Finite Group Databasebeta

← C151×#19302 #50324227

Subgroups — C151×#19302 #50324227

Order 38656.

616 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#487×C151C211yesmaximal, characteristic, complemented
2#3079×C151C211yesmaximal, characteristic
3#3079×C151C211yesmaximal, characteristic
4#2965×C151C211yesmaximal, characteristic
5#1704×C151C214yesmaximal, complemented
6#1703×C151C214yesmaximal, complemented
7#1566×C151C211yesmaximal, characteristic, complemented
8#1549×C151C211yesmaximal, characteristic, complemented
9#1548×C151C211yesmaximal, characteristic, complemented
10C2×C4⋊Q8×C151C2211yescharacteristic
11C2×C4⋊Q8×C151C2211yescharacteristic
12C4×#41×C151C2211yescharacteristic
13#487×C151—21no—
14#487×C151—21no—
15#487×C151C2214yes—
16#477×C151—21no—
17#477×C151C2212yes—
18#476×C151—21no—
19#476×C151C2212yes—
20#475×C151—21no—
21#475×C151C2212yes—
22#474×C151—21no—
23#474×C151C2212yes—
24#446×C151C2212yes—
25#436×C151C2212yes—
26#435×C151—22no—
27#431×C151—21no—
28#431×C151C2211yescharacteristic
29#428×C151—21no—
30#428×C151—21no—
31#423×C151C2211yescharacteristic
32#423×C151C2211yescharacteristic
33#417×C151—21no—
34#417×C151—21no—
35C2×#103×C151—22no—
36C4×M16×C151—21no—
37C2×C4×C8×C151C2211yescharacteristic
38#334×C151C2214yes—
39#333×C151C2214yes—
40#332×C151C2214yes—
41C2×#41×C151D411yescharacteristic
42C22×Q8×C151—21no—
43C22×Q8×C151—21no—
44C2×M16×C151—21no—
45C2×M16×C151—21no—
46C2×M16×C151—22no—
47C22×C8×C151D412yes—
48C4⋊Q8×C151—21no—
49C4⋊Q8×C151—21no—
50C4⋊Q8×C151—21no—
51C4⋊Q8×C151—21no—
52C4⋊Q8×C151—21no—
53C4⋊Q8×C151—21no—
54C4⋊Q8×C151C2312yes—
55C4⋊Q8×C151C2312yes—
56C4×Q8×C151D411yescharacteristic
57C4×Q8×C151C2311yescharacteristic
58C4×D4×C151—21no—
59C4×D4×C151—21no—
60C4×D4×C151D411yescharacteristic
61C4×D4×C151C2311yescharacteristic
62#117×C151—21no—
63#117×C151D411yescharacteristic
64C2×C4⋊C4×C151—21no—
65C2×C4⋊C4×C151—21no—
66C2×C4⋊C4×C151—21no—
67C2×C4⋊C4×C151—21no—
68C2×C42×C151—21no—
69C2×C42×C151C2311yescharacteristic
70#107×C151—22no—
71#107×C151—22no—
72#106×C151—22no—
73#106×C151—22no—
74C4⋊C8×C151—22no—
75C4⋊C8×C151—21no—
76C4⋊C8×C151—21no—
77C4⋊C8×C151C2312yes—
78C4⋊C8×C151C2312yes—
79C4⋊C8×C151C2312yes—
80#103×C151—24no—
81#103×C151—24no—
82#103×C151—22no—
83#103×C151—22no—
84#102×C151—22no—
85#102×C151—22no—
86C22⋊C8×C151—21no—
87C22⋊C8×C151—22no—
88#97×C151—22no—
89C4×C8×C151—21no—
90C4×C8×C151D411yescharacteristic
91C4×C8×C151D411yescharacteristic
92C4×C8×C151C2312yes—
93#41×C151—22no—
94#41×C151—22no—
95C2×Q8×C151—22no—
96C2×Q8×C151—22no—
97C2×Q8×C151—44no—
98C2×Q8×C151—41no—
99C2×Q8×C151—41no—
100C2×Q8×C151—82no—
101C2×Q8×C151C2×D411yescharacteristic
102C2×D4×C151—21no—
103C2×D4×C151C2×D411yescharacteristic
104C22×C4×C151—21no—
105C22×C4×C151—21no—
106C22×C4×C151—21no—
107C22×C4×C151—41no—
108C22×C4×C151—41no—
109C22×C4×C151C2×D411yescharacteristic
110C22×C4×C151C2×D411yescharacteristic
111C22×C4×C151#4111yescharacteristic
112M16×C151—44no—
113M16×C151—42no—
114M16×C151—42no—
115C2×C8×C151—22no—
116C2×C8×C151—22no—
117C2×C8×C151—22no—
118C2×C8×C151—42no—
119C2×C8×C151C2×D412yes—
120C2×C8×C151C2×D412yes—
121C4⋊C4×C151—21no—
122C4⋊C4×C151—21no—
123C4⋊C4×C151—22no—
124C4⋊C4×C151—22no—
125C4⋊C4×C151—22no—
126C4⋊C4×C151—22no—
127C4⋊C4×C151—41no—
128C4⋊C4×C151—41no—
129C4⋊C4×C151—41no—
130C4⋊C4×C151—41no—
131C4⋊C4×C151C2×D411yescharacteristic
132C4⋊C4×C151C2×D411yescharacteristic
133C22⋊C4×C151—21no—
134C22⋊C4×C151—21no—
135C22⋊C4×C151—21no—
136C42×C151—21no—
137C42×C151—21no—
138C42×C151—21no—
139C42×C151C2×D411yescharacteristic
140C42×C151C2×D411yescharacteristic
141C42×C151#4111yescharacteristic
142C42×C151C2411yescharacteristic
143C23×C151—21no—
144C23×C151#12111yescharacteristic
145Q8×C151—21no—
146Q8×C151—21no—
147Q8×C151—44no—
148Q8×C151—82no—
149Q8×C151—82no—
150Q8×C151—82no—
151D4×C151—21no—
152D4×C151—21no—
153D4×C151—42no—
154C2×C4×C151—22no—
155C2×C4×C151—22no—
156C2×C4×C151—21no—
157C2×C4×C151—21no—
158C2×C4×C151—21no—
159C2×C4×C151—42no—
160C2×C4×C151—42no—
161C2×C4×C151—42no—
162C2×C4×C151—42no—
163C2×C4×C151—42no—
164C2×C4×C151—82no—
165C2×C4×C151—82no—
166C2×C4×C151#12111yescharacteristic
167C2×C4×C151#12111yescharacteristic
168C2×C4×C151#12111yescharacteristic
169C2×C4×C151#13712yes—
170C2×C4×C151#13712yes—
171C2×C4×C151C22×D411yescharacteristic
172C2×C4×C151C22×D411yescharacteristic
173C2×C4×C151C2×#4111yescharacteristic
174C8×C151—22no—
175C8×C151—22no—
176C8×C151—42no—
177C8×C151—42no—
178C8×C151—42no—
179C22×C151—21no—
180C22×C151—21no—
181C22×C151—41no—
182C22×C151—41no—
183C22×C151—41no—
184C22×C151#47012yes—
185C22×C151C2×#12111yescharacteristic
186C4×C151—21no—
187C4×C151—21no—
188C4×C151—41no—
189C4×C151—41no—
190C4×C151—41no—
191C4×C151—82no—
192C4×C151—82no—
193C4×C151#47012yes—
194C4×C151#47112yes—
195C4×C151C2×#13711yescharacteristic
196C4×C151C2×#13711yescharacteristic
197C4×C151#57512yes—
198C2×C151—22no—
199C2×C151—81no—
200C2×C151#304011yescharacteristic
201C2×C151C2×#47011yescharacteristic
202C2×C151C2×#47111yescharacteristic
203#19302C15111yesmaximal, characteristic, direct product factor, Sylow
204C151#1930211yescharacteristic, direct product factor, Sylow
205C2×#487C2×C15111yescharacteristic, complemented
206#3079C2×C15111yescharacteristic
207#3079C2×C15111yescharacteristic
208#2965C2×C15111yescharacteristic
209#1704C2×C15114yescomplemented
210#1703C2×C15114yescomplemented
211#1566C2×C15111yescharacteristic, complemented
212#1549C2×C15111yescharacteristic, complemented
213#1548C2×C15111yescharacteristic, complemented
214C2×C4⋊Q8C22×C15111yescharacteristic
215C2×C4⋊Q8C22×C15111yescharacteristic
216C4×#41C22×C15111yescharacteristic
217#487—21no—
218#487—21no—
219#487C22×C15114yes—
220#477—21no—
221#477C22×C15112yes—
222#476—21no—
223#476C22×C15112yes—
224#475—21no—
225#475C22×C15112yes—
226#474—21no—
227#474C22×C15112yes—
228#446C22×C15112yes—
229#436C22×C15112yes—
230#435—22no—
231#431—21no—
232#431C22×C15111yescharacteristic
233#428—21no—
234#428—21no—
235#423C22×C15111yescharacteristic
236#423C22×C15111yescharacteristic
237#417—21no—
238#417—21no—
239C2×#103—22no—
240C4×M16—21no—
241C2×C4×C8C22×C15111yescharacteristic
242#334C22×C15114yes—
243#333C22×C15114yes—
244#332C22×C15114yes—
245C2×#41D4×C15111yescharacteristic
246C22×Q8—21no—
247C22×Q8—21no—
248C2×M16—21no—
249C2×M16—21no—
250C2×M16—22no—
251C22×C8D4×C15112yes—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8—21no—
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8C23×C15112yes—
259C4⋊Q8C23×C15112yes—
260C4×Q8D4×C15111yescharacteristic
261C4×Q8C23×C15111yescharacteristic
262C4×D4—21no—
263C4×D4—21no—
264C4×D4D4×C15111yescharacteristic
265C4×D4C23×C15111yescharacteristic
266#117—21no—
267#117D4×C15111yescharacteristic
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C42—21no—
273C2×C42C23×C15111yescharacteristic
274#107—22no—
275#107—22no—
276#106—22no—
277#106—22no—
278C4⋊C8—22no—
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8C23×C15112yes—
282C4⋊C8C23×C15112yes—
283C4⋊C8C23×C15112yes—
284#103—22no—
285#103—22no—
286#103—24no—
287#103—24no—
288#102—22no—
289#102—22no—
290C22⋊C8—21no—
291C22⋊C8—22no—
292#97—22no—
293C4×C8—21no—
294C4×C8D4×C15111yescharacteristic
295C4×C8D4×C15111yescharacteristic
296C4×C8C23×C15112yes—
297#41—22no—
298#41—22no—
299C2×Q8—22no—
300C2×Q8—22no—
301C2×Q8—44no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—82no—
305C2×Q8C2×D4×C15111yescharacteristic
306C2×D4—21no—
307C2×D4C2×D4×C15111yescharacteristic
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4C2×D4×C15111yescharacteristic
314C22×C4C2×D4×C15111yescharacteristic
315C22×C4#41×C15111yescharacteristic
316M16—44no—
317M16—42no—
318M16—42no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—42no—
323C2×C8C2×D4×C15112yes—
324C2×C8C2×D4×C15112yes—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4C2×D4×C15111yescharacteristic
336C4⋊C4C2×D4×C15111yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C42—21no—
341C42—21no—
342C42—21no—
343C42C2×D4×C15111yescharacteristic
344C42C2×D4×C15111yescharacteristic
345C42#41×C15111yescharacteristic
346C42C24×C15111yescharacteristic
347C23—21no—
348C23#121×C15111yescharacteristic
349Q8—21no—
350Q8—21no—
351Q8—44no—
352Q8—82no—
353Q8—82no—
354Q8—82no—
355D4—21no—
356D4—21no—
357D4—42no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4#121×C15111yescharacteristic
371C2×C4#121×C15111yescharacteristic
372C2×C4#121×C15111yescharacteristic
373C2×C4#137×C15112yes—
374C2×C4#137×C15112yes—
375C2×C4C22×D4×C15111yescharacteristic
376C2×C4C22×D4×C15111yescharacteristic
377C2×C4C2×#41×C15111yescharacteristic
378C8—22no—
379C8—22no—
380C8—42no—
381C8—42no—
382C8—42no—
383C22—21no—
384C22—21no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22#470×C15112yes—
389C22C2×#121×C15111yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—82no—
396C4—82no—
397C4#470×C15112yes—
398C4#471×C15112yes—
399C4C2×#137×C15111yescharacteristic
400C4C2×#137×C15111yescharacteristic
401C4#575×C15112yes—
402C2—22no—
403C2—81no—
404C2#3040×C15111yescharacteristic
405C2C2×#470×C15111yescharacteristic
406C2C2×#471×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radicalC2×#41×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
1. C2×#487×C151C2semidirect
5. #1704×C151C2semidirect
6. #1703×C151C2semidirect
7. #1566×C151C2semidirect
8. #1549×C151C2semidirect
9. #1548×C151C2semidirect
203. #19302C151direct (N × H)
204. C151#19302direct (N × H)
205. C2×#487C2×C151semidirect
209. #1704C2×C151semidirect
210. #1703C2×C151semidirect
211. #1566C2×C151semidirect
212. #1549C2×C151semidirect
213. #1548C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#487×C1512
#3079×C1512
#2965×C1512
#1704×C1512
#1703×C1512
#1566×C1512
#1549×C1512
#1548×C1512
#19302151