Finite Group Databasebeta

← C151×#19220 #50324145

Subgroups — C151×#19220 #50324145

Order 38656.

562 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3233×C151C212yesmaximal
2#3170×C151C211yesmaximal, characteristic, complemented
3#2966×C151C211yesmaximal, characteristic
4#1704×C151C212yesmaximal, complemented
5#1703×C151C212yesmaximal, complemented
6#1676×C151C211yesmaximal, characteristic, complemented
7#1675×C151C211yesmaximal, characteristic, complemented
8#1670×C151C211yesmaximal, characteristic, complemented
9#1669×C151C211yesmaximal, characteristic, complemented
10#1564×C151C211yesmaximal, characteristic, complemented
11#1554×C151C212yesmaximal, complemented
12#533×C151C2212yes—
13#529×C151C2211yescharacteristic
14#500×C151C2211yescharacteristic
15#499×C151—22no—
16#494×C151C2211yescharacteristic
17#488×C151—22no—
18#487×C151C2212yes—
19#485×C151—22no—
20#482×C151—22no—
21#477×C151C2212yes—
22#476×C151C2212yes—
23#475×C151C2212yes—
24#474×C151C2212yes—
25#467×C151—21no—
26#467×C151—21no—
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
37#431×C151C2212yes—
38#405×C151—21no—
39C2×C4×C8×C151C2211yescharacteristic
40#335×C151C2211yescharacteristic
41#335×C151C2211yescharacteristic
42#334×C151C2212yes—
43#333×C151C2212yes—
44#333×C151C2212yes—
45#332×C151C2212yes—
46#332×C151C2212yes—
47C2×Q16×C151—21no—
48C2×Q16×C151—21no—
49C2×M16×C151—21no—
50C22×C8×C151—21no—
51C22×C8×C151D411yescharacteristic
52C22×C8×C151D411yescharacteristic
53C4⋊Q8×C151C2312yes—
54C4⋊Q8×C151C2312yes—
55#126×C151—21no—
56#125×C151—22no—
57#125×C151D411yescharacteristic
58#124×C151D411yescharacteristic
59#123×C151—21no—
60C22⋊Q8×C151—22no—
61C22⋊Q8×C151—22no—
62C22⋊Q8×C151D411yescharacteristic
63#121×C151D411yescharacteristic
64C4×Q8×C151—22no—
65C4×Q8×C151—22no—
66C4×Q8×C151C2311yescharacteristic
67C4×D4×C151—21no—
68C4×D4×C151C2311yescharacteristic
69#117×C151—21no—
70#117×C151—22no—
71C2×C42×C151C2311yescharacteristic
72#107×C151—21no—
73#107×C151—21no—
74#107×C151—22no—
75#107×C151—22no—
76#106×C151—22no—
77#106×C151—22no—
78C4⋊C8×C151—21no—
79C4⋊C8×C151—21no—
80C4⋊C8×C151C2312yes—
81C4⋊C8×C151C2312yes—
82C4⋊C8×C151C2311yescharacteristic
83C4⋊C8×C151C2311yescharacteristic
84#103×C151—22no—
85#103×C151—22no—
86#103×C151—22no—
87#103×C151—22no—
88#102×C151—22no—
89#102×C151—22no—
90C22⋊C8×C151—22no—
91C22⋊C8×C151—21no—
92C22⋊C8×C151—21no—
93C22⋊C8×C151—21no—
94#97×C151—21no—
95#97×C151—21no—
96C4×C8×C151—21no—
97C4×C8×C151—22no—
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—
113M16×C151—42no—
114C2×C8×C151—22no—
115C2×C8×C151—21no—
116C2×C8×C151—22no—
117C2×C8×C151—22no—
118C2×C8×C151—21no—
119C2×C8×C151—41no—
120C2×C8×C151—42no—
121C2×C8×C151C2×D411yescharacteristic
122C2×C8×C151C2×D411yescharacteristic
123C2×C8×C151C2×D411yescharacteristic
124C2×C8×C151C2×D411yescharacteristic
125C4⋊C4×C151—21no—
126C4⋊C4×C151—21no—
127C4⋊C4×C151—21no—
128C4⋊C4×C151—21no—
129C4⋊C4×C151—22no—
130C4⋊C4×C151—22no—
131C4⋊C4×C151—22no—
132C4⋊C4×C151—22no—
133C4⋊C4×C151—42no—
134C4⋊C4×C151—42no—
135C4⋊C4×C151C2×D411yescharacteristic
136C4⋊C4×C151C2×D411yescharacteristic
137C22⋊C4×C151—21no—
138C22⋊C4×C151—21no—
139C22⋊C4×C151—21no—
140C22⋊C4×C151—21no—
141C22⋊C4×C151—21no—
142C22⋊C4×C151—42no—
143C42×C151—21no—
144C42×C151—42no—
145C42×C151C2×D411yescharacteristic
146C42×C151C2×D411yescharacteristic
147C42×C151#4111yescharacteristic
148C42×C151C2411yescharacteristic
149C23×C151—21no—
150C23×C151#12111yescharacteristic
151Q8×C151—21no—
152Q8×C151—21no—
153Q8×C151—42no—
154Q8×C151—42no—
155Q8×C151—82no—
156D4×C151—21no—
157D4×C151—21no—
158D4×C151—42no—
159C2×C4×C151—21no—
160C2×C4×C151—21no—
161C2×C4×C151—21no—
162C2×C4×C151—21no—
163C2×C4×C151—21no—
164C2×C4×C151—21no—
165C2×C4×C151—21no—
166C2×C4×C151—41no—
167C2×C4×C151—41no—
168C2×C4×C151—41no—
169C2×C4×C151—42no—
170C2×C4×C151—42no—
171C2×C4×C151#12111yescharacteristic
172C2×C4×C151#12111yescharacteristic
173C2×C4×C151#12111yescharacteristic
174C2×C4×C151C22×D411yescharacteristic
175C2×C4×C151C22×D411yescharacteristic
176C2×C4×C151C2×#4111yescharacteristic
177C8×C151—21no—
178C8×C151—21no—
179C8×C151—21no—
180C8×C151—41no—
181C8×C151—41no—
182C8×C151—42no—
183C8×C151—42no—
184C8×C151#13512yes—
185C22×C151—21no—
186C22×C151—21no—
187C22×C151—21no—
188C22×C151—41no—
189C22×C151—41no—
190C22×C151—41no—
191C22×C151C2×#12111yescharacteristic
192C4×C151—21no—
193C4×C151—21no—
194C4×C151—21no—
195C4×C151—21no—
196C4×C151—41no—
197C4×C151—41no—
198C4×C151—41no—
199C4×C151—82no—
200C4×C151—82no—
201C4×C151C2×#13511yescharacteristic
202C4×C151#57511yescharacteristic
203C4×C151#57811yescharacteristic
204C4×C151#57811yescharacteristic
205C2×C151—41no—
206C2×C151—81no—
207C2×C151#303511yescharacteristic
208C2×C151#305911yescharacteristic
209C2×C151#306711yescharacteristic
210#19220C15111yesmaximal, characteristic, direct product factor, Sylow
211C151#1922011yescharacteristic, direct product factor, Sylow
212#3233C2×C15112yes—
213#3170C2×C15111yescharacteristic, complemented
214#2966C2×C15111yescharacteristic
215#1704C2×C15112yescomplemented
216#1703C2×C15112yescomplemented
217#1676C2×C15111yescharacteristic, complemented
218#1675C2×C15111yescharacteristic, complemented
219#1670C2×C15111yescharacteristic, complemented
220#1669C2×C15111yescharacteristic, complemented
221#1564C2×C15111yescharacteristic, complemented
222#1554C2×C15112yescomplemented
223#533C22×C15112yes—
224#529C22×C15111yescharacteristic
225#500C22×C15111yescharacteristic
226#499—22no—
227#494C22×C15111yescharacteristic
228#488—22no—
229#487C22×C15112yes—
230#485—22no—
231#482—22no—
232#477C22×C15112yes—
233#476C22×C15112yes—
234#475C22×C15112yes—
235#474C22×C15112yes—
236#467—21no—
237#467—21no—
238#446C22×C15111yescharacteristic
239C8×Q8C22×C15111yescharacteristic
240C4×Q16—21no—
241C4×Q16—21no—
242#436C22×C15111yescharacteristic
243#435—21no—
244C8×D4—21no—
245C8×D4C22×C15111yescharacteristic
246#433—21no—
247#432C22×C15111yescharacteristic
248#431C22×C15112yes—
249#405—21no—
250C2×C4×C8C22×C15111yescharacteristic
251#335C22×C15111yescharacteristic
252#335C22×C15111yescharacteristic
253#334C22×C15112yes—
254#333C22×C15112yes—
255#333C22×C15112yes—
256#332C22×C15112yes—
257#332C22×C15112yes—
258C2×Q16—21no—
259C2×Q16—21no—
260C2×M16—21no—
261C22×C8—21no—
262C22×C8D4×C15111yescharacteristic
263C22×C8D4×C15111yescharacteristic
264C4⋊Q8C23×C15112yes—
265C4⋊Q8C23×C15112yes—
266#126—21no—
267#125—22no—
268#125D4×C15111yescharacteristic
269#124D4×C15111yescharacteristic
270#123—21no—
271C22⋊Q8—22no—
272C22⋊Q8—22no—
273C22⋊Q8D4×C15111yescharacteristic
274#121D4×C15111yescharacteristic
275C4×Q8—22no—
276C4×Q8—22no—
277C4×Q8C23×C15111yescharacteristic
278C4×D4—21no—
279C4×D4C23×C15111yescharacteristic
280#117—21no—
281#117—22no—
282C2×C42C23×C15111yescharacteristic
283#107—21no—
284#107—21no—
285#107—22no—
286#107—22no—
287#106—22no—
288#106—22no—
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8C23×C15111yescharacteristic
292C4⋊C8C23×C15111yescharacteristic
293C4⋊C8C23×C15112yes—
294C4⋊C8C23×C15112yes—
295#103—22no—
296#103—22no—
297#103—22no—
298#103—22no—
299#102—22no—
300#102—22no—
301C22⋊C8—22no—
302C22⋊C8—21no—
303C22⋊C8—21no—
304C22⋊C8—21no—
305#97—21no—
306#97—21no—
307C4×C8—21no—
308C4×C8—22no—
309C4×C8D4×C15111yescharacteristic
310C4×C8D4×C15111yescharacteristic
311C4×C8C23×C15111yescharacteristic
312C4×C8C23×C15111yescharacteristic
313C2×Q8—22no—
314C2×Q8—22no—
315C2×Q8C2×D4×C15111yescharacteristic
316C2×D4—21no—
317C2×D4C2×D4×C15111yescharacteristic
318C22×C4—21no—
319C22×C4C2×D4×C15111yescharacteristic
320C22×C4C2×D4×C15111yescharacteristic
321C22×C4#41×C15111yescharacteristic
322Q16—42no—
323Q16—42no—
324M16—42no—
325C2×C8—22no—
326C2×C8—21no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—21no—
330C2×C8—41no—
331C2×C8—42no—
332C2×C8C2×D4×C15111yescharacteristic
333C2×C8C2×D4×C15111yescharacteristic
334C2×C8C2×D4×C15111yescharacteristic
335C2×C8C2×D4×C15111yescharacteristic
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—42no—
345C4⋊C4—42no—
346C4⋊C4C2×D4×C15111yescharacteristic
347C4⋊C4C2×D4×C15111yescharacteristic
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—21no—
353C22⋊C4—42no—
354C42—21no—
355C42—42no—
356C42C2×D4×C15111yescharacteristic
357C42C2×D4×C15111yescharacteristic
358C42#41×C15111yescharacteristic
359C42C24×C15111yescharacteristic
360C23—21no—
361C23#121×C15111yescharacteristic
362Q8—21no—
363Q8—21no—
364Q8—42no—
365Q8—42no—
366Q8—82no—
367D4—21no—
368D4—21no—
369D4—42no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4#121×C15111yescharacteristic
383C2×C4#121×C15111yescharacteristic
384C2×C4#121×C15111yescharacteristic
385C2×C4C22×D4×C15111yescharacteristic
386C2×C4C22×D4×C15111yescharacteristic
387C2×C4C2×#41×C15111yescharacteristic
388C8—21no—
389C8—21no—
390C8—21no—
391C8—41no—
392C8—41no—
393C8—42no—
394C8—42no—
395C8#135×C15112yes—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22C2×#121×C15111yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—82no—
411C4—82no—
412C4C2×#135×C15111yescharacteristic
413C4#575×C15111yescharacteristic
414C4#578×C15111yescharacteristic
415C4#578×C15111yescharacteristic
416C2—41no—
417C2—81no—
418C2#3035×C15111yescharacteristic
419C2#3059×C15111yescharacteristic
420C2#3067×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. #1704×C151C2semidirect
5. #1703×C151C2semidirect
6. #1676×C151C2semidirect
7. #1675×C151C2semidirect
8. #1670×C151C2semidirect
9. #1669×C151C2semidirect
10. #1564×C151C2semidirect
11. #1554×C151C2semidirect
210. #19220C151direct (N × H)
211. C151#19220direct (N × H)
213. #3170C2×C151semidirect
215. #1704C2×C151semidirect
216. #1703C2×C151semidirect
217. #1676C2×C151semidirect
218. #1675C2×C151semidirect
219. #1670C2×C151semidirect
220. #1669C2×C151semidirect
221. #1564C2×C151semidirect
222. #1554C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3233×C1512
#3170×C1512
#2966×C1512
#1704×C1512
#1703×C1512
#1676×C1512
#1675×C1512
#1670×C1512
#1669×C1512
#1564×C1512
#1554×C1512
#19220151