Finite Group Databasebeta

← #34057528

Subgroups — #34057528

Order 19072.

332 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750352C211yesmaximal, characteristic, complemented
2#23750349C211yesmaximal, characteristic
3#23749986C211yesmaximal, characteristic
4#23749981C211yesmaximal, characteristic
5#23749934C211yesmaximal, characteristic, complemented
6#23749922C211yesmaximal, characteristic
7#23749918C211yesmaximal, characteristic, complemented
8#23749850C211yesmaximal, characteristic
9#23749850C211yesmaximal, characteristic
10#23749832C211yesmaximal, characteristic, complemented
11#23749753C211yesmaximal, characteristic, complemented
12#23749729C211yesmaximal, characteristic, complemented
13#23749727C211yesmaximal, characteristic
14#23749717C211yesmaximal, characteristic, complemented
15#491×C149C211yesmaximal, characteristic, complemented
16C2×#14558726C2211yescharacteristic
17C2×#14558726C2211yescharacteristic
18C2×#14558725C2211yescharacteristic
19#18011910—21no—
20#18011910C2211yescharacteristic
21#18011906—21no—
22#18011906—21no—
23#18011902C2211yescharacteristic
24#18011901—21no—
25#18011901—21no—
26#18011900C2211yescharacteristic
27#18011900C2211yescharacteristic
28#18011891—21no—
29Q8×Dic149C2211yescharacteristic
30Q8×Dic149C2211yescharacteristic
31C4×Dic298C2211yescharacteristic
32C4×Dic298C2211yescharacteristic
33#18011876—21no—
34#18011876C2211yescharacteristic
35#18011876C2211yescharacteristic
36C4×D596C2211yescharacteristic
37#18011869—21no—
38#18011845C2211yescharacteristic
39#18011844C2211yescharacteristic
40#18011842C2211yescharacteristic
41C4⋊#11924746C2211yescharacteristic
42#18011840C2211yescharacteristic
43#18011840C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011835C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011831C2211yescharacteristic
49#18011831C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C4⋊Q8×C149C2211yescharacteristic
53#125×C149C2211yescharacteristic
54#103×C149C2211yescharacteristic
55#103×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#97×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298D411yescharacteristic
61C2×Dic298C2311yescharacteristic
62C2×D596C2311yescharacteristic
63C2×C4×D149—21no—
64#14558726—22no—
65#14558726—22no—
66#14558725—22no—
67C2×#11924746C2311yescharacteristic
68C2×#11924746C2311yescharacteristic
69C4⋊Dic149—21no—
70C4⋊Dic149—21no—
71C4⋊Dic149—21no—
72C4⋊Dic149D411yescharacteristic
73C4⋊Dic149C2311yescharacteristic
74C4⋊Dic149C2311yescharacteristic
75#14558715—21no—
76#14558715—21no—
77#14558715—21no—
78#14558715—21no—
79#14558715—21no—
80#14558715D411yescharacteristic
81#14558715D411yescharacteristic
82#14558713—21no—
83#14558713—21no—
84#14558713—21no—
85#14558713—21no—
86#14558713—21no—
87C4×Dic149—21no—
88C4×Dic149—21no—
89C4×Dic149—21no—
90C4×Dic149—21no—
91C4×Dic149—21no—
92C4×Dic149C2311yescharacteristic
93C4×Dic149C2311yescharacteristic
94C2×Q8×C149C2311yescharacteristic
95C2×Q8×C149C2311yescharacteristic
96C2×C8×C149C2311yescharacteristic
97C2×C8×C149C2311yescharacteristic
98C4⋊C4×C149—21no—
99C4⋊C4×C149—21no—
100C4⋊C4×C149—21no—
101C4⋊C4×C149—21no—
102C4⋊C4×C149C2311yescharacteristic
103C4⋊C4×C149C2311yescharacteristic
104C42×C149C2311yescharacteristic
105C22×D149—21no—
106Dic298—21no—
107Dic298—41no—
108Dic298—42no—
109Dic298#4112yes—
110D596—21no—
111D596—21no—
112C2×Dic149—21no—
113C2×Dic149—21no—
114C2×Dic149—21no—
115C2×Dic149C2×D411yescharacteristic
116C2×Dic149C2×D411yescharacteristic
117C2×Dic149C2×D411yescharacteristic
118C2×Dic149C2×D411yescharacteristic
119C4×D149—42no—
120#11924746—21no—
121#11924746—21no—
122Q8×C149—21no—
123Q8×C149—21no—
124Q8×C149—21no—
125Q8×C149—21no—
126C2×C4×C149—21no—
127C2×C4×C149—21no—
128C2×C4×C149—21no—
129C2×C4×C149—21no—
130C2×C4×C149C2×D411yescharacteristic
131C2×C4×C149C2×D411yescharacteristic
132C2×C4×C149C2411yescharacteristic
133C8×C149—21no—
134C8×C149—21no—
135C22×C149C22×D411yescharacteristic
136C2×D149—41no—
137C2×D149—41no—
138C2×D149—41no—
139C4×C149—21no—
140C4×C149—21no—
141C4×C149—41no—
142C4×C149—41no—
143C4×C149—41no—
144C4×C149—41no—
145C4×C149C2×#4111yescharacteristic
146C4×C1492−1+411yescharacteristic
147Dic149—22no—
148Dic149—21no—
149Dic149—21no—
150Dic149—21no—
151Dic149—21no—
152Dic149—41no—
153Dic149—41no—
154C2×C149#54811yescharacteristic
155C2×C149#57511yescharacteristic
156C2×C149#57811yescharacteristic
157D149—81no—
158C149#337711yescharacteristic, complemented, Sylow
159#3377—1491nomaximal, Sylow
160#557—1491no—
161#556—1491no—
162#491D14911yescharacteristic, complemented
163#489—1491no—
164#488—1491no—
165#479—1491no—
166#478—1491no—
167#477—1491no—
168#464—1491no—
169#464—1491no—
170#462—1491no—
171#446—1491no—
172#441—1491no—
173#440—1491no—
174C4×Q16—1491no—
175C2×Q16—1491no—
176C2×Q16—1491no—
177C2×SD16—1491no—
178C4⋊Q8—2981no—
179C4⋊Q8—1491no—
180C4⋊Q8C2×D14911yescharacteristic
181#126—2981no—
182#126—2981no—
183#125—2981no—
184#125—2981no—
185#125—1491no—
186#125C2×D14911yescharacteristic
187#124—1491no—
188#124—1491no—
189C22⋊Q8—2981no—
190C4×Q8—2981no—
191C4×Q8—1491no—
192C4×Q8—1491no—
193C4×Q8—1491no—
194C4×Q8—1491no—
195C4×Q8—1491no—
196C4×Q8—1491no—
197C4×D4—1491no—
198#117—2981no—
199#107—1491no—
200#107—1491no—
201#106—1491no—
202C4⋊C8—1491no—
203C4⋊C8—1491no—
204C4⋊C8—1491no—
205#103—1491no—
206#103—1491no—
207#103—1491no—
208#103C2×D14911yescharacteristic
209#103C2×D14911yescharacteristic
210#103C2×D14911yescharacteristic
211#103C2×D14911yescharacteristic
212#102—1491no—
213#102—1491no—
214#102—1491no—
215#97—1491no—
216#97C2×D14911yescharacteristic
217C4×C8—1491no—
218C2×Q8—2981no—
219C2×Q8—1491no—
220C2×Q8—1491no—
221C2×Q8C22×D14911yescharacteristic
222C2×Q8C22×D14911yescharacteristic
223C2×D4—1491no—
224C22×C4—2981no—
225Q16—2982no—
226Q16—2982no—
227SD16—2982no—
228C2×C8—1491no—
229C2×C8—1491no—
230C2×C8C22×D14911yescharacteristic
231C2×C8C22×D14911yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—2981no—
237C4⋊C4—2981no—
238C4⋊C4—2981no—
239C4⋊C4—2981no—
240C4⋊C4—2981no—
241C4⋊C4—2981no—
242C4⋊C4—2981no—
243C4⋊C4—2981no—
244C4⋊C4—1491no—
245C4⋊C4—1491no—
246C4⋊C4—1491no—
247C4⋊C4—1491no—
248C4⋊C4—1491no—
249C4⋊C4C22×D14911yescharacteristic
250C4⋊C4C22×D14911yescharacteristic
251C22⋊C4—2981no—
252C22⋊C4—2981no—
253C22⋊C4—2981no—
254C22⋊C4—2981no—
255C22⋊C4—2981no—
256C42—2981no—
257C42—2981no—
258C42—2981no—
259C42—2981no—
260C42—2981no—
261C42—1491no—
262C42—1491no—
263C42C22×D14911yescharacteristic
264C23—2981no—
265Q8—21no—
266Q8—21no—
267Q8—21no—
268Q8—21no—
269Q8—2981no—
270Q8—5961no—
271Q8—5962no—
272Q8—1492no—
273D4—2981no—
274D4—2981no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—2981no—
280C2×C4—2981no—
281C2×C4—2981no—
282C2×C4—5962no—
283C2×C4—1491no—
284C2×C4—1491no—
285C2×C4—1491no—
286C2×C4—1491no—
287C2×C4D4×D14911yescharacteristic
288C2×C4D4×D14911yescharacteristic
289C2×C4C23×D14911yescharacteristic
290C8—21no—
291C8—21no—
292C8—2981no—
293C8—2981no—
294C22—5961no—
295C22—5961no—
296C22—5961no—
297C22C2×D4×D14911yescharacteristic
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—2981no—
305C4—2981no—
306C4—2981no—
307C4—2981no—
308C4—2982no—
309C4—5961no—
310C4—5961no—
311C4#41×D14911yescharacteristic
312C4#1801195811yescharacteristic
313C2—11921no—
314C2#2375028311yescharacteristic
315C2#2375042411yescharacteristic
316C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#491×C149C2
socleC22×C149C22×D4
prime radicalC2×D596C23
hypercenter#491D149
hypocenterC149#3377
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #23750352C2semidirect
5. #23749934C2semidirect
7. #23749918C2semidirect
10. #23749832C2semidirect
11. #23749753C2semidirect
12. #23749729C2semidirect
14. #23749717C2semidirect
15. #491×C149C2semidirect
158. C149#3377semidirect
162. #491D149semidirect

Maximal subgroups

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

subgroupindex
#237503522
#237503492
#237499862
#237499812
#237499342
#237499222
#237499182
#237498502
#237498322
#237497532
#237497292
#237497272
#237497172
#491×C1492
#3377149