Finite Group Databasebeta

← #34057453

Subgroups — #34057453

Order 19072.

344 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750353C211yesmaximal, characteristic, complemented
2#23749989C211yesmaximal, characteristic
3#23749984C211yesmaximal, characteristic, complemented
4#23749979C211yesmaximal, characteristic, complemented
5#23749932C211yesmaximal, characteristic, complemented
6#23749925C211yesmaximal, characteristic, complemented
7#23749915C211yesmaximal, characteristic, complemented
8#23749844C211yesmaximal, characteristic, complemented
9#23749844C211yesmaximal, characteristic, complemented
10#23749822C211yesmaximal, characteristic
11#23749756C211yesmaximal, characteristic, complemented
12#23749730C211yesmaximal, characteristic, complemented
13#23749725C211yesmaximal, characteristic, complemented
14C4×#14558724C211yesmaximal, characteristic, complemented
15#559×C149C211yesmaximal, characteristic
16C2×#14558726C2211yescharacteristic
17C2×#14558724C2211yescharacteristic
18C2×#14558724C2211yescharacteristic
19#18011911C2211yescharacteristic
20#18011909—21no—
21#18011903C2211yescharacteristic
22#18011903C2211yescharacteristic
23#18011901—21no—
24#18011901—21no—
25C4×Dic298C2211yescharacteristic
26C4×Dic298C2211yescharacteristic
27C4×Dic298C2211yescharacteristic
28#18011876—21no—
29#18011844C2211yescharacteristic
30#18011842C2211yescharacteristic
31#18011842C2211yescharacteristic
32C4⋊#11924746C2211yescharacteristic
33C4⋊#11924746C2211yescharacteristic
34C4⋊#11924746C2211yescharacteristic
35#18011835C2211yescharacteristic
36#18011835C2211yescharacteristic
37#18011835C2211yescharacteristic
38#18011834C2211yescharacteristic
39#18011832C2211yescharacteristic
40#18011832C2211yescharacteristic
41#18011832C2211yescharacteristic
42#18011832C2211yescharacteristic
43#18011832C2211yescharacteristic
44#18011832C2211yescharacteristic
45#18011822C2211yescharacteristic
46#18011822C2211yescharacteristic
47C4×#11924746C2211yescharacteristic
48#127×C149C2211yescharacteristic
49#124×C149—21no—
50#124×C149C2211yescharacteristic
51#124×C149C2211yescharacteristic
52#123×C149—21no—
53#123×C149—21no—
54C4×Q8×C149C2211yescharacteristic
55C4×Q8×C149C2211yescharacteristic
56C4×D4×C149—21no—
57C4×D4×C149C2211yescharacteristic
58C4×D4×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298C2311yescharacteristic
61#14558726—22no—
62#14558724—22no—
63#14558724—22no—
64C2×#11924746C2311yescharacteristic
65C2×#11924746C2311yescharacteristic
66C2×#11924746C2311yescharacteristic
67C2×#11924746C2311yescharacteristic
68C4⋊Dic149—21no—
69C4⋊Dic149C2311yescharacteristic
70C4⋊Dic149C2311yescharacteristic
71C4⋊Dic149C2311yescharacteristic
72#14558715—21no—
73#14558715—21no—
74#14558715—21no—
75#14558715—21no—
76#14558715—21no—
77#14558715—21no—
78#14558715—21no—
79C4×Dic149—21no—
80C4×Dic149—21no—
81C4×Dic149—21no—
82C2×Q8×C149D411yescharacteristic
83C2×Q8×C149C2311yescharacteristic
84C2×D4×C149—21no—
85C2×D4×C149—21no—
86C2×D4×C149C2311yescharacteristic
87C2×D4×C149C2311yescharacteristic
88C22×C4×C149—21no—
89C22×C4×C149—21no—
90C4⋊C4×C149—21no—
91C4⋊C4×C149D411yescharacteristic
92C4⋊C4×C149D411yescharacteristic
93C4⋊C4×C149D411yescharacteristic
94C4⋊C4×C149C2311yescharacteristic
95C22⋊C4×C149—21no—
96C22⋊C4×C149—21no—
97C22⋊C4×C149—21no—
98C22⋊C4×C149—21no—
99C22⋊C4×C149—21no—
100C22⋊C4×C149—21no—
101C42×C149—21no—
102C42×C149C2311yescharacteristic
103C42×C149C2311yescharacteristic
104C42×C149C2311yescharacteristic
105Dic298—21no—
106Dic298—42no—
107Dic298#4112yes—
108C2×Dic149—21no—
109C2×Dic149—21no—
110C2×Dic149—21no—
111C2×Dic149—21no—
112#11924746—21no—
113#11924746—21no—
114#11924746—21no—
115#11924746—21no—
116C23×C149—21no—
117C23×C149—21no—
118Q8×C149—21no—
119Q8×C149—21no—
120Q8×C149—41no—
121D4×C149—21no—
122D4×C149—21no—
123D4×C149—21no—
124D4×C149—21no—
125D4×C149—42no—
126D4×C149—81no—
127C2×C4×C149—21no—
128C2×C4×C149—21no—
129C2×C4×C149—81no—
130C2×C4×C149—81no—
131C2×C4×C149C2×D411yescharacteristic
132C2×C4×C149C2×D411yescharacteristic
133C2×C4×C149C2×D411yescharacteristic
134C2×C4×C149C2×D411yescharacteristic
135C2×C4×C149C2×D411yescharacteristic
136C2×C4×C149C2×D411yescharacteristic
137C2×C4×C149C2411yescharacteristic
138C22×C149—41no—
139C22×C149—41no—
140C22×C149—41no—
141C22×C149—41no—
142C22×C149—41no—
143C22×C149—41no—
144C22×C149C22×D411yescharacteristic
145C4×C149—21no—
146C4×C149—21no—
147C4×C149—21no—
148C4×C149—21no—
149C4×C149—21no—
150C4×C149—21no—
151C4×C149—41no—
152C4×C149—41no—
153C4×C149C2×#4111yescharacteristic
154C4×C1492−1+411yescharacteristic
155Dic149—22no—
156Dic149—41no—
157Dic149—41no—
158Dic149—41no—
159C2×C149—81no—
160C2×C149—81no—
161C2×C149#54811yescharacteristic
162C2×C149#57511yescharacteristic
163C2×C149#57711yescharacteristic
164C149#337111yescharacteristic, complemented, Sylow
165#3371—1491nomaximal, Sylow
166#559D14911yescharacteristic
167#557—1491no—
168#490—1491no—
169#489—1491no—
170#488—1491no—
171#479—1491no—
172#478—1491no—
173#476—1491no—
174#464—1491no—
175#464—1491no—
176#460—1491no—
177#446—1491no—
178#441—1491no—
179#440—1491no—
180C4×SD16—1491no—
181C2×Q16—1491no—
182C2×SD16—1491no—
183C2×SD16—1491no—
184C4⋊Q8—2981no—
185C4⋊Q8—1491no—
186#127C2×D14911yescharacteristic
187#125—2981no—
188#125—2981no—
189#125—1491no—
190#125—1491no—
191#124—21no—
192#124C2×D14911yescharacteristic
193#124C2×D14911yescharacteristic
194#123—21no—
195#123—21no—
196C4×Q8—2981no—
197C4×Q8—1491no—
198C4×Q8—1491no—
199C4×Q8—1491no—
200C4×Q8C2×D14911yescharacteristic
201C4×Q8C2×D14911yescharacteristic
202C4×D4—21no—
203C4×D4C2×D14911yescharacteristic
204C4×D4C2×D14911yescharacteristic
205#107—1491no—
206#106—1491no—
207#106—1491no—
208C4⋊C8—1491no—
209C4⋊C8—1491no—
210C4⋊C8—1491no—
211#103—1491no—
212#103—1491no—
213#103—1491no—
214#103—1491no—
215#102—1491no—
216#102—1491no—
217#102—1491no—
218#102—1491no—
219#102—1491no—
220#102—1491no—
221#97—1491no—
222#97—1491no—
223C4×C8—1491no—
224C2×Q8—2981no—
225C2×Q8—1491no—
226C2×Q8C22⋊D14911yescharacteristic
227C2×Q8C22×D14911yescharacteristic
228C2×D4—21no—
229C2×D4—21no—
230C2×D4C22×D14911yescharacteristic
231C2×D4C22×D14911yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
234Q16—2982no—
235SD16—2982no—
236SD16—2982no—
237C2×C8—1491no—
238C2×C8—1491no—
239C2×C8—1491no—
240C2×C8—1491no—
241C4⋊C4—21no—
242C4⋊C4—2981no—
243C4⋊C4—2981no—
244C4⋊C4—2981no—
245C4⋊C4—2981no—
246C4⋊C4—2981no—
247C4⋊C4—2981no—
248C4⋊C4—2981no—
249C4⋊C4—2981no—
250C4⋊C4—1491no—
251C4⋊C4—1491no—
252C4⋊C4—1491no—
253C4⋊C4C22⋊D14911yescharacteristic
254C4⋊C4C22⋊D14911yescharacteristic
255C4⋊C4C22⋊D14911yescharacteristic
256C4⋊C4C22×D14911yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C42—21no—
264C42—2981no—
265C42—2981no—
266C42—2981no—
267C42C22×D14911yescharacteristic
268C42C22×D14911yescharacteristic
269C42C22×D14911yescharacteristic
270C23—21no—
271C23—21no—
272Q8—21no—
273Q8—21no—
274Q8—41no—
275Q8—2981no—
276Q8—5962no—
277Q8—1492no—
278D4—21no—
279D4—21no—
280D4—21no—
281D4—21no—
282D4—42no—
283D4—81no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—2981no—
289C2×C4—2981no—
290C2×C4—2981no—
291C2×C4—2981no—
292C2×C4C2×C22⋊D14911yescharacteristic
293C2×C4C2×C22⋊D14911yescharacteristic
294C2×C4C2×C22⋊D14911yescharacteristic
295C2×C4C2×C22⋊D14911yescharacteristic
296C2×C4C2×C22⋊D14911yescharacteristic
297C2×C4C2×C22⋊D14911yescharacteristic
298C2×C4C23×D14911yescharacteristic
299C8—2981no—
300C8—2981no—
301C8—2981no—
302C8—2981no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22C22×C22⋊D14911yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—2982no—
319C4—5961no—
320C4—5961no—
321C4—5961no—
322C4#41×D14911yescharacteristic
323C4#1801195811yescharacteristic
324C2—81no—
325C2—81no—
326C2#2375028211yescharacteristic
327C2#2375042311yescharacteristic
328C2#2375043611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#559×C149C2
socleC22×C149C22×D4
prime radical#127×C149C22
hypercenter#559D149
hypocenterC149#3371
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #23750353C2semidirect
3. #23749984C2semidirect
4. #23749979C2semidirect
5. #23749932C2semidirect
6. #23749925C2semidirect
7. #23749915C2semidirect
8. #23749844C2semidirect
9. #23749844C2semidirect
11. #23749756C2semidirect
12. #23749730C2semidirect
13. #23749725C2semidirect
14. C4×#14558724C2semidirect
164. C149#3371semidirect

Maximal subgroups

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

subgroupindex
#237503532
#237499892
#237499842
#237499792
#237499322
#237499252
#237499152
#237498442
#237498222
#237497562
#237497302
#237497252
C4×#145587242
#559×C1492
#3371149