Finite Group Databasebeta

← #34057527

Subgroups — #34057527

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#23750353C211yesmaximal, characteristic, complemented
2#23749993C211yesmaximal, characteristic, complemented
3#23749984C211yesmaximal, characteristic
4#23749979C211yesmaximal, characteristic
5#23749932C211yesmaximal, characteristic, complemented
6#23749925C211yesmaximal, characteristic
7#23749920C211yesmaximal, characteristic, complemented
8#23749844C211yesmaximal, characteristic
9#23749844C211yesmaximal, characteristic
10#23749832C211yesmaximal, characteristic, complemented
11#23749756C211yesmaximal, characteristic, complemented
12#23749730C211yesmaximal, characteristic, complemented
13#23749725C211yesmaximal, characteristic
14C4×#14558726C211yesmaximal, characteristic, complemented
15#556×C149C211yesmaximal, characteristic
16C2×#14558726C2211yescharacteristic
17C2×#14558726C2211yescharacteristic
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#18011844C2211yescharacteristic
31#18011842C2211yescharacteristic
32C4⋊#11924746C2211yescharacteristic
33C4⋊#11924746C2211yescharacteristic
34C4⋊#11924746C2211yescharacteristic
35#18011835C2211yescharacteristic
36#18011835C2211yescharacteristic
37#18011835C2211yescharacteristic
38#18011835C2211yescharacteristic
39#18011835C2211yescharacteristic
40#18011835C2211yescharacteristic
41#18011834C2211yescharacteristic
42#18011832C2211yescharacteristic
43#18011832C2211yescharacteristic
44#18011832C2211yescharacteristic
45#18011822C2211yescharacteristic
46#18011822C2211yescharacteristic
47C4×#11924746C2211yescharacteristic
48C4⋊Q8×C149C2211yescharacteristic
49#126×C149—21no—
50#126×C149—21no—
51#124×C149C2211yescharacteristic
52#124×C149C2211yescharacteristic
53C22⋊Q8×C149—21no—
54C4×Q8×C149C2211yescharacteristic
55C4×Q8×C149C2211yescharacteristic
56C4×Q8×C149C2211yescharacteristic
57C4×D4×C149C2211yescharacteristic
58#117×C149—21no—
59C2×Dic298—21no—
60C2×Dic298C2311yescharacteristic
61#14558726—22no—
62#14558726—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×Q8×C149C2311yescharacteristic
85C2×D4×C149C2311yescharacteristic
86C22×C4×C149—21no—
87C4⋊C4×C149—21no—
88C4⋊C4×C149—21no—
89C4⋊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—
100C42×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—
117Q8×C149—21no—
118Q8×C149—21no—
119Q8×C149—21no—
120Q8×C149—21no—
121Q8×C149—41no—
122D4×C149—21no—
123D4×C149—21no—
124C2×C4×C149—21no—
125C2×C4×C149—21no—
126C2×C4×C149—21no—
127C2×C4×C149—42no—
128C2×C4×C149C2×D411yescharacteristic
129C2×C4×C149C2×D411yescharacteristic
130C2×C4×C149C2×D411yescharacteristic
131C2×C4×C149C2×D411yescharacteristic
132C2×C4×C149C2×D411yescharacteristic
133C2×C4×C149C2×D411yescharacteristic
134C2×C4×C149C2411yescharacteristic
135C22×C149—41no—
136C22×C149—41no—
137C22×C149—41no—
138C22×C149C22×D411yescharacteristic
139C4×C149—21no—
140C4×C149—21no—
141C4×C149—21no—
142C4×C149—21no—
143C4×C149—21no—
144C4×C149—21no—
145C4×C149—41no—
146C4×C149—41no—
147C4×C149—41no—
148C4×C149C2×#4111yescharacteristic
149C4×C1492−1+411yescharacteristic
150Dic149—22no—
151Dic149—41no—
152Dic149—41no—
153Dic149—41no—
154C2×C149—81no—
155C2×C149#54811yescharacteristic
156C2×C149#57511yescharacteristic
157C2×C149#57811yescharacteristic
158C149#337711yescharacteristic, complemented, Sylow
159#3377—1491nomaximal, Sylow
160#557—1491no—
161#556D14911yescharacteristic
162#491—1491no—
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—21no—
182#126—21no—
183#125—2981no—
184#125—2981no—
185#125—1491no—
186#125—1491no—
187#124C2×D14911yescharacteristic
188#124C2×D14911yescharacteristic
189C22⋊Q8—21no—
190C4×Q8—2981no—
191C4×Q8—1491no—
192C4×Q8—1491no—
193C4×Q8—1491no—
194C4×Q8C2×D14911yescharacteristic
195C4×Q8C2×D14911yescharacteristic
196C4×Q8C2×D14911yescharacteristic
197C4×D4C2×D14911yescharacteristic
198#117—21no—
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#103—1491no—
209#103—1491no—
210#103—1491no—
211#103—1491no—
212#102—1491no—
213#102—1491no—
214#102—1491no—
215#97—1491no—
216#97—1491no—
217C4×C8—1491no—
218C2×Q8—2981no—
219C2×Q8—1491no—
220C2×Q8C22⋊D14911yescharacteristic
221C2×Q8C22×D14911yescharacteristic
222C2×Q8C22×D14911yescharacteristic
223C2×D4C22×D14911yescharacteristic
224C22×C4—21no—
225Q16—2982no—
226Q16—2982no—
227SD16—2982no—
228C2×C8—1491no—
229C2×C8—1491no—
230C2×C8—1491no—
231C2×C8—1491no—
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⋊C4C22⋊D14911yescharacteristic
248C4⋊C4C22⋊D14911yescharacteristic
249C4⋊C4C22⋊D14911yescharacteristic
250C4⋊C4C22×D14911yescharacteristic
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—21no—
255C22⋊C4—21no—
256C42—21no—
257C42—21no—
258C42—2981no—
259C42—2981no—
260C42—2981no—
261C42C22×D14911yescharacteristic
262C42C22×D14911yescharacteristic
263C42C22×D14911yescharacteristic
264C23—21no—
265Q8—21no—
266Q8—21no—
267Q8—21no—
268Q8—21no—
269Q8—41no—
270Q8—2981no—
271Q8—5962no—
272Q8—1492no—
273D4—21no—
274D4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—42no—
279C2×C4—2981no—
280C2×C4—2981no—
281C2×C4—2981no—
282C2×C4—2981no—
283C2×C4C2×C22⋊D14911yescharacteristic
284C2×C4C2×C22⋊D14911yescharacteristic
285C2×C4C2×C22⋊D14911yescharacteristic
286C2×C4C2×C22⋊D14911yescharacteristic
287C2×C4C2×C22⋊D14911yescharacteristic
288C2×C4C2×C22⋊D14911yescharacteristic
289C2×C4C23×D14911yescharacteristic
290C8—2981no—
291C8—2981no—
292C8—2981no—
293C8—2981no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22C22×C22⋊D14911yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—2982no—
308C4—5961no—
309C4—5961no—
310C4—5961no—
311C4#41×D14911yescharacteristic
312C4#1801195811yescharacteristic
313C2—81no—
314C2#2375028211yescharacteristic
315C2#2375042311yescharacteristic
316C2#2375044011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#556×C149C2
socleC22×C149C22×D4
prime radicalC2×D4×C149C23
hypercenter#556D149
hypocenterC149#3377
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
1. #23750353C2semidirect
2. #23749993C2semidirect
5. #23749932C2semidirect
7. #23749920C2semidirect
10. #23749832C2semidirect
11. #23749756C2semidirect
12. #23749730C2semidirect
14. C4×#14558726C2semidirect
158. C149#3377semidirect

Maximal subgroups

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

subgroupindex
#237503532
#237499932
#237499842
#237499792
#237499322
#237499252
#237499202
#237498442
#237498322
#237497562
#237497302
#237497252
C4×#145587262
#556×C1492
#3377149