Finite Group Databasebeta

← #34053734

Subgroups — #34053734

Order 19072.

412 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750132C211yesmaximal, characteristic
2#23749701C211yesmaximal, characteristic, complemented
3#23749700C211yesmaximal, characteristic, complemented
4#23749699C211yesmaximal, characteristic, complemented
5#23749696C211yesmaximal, characteristic, complemented
6#23749694C211yesmaximal, characteristic, complemented
7#23749693C211yesmaximal, characteristic, complemented
8C8×C22⋊D149C211yesmaximal, characteristic, complemented
9#23749688C211yesmaximal, characteristic, complemented
10#23749683C211yesmaximal, characteristic, complemented
11#23749683C211yesmaximal, characteristic, complemented
12#23749592C211yesmaximal, characteristic, complemented
13#23749587C211yesmaximal, characteristic, complemented
14C22⋊C8×D149C211yesmaximal, characteristic, complemented
15#408×C149C211yesmaximal, characteristic, complemented
16C22×C4×D149C2211yescharacteristic
17C2×#14558720C2211yescharacteristic, complemented
18C2×#14558719C2211yescharacteristic
19C2×#14558719C2211yescharacteristic
20C22×#11924746C2211yescharacteristic, complemented
21C2×C8×D149C2211yescharacteristic
22C2×C8×D149C2211yescharacteristic
23#18011892C411yescharacteristic
24#18011892C411yescharacteristic
25#18011887C411yescharacteristic
26#18011887C411yescharacteristic
27#18011882C411yescharacteristic
28#18011882C411yescharacteristic
29#18011879C411yescharacteristic
30#18011879C411yescharacteristic
31C4×C22⋊D149C2211yescharacteristic
32C4×C22⋊D149C2211yescharacteristic
33C4×C22⋊D149C2211yescharacteristic
34C4×C22⋊D149C2211yescharacteristic
35#18011870C2211yescharacteristic
36#18011840C2211yescharacteristic, complemented
37#18011840C2211yescharacteristic, complemented
38#18011840C2211yescharacteristic, complemented
39#18011840C2211yescharacteristic, complemented
40C22⋊#11924746C2211yescharacteristic
41C22⋊#11924746C2211yescharacteristic
42C22⋊#11924746C2211yescharacteristic, complemented
43C22⋊#11924746C2211yescharacteristic, complemented
44#18011823C2211yescharacteristic
45#18011823C2211yescharacteristic
46#18011823C2211yescharacteristic
47#18011823C2211yescharacteristic
48#18011821C2211yescharacteristic, complemented
49#18011821C2211yescharacteristic, complemented
50C8×Dic149C2211yescharacteristic, complemented
51C8×Dic149C2211yescharacteristic, complemented
52C2×#41×C149C2211yescharacteristic
53C2×M16×C149C2211yescharacteristic, complemented
54C22×C8×C149C2211yescharacteristic, complemented
55C22⋊C8×C149C2211yescharacteristic
56C22⋊C8×C149C2211yescharacteristic
57C22⋊C8×C149C2211yescharacteristic, complemented
58C22⋊C8×C149C2211yescharacteristic, complemented
59C23×D149C2×C411yescharacteristic
60C2×C22⋊D149C2×C411yescharacteristic
61C2×C22⋊D149C2×C411yescharacteristic
62C2×C22⋊D149C2×C411yescharacteristic
63C2×C22⋊D149C2×C411yescharacteristic
64C22×Dic149C2×C411yescharacteristic
65C2×C4×D149—41no—
66C2×C4×D149—41no—
67C2×C4×D149C2×C411yescharacteristic
68C2×C4×D149C2×C411yescharacteristic
69C2×C4×D149C2311yescharacteristic
70C2×C4×D149C2311yescharacteristic
71#14558720—41no—
72#14558719—41no—
73#14558719—41no—
74C2×#11924746—41no—
75C2×#11924746C2311yescharacteristic
76C2×#11924746C2311yescharacteristic
77C2×#11924746C2311yescharacteristic
78C2×#11924746C2311yescharacteristic
79C8×D149—41no—
80C8×D149—41no—
81C4⋊Dic149C2×C411yescharacteristic
82C4⋊Dic149C2×C411yescharacteristic
83#14558715C2×C411yescharacteristic
84#14558715C2×C411yescharacteristic
85#14558715C2×C411yescharacteristic
86#14558715C2×C411yescharacteristic
87C22⋊Dic149C2×C411yescharacteristic
88C22⋊Dic149C2×C411yescharacteristic
89C22⋊Dic149C2×C411yescharacteristic
90C22⋊Dic149C2×C411yescharacteristic
91C22⋊Dic149C2×C411yescharacteristic
92C22⋊Dic149C2×C411yescharacteristic
93#14558713C2×C411yescharacteristic
94#14558713C2×C411yescharacteristic
95#14558713C2×C411yescharacteristic
96#14558713C2×C411yescharacteristic
97C4×Dic149C2311yescharacteristic
98C4×Dic149C2311yescharacteristic
99#41×C149—41no—
100#41×C149—41no—
101C2×Q8×C149C2×C411yescharacteristic
102C2×D4×C149C2×C411yescharacteristic
103C2×D4×C149C2×C411yescharacteristic
104C2×D4×C149C2×C411yescharacteristic
105C22×C4×C149C2311yescharacteristic
106C22×C4×C149C2311yescharacteristic
107C22×C4×C149C2311yescharacteristic
108M16×C149—41no—
109C2×C8×C149—41no—
110C2×C8×C149C2311yescharacteristic
111C2×C8×C149C2311yescharacteristic
112C2×C8×C149C2311yescharacteristic
113C2×C8×C149C2311yescharacteristic
114C22×D149—22no—
115C22×D149—41no—
116C22×D149—41no—
117C22×D149C22×C411yescharacteristic
118C22×D149C22×C411yescharacteristic
119C22⋊D149—22no—
120C22⋊D149—22no—
121C22⋊D149—41no—
122C22⋊D149—41no—
123C2×Dic149—41no—
124C2×Dic149C22×C411yescharacteristic
125C2×Dic149C22×C411yescharacteristic
126C2×Dic149C22×C411yescharacteristic
127C2×Dic149C22×C411yescharacteristic
128C2×Dic149C22×C411yescharacteristic
129C2×Dic149C22×C411yescharacteristic
130C4×D149—21no—
131C4×D149—21no—
132C4×D149—21no—
133C4×D149—21no—
134C4×D149—41no—
135C4×D149—41no—
136#11924746—21no—
137#11924746—21no—
138#11924746—21no—
139#11924746—21no—
140C23×C149C22×C411yescharacteristic
141C23×C149C22×C411yescharacteristic
142C23×C149C22×C411yescharacteristic
143Q8×C149—41no—
144D4×C149—41no—
145D4×C149—41no—
146D4×C149—41no—
147C2×C4×C149—21no—
148C2×C4×C149—21no—
149C2×C4×C149—21no—
150C2×C4×C149—21no—
151C2×C4×C149—21no—
152C2×C4×C149—21no—
153C2×C4×C149C22×C411yescharacteristic
154C2×C4×C149C22×C411yescharacteristic
155C2×C4×C149C22×C411yescharacteristic
156C2×C4×C149C2411yescharacteristic
157C8×C149—21no—
158C8×C149—21no—
159C8×C149—21no—
160C8×C149—21no—
161C22×C149—21no—
162C22×C149—21no—
163C22×C149—21no—
164C22×C149—21no—
165C22×C149—21no—
166C22×C149—21no—
167C22×C149—21no—
168C22×C149—21no—
169C22×C149—21no—
170C22×C149C23×C411yescharacteristic
171C2×D149—21no—
172C2×D149—21no—
173C2×D149—21no—
174C2×D149—21no—
175C2×D149—21no—
176C2×D149—44no—
177C2×D149#13112yes—
178C4×C149—21no—
179C4×C149—21no—
180C4×C149—21no—
181C4×C149H(5,𝔽2)11yescharacteristic
182C4×C149H(5,𝔽2)11yescharacteristic
183Dic149—21no—
184Dic149—21no—
185Dic149—21no—
186Dic149—21no—
187Dic149—21no—
188Dic149—21no—
189C2×C149—41no—
190C2×C149—41no—
191C2×C149—41no—
192C2×C149#51811yescharacteristic
193C2×C149C2×#13111yescharacteristic
194C2×C149#56811yescharacteristic
195D149—22no—
196D149—41no—
197C149#297611yescharacteristic, complemented, Sylow
198#2976—1491nomaximal, Sylow
199#525—1491no—
200#436—1491no—
201#436—1491no—
202#435—1491no—
203#435—1491no—
204#435—1491no—
205#435—1491no—
206C8×D4—1491no—
207C8×D4—1491no—
208#433—1491no—
209#433—1491no—
210#408—1491no—
211#408D14911yescharacteristic, complemented
212#407—1491no—
213C2×C22⋊C8—1491no—
214C2×#41C2×D14911yescharacteristic
215C23×C4—1491no—
216C2×M16—1491no—
217C2×M16—1491no—
218C2×M16—1491no—
219C2×M16C2×D14911yescharacteristic, complemented
220C22×C8—1491no—
221C22×C8—1491no—
222C22×C8—1491no—
223C22×C8C2×D14911yescharacteristic, complemented
224#123—1491no—
225#123—1491no—
226C22⋊Q8—1491no—
227C22⋊Q8—1491no—
228#121—1491no—
229#121—1491no—
230#120—1491no—
231#120—1491no—
232C4×D4—1491no—
233C4×D4—1491no—
234C4×D4—1491no—
235C4×D4—1491no—
236#117—1491no—
237C4⋊C8—1491no—
238C4⋊C8—1491no—
239C4⋊C8—1491no—
240C4⋊C8—1491no—
241C22⋊C8—1491no—
242C22⋊C8—1491no—
243C22⋊C8—1491no—
244C22⋊C8—1491no—
245C22⋊C8—1491no—
246C22⋊C8—1491no—
247C22⋊C8—1491no—
248C22⋊C8—1491no—
249C22⋊C8C2×D14911yescharacteristic
250C22⋊C8C2×D14911yescharacteristic
251C22⋊C8C2×D14911yescharacteristic, complemented
252C22⋊C8C2×D14911yescharacteristic, complemented
253#97—1491no—
254#97—1491no—
255C4×C8—1491no—
256C4×C8—1491no—
257C24—1491no—
258#41—41no—
259#41—41no—
260C2×Q8C4×D14911yescharacteristic
261C2×D4—1491no—
262C2×D4—1491no—
263C2×D4—1491no—
264C2×D4—1491no—
265C2×D4C4×D14911yescharacteristic
266C2×D4C4×D14911yescharacteristic
267C2×D4C4×D14911yescharacteristic
268C22×C4—5961no—
269C22×C4—5961no—
270C22×C4—1491no—
271C22×C4—1491no—
272C22×C4—1491no—
273C22×C4—1491no—
274C22×C4—1491no—
275C22×C4C22×D14911yescharacteristic
276C22×C4C22×D14911yescharacteristic
277C22×C4C22×D14911yescharacteristic
278M16—41no—
279M16—5961no—
280M16—5961no—
281M16—5961no—
282C2×C8—41no—
283C2×C8—5961no—
284C2×C8—5961no—
285C2×C8—5961no—
286C2×C8—1491no—
287C2×C8—1491no—
288C2×C8—1491no—
289C2×C8—1491no—
290C2×C8C22×D14911yescharacteristic
291C2×C8C22×D14911yescharacteristic
292C2×C8C22×D14911yescharacteristic
293C2×C8C22×D14911yescharacteristic
294C4⋊C4—1491no—
295C4⋊C4—1491no—
296C4⋊C4—1491no—
297C4⋊C4—1491no—
298C4⋊C4—1491no—
299C4⋊C4—1491no—
300C22⋊C4—1491no—
301C22⋊C4—1491no—
302C22⋊C4—1491no—
303C22⋊C4—1491no—
304C22⋊C4—1491no—
305C22⋊C4—1491no—
306C22⋊C4—1491no—
307C22⋊C4—1491no—
308C22⋊C4—1491no—
309C22⋊C4—1491no—
310C42—1491no—
311C42—1491no—
312C23—2982no—
313C23—5961no—
314C23—5961no—
315C23—1491no—
316C23—1491no—
317C23C2×C4×D14911yescharacteristic
318C23C2×C4×D14911yescharacteristic
319C23C2×C4×D14911yescharacteristic
320Q8—41no—
321D4—41no—
322D4—41no—
323D4—41no—
324D4—2982no—
325D4—2982no—
326D4—5961no—
327D4—5961no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—2981no—
335C2×C4—2981no—
336C2×C4—2981no—
337C2×C4—2981no—
338C2×C4—5961no—
339C2×C4—5961no—
340C2×C4—5961no—
341C2×C4—1491no—
342C2×C4—1491no—
343C2×C4—1491no—
344C2×C4—1491no—
345C2×C4—1491no—
346C2×C4—1491no—
347C2×C4C2×C4×D14911yescharacteristic
348C2×C4C2×C4×D14911yescharacteristic
349C2×C4C2×C4×D14911yescharacteristic
350C2×C4C23×D14911yescharacteristic
351C8—21no—
352C8—21no—
353C8—21no—
354C8—21no—
355C8—2981no—
356C8—2981no—
357C8—2981no—
358C8—2981no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—2981no—
369C22—2981no—
370C22—2981no—
371C22—2981no—
372C22—2981no—
373C22—5964no—
374C22—1492no—
375C22C22×C4×D14911yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—2981no—
380C4—2981no—
381C4—2981no—
382C4—2981no—
383C4—2981no—
384C4—2981no—
385C4#1801195611yescharacteristic
386C4#1801195611yescharacteristic
387C2—41no—
388C2—41no—
389C2—41no—
390C2—2982no—
391C2—5961no—
392C2#2375009811yescharacteristic
393C2#131×D14911yescharacteristic
394C2#2375039011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D149
commutator, socleC22×C149C23×C4
Fitting#408×C149C2
prime radical#23750132C2
cosocleC2×C4×C149C24
hypercenter#408D149
hypocenterC149#2976
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #23749701C2semidirect
3. #23749700C2semidirect
4. #23749699C2semidirect
5. #23749696C2semidirect
6. #23749694C2semidirect
7. #23749693C2semidirect
8. C8×C22⋊D149C2semidirect
9. #23749688C2semidirect
10. #23749683C2semidirect
11. #23749683C2semidirect
12. #23749592C2semidirect
13. #23749587C2semidirect
14. C22⋊C8×D149C2semidirect
15. #408×C149C2semidirect
17. C2×#14558720C22semidirect
20. C22×#11924746C22semidirect
36. #18011840C22semidirect
37. #18011840C22semidirect
38. #18011840C22semidirect
39. #18011840C22semidirect
42. C22⋊#11924746C22semidirect
43. C22⋊#11924746C22semidirect
48. #18011821C22semidirect
49. #18011821C22semidirect
50. C8×Dic149C22semidirect
51. C8×Dic149C22semidirect
53. C2×M16×C149C22semidirect
54. C22×C8×C149C22semidirect
57. C22⋊C8×C149C22semidirect
58. C22⋊C8×C149C22semidirect
197. C149#2976semidirect
211. #408D149semidirect
219. C2×M16C2×D149semidirect
223. C22×C8C2×D149semidirect
251. C22⋊C8C2×D149semidirect
252. C22⋊C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501322
#237497012
#237497002
#237496992
#237496962
#237496942
#237496932
C8×C22⋊D1492
#237496882
#237496832
#237495922
#237495872
C22⋊C8×D1492
#408×C1492
#2976149