Finite Group Databasebeta

← #34054910

Subgroups — #34054910

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#23750104C211yesmaximal, characteristic
3#23749962C211yesmaximal, characteristic, complemented
4#23749957C211yesmaximal, characteristic, complemented
5#23749929C211yesmaximal, characteristic, complemented
6#23749836C211yesmaximal, characteristic, complemented
7#23749830C211yesmaximal, characteristic, complemented
8#23749788C211yesmaximal, characteristic
9#23749788C211yesmaximal, characteristic
10#23749731C211yesmaximal, characteristic, complemented
11#23749722C211yesmaximal, characteristic, complemented
12#23749719C211yesmaximal, characteristic, complemented
13#23749716C211yesmaximal, characteristic, complemented
14#23749685C211yesmaximal, characteristic, complemented
15#478×C149C211yesmaximal, characteristic, complemented
16C2×#14558735C2211yescharacteristic
17C2×Dic596C2211yescharacteristic
18C2×Dic596C2211yescharacteristic
19C2×#14558724C2211yescharacteristic
20C2×#14558724C2211yescharacteristic
21#18011911C2211yescharacteristic
22#18011906—21no—
23#18011906—21no—
24#18011902—21no—
25#18011902—21no—
26#18011891C2211yescharacteristic
27#18011891C2211yescharacteristic
28C4×Dic298C2211yescharacteristic
29#18011876C2211yescharacteristic
30#18011876C2211yescharacteristic
31#18011876C2211yescharacteristic
32D4×Dic149C2211yescharacteristic
33C4×C22⋊D149—21no—
34#18011871—21no—
35#18011868C2211yescharacteristic
36#18011867—21no—
37C2×#14558715—21no—
38C4⋊C4×D149C2211yescharacteristic
39#18011844C2211yescharacteristic
40#18011842C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic
42#18011836C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011834C2211yescharacteristic
45#18011834C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011823C2211yescharacteristic
49#18011823C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52#125×C149C2211yescharacteristic
53C4×D4×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59#14558735—22no—
60#14558735—22no—
61C2×Dic298C2311yescharacteristic
62C2×Dic298C2311yescharacteristic
63C2×Dic298C2311yescharacteristic
64C2×C22⋊D149—21no—
65C22×Dic149—21no—
66C22×Dic149—21no—
67C2×C4×D149—21no—
68C2×C4×D149C2311yescharacteristic
69Dic596—22no—
70Dic596—22no—
71#14558724—22no—
72#14558724—22no—
73C2×#11924746C2311yescharacteristic
74C2×#11924746C2311yescharacteristic
75C4⋊Dic149—21no—
76C4⋊Dic149—21no—
77C4⋊Dic149—21no—
78C4⋊Dic149—21no—
79C4⋊Dic149C2311yescharacteristic
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715D411yescharacteristic
86#14558715D411yescharacteristic
87C22⋊Dic149—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713D411yescharacteristic
91#14558713D411yescharacteristic
92C4×Dic149—21no—
93C4×Dic149—21no—
94C4×Dic149—21no—
95C4×Dic149—21no—
96C4×Dic149C2311yescharacteristic
97C2×D4×C149C2311yescharacteristic
98C22×C4×C149—21no—
99C2×C8×C149C2311yescharacteristic
100C2×C8×C149C2311yescharacteristic
101C4⋊C4×C149—21no—
102C4⋊C4×C149—21no—
103C4⋊C4×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C4⋊C4×C149C2311yescharacteristic
106C22⋊C4×C149—21no—
107C42×C149C2311yescharacteristic
108C22×D149C2×D411yescharacteristic
109Dic298—21no—
110Dic298—21no—
111Dic298—21no—
112Dic298—21no—
113Dic298—21no—
114Dic298#4112yes—
115C22⋊D149—24no—
116C2×Dic149—24no—
117C2×Dic149—21no—
118C2×Dic149—21no—
119C2×Dic149—21no—
120C2×Dic149—21no—
121C2×Dic149—81no—
122C2×Dic149C2×D411yescharacteristic
123C2×Dic149C2×D411yescharacteristic
124C2×Dic149C2×D411yescharacteristic
125C4×D149—21no—
126C4×D149—21no—
127C4×D149—81no—
128#11924746—21no—
129#11924746—21no—
130C23×C149—21no—
131D4×C149—21no—
132D4×C149#4112yes—
133C2×C4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—81no—
137C2×C4×C149C2×D411yescharacteristic
138C2×C4×C149C2×D411yescharacteristic
139C2×C4×C149C2411yescharacteristic
140C8×C149—21no—
141C8×C149—21no—
142C22×C149—22no—
143C22×C149—41no—
144C22×C149—41no—
145C22×C149C22×D411yescharacteristic
146C2×D149—21no—
147C2×D149—21no—
148C2×D149—21no—
149C4×C149—21no—
150C4×C149—21no—
151C4×C149—41no—
152C4×C149—41no—
153C4×C149—41no—
154C4×C149C2×#4111yescharacteristic
155C4×C149C2×#4111yescharacteristic
156Dic149—21no—
157Dic149—22no—
158Dic149—21no—
159Dic149—21no—
160Dic149—41no—
161Dic149—41no—
162Dic149—41no—
163C2×C149—42no—
164C2×C149#52511yescharacteristic
165C2×C149#57711yescharacteristic
166C2×C149#57811yescharacteristic
167D149—41no—
168C149#312011yescharacteristic, complemented, Sylow
169#3120—1491nomaximal, Sylow
170#541—1491no—
171#520—1491no—
172#484—1491no—
173#483—1491no—
174#479—1491no—
175#478D14911yescharacteristic, complemented
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×Q8—1491no—
202C4×D4—2981no—
203C4×D4—2981no—
204C4×D4—1491no—
205C4×D4C2×D14911yescharacteristic
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#103—1491no—
221#103—1491no—
222#102C2×D14911yescharacteristic
223#102C2×D14911yescharacteristic
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×Q8—1491no—
233C2×D4—2981no—
234C2×D4C22×D14911yescharacteristic
235C22×C4—21no—
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—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—
276C42C22×D14911yescharacteristic
277C23—21no—
278C23—1491no—
279Q8—2981no—
280Q8—2981no—
281Q8—2981no—
282Q8—2981no—
283Q8—2981no—
284Q8—1492no—
285D4—21no—
286D4—2984no—
287D4#1455873712yes—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—81no—
292C2×C4—2984no—
293C2×C4—2981no—
294C2×C4—2981no—
295C2×C4—2981no—
296C2×C4—2981no—
297C2×C4—2981no—
298C2×C4—2981no—
299C2×C4—1491no—
300C2×C4—1491no—
301C2×C4—1491no—
302C2×C4—11921no—
303C2×C4—11921no—
304C2×C4D4×D14911yescharacteristic
305C2×C4D4×D14911yescharacteristic
306C2×C4C23×D14911yescharacteristic
307C8—21no—
308C8—21no—
309C8—2981no—
310C8—2981no—
311C22—22no—
312C22—41no—
313C22—41no—
314C22—2981no—
315C22—2981no—
316C22—2981no—
317C22C2×D4×D14911yescharacteristic
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—2981no—
324C4—2981no—
325C4—2981no—
326C4—2982no—
327C4—5961no—
328C4—5961no—
329C4—5961no—
330C4#41×D14911yescharacteristic
331C4C2×#1455873711yescharacteristic
332C2—42no—
333C2—5961no—
334C2#2375013811yescharacteristic
335C2#2375043511yescharacteristic
336C2#2375043911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#478×C149C2
socleC22×C149C22×D4
prime radicalC2×#14558735C22
hypercenter#478D149
hypocenterC149#3120
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #23750238C2semidirect
3. #23749962C2semidirect
4. #23749957C2semidirect
5. #23749929C2semidirect
6. #23749836C2semidirect
7. #23749830C2semidirect
10. #23749731C2semidirect
11. #23749722C2semidirect
12. #23749719C2semidirect
13. #23749716C2semidirect
14. #23749685C2semidirect
15. #478×C149C2semidirect
168. C149#3120semidirect
175. #478D149semidirect

Maximal subgroups

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

subgroupindex
#237502382
#237501042
#237499622
#237499572
#237499292
#237498362
#237498302
#237497882
#237497312
#237497222
#237497192
#237497162
#237496852
#478×C1492
#3120149