Finite Group Databasebeta

← #34056615

Subgroups — #34056615

Order 19072.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750338C211yesmaximal, characteristic, complemented
2#23750274C211yesmaximal, characteristic, complemented
3#23749974C211yesmaximal, characteristic, complemented
4#23749966C211yesmaximal, characteristic, complemented
5#23749964C211yesmaximal, characteristic, complemented
6#23749913C211yesmaximal, characteristic, complemented
7#23749857C211yesmaximal, characteristic, complemented
8#23749854C211yesmaximal, characteristic, complemented
9#23749829C211yesmaximal, characteristic, complemented
10#23749771C211yesmaximal, characteristic, complemented
11#23749770C211yesmaximal, characteristic, complemented
12#23749705C211yesmaximal, characteristic, complemented
13C8×C22⋊D149C211yesmaximal, characteristic, complemented
14#23749618C211yesmaximal, characteristic, complemented
15#416×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×#14558725C2211yescharacteristic
18C2×#14558723C2211yescharacteristic
19C2×#14558721C2211yescharacteristic
20C2×C8×D149C2211yescharacteristic
21#18011910C2211yescharacteristic
22#18011909C2211yescharacteristic
23#18011899—21no—
24#18011897—21no—
25#18011894—21no—
26#18011892—21no—
27#18011890C2211yescharacteristic
28#18011887C2211yescharacteristic
29#18011886C2211yescharacteristic
30#18011885C2211yescharacteristic
31#18011884—21no—
32#18011883—21no—
33D4×Dic149C2211yescharacteristic
34#18011873C2211yescharacteristic
35C4×C22⋊D149C2211yescharacteristic
36#18011869C2211yescharacteristic
37#18011868—21no—
38C2×#14558715—21no—
39#18011844C2211yescharacteristic
40#18011843C2211yescharacteristic
41#18011842C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011835C2211yescharacteristic
45#18011834C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011832C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011823C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×#41×C149C2211yescharacteristic
53C22×C8×C149C2211yescharacteristic
54#117×C149C2211yescharacteristic
55#103×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59#14558735—22no—
60#14558735—41no—
61C2×Dic298—21no—
62C2×Dic298C2311yescharacteristic
63C2×D596—21no—
64C2×D596C2311yescharacteristic
65C2×C22⋊D149—21no—
66C2×C22⋊D149—21no—
67C2×C22⋊D149D411yescharacteristic
68C22×Dic149—21no—
69C22×Dic149—21no—
70C2×C4×D149—21no—
71C2×C4×D149C2311yescharacteristic
72#14558725—41no—
73#14558723—41no—
74#14558721—22no—
75C2×#11924746C2311yescharacteristic
76C2×#11924746C2311yescharacteristic
77C8×D149—41no—
78C4⋊Dic149C2311yescharacteristic
79C4⋊Dic149C2311yescharacteristic
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715D411yescharacteristic
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C22⋊Dic149D411yescharacteristic
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713—21no—
94#14558713D411yescharacteristic
95C4×Dic149—21no—
96C4×Dic149C2311yescharacteristic
97#41×C149—22no—
98#41×C149—41no—
99C2×Q8×C149C2311yescharacteristic
100C2×D4×C149—21no—
101C2×D4×C149C2311yescharacteristic
102C22×C4×C149—21no—
103C22×C4×C149C2311yescharacteristic
104C2×C8×C149—41no—
105C2×C8×C149C2311yescharacteristic
106C2×C8×C149C2311yescharacteristic
107C4⋊C4×C149C2311yescharacteristic
108C4⋊C4×C149C2311yescharacteristic
109C22⋊C4×C149—21no—
110C42×C149—21no—
111C22×D149—21no—
112C22×D149C2×D411yescharacteristic
113Dic298—21no—
114Dic298—21no—
115Dic298—81no—
116D596—21no—
117D596—21no—
118D596—81no—
119C22⋊D149—22no—
120C22⋊D149—42no—
121C22⋊D149—81no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149—42no—
126C2×Dic149—42no—
127C2×Dic149C2×D411yescharacteristic
128C2×Dic149C2×D411yescharacteristic
129C2×Dic149C2×D411yescharacteristic
130C4×D149—21no—
131C4×D149—21no—
132C4×D149—42no—
133#11924746—21no—
134#11924746—21no—
135C23×C149—21no—
136C23×C149C2×D411yescharacteristic
137Q8×C149—21no—
138Q8×C149—21no—
139D4×C149—21no—
140D4×C149—42no—
141D4×C149#4112yes—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—21no—
145C2×C4×C149—21no—
146C2×C4×C149—21no—
147C2×C4×C149—42no—
148C2×C4×C149C2×D411yescharacteristic
149C2×C4×C149C2411yescharacteristic
150C8×C149—21no—
151C8×C149—21no—
152C22×C149—21no—
153C22×C149—22no—
154C22×C149—21no—
155C22×C149—21no—
156C22×C149—41no—
157C22×C149—41no—
158C22×C149C22×D411yescharacteristic
159C2×D149—21no—
160C2×D149—21no—
161C2×D149—21no—
162C2×D149—41no—
163C2×D149—41no—
164C2×D149—41no—
165C4×C149—21no—
166C4×C149—41no—
167C4×C149—41no—
168C4×C149—41no—
169C4×C149C2×#4111yescharacteristic
170C4×C149H(5,𝔽2)11yescharacteristic
171Dic149—21no—
172Dic149—21no—
173Dic149—41no—
174Dic149—41no—
175Dic149—41no—
176Dic149#13512yes—
177C2×C149—41no—
178C2×C149—42no—
179C2×C149#54611yescharacteristic
180C2×C149C2×#13511yescharacteristic
181C2×C149#57711yescharacteristic
182D149—41no—
183D149—81no—
184C149#330311yescharacteristic, complemented, Sylow
185#3303—1491nomaximal, Sylow
186#555—1491no—
187#547—1491no—
188#487—1491no—
189#485—1491no—
190#485—1491no—
191#476—1491no—
192#465—1491no—
193#465—1491no—
194#461—1491no—
195#449—1491no—
196#449—1491no—
197C4×D8—1491no—
198C8×D4—1491no—
199#416—1491no—
200#416D14911yescharacteristic, complemented
201C2×#41—1491no—
202C2×#41C2×D14911yescharacteristic
203C2×SD16—1491no—
204C2×SD16—1491no—
205C2×D8—1491no—
206C22×C8—1491no—
207C22×C8C2×D14911yescharacteristic
208C4⋊Q8—1491no—
209C4⋊Q8—1491no—
210#124—2981no—
211#124—2981no—
212#123—2981no—
213#123—2981no—
214C22⋊Q8—1491no—
215C22⋊Q8—1491no—
216#121—2981no—
217#121—2981no—
218#121—1491no—
219#121—1491no—
220C4×D4—1491no—
221C4×D4—1491no—
222C4×D4—1491no—
223#117—2981no—
224#117—1491no—
225#117C2×D14911yescharacteristic
226C2×C4⋊C4—2981no—
227#107—1491no—
228#106—1491no—
229#106—1491no—
230C4⋊C8—1491no—
231#103—1491no—
232#103—1491no—
233#103—1491no—
234#103—1491no—
235#103C2×D14911yescharacteristic
236#103C2×D14911yescharacteristic
237#102—1491no—
238#102—1491no—
239#102C2×D14911yescharacteristic
240#102C2×D14911yescharacteristic
241C22⋊C8—1491no—
242C22⋊C8—1491no—
243C4×C8—1491no—
244#41—22no—
245#41—41no—
246#41—2982no—
247#41—5961no—
248C2×Q8—2981no—
249C2×Q8—1491no—
250C2×Q8C22×D14911yescharacteristic
251C2×D4—21no—
252C2×D4—2981no—
253C2×D4—2981no—
254C2×D4—2981no—
255C2×D4—1491no—
256C2×D4—1491no—
257C2×D4C22×D14911yescharacteristic
258C22×C4—21no—
259C22×C4—2981no—
260C22×C4—2981no—
261C22×C4—2981no—
262C22×C4—1491no—
263C22×C4C22×D14911yescharacteristic
264SD16—5961no—
265SD16—5961no—
266D8—2982no—
267C2×C8—41no—
268C2×C8—5961no—
269C2×C8—1491no—
270C2×C8—1491no—
271C2×C8C22×D14911yescharacteristic
272C2×C8C22×D14911yescharacteristic
273C4⋊C4—2981no—
274C4⋊C4—2981no—
275C4⋊C4—2981no—
276C4⋊C4—2981no—
277C4⋊C4—2981no—
278C4⋊C4—1491no—
279C4⋊C4—1491no—
280C4⋊C4—1491no—
281C4⋊C4C22×D14911yescharacteristic
282C4⋊C4C22×D14911yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—2981no—
285C22⋊C4—2981no—
286C22⋊C4—2981no—
287C22⋊C4—2981no—
288C22⋊C4—2981no—
289C22⋊C4—2981no—
290C22⋊C4—2981no—
291C22⋊C4—1491no—
292C22⋊C4—1491no—
293C42—21no—
294C42—2981no—
295C42—1491no—
296C23—21no—
297C23—2981no—
298C23—1491no—
299C23D4×D14911yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—2981no—
303Q8—2981no—
304Q8—11921no—
305D4—21no—
306D4—42no—
307D4—2982no—
308D4—2981no—
309D4—2981no—
310D4—5962no—
311D4—11921no—
312D4—11921no—
313D4#1455873612yes—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—42no—
320C2×C4—2981no—
321C2×C4—2981no—
322C2×C4—2981no—
323C2×C4—2981no—
324C2×C4—2981no—
325C2×C4—5962no—
326C2×C4—5962no—
327C2×C4—5962no—
328C2×C4—1491no—
329C2×C4—1491no—
330C2×C4—1491no—
331C2×C4D4×D14911yescharacteristic
332C2×C4C23×D14911yescharacteristic
333C8—21no—
334C8—21no—
335C8—2981no—
336C8—2981no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—2981no—
344C22—2981no—
345C22—2981no—
346C22—5961no—
347C22—5961no—
348C22—5961no—
349C22C2×D4×D14911yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—2981no—
355C4—2981no—
356C4—5961no—
357C4—5961no—
358C4—5961no—
359C4—1492no—
360C4C2×#1455873611yescharacteristic
361C4#1801195611yescharacteristic
362C2—41no—
363C2—42no—
364C2—5961no—
365C2—11921no—
366C2#2375026511yescharacteristic
367C2#135×D14911yescharacteristic
368C2#2375043211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#416×C149C2
socleC22×C149C22×D4
hypercenter#416D149
hypocenterC149#3303
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #23750338C2semidirect
2. #23750274C2semidirect
3. #23749974C2semidirect
4. #23749966C2semidirect
5. #23749964C2semidirect
6. #23749913C2semidirect
7. #23749857C2semidirect
8. #23749854C2semidirect
9. #23749829C2semidirect
10. #23749771C2semidirect
11. #23749770C2semidirect
12. #23749705C2semidirect
13. C8×C22⋊D149C2semidirect
14. #23749618C2semidirect
15. #416×C149C2semidirect
184. C149#3303semidirect
200. #416D149semidirect

Maximal subgroups

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

subgroupindex
#237503382
#237502742
#237499742
#237499662
#237499642
#237499132
#237498572
#237498542
#237498292
#237497712
#237497702
#237497052
C8×C22⋊D1492
#237496182
#416×C1492
#3303149