Finite Group Databasebeta

← #34057602

Subgroups — #34057602

Order 19072.

340 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×Dic298C211yesmaximal, characteristic, complemented
2#23750334C211yesmaximal, characteristic
3#23750034C211yesmaximal, characteristic, complemented
4#23750033C211yesmaximal, characteristic, complemented
5#23750029C211yesmaximal, characteristic, complemented
6#23749932C211yesmaximal, characteristic, complemented
7#23749930C211yesmaximal, characteristic, complemented
8#23749918C211yesmaximal, characteristic, complemented
9#23749913C211yesmaximal, characteristic
10#23749905C211yesmaximal, characteristic
11#23749903C211yesmaximal, characteristic
12#23749753C211yesmaximal, characteristic, complemented
13#23749726C211yesmaximal, characteristic
14SD16×Dic149C211yesmaximal, characteristic
15#440×C149C211yesmaximal, characteristic
16#18011911—21no—
17#18011911C2211yescharacteristic
18#18011910—21no—
19#18011910—21no—
20#18011910C2211yescharacteristic
21#18011910C2211yescharacteristic
22#18011910C2211yescharacteristic
23#18011903C2211yescharacteristic
24#18011902C2211yescharacteristic
25#18011890—21no—
26#18011888—21no—
27#18011888—21no—
28Q8×Dic149C2211yescharacteristic
29Q8×Dic149C2211yescharacteristic
30C4×Dic298—21no—
31C4×Dic298C2211yescharacteristic
32D4×Dic149C2211yescharacteristic
33D4×Dic149C2211yescharacteristic
34C2×#14558715—21no—
35#18011845C2211yescharacteristic
36#18011845C2211yescharacteristic
37#18011844C2211yescharacteristic
38#18011844C2211yescharacteristic
39#18011844C2211yescharacteristic
40#18011843C2211yescharacteristic
41#18011843C2211yescharacteristic
42#18011842C2211yescharacteristic
43C4⋊#11924746C2211yescharacteristic
44#18011840C2211yescharacteristic
45#18011840C2211yescharacteristic
46#18011835C2211yescharacteristic
47#18011835C2211yescharacteristic
48#18011832C2211yescharacteristic
49#18011832C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×SD16×C149C2211yescharacteristic
53C4×Q8×C149C2211yescharacteristic
54C4×D4×C149C2211yescharacteristic
55#107×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#97×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298—21no—
61C2×Dic298—21no—
62C2×Dic298—21no—
63C2×Dic298D411yescharacteristic
64C22×Dic149—21no—
65C22×Dic149—21no—
66C2×#11924746C2311yescharacteristic
67C2×#11924746C2311yescharacteristic
68C4⋊Dic149—21no—
69C4⋊Dic149—21no—
70C4⋊Dic149—21no—
71C4⋊Dic149—21no—
72C4⋊Dic149D411yescharacteristic
73C4⋊Dic149C2311yescharacteristic
74C4⋊Dic149C2311yescharacteristic
75C4⋊Dic149C2311yescharacteristic
76C4⋊Dic149C2311yescharacteristic
77#14558715—21no—
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715—21no—
82#14558715—21no—
83#14558715D411yescharacteristic
84#14558715D411yescharacteristic
85C22⋊Dic149—21no—
86C22⋊Dic149—21no—
87C4×Dic149—21no—
88C4×Dic149—21no—
89C4×Dic149C2311yescharacteristic
90C4×Dic149C2311yescharacteristic
91C2×Q8×C149C2311yescharacteristic
92C2×D4×C149C2311yescharacteristic
93C22×C4×C149—21no—
94SD16×C149Q814yescomplemented
95C2×C8×C149C2311yescharacteristic
96C2×C8×C149C2311yescharacteristic
97C4⋊C4×C149—21no—
98C4⋊C4×C149C2311yescharacteristic
99C4⋊C4×C149C2311yescharacteristic
100C22⋊C4×C149—21no—
101C42×C149—21no—
102C42×C149C2311yescharacteristic
103Dic298—22no—
104Dic298—81no—
105Dic298—81no—
106Dic298—81no—
107Dic298—81no—
108C2×Dic149—21no—
109C2×Dic149—21no—
110C2×Dic149—21no—
111C2×Dic149—21no—
112C2×Dic149—42no—
113C2×Dic149—81no—
114C2×Dic149C2×D411yescharacteristic
115C2×Dic149C2×D411yescharacteristic
116C2×Dic149C2×D411yescharacteristic
117C2×Dic149C2×D411yescharacteristic
118#11924746—21no—
119#11924746—21no—
120C23×C149—21no—
121Q8×C149—21no—
122Q8×C149C2×Q812yes—
123D4×C149—21no—
124D4×C149C2×Q812yes—
125C2×C4×C149—21no—
126C2×C4×C149—21no—
127C2×C4×C149—21no—
128C2×C4×C149—81no—
129C2×C4×C149C2×D411yescharacteristic
130C2×C4×C149C2×D411yescharacteristic
131C2×C4×C149C2411yescharacteristic
132C8×C149—21no—
133C8×C149C2×Q812yes—
134C22×C149—22no—
135C22×C149—41no—
136C22×C149—41no—
137C22×C149C22×D411yescharacteristic
138C4×C149—22no—
139C4×C149—21no—
140C4×C149—21no—
141C4×C149—41no—
142C4×C149—41no—
143C4×C149C22×Q811yescharacteristic
144C4×C1492−1+411yescharacteristic
145Dic149—21no—
146Dic149—21no—
147Dic149—21no—
148Dic149—41no—
149Dic149—41no—
150Dic149—41no—
151Dic149—41no—
152Dic149#13712yes—
153C2×C149—42no—
154C2×C149D4×Q811yescharacteristic
155C2×C149C2×#13711yescharacteristic
156C2×C149#57611yescharacteristic
157C149#338511yescharacteristic, complemented, Sylow
158#3385—1491nomaximal, Sylow
159Q82—1491no—
160#554—1491no—
161#501—1491no—
162#501—1491no—
163#500—1491no—
164#479—1491no—
165#479—1491no—
166#477—1491no—
167#476—1491no—
168#474—1491no—
169#474—1491no—
170#446—1491no—
171#440—1491no—
172#440D14911yescharacteristic
173C4×SD16—1491no—
174C2×SD16C2×D14911yescharacteristic
175C4⋊Q8—2981no—
176C4⋊Q8—2981no—
177C4⋊Q8—2981no—
178C4⋊Q8—1491no—
179C4⋊Q8—1491no—
180C4⋊Q8—1491no—
181C4⋊Q8—1491no—
182#125—1491no—
183#125—1491no—
184C22⋊Q8—2981no—
185C22⋊Q8—2981no—
186C22⋊Q8—2981no—
187C4×Q8—2981no—
188C4×Q8—1491no—
189C4×Q8—1491no—
190C4×Q8—1491no—
191C4×Q8C2×D14911yescharacteristic
192C4×D4—1491no—
193C4×D4—1491no—
194C4×D4C2×D14911yescharacteristic
195C2×C4⋊C4—2981no—
196#107—1491no—
197#107—1491no—
198#107—1491no—
199#107—1491no—
200#107—1491no—
201#107C2×D14911yescharacteristic
202#106—1491no—
203#106—1491no—
204#106—1491no—
205C4⋊C8—1491no—
206C4⋊C8—1491no—
207C4⋊C8—1491no—
208#103—1491no—
209#103—1491no—
210#103C2×D14911yescharacteristic
211#102—1491no—
212#102—1491no—
213#102C2×D14911yescharacteristic
214#97—1491no—
215#97C2×D14911yescharacteristic
216C4×C8—1491no—
217C2×Q8—2981no—
218C2×Q8—2981no—
219C2×Q8—2981no—
220C2×Q8—2981no—
221C2×Q8—1491no—
222C2×Q8C22×D14911yescharacteristic
223C2×D4C22×D14911yescharacteristic
224C22×C4—21no—
225C22×C4—2981no—
226C22×C4—2981no—
227SD16Dic29814yescomplemented
228C2×C8—1491no—
229C2×C8—1491no—
230C2×C8C22×D14911yescharacteristic
231C2×C8C22×D14911yescharacteristic
232C4⋊C4—21no—
233C4⋊C4—2981no—
234C4⋊C4—2981no—
235C4⋊C4—2981no—
236C4⋊C4—2981no—
237C4⋊C4—2981no—
238C4⋊C4—2981no—
239C4⋊C4—2981no—
240C4⋊C4—2981no—
241C4⋊C4—2981no—
242C4⋊C4—2981no—
243C4⋊C4—1491no—
244C4⋊C4—1491no—
245C4⋊C4—1491no—
246C4⋊C4—1491no—
247C4⋊C4—1491no—
248C4⋊C4—1491no—
249C4⋊C4—1491no—
250C4⋊C4C22×D14911yescharacteristic
251C4⋊C4C22×D14911yescharacteristic
252C22⋊C4—21no—
253C22⋊C4—2981no—
254C22⋊C4—2981no—
255C42—21no—
256C42—2981no—
257C42—2981no—
258C42—1491no—
259C42—1491no—
260C42C22×D14911yescharacteristic
261C23—21no—
262Q8—21no—
263Q8—2982no—
264Q8—11921no—
265Q8—11921no—
266Q8—11921no—
267Q8—11921no—
268Q8C2×Dic29812yes—
269D4—21no—
270D4C2×Dic29812yes—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—81no—
275C2×C4—2981no—
276C2×C4—2981no—
277C2×C4—2981no—
278C2×C4—2981no—
279C2×C4—5962no—
280C2×C4—1491no—
281C2×C4—1491no—
282C2×C4—1491no—
283C2×C4—1491no—
284C2×C4—11921no—
285C2×C4D4×D14911yescharacteristic
286C2×C4D4×D14911yescharacteristic
287C2×C4C23×D14911yescharacteristic
288C8—21no—
289C8—2981no—
290C8—2981no—
291C8C2×Dic29812yes—
292C22—22no—
293C22—41no—
294C22—41no—
295C22C2×D4×D14911yescharacteristic
296C4—21no—
297C4—21no—
298C4—22no—
299C4—41no—
300C4—41no—
301C4—2981no—
302C4—2981no—
303C4—2981no—
304C4—5961no—
305C4—5961no—
306C4—5961no—
307C4—5961no—
308C4—1492no—
309C4C22×Dic29811yescharacteristic
310C4#1801195811yescharacteristic
311C2—42no—
312C2D4×Dic29811yescharacteristic
313C2#137×D14911yescharacteristic
314C2#2375042911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#440×C149C2
socleC22×C149C22×D4
prime radicalC2×D4×C149C23
hypercenter#440D149
hypocenterC149#3385
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. Q8×Dic298C2semidirect
3. #23750034C2semidirect
4. #23750033C2semidirect
5. #23750029C2semidirect
6. #23749932C2semidirect
7. #23749930C2semidirect
8. #23749918C2semidirect
12. #23749753C2semidirect
94. SD16×C149Q8semidirect
157. C149#3385semidirect
227. SD16Dic298semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic2982
#237503342
#237500342
#237500332
#237500292
#237499322
#237499302
#237499182
#237499132
#237499052
#237499032
#237497532
#237497262
SD16×Dic1492
#440×C1492
#3385149