Finite Group Databasebeta

← C151×#19527 #50324452

Subgroups — C151×#19527 #50324452

Order 38656.

574 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3255×C151C211yesmaximal, characteristic, complemented
2#3246×C151C211yesmaximal, characteristic
3#3210×C151C211yesmaximal, characteristic
4#2985×C151C211yesmaximal, characteristic, complemented
5#1700×C151C212yesmaximal, complemented
6#1686×C151C212yesmaximal, complemented
7#1682×C151C212yesmaximal, complemented
8#1670×C151C212yesmaximal, complemented
9#1571×C151C211yesmaximal, characteristic, complemented
10#1557×C151C211yesmaximal, characteristic
11#1552×C151C211yesmaximal, characteristic, complemented
12#533×C151C2211yescharacteristic
13#533×C151C2211yescharacteristic
14#532×C151C2211yescharacteristic
15#494×C151C2211yescharacteristic
16#492×C151C2211yescharacteristic
17#487×C151C2211yescharacteristic
18#486×C151C2211yescharacteristic
19#476×C151—21no—
20#475×C151—21no—
21#475×C151C2212yes—
22#475×C151C2212yes—
23#470×C151—22no—
24#465×C151—22no—
25#464×C151—22no—
26#462×C151—21no—
27#462×C151C2212yes—
28#461×C151—21no—
29#460×C151C2212yes—
30#452×C151—22no—
31#446×C151—22no—
32#446×C151C2212yes—
33C8×Q8×C151C2212yes—
34#433×C151—22no—
35#432×C151C2211yescharacteristic
36#431×C151C2211yescharacteristic
37#423×C151C2211yescharacteristic
38C2×C4⋊C8×C151C2211yescharacteristic
39#335×C151C2212yes—
40#335×C151C2212yes—
41#332×C151C2212yes—
42#332×C151C2212yes—
43#332×C151C2212yes—
44#331×C151C2212yes—
45C2×#41×C151—21no—
46C2×Q16×C151—22no—
47C2×Q16×C151—22no—
48C2×SD16×C151—22no—
49C2×SD16×C151—22no—
50C2×M16×C151—21no—
51C22×C8×C151—21no—
52C4⋊Q8×C151D411yescharacteristic
53C4⋊Q8×C151D411yescharacteristic
54C4⋊Q8×C151C2311yescharacteristic
55C4⋊Q8×C151C2311yescharacteristic
56C4⋊Q8×C151C2311yescharacteristic
57#127×C151C2311yescharacteristic
58#125×C151—21no—
59#125×C151—21no—
60#124×C151—21no—
61C22⋊Q8×C151—21no—
62C22⋊Q8×C151—21no—
63C22⋊Q8×C151—21no—
64C22⋊Q8×C151D412yes—
65#121×C151—21no—
66#121×C151—21no—
67C4×Q8×C151—21no—
68C4×Q8×C151—21no—
69C4×Q8×C151—21no—
70C4×Q8×C151C2312yes—
71C4×D4×C151—21no—
72C4×D4×C151—21no—
73#117×C151—21no—
74#117×C151—21no—
75C2×C42×C151C2311yescharacteristic
76#106×C151—22no—
77#106×C151—22no—
78C4⋊C8×C151—22no—
79C4⋊C8×C151—22no—
80C4⋊C8×C151—21no—
81C4⋊C8×C151—21no—
82C4⋊C8×C151D412yes—
83C4⋊C8×C151C2312yes—
84C4⋊C8×C151C2312yes—
85C4⋊C8×C151C2312yes—
86#103×C151—22no—
87#103×C151—22no—
88#103×C151—22no—
89#103×C151—22no—
90#102×C151—22no—
91#102×C151—22no—
92C22⋊C8×C151—21no—
93C22⋊C8×C151D412yes—
94#97×C151—22no—
95#97×C151—21no—
96C4×C8×C151—22no—
97C4×C8×C151C2311yescharacteristic
98C4×C8×C151C2311yescharacteristic
99#41×C151—82no—
100C2×Q8×C151—21no—
101C2×Q8×C151—21no—
102C2×Q8×C151—21no—
103C2×Q8×C151—21no—
104C2×Q8×C151C2×D412yes—
105C2×D4×C151—21no—
106C2×D4×C151—21no—
107C2×D4×C151—21no—
108C2×D4×C151—41no—
109C22×C4×C151—41no—
110C22×C4×C151C2×D411yescharacteristic
111C22×C4×C151C2×D411yescharacteristic
112C22×C4×C151#4111yescharacteristic
113Q16×C151—82no—
114Q16×C151—82no—
115SD16×C151—82no—
116SD16×C151—82no—
117M16×C151—81no—
118C2×C8×C151—22no—
119C2×C8×C151—22no—
120C2×C8×C151—22no—
121C2×C8×C151—81no—
122C2×C8×C151C2×D412yes—
123C2×C8×C151C2×D412yes—
124C4⋊C4×C151—21no—
125C4⋊C4×C151—21no—
126C4⋊C4×C151—21no—
127C4⋊C4×C151—22no—
128C4⋊C4×C151—22no—
129C4⋊C4×C151—21no—
130C4⋊C4×C151—21no—
131C4⋊C4×C151—21no—
132C4⋊C4×C151—21no—
133C4⋊C4×C151—21no—
134C4⋊C4×C151—21no—
135C4⋊C4×C151—41no—
136C4⋊C4×C151—41no—
137C4⋊C4×C151C2×D412yes—
138C22⋊C4×C151—22no—
139C22⋊C4×C151—41no—
140C22⋊C4×C151—41no—
141C22⋊C4×C151—41no—
142C42×C151—22no—
143C42×C151—41no—
144C42×C151C2×D411yescharacteristic
145C42×C151C2×D411yescharacteristic
146C42×C151#4111yescharacteristic
147C42×C151C2411yescharacteristic
148C23×C151—41no—
149C23×C151#12111yescharacteristic
150Q8×C151—22no—
151Q8×C151—22no—
152Q8×C151—41no—
153Q8×C151—42no—
154Q8×C151—42no—
155Q8×C151—41no—
156Q8×C151—81no—
157D4×C151—41no—
158D4×C151—42no—
159D4×C151—41no—
160D4×C151—81no—
161D4×C151—82no—
162C2×C4×C151—21no—
163C2×C4×C151—22no—
164C2×C4×C151—21no—
165C2×C4×C151—22no—
166C2×C4×C151—22no—
167C2×C4×C151—41no—
168C2×C4×C151—41no—
169C2×C4×C151—41no—
170C2×C4×C151—41no—
171C2×C4×C151—82no—
172C2×C4×C151#12111yescharacteristic
173C2×C4×C151#12111yescharacteristic
174C2×C4×C151#12111yescharacteristic
175C2×C4×C151C22×D411yescharacteristic
176C2×C4×C151C22×D411yescharacteristic
177C2×C4×C151C2×#4111yescharacteristic
178C8×C151—22no—
179C8×C151—22no—
180C8×C151—42no—
181C8×C151—42no—
182C8×C151—42no—
183C22×C151—21no—
184C22×C151—21no—
185C22×C151—21no—
186C22×C151—81no—
187C22×C151—81no—
188C22×C151—81no—
189C22×C151C2×#12111yescharacteristic
190C4×C151—21no—
191C4×C151—21no—
192C4×C151—21no—
193C4×C151—21no—
194C4×C151—42no—
195C4×C151—42no—
196C4×C151—81no—
197C4×C151—81no—
198C4×C151—81no—
199C4×C151#57611yescharacteristic
200C4×C151#57712yes—
201C4×C151#57811yescharacteristic
202C2×C151—41no—
203C2×C151—161no—
204C2×C151#304311yescharacteristic
205C2×C151#306111yescharacteristic
206C2×C151#306911yescharacteristic
207#19527C15111yesmaximal, characteristic, direct product factor, Sylow
208C151#1952711yescharacteristic, direct product factor, Sylow
209#3255C2×C15111yescharacteristic, complemented
210#3246C2×C15111yescharacteristic
211#3210C2×C15111yescharacteristic
212#2985C2×C15111yescharacteristic, complemented
213#1700C2×C15112yescomplemented
214#1686C2×C15112yescomplemented
215#1682C2×C15112yescomplemented
216#1670C2×C15112yescomplemented
217#1571C2×C15111yescharacteristic, complemented
218#1557C2×C15111yescharacteristic
219#1552C2×C15111yescharacteristic, complemented
220#533C22×C15111yescharacteristic
221#533C22×C15111yescharacteristic
222#532C22×C15111yescharacteristic
223#494C22×C15111yescharacteristic
224#492C22×C15111yescharacteristic
225#487C22×C15111yescharacteristic
226#486C22×C15111yescharacteristic
227#476—21no—
228#475—21no—
229#475C22×C15112yes—
230#475C22×C15112yes—
231#470—22no—
232#465—22no—
233#464—22no—
234#462—21no—
235#462C22×C15112yes—
236#461—21no—
237#460C22×C15112yes—
238#452—22no—
239#446—22no—
240#446C22×C15112yes—
241C8×Q8C22×C15112yes—
242#433—22no—
243#432C22×C15111yescharacteristic
244#431C22×C15111yescharacteristic
245#423C22×C15111yescharacteristic
246C2×C4⋊C8C22×C15111yescharacteristic
247#335C22×C15112yes—
248#335C22×C15112yes—
249#332C22×C15112yes—
250#332C22×C15112yes—
251#332C22×C15112yes—
252#331C22×C15112yes—
253C2×#41—21no—
254C2×Q16—22no—
255C2×Q16—22no—
256C2×SD16—22no—
257C2×SD16—22no—
258C2×M16—21no—
259C22×C8—21no—
260C4⋊Q8D4×C15111yescharacteristic
261C4⋊Q8D4×C15111yescharacteristic
262C4⋊Q8C23×C15111yescharacteristic
263C4⋊Q8C23×C15111yescharacteristic
264C4⋊Q8C23×C15111yescharacteristic
265#127C23×C15111yescharacteristic
266#125—21no—
267#125—21no—
268#124—21no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272C22⋊Q8D4×C15112yes—
273#121—21no—
274#121—21no—
275C4×Q8—21no—
276C4×Q8—21no—
277C4×Q8—21no—
278C4×Q8C23×C15112yes—
279C4×D4—21no—
280C4×D4—21no—
281#117—21no—
282#117—21no—
283C2×C42C23×C15111yescharacteristic
284#106—22no—
285#106—22no—
286C4⋊C8—22no—
287C4⋊C8—22no—
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8D4×C15112yes—
291C4⋊C8C23×C15112yes—
292C4⋊C8C23×C15112yes—
293C4⋊C8C23×C15112yes—
294#103—22no—
295#103—22no—
296#103—22no—
297#103—22no—
298#102—22no—
299#102—22no—
300C22⋊C8—21no—
301C22⋊C8D4×C15112yes—
302#97—22no—
303#97—21no—
304C4×C8—22no—
305C4×C8C23×C15111yescharacteristic
306C4×C8C23×C15111yescharacteristic
307#41—82no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8C2×D4×C15112yes—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C22×C4—41no—
318C22×C4C2×D4×C15111yescharacteristic
319C22×C4C2×D4×C15111yescharacteristic
320C22×C4#41×C15111yescharacteristic
321Q16—82no—
322Q16—82no—
323SD16—82no—
324SD16—82no—
325M16—81no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—22no—
329C2×C8—81no—
330C2×C8C2×D4×C15112yes—
331C2×C8C2×D4×C15112yes—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4C2×D4×C15112yes—
346C22⋊C4—22no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C42—22no—
351C42—41no—
352C42C2×D4×C15111yescharacteristic
353C42C2×D4×C15111yescharacteristic
354C42#41×C15111yescharacteristic
355C42C24×C15111yescharacteristic
356C23—41no—
357C23#121×C15111yescharacteristic
358Q8—22no—
359Q8—22no—
360Q8—41no—
361Q8—42no—
362Q8—42no—
363Q8—41no—
364Q8—81no—
365D4—41no—
366D4—42no—
367D4—41no—
368D4—81no—
369D4—82no—
370C2×C4—21no—
371C2×C4—22no—
372C2×C4—21no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—82no—
380C2×C4#121×C15111yescharacteristic
381C2×C4#121×C15111yescharacteristic
382C2×C4#121×C15111yescharacteristic
383C2×C4C22×D4×C15111yescharacteristic
384C2×C4C22×D4×C15111yescharacteristic
385C2×C4C2×#41×C15111yescharacteristic
386C8—22no—
387C8—22no—
388C8—42no—
389C8—42no—
390C8—42no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22C2×#121×C15111yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—42no—
403C4—42no—
404C4—81no—
405C4—81no—
406C4—81no—
407C4#576×C15111yescharacteristic
408C4#577×C15112yes—
409C4#578×C15111yescharacteristic
410C2—41no—
411C2—161no—
412C2#3043×C15111yescharacteristic
413C2#3061×C15111yescharacteristic
414C2#3069×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#532×C151C22
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. #3255×C151C2semidirect
4. #2985×C151C2semidirect
5. #1700×C151C2semidirect
6. #1686×C151C2semidirect
7. #1682×C151C2semidirect
8. #1670×C151C2semidirect
9. #1571×C151C2semidirect
11. #1552×C151C2semidirect
207. #19527C151direct (N × H)
208. C151#19527direct (N × H)
209. #3255C2×C151semidirect
212. #2985C2×C151semidirect
213. #1700C2×C151semidirect
214. #1686C2×C151semidirect
215. #1682C2×C151semidirect
216. #1670C2×C151semidirect
217. #1571C2×C151semidirect
219. #1552C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3255×C1512
#3246×C1512
#3210×C1512
#2985×C1512
#1700×C1512
#1686×C1512
#1682×C1512
#1670×C1512
#1571×C1512
#1557×C1512
#1552×C1512
#19527151