Finite Group Databasebeta

← #34057596

Subgroups — #34057596

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
1#23750355C211yesmaximal, characteristic, complemented
2#23750334C211yesmaximal, characteristic
3#23750033C211yesmaximal, characteristic, complemented
4#23750031C211yesmaximal, characteristic, complemented
5#23750029C211yesmaximal, characteristic, complemented
6#23749933C211yesmaximal, characteristic, complemented
7#23749931C211yesmaximal, characteristic, complemented
8#23749919C211yesmaximal, characteristic, complemented
9#23749913C211yesmaximal, characteristic
10#23749903C211yesmaximal, characteristic
11#23749754C211yesmaximal, characteristic, complemented
12#23749725C211yesmaximal, characteristic
13#23749722C211yesmaximal, characteristic
14#23749716C211yesmaximal, characteristic
15#474×C149C211yesmaximal, characteristic
16C2×#14558724C2211yescharacteristic
17#18011910—21no—
18#18011910C2211yescharacteristic
19#18011910C2211yescharacteristic
20#18011910C2211yescharacteristic
21#18011909—21no—
22#18011909—21no—
23#18011903C2211yescharacteristic
24#18011902C2211yescharacteristic
25#18011890—21no—
26#18011888—21no—
27#18011888—21no—
28C4×Dic298C2211yescharacteristic
29C4×Dic298C2211yescharacteristic
30#18011876—21no—
31#18011876C2211yescharacteristic
32#18011876C2211yescharacteristic
33D4×Dic149C2211yescharacteristic
34D4×Dic149C2211yescharacteristic
35C2×#14558715—21no—
36#18011845C2211yescharacteristic
37#18011844C2211yescharacteristic
38#18011844C2211yescharacteristic
39#18011844C2211yescharacteristic
40#18011843C2211yescharacteristic
41#18011842C2211yescharacteristic
42#18011842C2211yescharacteristic
43#18011840C2211yescharacteristic
44#18011840C2211yescharacteristic
45#18011836C2211yescharacteristic
46#18011836C2211yescharacteristic
47#18011834C2211yescharacteristic
48#18011832C2211yescharacteristic
49#18011822C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C4⋊Q8×C149C2211yescharacteristic
53C4×D4×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic
55#107×C149C2211yescharacteristic
56C4⋊C8×C149C2211yescharacteristic
57#102×C149C2211yescharacteristic
58#102×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298—21no—
61C2×Dic298—21no—
62C2×Dic298D411yescharacteristic
63C2×Dic298C2311yescharacteristic
64C22×Dic149—21no—
65C22×Dic149—21no—
66#14558724Q814yescomplemented
67C2×#11924746C2311yescharacteristic
68C2×#11924746C2311yescharacteristic
69C4⋊Dic149—21no—
70C4⋊Dic149D411yescharacteristic
71C4⋊Dic149C2311yescharacteristic
72C4⋊Dic149C2311yescharacteristic
73C4⋊Dic149C2311yescharacteristic
74#14558715—21no—
75#14558715—21no—
76#14558715—21no—
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×Dic149—21no—
90C4×Dic149C2311yescharacteristic
91C4×Dic149C2311yescharacteristic
92C2×Q8×C149—21no—
93C2×D4×C149C2311yescharacteristic
94C22×C4×C149—21no—
95C2×C8×C149C2311yescharacteristic
96C2×C8×C149C2311yescharacteristic
97C4⋊C4×C149—21no—
98C4⋊C4×C149C2311yescharacteristic
99C4⋊C4×C149C2311yescharacteristic
100C4⋊C4×C149C2311yescharacteristic
101C22⋊C4×C149—21no—
102C42×C149C2311yescharacteristic
103Dic298—21no—
104Dic298—22no—
105Dic298—81no—
106Dic298—81no—
107Dic298—81no—
108Dic298C2×Q812yes—
109C2×Dic149—21no—
110C2×Dic149—21no—
111C2×Dic149—21no—
112C2×Dic149—21no—
113C2×Dic149—42no—
114C2×Dic149—81no—
115C2×Dic149C2×D411yescharacteristic
116C2×Dic149C2×D411yescharacteristic
117C2×Dic149C2×D411yescharacteristic
118C2×Dic149C2×D411yescharacteristic
119#11924746—21no—
120#11924746C2×Q812yes—
121C23×C149—21no—
122Q8×C149—81no—
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×C149—21no—
134C22×C149—22no—
135C22×C149—41no—
136C22×C149—41no—
137C22×C149C22×D411yescharacteristic
138C4×C149—21no—
139C4×C149—21no—
140C4×C149—41no—
141C4×C149—41no—
142C4×C149—41no—
143C4×C149C22×Q811yescharacteristic
144C4×C1492−1+411yescharacteristic
145Dic149—22no—
146Dic149—21no—
147Dic149—21no—
148Dic149—21no—
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#474D14911yescharacteristic
170#446—1491no—
171#440—1491no—
172#440—1491no—
173C4×SD16—1491no—
174C2×SD16—1491no—
175C4⋊Q8—2981no—
176C4⋊Q8—2981no—
177C4⋊Q8—2981no—
178C4⋊Q8—1491no—
179C4⋊Q8—1491no—
180C4⋊Q8—1491no—
181C4⋊Q8C2×D14911yescharacteristic
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×Q8—1491no—
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#107C2×D14911yescharacteristic
201#107C2×D14911yescharacteristic
202#106—1491no—
203#106—1491no—
204#106—1491no—
205C4⋊C8—1491no—
206C4⋊C8—1491no—
207C4⋊C8C2×D14911yescharacteristic
208#103—1491no—
209#103—1491no—
210#103—1491no—
211#102—1491no—
212#102C2×D14911yescharacteristic
213#102C2×D14911yescharacteristic
214#97—1491no—
215#97—1491no—
216C4×C8—1491no—
217C2×Q8—21no—
218C2×Q8—2981no—
219C2×Q8—2981no—
220C2×Q8—2981no—
221C2×Q8—1491no—
222C2×Q8—1491no—
223C2×D4C22×D14911yescharacteristic
224C22×C4—21no—
225C22×C4—2981no—
226C22×C4—2981no—
227SD16—1494no—
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⋊C4C22×D14911yescharacteristic
250C4⋊C4C22×D14911yescharacteristic
251C4⋊C4C22×D14911yescharacteristic
252C22⋊C4—21no—
253C22⋊C4—2981no—
254C22⋊C4—2981no—
255C42—2981no—
256C42—2981no—
257C42—2981no—
258C42—1491no—
259C42—1491no—
260C42C22×D14911yescharacteristic
261C23—21no—
262Q8—81no—
263Q8—2982no—
264Q8—2981no—
265Q8—1492no—
266Q8—11921no—
267Q8—11921no—
268Q8—11921no—
269D4—21no—
270D4Q8×D14912yes—
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—21no—
290C8—2981no—
291C8—1492no—
292C22—22no—
293C22—41no—
294C22—41no—
295C22C2×D4×D14911yescharacteristic
296C4—21no—
297C4—21no—
298C4—41no—
299C4—41no—
300C4—41no—
301C4—2981no—
302C4—2981no—
303C4—2981no—
304C4—2982no—
305C4—5961no—
306C4—5961no—
307C4—5961no—
308C4—1492no—
309C4C2×Q8×D14911yescharacteristic
310C4#1801195811yescharacteristic
311C2—42no—
312C2#2375028811yescharacteristic
313C2#137×D14911yescharacteristic
314C2#2375042611yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#474×C149C2
socleC22×C149C22×D4
prime radicalC2×D4×C149C23
hypercenter#474D149
hypocenterC149#3385
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #23750355C2semidirect
3. #23750033C2semidirect
4. #23750031C2semidirect
5. #23750029C2semidirect
6. #23749933C2semidirect
7. #23749931C2semidirect
8. #23749919C2semidirect
11. #23749754C2semidirect
66. #14558724Q8semidirect
157. C149#3385semidirect

Maximal subgroups

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

subgroupindex
#237503552
#237503342
#237500332
#237500312
#237500292
#237499332
#237499312
#237499192
#237499132
#237499032
#237497542
#237497252
#237497222
#237497162
#474×C1492
#3385149