Finite Group Databasebeta

← #34056604

Subgroups — #34056604

Order 19072.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750343C211yesmaximal, characteristic, complemented
2#23750274C211yesmaximal, characteristic
3#23749974C211yesmaximal, characteristic, complemented
4#23749966C211yesmaximal, characteristic, complemented
5#23749965C211yesmaximal, characteristic, complemented
6#23749903C211yesmaximal, characteristic, complemented
7#23749866C211yesmaximal, characteristic, complemented
8#23749865C211yesmaximal, characteristic, complemented
9#23749834C211yesmaximal, characteristic, complemented
10#23749788C211yesmaximal, characteristic, complemented
11#23749787C211yesmaximal, characteristic, complemented
12#23749716C211yesmaximal, characteristic, complemented
13C8×C22⋊D149C211yesmaximal, characteristic, complemented
14#23749618C211yesmaximal, characteristic, complemented
15#416×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×Dic596C2211yescharacteristic
18C2×#14558726C2211yescharacteristic
19C2×#14558724C2211yescharacteristic
20C2×C8×D149C2211yescharacteristic
21#18011910C2211yescharacteristic
22#18011909C2211yescharacteristic
23#18011905—21no—
24#18011904—21no—
25#18011897—21no—
26#18011894—21no—
27#18011892—21no—
28#18011891C2211yescharacteristic
29#18011890C2211yescharacteristic
30#18011890C2211yescharacteristic
31#18011887C2211yescharacteristic
32#18011883—21no—
33C4×Dic298—21no—
34#18011876C2211yescharacteristic
35D4×Dic149C2211yescharacteristic
36C4×C22⋊D149C2211yescharacteristic
37#18011869C2211yescharacteristic
38C2×#14558715—21no—
39#18011845C2211yescharacteristic
40#18011844C2211yescharacteristic
41#18011842C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011834C2211yescharacteristic
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×Dic298C2311yescharacteristic
64C2×C22⋊D149—21no—
65C2×C22⋊D149D411yescharacteristic
66C22×Dic149—21no—
67C22×Dic149—21no—
68C2×C4×D149C2311yescharacteristic
69Dic596—41no—
70#14558726—41no—
71#14558724—22no—
72C2×#11924746C2311yescharacteristic
73C2×#11924746C2311yescharacteristic
74C8×D149—41no—
75C4⋊Dic149—21no—
76C4⋊Dic149C2311yescharacteristic
77C4⋊Dic149C2311yescharacteristic
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715D411yescharacteristic
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88C22⋊Dic149—21no—
89C22⋊Dic149D411yescharacteristic
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93#14558713D411yescharacteristic
94C4×Dic149—21no—
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×D149C2×D411yescharacteristic
112Dic298—21no—
113Dic298—21no—
114Dic298—21no—
115Dic298—21no—
116Dic298—42no—
117C22⋊D149—22no—
118C22⋊D149—42no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—42no—
124C2×Dic149—42no—
125C2×Dic149C2×D411yescharacteristic
126C2×Dic149C2×D411yescharacteristic
127C2×Dic149C2×D411yescharacteristic
128C4×D149—21no—
129C4×D149—21no—
130#11924746—21no—
131#11924746—21no—
132C23×C149—21no—
133C23×C149C2×D411yescharacteristic
134Q8×C149—21no—
135Q8×C149—21no—
136D4×C149—21no—
137D4×C149—42no—
138D4×C149#4112yes—
139C2×C4×C149—21no—
140C2×C4×C149—21no—
141C2×C4×C149—21no—
142C2×C4×C149—21no—
143C2×C4×C149—21no—
144C2×C4×C149—42no—
145C2×C4×C149C2×D411yescharacteristic
146C2×C4×C149C2411yescharacteristic
147C8×C149—21no—
148C8×C149—21no—
149C22×C149—21no—
150C22×C149—22no—
151C22×C149—21no—
152C22×C149—21no—
153C22×C149—41no—
154C22×C149—41no—
155C22×C149C22×D411yescharacteristic
156C2×D149—21no—
157C2×D149—21no—
158C2×D149—21no—
159C4×C149—21no—
160C4×C149—41no—
161C4×C149—41no—
162C4×C149—41no—
163C4×C149C2×#4111yescharacteristic
164C4×C149H(5,𝔽2)11yescharacteristic
165Dic149—21no—
166Dic149—21no—
167Dic149—41no—
168Dic149—41no—
169Dic149—41no—
170Dic149—41no—
171Dic149#13512yes—
172C2×C149—41no—
173C2×C149—42no—
174C2×C149#54611yescharacteristic
175C2×C149C2×#13511yescharacteristic
176C2×C149#57811yescharacteristic
177D149—41no—
178C149#330211yescharacteristic, complemented, Sylow
179#3302—1491nomaximal, Sylow
180#556—1491no—
181#547—1491no—
182#487—1491no—
183#485—1491no—
184#485—1491no—
185#474—1491no—
186#467—1491no—
187#467—1491no—
188#462—1491no—
189#452—1491no—
190#452—1491no—
191C4×SD16—1491no—
192C8×D4—1491no—
193#416—1491no—
194#416D14911yescharacteristic, complemented
195C2×#41—1491no—
196C2×#41C2×D14911yescharacteristic
197C2×Q16—1491no—
198C2×Q16—1491no—
199C2×SD16—1491no—
200C22×C8—1491no—
201C22×C8C2×D14911yescharacteristic
202C4⋊Q8—1491no—
203C4⋊Q8—1491no—
204#126—2981no—
205#126—2981no—
206#124—2981no—
207#123—2981no—
208#123—2981no—
209C22⋊Q8—1491no—
210C22⋊Q8—1491no—
211C22⋊Q8—1491no—
212C22⋊Q8—1491no—
213#121—2981no—
214C4×Q8—2981no—
215C4×Q8—1491no—
216C4×D4—1491no—
217C4×D4—1491no—
218#117—1491no—
219#117C2×D14911yescharacteristic
220C2×C4⋊C4—2981no—
221#107—1491no—
222#107—1491no—
223#106—1491no—
224C4⋊C8—1491no—
225#103—1491no—
226#103—1491no—
227#103—1491no—
228#103—1491no—
229#103—1491no—
230#103C2×D14911yescharacteristic
231#103C2×D14911yescharacteristic
232#102—1491no—
233#102C2×D14911yescharacteristic
234#102C2×D14911yescharacteristic
235C22⋊C8—1491no—
236C22⋊C8—1491no—
237C4×C8—1491no—
238#41—22no—
239#41—41no—
240#41—2982no—
241#41—5961no—
242C2×Q8—2981no—
243C2×Q8—1491no—
244C2×Q8—1491no—
245C2×Q8C22×D14911yescharacteristic
246C2×D4—21no—
247C2×D4—2981no—
248C2×D4—1491no—
249C2×D4C22×D14911yescharacteristic
250C22×C4—21no—
251C22×C4—2981no—
252C22×C4—2981no—
253C22×C4—1491no—
254C22×C4C22×D14911yescharacteristic
255Q16—5961no—
256Q16—5961no—
257SD16—2982no—
258C2×C8—41no—
259C2×C8—5961no—
260C2×C8—1491no—
261C2×C8—1491no—
262C2×C8C22×D14911yescharacteristic
263C2×C8C22×D14911yescharacteristic
264C4⋊C4—2981no—
265C4⋊C4—2981no—
266C4⋊C4—2981no—
267C4⋊C4—2981no—
268C4⋊C4—2981no—
269C4⋊C4—2981no—
270C4⋊C4—2981no—
271C4⋊C4—2981no—
272C4⋊C4—1491no—
273C4⋊C4—1491no—
274C4⋊C4—1491no—
275C4⋊C4C22×D14911yescharacteristic
276C4⋊C4C22×D14911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—2981no—
279C22⋊C4—2981no—
280C22⋊C4—2981no—
281C22⋊C4—2981no—
282C22⋊C4—2981no—
283C22⋊C4—2981no—
284C22⋊C4—1491no—
285C22⋊C4—1491no—
286C42—21no—
287C42—2981no—
288C42—2981no—
289C42—1491no—
290C23—21no—
291C23—1491no—
292C23D4×D14911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—2981no—
296Q8—2981no—
297Q8—2981no—
298Q8—2981no—
299Q8—5962no—
300D4—21no—
301D4—42no—
302D4—2982no—
303D4—5962no—
304D4#1455873612yes—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—2981no—
312C2×C4—2981no—
313C2×C4—2981no—
314C2×C4—2981no—
315C2×C4—2981no—
316C2×C4—2981no—
317C2×C4—5962no—
318C2×C4—5962no—
319C2×C4—1491no—
320C2×C4—1491no—
321C2×C4—1491no—
322C2×C4D4×D14911yescharacteristic
323C2×C4C23×D14911yescharacteristic
324C8—21no—
325C8—21no—
326C8—2981no—
327C8—2981no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—2981no—
335C22—2981no—
336C22—2981no—
337C22C2×D4×D14911yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—2981no—
343C4—2981no—
344C4—5961no—
345C4—5961no—
346C4—5961no—
347C4—5961no—
348C4—1492no—
349C4C2×#1455873611yescharacteristic
350C4#1801195611yescharacteristic
351C2—41no—
352C2—42no—
353C2—5961no—
354C2#2375026511yescharacteristic
355C2#135×D14911yescharacteristic
356C2#2375043911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#416×C149C2
socleC22×C149C22×D4
prime radical#23750274C2
hypercenter#416D149
hypocenterC149#3302
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. #23750343C2semidirect
3. #23749974C2semidirect
4. #23749966C2semidirect
5. #23749965C2semidirect
6. #23749903C2semidirect
7. #23749866C2semidirect
8. #23749865C2semidirect
9. #23749834C2semidirect
10. #23749788C2semidirect
11. #23749787C2semidirect
12. #23749716C2semidirect
13. C8×C22⋊D149C2semidirect
14. #23749618C2semidirect
15. #416×C149C2semidirect
178. C149#3302semidirect
194. #416D149semidirect

Maximal subgroups

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

subgroupindex
#237503432
#237502742
#237499742
#237499662
#237499652
#237499032
#237498662
#237498652
#237498342
#237497882
#237497872
#237497162
C8×C22⋊D1492
#237496182
#416×C1492
#3302149