Finite Group Databasebeta

← C151×#12794 #50317719

Subgroups — C151×#12794 #50317719

Order 38656.

540 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#123×C151C211yesmaximal, characteristic
2C2×#352×C151C212yesmaximal
3#1800×C151C211yesmaximal, characteristic
4#1799×C151C211yesmaximal, characteristic
5#1390×C151C212yesmaximal
6C2×#123×C151C2211yescharacteristic
7C2×C4×D4×C151C2211yescharacteristic
8C22×C42×C151C411yescharacteristic, complemented
9#423×C151—21no—
10C2×#100×C151C2212yes—
11C2×#99×C151C2212yes—
12#388×C151—21no—
13#387×C151—21no—
14#386×C151C2211yescharacteristic
15#385×C151C411yescharacteristic, complemented
16#381×C151C411yescharacteristic, complemented
17#380×C151—21no—
18C4×C4⋊C4×C151—21no—
19C4×C22⋊C4×C151—21no—
20C4×C22⋊C4×C151C411yescharacteristic, complemented
21#352×C151—24no—
22#343×C151—21no—
23#342×C151—21no—
24C22×D4×C151C2311yescharacteristic
25C23×C4×C151C2×C411yescharacteristic
26C23×C4×C151C2×C411yescharacteristic
27C23×C4×C151C2×C411yescharacteristic
28C23×C4×C151D411yescharacteristic
29C2×M16×C151—22no—
30#123×C151—21no—
31#123×C151—21no—
32#123×C151D412yes—
33#123×C151Q812yes—
34C4×D4×C151—41no—
35C4×D4×C151—41no—
36C2×C4⋊C4×C151—21no—
37C2×C4⋊C4×C151—21no—
38C2×C4⋊C4×C151—41no—
39C2×C4⋊C4×C151D411yescharacteristic
40C2×C22⋊C4×C151—21no—
41C2×C22⋊C4×C151—21no—
42C2×C22⋊C4×C151—22no—
43C2×C22⋊C4×C151C2×C411yescharacteristic
44C2×C22⋊C4×C151C2×C411yescharacteristic
45C2×C22⋊C4×C151C2×C411yescharacteristic
46C2×C22⋊C4×C151D411yescharacteristic
47C2×C42×C151—21no—
48C2×C42×C151—21no—
49C2×C42×C151—21no—
50C2×C42×C151—41no—
51C2×C42×C151—41no—
52C2×C42×C151D411yescharacteristic
53C4⋊C8×C151—41no—
54C4⋊C8×C151—41no—
55#100×C151—22no—
56#100×C151—22no—
57#99×C151—22no—
58#99×C151—22no—
59#95×C151—21no—
60#95×C151—21no—
61#95×C151—21no—
62#95×C151—21no—
63#95×C151—21no—
64#95×C151—41no—
65C24×C151C22×C411yescharacteristic
66C24×C151C2×D411yescharacteristic
67C2×D4×C151—41no—
68C2×D4×C151—41no—
69C2×D4×C151C2×D411yescharacteristic
70C2×D4×C151C2×Q811yescharacteristic
71C2×D4×C151#4111yescharacteristic
72C2×D4×C151#4111yescharacteristic
73C22×C4×C151—21no—
74C22×C4×C151—21no—
75C22×C4×C151—21no—
76C22×C4×C151—21no—
77C22×C4×C151—21no—
78C22×C4×C151—21no—
79C22×C4×C151—21no—
80C22×C4×C151—21no—
81C22×C4×C151—21no—
82C22×C4×C151—42no—
83C22×C4×C151—42no—
84C22×C4×C151—42no—
85C22×C4×C151—41no—
86C22×C4×C151—41no—
87C22×C4×C151—41no—
88C22×C4×C151—42no—
89C22×C4×C151C22⋊C411yescharacteristic
90C22×C4×C151C22⋊C411yescharacteristic
91C22×C4×C151C22⋊C411yescharacteristic
92C22×C4×C151C22⋊C411yescharacteristic
93C22×C4×C151C4⋊C412yescomplemented
94C22×C4×C151C2×D411yescharacteristic
95M16×C151—42no—
96M16×C151—42no—
97C2×C8×C151—42no—
98C4⋊C4×C151—22no—
99C4⋊C4×C151—22no—
100C4⋊C4×C151—41no—
101C4⋊C4×C151—42no—
102C4⋊C4×C151—82no—
103C22⋊C4×C151—21no—
104C22⋊C4×C151—22no—
105C22⋊C4×C151—22no—
106C22⋊C4×C151—41no—
107C22⋊C4×C151—41no—
108C22⋊C4×C151—42no—
109C22⋊C4×C151—41no—
110C22⋊C4×C151—42no—
111C22⋊C4×C151—42no—
112C22⋊C4×C151C4⋊C412yescomplemented
113C42×C151—21no—
114C42×C151—21no—
115C42×C151—42no—
116C42×C151—42no—
117C42×C151—41no—
118C42×C151—41no—
119C23×C151—21no—
120C23×C151—21no—
121C23×C151—21no—
122C23×C151—21no—
123C23×C151—41no—
124C23×C151—41no—
125C23×C151—41no—
126C23×C151—41no—
127C23×C151C2×C22⋊C411yescharacteristic
128C23×C151C2×C4⋊C411yescharacteristic
129C23×C151#11711yescharacteristic
130C23×C151#12111yescharacteristic
131C23×C151C22⋊Q811yescharacteristic
132D4×C151—41no—
133D4×C151—41no—
134D4×C151—41no—
135D4×C151—41no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—22no—
139C2×C4×C151—22no—
140C2×C4×C151—22no—
141C2×C4×C151—22no—
142C2×C4×C151—21no—
143C2×C4×C151—21no—
144C2×C4×C151—21no—
145C2×C4×C151—42no—
146C2×C4×C151—41no—
147C2×C4×C151—41no—
148C2×C4×C151—42no—
149C2×C4×C151—41no—
150C2×C4×C151—42no—
151C2×C4×C151—41no—
152C2×C4×C151—41no—
153C2×C4×C151—41no—
154C2×C4×C151—42no—
155C2×C4×C151—42no—
156C2×C4×C151—41no—
157C2×C4×C151—41no—
158C2×C4×C151—41no—
159C2×C4×C151—42no—
160C2×C4×C151—42no—
161C2×C4×C151—41no—
162C2×C4×C151—41no—
163C2×C4×C151—41no—
164C2×C4×C151—81no—
165C2×C4×C151—82no—
166C2×C4×C151—82no—
167C2×C4×C151—82no—
168C2×C4×C151#9911yescharacteristic
169C2×C4×C151#9911yescharacteristic
170C2×C4×C151#12111yescharacteristic
171C2×C4×C151C22⋊Q811yescharacteristic
172C8×C151—82no—
173C22×C151—21no—
174C22×C151—21no—
175C22×C151—21no—
176C22×C151—21no—
177C22×C151—21no—
178C22×C151—21no—
179C22×C151—41no—
180C22×C151—41no—
181C22×C151—41no—
182C22×C151—41no—
183C22×C151—42no—
184C22×C151—41no—
185C22×C151—41no—
186C22×C151—41no—
187C22×C151—41no—
188C22×C151—81no—
189C22×C151#38011yescharacteristic
190C22×C151C2×#9911yescharacteristic
191C22×C151#41011yescharacteristic
192C4×C151—21no—
193C4×C151—21no—
194C4×C151—21no—
195C4×C151—42no—
196C4×C151—42no—
197C4×C151—41no—
198C4×C151—41no—
199C4×C151—41no—
200C4×C151—42no—
201C4×C151—81no—
202C4×C151—162no—
203C4×C151#35212yescomplemented
204C2×C151—21no—
205C2×C151—21no—
206C2×C151—41no—
207C2×C151—41no—
208C2×C151—41no—
209C2×C151—41no—
210C2×C151#179911yescharacteristic
211C2×C151C2×#35211yescharacteristic
212C2×C151#212011yescharacteristic
213#12794C15111yesmaximal, characteristic, direct product factor, Sylow
214C151#1279411yescharacteristic, direct product factor, Sylow
215C4×#123C2×C15111yescharacteristic
216C2×#352C2×C15112yes—
217#1800C2×C15111yescharacteristic
218#1799C2×C15111yescharacteristic
219#1390C2×C15112yes—
220C2×#123C22×C15111yescharacteristic
221C2×C4×D4C22×C15111yescharacteristic
222C22×C42C4×C15111yescharacteristic, complemented
223#423—21no—
224C2×#100C22×C15112yes—
225C2×#99C22×C15112yes—
226#388—21no—
227#387—21no—
228#386C22×C15111yescharacteristic
229#385C4×C15111yescharacteristic, complemented
230#381C4×C15111yescharacteristic, complemented
231#380—21no—
232C4×C4⋊C4—21no—
233C4×C22⋊C4—21no—
234C4×C22⋊C4C4×C15111yescharacteristic, complemented
235#352—24no—
236#343—21no—
237#342—21no—
238C22×D4C23×C15111yescharacteristic
239C23×C4C2×C4×C15111yescharacteristic
240C23×C4C2×C4×C15111yescharacteristic
241C23×C4C2×C4×C15111yescharacteristic
242C23×C4D4×C15111yescharacteristic
243C2×M16—22no—
244#123—21no—
245#123—21no—
246#123D4×C15112yes—
247#123Q8×C15112yes—
248C4×D4—41no—
249C4×D4—41no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—41no—
253C2×C4⋊C4D4×C15111yescharacteristic
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—22no—
257C2×C22⋊C4C2×C4×C15111yescharacteristic
258C2×C22⋊C4C2×C4×C15111yescharacteristic
259C2×C22⋊C4C2×C4×C15111yescharacteristic
260C2×C22⋊C4D4×C15111yescharacteristic
261C2×C42—21no—
262C2×C42—21no—
263C2×C42—21no—
264C2×C42—41no—
265C2×C42—41no—
266C2×C42D4×C15111yescharacteristic
267C4⋊C8—41no—
268C4⋊C8—41no—
269#100—22no—
270#100—22no—
271#99—22no—
272#99—22no—
273#95—21no—
274#95—21no—
275#95—21no—
276#95—21no—
277#95—21no—
278#95—41no—
279C24C22×C4×C15111yescharacteristic
280C24C2×D4×C15111yescharacteristic
281C2×D4—41no—
282C2×D4—41no—
283C2×D4C2×D4×C15111yescharacteristic
284C2×D4C2×Q8×C15111yescharacteristic
285C2×D4#41×C15111yescharacteristic
286C2×D4#41×C15111yescharacteristic
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—42no—
303C22×C4C22⋊C4×C15111yescharacteristic
304C22×C4C22⋊C4×C15111yescharacteristic
305C22×C4C22⋊C4×C15111yescharacteristic
306C22×C4C22⋊C4×C15111yescharacteristic
307C22×C4C4⋊C4×C15112yescomplemented
308C22×C4C2×D4×C15111yescharacteristic
309M16—42no—
310M16—42no—
311C2×C8—42no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—42no—
316C4⋊C4—82no—
317C22⋊C4—21no—
318C22⋊C4—22no—
319C22⋊C4—22no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—42no—
323C22⋊C4—41no—
324C22⋊C4—42no—
325C22⋊C4—42no—
326C22⋊C4C4⋊C4×C15112yescomplemented
327C42—21no—
328C42—21no—
329C42—42no—
330C42—42no—
331C42—41no—
332C42—41no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23C2×C22⋊C4×C15111yescharacteristic
342C23C2×C4⋊C4×C15111yescharacteristic
343C23#117×C15111yescharacteristic
344C23#121×C15111yescharacteristic
345C23C22⋊Q8×C15111yescharacteristic
346D4—41no—
347D4—41no—
348D4—41no—
349D4—41no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—81no—
379C2×C4—82no—
380C2×C4—82no—
381C2×C4—82no—
382C2×C4#99×C15111yescharacteristic
383C2×C4#99×C15111yescharacteristic
384C2×C4#121×C15111yescharacteristic
385C2×C4C22⋊Q8×C15111yescharacteristic
386C8—82no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—42no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—81no—
403C22#380×C15111yescharacteristic
404C22C2×#99×C15111yescharacteristic
405C22#410×C15111yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—42no—
410C4—41no—
411C4—41no—
412C4—42no—
413C4—41no—
414C4—42no—
415C4—81no—
416C4—162no—
417C4#352×C15112yescomplemented
418C2—21no—
419C2—21no—
420C2—41no—
421C2—41no—
422C2—41no—
423C2—41no—
424C2#1799×C15111yescharacteristic
425C2C2×#352×C15111yescharacteristic
426C2#2120×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#99
commutatorC24C22×C4×C151
Frattini, cosocleC22×D4C23×C151
prime radicalC22×D4×C151C23
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
8. C22×C42×C151C4semidirect
15. #385×C151C4semidirect
16. #381×C151C4semidirect
20. C4×C22⋊C4×C151C4semidirect
93. C22×C4×C151C4⋊C4semidirect
112. C22⋊C4×C151C4⋊C4semidirect
203. C4×C151#352semidirect
213. #12794C151direct (N × H)
214. C151#12794direct (N × H)
222. C22×C42C4×C151semidirect
229. #385C4×C151semidirect
230. #381C4×C151semidirect
234. C4×C22⋊C4C4×C151semidirect
307. C22×C4C4⋊C4×C151semidirect
326. C22⋊C4C4⋊C4×C151semidirect
417. C4#352×C151semidirect

Maximal subgroups

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

subgroupindex
C4×#123×C1512
C2×#352×C1512
#1800×C1512
#1799×C1512
#1390×C1512
#12794151