Finite Group Databasebeta

← #34071968

Subgroups — #34071968

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×#18012695C211yesmaximal, characteristic
2#23752099C211yesmaximal, characteristic, complemented
3#23752099C211yesmaximal, characteristic, complemented
4#23752093C211yesmaximal, characteristic, complemented
5#23752093C211yesmaximal, characteristic, complemented
6#23752087C211yesmaximal, characteristic
7#23752079C211yesmaximal, characteristic, complemented
8#23752077C211yesmaximal, characteristic, complemented
9#23752073C211yesmaximal, characteristic
10C4⋊C4×Dic151C211yesmaximal, characteristic, complemented
11C22⋊C4×Dic151C211yesmaximal, characteristic
12C4×C22⋊Dic151C211yesmaximal, characteristic
13#23752057C211yesmaximal, characteristic, complemented
14C2×C151⋊#95C211yesmaximal, characteristic
15#385×C151C211yesmaximal, characteristic
16C23×Dic151C2211yescharacteristic
17C23×Dic151C2211yescharacteristic
18#18012695C418yescomplemented
19C2×C4⋊Dic151C2211yescharacteristic
20C2×C4⋊Dic151C2211yescharacteristic
21C2×Dic151⋊C4C2211yescharacteristic
22C2×Dic151⋊C4C2211yescharacteristic
23C2×C22⋊Dic151C2211yescharacteristic
24C2×C22⋊Dic151C2211yescharacteristic
25C2×C4×Dic151C2211yescharacteristic
26C2×C4×Dic151C2211yescharacteristic
27C2×C4×Dic151C2211yescharacteristic
28C2×C4×Dic151C2211yescharacteristic
29C2×C4×Dic151C2211yescharacteristic
30C2×C4×Dic151C2211yescharacteristic
31C151⋊#95C2211yescharacteristic
32C151⋊#95C2211yescharacteristic
33C151⋊#95C2211yescharacteristic
34C151⋊#95C2211yescharacteristic
35C151⋊#95C2211yescharacteristic
36C151⋊#95C2211yescharacteristic
37C151⋊#95C2211yescharacteristic
38C151⋊#95C2211yescharacteristic
39C151⋊#95C2211yescharacteristic
40C151⋊#95C2211yescharacteristic
41C151⋊#95C2211yescharacteristic
42C151⋊#95C2211yescharacteristic
43C151⋊#95C2211yescharacteristic
44C151⋊#95C2211yescharacteristic
45C23×C4×C151C2211yescharacteristic
46C2×C4⋊C4×C151C2211yescharacteristic
47C2×C4⋊C4×C151C2211yescharacteristic
48C2×C22⋊C4×C151C2211yescharacteristic
49C2×C22⋊C4×C151C2211yescharacteristic
50#95×C151C2211yescharacteristic
51#95×C151C2211yescharacteristic
52C22×Dic151—22no—
53C22×Dic151—22no—
54C22×Dic151—22no—
55C22×Dic151—22no—
56C22×Dic151—41no—
57C22×Dic151C2×C414yes—
58C22×Dic151C2311yescharacteristic
59C22×Dic151C2311yescharacteristic
60C22×Dic151C2311yescharacteristic
61C22×Dic151C2311yescharacteristic
62C22×Dic151C2311yescharacteristic
63C22×Dic151C2311yescharacteristic
64C22×Dic151C2311yescharacteristic
65C22×Dic151C2311yescharacteristic
66C4⋊Dic151—22no—
67C4⋊Dic151—41no—
68Dic151⋊C4C2×C414yescomplemented
69Dic151⋊C4C2×C414yescomplemented
70C22⋊Dic151—22no—
71C22⋊Dic151C2×C414yes—
72C4×Dic151—22no—
73C4×Dic151—22no—
74C4×Dic151—41no—
75C4×Dic151—41no—
76C4×Dic151C2×C414yescomplemented
77C4×Dic151C2×C414yescomplemented
78C24×C151C2311yescharacteristic
79C22×C4×C151—22no—
80C22×C4×C151—22no—
81C22×C4×C151—41no—
82C22×C4×C151C2311yescharacteristic
83C22×C4×C151C2311yescharacteristic
84C22×C4×C151C2311yescharacteristic
85C22×C4×C151C2311yescharacteristic
86C22×C4×C151C2311yescharacteristic
87C22×C4×C151C2311yescharacteristic
88C4⋊C4×C151—22no—
89C4⋊C4×C151—41no—
90C22⋊C4×C151—22no—
91C22⋊C4×C151C2×C414yes—
92C2×Dic151—28no—
93C2×Dic151—21no—
94C2×Dic151—21no—
95C2×Dic151—21no—
96C2×Dic151—21no—
97C2×Dic151—21no—
98C2×Dic151—21no—
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—44no—
113C2×Dic151C22×C412yes—
114C2×Dic151C22×C412yes—
115C2×Dic151C22×C412yes—
116C2×Dic151C22×C412yes—
117C2×Dic151#4112yes—
118C23×C151—21no—
119C23×C151—21no—
120C23×C151—21no—
121C23×C151—21no—
122C23×C151C22×C412yes—
123C23×C151#4112yes—
124C23×C151#4112yes—
125C23×C151C2411yescharacteristic
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×C151—44no—
142C2×C4×C151C22×C412yes—
143C2×C4×C151C22×C412yes—
144C2×C4×C151#4112yes—
145C22×C151—22no—
146C22×C151—22no—
147C22×C151—22no—
148C22×C151—22no—
149C22×C151—22no—
150C22×C151—22no—
151C22×C151#11714yes—
152C22×C151C23×C411yescharacteristic
153C22×C151C2×#4111yescharacteristic
154C22×C151C2×#4111yescharacteristic
155C22×C151C2×#4111yescharacteristic
156C22×C151C2×#4111yescharacteristic
157C22×C151H(5,𝔽2)11yescharacteristic
158C22×C1512−1+411yescharacteristic
159C4×C151—22no—
160C4×C151—22no—
161C4×C151—22no—
162C4×C151—41no—
163C4×C151—41no—
164C4×C151—41no—
165Dic151—22no—
166Dic151—22no—
167Dic151—22no—
168Dic151—22no—
169Dic151—22no—
170Dic151—41no—
171Dic151—41no—
172Dic151—41no—
173C2×C151—24no—
174C2×C151C2×#11711yescharacteristic
175C2×C151C4×#4111yescharacteristic
176C2×C151#52011yescharacteristic
177C2×C151#55111yescharacteristic
178C2×C151#55111yescharacteristic
179C2×C151#55211yescharacteristic
180C2×C151#55211yescharacteristic
181C151#234311yescharacteristic, complemented, Sylow
182#2343—1511nomaximal, Sylow
183C2×#117—1511no—
184#387—1511no—
185#387—1511no—
186#387—1511no—
187#387—1511no—
188#385—1511no—
189#385D15111yescharacteristic
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×C4C2×D15111yescharacteristic
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⋊C4C2×D15111yescharacteristic
211C2×C22⋊C4C2×D15111yescharacteristic
212C2×C42—1511no—
213C2×C42—1511no—
214C2×C42—1511no—
215C2×C42—1511no—
216C2×C42—1511no—
217C2×C42—1511no—
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#95—1511no—
231#95—1511no—
232#95C2×D15111yescharacteristic
233#95C2×D15111yescharacteristic
234C24C22×D15111yescharacteristic
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—41no—
238C22×C4—3022no—
239C22×C4—3022no—
240C22×C4—3022no—
241C22×C4—3022no—
242C22×C4—6041no—
243C22×C4—1511no—
244C22×C4—1511no—
245C22×C4—1511no—
246C22×C4—1514no—
247C22×C4—1511no—
248C22×C4—1511no—
249C22×C4—1511no—
250C22×C4—1511no—
251C22×C4—1511no—
252C22×C4C22×D15111yescharacteristic
253C22×C4C22×D15111yescharacteristic
254C22×C4C22×D15111yescharacteristic
255C22×C4C22×D15111yescharacteristic
256C22×C4C22×D15111yescharacteristic
257C22×C4C22×D15111yescharacteristic
258C4⋊C4—22no—
259C4⋊C4—41no—
260C4⋊C4—3022no—
261C4⋊C4—6041no—
262C4⋊C4—1514no—
263C4⋊C4—1514no—
264C22⋊C4—22no—
265C22⋊C4—3022no—
266C22⋊C4—1514no—
267C22⋊C4C4×D15114yes—
268C42—3022no—
269C42—3022no—
270C42—6041no—
271C42—6041no—
272C42—1514no—
273C42—1514no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23C2×C4×D15112yes—
279C23#1455900312yes—
280C23#1455900512yes—
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—44no—
298C2×C4—3028no—
299C2×C4—3021no—
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—3021no—
318C2×C4—6044no—
319C2×C4—1512no—
320C2×C4—1512no—
321C2×C4—1512no—
322C2×C4—1512no—
323C2×C4—1512no—
324C2×C4C2×C4×D15112yes—
325C2×C4C2×C4×D15112yes—
326C2×C4#1455900312yes—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—22no—
331C22—22no—
332C22—22no—
333C22#1801269714yes—
334C22C22×C4×D15111yescharacteristic
335C22#41×D15111yescharacteristic
336C22C2×#1455900311yescharacteristic
337C22C2×#1455900311yescharacteristic
338C22C2×#1455900511yescharacteristic
339C22#1801278411yescharacteristic
340C22#1801278611yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—3022no—
348C4—3022no—
349C4—3022no—
350C4—3022no—
351C4—3022no—
352C4—6041no—
353C4—6041no—
354C4—6041no—
355C2—24no—
356C2C2×#1801269711yescharacteristic
357C2C4×#1455900311yescharacteristic
358C2#2375269111yescharacteristic
359C2#2375288911yescharacteristic
360C2#2375289311yescharacteristic
361C2#2375289911yescharacteristic
362C2#2375290411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutatorC22×C151C23×C4
Fitting#385×C151C2
socle, cosocleC23×C151C24
prime radicalC24×C151C23
hypercenter#385D151
hypocenterC151#2343
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. #23752099C2semidirect
3. #23752099C2semidirect
4. #23752093C2semidirect
5. #23752093C2semidirect
7. #23752079C2semidirect
8. #23752077C2semidirect
10. C4⋊C4×Dic151C2semidirect
13. #23752057C2semidirect
18. #18012695C4semidirect
68. Dic151⋊C4C2×C4semidirect
69. Dic151⋊C4C2×C4semidirect
76. C4×Dic151C2×C4semidirect
77. C4×Dic151C2×C4semidirect
181. C151#2343semidirect

Maximal subgroups

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

subgroupindex
C2×#180126952
#237520992
#237520932
#237520872
#237520792
#237520772
#237520732
C4⋊C4×Dic1512
C22⋊C4×Dic1512
C4×C22⋊Dic1512
#237520572
C2×C151⋊#952
#385×C1512
#2343151