Finite Group Databasebeta

← #34056159

Subgroups — #34056159

Order 19072.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750247C211yesmaximal, characteristic, complemented
2#23750244C211yesmaximal, characteristic, complemented
3#23749916C211yesmaximal, characteristic, complemented
4#23749913C211yesmaximal, characteristic, complemented
5#23749910C211yesmaximal, characteristic, complemented
6#23749908C211yesmaximal, characteristic, complemented
7#23749880C211yesmaximal, characteristic, complemented
8#23749877C211yesmaximal, characteristic
9#23749857C211yesmaximal, characteristic, complemented
10#23749851C211yesmaximal, characteristic, complemented
11#23749849C211yesmaximal, characteristic, complemented
12#23749842C211yesmaximal, characteristic, complemented
13#23749837C211yesmaximal, characteristic, complemented
14#23749650C211yesmaximal, characteristic, complemented
15#464×C149C211yesmaximal, characteristic, complemented
16C2×#14558723C2211yescharacteristic
17C2×#14558721C2211yescharacteristic
18C2×#14558719C2211yescharacteristic
19C2×C8×D149C2211yescharacteristic
20#18011911C2211yescharacteristic
21#18011910C2211yescharacteristic
22#18011905—21no—
23#18011904—21no—
24#18011900C2211yescharacteristic
25#18011899—21no—
26#18011897—21no—
27#18011896—21no—
28#18011895—21no—
29#18011889—21no—
30#18011888—21no—
31#18011887C2211yescharacteristic
32#18011887C2211yescharacteristic
33#18011886C2211yescharacteristic
34#18011882C2211yescharacteristic
35Q8×Dic149C2211yescharacteristic
36C4×D596C2211yescharacteristic
37D4×Dic149C2211yescharacteristic
38#18011868C2211yescharacteristic
39#18011843C2211yescharacteristic
40#18011843C2211yescharacteristic
41#18011842C2211yescharacteristic
42#18011842C2211yescharacteristic
43C4⋊#11924746C2211yescharacteristic
44#18011840C2211yescharacteristic
45#18011840C2211yescharacteristic
46#18011835C2211yescharacteristic
47#18011835C2211yescharacteristic
48#18011835C2211yescharacteristic
49#18011833C2211yescharacteristic
50#18011833C2211yescharacteristic
51#18011832C2211yescharacteristic
52C2×Q16×C149C2211yescharacteristic
53C2×SD16×C149C2211yescharacteristic
54#124×C149C2211yescharacteristic
55C4×Q8×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298—21no—
61C2×D596—21no—
62C2×D596C2311yescharacteristic
63C2×C22⋊D149—21no—
64C22×Dic149—21no—
65C2×C4×D149—21no—
66C2×C4×D149C2311yescharacteristic
67#14558723—41no—
68#14558721—41no—
69#14558719—41no—
70C2×#11924746C2311yescharacteristic
71C2×#11924746C2311yescharacteristic
72C8×D149—41no—
73C4⋊Dic149—21no—
74C4⋊Dic149—21no—
75C4⋊Dic149C2311yescharacteristic
76C4⋊Dic149C2311yescharacteristic
77C4⋊Dic149C2311yescharacteristic
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715D411yescharacteristic
82#14558715D411yescharacteristic
83C22⋊Dic149—21no—
84C22⋊Dic149—21no—
85#14558713—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713D411yescharacteristic
92#14558713D411yescharacteristic
93C4×Dic149—21no—
94C4×Dic149C2311yescharacteristic
95C2×Q8×C149C2311yescharacteristic
96C2×Q8×C149C2311yescharacteristic
97C2×D4×C149C2311yescharacteristic
98Q16×C149—41no—
99SD16×C149—41no—
100C2×C8×C149C2311yescharacteristic
101C2×C8×C149C2311yescharacteristic
102C4⋊C4×C149—21no—
103C4⋊C4×C149C2311yescharacteristic
104C22⋊C4×C149—21no—
105C22⋊C4×C149—21no—
106C42×C149—21no—
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109C22×D149C2×D411yescharacteristic
110Dic298—81no—
111Dic298—81no—
112D596—21no—
113D596—21no—
114D596—81no—
115C22⋊D149—81no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C2×Dic149—21no—
119C2×Dic149—81no—
120C2×Dic149C2×D411yescharacteristic
121C2×Dic149C2×D411yescharacteristic
122C2×Dic149C2×D411yescharacteristic
123C4×D149—21no—
124C4×D149—21no—
125C4×D149—81no—
126#11924746—21no—
127#11924746—21no—
128C23×C149—21no—
129Q8×C149—21no—
130Q8×C149—21no—
131Q8×C149—21no—
132Q8×C149—21no—
133D4×C149—21no—
134D4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149C2×D411yescharacteristic
139C2×C4×C149C2×D411yescharacteristic
140C2×C4×C149C2411yescharacteristic
141C8×C149—21no—
142C8×C149—21no—
143C22×C149—41no—
144C22×C149—41no—
145C22×C149—41no—
146C22×C149C22×D411yescharacteristic
147C2×D149—21no—
148C2×D149—21no—
149C2×D149—21no—
150C2×D149—41no—
151C2×D149—41no—
152C2×D149—41no—
153C4×C149—21no—
154C4×C149—21no—
155C4×C149—41no—
156C4×C149—41no—
157C4×C149—41no—
158C4×C149H(5,𝔽2)11yescharacteristic
159C4×C1492−1+411yescharacteristic
160Dic149—21no—
161Dic149—21no—
162Dic149—21no—
163Dic149—41no—
164Dic149—41no—
165Dic149—41no—
166C2×C149—81no—
167C2×C149#53711yescharacteristic
168C2×C149#57711yescharacteristic
169C2×C149#57711yescharacteristic
170D149—41no—
171D149—81no—
172C149#326311yescharacteristic, complemented, Sylow
173#3263—1491nomaximal, Sylow
174#542—1491no—
175#542—1491no—
176#476—1491no—
177#476—1491no—
178#475—1491no—
179#475—1491no—
180#470—1491no—
181#469—1491no—
182#465—1491no—
183#465—1491no—
184#464—1491no—
185#464D14911yescharacteristic, complemented
186#463—1491no—
187#463—1491no—
188#424—1491no—
189C2×Q16C2×D14911yescharacteristic
190C2×SD16—1491no—
191C2×SD16C2×D14911yescharacteristic
192C2×D8—1491no—
193C2×M16—1491no—
194C22×C8—1491no—
195C4⋊Q8—1491no—
196C4⋊Q8—1491no—
197#126—2981no—
198#126—2981no—
199#124—2981no—
200#124—2981no—
201#124—1491no—
202#124C2×D14911yescharacteristic
203#123—2981no—
204#123—2981no—
205C22⋊Q8—2981no—
206C22⋊Q8—2981no—
207C22⋊Q8—1491no—
208C22⋊Q8—1491no—
209#121—1491no—
210#121—1491no—
211C4×Q8—1491no—
212C4×Q8C2×D14911yescharacteristic
213C4×D4—1491no—
214C4×D4—1491no—
215#117—1491no—
216#106—1491no—
217#106—1491no—
218#106—1491no—
219#106—1491no—
220C4⋊C8—1491no—
221C4⋊C8—1491no—
222C4⋊C8—1491no—
223C4⋊C8C2×D14911yescharacteristic
224#103—1491no—
225#103—1491no—
226#103—1491no—
227#103C2×D14911yescharacteristic
228#102—1491no—
229#102—1491no—
230#102—1491no—
231#102C2×D14911yescharacteristic
232C2×Q8—2981no—
233C2×Q8—2981no—
234C2×Q8C22×D14911yescharacteristic
235C2×Q8C22×D14911yescharacteristic
236C2×D4—2981no—
237C2×D4—2981no—
238C2×D4—1491no—
239C2×D4C22×D14911yescharacteristic
240C22×C4—2981no—
241C22×C4—2981no—
242C22×C4—1491no—
243Q16—41no—
244SD16—41no—
245SD16—5961no—
246D8—5961no—
247M16—5961no—
248C2×C8—5961no—
249C2×C8—1491no—
250C2×C8—1491no—
251C2×C8C22×D14911yescharacteristic
252C2×C8C22×D14911yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—2981no—
255C4⋊C4—2981no—
256C4⋊C4—2981no—
257C4⋊C4—2981no—
258C4⋊C4—2981no—
259C4⋊C4—1491no—
260C4⋊C4—1491no—
261C4⋊C4—1491no—
262C4⋊C4—1491no—
263C4⋊C4—1491no—
264C4⋊C4C22×D14911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—2981no—
268C22⋊C4—2981no—
269C22⋊C4—2981no—
270C22⋊C4—2981no—
271C22⋊C4—2981no—
272C22⋊C4—2981no—
273C22⋊C4—2981no—
274C22⋊C4—2981no—
275C22⋊C4—1491no—
276C22⋊C4—1491no—
277C42—21no—
278C42—2981no—
279C42—1491no—
280C42C22×D14911yescharacteristic
281C23—21no—
282C23—2981no—
283C23—1491no—
284Q8—21no—
285Q8—21no—
286Q8—21no—
287Q8—21no—
288Q8—11921no—
289Q8—11921no—
290D4—21no—
291D4—21no—
292D4—2981no—
293D4—2981no—
294D4—11921no—
295D4—11921no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—2981no—
300C2×C4—2981no—
301C2×C4—2981no—
302C2×C4—2981no—
303C2×C4—2981no—
304C2×C4—1491no—
305C2×C4—1491no—
306C2×C4—1491no—
307C2×C4—11921no—
308C2×C4—11921no—
309C2×C4D4×D14911yescharacteristic
310C2×C4D4×D14911yescharacteristic
311C2×C4C23×D14911yescharacteristic
312C8—21no—
313C8—21no—
314C8—2981no—
315C8—2981no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—2981no—
320C22—2981no—
321C22—2981no—
322C22—5961no—
323C22—5961no—
324C22—5961no—
325C22C2×D4×D14911yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—2981no—
332C4—2981no—
333C4—2981no—
334C4—5961no—
335C4—5961no—
336C4—5961no—
337C4#1801195611yescharacteristic
338C4#1801195811yescharacteristic
339C2—81no—
340C2—5961no—
341C2—11921no—
342C2#2375020411yescharacteristic
343C2#2375043211yescharacteristic
344C2#2375043411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#464×C149C2
socleC22×C149C22×D4
prime radical#23749877C2
hypercenter#464D149
hypocenterC149#3263
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #23750247C2semidirect
2. #23750244C2semidirect
3. #23749916C2semidirect
4. #23749913C2semidirect
5. #23749910C2semidirect
6. #23749908C2semidirect
7. #23749880C2semidirect
9. #23749857C2semidirect
10. #23749851C2semidirect
11. #23749849C2semidirect
12. #23749842C2semidirect
13. #23749837C2semidirect
14. #23749650C2semidirect
15. #464×C149C2semidirect
172. C149#3263semidirect
185. #464D149semidirect

Maximal subgroups

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

subgroupindex
#237502472
#237502442
#237499162
#237499132
#237499102
#237499082
#237498802
#237498772
#237498572
#237498512
#237498492
#237498422
#237498372
#237496502
#464×C1492
#3263149