Finite Group Databasebeta

← #34054908

Subgroups — #34054908

Order 19072.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750235C211yesmaximal, characteristic, complemented
2#23750106C211yesmaximal, characteristic
3#23749960C211yesmaximal, characteristic, complemented
4#23749935C211yesmaximal, characteristic, complemented
5#23749924C211yesmaximal, characteristic, complemented
6#23749834C211yesmaximal, characteristic, complemented
7#23749829C211yesmaximal, characteristic, complemented
8#23749789C211yesmaximal, characteristic
9#23749785C211yesmaximal, characteristic
10#23749731C211yesmaximal, characteristic, complemented
11#23749728C211yesmaximal, characteristic, complemented
12#23749717C211yesmaximal, characteristic, complemented
13#23749712C211yesmaximal, characteristic, complemented
14#23749683C211yesmaximal, characteristic, complemented
15#483×C149C211yesmaximal, characteristic, complemented
16C2×#14558736C2211yescharacteristic
17C2×Dic596C2211yescharacteristic
18C2×#14558726C2211yescharacteristic
19C2×#14558725C2211yescharacteristic
20C2×#14558723C2211yescharacteristic
21#18011909C2211yescharacteristic
22#18011904—21no—
23#18011904—21no—
24#18011902—21no—
25#18011902C2211yescharacteristic
26#18011901—21no—
27#18011890C2211yescharacteristic
28Q8×Dic149C2211yescharacteristic
29#18011876C2211yescharacteristic
30#18011876C2211yescharacteristic
31#18011876C2211yescharacteristic
32#18011873C2211yescharacteristic
33#18011873C2211yescharacteristic
34C4×C22⋊D149—21no—
35C4×C22⋊D149—21no—
36#18011870C2211yescharacteristic
37#18011869—21no—
38C4⋊C4×D149—21no—
39#18011844C2211yescharacteristic
40#18011844C2211yescharacteristic
41#18011840C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011834C2211yescharacteristic
45#18011834C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011831C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C22⋊Q8×C149C2211yescharacteristic
53C2×C4⋊C4×C149C2211yescharacteristic
54#106×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58C22⋊C8×C149C2211yescharacteristic
59#14558736—22no—
60#14558736—22no—
61C2×Dic298C2311yescharacteristic
62C2×Dic298C2311yescharacteristic
63C2×D596C2311yescharacteristic
64C2×C22⋊D149—21no—
65C2×C4×D149—21no—
66C2×C4×D149—21no—
67C2×C4×D149—21no—
68Dic596—22no—
69#14558726—22no—
70#14558725—22no—
71#14558723—22no—
72C2×#11924746C2311yescharacteristic
73C2×#11924746C2311yescharacteristic
74C4⋊Dic149—21no—
75C4⋊Dic149—21no—
76C4⋊Dic149D411yescharacteristic
77C4⋊Dic149D411yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79#14558715—21no—
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149D411yescharacteristic
88C22⋊Dic149D411yescharacteristic
89#14558713—21no—
90#14558713—21no—
91C4×Dic149—21no—
92C4×Dic149—21no—
93C4×Dic149—21no—
94C4×Dic149—21no—
95C4×Dic149C2311yescharacteristic
96C4×Dic149C2311yescharacteristic
97C2×Q8×C149C2311yescharacteristic
98C22×C4×C149—21no—
99C22×C4×C149C2311yescharacteristic
100C2×C8×C149C2311yescharacteristic
101C2×C8×C149C2311yescharacteristic
102C4⋊C4×C149—21no—
103C4⋊C4×C149—21no—
104C4⋊C4×C149C2311yescharacteristic
105C4⋊C4×C149C2311yescharacteristic
106C4⋊C4×C149C2311yescharacteristic
107C22⋊C4×C149—21no—
108C22×D149—21no—
109Dic298—21no—
110Dic298—21no—
111Dic298—21no—
112Dic298#4112yes—
113D596—21no—
114D596#4112yes—
115C22⋊D149—24no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C2×Dic149—21no—
119C2×Dic149C2×D411yescharacteristic
120C2×Dic149C2×D411yescharacteristic
121C2×Dic149C2×D411yescharacteristic
122C2×Dic149C2×D411yescharacteristic
123C4×D149—24no—
124C4×D149—81no—
125C4×D149—81no—
126#11924746—21no—
127#11924746—21no—
128C23×C149C2×D411yescharacteristic
129Q8×C149—21no—
130Q8×C149—21no—
131C2×C4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—21no—
137C2×C4×C149—81no—
138C2×C4×C149C2×D411yescharacteristic
139C2×C4×C149C2411yescharacteristic
140C8×C149—21no—
141C8×C149—21no—
142C22×C149—21no—
143C22×C149—21no—
144C22×C149—21no—
145C22×C149C22×D411yescharacteristic
146C2×D149—22no—
147C2×D149—41no—
148C2×D149—41no—
149C4×C149—21no—
150C4×C149—41no—
151C4×C149—41no—
152C4×C149—41no—
153C4×C149—41no—
154C4×C149C2×#4111yescharacteristic
155C4×C149C2×#4111yescharacteristic
156Dic149—22no—
157Dic149—21no—
158Dic149—21no—
159Dic149—21no—
160Dic149—21no—
161Dic149—41no—
162Dic149—41no—
163C2×C149—41no—
164C2×C149#52511yescharacteristic
165C2×C149#57711yescharacteristic
166C2×C149#57811yescharacteristic
167D149—42no—
168C149#312011yescharacteristic, complemented, Sylow
169#3120—1491nomaximal, Sylow
170#541—1491no—
171#520—1491no—
172#484—1491no—
173#483D14911yescharacteristic, complemented
174#479—1491no—
175#478—1491no—
176#462—1491no—
177#461—1491no—
178#452—1491no—
179#452—1491no—
180#441—1491no—
181#440—1491no—
182C4×Q16—1491no—
183C4×SD16—1491no—
184#433—1491no—
185C2×#41—1491no—
186C2×Q16—1491no—
187C2×Q16—1491no—
188C2×SD16—1491no—
189C2×SD16—1491no—
190C4⋊Q8—1491no—
191#126—2981no—
192#126—2981no—
193#125—2981no—
194#125—2981no—
195#125—1491no—
196C22⋊Q8—1491no—
197C22⋊Q8C2×D14911yescharacteristic
198C4×Q8—1491no—
199C4×Q8—1491no—
200C4×Q8—1491no—
201C4×Q8—1491no—
202C4×D4—2981no—
203C4×D4—2981no—
204C4×D4—1491no—
205C4×D4—1491no—
206#117—2981no—
207#117—1491no—
208C2×C4⋊C4—2981no—
209C2×C4⋊C4C2×D14911yescharacteristic
210#107—1491no—
211#107—1491no—
212#106C2×D14911yescharacteristic
213#106C2×D14911yescharacteristic
214C4⋊C8—1491no—
215C4⋊C8—1491no—
216#103—1491no—
217#103—1491no—
218#103—1491no—
219#103—1491no—
220#103C2×D14911yescharacteristic
221#103C2×D14911yescharacteristic
222#102—1491no—
223#102—1491no—
224C22⋊C8—1491no—
225C22⋊C8C2×D14911yescharacteristic
226#97—1491no—
227C4×C8—1491no—
228#41—2982no—
229#41—2982no—
230C2×Q8—1491no—
231C2×Q8—1491no—
232C2×Q8C22×D14911yescharacteristic
233C2×D4—2981no—
234C2×D4—1491no—
235C22×C4—21no—
236C22×C4—2981no—
237C22×C4—2981no—
238C22×C4—2981no—
239C22×C4C22×D14911yescharacteristic
240Q16—2982no—
241Q16—2982no—
242SD16—2982no—
243SD16—2982no—
244C2×C8—1491no—
245C2×C8—1491no—
246C2×C8C22×D14911yescharacteristic
247C2×C8C22×D14911yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—2981no—
251C4⋊C4—2981no—
252C4⋊C4—2981no—
253C4⋊C4—2981no—
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⋊C4C22×D14911yescharacteristic
263C4⋊C4C22×D14911yescharacteristic
264C4⋊C4C22×D14911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—2981no—
267C22⋊C4—2981no—
268C22⋊C4—2981no—
269C22⋊C4—1491no—
270C22⋊C4—1491no—
271C42—2981no—
272C42—2981no—
273C42—2981no—
274C42—2981no—
275C42—1491no—
276C42—1491no—
277C23—2981no—
278C23D4×D14911yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—2981no—
282Q8—2981no—
283Q8—2981no—
284Q8—1492no—
285D4—2984no—
286D4—2981no—
287D4—1492no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—2984no—
296C2×C4—2981no—
297C2×C4—2981no—
298C2×C4—2981no—
299C2×C4—1491no—
300C2×C4—1491no—
301C2×C4—1491no—
302C2×C4—1491no—
303C2×C4—11921no—
304C2×C4—11921no—
305C2×C4D4×D14911yescharacteristic
306C2×C4C23×D14911yescharacteristic
307C8—21no—
308C8—21no—
309C8—2981no—
310C8—2981no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—2982no—
315C22—5961no—
316C22—5961no—
317C22C2×D4×D14911yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—2981no—
324C4—2981no—
325C4—2981no—
326C4—2981no—
327C4—2982no—
328C4—5961no—
329C4—5961no—
330C4#41×D14911yescharacteristic
331C4#41×D14911yescharacteristic
332C2—41no—
333C2—5962no—
334C2#2375013311yescharacteristic
335C2#2375043111yescharacteristic
336C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#483×C149C2
socleC22×C149C22×D4
prime radicalC2×#14558736C22
hypercenter#483D149
hypocenterC149#3120
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #23750235C2semidirect
3. #23749960C2semidirect
4. #23749935C2semidirect
5. #23749924C2semidirect
6. #23749834C2semidirect
7. #23749829C2semidirect
10. #23749731C2semidirect
11. #23749728C2semidirect
12. #23749717C2semidirect
13. #23749712C2semidirect
14. #23749683C2semidirect
15. #483×C149C2semidirect
168. C149#3120semidirect
173. #483D149semidirect

Maximal subgroups

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

subgroupindex
#237502352
#237501062
#237499602
#237499352
#237499242
#237498342
#237498292
#237497892
#237497852
#237497312
#237497282
#237497172
#237497122
#237496832
#483×C1492
#3120149