Finite Group Databasebeta

← #34071844

Subgroups — #34071844

Order 19328.

528 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012717C211yesmaximal, characteristic
2#23752117C211yesmaximal, characteristic, complemented
3#23752116C211yesmaximal, characteristic, complemented
4#23752107C211yesmaximal, characteristic, complemented
5#23752099C211yesmaximal, characteristic, complemented
6#23752098C211yesmaximal, characteristic, complemented
7#23752096C211yesmaximal, characteristic, complemented
8#23752093C211yesmaximal, characteristic, complemented
9#23752083C211yesmaximal, characteristic
10#23752083C211yesmaximal, characteristic
11#23752069C211yesmaximal, characteristic
12C4×(C2×D151)⋊C4C211yesmaximal, characteristic
13#23752059C211yesmaximal, characteristic
14#95×D151C211yesmaximal, characteristic
15#389×C151C211yesmaximal, characteristic, complemented
16C22×Dic302C2211yescharacteristic
17C22×C4×D151C2211yescharacteristic
18C22×C4×D151C2211yescharacteristic
19C22×C4×D151C2211yescharacteristic
20#18012717C418yescomplemented
21C2×C4⋊Dic151C2211yescharacteristic
22C2×Dic151⋊C4C2211yescharacteristic
23C2×Dic151⋊C4C2211yescharacteristic
24C2×Dic151⋊C4C2211yescharacteristic
25C2×Dic151⋊C4C2211yescharacteristic
26C2×(C2×D151)⋊C4C2211yescharacteristic
27C2×(C2×D151)⋊C4C2211yescharacteristic
28C2×(C2×D151)⋊C4C2211yescharacteristic
29C2×(C2×D151)⋊C4C2211yescharacteristic
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×C4⋊C4×C151C2211yescharacteristic
48C2×C4⋊C4×C151C2211yescharacteristic
49C2×C42×C151C2211yescharacteristic
50#95×C151C2211yescharacteristic
51#95×C151C2211yescharacteristic
52C23×D151C2311yescharacteristic
53C2×Dic302—41no—
54C2×Dic302—41no—
55C2×Dic302C2×C414yescomplemented
56C22×Dic151C2311yescharacteristic
57C22×Dic151C2311yescharacteristic
58C22×Dic151C2311yescharacteristic
59C22×Dic151C2311yescharacteristic
60C22×Dic151C2311yescharacteristic
61C22×Dic151C2311yescharacteristic
62C22×Dic151C2311yescharacteristic
63C2×C4×D151—22no—
64C2×C4×D151—41no—
65C2×C4×D151—41no—
66C2×C4×D151—41no—
67C2×C4×D151—41no—
68C2×C4×D151—41no—
69C2×C4×D151—41no—
70C2×C4×D151C2×C414yes—
71C2×C4×D151Q814yescomplemented
72C4⋊Dic151—41no—
73Dic151⋊C4—41no—
74Dic151⋊C4—41no—
75Dic151⋊C4C2×C414yescomplemented
76Dic151⋊C4C2×C414yescomplemented
77(C2×D151)⋊C4—22no—
78(C2×D151)⋊C4—22no—
79(C2×D151)⋊C4C2×C414yes—
80(C2×D151)⋊C4C2×C414yes—
81C4×Dic151—41no—
82C4×Dic151—41no—
83C4×Dic151—41no—
84C22×C4×C151C2311yescharacteristic
85C22×C4×C151C2311yescharacteristic
86C22×C4×C151C2311yescharacteristic
87C22×C4×C151C2311yescharacteristic
88C22×C4×C151C2311yescharacteristic
89C22×C4×C151C2311yescharacteristic
90C22×C4×C151C2311yescharacteristic
91C4⋊C4×C151—41no—
92C4⋊C4×C151—41no—
93C4⋊C4×C151—41no—
94C4⋊C4×C151C2×C414yescomplemented
95C42×C151—41no—
96C22×D151—21no—
97C22×D151—21no—
98C22×D151—21no—
99C22×D151—21no—
100C22×D151C22×C412yes—
101C22×D151C2×Q812yes—
102C22×D151#4112yes—
103Dic302—44no—
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×Dic151—21no—
117C2×Dic151—21no—
118C2×Dic151—21no—
119C2×Dic151—21no—
120C2×Dic151—21no—
121C2×Dic151C22×C412yes—
122C2×Dic151C22×C412yes—
123C2×Dic151C22×C412yes—
124C2×Dic151C2×Q812yes—
125C4×D151—44no—
126C4×D151—44no—
127C4×D151—44no—
128C23×C151C2411yescharacteristic
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—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151C22×C412yes—
147C2×C4×C151C22×C412yes—
148C2×C4×C151C22×C412yes—
149C2×C4×C151C2×Q812yes—
150C22×C151C23×C411yescharacteristic
151C22×C151C22×Q811yescharacteristic
152C22×C151C2×#4111yescharacteristic
153C22×C151H(5,𝔽2)11yescharacteristic
154C22×C151H(5,𝔽2)11yescharacteristic
155C22×C151H(5,𝔽2)11yescharacteristic
156C22×C1512−1+411yescharacteristic
157C2×D151—22no—
158C2×D151—22no—
159C2×D151—22no—
160C2×D151—22no—
161C2×D151—22no—
162C2×D151—22no—
163C2×D151C4×Q814yes—
164C4×C151—22no—
165C4×C151—22no—
166C4×C151—22no—
167C4×C151—22no—
168C4×C151—41no—
169C4×C151—41no—
170C4×C151—41no—
171Dic151—22no—
172Dic151—22no—
173Dic151—22no—
174Dic151—22no—
175Dic151—41no—
176Dic151—41no—
177Dic151—41no—
178C2×C151C2×C4×Q811yescharacteristic
179C2×C151#51811yescharacteristic
180C2×C151#52011yescharacteristic
181C2×C151#53811yescharacteristic
182C2×C151#53911yescharacteristic
183C2×C151#54311yescharacteristic
184C2×C151#54411yescharacteristic
185D151—24no—
186C151#232911yescharacteristic, complemented, Sylow
187#2329—1511nomaximal, Sylow
188C2×C22⋊Q8—1511no—
189#391—1511no—
190#391—1511no—
191#389—1511no—
192#389D15111yescharacteristic, complemented
193#387—1511no—
194#387—1511no—
195#387—1511no—
196#387—1511no—
197#385—1511no—
198#385—1511no—
199#380—1511no—
200C4×C22⋊C4—1511no—
201C4×C22⋊C4—1511no—
202C2×#95—1511no—
203C22×Q8—1511no—
204C23×C4—1511no—
205C23×C4—1511no—
206C23×C4—1511no—
207C22⋊Q8—1518no—
208C2×C4⋊C4—1511no—
209C2×C4⋊C4—1511no—
210C2×C4⋊C4—1511no—
211C2×C4⋊C4—1511no—
212C2×C4⋊C4—1511no—
213C2×C4⋊C4C2×D15111yescharacteristic
214C2×C4⋊C4C2×D15111yescharacteristic
215C2×C4⋊C4C2×D15111yescharacteristic
216C2×C4⋊C4C2×D15111yescharacteristic
217C2×C22⋊C4—1511no—
218C2×C22⋊C4—1511no—
219C2×C22⋊C4—1511no—
220C2×C22⋊C4—1511no—
221C2×C42—1511no—
222C2×C42—1511no—
223C2×C42—1511no—
224C2×C42C2×D15111yescharacteristic
225#95—1511no—
226#95—1511no—
227#95—1511no—
228#95—1511no—
229#95—1511no—
230#95—1511no—
231#95—1511no—
232#95—1511no—
233#95—1511no—
234#95—1511no—
235#95—1511no—
236#95—1511no—
237#95C2×D15111yescharacteristic
238#95C2×D15111yescharacteristic
239C24—1511no—
240C2×Q8—6041no—
241C2×Q8—6041no—
242C2×Q8—1514no—
243C22×C4—3022no—
244C22×C4—6041no—
245C22×C4—6041no—
246C22×C4—6041no—
247C22×C4—6041no—
248C22×C4—6041no—
249C22×C4—6041no—
250C22×C4—1511no—
251C22×C4—1511no—
252C22×C4—1511no—
253C22×C4—1511no—
254C22×C4—1511no—
255C22×C4—1511no—
256C22×C4—1511no—
257C22×C4—1514no—
258C22×C4—1514no—
259C22×C4C22×D15111yescharacteristic
260C22×C4C22×D15111yescharacteristic
261C22×C4C22×D15111yescharacteristic
262C22×C4C22×D15111yescharacteristic
263C22×C4C22×D15111yescharacteristic
264C22×C4C22×D15111yescharacteristic
265C22×C4C22×D15111yescharacteristic
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—6041no—
270C4⋊C4—6041no—
271C4⋊C4—6041no—
272C4⋊C4—1514no—
273C4⋊C4—1514no—
274C4⋊C4C4×D15114yescomplemented
275C22⋊C4—3022no—
276C22⋊C4—3022no—
277C22⋊C4—1514no—
278C22⋊C4—1514no—
279C42—41no—
280C42—6041no—
281C42—6041no—
282C42—6041no—
283C23—3021no—
284C23—3021no—
285C23—3021no—
286C23—3021no—
287C23—1512no—
288C23—1512no—
289C23—1512no—
290C23C23×D15111yescharacteristic
291Q8—6044no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
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—3021no—
319C2×C4—3021no—
320C2×C4—3021no—
321C2×C4—3021no—
322C2×C4—3021no—
323C2×C4—3021no—
324C2×C4—3021no—
325C2×C4—3021no—
326C2×C4—6044no—
327C2×C4—6044no—
328C2×C4—6044no—
329C2×C4—1512no—
330C2×C4—1512no—
331C2×C4—1512no—
332C2×C4—1512no—
333C2×C4C2×C4×D15112yes—
334C2×C4C2×C4×D15112yes—
335C2×C4C2×C4×D15112yes—
336C2×C4Q8×D15112yes—
337C22—3022no—
338C22—3022no—
339C22—3022no—
340C22—3022no—
341C22—3022no—
342C22—3022no—
343C22—1514no—
344C22C22×C4×D15111yescharacteristic
345C22C2×Q8×D15111yescharacteristic
346C22#41×D15111yescharacteristic
347C22#1801278411yescharacteristic
348C22#1801278411yescharacteristic
349C22#1801278511yescharacteristic
350C22#1801278711yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—3022no—
359C4—3022no—
360C4—3022no—
361C4—3022no—
362C4—6041no—
363C4—6041no—
364C4—6041no—
365C2—3024no—
366C2C4×Q8×D15111yescharacteristic
367C2#2375268411yescharacteristic
368C2#2375269311yescharacteristic
369C2#2375279411yescharacteristic
370C2#2375281011yescharacteristic
371C2#2375283711yescharacteristic
372C2#2375283911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutatorC22×C151C23×C4
Fitting#389×C151C2
socle, cosocleC23×C151C24
prime radicalC23×D151C23
hypercenter#389D151
hypocenterC151#2329
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
2. #23752117C2semidirect
3. #23752116C2semidirect
4. #23752107C2semidirect
5. #23752099C2semidirect
6. #23752098C2semidirect
7. #23752096C2semidirect
8. #23752093C2semidirect
15. #389×C151C2semidirect
20. #18012717C4semidirect
55. C2×Dic302C2×C4semidirect
71. C2×C4×D151Q8semidirect
75. Dic151⋊C4C2×C4semidirect
76. Dic151⋊C4C2×C4semidirect
94. C4⋊C4×C151C2×C4semidirect
186. C151#2329semidirect
192. #389D151semidirect
274. C4⋊C4C4×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127172
#237521172
#237521162
#237521072
#237520992
#237520982
#237520962
#237520932
#237520832
#237520692
C4×(C2×D151)⋊C42
#237520592
#95×D1512
#389×C1512
#2329151