Finite Group Databasebeta

← #34057146

Subgroups — #34057146

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#23750332C211yesmaximal, characteristic
2#23750035C211yesmaximal, characteristic, complemented
3#23749966C211yesmaximal, characteristic, complemented
4#23749958C211yesmaximal, characteristic, complemented
5#23749955C211yesmaximal, characteristic, complemented
6#23749953C211yesmaximal, characteristic, complemented
7#23749929C211yesmaximal, characteristic, complemented
8#23749910C211yesmaximal, characteristic, complemented
9#23749881C211yesmaximal, characteristic, complemented
10#23749864C211yesmaximal, characteristic, complemented
11#23749730C211yesmaximal, characteristic, complemented
12#23749697C211yesmaximal, characteristic
13#23749668C211yesmaximal, characteristic, complemented
14C2×#18011842C211yesmaximal, characteristic, complemented
15#552×C149C211yesmaximal, characteristic
16C2×#14558726C2211yescharacteristic
17C2×#14558720C2211yescharacteristic
18C22×#11924746C2211yescharacteristic
19#18011911C2211yescharacteristic
20#18011902—21no—
21#18011890C2211yescharacteristic
22#18011890C2211yescharacteristic
23#18011888—21no—
24#18011888—21no—
25C4×Dic298C2211yescharacteristic
26D4×Dic149—21no—
27C2×C4⋊Dic149C2211yescharacteristic
28C2×C4⋊Dic149C2211yescharacteristic
29#18011844C2211yescharacteristic
30#18011844C2211yescharacteristic
31#18011844C2211yescharacteristic
32#18011842C2211yescharacteristic
33#18011842C2211yescharacteristic
34#18011842C2211yescharacteristic
35#18011842C2211yescharacteristic
36#18011842C2211yescharacteristic
37#18011842C2211yescharacteristic
38C4⋊#11924746C2211yescharacteristic
39#18011835C2211yescharacteristic
40#18011835C2211yescharacteristic
41#18011835C2211yescharacteristic
42#18011834C2211yescharacteristic
43#18011834C2211yescharacteristic
44#18011834C2211yescharacteristic
45C22⋊#11924746C2211yescharacteristic
46C22⋊#11924746C2211yescharacteristic
47#18011822C2211yescharacteristic
48#126×C149—21no—
49#125×C149—21no—
50#125×C149C2211yescharacteristic
51#123×C149—21no—
52C22⋊Q8×C149C2211yescharacteristic
53C22⋊Q8×C149C2211yescharacteristic
54C4×Q8×C149C2211yescharacteristic
55C4×D4×C149C2211yescharacteristic
56#117×C149—21no—
57#117×C149C2211yescharacteristic
58C2×C4⋊C4×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298C2311yescharacteristic
61C22×Dic149—21no—
62C22×Dic149—21no—
63#14558726—22no—
64#14558720—22no—
65C2×#11924746—22no—
66C2×#11924746C2311yescharacteristic
67C2×#11924746C2311yescharacteristic
68C2×#11924746C2311yescharacteristic
69C2×#11924746C2311yescharacteristic
70C4⋊Dic149—21no—
71C4⋊Dic149—21no—
72C4⋊Dic149—21no—
73C4⋊Dic149C2311yescharacteristic
74C4⋊Dic149C2311yescharacteristic
75C4⋊Dic149C2311yescharacteristic
76#14558715—21no—
77#14558715—21no—
78#14558715—21no—
79C22⋊Dic149—21no—
80C22⋊Dic149—21no—
81C4×Dic149—21no—
82C2×Q8×C149C2311yescharacteristic
83C2×D4×C149D411yescharacteristic
84C22×C4×C149—21no—
85C22×C4×C149C2311yescharacteristic
86C22×C4×C149C2311yescharacteristic
87C4⋊C4×C149—21no—
88C4⋊C4×C149—21no—
89C4⋊C4×C149—21no—
90C4⋊C4×C149—21no—
91C4⋊C4×C149—21no—
92C4⋊C4×C149—21no—
93C4⋊C4×C149D411yescharacteristic
94C4⋊C4×C149C2311yescharacteristic
95C4⋊C4×C149C2311yescharacteristic
96C4⋊C4×C149C2311yescharacteristic
97C22⋊C4×C149—21no—
98C22⋊C4×C149—21no—
99C22⋊C4×C149—21no—
100C22⋊C4×C149D411yescharacteristic
101C22⋊C4×C149D411yescharacteristic
102C42×C149—21no—
103C42×C149—21no—
104C42×C149C2311yescharacteristic
105Dic298—21no—
106Dic298—21no—
107Dic298—81no—
108C2×Dic149—21no—
109C2×Dic149—21no—
110C2×Dic149—21no—
111C2×Dic149—21no—
112C2×Dic149—81no—
113C2×Dic149—81no—
114#11924746—21no—
115#11924746—21no—
116#11924746—21no—
117#11924746#4112yes—
118C23×C149C2×D411yescharacteristic
119C23×C149C2×D411yescharacteristic
120Q8×C149—21no—
121Q8×C149—21no—
122D4×C149—22no—
123C2×C4×C149—21no—
124C2×C4×C149—21no—
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×C149C2×D411yescharacteristic
133C2×C4×C149C2×D411yescharacteristic
134C2×C4×C149C2×D411yescharacteristic
135C2×C4×C149C2×D411yescharacteristic
136C2×C4×C149C2411yescharacteristic
137C22×C149—21no—
138C22×C149—21no—
139C22×C149—21no—
140C22×C149—21no—
141C22×C149—21no—
142C22×C149#13712yes—
143C22×C149C22×D411yescharacteristic
144C4×C149—21no—
145C4×C149—21no—
146C4×C149—21no—
147C4×C149—21no—
148C4×C149—41no—
149C4×C149—41no—
150C4×C149—41no—
151C4×C149—41no—
152C4×C149C2×#4111yescharacteristic
153C4×C1492−1+411yescharacteristic
154Dic149—41no—
155Dic149—41no—
156Dic149—41no—
157Dic149—41no—
158C2×C149—22no—
159C2×C149—41no—
160C2×C149#54711yescharacteristic
161C2×C149C2×#13711yescharacteristic
162C2×C149#57711yescharacteristic
163C149#334411yescharacteristic, complemented, Sylow
164#3344—1491nomaximal, Sylow
165#554—1491no—
166#552D14911yescharacteristic
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×#106—1491no—
180C2×Q16—1491no—
181C2×M16—1491no—
182C22×C8—1491no—
183C4⋊Q8—1491no—
184#126—21no—
185#125—21no—
186#125—2981no—
187#125C2×D14911yescharacteristic
188#123—21no—
189C22⋊Q8—2981no—
190C22⋊Q8—2981no—
191C22⋊Q8—1491no—
192C22⋊Q8—1491no—
193C22⋊Q8C2×D14911yescharacteristic
194C22⋊Q8C2×D14911yescharacteristic
195C4×Q8—1491no—
196C4×Q8C2×D14911yescharacteristic
197C4×D4—2981no—
198C4×D4C2×D14911yescharacteristic
199#117—21no—
200#117C2×D14911yescharacteristic
201C2×C4⋊C4—1491no—
202C2×C4⋊C4—1491no—
203C2×C4⋊C4C2×D14911yescharacteristic
204#107—1491no—
205#107—1491no—
206#107—1491no—
207#106—1491no—
208#106—1491no—
209#106—1491no—
210#106—1491no—
211#106—1491no—
212#106—1491no—
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×Q8C22×D14911yescharacteristic
226C2×D4C22⋊D14911yescharacteristic
227C22×C4—21no—
228C22×C4—2981no—
229C22×C4—2981no—
230C22×C4C22×D14911yescharacteristic
231C22×C4C22×D14911yescharacteristic
232Q16—2982no—
233M16—2982no—
234C2×C8—2982no—
235C2×C8—1491no—
236C2×C8—1491no—
237C2×C8—1491no—
238C2×C8—1491no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
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—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—2981no—
262C22⋊C4—2981no—
263C22⋊C4C22⋊D14911yescharacteristic
264C22⋊C4C22⋊D14911yescharacteristic
265C42—21no—
266C42—21no—
267C42—2981no—
268C42C22×D14911yescharacteristic
269C23C2×C22⋊D14911yescharacteristic
270C23C2×C22⋊D14911yescharacteristic
271Q8—21no—
272Q8—21no—
273Q8—2981no—
274Q8—2981no—
275Q8—11921no—
276D4—22no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—42no—
286C2×C4—2981no—
287C2×C4—2981no—
288C2×C4—2981no—
289C2×C4—2981no—
290C2×C4—11921no—
291C2×C4—11921no—
292C2×C4C2×C22⋊D14911yescharacteristic
293C2×C4C2×C22⋊D14911yescharacteristic
294C2×C4C2×C22⋊D14911yescharacteristic
295C2×C4C2×C22⋊D14911yescharacteristic
296C2×C4C23×D14911yescharacteristic
297C8—2981no—
298C8—2981no—
299C8—2981no—
300C8—1492no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22#1801194112yes—
307C22C22×C22⋊D14911yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—5961no—
317C4—5961no—
318C4—5961no—
319C4—5961no—
320C4#41×D14911yescharacteristic
321C4#1801195811yescharacteristic
322C2—22no—
323C2—41no—
324C2#2375027411yescharacteristic
325C2C2×#1801194111yescharacteristic
326C2#2375043311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#552×C149C2
socleC22×C149C22×D4
prime radicalC2×D4×C149D4
hypercenter#552D149
hypocenterC149#3344
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #23750035C2semidirect
3. #23749966C2semidirect
4. #23749958C2semidirect
5. #23749955C2semidirect
6. #23749953C2semidirect
7. #23749929C2semidirect
8. #23749910C2semidirect
9. #23749881C2semidirect
10. #23749864C2semidirect
11. #23749730C2semidirect
13. #23749668C2semidirect
14. C2×#18011842C2semidirect
163. C149#3344semidirect

Maximal subgroups

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

subgroupindex
#237503322
#237500352
#237499662
#237499582
#237499552
#237499532
#237499292
#237499102
#237498812
#237498642
#237497302
#237496972
#237496682
C2×#180118422
#552×C1492
#3344149