Finite Group Databasebeta

← #34055293

Subgroups — #34055293

Order 19072.

364 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#23750179C211yesmaximal, characteristic, complemented
2#23750157C211yesmaximal, characteristic
3#23750032C211yesmaximal, characteristic, complemented
4#23750016C211yesmaximal, characteristic, complemented
5#23749992C211yesmaximal, characteristic, complemented
6#23749983C211yesmaximal, characteristic, complemented
7#23749884C211yesmaximal, characteristic, complemented
8#23749882C211yesmaximal, characteristic, complemented
9#23749870C211yesmaximal, characteristic
10#23749868C211yesmaximal, characteristic
11C4×Dic596C211yesmaximal, characteristic, complemented
12C4×#14558726C211yesmaximal, characteristic, complemented
13C4×#14558724C211yesmaximal, characteristic, complemented
14C4×#14558719C211yesmaximal, characteristic, complemented
15C4×SD16×C149C211yesmaximal, characteristic, complemented
16C2×Dic596C2211yescharacteristic
17C2×#14558726C2211yescharacteristic
18C2×#14558724C2211yescharacteristic
19C2×#14558719C2211yescharacteristic
20C2×#14558719C2211yescharacteristic
21#18011910C2211yescharacteristic
22#18011909C2211yescharacteristic
23#18011904—21no—
24#18011902C2211yescharacteristic
25#18011901—21no—
26#18011898C2211yescharacteristic
27#18011893—21no—
28#18011891C2211yescharacteristic
29#18011891C2211yescharacteristic
30#18011889—21no—
31#18011887C2211yescharacteristic
32#18011882C2211yescharacteristic
33C4×Dic298—21no—
34C4×Dic298C2211yescharacteristic
35C4×Dic298C2211yescharacteristic
36C4×C22⋊D149—21no—
37#18011870—21no—
38#18011868—21no—
39C42×D149C2211yescharacteristic
40#18011845C2211yescharacteristic
41#18011844C2211yescharacteristic
42#18011842C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011832C2211yescharacteristic
49#18011821C2211yescharacteristic
50#18011821C2211yescharacteristic
51C4×#11924746C2211yescharacteristic
52C2×SD16×C149C2211yescharacteristic
53C4×Q8×C149C2211yescharacteristic
54C4×D4×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298C2311yescharacteristic
61C2×Dic298C2311yescharacteristic
62C2×C22⋊D149—21no—
63C2×C4×D149D411yescharacteristic
64C2×C4×D149D411yescharacteristic
65C2×C4×D149C2311yescharacteristic
66Dic596—22no—
67#14558726—22no—
68#14558724—22no—
69#14558719—22no—
70#14558719—22no—
71C2×#11924746C2311yescharacteristic
72C2×#11924746C2311yescharacteristic
73C4⋊Dic149—21no—
74C4⋊Dic149—21no—
75C4⋊Dic149—21no—
76C4⋊Dic149C2311yescharacteristic
77C4⋊Dic149C2311yescharacteristic
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85C22⋊Dic149—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91C4×Dic149—21no—
92C4×Dic149—21no—
93C4×Dic149D411yescharacteristic
94C4×Dic149D411yescharacteristic
95C4×Dic149C2311yescharacteristic
96C2×Q8×C149C2311yescharacteristic
97C2×D4×C149C2311yescharacteristic
98C22×C4×C149—21no—
99SD16×C149—22no—
100C2×C8×C149C2311yescharacteristic
101C2×C8×C149C2311yescharacteristic
102C4⋊C4×C149—21no—
103C4⋊C4×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C22⋊C4×C149—21no—
106C42×C149—21no—
107C42×C149C2311yescharacteristic
108C22×D149C2×D411yescharacteristic
109Dic298—21no—
110Dic298—21no—
111Dic298—21no—
112Dic298—21no—
113Dic298—42no—
114C22⋊D149—42no—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C2×Dic149—21no—
118C2×Dic149—21no—
119C2×Dic149C2×D411yescharacteristic
120C2×Dic149C2×D411yescharacteristic
121C2×Dic149C2×D411yescharacteristic
122C4×D149—22no—
123C4×D149—21no—
124C4×D149—21no—
125C4×D149—41no—
126#11924746—21no—
127#11924746#4112yes—
128C23×C149—21no—
129Q8×C149—21no—
130Q8×C149—21no—
131D4×C149—21no—
132D4×C149—21no—
133C2×C4×C149—21no—
134C2×C4×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—42no—
137C2×C4×C149C2×D411yescharacteristic
138C2×C4×C149C2×D411yescharacteristic
139C2×C4×C149C2411yescharacteristic
140C8×C149—21no—
141C8×C149#4112yes—
142C22×C149—41no—
143C22×C149—41no—
144C22×C149—41no—
145C22×C149C22×D411yescharacteristic
146C2×D149—21no—
147C2×D149—21no—
148C2×D149—21no—
149C4×C149—21no—
150C4×C149—41no—
151C4×C149—41no—
152C4×C149—41no—
153C4×C149#13712yes—
154C4×C149C2×#4111yescharacteristic
155C4×C149C2×#4111yescharacteristic
156Dic149—21no—
157Dic149—21no—
158Dic149—21no—
159Dic149—41no—
160Dic149—41no—
161Dic149—41no—
162Dic149—41no—
163C2×C149—81no—
164C2×C149#53211yescharacteristic
165C2×C149C2×#13711yescharacteristic
166C2×C149#57511yescharacteristic
167D149—41no—
168C149#317211yescharacteristic, complemented, Sylow
169#3172—1491nomaximal, Sylow
170#533—1491no—
171#529—1491no—
172#501—1491no—
173#497—1491no—
174#491—1491no—
175#489—1491no—
176#470—1491no—
177#470—1491no—
178#468—1491no—
179#468—1491no—
180C4×Q16—1491no—
181C4×Q16—1491no—
182C4×SD16—1491no—
183C4×SD16D14911yescharacteristic, complemented
184C4×M16—1491no—
185C2×Q16—1491no—
186C2×Q16—1491no—
187C2×SD16—1491no—
188C2×SD16C2×D14911yescharacteristic
189C2×M16—1491no—
190C2×M16—1491no—
191C4⋊Q8—1491no—
192C4⋊Q8—1491no—
193#126—2981no—
194#125—2981no—
195#125—1491no—
196#124—1491no—
197#123—2981no—
198C22⋊Q8—2981no—
199C22⋊Q8—1491no—
200C22⋊Q8—1491no—
201C22⋊Q8—1491no—
202#121—1491no—
203C4×Q8—2981no—
204C4×Q8—1491no—
205C4×Q8—1491no—
206C4×Q8C2×D14911yescharacteristic
207C4×D4—2981no—
208C4×D4C2×D14911yescharacteristic
209#117—2981no—
210#117—2981no—
211C2×C42—1491no—
212#107—1491no—
213#107—1491no—
214#106—1491no—
215#106C2×D14911yescharacteristic
216#103—1491no—
217#103—1491no—
218#103—1491no—
219#103—1491no—
220#103—1491no—
221#103C2×D14911yescharacteristic
222#102—1491no—
223#102C2×D14911yescharacteristic
224#97—1491no—
225#97—1491no—
226C4×C8—1491no—
227C4×C8C2×D14911yescharacteristic
228C2×Q8—2981no—
229C2×Q8—1491no—
230C2×Q8—1491no—
231C2×Q8C22×D14911yescharacteristic
232C2×D4—2981no—
233C2×D4C22×D14911yescharacteristic
234C22×C4—21no—
235C22×C4—1491no—
236C22×C4—1491no—
237C22×C4—1491no—
238Q16—2982no—
239Q16—2982no—
240SD16—22no—
241SD16—2982no—
242M16—2982no—
243M16—2982no—
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—2981no—
258C4⋊C4—2981no—
259C4⋊C4—1491no—
260C4⋊C4—1491no—
261C4⋊C4C22×D14911yescharacteristic
262C4⋊C4C22×D14911yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—2981no—
265C22⋊C4—2981no—
266C22⋊C4—2981no—
267C22⋊C4—2981no—
268C22⋊C4—2981no—
269C22⋊C4—2981no—
270C42—21no—
271C42—2981no—
272C42—2981no—
273C42—1491no—
274C42—1491no—
275C42—1491no—
276C42C22×D14911yescharacteristic
277C23—21no—
278C23—1491no—
279Q8—21no—
280Q8—21no—
281Q8—2981no—
282Q8—2981no—
283Q8—2981no—
284Q8—2981no—
285Q8—5962no—
286D4—21no—
287D4—21no—
288D4—5962no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—42no—
293C2×C4—2982no—
294C2×C4—2981no—
295C2×C4—2981no—
296C2×C4—2981no—
297C2×C4—2981no—
298C2×C4—2981no—
299C2×C4—2981no—
300C2×C4—5961no—
301C2×C4—1491no—
302C2×C4—1491no—
303C2×C4—1491no—
304C2×C4D4×D14911yescharacteristic
305C2×C4D4×D14911yescharacteristic
306C2×C4C23×D14911yescharacteristic
307C8—21no—
308C8—2981no—
309C8—1492no—
310C8#1455873612yes—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—2981no—
315C22—2981no—
316C22—2981no—
317C22C2×D4×D14911yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—2981no—
323C4—2981no—
324C4—2981no—
325C4—5961no—
326C4—5961no—
327C4—5961no—
328C4—5961no—
329C4#1801194012yes—
330C4#41×D14911yescharacteristic
331C4C2×#1455873611yescharacteristic
332C2—81no—
333C2—5961no—
334C2#2375017211yescharacteristic
335C2C2×#1801194011yescharacteristic
336C2#2375042211yescharacteristic
subgroupG/H
centerC2×C4D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC4×SD16×C149C2
socleC22×C149C22×D4
prime radical#18011882C22
hypercenterC4×SD16D149
hypocenterC149#3172
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #23750179C2semidirect
3. #23750032C2semidirect
4. #23750016C2semidirect
5. #23749992C2semidirect
6. #23749983C2semidirect
7. #23749884C2semidirect
8. #23749882C2semidirect
11. C4×Dic596C2semidirect
12. C4×#14558726C2semidirect
13. C4×#14558724C2semidirect
14. C4×#14558719C2semidirect
15. C4×SD16×C149C2semidirect
168. C149#3172semidirect
183. C4×SD16D149semidirect

Maximal subgroups

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

subgroupindex
#237501792
#237501572
#237500322
#237500162
#237499922
#237499832
#237498842
#237498822
#237498702
#237498682
C4×Dic5962
C4×#145587262
C4×#145587242
C4×#145587192
C4×SD16×C1492
#3172149