Finite Group Databasebeta

← #2481×C151 #34065813

Subgroups — #2481×C151 #34065813

Order 19328.

546 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#126×C151C211yesmaximal, characteristic, complemented
2C22×C4⋊C4×C151C211yesmaximal, characteristic, complemented
3#400×C151C211yesmaximal, characteristic, complemented
4#400×C151C211yesmaximal, characteristic, complemented
5#397×C151C211yesmaximal, characteristic, complemented
6#396×C151C211yesmaximal, characteristic, complemented
7#388×C151C211yesmaximal, characteristic, complemented
8#387×C151C211yesmaximal, characteristic, complemented
9#387×C151C211yesmaximal, characteristic, complemented
10#386×C151C211yesmaximal, characteristic
11#386×C151C211yesmaximal, characteristic
12#386×C151C211yesmaximal, characteristic
13#385×C151C211yesmaximal, characteristic, complemented
14#380×C151C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C151C211yesmaximal, characteristic, complemented
16C22×D4×C151C2211yescharacteristic
17C23×C4×C151C2211yescharacteristic
18C23×C4×C151C2211yescharacteristic
19C23×C4×C151C2211yescharacteristic
20#126×C151—24no—
21C2×C4⋊C4×C151—24no—
22C2×C4⋊C4×C151C2211yescharacteristic
23C2×C4⋊C4×C151C2211yescharacteristic
24C2×C4⋊C4×C151C2211yescharacteristic
25C2×C4⋊C4×C151C2211yescharacteristic
26C2×C4⋊C4×C151C2211yescharacteristic
27C2×C4⋊C4×C151C2211yescharacteristic
28C2×C4⋊C4×C151C2211yescharacteristic
29C2×C4⋊C4×C151C2211yescharacteristic
30C2×C22⋊C4×C151C2211yescharacteristic
31C2×C22⋊C4×C151C2211yescharacteristic
32C2×C22⋊C4×C151C2211yescharacteristic
33C2×C22⋊C4×C151C2211yescharacteristic
34C2×C22⋊C4×C151C2211yescharacteristic
35C2×C22⋊C4×C151C2211yescharacteristic
36C2×C22⋊C4×C151C2211yescharacteristic
37C2×C22⋊C4×C151C2211yescharacteristic
38C2×C22⋊C4×C151C2211yescharacteristic
39C2×C42×C151C2211yescharacteristic
40C2×C42×C151C2211yescharacteristic
41#95×C151C2211yescharacteristic
42#95×C151C2211yescharacteristic
43#95×C151C2211yescharacteristic
44#95×C151C2211yescharacteristic
45#95×C151C2211yescharacteristic
46#95×C151C2211yescharacteristic
47#95×C151C2211yescharacteristic
48#95×C151C2211yescharacteristic
49#95×C151C2211yescharacteristic
50#95×C151C2211yescharacteristic
51#95×C151C2211yescharacteristic
52#95×C151C2211yescharacteristic
53C24×C151C2311yescharacteristic
54C24×C151C2311yescharacteristic
55C2×D4×C151—22no—
56C2×D4×C151—22no—
57C2×D4×C151—22no—
58C22×C4×C151—22no—
59C22×C4×C151—22no—
60C22×C4×C151—22no—
61C22×C4×C151—22no—
62C22×C4×C151—22no—
63C22×C4×C151—22no—
64C22×C4×C151—22no—
65C22×C4×C151—41no—
66C22×C4×C151—41no—
67C22×C4×C151C2311yescharacteristic
68C22×C4×C151C2311yescharacteristic
69C22×C4×C151C2311yescharacteristic
70C22×C4×C151C2311yescharacteristic
71C22×C4×C151C2311yescharacteristic
72C22×C4×C151C2311yescharacteristic
73C22×C4×C151C2311yescharacteristic
74C22×C4×C151C2311yescharacteristic
75C22×C4×C151C2311yescharacteristic
76C22×C4×C151C2311yescharacteristic
77C22×C4×C151C2311yescharacteristic
78C22×C4×C151C2311yescharacteristic
79C22×C4×C151C2311yescharacteristic
80C4⋊C4×C151—22no—
81C4⋊C4×C151—22no—
82C4⋊C4×C151—22no—
83C4⋊C4×C151—22no—
84C4⋊C4×C151—22no—
85C4⋊C4×C151—22no—
86C4⋊C4×C151—41no—
87C4⋊C4×C151D414yescomplemented
88C22⋊C4×C151—22no—
89C22⋊C4×C151—22no—
90C22⋊C4×C151—22no—
91C22⋊C4×C151—22no—
92C22⋊C4×C151—22no—
93C22⋊C4×C151—22no—
94C22⋊C4×C151—22no—
95C22⋊C4×C151—41no—
96C22⋊C4×C151—41no—
97C42×C151—22no—
98C42×C151—41no—
99C23×C151—21no—
100C23×C151—21no—
101C23×C151—21no—
102C23×C151—21no—
103C23×C151—21no—
104C23×C151—21no—
105C23×C151—21no—
106C23×C151—21no—
107C23×C151—21no—
108C23×C151—21no—
109C23×C151—21no—
110C23×C151#4112yes—
111C23×C151#4112yes—
112C23×C151#4112yes—
113C23×C151C2411yescharacteristic
114D4×C151—44no—
115C2×C4×C151—28no—
116C2×C4×C151—21no—
117C2×C4×C151—21no—
118C2×C4×C151—21no—
119C2×C4×C151—21no—
120C2×C4×C151—21no—
121C2×C4×C151—21no—
122C2×C4×C151—21no—
123C2×C4×C151—21no—
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×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—21no—
146C2×C4×C151—21no—
147C2×C4×C151—21no—
148C2×C4×C151—21no—
149C2×C4×C151—21no—
150C2×C4×C151—21no—
151C2×C4×C151—44no—
152C2×C4×C151—44no—
153C2×C4×C151C2×D412yes—
154C2×C4×C151C2×D412yes—
155C2×C4×C151C2×D412yes—
156C2×C4×C151#4112yes—
157C22×C151—22no—
158C22×C151—22no—
159C22×C151—22no—
160C22×C151—22no—
161C22×C151—22no—
162C22×C151—22no—
163C22×C151—41no—
164C22×C151—41no—
165C22×C151—41no—
166C22×C151—41no—
167C22×C151—41no—
168C22×C151—41no—
169C22×C151—41no—
170C22×C151#12614yescomplemented
171C22×C151C22×D411yescharacteristic
172C22×C151C2×#4111yescharacteristic
173C22×C151C2×#4111yescharacteristic
174C22×C151C2×#4111yescharacteristic
175C22×C151C2×#4111yescharacteristic
176C22×C151H(5,𝔽2)11yescharacteristic
177C22×C1512−1+411yescharacteristic
178C4×C151—22no—
179C4×C151—22no—
180C4×C151—22no—
181C4×C151—22no—
182C4×C151—41no—
183C4×C151—41no—
184C4×C151—41no—
185C4×C151—41no—
186C4×C151—41no—
187C4×C151—41no—
188C4×C151—41no—
189C4×C151—41no—
190C4×C151—41no—
191C2×C151—24no—
192C2×C151—81no—
193C2×C151#52511yescharacteristic
194C2×C151C2×#12611yescharacteristic
195C2×C151#53911yescharacteristic
196C2×C151#54611yescharacteristic
197C2×C151#54811yescharacteristic
198C2×C151#55211yescharacteristic
199C2×C151#55311yescharacteristic
200C151#248111yescharacteristic, direct product factor, Sylow
201#2481C15111yesmaximal, characteristic, direct product factor, Sylow
202C2×#126C2×C15111yescharacteristic, complemented
203C22×C4⋊C4C2×C15111yescharacteristic, complemented
204#400C2×C15111yescharacteristic, complemented
205#400C2×C15111yescharacteristic, complemented
206#397C2×C15111yescharacteristic, complemented
207#396C2×C15111yescharacteristic, complemented
208#388C2×C15111yescharacteristic, complemented
209#387C2×C15111yescharacteristic, complemented
210#387C2×C15111yescharacteristic, complemented
211#386C2×C15111yescharacteristic
212#386C2×C15111yescharacteristic
213#386C2×C15111yescharacteristic
214#385C2×C15111yescharacteristic, complemented
215#380C2×C15111yescharacteristic, complemented
216C4×C22⋊C4C2×C15111yescharacteristic, complemented
217C22×D4C22×C15111yescharacteristic
218C23×C4C22×C15111yescharacteristic
219C23×C4C22×C15111yescharacteristic
220C23×C4C22×C15111yescharacteristic
221#126—24no—
222C2×C4⋊C4—24no—
223C2×C4⋊C4C22×C15111yescharacteristic
224C2×C4⋊C4C22×C15111yescharacteristic
225C2×C4⋊C4C22×C15111yescharacteristic
226C2×C4⋊C4C22×C15111yescharacteristic
227C2×C4⋊C4C22×C15111yescharacteristic
228C2×C4⋊C4C22×C15111yescharacteristic
229C2×C4⋊C4C22×C15111yescharacteristic
230C2×C4⋊C4C22×C15111yescharacteristic
231C2×C22⋊C4C22×C15111yescharacteristic
232C2×C22⋊C4C22×C15111yescharacteristic
233C2×C22⋊C4C22×C15111yescharacteristic
234C2×C22⋊C4C22×C15111yescharacteristic
235C2×C22⋊C4C22×C15111yescharacteristic
236C2×C22⋊C4C22×C15111yescharacteristic
237C2×C22⋊C4C22×C15111yescharacteristic
238C2×C22⋊C4C22×C15111yescharacteristic
239C2×C22⋊C4C22×C15111yescharacteristic
240C2×C42C22×C15111yescharacteristic
241C2×C42C22×C15111yescharacteristic
242#95C22×C15111yescharacteristic
243#95C22×C15111yescharacteristic
244#95C22×C15111yescharacteristic
245#95C22×C15111yescharacteristic
246#95C22×C15111yescharacteristic
247#95C22×C15111yescharacteristic
248#95C22×C15111yescharacteristic
249#95C22×C15111yescharacteristic
250#95C22×C15111yescharacteristic
251#95C22×C15111yescharacteristic
252#95C22×C15111yescharacteristic
253#95C22×C15111yescharacteristic
254C24C23×C15111yescharacteristic
255C24C23×C15111yescharacteristic
256C2×D4—22no—
257C2×D4—22no—
258C2×D4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4C23×C15111yescharacteristic
269C22×C4C23×C15111yescharacteristic
270C22×C4C23×C15111yescharacteristic
271C22×C4C23×C15111yescharacteristic
272C22×C4C23×C15111yescharacteristic
273C22×C4C23×C15111yescharacteristic
274C22×C4C23×C15111yescharacteristic
275C22×C4C23×C15111yescharacteristic
276C22×C4C23×C15111yescharacteristic
277C22×C4C23×C15111yescharacteristic
278C22×C4C23×C15111yescharacteristic
279C22×C4C23×C15111yescharacteristic
280C22×C4C23×C15111yescharacteristic
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—41no—
288C4⋊C4D4×C15114yescomplemented
289C22⋊C4—22no—
290C22⋊C4—22no—
291C22⋊C4—22no—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C22⋊C4—22no—
295C22⋊C4—22no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C42—22no—
299C42—41no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23#41×C15112yes—
312C23#41×C15112yes—
313C23#41×C15112yes—
314C23C24×C15111yescharacteristic
315D4—44no—
316C2×C4—28no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4C2×D4×C15112yes—
355C2×C4C2×D4×C15112yes—
356C2×C4C2×D4×C15112yes—
357C2×C4#41×C15112yes—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22#126×C15114yescomplemented
372C22C22×D4×C15111yescharacteristic
373C22C2×#41×C15111yescharacteristic
374C22C2×#41×C15111yescharacteristic
375C22C2×#41×C15111yescharacteristic
376C22C2×#41×C15111yescharacteristic
377C22H(5,𝔽2)×C15111yescharacteristic
378C222−1+4×C15111yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—22no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—41no—
392C2—24no—
393C2—81no—
394C2#525×C15111yescharacteristic
395C2C2×#126×C15111yescharacteristic
396C2#539×C15111yescharacteristic
397C2#546×C15111yescharacteristic
398C2#548×C15111yescharacteristic
399C2#552×C15111yescharacteristic
400C2#553×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C24
commutator, Frattini, cosocleC23C24×C151
prime radicalC22×D4×C151C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#126×C151C2semidirect
2. C22×C4⋊C4×C151C2semidirect
3. #400×C151C2semidirect
4. #400×C151C2semidirect
5. #397×C151C2semidirect
6. #396×C151C2semidirect
7. #388×C151C2semidirect
8. #387×C151C2semidirect
9. #387×C151C2semidirect
13. #385×C151C2semidirect
14. #380×C151C2semidirect
15. C4×C22⋊C4×C151C2semidirect
87. C4⋊C4×C151D4semidirect
170. C22×C151#126semidirect
200. C151#2481direct (N × H)
201. #2481C151direct (N × H)
202. C2×#126C2×C151semidirect
203. C22×C4⋊C4C2×C151semidirect
204. #400C2×C151semidirect
205. #400C2×C151semidirect
206. #397C2×C151semidirect
207. #396C2×C151semidirect
208. #388C2×C151semidirect
209. #387C2×C151semidirect
210. #387C2×C151semidirect
214. #385C2×C151semidirect
215. #380C2×C151semidirect
216. C4×C22⋊C4C2×C151semidirect
288. C4⋊C4D4×C151semidirect
371. C22#126×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#126×C1512
C22×C4⋊C4×C1512
#400×C1512
#397×C1512
#396×C1512
#388×C1512
#387×C1512
#386×C1512
#385×C1512
#380×C1512
C4×C22⋊C4×C1512
#2481151