Finite Group Databasebeta

← #34057142

Subgroups — #34057142

Order 19072.

344 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750330C211yesmaximal, characteristic
2#23750310C211yesmaximal, characteristic
3#23750032C211yesmaximal, characteristic, complemented
4#23749969C211yesmaximal, characteristic, complemented
5#23749960C211yesmaximal, characteristic, complemented
6#23749957C211yesmaximal, characteristic, complemented
7#23749955C211yesmaximal, characteristic, complemented
8#23749935C211yesmaximal, characteristic, complemented
9#23749909C211yesmaximal, characteristic, complemented
10#23749884C211yesmaximal, characteristic, complemented
11#23749866C211yesmaximal, characteristic, complemented
12#23749731C211yesmaximal, characteristic, complemented
13#23749696C211yesmaximal, characteristic
14#23749664C211yesmaximal, characteristic, complemented
15C2×#106×C149C211yesmaximal, characteristic, complemented
16C2×Dic596C2211yescharacteristic
17C2×#14558719C2211yescharacteristic
18#18011910C2211yescharacteristic
19#18011906—21no—
20#18011902C2211yescharacteristic
21#18011901—21no—
22#18011901—21no—
23#18011894—21no—
24#18011891C2211yescharacteristic
25#18011891C2211yescharacteristic
26#18011890—21no—
27#18011890C2211yescharacteristic
28#18011890C2211yescharacteristic
29#18011889—21no—
30#18011876C2211yescharacteristic
31#18011876C2211yescharacteristic
32C4×C22⋊D149—21no—
33C4×C22⋊D149C2211yescharacteristic
34#18011870—21no—
35#18011869C2211yescharacteristic
36C4⋊C4×D149C2211yescharacteristic
37#18011845C2211yescharacteristic
38#18011844C2211yescharacteristic
39#18011844C2211yescharacteristic
40#18011842C2211yescharacteristic
41#18011842C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011834C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011834C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011821C2211yescharacteristic
52C22×C8×C149C2211yescharacteristic
53C2×C4⋊C4×C149C2211yescharacteristic
54C2×C4⋊C4×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56#106×C149C2211yescharacteristic
57#106×C149C2211yescharacteristic
58#106×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298C2311yescharacteristic
61C2×Dic298C2311yescharacteristic
62C2×C22⋊D149D411yescharacteristic
63C2×C4×D149—21no—
64C2×C4×D149C2311yescharacteristic
65Dic596—22no—
66#14558719—22no—
67C2×#11924746C2311yescharacteristic
68C2×#11924746C2311yescharacteristic
69C4⋊Dic149—21no—
70C4⋊Dic149—21no—
71C4⋊Dic149—21no—
72C4⋊Dic149C2311yescharacteristic
73C4⋊Dic149C2311yescharacteristic
74#14558715—21no—
75#14558715—21no—
76#14558715—21no—
77#14558715—21no—
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715D411yescharacteristic
82C22⋊Dic149—21no—
83C22⋊Dic149—21no—
84C22⋊Dic149D411yescharacteristic
85#14558713—21no—
86#14558713—21no—
87#14558713—21no—
88#14558713D411yescharacteristic
89C4×Dic149—21no—
90C4×Dic149—21no—
91C4×Dic149—21no—
92C4×Dic149C2311yescharacteristic
93C22×C4×C149—21no—
94C22×C4×C149—21no—
95C22×C4×C149C2311yescharacteristic
96C2×C8×C149—22no—
97C2×C8×C149C2311yescharacteristic
98C2×C8×C149C2311yescharacteristic
99C4⋊C4×C149—21no—
100C4⋊C4×C149—21no—
101C4⋊C4×C149C2311yescharacteristic
102C4⋊C4×C149C2311yescharacteristic
103C4⋊C4×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C22×D149C2×D411yescharacteristic
106Dic298—21no—
107Dic298—21no—
108Dic298—21no—
109Dic298—21no—
110Dic298—81no—
111C22⋊D149—22no—
112C2×Dic149—21no—
113C2×Dic149—21no—
114C2×Dic149—21no—
115C2×Dic149—21no—
116C2×Dic149C2×D411yescharacteristic
117C2×Dic149C2×D411yescharacteristic
118C2×Dic149C2×D411yescharacteristic
119C4×D149—21no—
120C4×D149—21no—
121C4×D149—81no—
122#11924746—21no—
123#11924746—21no—
124C23×C149C2×D411yescharacteristic
125C2×C4×C149—21no—
126C2×C4×C149—21no—
127C2×C4×C149—21no—
128C2×C4×C149—21no—
129C2×C4×C149—21no—
130C2×C4×C149—21no—
131C2×C4×C149—42no—
132C2×C4×C149—81no—
133C2×C4×C149C2×D411yescharacteristic
134C2×C4×C149C2411yescharacteristic
135C8×C149—21no—
136C8×C149#4112yes—
137C22×C149—21no—
138C22×C149—21no—
139C22×C149#13712yes—
140C22×C149C22×D411yescharacteristic
141C2×D149—21no—
142C2×D149—21no—
143C2×D149—21no—
144C4×C149—21no—
145C4×C149—41no—
146C4×C149—41no—
147C4×C149—41no—
148C4×C149—41no—
149C4×C149C2×#4111yescharacteristic
150C4×C1492−1+411yescharacteristic
151Dic149—21no—
152Dic149—21no—
153Dic149—21no—
154Dic149—41no—
155Dic149—41no—
156Dic149—41no—
157Dic149—41no—
158C2×C149—22no—
159C2×C149#54711yescharacteristic
160C2×C149C2×#13711yescharacteristic
161C2×C149#57711yescharacteristic
162D149—41no—
163C149#334411yescharacteristic, complemented, Sylow
164#3344—1491nomaximal, Sylow
165#554—1491no—
166#552—1491no—
167#501—1491no—
168#485—1491no—
169#484—1491no—
170#483—1491no—
171#483—1491no—
172#479—1491no—
173#475—1491no—
174#470—1491no—
175#467—1491no—
176#441—1491no—
177#435—1491no—
178#428—1491no—
179C2×#106D14911yescharacteristic, complemented
180C2×Q16—1491no—
181C2×M16—1491no—
182C22×C8C2×D14911yescharacteristic
183C4⋊Q8—1491no—
184#126—2981no—
185#125—2981no—
186#125—2981no—
187#125—1491no—
188#123—2981no—
189C22⋊Q8—2981no—
190C22⋊Q8—2981no—
191C22⋊Q8—1491no—
192C22⋊Q8—1491no—
193C22⋊Q8—1491no—
194C22⋊Q8—1491no—
195C4×Q8—1491no—
196C4×Q8—1491no—
197C4×D4—2981no—
198C4×D4—1491no—
199#117—2981no—
200#117—1491no—
201C2×C4⋊C4—1491no—
202C2×C4⋊C4C2×D14911yescharacteristic
203C2×C4⋊C4C2×D14911yescharacteristic
204#107—1491no—
205#107—1491no—
206#107—1491no—
207#106—1491no—
208#106—1491no—
209#106C2×D14911yescharacteristic
210#106C2×D14911yescharacteristic
211#106C2×D14911yescharacteristic
212#106C2×D14911yescharacteristic
213C4⋊C8—1491no—
214#103—1491no—
215#103—1491no—
216#103—1491no—
217#103—1491no—
218#103—1491no—
219#103—1491no—
220C22⋊C8—1491no—
221C22⋊C8—1491no—
222#97—1491no—
223C2×Q8—2981no—
224C2×Q8—1491no—
225C2×Q8—1491no—
226C2×D4—1491no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—2981no—
230C22×C4—1491no—
231C22×C4C22×D14911yescharacteristic
232Q16—2982no—
233M16—2982no—
234C2×C8—22no—
235C2×C8—1491no—
236C2×C8—1491no—
237C2×C8C22×D14911yescharacteristic
238C2×C8C22×D14911yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—2981no—
242C4⋊C4—2981no—
243C4⋊C4—2981no—
244C4⋊C4—2981no—
245C4⋊C4—2981no—
246C4⋊C4—2981no—
247C4⋊C4—2981no—
248C4⋊C4—2981no—
249C4⋊C4—2981no—
250C4⋊C4—2981no—
251C4⋊C4—1491no—
252C4⋊C4—1491no—
253C4⋊C4—1491no—
254C4⋊C4C22×D14911yescharacteristic
255C4⋊C4C22×D14911yescharacteristic
256C4⋊C4C22×D14911yescharacteristic
257C4⋊C4C22×D14911yescharacteristic
258C22⋊C4—2981no—
259C22⋊C4—2981no—
260C22⋊C4—2981no—
261C22⋊C4—2981no—
262C22⋊C4—2981no—
263C22⋊C4—1491no—
264C22⋊C4—1491no—
265C42—2981no—
266C42—2981no—
267C42—2981no—
268C42—1491no—
269C23—1491no—
270C23D4×D14911yescharacteristic
271Q8—2981no—
272Q8—2981no—
273Q8—2981no—
274Q8—2981no—
275Q8—11921no—
276D4—2982no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—42no—
284C2×C4—81no—
285C2×C4—2981no—
286C2×C4—2981no—
287C2×C4—2981no—
288C2×C4—2981no—
289C2×C4—2981no—
290C2×C4—2981no—
291C2×C4—1491no—
292C2×C4—1491no—
293C2×C4—1491no—
294C2×C4—11921no—
295C2×C4D4×D14911yescharacteristic
296C2×C4C23×D14911yescharacteristic
297C8—21no—
298C8—2981no—
299C8—2981no—
300C8#1455873612yes—
301C22—21no—
302C22—21no—
303C22—2981no—
304C22—2981no—
305C22—2981no—
306C22#1801194012yes—
307C22C2×D4×D14911yescharacteristic
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—2981no—
314C4—2981no—
315C4—2981no—
316C4—5961no—
317C4—5961no—
318C4—5961no—
319C4—5961no—
320C4C2×#1455873611yescharacteristic
321C4#1801195911yescharacteristic
322C2—22no—
323C2—5961no—
324C2#2375027611yescharacteristic
325C2C2×#1801194011yescharacteristic
326C2#2375043111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#106×C149C2
socleC22×C149C22×D4
prime radicalC2×C22⋊D149D4
hypercenterC2×#106D149
hypocenterC149#3344
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
3. #23750032C2semidirect
4. #23749969C2semidirect
5. #23749960C2semidirect
6. #23749957C2semidirect
7. #23749955C2semidirect
8. #23749935C2semidirect
9. #23749909C2semidirect
10. #23749884C2semidirect
11. #23749866C2semidirect
12. #23749731C2semidirect
14. #23749664C2semidirect
15. C2×#106×C149C2semidirect
163. C149#3344semidirect
179. C2×#106D149semidirect

Maximal subgroups

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

subgroupindex
#237503302
#237503102
#237500322
#237499692
#237499602
#237499572
#237499552
#237499352
#237499092
#237498842
#237498662
#237497312
#237496962
#237496642
C2×#106×C1492
#3344149