Finite Group Databasebeta

← C151×#11808 #50316733

Subgroups — C151×#11808 #50316733

Order 38656.

680 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 680 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#393×C151C211yesmaximal, characteristic
2#1819×C151C211yesmaximal, characteristic
3#1462×C151C211yesmaximal, characteristic
4#1351×C151C214yesmaximal, complemented
5C23×Q8×C151C411yescharacteristic, complemented
6C22×C22⋊C4×C151—21no—
7C22×C22⋊C4×C151C2211yescharacteristic
8#407×C151—21no—
9#393×C151—21no—
10#393×C151—21no—
11#393×C151C412yescomplemented
12#393×C151C2212yes—
13#379×C151—21no—
14C2×#95×C151—21no—
15C2×#95×C151C411yescharacteristic, complemented
16#342×C151—21no—
17#342×C151C2212yes—
18#323×C151—21no—
19#323×C151C2212yes—
20C25×C151D411yescharacteristic
21C22×Q8×C151—21no—
22C22×Q8×C151—41no—
23C22×Q8×C151—41no—
24C22×Q8×C151—44no—
25C22×Q8×C151C2×C412yes—
26C23×C4×C151—21no—
27C23×C4×C151—21no—
28C23×C4×C151C2×C411yescharacteristic
29C23×C4×C151D411yescharacteristic
30C2×M16×C151—41no—
31C2×C22⋊C4×C151—22no—
32C2×C22⋊C4×C151—22no—
33C2×C22⋊C4×C151—22no—
34C2×C22⋊C4×C151—41no—
35C2×C22⋊C4×C151—41no—
36C2×C22⋊C4×C151—41no—
37C2×C22⋊C4×C151—41no—
38C2×C22⋊C4×C151—44no—
39C2×C22⋊C4×C151C2×C411yescharacteristic
40C2×C22⋊C4×C151D411yescharacteristic
41C2×C22⋊C4×C151D411yescharacteristic
42C2×C22⋊C4×C151C2311yescharacteristic
43C22⋊C8×C151—22no—
44C22⋊C8×C151—41no—
45#95×C151—22no—
46#95×C151—21no—
47#95×C151—22no—
48#95×C151C2×C412yes—
49C24×C151—22no—
50C24×C151—21no—
51C24×C151—21no—
52C24×C151—41no—
53C24×C151—42no—
54C24×C151—42no—
55C24×C151C22⋊C411yescharacteristic
56C24×C151C22⋊C411yescharacteristic
57C24×C151C2×D411yescharacteristic
58C2×Q8×C151—44no—
59C2×Q8×C151—44no—
60C2×Q8×C151—42no—
61C2×Q8×C151—42no—
62C2×Q8×C151—48no—
63C2×Q8×C151—44no—
64C2×Q8×C151—44no—
65C22×C4×C151—24no—
66C22×C4×C151—21no—
67C22×C4×C151—21no—
68C22×C4×C151—21no—
69C22×C4×C151—22no—
70C22×C4×C151—21no—
71C22×C4×C151—22no—
72C22×C4×C151—42no—
73C22×C4×C151—41no—
74C22×C4×C151—41no—
75C22×C4×C151—42no—
76C22×C4×C151—42no—
77C22×C4×C151—42no—
78C22×C4×C151—42no—
79C22×C4×C151—42no—
80C22×C4×C151—42no—
81C22×C4×C151C22⋊C411yescharacteristic
82C22×C4×C151C22⋊C411yescharacteristic
83C22×C4×C151C22×C411yescharacteristic
84C22×C4×C151C2×D411yescharacteristic
85M16×C151—82no—
86C2×C8×C151—42no—
87C22⋊C4×C151—41no—
88C22⋊C4×C151—41no—
89C22⋊C4×C151—41no—
90C22⋊C4×C151—41no—
91C22⋊C4×C151—44no—
92C22⋊C4×C151—44no—
93C22⋊C4×C151—42no—
94C22⋊C4×C151—42no—
95C22⋊C4×C151—82no—
96C22⋊C4×C151—82no—
97C23×C151—22no—
98C23×C151—22no—
99C23×C151—21no—
100C23×C151—21no—
101C23×C151—21no—
102C23×C151—21no—
103C23×C151—21no—
104C23×C151—21no—
105C23×C151—21no—
106C23×C151—42no—
107C23×C151—42no—
108C23×C151—41no—
109C23×C151—41no—
110C23×C151—41no—
111C23×C151—41no—
112C23×C151—48no—
113C23×C151—42no—
114C23×C151—42no—
115C23×C151—81no—
116C23×C151—81no—
117C23×C151—84no—
118C23×C151#9911yescharacteristic
119C23×C151#9911yescharacteristic
120C23×C151C2×C22⋊C411yescharacteristic
121C23×C151#13712yes—
122Q8×C151—44no—
123Q8×C151—44no—
124Q8×C151—48no—
125C2×C4×C151—24no—
126C2×C4×C151—21no—
127C2×C4×C151—21no—
128C2×C4×C151—21no—
129C2×C4×C151—21no—
130C2×C4×C151—42no—
131C2×C4×C151—44no—
132C2×C4×C151—42no—
133C2×C4×C151—42no—
134C2×C4×C151—44no—
135C2×C4×C151—42no—
136C2×C4×C151—42no—
137C2×C4×C151—41no—
138C2×C4×C151—41no—
139C2×C4×C151—41no—
140C2×C4×C151—41no—
141C2×C4×C151—42no—
142C2×C4×C151—42no—
143C2×C4×C151—42no—
144C2×C4×C151—81no—
145C2×C4×C151—84no—
146C2×C4×C151—82no—
147C2×C4×C151—82no—
148C2×C4×C151—82no—
149C8×C151—82no—
150C22×C151—24no—
151C22×C151—24no—
152C22×C151—21no—
153C22×C151—21no—
154C22×C151—21no—
155C22×C151—21no—
156C22×C151—21no—
157C22×C151—21no—
158C22×C151—22no—
159C22×C151—42no—
160C22×C151—42no—
161C22×C151—41no—
162C22×C151—41no—
163C22×C151—41no—
164C22×C151—41no—
165C22×C151—41no—
166C22×C151—81no—
167C22×C151—84no—
168C22×C151—84no—
169C22×C151—81no—
170C22×C151AΣL(1,𝔽16)12yes—
171C22×C151#35412yes—
172C22×C151C2×#9911yescharacteristic
173C22×C151#41911yescharacteristic
174C22×C151#42111yescharacteristic
175C4×C151—44no—
176C4×C151—41no—
177C4×C151—41no—
178C4×C151—41no—
179C4×C151—41no—
180C4×C151—82no—
181C4×C151—162no—
182C2×C151—21no—
183C2×C151—21no—
184C2×C151—22no—
185C2×C151—22no—
186C2×C151—42no—
187C2×C151—81no—
188C2×C151#151111yescharacteristic
189C2×C151C2×AΣL(1,𝔽16)11yescharacteristic
190C2×C151C2×#35411yescharacteristic
191#11808C15111yesmaximal, characteristic, direct product factor, Sylow
192C151#1180811yescharacteristic, direct product factor, Sylow
193C2×#393C2×C15111yescharacteristic
194#1819C2×C15111yescharacteristic
195#1462C2×C15111yescharacteristic
196#1351C2×C15114yescomplemented
197C23×Q8C4×C15111yescharacteristic, complemented
198C22×C22⋊C4—21no—
199C22×C22⋊C4C22×C15111yescharacteristic
200#407—21no—
201#393—21no—
202#393—21no—
203#393C4×C15112yescomplemented
204#393C22×C15112yes—
205#379—21no—
206C2×#95—21no—
207C2×#95C4×C15111yescharacteristic, complemented
208#342—21no—
209#342C22×C15112yes—
210#323—21no—
211#323C22×C15112yes—
212C25D4×C15111yescharacteristic
213C22×Q8—21no—
214C22×Q8—44no—
215C22×Q8—41no—
216C22×Q8—41no—
217C22×Q8C2×C4×C15112yes—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4C2×C4×C15111yescharacteristic
221C23×C4D4×C15111yescharacteristic
222C2×M16—41no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—22no—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—41no—
227C2×C22⋊C4—41no—
228C2×C22⋊C4—44no—
229C2×C22⋊C4—41no—
230C2×C22⋊C4—41no—
231C2×C22⋊C4C2×C4×C15111yescharacteristic
232C2×C22⋊C4D4×C15111yescharacteristic
233C2×C22⋊C4D4×C15111yescharacteristic
234C2×C22⋊C4C23×C15111yescharacteristic
235C22⋊C8—22no—
236C22⋊C8—41no—
237#95—22no—
238#95—21no—
239#95—22no—
240#95C2×C4×C15112yes—
241C24—22no—
242C24—21no—
243C24—21no—
244C24—41no—
245C24—42no—
246C24—42no—
247C24C22⋊C4×C15111yescharacteristic
248C24C22⋊C4×C15111yescharacteristic
249C24C2×D4×C15111yescharacteristic
250C2×Q8—44no—
251C2×Q8—44no—
252C2×Q8—42no—
253C2×Q8—42no—
254C2×Q8—48no—
255C2×Q8—44no—
256C2×Q8—44no—
257C22×C4—24no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—22no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—42no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4C22⋊C4×C15111yescharacteristic
274C22×C4C22⋊C4×C15111yescharacteristic
275C22×C4C22×C4×C15111yescharacteristic
276C22×C4C2×D4×C15111yescharacteristic
277M16—82no—
278C2×C8—42no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—44no—
284C22⋊C4—44no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—82no—
288C22⋊C4—82no—
289C23—22no—
290C23—22no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—42no—
299C23—42no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—48no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—81no—
309C23—84no—
310C23#99×C15111yescharacteristic
311C23#99×C15111yescharacteristic
312C23C2×C22⋊C4×C15111yescharacteristic
313C23#137×C15112yes—
314Q8—44no—
315Q8—44no—
316Q8—48no—
317C2×C4—24no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—44no—
324C2×C4—42no—
325C2×C4—44no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—81no—
337C2×C4—84no—
338C2×C4—82no—
339C2×C4—82no—
340C2×C4—82no—
341C8—82no—
342C22—24no—
343C22—24no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—42no—
352C22—42no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—81no—
359C22—84no—
360C22—84no—
361C22—81no—
362C22AΣL(1,𝔽16)×C15112yes—
363C22#354×C15112yes—
364C22C2×#99×C15111yescharacteristic
365C22#419×C15111yescharacteristic
366C22#421×C15111yescharacteristic
367C4—44no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—82no—
373C4—162no—
374C2—21no—
375C2—21no—
376C2—22no—
377C2—22no—
378C2—42no—
379C2—81no—
380C2#1511×C15111yescharacteristic
381C2C2×AΣL(1,𝔽16)×C15111yescharacteristic
382C2C2×#354×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#99
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C22⋊C4C23×C151
prime radicalC25×C151D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C24×C151 ◁ C22×C22⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1351×C151C2semidirect
5. C23×Q8×C151C4semidirect
11. #393×C151C4semidirect
15. C2×#95×C151C4semidirect
191. #11808C151direct (N × H)
192. C151#11808direct (N × H)
196. #1351C2×C151semidirect
197. C23×Q8C4×C151semidirect
203. #393C4×C151semidirect
207. C2×#95C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#393×C1512
#1819×C1512
#1462×C1512
#1351×C1512
#11808151