22×C181—21no—
159C22×C181—21no—
160C22×C181—21no—
161C22×C181—21no—
162C22×C181—21no—
163C22×C181—21no—
164C22×C181—21no—
165C22×C181—21no—
166C22×C181—21no—
167C22×C181C22×D411yescharacteristic
168C2×D181—41no—
169C2×D181—41no—
170C2×D181—41no—
171C4×C181—21no—
172C4×C181—21no—
173C4×C181—21no—
174C4×C181H(5,𝔽2)11yescharacteristic
175C4×C181H(5,𝔽2)11yescharacteristic
176Dic181—41no—
177Dic181—41no—
178Dic181—41no—
179Dic181—41no—
180Dic181—41no—
181Dic181—41no—
182Dic181—41no—
183C2×C181—41no—
184C2×C181—41no—
185C2×C181—41no—
186C2×C181#53411yescharacteristic
187C2×C181#57711yescharacteristic
188C2×C181#57811yescharacteristic
189D181—81no—
190C181#320111yescharacteristic, complemented, Sylow
191#3201—1811nomaximal, Sylow
192#537—1811no—
193#536—1811no—
194#485—1811no—
195#484—1811no—
196#483—1811no—
197#482—1811no—
198#470—1811no—
199#468—1811no—
200#467—1811no—
201#465—1811no—
202#452—1811no—
203#452—1811no—
204#451—1811no—
205#448—1811no—
206#408D18111yescharacteristic, complemented
207C2×#41—1811no—
208C2×#41C2×D18111yescharacteristic
209C22×Q8—1811no—
210C2×Q16—1811no—
211C2×Q16—1811no—
212C2×SD16—1811no—
213C2×SD16—1811no—
214C2×M16C2×D18111yescharacteristic
215C22×C8C2×D18111yescharacteristic
216C4⋊Q8—3621no—
217#124—3621no—
218#123—3621no—
219#123—3621no—
220C22⋊Q8—3621no—
221C22⋊Q8—1811no—
222C22⋊Q8—1811no—
223C22⋊Q8—1811no—
224C22⋊Q8—1811no—
225C22⋊Q8—1811no—
226C22⋊Q8—1811no—
227#121—3621no—
228#121—3621no—
229#121—3621no—
230#121—1811no—
231#121—1811no—
232#117—1811no—
233C2×C4⋊C4—1811no—
234#107—1811no—
235#107—1811no—
236#106—1811no—
237#106—1811no—
238#103—1811no—
239#103—1811no—
240#103—1811no—
241#103—1811no—
242#103—1811no—
243#103—1811no—
244#102—1811no—
245#102—1811no—
246C22⋊C8C2×D18111yescharacteristic
247C22⋊C8C2×D18111yescharacteristic
248C22⋊C8C2×D18111yescharacteristic
249C22⋊C8C2×D18111yescharacteristic
250#41—41no—
251#41—41no—
252#41—7241no—
253#41—7241no—
254C2×Q8—3621no—
255C2×Q8—1811no—
256C2×Q8—1811no—
257C2×Q8—1811no—
258C2×Q8—7241no—
259C2×Q8—7241no—
260C2×Q8D72411yescharacteristic
261C2×D4—3621no—
262C2×D4—3621no—
263C2×D4—3621no—
264C2×D4—1811no—
265C2×D4D72411yescharacteristic
266C2×D4D72411yescharacteristic
267C2×D4D72411yescharacteristic
268C22×C4—3621no—
269C22×C4—3621no—
270C22×C4—3621no—
271C22×C4C22×D18111yescharacteristic
272C22×C4C22×D18111yescharacteristic
273C22×C4C22×D18111yescharacteristic
274Q16—7241no—
275Q16—7241no—
276SD16—7241no—
277SD16—7241no—
278M16—41no—
279C2×C8—41no—
280C2×C8C22×D18111yescharacteristic
281C2×C8C22×D18111yescharacteristic
282C2×C8C22×D18111yescharacteristic
283C2×C8C22×D18111yescharacteristic
284C4⋊C4—3621no—
285C4⋊C4—3621no—
286C4⋊C4—3621no—
287C4⋊C4—3621no—
288C4⋊C4—3621no—
289C4⋊C4—3621no—
290C4⋊C4—3621no—
291C4⋊C4—1811no—
292C4⋊C4—1811no—
293C4⋊C4—1811no—
294C4⋊C4—1811no—
295C22⋊C4—3621no—
296C22⋊C4—3621no—
297C22⋊C4—3621no—
298C22⋊C4—3621no—
299C22⋊C4—3621no—
300C22⋊C4—3621no—
301C22⋊C4—3621no—
302C22⋊C4—3621no—
303C22⋊C4—3621no—
304C42—3621no—
305C23—3621no—
306C23C2×D72411yescharacteristic
307C23C2×D72411yescharacteristic
308C23C2×D72411yescharacteristic
309Q8—41no—
310Q8—3621no—
311Q8—3621no—
312Q8—3621no—
313Q8—3621no—
314Q8—3621no—
315Q8—3621no—
316Q8—7242no—
317D4—41no—
318D4—41no—
319D4—41no—
320D4—3621no—
321D4—3621no—
322D4—14481no—
323D4—14481no—
324D4—7242no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—3621no—
332C2×C4—3621no—
333C2×C4—3621no—
334C2×C4—3621no—
335C2×C4—3621no—
336C2×C4—3621no—
337C2×C4—3621no—
338C2×C4—14481no—
339C2×C4—7242no—
340C2×C4—7242no—
341C2×C4C2×D72411yescharacteristic
342C2×C4C2×D72411yescharacteristic
343C2×C4C2×D72411yescharacteristic
344C2×C4C23×D18111yescharacteristic
345C8—21no—
346C8—21no—
347C8—21no—
348C8—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—7241no—
359C22—7241no—
360C22—7241no—
361C22C22×D72411yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—7241no—
366C4—7241no—
367C4—7241no—
368C4—7241no—
369C4—7241no—
370C4—7241no—
371C4—7241no—
372C4#1915386111yescharacteristic
373C4#1915386111yescharacteristic
374C2—41no—
375C2—41no—
376C2—41no—
377C2—14481no—
378C2#2604184111yescharacteristic
379C2#2604209111yescharacteristic
380C2#2604209611yescharacteristic
subgroupG/H
centerC22C22×D724
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#408×C181C2
socleC22×C181C22×D4
prime radical#26041857C2
hypercenter#408D181
hypocenterC181#3201
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #26041850C2semidirect
3. #26041621C2semidirect
4. #26041615C2semidirect
5. #26041610C2semidirect
6. #26041604C2semidirect
7. #26041537C2semidirect
8. #26041525C2semidirect
9. #26041520C2semidirect
10. #26041508C2semidirect
11. #26041443C2semidirect
12. #26041443C2semidirect
13. #26041437C2semidirect
14. #26041420C2semidirect
15. #408×C181C2semidirect
190. C181#3201semidirect
206. #408D181semidirect

Maximal subgroups

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

subgroupindex
#260418572
#260418502
#260416212
#260416152
#260416102
#260416042
#260415372
#260415252
#260415202
#260415082
#260414432
#260414372
#260414202
#408×C1812
#3201181