Finite Group Databasebeta

← #34057182

Subgroups — #34057182

Order 19072.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750333C211yesmaximal, characteristic, complemented
2#23750327C211yesmaximal, characteristic
3#23750032C211yesmaximal, characteristic, complemented
4#23749965C211yesmaximal, characteristic, complemented
5#23749958C211yesmaximal, characteristic, complemented
6#23749941C211yesmaximal, characteristic, complemented
7#23749937C211yesmaximal, characteristic, complemented
8#23749934C211yesmaximal, characteristic, complemented
9#23749903C211yesmaximal, characteristic, complemented
10#23749868C211yesmaximal, characteristic, complemented
11#23749726C211yesmaximal, characteristic, complemented
12#23749696C211yesmaximal, characteristic, complemented
13#23749664C211yesmaximal, characteristic, complemented
14C2×#18011845C211yesmaximal, characteristic, complemented
15#465×C149C211yesmaximal, characteristic, complemented
16C2×#14558719C2211yescharacteristic
17#18011910C2211yescharacteristic
18#18011904—21no—
19#18011902C2211yescharacteristic
20#18011901—21no—
21#18011895—21no—
22#18011891—21no—
23#18011888—21no—
24#18011887C2211yescharacteristic
25#18011883—21no—
26#18011882C2211yescharacteristic
27Q8×Dic149C2211yescharacteristic
28D4×Dic149—21no—
29D4×Dic149C2211yescharacteristic
30C4×C22⋊D149C2211yescharacteristic
31#18011871—21no—
32#18011869C2211yescharacteristic
33C2×C4⋊Dic149C2211yescharacteristic
34C2×C4⋊Dic149C2211yescharacteristic
35C4⋊C4×D149C2211yescharacteristic
36#18011845C2211yescharacteristic
37#18011845C2211yescharacteristic
38#18011845C2211yescharacteristic
39#18011845C2211yescharacteristic
40#18011844C2211yescharacteristic
41#18011844C2211yescharacteristic
42#18011842C2211yescharacteristic
43#18011842C2211yescharacteristic
44#18011840C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011835C2211yescharacteristic
47#18011832C2211yescharacteristic
48#18011832C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011823C2211yescharacteristic
51#18011821C2211yescharacteristic
52C2×SD16×C149C2211yescharacteristic
53C22×C8×C149C2211yescharacteristic
54C22⋊Q8×C149C2211yescharacteristic
55#121×C149C2211yescharacteristic
56#106×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×C22⋊D149—21no—
61C2×C22⋊D149D411yescharacteristic
62C22×Dic149—21no—
63C22×Dic149—21no—
64C22×Dic149—21no—
65C2×C4×D149—21no—
66C2×C4×D149C2311yescharacteristic
67#14558719—22no—
68C2×#11924746C2311yescharacteristic
69C2×#11924746C2311yescharacteristic
70C4⋊Dic149—21no—
71C4⋊Dic149—21no—
72C4⋊Dic149—21no—
73C4⋊Dic149—21no—
74C4⋊Dic149C2311yescharacteristic
75C4⋊Dic149C2311yescharacteristic
76C4⋊Dic149C2311yescharacteristic
77C4⋊Dic149C2311yescharacteristic
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715—21no—
82#14558715D411yescharacteristic
83C22⋊Dic149—21no—
84C22⋊Dic149—21no—
85C22⋊Dic149D411yescharacteristic
86#14558713—21no—
87#14558713—21no—
88#14558713D411yescharacteristic
89C4×Dic149—21no—
90C4×Dic149—21no—
91C4×Dic149C2311yescharacteristic
92C2×Q8×C149C2311yescharacteristic
93C2×D4×C149—21no—
94C2×D4×C149C2311yescharacteristic
95C22×C4×C149C2311yescharacteristic
96SD16×C149—22no—
97C2×C8×C149—22no—
98C2×C8×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C4⋊C4×C149—21no—
101C4⋊C4×C149C2311yescharacteristic
102C4⋊C4×C149C2311yescharacteristic
103C22⋊C4×C149—21no—
104C22⋊C4×C149—21no—
105C22×D149C2×D411yescharacteristic
106Dic298—81no—
107C22⋊D149—22no—
108C22⋊D149—81no—
109C2×Dic149—21no—
110C2×Dic149—21no—
111C2×Dic149—21no—
112C2×Dic149—21no—
113C2×Dic149—81no—
114C2×Dic149—81no—
115C2×Dic149—81no—
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×C149—21no—
125C23×C149C2×D411yescharacteristic
126Q8×C149—21no—
127Q8×C149—21no—
128D4×C149—21no—
129D4×C149—21no—
130D4×C149—42no—
131C2×C4×C149—21no—
132C2×C4×C149—21no—
133C2×C4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149C2×D411yescharacteristic
137C2×C4×C149C2411yescharacteristic
138C8×C149—21no—
139C8×C149#4112yes—
140C22×C149—21no—
141C22×C149—21no—
142C22×C149—41no—
143C22×C149—41no—
144C22×C149—41no—
145C22×C149#13712yes—
146C22×C149C22×D411yescharacteristic
147C2×D149—21no—
148C2×D149—21no—
149C2×D149—21no—
150C4×C149—21no—
151C4×C149—41no—
152C4×C149—41no—
153C4×C149—41no—
154C4×C149C2×#4111yescharacteristic
155C4×C1492−1+411yescharacteristic
156Dic149—21no—
157Dic149—21no—
158Dic149—21no—
159Dic149—41no—
160Dic149—41no—
161Dic149—41no—
162Dic149—41no—
163C2×C149—22no—
164C2×C149—81no—
165C2×C149#54711yescharacteristic
166C2×C149C2×#13711yescharacteristic
167C2×C149#57611yescharacteristic
168D149—41no—
169C149#334611yescharacteristic, complemented, Sylow
170#3346—1491nomaximal, Sylow
171#554—1491no—
172#553—1491no—
173#501—1491no—
174#485—1491no—
175#484—1491no—
176#481—1491no—
177#480—1491no—
178#479—1491no—
179#474—1491no—
180#468—1491no—
181#465D14911yescharacteristic, complemented
182#440—1491no—
183#435—1491no—
184#428—1491no—
185C2×#107—1491no—
186C2×SD16C2×D14911yescharacteristic
187C2×M16—1491no—
188C22×C8C2×D14911yescharacteristic
189C4⋊Q8—1491no—
190#126—2981no—
191#125—2981no—
192#125—1491no—
193#123—2981no—
194C22⋊Q8—2981no—
195C22⋊Q8—2981no—
196C22⋊Q8—1491no—
197C22⋊Q8C2×D14911yescharacteristic
198#121—2981no—
199#121—1491no—
200#121C2×D14911yescharacteristic
201C4×Q8—1491no—
202C4×D4—2981no—
203C4×D4—2981no—
204C4×D4—1491no—
205C4×D4—1491no—
206#117—1491no—
207C2×C4⋊C4—1491no—
208C2×C4⋊C4—1491no—
209C2×C4⋊C4—1491no—
210#107—1491no—
211#107—1491no—
212#107—1491no—
213#107—1491no—
214#107—1491no—
215#107—1491no—
216#106—1491no—
217#106—1491no—
218#106C2×D14911yescharacteristic
219C4⋊C8—1491no—
220#103—1491no—
221#103—1491no—
222#103C2×D14911yescharacteristic
223#102—1491no—
224#102—1491no—
225#102C2×D14911yescharacteristic
226C22⋊C8—1491no—
227C22⋊C8—1491no—
228#97—1491no—
229C2×Q8—2981no—
230C2×Q8C22×D14911yescharacteristic
231C2×D4—21no—
232C2×D4—2981no—
233C2×D4—1491no—
234C2×D4C22×D14911yescharacteristic
235C22×C4—2981no—
236C22×C4—2981no—
237C22×C4—2981no—
238C22×C4—2981no—
239C22×C4—1491no—
240C22×C4C22×D14911yescharacteristic
241SD16—22no—
242M16—2982no—
243C2×C8—22no—
244C2×C8—1491no—
245C2×C8—1491no—
246C2×C8C22×D14911yescharacteristic
247C2×C8C22×D14911yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—2981no—
250C4⋊C4—2981no—
251C4⋊C4—2981no—
252C4⋊C4—2981no—
253C4⋊C4—2981no—
254C4⋊C4—2981no—
255C4⋊C4—2981no—
256C4⋊C4—2981no—
257C4⋊C4—1491no—
258C4⋊C4—1491no—
259C4⋊C4—1491no—
260C4⋊C4—1491no—
261C4⋊C4—1491no—
262C4⋊C4C22×D14911yescharacteristic
263C4⋊C4C22×D14911yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—2981no—
267C22⋊C4—2981no—
268C22⋊C4—2981no—
269C22⋊C4—2981no—
270C22⋊C4—1491no—
271C22⋊C4—1491no—
272C42—2981no—
273C42—2981no—
274C42—1491no—
275C23—21no—
276C23—1491no—
277C23D4×D14911yescharacteristic
278Q8—21no—
279Q8—21no—
280Q8—11921no—
281D4—21no—
282D4—21no—
283D4—42no—
284D4—2982no—
285D4—11921no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—2981no—
292C2×C4—2981no—
293C2×C4—2981no—
294C2×C4—2981no—
295C2×C4—2981no—
296C2×C4—2981no—
297C2×C4—1491no—
298C2×C4—1491no—
299C2×C4—1491no—
300C2×C4—11921no—
301C2×C4—11921no—
302C2×C4—11921no—
303C2×C4—11921no—
304C2×C4D4×D14911yescharacteristic
305C2×C4C23×D14911yescharacteristic
306C8—21no—
307C8—2981no—
308C8—2981no—
309C8#1455873512yes—
310C22—21no—
311C22—21no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—2981no—
316C22—2981no—
317C22—2981no—
318C22#1801194012yes—
319C22C2×D4×D14911yescharacteristic
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—2981no—
325C4—2981no—
326C4—2981no—
327C4—5961no—
328C4—5961no—
329C4—5961no—
330C4—5961no—
331C4C2×#1455873511yescharacteristic
332C4#1801195811yescharacteristic
333C2—22no—
334C2—81no—
335C2—5961no—
336C2#2375027511yescharacteristic
337C2C2×#1801194011yescharacteristic
338C2#2375042711yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#465×C149C2
socleC22×C149C22×D4
prime radical#23750327C2
hypercenter#465D149
hypocenterC149#3346
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #23750333C2semidirect
3. #23750032C2semidirect
4. #23749965C2semidirect
5. #23749958C2semidirect
6. #23749941C2semidirect
7. #23749937C2semidirect
8. #23749934C2semidirect
9. #23749903C2semidirect
10. #23749868C2semidirect
11. #23749726C2semidirect
12. #23749696C2semidirect
13. #23749664C2semidirect
14. C2×#18011845C2semidirect
15. #465×C149C2semidirect
169. C149#3346semidirect
181. #465D149semidirect

Maximal subgroups

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

subgroupindex
#237503332
#237503272
#237500322
#237499652
#237499582
#237499412
#237499372
#237499342
#237499032
#237498682
#237497262
#237496962
#237496642
C2×#180118452
#465×C1492
#3346149