Finite Group Databasebeta

← C2×#1344×C151 #50316615

Subgroups — C2×#1344×C151 #50316615

Order 38656.

668 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C151C211yesmaximal, characteristic
2C2×#342×C151C211yesmaximal, characteristic
3C2×#323×C151C211yesmaximal, characteristic
4#1344×C151C214yesmaximal, direct product factor
5C22×C4⋊C4×C151C411yescharacteristic, complemented
6C22×C22⋊C4×C151—21no—
7C22×C22⋊C4×C151—21no—
8C22×C22⋊C4×C151C2211yescharacteristic
9C2×C22⋊C8×C151—21no—
10#397×C151—21no—
11#397×C151—21no—
12#397×C151C412yescomplemented
13#397×C151C2212yes—
14C2×#95×C151—21no—
15C2×#95×C151C411yescharacteristic, complemented
16#342×C151—21no—
17#342×C151C2212yes—
18#323×C151—21no—
19#323×C151C2212yes—
20C25×C151D411yescharacteristic
21C23×C4×C151—21no—
22C23×C4×C151—21no—
23C23×C4×C151—41no—
24C23×C4×C151C2×C411yescharacteristic
25C23×C4×C151D411yescharacteristic
26C22×C8×C151—41no—
27C2×C4⋊C4×C151—21no—
28C2×C4⋊C4×C151—41no—
29C2×C4⋊C4×C151—41no—
30C2×C4⋊C4×C151C2×C412yescomplemented
31C2×C22⋊C4×C151—24no—
32C2×C22⋊C4×C151—22no—
33C2×C22⋊C4×C151—22no—
34C2×C22⋊C4×C151—22no—
35C2×C22⋊C4×C151—41no—
36C2×C22⋊C4×C151—41no—
37C2×C22⋊C4×C151—41no—
38C2×C22⋊C4×C151—42no—
39C2×C22⋊C4×C151—42no—
40C2×C22⋊C4×C151—42no—
41C2×C22⋊C4×C151C2×C411yescharacteristic
42C2×C22⋊C4×C151D411yescharacteristic
43C2×C22⋊C4×C151D411yescharacteristic
44C2×C22⋊C4×C151C2311yescharacteristic
45C22⋊C8×C151—22no—
46C22⋊C8×C151—41no—
47#95×C151—22no—
48#95×C151—21no—
49#95×C151—22no—
50#95×C151C2×C412yescomplemented
51C24×C151—21no—
52C24×C151—21no—
53C24×C151—22no—
54C24×C151—42no—
55C24×C151—42no—
56C24×C151C22⋊C411yescharacteristic
57C24×C151C22⋊C411yescharacteristic
58C24×C151D812yes—
59C24×C151SD1612yes—
60C24×C151C2×D411yescharacteristic
61C22×C4×C151—21no—
62C22×C4×C151—21no—
63C22×C4×C151—21no—
64C22×C4×C151—21no—
65C22×C4×C151—22no—
66C22×C4×C151—22no—
67C22×C4×C151—42no—
68C22×C4×C151—42no—
69C22×C4×C151—44no—
70C22×C4×C151—42no—
71C22×C4×C151—42no—
72C22×C4×C151—42no—
73C22×C4×C151—41no—
74C22×C4×C151—41no—
75C22×C4×C151—42no—
76C22×C4×C151—42no—
77C22×C4×C151—42no—
78C22×C4×C151—82no—
79C22×C4×C151—82no—
80C22×C4×C151C22⋊C411yescharacteristic
81C22×C4×C151C22⋊C411yescharacteristic
82C22×C4×C151C22×C411yescharacteristic
83C22×C4×C151C2×D411yescharacteristic
84C2×C8×C151—42no—
85C2×C8×C151—82no—
86C4⋊C4×C151—42no—
87C4⋊C4×C151—42no—
88C22⋊C4×C151—24no—
89C22⋊C4×C151—41no—
90C22⋊C4×C151—41no—
91C22⋊C4×C151—41no—
92C22⋊C4×C151—41no—
93C22⋊C4×C151—44no—
94C22⋊C4×C151—44no—
95C22⋊C4×C151—42no—
96C22⋊C4×C151—42no—
97C22⋊C4×C151—42no—
98C23×C151—22no—
99C23×C151—22no—
100C23×C151—22no—
101C23×C151—22no—
102C23×C151—21no—
103C23×C151—21no—
104C23×C151—22no—
105C23×C151—22no—
106C23×C151—21no—
107C23×C151—21no—
108C23×C151—41no—
109C23×C151—41no—
110C23×C151—44no—
111C23×C151—44no—
112C23×C151—41no—
113C23×C151—41no—
114C23×C151—42no—
115C23×C151—42no—
116C23×C151—84no—
117C23×C151—81no—
118C23×C151—81no—
119C23×C151#9911yescharacteristic
120C23×C151#9911yescharacteristic
121C23×C151#10212yes—
122C23×C151#10212yes—
123C23×C151#10412yes—
124C23×C151C2×C22⋊C411yescharacteristic
125C23×C151C2×D811yescharacteristic
126C23×C151C2×SD1611yescharacteristic
127C2×C4×C151—21no—
128C2×C4×C151—21no—
129C2×C4×C151—21no—
130C2×C4×C151—21no—
131C2×C4×C151—42no—
132C2×C4×C151—42no—
133C2×C4×C151—42no—
134C2×C4×C151—41no—
135C2×C4×C151—41no—
136C2×C4×C151—41no—
137C2×C4×C151—41no—
138C2×C4×C151—44no—
139C2×C4×C151—42no—
140C2×C4×C151—42no—
141C2×C4×C151—42no—
142C2×C4×C151—42no—
143C2×C4×C151—42no—
144C2×C4×C151—42no—
145C2×C4×C151—81no—
146C2×C4×C151—84no—
147C2×C4×C151—88no—
148C2×C4×C151—82no—
149C2×C4×C151—82no—
150C2×C4×C151—82no—
151C2×C4×C151—82no—
152C8×C151—82no—
153C22×C151—24no—
154C22×C151—24no—
155C22×C151—21no—
156C22×C151—21no—
157C22×C151—21no—
158C22×C151—21no—
159C22×C151—21no—
160C22×C151—22no—
161C22×C151—21no—
162C22×C151—42no—
163C22×C151—41no—
164C22×C151—41no—
165C22×C151—44no—
166C22×C151—44no—
167C22×C151—41no—
168C22×C151—41no—
169C22×C151—41no—
170C22×C151—41no—
171C22×C151—82no—
172C22×C151—82no—
173C22×C151—81no—
174C22×C151—81no—
175C22×C151#32712yes—
176C22×C151#32712yes—
177C22×C151#35212yes—
178C22×C151#35412yes—
179C22×C151C2×#9911yescharacteristic
180C22×C151C2×#10211yescharacteristic
181C22×C151C2×#10411yescharacteristic
182C4×C151—41no—
183C4×C151—41no—
184C4×C151—41no—
185C4×C151—41no—
186C4×C151—82no—
187C4×C151—84no—
188C4×C151—82no—
189C2×C151—21no—
190C2×C151—22no—
191C2×C151—21no—
192C2×C151—41no—
193C2×C151—42no—
194C2×C151—41no—
195C2×C151#134414yesdirect product factor
196C2×C151C2×#32711yescharacteristic
197C2×C151C2×#35211yescharacteristic
198C2×C151C2×#35411yescharacteristic
199C2×#1344C15111yesmaximal, characteristic, direct product factor, Sylow
200C151C2×#134411yescharacteristic, direct product factor, Sylow
201C2×#397C2×C15111yescharacteristic
202C2×#342C2×C15111yescharacteristic
203C2×#323C2×C15111yescharacteristic
204#1344C2×C15114yesdirect product factor
205C22×C4⋊C4C4×C15111yescharacteristic, complemented
206C22×C22⋊C4—21no—
207C22×C22⋊C4—21no—
208C22×C22⋊C4C22×C15111yescharacteristic
209C2×C22⋊C8—21no—
210#397—21no—
211#397—21no—
212#397C4×C15112yescomplemented
213#397C22×C15112yes—
214C2×#95—21no—
215C2×#95C4×C15111yescharacteristic, complemented
216#342—21no—
217#342C22×C15112yes—
218#323—21no—
219#323C22×C15112yes—
220C25D4×C15111yescharacteristic
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—41no—
224C23×C4C2×C4×C15111yescharacteristic
225C23×C4D4×C15111yescharacteristic
226C22×C8—41no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—41no—
229C2×C4⋊C4—41no—
230C2×C4⋊C4C2×C4×C15112yescomplemented
231C2×C22⋊C4—24no—
232C2×C22⋊C4—22no—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—41no—
236C2×C22⋊C4—41no—
237C2×C22⋊C4—41no—
238C2×C22⋊C4—42no—
239C2×C22⋊C4—42no—
240C2×C22⋊C4—42no—
241C2×C22⋊C4C2×C4×C15111yescharacteristic
242C2×C22⋊C4D4×C15111yescharacteristic
243C2×C22⋊C4D4×C15111yescharacteristic
244C2×C22⋊C4C23×C15111yescharacteristic
245C22⋊C8—22no—
246C22⋊C8—41no—
247#95—22no—
248#95—21no—
249#95—22no—
250#95C2×C4×C15112yescomplemented
251C24—21no—
252C24—21no—
253C24—22no—
254C24—42no—
255C24—42no—
256C24C22⋊C4×C15111yescharacteristic
257C24C22⋊C4×C15111yescharacteristic
258C24D8×C15112yes—
259C24SD16×C15112yes—
260C24C2×D4×C15111yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—44no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—82no—
279C22×C4—82no—
280C22×C4C22⋊C4×C15111yescharacteristic
281C22×C4C22⋊C4×C15111yescharacteristic
282C22×C4C22×C4×C15111yescharacteristic
283C22×C4C2×D4×C15111yescharacteristic
284C2×C8—42no—
285C2×C8—82no—
286C4⋊C4—42no—
287C4⋊C4—42no—
288C22⋊C4—24no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—44no—
294C22⋊C4—44no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—42no—
298C23—22no—
299C23—22no—
300C23—21no—
301C23—21no—
302C23—22no—
303C23—22no—
304C23—21no—
305C23—21no—
306C23—22no—
307C23—22no—
308C23—41no—
309C23—41no—
310C23—44no—
311C23—44no—
312C23—41no—
313C23—41no—
314C23—42no—
315C23—42no—
316C23—84no—
317C23—81no—
318C23—81no—
319C23#99×C15111yescharacteristic
320C23#99×C15111yescharacteristic
321C23#102×C15112yes—
322C23#102×C15112yes—
323C23#104×C15112yes—
324C23C2×C22⋊C4×C15111yescharacteristic
325C23C2×D8×C15111yescharacteristic
326C23C2×SD16×C15111yescharacteristic
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—44no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—81no—
346C2×C4—84no—
347C2×C4—88no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—82no—
352C8—82no—
353C22—24no—
354C22—24no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—21no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—44no—
366C22—44no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—81no—
372C22—81no—
373C22—82no—
374C22—82no—
375C22#327×C15112yes—
376C22#327×C15112yes—
377C22#352×C15112yes—
378C22#354×C15112yes—
379C22C2×#99×C15111yescharacteristic
380C22C2×#102×C15111yescharacteristic
381C22C2×#104×C15111yescharacteristic
382C4—41no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—82no—
387C4—84no—
388C4—82no—
389C2—21no—
390C2—21no—
391C2—22no—
392C2—41no—
393C2—42no—
394C2—41no—
395C2#1344×C15114yesdirect product factor
396C2C2×#327×C15111yescharacteristic
397C2C2×#352×C15111yescharacteristic
398C2C2×#354×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#99
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C22⋊C4C23×C151
prime radicalC25×C151D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C24×C151 ◁ C22×C22⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1344×C151C2direct (N × H)
5. C22×C4⋊C4×C151C4semidirect
12. #397×C151C4semidirect
15. C2×#95×C151C4semidirect
30. C2×C4⋊C4×C151C2×C4semidirect
50. #95×C151C2×C4semidirect
195. C2×C151#1344direct (N × H)
199. C2×#1344C151direct (N × H)
200. C151C2×#1344direct (N × H)
204. #1344C2×C151direct (N × H)
205. C22×C4⋊C4C4×C151semidirect
212. #397C4×C151semidirect
215. C2×#95C4×C151semidirect
230. C2×C4⋊C4C2×C4×C151semidirect
250. #95C2×C4×C151semidirect
395. C2#1344×C151direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#397×C1512
C2×#342×C1512
C2×#323×C1512
#1344×C1512
C2×#1344151