Finite Group Databasebeta

← #34071965

Subgroups — #34071965

Order 19328.

532 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012697C211yesmaximal, characteristic
2#23752098C211yesmaximal, characteristic, complemented
3#23752097C211yesmaximal, characteristic, complemented
4#23752095C211yesmaximal, characteristic, complemented
5#23752086C211yesmaximal, characteristic
6#23752083C211yesmaximal, characteristic
7#23752079C211yesmaximal, characteristic, complemented
8#23752076C211yesmaximal, characteristic, complemented
9#23752074C211yesmaximal, characteristic
10C4⋊C4×Dic151C211yesmaximal, characteristic, complemented
11C4×(C2×D151)⋊C4C211yesmaximal, characteristic
12#23752059C211yesmaximal, characteristic
13#23752058C211yesmaximal, characteristic, complemented
14#95×D151C211yesmaximal, characteristic
15#387×C151C211yesmaximal, characteristic, complemented
16C22×C4×D151C2211yescharacteristic
17C22×C4×D151C2211yescharacteristic
18C22×C4×D151C2211yescharacteristic
19#18012697C418yescomplemented
20C2×C4⋊Dic151C2211yescharacteristic
21C2×C4⋊Dic151C2211yescharacteristic
22C2×Dic151⋊C4C2211yescharacteristic
23C2×Dic151⋊C4C2211yescharacteristic
24C2×(C2×D151)⋊C4C2211yescharacteristic
25C2×(C2×D151)⋊C4C2211yescharacteristic
26C2×(C2×D151)⋊C4C2211yescharacteristic
27C2×(C2×D151)⋊C4C2211yescharacteristic
28C2×C4×Dic151C2211yescharacteristic
29C2×C4×Dic151C2211yescharacteristic
30C2×C4×Dic151C2211yescharacteristic
31C2×C4×Dic151C2211yescharacteristic
32C2×C4×Dic151C2211yescharacteristic
33C151⋊#95C2211yescharacteristic
34C151⋊#95C2211yescharacteristic
35C151⋊#95C2211yescharacteristic
36C151⋊#95C2211yescharacteristic
37C151⋊#95C2211yescharacteristic
38C151⋊#95C2211yescharacteristic
39C151⋊#95C2211yescharacteristic
40C151⋊#95C2211yescharacteristic
41C151⋊#95C2211yescharacteristic
42C151⋊#95C2211yescharacteristic
43C151⋊#95C2211yescharacteristic
44C151⋊#95C2211yescharacteristic
45C2×C4⋊C4×C151C2211yescharacteristic
46C2×C4⋊C4×C151C2211yescharacteristic
47C2×C42×C151C2211yescharacteristic
48#95×C151C2211yescharacteristic
49#95×C151C2211yescharacteristic
50#95×C151C2211yescharacteristic
51#95×C151C2211yescharacteristic
52C23×D151C2311yescharacteristic
53C22×Dic151C2311yescharacteristic
54C22×Dic151C2311yescharacteristic
55C22×Dic151C2311yescharacteristic
56C22×Dic151C2311yescharacteristic
57C22×Dic151C2311yescharacteristic
58C22×Dic151C2311yescharacteristic
59C22×Dic151C2311yescharacteristic
60C2×C4×D151—22no—
61C2×C4×D151—22no—
62C2×C4×D151—22no—
63C2×C4×D151—22no—
64C2×C4×D151—22no—
65C2×C4×D151—22no—
66C2×C4×D151—41no—
67C2×C4×D151—41no—
68C2×C4×D151C2×C414yes—
69C4⋊Dic151—22no—
70C4⋊Dic151C2×C414yescomplemented
71Dic151⋊C4—41no—
72Dic151⋊C4—41no—
73(C2×D151)⋊C4—22no—
74(C2×D151)⋊C4—22no—
75(C2×D151)⋊C4C2×C414yes—
76(C2×D151)⋊C4C2×C414yes—
77C4×Dic151—22no—
78C4×Dic151—41no—
79C4×Dic151—41no—
80C4×Dic151C2×C414yescomplemented
81C4×Dic151C2×C414yescomplemented
82C22×C4×C151C2311yescharacteristic
83C22×C4×C151C2311yescharacteristic
84C22×C4×C151C2311yescharacteristic
85C22×C4×C151C2311yescharacteristic
86C22×C4×C151C2311yescharacteristic
87C22×C4×C151C2311yescharacteristic
88C22×C4×C151C2311yescharacteristic
89C4⋊C4×C151—22no—
90C4⋊C4×C151C2×C414yescomplemented
91C42×C151—22no—
92C22×D151—21no—
93C22×D151—21no—
94C22×D151—21no—
95C22×D151—21no—
96C22×D151C22×C412yes—
97C22×D151#4112yes—
98C22×D151#4112yes—
99C2×Dic151—21no—
100C2×Dic151—21no—
101C2×Dic151—21no—
102C2×Dic151—21no—
103C2×Dic151—21no—
104C2×Dic151—21no—
105C2×Dic151—21no—
106C2×Dic151—21no—
107C2×Dic151—21no—
108C2×Dic151—21no—
109C2×Dic151—21no—
110C2×Dic151—21no—
111C2×Dic151—21no—
112C2×Dic151—21no—
113C2×Dic151—21no—
114C2×Dic151—21no—
115C2×Dic151—21no—
116C2×Dic151C22×C412yes—
117C2×Dic151C22×C412yes—
118C2×Dic151C22×C412yes—
119C2×Dic151#4112yes—
120C4×D151—28no—
121C4×D151—44no—
122C4×D151—44no—
123C23×C151C2411yescharacteristic
124C2×C4×C151—21no—
125C2×C4×C151—21no—
126C2×C4×C151—21no—
127C2×C4×C151—21no—
128C2×C4×C151—21no—
129C2×C4×C151—21no—
130C2×C4×C151—21no—
131C2×C4×C151—21no—
132C2×C4×C151—21no—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151C22×C412yes—
142C2×C4×C151C22×C412yes—
143C2×C4×C151C22×C412yes—
144C2×C4×C151#4112yes—
145C22×C151C23×C411yescharacteristic
146C22×C151C2×#4111yescharacteristic
147C22×C151C2×#4111yescharacteristic
148C22×C151C2×#4111yescharacteristic
149C22×C151C2×#4111yescharacteristic
150C22×C151H(5,𝔽2)11yescharacteristic
151C22×C1512−1+411yescharacteristic
152C2×D151—22no—
153C2×D151—22no—
154C2×D151—22no—
155C2×D151—22no—
156C2×D151—22no—
157C2×D151—22no—
158C2×D151#11714yes—
159C4×C151—22no—
160C4×C151—22no—
161C4×C151—22no—
162C4×C151—22no—
163C4×C151—41no—
164C4×C151—41no—
165C4×C151—41no—
166Dic151—22no—
167Dic151—22no—
168Dic151—22no—
169Dic151—22no—
170Dic151—41no—
171Dic151—41no—
172Dic151—41no—
173C2×C151C2×#11711yescharacteristic
174C2×C151C4×#4111yescharacteristic
175C2×C151#52011yescharacteristic
176C2×C151#55111yescharacteristic
177C2×C151#55111yescharacteristic
178C2×C151#55211yescharacteristic
179C2×C151#55211yescharacteristic
180D151—24no—
181C151#234311yescharacteristic, complemented, Sylow
182#2343—1511nomaximal, Sylow
183C2×#117—1511no—
184#387—1511no—
185#387—1511no—
186#387—1511no—
187#387D15111yescharacteristic, complemented
188#385—1511no—
189#385—1511no—
190#383—1511no—
191#382—1511no—
192#381—1511no—
193C4×C4⋊C4—1511no—
194C4×C22⋊C4—1511no—
195C4×C22⋊C4—1511no—
196#376—1511no—
197C2×#95—1511no—
198C23×C4—1511no—
199C23×C4—1511no—
200C23×C4—1511no—
201#117—1518no—
202C2×C4⋊C4—1511no—
203C2×C4⋊C4—1511no—
204C2×C4⋊C4—1511no—
205C2×C4⋊C4—1511no—
206C2×C4⋊C4C2×D15111yescharacteristic
207C2×C4⋊C4C2×D15111yescharacteristic
208C2×C22⋊C4—1511no—
209C2×C22⋊C4—1511no—
210C2×C22⋊C4—1511no—
211C2×C22⋊C4—1511no—
212C2×C42—1511no—
213C2×C42—1511no—
214C2×C42—1511no—
215C2×C42—1511no—
216C2×C42—1511no—
217C2×C42C2×D15111yescharacteristic
218#95—1511no—
219#95—1511no—
220#95—1511no—
221#95—1511no—
222#95—1511no—
223#95—1511no—
224#95—1511no—
225#95—1511no—
226#95—1511no—
227#95—1511no—
228#95—1511no—
229#95—1511no—
230#95C2×D15111yescharacteristic
231#95C2×D15111yescharacteristic
232#95C2×D15111yescharacteristic
233#95C2×D15111yescharacteristic
234C24—1511no—
235C22×C4—3022no—
236C22×C4—3022no—
237C22×C4—3022no—
238C22×C4—3022no—
239C22×C4—3022no—
240C22×C4—3022no—
241C22×C4—6041no—
242C22×C4—6041no—
243C22×C4—1511no—
244C22×C4—1511no—
245C22×C4—1511no—
246C22×C4—1511no—
247C22×C4—1511no—
248C22×C4—1511no—
249C22×C4—1511no—
250C22×C4—1514no—
251C22×C4C22×D15111yescharacteristic
252C22×C4C22×D15111yescharacteristic
253C22×C4C22×D15111yescharacteristic
254C22×C4C22×D15111yescharacteristic
255C22×C4C22×D15111yescharacteristic
256C22×C4C22×D15111yescharacteristic
257C22×C4C22×D15111yescharacteristic
258C4⋊C4—22no—
259C4⋊C4—3022no—
260C4⋊C4—6041no—
261C4⋊C4—6041no—
262C4⋊C4—1514no—
263C4⋊C4C4×D15114yescomplemented
264C22⋊C4—3022no—
265C22⋊C4—3022no—
266C22⋊C4—1514no—
267C22⋊C4—1514no—
268C42—22no—
269C42—3022no—
270C42—6041no—
271C42—6041no—
272C42—1514no—
273C42—1514no—
274C23—3021no—
275C23—3021no—
276C23—3021no—
277C23—3021no—
278C23—1512no—
279C23—1512no—
280C23—1512no—
281C23C23×D15111yescharacteristic
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—3028no—
300C2×C4—3021no—
301C2×C4—3021no—
302C2×C4—3021no—
303C2×C4—3021no—
304C2×C4—3021no—
305C2×C4—3021no—
306C2×C4—3021no—
307C2×C4—3021no—
308C2×C4—3021no—
309C2×C4—3021no—
310C2×C4—3021no—
311C2×C4—3021no—
312C2×C4—3021no—
313C2×C4—3021no—
314C2×C4—3021no—
315C2×C4—3021no—
316C2×C4—3021no—
317C2×C4—6044no—
318C2×C4—6044no—
319C2×C4—1512no—
320C2×C4—1512no—
321C2×C4—1512no—
322C2×C4—1512no—
323C2×C4C2×C4×D15112yes—
324C2×C4C2×C4×D15112yes—
325C2×C4C2×C4×D15112yes—
326C2×C4#1455900312yes—
327C22—3022no—
328C22—3022no—
329C22—3022no—
330C22—3022no—
331C22—3022no—
332C22—3022no—
333C22—1514no—
334C22C22×C4×D15111yescharacteristic
335C22#41×D15111yescharacteristic
336C22#41×D15111yescharacteristic
337C22#41×D15111yescharacteristic
338C22C2×#1455900311yescharacteristic
339C22#1801278511yescharacteristic
340C22#1801278711yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—22no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—3022no—
349C4—3022no—
350C4—3022no—
351C4—3022no—
352C4—6041no—
353C4—6041no—
354C4—6041no—
355C2—3024no—
356C2#117×D15111yescharacteristic
357C2C4×#1455900311yescharacteristic
358C2#2375269411yescharacteristic
359C2#2375288511yescharacteristic
360C2#2375288711yescharacteristic
361C2#2375289411yescharacteristic
362C2#2375289611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutatorC22×C151C23×C4
Fitting#387×C151C2
socle, cosocleC23×C151C24
prime radicalC23×D151C23
hypercenter#387D151
hypocenterC151#2343
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #23752098C2semidirect
3. #23752097C2semidirect
4. #23752095C2semidirect
7. #23752079C2semidirect
8. #23752076C2semidirect
10. C4⋊C4×Dic151C2semidirect
13. #23752058C2semidirect
15. #387×C151C2semidirect
19. #18012697C4semidirect
70. C4⋊Dic151C2×C4semidirect
80. C4×Dic151C2×C4semidirect
81. C4×Dic151C2×C4semidirect
90. C4⋊C4×C151C2×C4semidirect
181. C151#2343semidirect
187. #387D151semidirect
263. C4⋊C4C4×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180126972
#237520982
#237520972
#237520952
#237520862
#237520832
#237520792
#237520762
#237520742
C4⋊C4×Dic1512
C4×(C2×D151)⋊C42
#237520592
#237520582
#95×D1512
#387×C1512
#2343151