Finite Group Databasebeta

← #34054912

Subgroups — #34054912

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#23750238C211yesmaximal, characteristic, complemented
2#23750107C211yesmaximal, characteristic
3#23749962C211yesmaximal, characteristic, complemented
4#23749957C211yesmaximal, characteristic, complemented
5#23749922C211yesmaximal, characteristic, complemented
6#23749835C211yesmaximal, characteristic, complemented
7#23749831C211yesmaximal, characteristic, complemented
8#23749790C211yesmaximal, characteristic
9#23749790C211yesmaximal, characteristic
10#23749729C211yesmaximal, characteristic, complemented
11#23749724C211yesmaximal, characteristic, complemented
12#23749717C211yesmaximal, characteristic, complemented
13#23749712C211yesmaximal, characteristic, complemented
14#23749685C211yesmaximal, characteristic, complemented
15#479×C149C211yesmaximal, characteristic, complemented
16C2×#14558737C2211yescharacteristic
17C2×#14558726C2211yescharacteristic
18C2×#14558726C2211yescharacteristic
19C2×#14558725C2211yescharacteristic
20C2×#14558725C2211yescharacteristic
21#18011911C2211yescharacteristic
22#18011906—21no—
23#18011906—21no—
24#18011902—21no—
25#18011902—21no—
26#18011891C2211yescharacteristic
27#18011891C2211yescharacteristic
28Q8×Dic149C2211yescharacteristic
29#18011876C2211yescharacteristic
30#18011876C2211yescharacteristic
31C4×D596—21no—
32C4×D596C2211yescharacteristic
33#18011873—21no—
34#18011873C2211yescharacteristic
35#18011868—21no—
36#18011868C2211yescharacteristic
37C4⋊C4×D149—21no—
38C4⋊C4×D149C2211yescharacteristic
39#18011844C2211yescharacteristic
40#18011842C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic
42#18011836C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011834C2211yescharacteristic
45#18011834C2211yescharacteristic
46#18011831C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52#125×C149C2211yescharacteristic
53C4×Q8×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#103×C149C2211yescharacteristic
59#14558737—22no—
60#14558737—22no—
61C2×Dic298C2311yescharacteristic
62C2×Dic298C2311yescharacteristic
63C2×D596—21no—
64C2×D596C2311yescharacteristic
65C2×C4×D149—21no—
66C2×C4×D149—21no—
67C2×C4×D149—21no—
68C2×C4×D149—21no—
69C2×C4×D149C2311yescharacteristic
70#14558726—22no—
71#14558726—22no—
72#14558725—22no—
73#14558725—22no—
74C2×#11924746C2311yescharacteristic
75C2×#11924746C2311yescharacteristic
76C4⋊Dic149—21no—
77C4⋊Dic149—21no—
78C4⋊Dic149—21no—
79C4⋊Dic149—21no—
80C4⋊Dic149—21no—
81C4⋊Dic149C2311yescharacteristic
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715D411yescharacteristic
86#14558715D411yescharacteristic
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91#14558713D411yescharacteristic
92#14558713D411yescharacteristic
93C4×Dic149—21no—
94C4×Dic149—21no—
95C4×Dic149—21no—
96C4×Dic149C2311yescharacteristic
97C2×Q8×C149C2311yescharacteristic
98C2×C8×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C4⋊C4×C149—21no—
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×D149C2×D411yescharacteristic
110Dic298—21no—
111Dic298—21no—
112Dic298—21no—
113Dic298—21no—
114D596—24no—
115D596—21no—
116D596#4112yes—
117C2×Dic149—21no—
118C2×Dic149—21no—
119C2×Dic149—21no—
120C2×Dic149C2×D411yescharacteristic
121C2×Dic149C2×D411yescharacteristic
122C2×Dic149C2×D411yescharacteristic
123C4×D149—24no—
124C4×D149—21no—
125C4×D149—21no—
126C4×D149—81no—
127C4×D149—81no—
128C4×D149—81no—
129#11924746—21no—
130#11924746—21no—
131Q8×C149—21no—
132Q8×C149#4112yes—
133C2×C4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—21no—
137C2×C4×C149C2×D411yescharacteristic
138C2×C4×C149C2×D411yescharacteristic
139C2×C4×C149C2411yescharacteristic
140C8×C149—21no—
141C8×C149—21no—
142C22×C149C22×D411yescharacteristic
143C2×D149—21no—
144C2×D149—22no—
145C2×D149—21no—
146C2×D149—21no—
147C2×D149—41no—
148C2×D149—41no—
149C4×C149—22no—
150C4×C149—21no—
151C4×C149—21no—
152C4×C149—41no—
153C4×C149—41no—
154C4×C149—41no—
155C4×C149C2×#4111yescharacteristic
156C4×C149C2×#4111yescharacteristic
157Dic149—21no—
158Dic149—21no—
159Dic149—21no—
160Dic149—41no—
161Dic149—41no—
162Dic149—41no—
163C2×C149#52511yescharacteristic
164C2×C149#57711yescharacteristic
165C2×C149#57811yescharacteristic
166D149—41no—
167D149—42no—
168C149#312011yescharacteristic, complemented, Sylow
169#3120—1491nomaximal, Sylow
170#541—1491no—
171#520—1491no—
172#484—1491no—
173#483—1491no—
174#479D14911yescharacteristic, complemented
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#125C2×D14911yescharacteristic
196C22⋊Q8—1491no—
197C22⋊Q8—1491no—
198C4×Q8—1491no—
199C4×Q8—1491no—
200C4×Q8—1491no—
201C4×Q8C2×D14911yescharacteristic
202C4×D4—2981no—
203C4×D4—2981no—
204C4×D4—1491no—
205C4×D4—1491no—
206#117—2981no—
207#117—1491no—
208C2×C4⋊C4—2981no—
209C2×C4⋊C4—1491no—
210#107—1491no—
211#107C2×D14911yescharacteristic
212#106—1491no—
213#106C2×D14911yescharacteristic
214C4⋊C8—1491no—
215C4⋊C8C2×D14911yescharacteristic
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⋊C8—1491no—
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—2981no—
236C22×C4—2981no—
237C22×C4—2981no—
238C22×C4—2981no—
239C22×C4—1491no—
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—21no—
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—2981no—
266C22⋊C4—2981no—
267C22⋊C4—2981no—
268C22⋊C4—2981no—
269C22⋊C4—1491no—
270C22⋊C4—1491no—
271C42—21no—
272C42—2981no—
273C42—2981no—
274C42—2981no—
275C42—1491no—
276C42C22×D14911yescharacteristic
277C23—2981no—
278C23—1491no—
279Q8—21no—
280Q8—2981no—
281Q8—2981no—
282Q8—2981no—
283Q8—2981no—
284Q8#1455873712yes—
285D4—2984no—
286D4—2981no—
287D4—1492no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—2984no—
293C2×C4—2981no—
294C2×C4—2981no—
295C2×C4—2981no—
296C2×C4—2981no—
297C2×C4—2981no—
298C2×C4—1491no—
299C2×C4—1491no—
300C2×C4—1491no—
301C2×C4—11921no—
302C2×C4—11921no—
303C2×C4—11921no—
304C2×C4D4×D14911yescharacteristic
305C2×C4D4×D14911yescharacteristic
306C2×C4C23×D14911yescharacteristic
307C8—21no—
308C8—21no—
309C8—2981no—
310C8—2981no—
311C22—2981no—
312C22—2981no—
313C22—2981no—
314C22—2982no—
315C22—5961no—
316C22—5961no—
317C22C2×D4×D14911yescharacteristic
318C4—21no—
319C4—21no—
320C4—22no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—2981no—
325C4—2981no—
326C4—2981no—
327C4—5961no—
328C4—5961no—
329C4—5961no—
330C4#41×D14911yescharacteristic
331C4C2×#1455873711yescharacteristic
332C2—5961no—
333C2—5962no—
334C2#2375013811yescharacteristic
335C2#2375043211yescharacteristic
336C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#479×C149C2
socleC22×C149C22×D4
prime radicalC2×#14558737C22
hypercenter#479D149
hypocenterC149#3120
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #23750238C2semidirect
3. #23749962C2semidirect
4. #23749957C2semidirect
5. #23749922C2semidirect
6. #23749835C2semidirect
7. #23749831C2semidirect
10. #23749729C2semidirect
11. #23749724C2semidirect
12. #23749717C2semidirect
13. #23749712C2semidirect
14. #23749685C2semidirect
15. #479×C149C2semidirect
168. C149#3120semidirect
174. #479D149semidirect

Maximal subgroups

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

subgroupindex
#237502382
#237501072
#237499622
#237499572
#237499222
#237498352
#237498312
#237497902
#237497292
#237497242
#237497172
#237497122
#237496852
#479×C1492
#3120149