Finite Group Databasebeta

← #34054922

Subgroups — #34054922

Order 19072.

370 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#23750246C211yesmaximal, characteristic
2#23750102C211yesmaximal, characteristic, complemented
3#23749967C211yesmaximal, characteristic, complemented
4#23749950C211yesmaximal, characteristic
5#23749921C211yesmaximal, characteristic, complemented
6#23749911C211yesmaximal, characteristic, complemented
7#23749848C211yesmaximal, characteristic, complemented
8#23749848C211yesmaximal, characteristic, complemented
9#23749783C211yesmaximal, characteristic, complemented
10#23749766C211yesmaximal, characteristic
11#23749733C211yesmaximal, characteristic, complemented
12#23749727C211yesmaximal, characteristic, complemented
13C4×Dic596C211yesmaximal, characteristic, complemented
14C4×#14558725C211yesmaximal, characteristic, complemented
15#433×C149C211yesmaximal, characteristic, complemented
16C22×Dic298C2211yescharacteristic
17C2×Dic596C2211yescharacteristic
18C2×Dic596C2211yescharacteristic
19C2×#14558725C2211yescharacteristic
20C2×#14558725C2211yescharacteristic
21#18011911C2211yescharacteristic
22#18011906—21no—
23#18011899C2211yescharacteristic
24#18011897—21no—
25#18011893—21no—
26#18011890C2211yescharacteristic
27#18011889—21no—
28#18011885C2211yescharacteristic
29C4×Dic298C2211yescharacteristic
30C4×Dic298C2211yescharacteristic
31C4×Dic298C2211yescharacteristic
32C4×Dic298C2211yescharacteristic
33C4×Dic298C2211yescharacteristic
34#18011876—21no—
35#18011876—21no—
36C4×D596C2211yescharacteristic
37#18011870C2211yescharacteristic
38#18011867—21no—
39#18011867—21no—
40#18011845C2211yescharacteristic
41#18011845C2211yescharacteristic
42#18011843C2211yescharacteristic
43#18011843C2211yescharacteristic
44#18011836C2211yescharacteristic
45#18011836C2211yescharacteristic
46#18011836C2211yescharacteristic
47#18011836C2211yescharacteristic
48#18011836C2211yescharacteristic
49#18011836C2211yescharacteristic
50#18011833C2211yescharacteristic
51#18011833C2211yescharacteristic
52#117×C149C2211yescharacteristic
53C4⋊C8×C149C2211yescharacteristic
54C4⋊C8×C149C2211yescharacteristic
55C22⋊C8×C149C2211yescharacteristic
56C22⋊C8×C149C2211yescharacteristic
57#97×C149C2211yescharacteristic
58C4×C8×C149C2211yescharacteristic
59C2×Dic298—22no—
60C2×Dic298—22no—
61C2×Dic298—21no—
62C2×Dic298—21no—
63C2×Dic298C2311yescharacteristic
64C2×Dic298C2311yescharacteristic
65C2×Dic298C2311yescharacteristic
66C2×D596C2311yescharacteristic
67C2×C22⋊D149—21no—
68C22×Dic149—21no—
69C2×C4×D149—21no—
70Dic596—22no—
71Dic596—22no—
72#14558725—22no—
73#14558725—22no—
74C4⋊Dic149—21no—
75C4⋊Dic149C2311yescharacteristic
76C4⋊Dic149C2311yescharacteristic
77C4⋊Dic149C2311yescharacteristic
78C4⋊Dic149C2311yescharacteristic
79#14558715—21no—
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85C22⋊Dic149—21no—
86C22⋊Dic149—21no—
87#14558713—21no—
88#14558713—21no—
89#14558713—21no—
90#14558713—21no—
91C4×Dic149—21no—
92C4×Dic149—21no—
93C4×Dic149—21no—
94C4×Dic149—21no—
95C4×Dic149—21no—
96C4×Dic149—21no—
97C22×C4×C149C2311yescharacteristic
98C2×C8×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C2×C8×C149C2311yescharacteristic
101C2×C8×C149C2311yescharacteristic
102C4⋊C4×C149D411yescharacteristic
103C4⋊C4×C149D411yescharacteristic
104C22⋊C4×C149D411yescharacteristic
105C22⋊C4×C149D411yescharacteristic
106C42×C149C2311yescharacteristic
107C42×C149C2311yescharacteristic
108C22×D149—21no—
109Dic298—24no—
110Dic298—21no—
111Dic298—21no—
112Dic298—21no—
113Dic298—21no—
114Dic298—81no—
115Dic298#4112yes—
116Dic298#4112yes—
117D596—21no—
118D596—21no—
119C22⋊D149—81no—
120C2×Dic149—24no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149—21no—
125C2×Dic149—21no—
126C2×Dic149—21no—
127C2×Dic149—21no—
128C4×D149—81no—
129C23×C149C2×D411yescharacteristic
130C2×C4×C149—21no—
131C2×C4×C149—21no—
132C2×C4×C149C2×D411yescharacteristic
133C2×C4×C149C2×D411yescharacteristic
134C2×C4×C149C2×D411yescharacteristic
135C2×C4×C149C2×D411yescharacteristic
136C2×C4×C149C2×D411yescharacteristic
137C2×C4×C149C2411yescharacteristic
138C8×C149—21no—
139C8×C149—21no—
140C8×C149—21no—
141C8×C149—21no—
142C22×C149—21no—
143C22×C149—21no—
144C22×C149—21no—
145C22×C149C22×D411yescharacteristic
146C2×D149—41no—
147C2×D149—41no—
148C2×D149—41no—
149C4×C149—21no—
150C4×C149—21no—
151C4×C149—21no—
152C4×C149—21no—
153C4×C149—21no—
154C4×C149C2×#4111yescharacteristic
155C4×C149C2×#4111yescharacteristic
156Dic149—22no—
157Dic149—22no—
158Dic149—41no—
159Dic149—41no—
160Dic149—41no—
161Dic149—41no—
162Dic149—41no—
163C2×C149—41no—
164C2×C149#52511yescharacteristic
165C2×C149#57711yescharacteristic
166C2×C149#57811yescharacteristic
167D149—81no—
168C149#312111yescharacteristic, complemented, Sylow
169#3121—1491nomaximal, Sylow
170#542—1491no—
171#519—1491no—
172#485—1491no—
173#482—1491no—
174#477—1491no—
175#475—1491no—
176#464—1491no—
177#464—1491no—
178#451—1491no—
179#448—1491no—
180#441—1491no—
181#440—1491no—
182C4×Q16—1491no—
183C4×SD16—1491no—
184#433D14911yescharacteristic, complemented
185C22×Q8—1491no—
186C2×Q16—1491no—
187C2×Q16—1491no—
188C2×SD16—1491no—
189C2×SD16—1491no—
190C4⋊Q8—1491no—
191#126—2981no—
192#124—2981no—
193#124—1491no—
194#123—2981no—
195C22⋊Q8—2981no—
196C22⋊Q8—1491no—
197#121—1491no—
198C4×Q8—2981no—
199C4×Q8—2981no—
200C4×Q8—1491no—
201C4×Q8—1491no—
202C4×Q8—1491no—
203C4×Q8—1491no—
204C4×Q8—1491no—
205C4×D4—1491no—
206#117—2981no—
207#117—2981no—
208#117—1491no—
209#117C2×D14911yescharacteristic
210#107—1491no—
211#107—1491no—
212#106—1491no—
213#106—1491no—
214C4⋊C8C2×D14911yescharacteristic
215C4⋊C8C2×D14911yescharacteristic
216#103—1491no—
217#103—1491no—
218#103—1491no—
219#103—1491no—
220#103—1491no—
221#103—1491no—
222#102—1491no—
223#102—1491no—
224C22⋊C8C2×D14911yescharacteristic
225C22⋊C8C2×D14911yescharacteristic
226#97C2×D14911yescharacteristic
227C4×C8C2×D14911yescharacteristic
228C2×Q8—2982no—
229C2×Q8—2982no—
230C2×Q8—2981no—
231C2×Q8—2981no—
232C2×Q8—1491no—
233C2×Q8—1491no—
234C2×Q8—1491no—
235C2×D4—2981no—
236C2×D4—1491no—
237C22×C4—2981no—
238C22×C4—2981no—
239C22×C4C22×D14911yescharacteristic
240Q16—2982no—
241Q16—2982no—
242SD16—2982no—
243SD16—2982no—
244C2×C8C22×D14911yescharacteristic
245C2×C8C22×D14911yescharacteristic
246C2×C8C22×D14911yescharacteristic
247C2×C8C22×D14911yescharacteristic
248C4⋊C4—2981no—
249C4⋊C4—2981no—
250C4⋊C4—2981no—
251C4⋊C4—2981no—
252C4⋊C4—2981no—
253C4⋊C4—2981no—
254C4⋊C4—2981no—
255C4⋊C4—1491no—
256C4⋊C4—1491no—
257C4⋊C4—1491no—
258C4⋊C4—1491no—
259C4⋊C4D59611yescharacteristic
260C4⋊C4D59611yescharacteristic
261C22⋊C4—2981no—
262C22⋊C4—2981no—
263C22⋊C4—2981no—
264C22⋊C4—2981no—
265C22⋊C4—2981no—
266C22⋊C4—2981no—
267C22⋊C4D59611yescharacteristic
268C22⋊C4D59611yescharacteristic
269C42—2981no—
270C42—2981no—
271C42—2981no—
272C42—2981no—
273C42—2981no—
274C42—2981no—
275C42C22×D14911yescharacteristic
276C42C22×D14911yescharacteristic
277C23—2981no—
278C23C2×D59611yescharacteristic
279Q8—2984no—
280Q8—2981no—
281Q8—2981no—
282Q8—2981no—
283Q8—2981no—
284Q8—1492no—
285Q8—1492no—
286Q8—11921no—
287D4—2981no—
288D4—2981no—
289D4—11921no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—2984no—
293C2×C4—2981no—
294C2×C4—2981no—
295C2×C4—2981no—
296C2×C4—2981no—
297C2×C4—2981no—
298C2×C4—2981no—
299C2×C4—2981no—
300C2×C4—11921no—
301C2×C4C2×D59611yescharacteristic
302C2×C4C2×D59611yescharacteristic
303C2×C4C2×D59611yescharacteristic
304C2×C4C2×D59611yescharacteristic
305C2×C4C2×D59611yescharacteristic
306C2×C4C23×D14911yescharacteristic
307C8—21no—
308C8—21no—
309C8—21no—
310C8—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—5961no—
315C22—5961no—
316C22—5961no—
317C22C22×D59611yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—2982no—
324C4—2982no—
325C4—5961no—
326C4—5961no—
327C4—5961no—
328C4—5961no—
329C4—5961no—
330C4#41×D14911yescharacteristic
331C4#41×D14911yescharacteristic
332C2—41no—
333C2—11921no—
334C2#2375013711yescharacteristic
335C2#2375043711yescharacteristic
336C2#2375044211yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#433×C149C2
socleC22×C149C22×D4
prime radical#18011885C22
hypercenter#433D149
hypocenterC149#3121
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #23750102C2semidirect
3. #23749967C2semidirect
5. #23749921C2semidirect
6. #23749911C2semidirect
7. #23749848C2semidirect
8. #23749848C2semidirect
9. #23749783C2semidirect
11. #23749733C2semidirect
12. #23749727C2semidirect
13. C4×Dic596C2semidirect
14. C4×#14558725C2semidirect
15. #433×C149C2semidirect
168. C149#3121semidirect
184. #433D149semidirect

Maximal subgroups

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

subgroupindex
#237502462
#237501022
#237499672
#237499502
#237499212
#237499112
#237498482
#237497832
#237497662
#237497332
#237497272
C4×Dic5962
C4×#145587252
#433×C1492
#3121149