Finite Group Databasebeta

← #37544629

Subgroups — #37544629

Order 23168.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041859C211yesmaximal, characteristic, complemented
2#26041857C211yesmaximal, characteristic, complemented
3#26041608C211yesmaximal, characteristic, complemented
4#26041607C211yesmaximal, characteristic, complemented
5#26041598C211yesmaximal, characteristic, complemented
6#26041596C211yesmaximal, characteristic, complemented
7#26041534C211yesmaximal, characteristic, complemented
8#26041531C211yesmaximal, characteristic, complemented
9#26041511C211yesmaximal, characteristic, complemented
10#26041505C211yesmaximal, characteristic, complemented
11#26041440C211yesmaximal, characteristic, complemented
12#26041424C211yesmaximal, characteristic, complemented
13#26041423C211yesmaximal, characteristic, complemented
14#26041244C211yesmaximal, characteristic, complemented
15#452×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668449C2211yescharacteristic
18C2×#15668436C2211yescharacteristic
19C2×#15668434C2211yescharacteristic
20C2×#15668432C2211yescharacteristic
21C2×C8×D181C2211yescharacteristic
22#19153795—21no—
23#19153794—21no—
24#19153792C2211yescharacteristic
25#19153792C2211yescharacteristic
26#19153792C2211yescharacteristic
27#19153791—21no—
28#19153791C2211yescharacteristic
29#19153790—21no—
30#19153790C2211yescharacteristic
31#19153789—21no—
32#19153789—21no—
33#19153788—21no—
34#19153788—21no—
35#19153787C2211yescharacteristic
36#19153787C2211yescharacteristic
37C2×C4⋊Dic181C2211yescharacteristic
38C4⋊C4×D181C2211yescharacteristic
39#19153748C2211yescharacteristic
40#19153748C2211yescharacteristic
41#19153747C2211yescharacteristic
42#19153747C2211yescharacteristic
43#19153740C2211yescharacteristic
44#19153740C2211yescharacteristic
45#19153740C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153738C2211yescharacteristic
48#19153737C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153728C2211yescharacteristic
52C2×#41×C181C2211yescharacteristic
53C2×Q16×C181C2211yescharacteristic
54C2×SD16×C181C2211yescharacteristic
55C22⋊Q8×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59#15668450—41no—
60#15668450—41no—
61#15668449—41no—
62#15668449—41no—
63C2×Dic362D411yescharacteristic
64C2×D724—21no—
65C2×D724—21no—
66C2×D724D411yescharacteristic
67C2×D724C2311yescharacteristic
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C22⋊D181—21no—
71C2×C22⋊D181D411yescharacteristic
72C2×C22⋊D181D411yescharacteristic
73C22×Dic181—21no—
74C2×C4×D181—21no—
75C2×C4×D181—21no—
76C2×C4×D181C2311yescharacteristic
77C2×C4×D181C2311yescharacteristic
78#15668436—41no—
79#15668434—41no—
80#15668432—41no—
81C2×#13089678C2311yescharacteristic
82C2×#13089678C2311yescharacteristic
83C8×D181—41no—
84C4⋊Dic181—21no—
85C4⋊Dic181C2311yescharacteristic
86C4⋊Dic181C2311yescharacteristic
87C4⋊Dic181C2311yescharacteristic
88#15668428—21no—
89#15668428—21no—
90#15668428—21no—
91#15668428—21no—
92C22⋊Dic181—21no—
93C22⋊Dic181—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426—21no—
97#15668426—21no—
98#15668426—21no—
99#41×C181—41no—
100#41×C181—41no—
101C2×Q8×C181C2311yescharacteristic
102C2×Q8×C181C2311yescharacteristic
103C2×D4×C181—21no—
104C2×D4×C181C2311yescharacteristic
105C22×C4×C181—21no—
106C22×C4×C181C2311yescharacteristic
107Q16×C181—41no—
108SD16×C181—41no—
109C2×C8×C181C2311yescharacteristic
110C2×C8×C181C2311yescharacteristic
111C4⋊C4×C181—21no—
112C4⋊C4×C181C2311yescharacteristic
113C22⋊C4×C181—21no—
114C22×D181—21no—
115C22×D181C2×D411yescharacteristic
116C22×D181C2×D411yescharacteristic
117Dic362—41no—
118D724—21no—
119D724—21no—
120D724—41no—
121D724—42no—
122D724—81no—
123C22⋊D181—41no—
124C22⋊D181—41no—
125C22⋊D181—81no—
126C22⋊D181—81no—
127C22⋊D181—81no—
128C2×Dic181—21no—
129C2×Dic181—21no—
130C2×Dic181—21no—
131C2×Dic181—81no—
132C2×Dic181C2×D411yescharacteristic
133C2×Dic181C2×D411yescharacteristic
134C4×D181—21no—
135C4×D181—21no—
136C4×D181—21no—
137C4×D181—21no—
138C4×D181—42no—
139C4×D181—81no—
140#13089678—21no—
141#13089678—21no—
142C23×C181—21no—
143C23×C181C2×D411yescharacteristic
144Q8×C181—21no—
145Q8×C181—21no—
146Q8×C181—21no—
147Q8×C181—21no—
148D4×C181—21no—
149D4×C181—21no—
150D4×C181—42no—
151C2×C4×C181—21no—
152C2×C4×C181—21no—
153C2×C4×C181—21no—
154C2×C4×C181—21no—
155C2×C4×C181—21no—
156C2×C4×C181—42no—
157C2×C4×C181C2×D411yescharacteristic
158C2×C4×C181C2411yescharacteristic
159C8×C181—21no—
160C8×C181—21no—
161C22×C181—21no—
162C22×C181—21no—
163C22×C181—21no—
164C22×C181—41no—
165C22×C181—41no—
166C22×C181—41no—
167C22×C181C22×D411yescharacteristic
168C2×D181—21no—
169C2×D181—21no—
170C2×D181—21no—
171C2×D181—21no—
172C2×D181—21no—
173C2×D181—21no—
174C2×D181—41no—
175C2×D181—41no—
176C2×D181—41no—
177C4×C181—21no—
178C4×C181—41no—
179C4×C181—41no—
180C4×C181—41no—
181C4×C181H(5,𝔽2)11yescharacteristic
182C4×C181H(5,𝔽2)11yescharacteristic
183Dic181—21no—
184Dic181—21no—
185Dic181—41no—
186Dic181—41no—
187Dic181—41no—
188C2×C181—41no—
189C2×C181—81no—
190C2×C181#53411yescharacteristic
191C2×C181#57711yescharacteristic
192C2×C181#57711yescharacteristic
193D181—41no—
194D181—41no—
195D181—81no—
196C181#320411yescharacteristic, complemented, Sylow
197#3204—1811nomaximal, Sylow
198#537—1811no—
199#537—1811no—
200#483—1811no—
201#483—1811no—
202#481—1811no—
203#481—1811no—
204#470—1811no—
205#469—1811no—
206#465—1811no—
207#465—1811no—
208#452—1811no—
209#452D18111yescharacteristic, complemented
210#449—1811no—
211#449—1811no—
212#408—1811no—
213C2×#41—1811no—
214C2×#41—1811no—
215C2×#41C2×D18111yescharacteristic
216C2×Q16C2×D18111yescharacteristic
217C2×SD16—1811no—
218C2×SD16C2×D18111yescharacteristic
219C2×D8—1811no—
220C2×M16—1811no—
221C22×C8—1811no—
222C22⋊Q8—3621no—
223C22⋊Q8—3621no—
224C22⋊Q8—1811no—
225C22⋊Q8—1811no—
226C22⋊Q8—1811no—
227C22⋊Q8C2×D18111yescharacteristic
228#121—3621no—
229#121—3621no—
230#121—3621no—
231#121—3621no—
232#121—3621no—
233#121—3621no—
234#121—1811no—
235#121—1811no—
236#121—1811no—
237#121—1811no—
238C2×C4⋊C4—1811no—
239C2×C4⋊C4—1811no—
240#106—1811no—
241#106—1811no—
242#106—1811no—
243#106—1811no—
244#103—1811no—
245#103—1811no—
246#103—1811no—
247#103C2×D18111yescharacteristic
248#102—1811no—
249#102—1811no—
250#102—1811no—
251#102C2×D18111yescharacteristic
252C22⋊C8—1811no—
253C22⋊C8—1811no—
254C22⋊C8—1811no—
255C22⋊C8C2×D18111yescharacteristic
256#41—41no—
257#41—41no—
258#41—7241no—
259#41—7241no—
260#41—7241no—
261#41—7241no—
262C2×Q8—1811no—
263C2×Q8C22×D18111yescharacteristic
264C2×Q8C22×D18111yescharacteristic
265C2×D4—21no—
266C2×D4—3621no—
267C2×D4—3621no—
268C2×D4—3621no—
269C2×D4—3621no—
270C2×D4—3621no—
271C2×D4—1811no—
272C2×D4—1811no—
273C2×D4—1811no—
274C2×D4—1811no—
275C2×D4C22×D18111yescharacteristic
276C22×C4—21no—
277C22×C4—3621no—
278C22×C4—3621no—
279C22×C4—3621no—
280C22×C4—1811no—
281C22×C4—1811no—
282C22×C4C22×D18111yescharacteristic
283Q16—41no—
284SD16—41no—
285SD16—7241no—
286D8—7241no—
287M16—7241no—
288C2×C8—1811no—
289C2×C8—1811no—
290C2×C8—7241no—
291C2×C8C22×D18111yescharacteristic
292C2×C8C22×D18111yescharacteristic
293C4⋊C4—21no—
294C4⋊C4—3621no—
295C4⋊C4—3621no—
296C4⋊C4—3621no—
297C4⋊C4—3621no—
298C4⋊C4—3621no—
299C4⋊C4—1811no—
300C4⋊C4—1811no—
301C4⋊C4—1811no—
302C4⋊C4C22×D18111yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—3621no—
305C22⋊C4—3621no—
306C22⋊C4—3621no—
307C22⋊C4—3621no—
308C22⋊C4—3621no—
309C22⋊C4—3621no—
310C22⋊C4—3621no—
311C23—21no—
312C23—3621no—
313C23—1811no—
314C23—1811no—
315C23D4×D18111yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—21no—
319Q8—21no—
320Q8—7241no—
321D4—21no—
322D4—21no—
323D4—42no—
324D4—3621no—
325D4—3621no—
326D4—14481no—
327D4—14481no—
328D4—14481no—
329D4—14481no—
330D4—7241no—
331D4—7242no—
332D4—7241no—
333D4—7241no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—3621no—
341C2×C4—3621no—
342C2×C4—3621no—
343C2×C4—3621no—
344C2×C4—3621no—
345C2×C4—3621no—
346C2×C4—3621no—
347C2×C4—14481no—
348C2×C4—14481no—
349C2×C4—1811no—
350C2×C4—1811no—
351C2×C4—7242no—
352C2×C4D4×D18111yescharacteristic
353C2×C4C23×D18111yescharacteristic
354C8—21no—
355C8—21no—
356C8—3621no—
357C8—3621no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—3621no—
365C22—3621no—
366C22—3621no—
367C22—3621no—
368C22—3621no—
369C22—3621no—
370C22—7241no—
371C22—7241no—
372C22—7241no—
373C22C2×D4×D18111yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—3621no—
379C4—3621no—
380C4—7241no—
381C4—7241no—
382C4—7241no—
383C4#1915386111yescharacteristic
384C4#1915386111yescharacteristic
385C2—41no—
386C2—81no—
387C2—14481no—
388C2—7241no—
389C2—7241no—
390C2#2604183911yescharacteristic
391C2#2604208611yescharacteristic
392C2#2604208811yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#452×C181C2
socleC22×C181C22×D4
hypercenter#452D181
hypocenterC181#3204
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #26041859C2semidirect
2. #26041857C2semidirect
3. #26041608C2semidirect
4. #26041607C2semidirect
5. #26041598C2semidirect
6. #26041596C2semidirect
7. #26041534C2semidirect
8. #26041531C2semidirect
9. #26041511C2semidirect
10. #26041505C2semidirect
11. #26041440C2semidirect
12. #26041424C2semidirect
13. #26041423C2semidirect
14. #26041244C2semidirect
15. #452×C181C2semidirect
196. C181#3204semidirect
209. #452D181semidirect

Maximal subgroups

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

subgroupindex
#260418592
#260418572
#260416082
#260416072
#260415982
#260415962
#260415342
#260415312
#260415112
#260415052
#260414402
#260414242
#260414232
#260412442
#452×C1812
#3204181