Finite Group Databasebeta

← #34047248

Subgroups — #34047248

Order 19072.

484 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18011901C211yesmaximal, characteristic
2#23749522C211yesmaximal, characteristic
3#23749520C211yesmaximal, characteristic
4#23749512C211yesmaximal, characteristic
5#23749509C211yesmaximal, characteristic
6#23749508C211yesmaximal, characteristic
7#23749489C211yesmaximal, characteristic
8C4⋊C4×Dic149C211yesmaximal, characteristic
9C4⋊C4×Dic149C211yesmaximal, characteristic
10#23749476C211yesmaximal, characteristic
11#23749476C211yesmaximal, characteristic
12#23749476C211yesmaximal, characteristic
13#23749476C211yesmaximal, characteristic
14C42×Dic149C211yesmaximal, characteristic
15#387×C149C211yesmaximal, characteristic
16#18011901C418yescomplemented
17C2×C4⋊Dic149C2211yescharacteristic
18C2×C4⋊Dic149C2211yescharacteristic
19C2×#14558715C2211yescharacteristic
20C2×#14558715C2211yescharacteristic
21C2×#14558715C2211yescharacteristic
22C2×#14558715C2211yescharacteristic
23C2×#14558715C2211yescharacteristic
24C2×#14558715C2211yescharacteristic
25C2×#14558715C2211yescharacteristic
26C2×#14558715C2211yescharacteristic
27C2×C4×Dic149C2211yescharacteristic
28C2×C4×Dic149C2211yescharacteristic
29C2×C4×Dic149C2211yescharacteristic
30C2×C4×Dic149C2211yescharacteristic
31C2×C4×Dic149C2211yescharacteristic
32C2×C4×Dic149C2211yescharacteristic
33C2×C4×Dic149C2211yescharacteristic
34C2×C4×Dic149C2211yescharacteristic
35C2×C4×Dic149C2211yescharacteristic
36C2×C4×Dic149C2211yescharacteristic
37#18011818C2211yescharacteristic
38#18011818C2211yescharacteristic
39#18011818C2211yescharacteristic
40#18011818C2211yescharacteristic
41#18011818C2211yescharacteristic
42#18011818C2211yescharacteristic
43#18011818C2211yescharacteristic
44#18011818C2211yescharacteristic
45C2×C4⋊C4×C149C2211yescharacteristic
46C2×C4⋊C4×C149C2211yescharacteristic
47C2×C42×C149C2211yescharacteristic
48#95×C149C2211yescharacteristic
49#95×C149C2211yescharacteristic
50#95×C149C2211yescharacteristic
51#95×C149C2211yescharacteristic
52C22×Dic149C2311yescharacteristic
53C22×Dic149C2311yescharacteristic
54C22×Dic149C2311yescharacteristic
55C22×Dic149C2311yescharacteristic
56C22×Dic149C2311yescharacteristic
57C22×Dic149C2311yescharacteristic
58C22×Dic149C2311yescharacteristic
59C22×Dic149C2311yescharacteristic
60C4⋊Dic149—22no—
61C4⋊Dic149C2×C414yes—
62#14558715—22no—
63#14558715—22no—
64#14558715—22no—
65#14558715—22no—
66#14558715C2×C414yes—
67#14558715C2×C414yes—
68#14558715C2×C414yes—
69#14558715C2×C414yes—
70C4×Dic149—22no—
71C4×Dic149—22no—
72C4×Dic149—22no—
73C4×Dic149—22no—
74C4×Dic149—22no—
75C4×Dic149—22no—
76C4×Dic149—22no—
77C4×Dic149—22no—
78C4×Dic149C2×C414yes—
79C4×Dic149Q814yes—
80C22×C4×C149C2311yescharacteristic
81C22×C4×C149C2311yescharacteristic
82C22×C4×C149C2311yescharacteristic
83C22×C4×C149C2311yescharacteristic
84C22×C4×C149C2311yescharacteristic
85C22×C4×C149C2311yescharacteristic
86C22×C4×C149C2311yescharacteristic
87C4⋊C4×C149—22no—
88C4⋊C4×C149C2×C414yes—
89C42×C149—22no—
90C2×Dic149—21no—
91C2×Dic149—21no—
92C2×Dic149—21no—
93C2×Dic149—21no—
94C2×Dic149—21no—
95C2×Dic149—21no—
96C2×Dic149—21no—
97C2×Dic149—21no—
98C2×Dic149—21no—
99C2×Dic149—21no—
100C2×Dic149—21no—
101C2×Dic149—21no—
102C2×Dic149—21no—
103C2×Dic149—21no—
104C2×Dic149C22×C412yes—
105C2×Dic149C22×C412yes—
106C2×Dic149C22×C412yes—
107C2×Dic149C22×C412yes—
108C2×Dic149C2×Q812yes—
109C2×Dic149C2×Q812yes—
110C2×Dic149#4112yes—
111C2×Dic149#4112yes—
112C2×Dic149#4112yes—
113C2×Dic149#4112yes—
114C23×C149C2411yescharacteristic
115C2×C4×C149—21no—
116C2×C4×C149—21no—
117C2×C4×C149—21no—
118C2×C4×C149—21no—
119C2×C4×C149—21no—
120C2×C4×C149—21no—
121C2×C4×C149—21no—
122C2×C4×C149—21no—
123C2×C4×C149—21no—
124C2×C4×C149—21no—
125C2×C4×C149—21no—
126C2×C4×C149—21no—
127C2×C4×C149—21no—
128C2×C4×C149—21no—
129C2×C4×C149—21no—
130C2×C4×C149—21no—
131C2×C4×C149C22×C412yes—
132C2×C4×C149C22×C412yes—
133C2×C4×C149C22×C412yes—
134C2×C4×C149C2×Q812yes—
135C2×C4×C149#4112yes—
136C22×C149C23×C411yescharacteristic
137C22×C149C22×Q811yescharacteristic
138C22×C149C2×#4111yescharacteristic
139C22×C149C2×#4111yescharacteristic
140C22×C149C2×#4111yescharacteristic
141C22×C149C2×#4111yescharacteristic
142C22×C149C2×#4111yescharacteristic
143C4×C149—22no—
144C4×C149—22no—
145C4×C149—22no—
146C4×C149—22no—
147C4×C149—22no—
148C4×C149—41no—
149C4×C149—41no—
150Dic149—22no—
151Dic149—22no—
152Dic149—22no—
153Dic149—22no—
154Dic149—41no—
155Dic149—41no—
156Dic149C4×Q814yes—
157Dic149#12514yescomplemented
158C2×C149C2×C4×Q811yescharacteristic
159C2×C149C4×#4111yescharacteristic
160C2×C149C4×#4111yescharacteristic
161C2×C149C2×#12511yescharacteristic
162C2×C149#52911yescharacteristic
163C2×C149#52911yescharacteristic
164C2×C149#53311yescharacteristic
165C149C4×#12511yescharacteristic, complemented, Sylow
166C4×#125—1491nomaximal, Sylow
167C2×#125—1491no—
168#389—1491no—
169#389—1491no—
170#387—1491no—
171#387—1491no—
172#387—1491no—
173#387D14911yescharacteristic
174#382—1491no—
175C4×C4⋊C4—1491no—
176C4×C4⋊C4—1491no—
177C4×C4⋊C4—1491no—
178C4×C4⋊C4—1491no—
179C4×C4⋊C4—1491no—
180C4×C4⋊C4—1491no—
181C43—1491no—
182#125—1498no—
183C2×C4⋊C4—1491no—
184C2×C4⋊C4—1491no—
185C2×C4⋊C4—1491no—
186C2×C4⋊C4—1491no—
187C2×C4⋊C4—1491no—
188C2×C4⋊C4—1491no—
189C2×C4⋊C4—1491no—
190C2×C4⋊C4—1491no—
191C2×C4⋊C4—1491no—
192C2×C4⋊C4—1491no—
193C2×C4⋊C4C2×D14911yescharacteristic
194C2×C4⋊C4C2×D14911yescharacteristic
195C2×C42—1491no—
196C2×C42—1491no—
197C2×C42—1491no—
198C2×C42—1491no—
199C2×C42—1491no—
200C2×C42—1491no—
201C2×C42—1491no—
202C2×C42—1491no—
203C2×C42—1491no—
204C2×C42—1491no—
205C2×C42C2×D14911yescharacteristic
206#95—1491no—
207#95—1491no—
208#95—1491no—
209#95—1491no—
210#95—1491no—
211#95—1491no—
212#95—1491no—
213#95—1491no—
214#95C2×D14911yescharacteristic
215#95C2×D14911yescharacteristic
216#95C2×D14911yescharacteristic
217#95C2×D14911yescharacteristic
218C22×C4—1491no—
219C22×C4—1491no—
220C22×C4—1491no—
221C22×C4—1491no—
222C22×C4—1491no—
223C22×C4—1491no—
224C22×C4—1491no—
225C22×C4—1491no—
226C22×C4C22×D14911yescharacteristic
227C22×C4C22×D14911yescharacteristic
228C22×C4C22×D14911yescharacteristic
229C22×C4C22×D14911yescharacteristic
230C22×C4C22×D14911yescharacteristic
231C22×C4C22×D14911yescharacteristic
232C22×C4C22×D14911yescharacteristic
233C4⋊C4—22no—
234C4⋊C4—2982no—
235C4⋊C4—2982no—
236C4⋊C4—2982no—
237C4⋊C4—2982no—
238C4⋊C4—2982no—
239C4⋊C4—1494no—
240C4⋊C4—1494no—
241C4⋊C4—1494no—
242C4⋊C4—1494no—
243C4⋊C4—1494no—
244C4⋊C4C4×D14914yes—
245C42—22no—
246C42—2982no—
247C42—2982no—
248C42—2982no—
249C42—2982no—
250C42—2982no—
251C42—2982no—
252C42—2982no—
253C42—2982no—
254C42—1494no—
255C42—1494no—
256C23C23×D14911yescharacteristic
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—2981no—
274C2×C4—2981no—
275C2×C4—2981no—
276C2×C4—2981no—
277C2×C4—2981no—
278C2×C4—2981no—
279C2×C4—2981no—
280C2×C4—2981no—
281C2×C4—2981no—
282C2×C4—2981no—
283C2×C4—2981no—
284C2×C4—2981no—
285C2×C4—2981no—
286C2×C4—2981no—
287C2×C4—1492no—
288C2×C4—1492no—
289C2×C4—1492no—
290C2×C4—1492no—
291C2×C4—1492no—
292C2×C4—1492no—
293C2×C4—1492no—
294C2×C4—1492no—
295C2×C4—1492no—
296C2×C4—1492no—
297C2×C4C2×C4×D14912yes—
298C2×C4C2×C4×D14912yes—
299C2×C4C2×C4×D14912yes—
300C2×C4Q8×D14912yes—
301C2×C4#1455873512yes—
302C22C22×C4×D14911yescharacteristic
303C22C2×Q8×D14911yescharacteristic
304C22#41×D14911yescharacteristic
305C22#41×D14911yescharacteristic
306C22#41×D14911yescharacteristic
307C22#41×D14911yescharacteristic
308C22C2×#1455873511yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—22no—
314C4—41no—
315C4—41no—
316C4—2982no—
317C4—2982no—
318C4—2982no—
319C4—2982no—
320C4—5961no—
321C4—5961no—
322C4—1494no—
323C4—1494no—
324C2C4×Q8×D14911yescharacteristic
325C2C4×#1455873511yescharacteristic
326C2#2375009311yescharacteristic
327C2#125×D14911yescharacteristic
328C2#2375015211yescharacteristic
329C2#2375015811yescharacteristic
330C2#2375017711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#387×C149C2
socle, prime radical, cosocleC23×C149C24
hypercenter#387D149
hypocenterC149C4×#125
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
16. #18011901C4semidirect
157. Dic149#125semidirect
165. C149C4×#125semidirect

Maximal subgroups

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

subgroupindex
C2×#180119012
#237495222
#237495202
#237495122
#237495092
#237495082
#237494892
C4⋊C4×Dic1492
#237494762
C42×Dic1492
#387×C1492
C4×#125149