Finite Group Databasebeta

← #34054975

Subgroups — #34054975

Order 19072.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750249C211yesmaximal, characteristic, complemented
2#23750107C211yesmaximal, characteristic, complemented
3#23749957C211yesmaximal, characteristic, complemented
4#23749945C211yesmaximal, characteristic, complemented
5#23749912C211yesmaximal, characteristic, complemented
6#23749847C211yesmaximal, characteristic, complemented
7#23749841C211yesmaximal, characteristic, complemented
8#23749790C211yesmaximal, characteristic, complemented
9#23749773C211yesmaximal, characteristic
10#23749736C211yesmaximal, characteristic, complemented
11#23749729C211yesmaximal, characteristic, complemented
12#23749712C211yesmaximal, characteristic, complemented
13#23749710C211yesmaximal, characteristic, complemented
14#23749685C211yesmaximal, characteristic, complemented
15#475×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558726C2211yescharacteristic
18C2×#14558725C2211yescharacteristic
19C2×#14558723C2211yescharacteristic
20C2×D1192C2211yescharacteristic
21#18011906—21no—
22#18011900—21no—
23#18011899C2211yescharacteristic
24#18011896—21no—
25#18011891C2211yescharacteristic
26#18011887—21no—
27#18011886C2211yescharacteristic
28Q8×Dic149C2211yescharacteristic
29#18011876C2211yescharacteristic
30C4×D596—21no—
31C4×D596C2211yescharacteristic
32#18011873—21no—
33#18011873C2211yescharacteristic
34#18011873C2211yescharacteristic
35#18011868—21no—
36#18011868C2211yescharacteristic
37C4⋊C4×D149—21no—
38C4⋊C4×D149C2211yescharacteristic
39#18011842C2211yescharacteristic
40#18011842C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic
42#18011836C2211yescharacteristic
43#18011834C2211yescharacteristic
44#18011833C2211yescharacteristic
45#18011831C2211yescharacteristic
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C4⋊Q8×C149C2211yescharacteristic
53C4×Q8×C149C2211yescharacteristic
54#106×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#103×C149C2211yescharacteristic
59#14558737—22no—
60#14558737—22no—
61C2×Dic298C2311yescharacteristic
62C2×D596—21no—
63C2×D596—21no—
64C2×D596C2311yescharacteristic
65C2×D596C2311yescharacteristic
66C2×C4×D149—21no—
67C2×C4×D149—21no—
68C2×C4×D149—21no—
69C2×C4×D149—21no—
70C2×C4×D149—21no—
71C2×C4×D149C2311yescharacteristic
72#14558726—22no—
73#14558725—22no—
74#14558723—22no—
75D1192—22no—
76C2×#11924746C2311yescharacteristic
77C2×#11924746C2311yescharacteristic
78C4⋊Dic149—21no—
79C4⋊Dic149—21no—
80C4⋊Dic149C2311yescharacteristic
81#14558715—21no—
82#14558715—21no—
83#14558715D411yescharacteristic
84#14558715D411yescharacteristic
85#14558713—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713D411yescharacteristic
93#14558713D411yescharacteristic
94C4×Dic149—21no—
95C4×Dic149—21no—
96C4×Dic149C2311yescharacteristic
97C2×Q8×C149—21no—
98C2×Q8×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C2×C8×C149C2311yescharacteristic
101C4⋊C4×C149—21no—
102C4⋊C4×C149—21no—
103C4⋊C4×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C4⋊C4×C149C2311yescharacteristic
106C42×C149—21no—
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109C22×D149—21no—
110C22×D149C2×D411yescharacteristic
111Dic298—21no—
112Dic298—21no—
113D596—24no—
114D596—21no—
115D596—21no—
116D596—21no—
117D596—81no—
118D596#4112yes—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149C2×D411yescharacteristic
122C2×Dic149C2×D411yescharacteristic
123C2×Dic149C2×D411yescharacteristic
124C4×D149—24no—
125C4×D149—21no—
126C4×D149—21no—
127C4×D149—81no—
128C4×D149—81no—
129C4×D149—81no—
130C4×D149—81no—
131#11924746—21no—
132#11924746—21no—
133Q8×C149—21no—
134Q8×C149—81no—
135Q8×C149#4112yes—
136C2×C4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149—21no—
139C2×C4×C149—21no—
140C2×C4×C149C2×D411yescharacteristic
141C2×C4×C149C2×D411yescharacteristic
142C2×C4×C149C2411yescharacteristic
143C8×C149—21no—
144C8×C149—21no—
145C22×C149C22×D411yescharacteristic
146C2×D149—21no—
147C2×D149—22no—
148C2×D149—21no—
149C2×D149—21no—
150C2×D149—41no—
151C2×D149—41no—
152C2×D149—41no—
153C2×D149—41no—
154C2×D149—41no—
155C4×C149—22no—
156C4×C149—21no—
157C4×C149—21no—
158C4×C149—41no—
159C4×C149—41no—
160C4×C149—41no—
161C4×C149C2×#4111yescharacteristic
162C4×C149C2×#4111yescharacteristic
163Dic149—21no—
164Dic149—21no—
165Dic149—21no—
166Dic149—41no—
167Dic149—41no—
168C2×C149#52511yescharacteristic
169C2×C149#57711yescharacteristic
170C2×C149#57711yescharacteristic
171D149—41no—
172D149—42no—
173D149—81no—
174C149#312511yescharacteristic, complemented, Sylow
175#3125—1491nomaximal, Sylow
176#542—1491no—
177#520—1491no—
178#483—1491no—
179#481—1491no—
180#476—1491no—
181#475D14911yescharacteristic, complemented
182#464—1491no—
183#463—1491no—
184#452—1491no—
185#449—1491no—
186#442—1491no—
187#441—1491no—
188C4×SD16—1491no—
189C4×SD16—1491no—
190#433—1491no—
191C2×#41—1491no—
192C2×Q16—1491no—
193C2×SD16—1491no—
194C2×SD16—1491no—
195C2×D8—1491no—
196C4⋊Q8C2×D14911yescharacteristic
197#126—2981no—
198#124—2981no—
199#124—1491no—
200#123—2981no—
201C22⋊Q8—2981no—
202C22⋊Q8—1491no—
203#121—1491no—
204C4×Q8—1491no—
205C4×Q8—1491no—
206C4×Q8C2×D14911yescharacteristic
207C4×D4—2981no—
208C4×D4—2981no—
209C4×D4—1491no—
210C4×D4—1491no—
211C4×D4—1491no—
212#117—2981no—
213#117—1491no—
214C2×C4⋊C4—2981no—
215C2×C4⋊C4—1491no—
216#106—1491no—
217#106—1491no—
218#106C2×D14911yescharacteristic
219#106C2×D14911yescharacteristic
220C4⋊C8—1491no—
221C4⋊C8C2×D14911yescharacteristic
222#103—1491no—
223#103—1491no—
224#103C2×D14911yescharacteristic
225#103C2×D14911yescharacteristic
226#102—1491no—
227#102—1491no—
228#102—1491no—
229#102—1491no—
230C22⋊C8—1491no—
231C22⋊C8—1491no—
232#97—1491no—
233C4×C8—1491no—
234#41—2982no—
235#41—2982no—
236C2×Q8—21no—
237C2×Q8—1491no—
238C2×Q8C22×D14911yescharacteristic
239C2×D4—2981no—
240C2×D4—2981no—
241C2×D4—1491no—
242C2×D4—1491no—
243C22×C4—2981no—
244C22×C4—2981no—
245C22×C4—2981no—
246C22×C4—2981no—
247C22×C4—2981no—
248C22×C4—1491no—
249Q16—2982no—
250SD16—2982no—
251SD16—2982no—
252D8—2982no—
253C2×C8—1491no—
254C2×C8—1491no—
255C2×C8C22×D14911yescharacteristic
256C2×C8C22×D14911yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—2981no—
260C4⋊C4—2981no—
261C4⋊C4—2981no—
262C4⋊C4—2981no—
263C4⋊C4—1491no—
264C4⋊C4—1491no—
265C4⋊C4—1491no—
266C4⋊C4C22×D14911yescharacteristic
267C4⋊C4C22×D14911yescharacteristic
268C4⋊C4C22×D14911yescharacteristic
269C22⋊C4—2981no—
270C22⋊C4—2981no—
271C22⋊C4—2981no—
272C22⋊C4—2981no—
273C22⋊C4—2981no—
274C22⋊C4—2981no—
275C22⋊C4—2981no—
276C22⋊C4—1491no—
277C22⋊C4—1491no—
278C42—21no—
279C42—2981no—
280C42—2981no—
281C42—1491no—
282C42C22×D14911yescharacteristic
283C23—2981no—
284C23—2981no—
285C23—1491no—
286Q8—21no—
287Q8—81no—
288Q8—2981no—
289Q8—2981no—
290Q8#1455873712yes—
291D4—2984no—
292D4—2981no—
293D4—2981no—
294D4—2981no—
295D4—1492no—
296D4—11921no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—2984no—
302C2×C4—2981no—
303C2×C4—2981no—
304C2×C4—2981no—
305C2×C4—2981no—
306C2×C4—1491no—
307C2×C4—1491no—
308C2×C4—1491no—
309C2×C4—11921no—
310C2×C4—11921no—
311C2×C4—11921no—
312C2×C4—11921no—
313C2×C4D4×D14911yescharacteristic
314C2×C4D4×D14911yescharacteristic
315C2×C4C23×D14911yescharacteristic
316C8—21no—
317C8—21no—
318C8—2981no—
319C8—2981no—
320C22—2981no—
321C22—2981no—
322C22—2981no—
323C22—2982no—
324C22—5961no—
325C22—5961no—
326C22—5961no—
327C22—5961no—
328C22—5961no—
329C22C2×D4×D14911yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—2981no—
337C4—2981no—
338C4—2981no—
339C4—5961no—
340C4—5961no—
341C4#41×D14911yescharacteristic
342C4C2×#1455873711yescharacteristic
343C2—5961no—
344C2—5962no—
345C2—11921no—
346C2#2375013811yescharacteristic
347C2#2375043111yescharacteristic
348C2#2375043411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#475×C149C2
socleC22×C149C22×D4
prime radical#23749773C2
hypercenter#475D149
hypocenterC149#3125
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #23750249C2semidirect
2. #23750107C2semidirect
3. #23749957C2semidirect
4. #23749945C2semidirect
5. #23749912C2semidirect
6. #23749847C2semidirect
7. #23749841C2semidirect
8. #23749790C2semidirect
10. #23749736C2semidirect
11. #23749729C2semidirect
12. #23749712C2semidirect
13. #23749710C2semidirect
14. #23749685C2semidirect
15. #475×C149C2semidirect
174. C149#3125semidirect
181. #475D149semidirect

Maximal subgroups

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

subgroupindex
#237502492
#237501072
#237499572
#237499452
#237499122
#237498472
#237498412
#237497902
#237497732
#237497362
#237497292
#237497122
#237497102
#237496852
#475×C1492
#3125149