Finite Group Databasebeta

← #34061231

Subgroups — #34061231

Order 19072.

512 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750577C211yesmaximal, characteristic
2#23750576C212yesmaximal, complemented
3#23750575C212yesmaximal, complemented
4#23750575C212yesmaximal, complemented
5#23750574C212yesmaximal, complemented
6#23750573C211yesmaximal, characteristic
7#23750572C212yesmaximal, complemented
8#23750567C212yesmaximal, complemented
9#123×D149C211yesmaximal, characteristic
10C23×#10597010C2211yescharacteristic
11C2×C4⋊#10597010C2212yes—
12C2×C4⋊#10597010C2212yes—
13C2×C4⋊#10597010C2212yes—
14C2×C4⋊#10597010C2211yescharacteristic
15C2×C22⋊#10597010C2212yes—
16C2×C22⋊#10597010C2212yes—
17C2×C22⋊#10597010C2212yes—
18C2×C22⋊#10597010C2211yescharacteristic
19C2×C4×#10597010C2211yescharacteristic
20C2×C4×#10597010C2212yes—
21(C2×#10597010)⋊C4C2212yes—
22(C2×#10597010)⋊C4C2212yes—
23(C2×#10597010)⋊C4C2212yes—
24(C2×#10597010)⋊C4C2212yes—
25(C2×#10597010)⋊C4C2212yes—
26C2×D4×D149C2211yescharacteristic
27C22×C4×D149C2211yescharacteristic
28#18011896C412yescomplemented
29#18011895C411yescharacteristic, complemented
30#18011894C411yescharacteristic, complemented
31#18011893C412yescomplemented
32#18011892C411yescharacteristic, complemented
33C4⋊C4×D149C2212yes—
34C22⋊C4×D149C2212yes—
35C22⋊C4×D149C2211yescharacteristic
36#123×C149C411yescharacteristic, complemented
37C22×#10597010—41no—
38C22×#10597010—42no—
39C22×#10597010C2312yes—
40C22×#10597010C2312yes—
41C22×#10597010C2312yes—
42C22×#10597010C2312yes—
43C4⋊#10597010—42no—
44C4⋊#10597010—42no—
45C4⋊#10597010—41no—
46C4⋊#10597010—42no—
47C22⋊#10597010—41no—
48C22⋊#10597010—42no—
49C22⋊#10597010—42no—
50C22⋊#10597010—42no—
51C4×#10597010—41no—
52C4×#10597010—42no—
53C23×D149C2311yescharacteristic
54C23×D149C2311yescharacteristic
55C2×D596C2×C411yescharacteristic
56C2×C22⋊D149C2×C411yescharacteristic
57C2×C22⋊D149C2×C411yescharacteristic
58D4×D149—41no—
59D4×D149—41no—
60C22×Dic149C2×C411yescharacteristic, complemented
61C2×C4×D149—41no—
62C2×C4×D149—41no—
63C2×C4×D149C2×C412yescomplemented
64C2×C4×D149C2312yes—
65C2×C4×D149C2311yescharacteristic
66C2×C4×D149C2312yes—
67C4⋊Dic149C2×C412yescomplemented
68#14558715C2×C412yescomplemented
69#14558715C2×C412yescomplemented
70C22⋊Dic149C2×C412yes—
71C22⋊Dic149C2×C411yescharacteristic, complemented
72#14558713C2×C412yes—
73#14558713C2×C412yes—
74#14558713C2×C412yescomplemented
75C2×D4×C149C2×C411yescharacteristic
76C22×C4×C149C2×C411yescharacteristic, complemented
77C4⋊C4×C149C2×C412yescomplemented
78C22⋊C4×C149C2×C412yes—
79C22⋊C4×C149C2×C411yescharacteristic, complemented
80C2×#10597010—22no—
81C2×#10597010—22no—
82C2×#10597010—22no—
83C2×#10597010—22no—
84C2×#10597010—22no—
85C2×#10597010—22no—
86C2×#10597010—22no—
87C2×#10597010—22no—
88C2×#10597010—22no—
89C2×#10597010—22no—
90C2×#10597010—22no—
91C2×#10597010—22no—
92C2×#10597010—44no—
93C22×D149—21no—
94C22×D149—21no—
95C22×D149—21no—
96C22×D149—21no—
97C22×D149—22no—
98C22×D149—22no—
99C22×D149—22no—
100C22×D149—22no—
101C22×D149C22×C411yescharacteristic
102C22×D149C22×C411yescharacteristic
103C22×D149C2411yescharacteristic
104D596—41no—
105C22⋊D149—41no—
106C22⋊D149—41no—
107C2×Dic149—41no—
108C2×Dic149C22×C412yes—
109C2×Dic149C22×C411yescharacteristic
110C2×Dic149C22×C412yes—
111C4×D149—22no—
112C4×D149—22no—
113C4×D149—21no—
114C4×D149—21no—
115C4×D149—22no—
116C4×D149—22no—
117C4×D149—42no—
118C23×C149C22×C411yescharacteristic
119C23×C149C22×C411yescharacteristic
120D4×C149—41no—
121C2×C4×C149—41no—
122C2×C4×C149C22×C412yes—
123C2×C4×C149C22×C411yescharacteristic
124C2×C4×C149C22×C412yes—
125C22×C149—21no—
126C22×C149—21no—
127C22×C149—22no—
128C22×C149—22no—
129C22×C149C23×C411yescharacteristic
130C2×D149—21no—
131C2×D149—21no—
132C2×D149—22no—
133C2×D149—22no—
134C2×D149—41no—
135C2×D149—41no—
136C2×D149—42no—
137C2×D149—42no—
138C2×D149—41no—
139C2×D149—41no—
140C2×D149H(5,𝔽2)12yes—
141C2×D149H(5,𝔽2)11yescharacteristic
142C2×D149H(5,𝔽2)11yescharacteristic
143C2×D1492−1+412yes—
144#10597010—42no—
145#10597010—42no—
146#10597010—42no—
147#10597010—42no—
148C4×C149—22no—
149C4×C149—21no—
150C4×C149—22no—
151Dic149—22no—
152Dic149—21no—
153Dic149—22no—
154C2×C149—41no—
155C2×C149—41no—
156C2×C149#51811yescharacteristic
157C2×C149#52012yes—
158D149—41no—
159D149—41no—
160D149#56011yescharacteristic
161D149#56212yes—
162D149#56311yescharacteristic
163C149#237611yescharacteristic, complemented, Sylow
164#2376—1491nomaximal, Sylow
165C2×#123—1491no—
166#390—1491no—
167#389—1492no—
168#388—1492no—
169#388—1492no—
170#387—1492no—
171#386—1491no—
172#385—1492no—
173#380—1492no—
174C22×D4—1491no—
175C23×C4—1491no—
176C23×C4—1491no—
177#123—1491no—
178#123—1491no—
179#123—1492no—
180#123—1492no—
181#123—1491no—
182#123#1059701011yescharacteristic, complemented
183C2×C4⋊C4—1492no—
184C2×C4⋊C4—1492no—
185C2×C4⋊C4—1492no—
186C2×C4⋊C4—1491no—
187C2×C4⋊C4—1492no—
188C2×C22⋊C4—1492no—
189C2×C22⋊C4—1492no—
190C2×C22⋊C4—1492no—
191C2×C22⋊C4—1491no—
192C2×C22⋊C4—1492no—
193C2×C22⋊C4—1491no—
194C2×C42—1491no—
195C2×C42—1492no—
196#95—1492no—
197#95—1492no—
198#95—1492no—
199#95—1492no—
200#95—1492no—
201C24—1491no—
202C24—1491no—
203C2×D4—5961no—
204C2×D4—5961no—
205C2×D4—1491no—
206C2×D4—1491no—
207C2×D4—1491no—
208C2×D4C2×#1059701011yescharacteristic
209C22×C4—5961no—
210C22×C4—5961no—
211C22×C4—5962no—
212C22×C4—5961no—
213C22×C4—1492no—
214C22×C4—1492no—
215C22×C4—1492no—
216C22×C4—1492no—
217C22×C4—1492no—
218C22×C4—1491no—
219C22×C4—1492no—
220C22×C4—1491no—
221C22×C4—1492no—
222C22×C4C2×#1059701011yescharacteristic, complemented
223C4⋊C4—5962no—
224C4⋊C4—5962no—
225C4⋊C4—5962no—
226C4⋊C4—5961no—
227C4⋊C4—1492no—
228C4⋊C4—1492no—
229C4⋊C4—1492no—
230C4⋊C4C2×#1059701012yescomplemented
231C22⋊C4—5962no—
232C22⋊C4—5962no—
233C22⋊C4—5962no—
234C22⋊C4—5961no—
235C22⋊C4—1492no—
236C22⋊C4—1491no—
237C22⋊C4—1492no—
238C22⋊C4—1492no—
239C22⋊C4—1492no—
240C22⋊C4C2×#1059701012yes—
241C22⋊C4C2×#1059701011yescharacteristic, complemented
242C42—5962no—
243C42—5961no—
244C23—2982no—
245C23—2982no—
246C23—2981no—
247C23—2981no—
248C23—2981no—
249C23—2981no—
250C23—2982no—
251C23—2982no—
252C23—1491no—
253C23—1491no—
254C23—1491no—
255C23C22×#1059701011yescharacteristic
256C23C22×#1059701011yescharacteristic
257D4—41no—
258D4—5961no—
259D4—5961no—
260D4—5961no—
261C2×C4—41no—
262C2×C4—2982no—
263C2×C4—2981no—
264C2×C4—2982no—
265C2×C4—2982no—
266C2×C4—2981no—
267C2×C4—2982no—
268C2×C4—2982no—
269C2×C4—2982no—
270C2×C4—2982no—
271C2×C4—2982no—
272C2×C4—2982no—
273C2×C4—2982no—
274C2×C4—2982no—
275C2×C4—2982no—
276C2×C4—2982no—
277C2×C4—2982no—
278C2×C4—2982no—
279C2×C4—2982no—
280C2×C4—5962no—
281C2×C4—5961no—
282C2×C4—5964no—
283C2×C4—1492no—
284C2×C4—1492no—
285C2×C4—1491no—
286C2×C4C22×#1059701012yes—
287C2×C4C22×#1059701012yes—
288C2×C4C22×#1059701011yescharacteristic
289C22—21no—
290C22—21no—
291C22—22no—
292C22—22no—
293C22—2981no—
294C22—2981no—
295C22—2982no—
296C22—2982no—
297C22—5961no—
298C22—5961no—
299C22—5962no—
300C22—5962no—
301C22—5961no—
302C22—5961no—
303C22—1491no—
304C22—1491no—
305C22—1492no—
306C22—1492no—
307C22C23×#1059701011yescharacteristic
308C4—22no—
309C4—21no—
310C4—22no—
311C4—2982no—
312C4—2981no—
313C4—2982no—
314C4—5962no—
315C4—5962no—
316C4—5962no—
317C4—5962no—
318C2—41no—
319C2—41no—
320C2—5961no—
321C2—5961no—
322C2—1491no—
323C2—1492no—
324C2—1491no—
325C2#2375069211yescharacteristic
326C2#2375069412yes—
subgroupG/H
center, FrattiniC22C23×#10597010
commutator, socleC22×C149C23×C4
Fitting#123×C149C4
prime radicalC2×D4×D149C22
cosocleC22×D149C24
hypercenter#123#10597010
hypocenterC149#2376
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
2. #23750576C2semidirect
3. #23750575C2semidirect
4. #23750575C2semidirect
5. #23750574C2semidirect
7. #23750572C2semidirect
8. #23750567C2semidirect
28. #18011896C4semidirect
29. #18011895C4semidirect
30. #18011894C4semidirect
31. #18011893C4semidirect
32. #18011892C4semidirect
36. #123×C149C4semidirect
60. C22×Dic149C2×C4semidirect
63. C2×C4×D149C2×C4semidirect
67. C4⋊Dic149C2×C4semidirect
68. #14558715C2×C4semidirect
69. #14558715C2×C4semidirect
71. C22⋊Dic149C2×C4semidirect
74. #14558713C2×C4semidirect
76. C22×C4×C149C2×C4semidirect
77. C4⋊C4×C149C2×C4semidirect
79. C22⋊C4×C149C2×C4semidirect
163. C149#2376semidirect
182. #123#10597010semidirect
222. C22×C4C2×#10597010semidirect
230. C4⋊C4C2×#10597010semidirect
241. C22⋊C4C2×#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505772
#237505762
#237505752
#237505742
#237505732
#237505722
#237505672
#123×D1492
#2376149