Finite Group Databasebeta

← #34057432

Subgroups — #34057432

Order 19072.

338 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×Dic298C211yesmaximal, characteristic, complemented
2#23750347C211yesmaximal, characteristic
3#23749986C211yesmaximal, characteristic
4#23749985C211yesmaximal, characteristic
5#23749974C211yesmaximal, characteristic, complemented
6#23749914C211yesmaximal, characteristic
7#23749910C211yesmaximal, characteristic, complemented
8#23749909C211yesmaximal, characteristic, complemented
9#23749849C211yesmaximal, characteristic
10#23749847C211yesmaximal, characteristic
11#23749833C211yesmaximal, characteristic, complemented
12#23749753C211yesmaximal, characteristic, complemented
13#23749729C211yesmaximal, characteristic, complemented
14#23749710C211yesmaximal, characteristic
15#441×C149C211yesmaximal, characteristic, complemented
16C2×#14558726C2211yescharacteristic
17C2×#14558723C2211yescharacteristic
18#18011911—21no—
19#18011911C2211yescharacteristic
20#18011910—21no—
21#18011910—21no—
22#18011910C2211yescharacteristic
23#18011910C2211yescharacteristic
24#18011909C2211yescharacteristic
25#18011906—21no—
26#18011905—21no—
27#18011900C2211yescharacteristic
28#18011899C2211yescharacteristic
29#18011889—21no—
30Q8×Dic149C2211yescharacteristic
31Q8×Dic149C2211yescharacteristic
32C4×Dic298—21no—
33C4×Dic298C2211yescharacteristic
34#18011876C2211yescharacteristic
35#18011873C2211yescharacteristic
36#18011868—21no—
37#18011842C2211yescharacteristic
38#18011842C2211yescharacteristic
39C4⋊#11924746C2211yescharacteristic
40#18011840C2211yescharacteristic
41#18011840C2211yescharacteristic
42#18011836C2211yescharacteristic
43#18011836C2211yescharacteristic
44#18011835C2211yescharacteristic
45#18011835C2211yescharacteristic
46#18011834C2211yescharacteristic
47#18011833C2211yescharacteristic
48#18011833C2211yescharacteristic
49#18011831C2211yescharacteristic
50#18011821C2211yescharacteristic
51C8×Dic149C2211yescharacteristic
52C2×Q16×C149C2211yescharacteristic
53C4×Q8×C149C2211yescharacteristic
54C4×Q8×C149C2211yescharacteristic
55#106×C149C2211yescharacteristic
56#103×C149C2211yescharacteristic
57#103×C149C2211yescharacteristic
58#97×C149C2211yescharacteristic
59C2×Dic298—21no—
60C2×Dic298—21no—
61C2×Dic298—21no—
62C2×Dic298D411yescharacteristic
63C2×Dic298C2311yescharacteristic
64C2×D596C2311yescharacteristic
65C2×C4×D149—21no—
66#14558726—22no—
67#14558723—22no—
68C2×#11924746C2311yescharacteristic
69C2×#11924746C2311yescharacteristic
70C4⋊Dic149—21no—
71C4⋊Dic149—21no—
72C4⋊Dic149—21no—
73C4⋊Dic149D411yescharacteristic
74C4⋊Dic149C2311yescharacteristic
75C4⋊Dic149C2311yescharacteristic
76#14558715—21no—
77#14558715—21no—
78#14558715—21no—
79#14558715—21no—
80#14558715—21no—
81#14558715D411yescharacteristic
82#14558715D411yescharacteristic
83#14558713—21no—
84#14558713—21no—
85#14558713—21no—
86#14558713—21no—
87#14558713—21no—
88C4×Dic149—21no—
89C4×Dic149—21no—
90C4×Dic149—21no—
91C4×Dic149C2311yescharacteristic
92C4×Dic149C2311yescharacteristic
93C2×Q8×C149C2311yescharacteristic
94C2×Q8×C149C2311yescharacteristic
95Q16×C149—22no—
96C2×C8×C149C2311yescharacteristic
97C2×C8×C149C2311yescharacteristic
98C4⋊C4×C149—21no—
99C4⋊C4×C149—21no—
100C4⋊C4×C149C2311yescharacteristic
101C4⋊C4×C149C2311yescharacteristic
102C42×C149—21no—
103C42×C149—21no—
104C42×C149C2311yescharacteristic
105C22×D149—21no—
106Dic298—22no—
107Dic298—21no—
108Dic298—21no—
109Dic298—81no—
110Dic298—81no—
111Dic298—81no—
112D596—21no—
113D596—21no—
114C2×Dic149—21no—
115C2×Dic149—21no—
116C2×Dic149—21no—
117C2×Dic149C2×D411yescharacteristic
118C2×Dic149C2×D411yescharacteristic
119C2×Dic149C2×D411yescharacteristic
120C2×Dic149C2×D411yescharacteristic
121C4×D149—42no—
122#11924746—21no—
123#11924746—21no—
124Q8×C149—21no—
125Q8×C149—21no—
126Q8×C149—21no—
127Q8×C149#4112yes—
128C2×C4×C149—21no—
129C2×C4×C149—21no—
130C2×C4×C149—21no—
131C2×C4×C149—21no—
132C2×C4×C149C2×D411yescharacteristic
133C2×C4×C149C2×D411yescharacteristic
134C2×C4×C149C2411yescharacteristic
135C8×C149—21no—
136C8×C149—21no—
137C22×C149C22×D411yescharacteristic
138C2×D149—41no—
139C2×D149—41no—
140C2×D149—41no—
141C4×C149—22no—
142C4×C149—21no—
143C4×C149—21no—
144C4×C149—41no—
145C4×C149—41no—
146C4×C149—41no—
147C4×C149C2×#4111yescharacteristic
148C4×C1492−1+411yescharacteristic
149Dic149—21no—
150Dic149—21no—
151Dic149—21no—
152Dic149—41no—
153Dic149—41no—
154Dic149—41no—
155Dic149#13712yes—
156C2×C149#54811yescharacteristic
157C2×C149C2×#13711yescharacteristic
158C2×C149#57711yescharacteristic
159D149—81no—
160C149#336911yescharacteristic, complemented, Sylow
161#3369—1491nomaximal, Sylow
162Q82—1491no—
163#556—1491no—
164#489—1491no—
165#489—1491no—
166#487—1491no—
167#476—1491no—
168#475—1491no—
169#475—1491no—
170#464—1491no—
171#464—1491no—
172#462—1491no—
173#446—1491no—
174#441—1491no—
175#441D14911yescharacteristic, complemented
176C4×SD16—1491no—
177C2×Q16—1491no—
178C2×Q16C2×D14911yescharacteristic
179C2×SD16—1491no—
180C4⋊Q8—2981no—
181C4⋊Q8—2981no—
182C4⋊Q8—2981no—
183C4⋊Q8—1491no—
184C4⋊Q8—1491no—
185C4⋊Q8—1491no—
186C4⋊Q8—1491no—
187#126—2981no—
188#126—2981no—
189#124—1491no—
190#124—1491no—
191C22⋊Q8—2981no—
192C4×Q8—2981no—
193C4×Q8—1491no—
194C4×Q8—1491no—
195C4×Q8—1491no—
196C4×Q8—1491no—
197C4×Q8C2×D14911yescharacteristic
198C4×Q8C2×D14911yescharacteristic
199C4×D4—1491no—
200#117—2981no—
201#106—1491no—
202#106—1491no—
203#106C2×D14911yescharacteristic
204C4⋊C8—1491no—
205C4⋊C8—1491no—
206C4⋊C8—1491no—
207#103—1491no—
208#103—1491no—
209#103—1491no—
210#103—1491no—
211#103—1491no—
212#103C2×D14911yescharacteristic
213#103C2×D14911yescharacteristic
214#102—1491no—
215#102—1491no—
216#102—1491no—
217#97—1491no—
218#97C2×D14911yescharacteristic
219C4×C8—1491no—
220C2×Q8—2981no—
221C2×Q8—2981no—
222C2×Q8—2981no—
223C2×Q8—1491no—
224C2×Q8—1491no—
225C2×Q8C22×D14911yescharacteristic
226C2×Q8C22×D14911yescharacteristic
227C2×D4—1491no—
228C22×C4—2981no—
229Q16—22no—
230Q16—2982no—
231SD16—2982no—
232C2×C8—1491no—
233C2×C8—1491no—
234C2×C8C22×D14911yescharacteristic
235C2×C8C22×D14911yescharacteristic
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—2981no—
239C4⋊C4—2981no—
240C4⋊C4—2981no—
241C4⋊C4—2981no—
242C4⋊C4—2981no—
243C4⋊C4—2981no—
244C4⋊C4—2981no—
245C4⋊C4—2981no—
246C4⋊C4—1491no—
247C4⋊C4—1491no—
248C4⋊C4—1491no—
249C4⋊C4—1491no—
250C4⋊C4—1491no—
251C4⋊C4C22×D14911yescharacteristic
252C4⋊C4C22×D14911yescharacteristic
253C22⋊C4—2981no—
254C22⋊C4—2981no—
255C22⋊C4—2981no—
256C22⋊C4—2981no—
257C22⋊C4—2981no—
258C42—21no—
259C42—21no—
260C42—2981no—
261C42—2981no—
262C42—2981no—
263C42—1491no—
264C42—1491no—
265C42C22×D14911yescharacteristic
266C23—2981no—
267Q8—21no—
268Q8—21no—
269Q8—21no—
270Q8—2982no—
271Q8—2981no—
272Q8—2981no—
273Q8—11921no—
274Q8—11921no—
275Q8—11921no—
276Q8#1455873612yes—
277D4—2981no—
278D4—2981no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—2981no—
284C2×C4—2981no—
285C2×C4—2981no—
286C2×C4—5962no—
287C2×C4—1491no—
288C2×C4—1491no—
289C2×C4—1491no—
290C2×C4—1491no—
291C2×C4D4×D14911yescharacteristic
292C2×C4D4×D14911yescharacteristic
293C2×C4C23×D14911yescharacteristic
294C8—21no—
295C8—21no—
296C8—2981no—
297C8—2981no—
298C22—5961no—
299C22—5961no—
300C22—5961no—
301C22C2×D4×D14911yescharacteristic
302C4—21no—
303C4—21no—
304C4—22no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—2981no—
309C4—2981no—
310C4—2981no—
311C4—5961no—
312C4—5961no—
313C4—5961no—
314C4—1492no—
315C4C2×#1455873611yescharacteristic
316C4#1801195811yescharacteristic
317C2—11921no—
318C2#2375028411yescharacteristic
319C2#137×D14911yescharacteristic
320C2#2375043411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#441×C149C2
socleC22×C149C22×D4
prime radicalC2×D596C23
hypercenter#441D149
hypocenterC149#3369
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. Q8×Dic298C2semidirect
5. #23749974C2semidirect
7. #23749910C2semidirect
8. #23749909C2semidirect
11. #23749833C2semidirect
12. #23749753C2semidirect
13. #23749729C2semidirect
15. #441×C149C2semidirect
160. C149#3369semidirect
175. #441D149semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic2982
#237503472
#237499862
#237499852
#237499742
#237499142
#237499102
#237499092
#237498492
#237498472
#237498332
#237497532
#237497292
#237497102
#441×C1492
#3369149