Finite Group Databasebeta

← C151×#9338 #50314263

Subgroups — C151×#9338 #50314263

Order 38656.

400 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3238×C151C211yesmaximal, characteristic
2#2995×C151C211yesmaximal, characteristic
3#1997×C151C211yesmaximal, characteristic, complemented
4#1556×C151C211yesmaximal, characteristic, complemented
5#1529×C151C211yesmaximal, characteristic
6#1307×C151C211yesmaximal, characteristic, complemented
7#1291×C151C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C151C2211yescharacteristic
9#529×C151C2211yescharacteristic
10#501×C151—21no—
11#489×C151—21no—
12#483×C151C412yes—
13#480×C151C412yes—
14#477×C151—21no—
15#476×C151—21no—
16#446×C151—21no—
17#436×C151—21no—
18#435×C151—21no—
19#435×C151—21no—
20#433×C151—21no—
21#432×C151C2211yescharacteristic
22#432×C151C2211yescharacteristic
23#432×C151C2211yescharacteristic
24#424×C151—21no—
25#423×C151C2211yescharacteristic
26C4×M16×C151C2211yescharacteristic
27#343×C151—21no—
28#343×C151—21no—
29#332×C151—21no—
30#332×C151—21no—
31#330×C151—21no—
32#329×C151—21no—
33C22×Q8×C151—21no—
34C2×M16×C151—21no—
35C2×M16×C151—21no—
36C2×M16×C151D411yescharacteristic
37C2×M16×C151D411yescharacteristic
38C22×C8×C151—21no—
39C4⋊Q8×C151—21no—
40C4⋊Q8×C151—21no—
41C4⋊Q8×C151—21no—
42C4⋊Q8×C151—21no—
43#126×C151—21no—
44#125×C151D411yescharacteristic
45#124×C151D411yescharacteristic
46#123×C151—21no—
47C22⋊Q8×C151C2×C411yescharacteristic
48#121×C151C2×C411yescharacteristic
49C4×Q8×C151D411yescharacteristic
50C4×D4×C151—21no—
51C4×D4×C151D411yescharacteristic
52#117×C151—21no—
53C2×C4⋊C4×C151—21no—
54C2×C4⋊C4×C151C2×C412yes—
55C2×C42×C151C2311yescharacteristic
56#107×C151—22no—
57#106×C151—22no—
58C4⋊C8×C151—21no—
59C4⋊C8×C151—21no—
60C4⋊C8×C151—21no—
61C4⋊C8×C151—21no—
62C4⋊C8×C151—21no—
63C4⋊C8×C151—21no—
64C4⋊C8×C151D411yescharacteristic
65C4⋊C8×C151D411yescharacteristic
66#103×C151—22no—
67#102×C151—22no—
68C22⋊C8×C151—21no—
69C22⋊C8×C151—21no—
70C22⋊C8×C151—21no—
71C22⋊C8×C151—21no—
72C22⋊C8×C151C2×C412yes—
73#97×C151—21no—
74#97×C151—21no—
75#97×C151—21no—
76#97×C151—21no—
77#97×C151—21no—
78C4×C8×C151—21no—
79C4×C8×C151—21no—
80C2×Q8×C151—41no—
81C2×Q8×C151—41no—
82C2×Q8×C151—82no—
83C2×Q8×C151C22⋊C411yescharacteristic
84C2×D4×C151—21no—
85C2×D4×C151C22⋊C411yescharacteristic
86C22×C4×C151—21no—
87C22×C4×C151—22no—
88C22×C4×C151C22×C411yescharacteristic
89C22×C4×C151C2×D411yescharacteristic
90C22×C4×C151#4111yescharacteristic
91M16×C151—22no—
92M16×C151—41no—
93M16×C151—41no—
94M16×C151—41no—
95M16×C151—81no—
96C2×C8×C151—22no—
97C2×C8×C151—21no—
98C2×C8×C151—21no—
99C2×C8×C151—21no—
100C2×C8×C151—21no—
101C2×C8×C151—41no—
102C2×C8×C151—41no—
103C2×C8×C151—81no—
104C4⋊C4×C151—21no—
105C4⋊C4×C151—21no—
106C4⋊C4×C151—21no—
107C4⋊C4×C151—21no—
108C4⋊C4×C151—22no—
109C4⋊C4×C151—22no—
110C4⋊C4×C151—41no—
111C4⋊C4×C151—41no—
112C4⋊C4×C151C22⋊C411yescharacteristic
113C4⋊C4×C151C22⋊C411yescharacteristic
114C22⋊C4×C151—21no—
115C22⋊C4×C151—21no—
116C22⋊C4×C151—21no—
117C22⋊C4×C151—21no—
118C22⋊C4×C151—21no—
119C42×C151—21no—
120C42×C151C2×D411yescharacteristic
121C42×C151C2×D411yescharacteristic
122C42×C151C2×D411yescharacteristic
123C42×C151#4111yescharacteristic
124C23×C151—21no—
125C23×C151C4×D411yescharacteristic
126Q8×C151—41no—
127Q8×C151—82no—
128Q8×C151—82no—
129D4×C151—41no—
130D4×C151—81no—
131C2×C4×C151—21no—
132C2×C4×C151—21no—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—41no—
137C2×C4×C151—41no—
138C2×C4×C151—41no—
139C2×C4×C151—41no—
140C2×C4×C151—42no—
141C2×C4×C151—82no—
142C2×C4×C151C2×C22⋊C411yescharacteristic
143C2×C4×C151C4×D411yescharacteristic
144C2×C4×C151#12011yescharacteristic
145C2×C4×C151#12111yescharacteristic
146C2×C4×C151#12111yescharacteristic
147C2×C4×C151#12311yescharacteristic
148C8×C151—42no—
149C8×C151—42no—
150C8×C151—41no—
151C8×C151—41no—
152C8×C151—41no—
153C8×C151—41no—
154C8×C151—81no—
155C22×C151—21no—
156C22×C151—21no—
157C22×C151—21no—
158C22×C151—41no—
159C22×C151—41no—
160C22×C151—41no—
161C22×C151#38611yescharacteristic
162C4×C151—21no—
163C4×C151—21no—
164C4×C151—21no—
165C4×C151—21no—
166C4×C151—21no—
167C4×C151—41no—
168C4×C151—41no—
169C4×C151—41no—
170C4×C151—82no—
171C4×C151#45511yescharacteristic
172C4×C151#45611yescharacteristic
173C2×C151—41no—
174C2×C151—81no—
175C2×C151#188211yescharacteristic
176C2×C151#190311yescharacteristic
177C2×C151#191511yescharacteristic
178#9338C15111yesmaximal, characteristic, direct product factor, Sylow
179C151#933811yescharacteristic, direct product factor, Sylow
180#3238C2×C15111yescharacteristic
181#2995C2×C15111yescharacteristic
182#1997C2×C15111yescharacteristic, complemented
183#1556C2×C15111yescharacteristic, complemented
184#1529C2×C15111yescharacteristic
185#1307C2×C15111yescharacteristic, complemented
186#1291C2×C15111yescharacteristic, complemented
187C2×C4⋊Q8C22×C15111yescharacteristic
188#529C22×C15111yescharacteristic
189#501—21no—
190#489—21no—
191#483C4×C15112yes—
192#480C4×C15112yes—
193#477—21no—
194#476—21no—
195#446—21no—
196#436—21no—
197#435—21no—
198#435—21no—
199#433—21no—
200#432C22×C15111yescharacteristic
201#432C22×C15111yescharacteristic
202#432C22×C15111yescharacteristic
203#424—21no—
204#423C22×C15111yescharacteristic
205C4×M16C22×C15111yescharacteristic
206#343—21no—
207#343—21no—
208#332—21no—
209#332—21no—
210#330—21no—
211#329—21no—
212C22×Q8—21no—
213C2×M16—21no—
214C2×M16—21no—
215C2×M16D4×C15111yescharacteristic
216C2×M16D4×C15111yescharacteristic
217C22×C8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222#126—21no—
223#125D4×C15111yescharacteristic
224#124D4×C15111yescharacteristic
225#123—21no—
226C22⋊Q8C2×C4×C15111yescharacteristic
227#121C2×C4×C15111yescharacteristic
228C4×Q8D4×C15111yescharacteristic
229C4×D4—21no—
230C4×D4D4×C15111yescharacteristic
231#117—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4C2×C4×C15112yes—
234C2×C42C23×C15111yescharacteristic
235#107—22no—
236#106—22no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8D4×C15111yescharacteristic
244C4⋊C8D4×C15111yescharacteristic
245#103—22no—
246#102—22no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249C22⋊C8—21no—
250C22⋊C8—21no—
251C22⋊C8C2×C4×C15112yes—
252#97—21no—
253#97—21no—
254#97—21no—
255#97—21no—
256#97—21no—
257C4×C8—21no—
258C4×C8—21no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×Q8—82no—
262C2×Q8C22⋊C4×C15111yescharacteristic
263C2×D4—21no—
264C2×D4C22⋊C4×C15111yescharacteristic
265C22×C4—21no—
266C22×C4—22no—
267C22×C4C22×C4×C15111yescharacteristic
268C22×C4C2×D4×C15111yescharacteristic
269C22×C4#41×C15111yescharacteristic
270M16—22no—
271M16—41no—
272M16—41no—
273M16—41no—
274M16—81no—
275C2×C8—22no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—81no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4C22⋊C4×C15111yescharacteristic
292C4⋊C4C22⋊C4×C15111yescharacteristic
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—21no—
298C42—21no—
299C42C2×D4×C15111yescharacteristic
300C42C2×D4×C15111yescharacteristic
301C42C2×D4×C15111yescharacteristic
302C42#41×C15111yescharacteristic
303C23—21no—
304C23C4×D4×C15111yescharacteristic
305Q8—41no—
306Q8—82no—
307Q8—82no—
308D4—41no—
309D4—81no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—82no—
321C2×C4C2×C22⋊C4×C15111yescharacteristic
322C2×C4C4×D4×C15111yescharacteristic
323C2×C4#120×C15111yescharacteristic
324C2×C4#121×C15111yescharacteristic
325C2×C4#121×C15111yescharacteristic
326C2×C4#123×C15111yescharacteristic
327C8—42no—
328C8—42no—
329C8—41no—
330C8—41no—
331C8—41no—
332C8—41no—
333C8—81no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22#386×C15111yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—82no—
350C4#455×C15111yescharacteristic
351C4#456×C15111yescharacteristic
352C2—41no—
353C2—81no—
354C2#1882×C15111yescharacteristic
355C2#1903×C15111yescharacteristic
356C2#1915×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#386
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radical#121×C151C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1997×C151C2semidirect
4. #1556×C151C2semidirect
6. #1307×C151C2semidirect
7. #1291×C151C2semidirect
178. #9338C151direct (N × H)
179. C151#9338direct (N × H)
182. #1997C2×C151semidirect
183. #1556C2×C151semidirect
185. #1307C2×C151semidirect
186. #1291C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3238×C1512
#2995×C1512
#1997×C1512
#1556×C1512
#1529×C1512
#1307×C1512
#1291×C1512
#9338151