Finite Group Databasebeta

← C151×#19223 #50324148

Subgroups — C151×#19223 #50324148

Order 38656.

584 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3248×C151C212yesmaximal
2#3170×C151C211yesmaximal, characteristic, complemented
3#2966×C151C211yesmaximal, characteristic
4#1700×C151C212yesmaximal, complemented
5#1699×C151C212yesmaximal, complemented
6#1674×C151C211yesmaximal, characteristic, complemented
7#1673×C151C211yesmaximal, characteristic, complemented
8#1670×C151C211yesmaximal, characteristic, complemented
9#1669×C151C211yesmaximal, characteristic, complemented
10C2×#335×C151C211yesmaximal, characteristic, complemented
11#1552×C151C212yesmaximal, complemented
12#533×C151C2212yes—
13#529×C151C2211yescharacteristic
14#500×C151C2211yescharacteristic
15#494×C151C2211yescharacteristic
16#487×C151C2212yes—
17#479×C151—22no—
18#475×C151C2212yes—
19#474×C151C2212yes—
20#467×C151—21no—
21#467×C151—21no—
22#467×C151—22no—
23#465×C151—22no—
24#464×C151—22no—
25#462×C151C2212yes—
26#461×C151C2212yes—
27#446×C151C2211yescharacteristic
28C8×Q8×C151C2211yescharacteristic
29C4×Q16×C151—21no—
30C4×Q16×C151—21no—
31#436×C151C2211yescharacteristic
32#435×C151—21no—
33C8×D4×C151—21no—
34C8×D4×C151C2211yescharacteristic
35#433×C151—21no—
36#432×C151C2211yescharacteristic
37C2×C4⋊C8×C151C2212yes—
38#405×C151—21no—
39C2×C4×C8×C151C2211yescharacteristic
40#335×C151C2211yescharacteristic
41#335×C151C2211yescharacteristic
42#335×C151C2212yes—
43#332×C151C2212yes—
44#332×C151C2212yes—
45#332×C151C2212yes—
46#332×C151C2212yes—
47C2×Q16×C151—21no—
48C2×Q16×C151—21no—
49C2×Q16×C151—22no—
50C2×SD16×C151—22no—
51C2×M16×C151—21no—
52C22×C8×C151—22no—
53C22×C8×C151—21no—
54C22×C8×C151D411yescharacteristic
55C22×C8×C151D411yescharacteristic
56C4⋊Q8×C151C2312yes—
57C4⋊Q8×C151C2312yes—
58#126×C151—21no—
59#125×C151—22no—
60#125×C151D411yescharacteristic
61#124×C151D411yescharacteristic
62#123×C151—21no—
63C22⋊Q8×C151—22no—
64C22⋊Q8×C151—22no—
65C22⋊Q8×C151D411yescharacteristic
66#121×C151D411yescharacteristic
67C4×Q8×C151—22no—
68C4×Q8×C151—22no—
69C4×Q8×C151C2311yescharacteristic
70C4×D4×C151—21no—
71C4×D4×C151C2311yescharacteristic
72#117×C151—21no—
73#117×C151—22no—
74C2×C42×C151C2311yescharacteristic
75#107×C151—21no—
76#107×C151—21no—
77#107×C151—22no—
78#106×C151—22no—
79C4⋊C8×C151—21no—
80C4⋊C8×C151—21no—
81C4⋊C8×C151—22no—
82C4⋊C8×C151C2312yes—
83C4⋊C8×C151C2312yes—
84C4⋊C8×C151C2311yescharacteristic
85C4⋊C8×C151C2311yescharacteristic
86#103×C151—22no—
87#103×C151—22no—
88#103×C151—22no—
89#103×C151—22no—
90#103×C151—22no—
91#102×C151—22no—
92C22⋊C8×C151—21no—
93C22⋊C8×C151—21no—
94C22⋊C8×C151—21no—
95#97×C151—21no—
96#97×C151—21no—
97C4×C8×C151—21no—
98C4×C8×C151D411yescharacteristic
99C4×C8×C151D411yescharacteristic
100C4×C8×C151C2311yescharacteristic
101C4×C8×C151C2311yescharacteristic
102C2×Q8×C151—22no—
103C2×Q8×C151—22no—
104C2×Q8×C151C2×D411yescharacteristic
105C2×D4×C151—21no—
106C2×D4×C151C2×D411yescharacteristic
107C22×C4×C151—21no—
108C22×C4×C151C2×D411yescharacteristic
109C22×C4×C151C2×D411yescharacteristic
110C22×C4×C151#4111yescharacteristic
111Q16×C151—42no—
112Q16×C151—42no—
113Q16×C151—82no—
114SD16×C151—82no—
115M16×C151—42no—
116C2×C8×C151—22no—
117C2×C8×C151—21no—
118C2×C8×C151—21no—
119C2×C8×C151—22no—
120C2×C8×C151—22no—
121C2×C8×C151—41no—
122C2×C8×C151—42no—
123C2×C8×C151—82no—
124C2×C8×C151C2×D411yescharacteristic
125C2×C8×C151C2×D411yescharacteristic
126C2×C8×C151C2×D411yescharacteristic
127C2×C8×C151C2×D411yescharacteristic
128C4⋊C4×C151—21no—
129C4⋊C4×C151—21no—
130C4⋊C4×C151—21no—
131C4⋊C4×C151—21no—
132C4⋊C4×C151—22no—
133C4⋊C4×C151—22no—
134C4⋊C4×C151—22no—
135C4⋊C4×C151—22no—
136C4⋊C4×C151—42no—
137C4⋊C4×C151—42no—
138C4⋊C4×C151C2×D411yescharacteristic
139C4⋊C4×C151C2×D411yescharacteristic
140C22⋊C4×C151—21no—
141C22⋊C4×C151—21no—
142C22⋊C4×C151—21no—
143C22⋊C4×C151—21no—
144C22⋊C4×C151—21no—
145C22⋊C4×C151—42no—
146C42×C151—21no—
147C42×C151—42no—
148C42×C151C2×D411yescharacteristic
149C42×C151C2×D411yescharacteristic
150C42×C151#4111yescharacteristic
151C42×C151C2411yescharacteristic
152C23×C151—21no—
153C23×C151#12111yescharacteristic
154Q8×C151—21no—
155Q8×C151—21no—
156Q8×C151—42no—
157Q8×C151—42no—
158Q8×C151—42no—
159Q8×C151—42no—
160D4×C151—21no—
161D4×C151—21no—
162D4×C151—42no—
163C2×C4×C151—22no—
164C2×C4×C151—21no—
165C2×C4×C151—21no—
166C2×C4×C151—21no—
167C2×C4×C151—21no—
168C2×C4×C151—21no—
169C2×C4×C151—21no—
170C2×C4×C151—21no—
171C2×C4×C151—41no—
172C2×C4×C151—41no—
173C2×C4×C151—42no—
174C2×C4×C151—42no—
175C2×C4×C151#12111yescharacteristic
176C2×C4×C151#12111yescharacteristic
177C2×C4×C151#12111yescharacteristic
178C2×C4×C151C22×D411yescharacteristic
179C2×C4×C151C22×D411yescharacteristic
180C2×C4×C151C2×#4111yescharacteristic
181C8×C151—21no—
182C8×C151—21no—
183C8×C151—21no—
184C8×C151—41no—
185C8×C151—41no—
186C8×C151—42no—
187C8×C151—42no—
188C8×C151#13512yes—
189C22×C151—21no—
190C22×C151—21no—
191C22×C151—41no—
192C22×C151—41no—
193C22×C151—41no—
194C22×C151#47312yes—
195C22×C151C2×#12111yescharacteristic
196C4×C151—21no—
197C4×C151—21no—
198C4×C151—21no—
199C4×C151—21no—
200C4×C151—41no—
201C4×C151—41no—
202C4×C151—41no—
203C4×C151—82no—
204C4×C151—82no—
205C4×C151C2×#13511yescharacteristic
206C4×C151#57511yescharacteristic
207C4×C151#57611yescharacteristic
208C4×C151#57811yescharacteristic
209C2×C151—22no—
210C2×C151—81no—
211C2×C151#303511yescharacteristic
212C2×C151#306111yescharacteristic
213C2×C151C2×#47311yescharacteristic
214#19223C15111yesmaximal, characteristic, direct product factor, Sylow
215C151#1922311yescharacteristic, direct product factor, Sylow
216#3248C2×C15112yes—
217#3170C2×C15111yescharacteristic, complemented
218#2966C2×C15111yescharacteristic
219#1700C2×C15112yescomplemented
220#1699C2×C15112yescomplemented
221#1674C2×C15111yescharacteristic, complemented
222#1673C2×C15111yescharacteristic, complemented
223#1670C2×C15111yescharacteristic, complemented
224#1669C2×C15111yescharacteristic, complemented
225C2×#335C2×C15111yescharacteristic, complemented
226#1552C2×C15112yescomplemented
227#533C22×C15112yes—
228#529C22×C15111yescharacteristic
229#500C22×C15111yescharacteristic
230#494C22×C15111yescharacteristic
231#487C22×C15112yes—
232#479—22no—
233#475C22×C15112yes—
234#474C22×C15112yes—
235#467—21no—
236#467—21no—
237#467—22no—
238#465—22no—
239#464—22no—
240#462C22×C15112yes—
241#461C22×C15112yes—
242#446C22×C15111yescharacteristic
243C8×Q8C22×C15111yescharacteristic
244C4×Q16—21no—
245C4×Q16—21no—
246#436C22×C15111yescharacteristic
247#435—21no—
248C8×D4—21no—
249C8×D4C22×C15111yescharacteristic
250#433—21no—
251#432C22×C15111yescharacteristic
252C2×C4⋊C8C22×C15112yes—
253#405—21no—
254C2×C4×C8C22×C15111yescharacteristic
255#335C22×C15111yescharacteristic
256#335C22×C15111yescharacteristic
257#335C22×C15112yes—
258#332C22×C15112yes—
259#332C22×C15112yes—
260#332C22×C15112yes—
261#332C22×C15112yes—
262C2×Q16—22no—
263C2×Q16—21no—
264C2×Q16—21no—
265C2×SD16—22no—
266C2×M16—21no—
267C22×C8—22no—
268C22×C8—21no—
269C22×C8D4×C15111yescharacteristic
270C22×C8D4×C15111yescharacteristic
271C4⋊Q8C23×C15112yes—
272C4⋊Q8C23×C15112yes—
273#126—21no—
274#125—22no—
275#125D4×C15111yescharacteristic
276#124D4×C15111yescharacteristic
277#123—21no—
278C22⋊Q8—22no—
279C22⋊Q8—22no—
280C22⋊Q8D4×C15111yescharacteristic
281#121D4×C15111yescharacteristic
282C4×Q8—22no—
283C4×Q8—22no—
284C4×Q8C23×C15111yescharacteristic
285C4×D4—21no—
286C4×D4C23×C15111yescharacteristic
287#117—21no—
288#117—22no—
289C2×C42C23×C15111yescharacteristic
290#107—21no—
291#107—21no—
292#107—22no—
293#106—22no—
294C4⋊C8—21no—
295C4⋊C8—21no—
296C4⋊C8—22no—
297C4⋊C8C23×C15111yescharacteristic
298C4⋊C8C23×C15111yescharacteristic
299C4⋊C8C23×C15112yes—
300C4⋊C8C23×C15112yes—
301#103—22no—
302#103—22no—
303#103—22no—
304#103—22no—
305#103—22no—
306#102—22no—
307C22⋊C8—21no—
308C22⋊C8—21no—
309C22⋊C8—21no—
310#97—21no—
311#97—21no—
312C4×C8—21no—
313C4×C8D4×C15111yescharacteristic
314C4×C8D4×C15111yescharacteristic
315C4×C8C23×C15111yescharacteristic
316C4×C8C23×C15111yescharacteristic
317C2×Q8—22no—
318C2×Q8—22no—
319C2×Q8C2×D4×C15111yescharacteristic
320C2×D4—21no—
321C2×D4C2×D4×C15111yescharacteristic
322C22×C4—21no—
323C22×C4C2×D4×C15111yescharacteristic
324C22×C4C2×D4×C15111yescharacteristic
325C22×C4#41×C15111yescharacteristic
326Q16—42no—
327Q16—42no—
328Q16—82no—
329SD16—82no—
330M16—42no—
331C2×C8—22no—
332C2×C8—21no—
333C2×C8—21no—
334C2×C8—22no—
335C2×C8—22no—
336C2×C8—41no—
337C2×C8—42no—
338C2×C8—82no—
339C2×C8C2×D4×C15111yescharacteristic
340C2×C8C2×D4×C15111yescharacteristic
341C2×C8C2×D4×C15111yescharacteristic
342C2×C8C2×D4×C15111yescharacteristic
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—42no—
352C4⋊C4—42no—
353C4⋊C4C2×D4×C15111yescharacteristic
354C4⋊C4C2×D4×C15111yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—21no—
357C22⋊C4—21no—
358C22⋊C4—21no—
359C22⋊C4—21no—
360C22⋊C4—42no—
361C42—21no—
362C42—42no—
363C42C2×D4×C15111yescharacteristic
364C42C2×D4×C15111yescharacteristic
365C42#41×C15111yescharacteristic
366C42C24×C15111yescharacteristic
367C23—21no—
368C23#121×C15111yescharacteristic
369Q8—21no—
370Q8—21no—
371Q8—42no—
372Q8—42no—
373Q8—42no—
374Q8—42no—
375D4—21no—
376D4—21no—
377D4—42no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4#121×C15111yescharacteristic
391C2×C4#121×C15111yescharacteristic
392C2×C4#121×C15111yescharacteristic
393C2×C4C22×D4×C15111yescharacteristic
394C2×C4C22×D4×C15111yescharacteristic
395C2×C4C2×#41×C15111yescharacteristic
396C8—21no—
397C8—21no—
398C8—21no—
399C8—41no—
400C8—41no—
401C8—42no—
402C8—42no—
403C8#135×C15112yes—
404C22—21no—
405C22—21no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22#473×C15112yes—
410C22C2×#121×C15111yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—41no—
416C4—41no—
417C4—41no—
418C4—82no—
419C4—82no—
420C4C2×#135×C15111yescharacteristic
421C4#575×C15111yescharacteristic
422C4#576×C15111yescharacteristic
423C4#578×C15111yescharacteristic
424C2—22no—
425C2—81no—
426C2#3035×C15111yescharacteristic
427C2#3061×C15111yescharacteristic
428C2C2×#473×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#121×C151D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3170×C151C2semidirect
4. #1700×C151C2semidirect
5. #1699×C151C2semidirect
6. #1674×C151C2semidirect
7. #1673×C151C2semidirect
8. #1670×C151C2semidirect
9. #1669×C151C2semidirect
10. C2×#335×C151C2semidirect
11. #1552×C151C2semidirect
214. #19223C151direct (N × H)
215. C151#19223direct (N × H)
217. #3170C2×C151semidirect
219. #1700C2×C151semidirect
220. #1699C2×C151semidirect
221. #1674C2×C151semidirect
222. #1673C2×C151semidirect
223. #1670C2×C151semidirect
224. #1669C2×C151semidirect
225. C2×#335C2×C151semidirect
226. #1552C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3248×C1512
#3170×C1512
#2966×C1512
#1700×C1512
#1699×C1512
#1674×C1512
#1673×C1512
#1670×C1512
#1669×C1512
C2×#335×C1512
#1552×C1512
#19223151