Finite Group Databasebeta

← C151×#11805 #50316730

Subgroups — C151×#11805 #50316730

Order 38656.

448 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 98 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
1#2618×C151C211yesmaximal, characteristic
2#1821×C151C211yesmaximal, characteristic, complemented
3#1463×C151C211yesmaximal, characteristic, complemented
4#1346×C151C212yesmaximal, complemented
5#1345×C151C212yesmaximal, complemented
6C2×#123×C151—21no—
7C2×#121×C151C411yescharacteristic
8C22×C4⋊C4×C151C2211yescharacteristic
9#407×C151—21no—
10#407×C151—21no—
11#398×C151C411yescharacteristic
12#398×C151C2211yescharacteristic
13#396×C151—21no—
14#396×C151—21no—
15#394×C151C411yescharacteristic
16#394×C151C2211yescharacteristic
17#386×C151—21no—
18#380×C151C411yescharacteristic
19#343×C151—21no—
20#343×C151C2212yes—
21#324×C151—21no—
22#324×C151C2212yes—
23C22×D4×C151—21no—
24C22×D4×C151C2×C411yescharacteristic
25C23×C4×C151C2×C411yescharacteristic
26C23×C4×C151D411yescharacteristic
27C23×C4×C151D411yescharacteristic
28C2×M16×C151—22no—
29C2×M16×C151—41no—
30#123×C151—44no—
31#121×C151—41no—
32#121×C151—41no—
33C2×C4⋊C4×C151—21no—
34C2×C4⋊C4×C151—21no—
35C2×C4⋊C4×C151—21no—
36C2×C4⋊C4×C151—41no—
37C2×C4⋊C4×C151—41no—
38C2×C4⋊C4×C151C2×C411yescharacteristic
39C2×C4⋊C4×C151C2×C411yescharacteristic
40C2×C4⋊C4×C151D411yescharacteristic
41C2×C4⋊C4×C151D411yescharacteristic
42C2×C4⋊C4×C151C2311yescharacteristic
43C2×C22⋊C4×C151—21no—
44C2×C22⋊C4×C151—21no—
45C2×C22⋊C4×C151—21no—
46C2×C22⋊C4×C151—21no—
47C2×C22⋊C4×C151—21no—
48C2×C22⋊C4×C151—21no—
49C22⋊C8×C151—22no—
50C22⋊C8×C151—41no—
51C22⋊C8×C151—41no—
52C22⋊C8×C151—41no—
53#95×C151—21no—
54#95×C151—21no—
55#95×C151C2×C411yescharacteristic
56#95×C151C2×C411yescharacteristic
57C24×C151—21no—
58C24×C151C22⋊C411yescharacteristic
59C2×D4×C151—41no—
60C2×D4×C151—42no—
61C2×D4×C151—42no—
62C2×D4×C151—41no—
63C2×D4×C151—41no—
64C2×D4×C151—81no—
65C22×C4×C151—21no—
66C22×C4×C151—21no—
67C22×C4×C151—21no—
68C22×C4×C151—21no—
69C22×C4×C151—21no—
70C22×C4×C151—21no—
71C22×C4×C151—22no—
72C22×C4×C151—21no—
73C22×C4×C151—21no—
74C22×C4×C151—21no—
75C22×C4×C151—41no—
76C22×C4×C151—81no—
77C22×C4×C151—81no—
78C22×C4×C151C22⋊C411yescharacteristic
79C22×C4×C151C22⋊C411yescharacteristic
80C22×C4×C151C22⋊C411yescharacteristic
81C22×C4×C151C22×C411yescharacteristic
82C22×C4×C151C2×D411yescharacteristic
83C22×C4×C151C2×D411yescharacteristic
84M16×C151—42no—
85M16×C151—42no—
86M16×C151—82no—
87C2×C8×C151—42no—
88C2×C8×C151—42no—
89C4⋊C4×C151—41no—
90C4⋊C4×C151—41no—
91C4⋊C4×C151—41no—
92C4⋊C4×C151—41no—
93C4⋊C4×C151—41no—
94C4⋊C4×C151—42no—
95C4⋊C4×C151—42no—
96C4⋊C4×C151—81no—
97C22⋊C4×C151—42no—
98C22⋊C4×C151—42no—
99C22⋊C4×C151—42no—
100C22⋊C4×C151—42no—
101C22⋊C4×C151—81no—
102C22⋊C4×C151—81no—
103C23×C151—21no—
104C23×C151—21no—
105C23×C151—41no—
106C23×C151—41no—
107C23×C151—41no—
108C23×C151—41no—
109C23×C151—41no—
110C23×C151—41no—
111C23×C151—41no—
112C23×C151—41no—
113C23×C151—41no—
114C23×C151#9911yescharacteristic
115C23×C151#9911yescharacteristic
116C23×C151C2×C22⋊C411yescharacteristic
117D4×C151—82no—
118D4×C151—82no—
119D4×C151—82no—
120C2×C4×C151—21no—
121C2×C4×C151—21no—
122C2×C4×C151—21no—
123C2×C4×C151—21no—
124C2×C4×C151—21no—
125C2×C4×C151—21no—
126C2×C4×C151—21no—
127C2×C4×C151—21no—
128C2×C4×C151—21no—
129C2×C4×C151—42no—
130C2×C4×C151—42no—
131C2×C4×C151—42no—
132C2×C4×C151—41no—
133C2×C4×C151—41no—
134C2×C4×C151—41no—
135C2×C4×C151—41no—
136C2×C4×C151—41no—
137C2×C4×C151—41no—
138C2×C4×C151—41no—
139C2×C4×C151—41no—
140C2×C4×C151—41no—
141C2×C4×C151—41no—
142C2×C4×C151—41no—
143C2×C4×C151—41no—
144C2×C4×C151—41no—
145C2×C4×C151—81no—
146C2×C4×C151—81no—
147C2×C4×C151—81no—
148C2×C4×C151AGL(1,ℤ/8)12yes—
149C8×C151—82no—
150C8×C151—82no—
151C22×C151—21no—
152C22×C151—21no—
153C22×C151—21no—
154C22×C151—21no—
155C22×C151—21no—
156C22×C151—21no—
157C22×C151—21no—
158C22×C151—21no—
159C22×C151—42no—
160C22×C151—42no—
161C22×C151—81no—
162C22×C151—81no—
163C22×C151—81no—
164C22×C151—81no—
165C22×C151—81no—
166C22×C151—81no—
167C22×C151—81no—
168C22×C151C2×#9911yescharacteristic
169C22×C151#41811yescharacteristic
170C22×C151#42111yescharacteristic
171C4×C151—22no—
172C4×C151—41no—
173C4×C151—41no—
174C4×C151—41no—
175C4×C151—41no—
176C4×C151—41no—
177C4×C151—81no—
178C4×C151—81no—
179C4×C151—81no—
180C2×C151—21no—
181C2×C151—21no—
182C2×C151—41no—
183C2×C151—41no—
184C2×C151—161no—
185C2×C151#151011yescharacteristic
186C2×C151#212111yescharacteristic
187C2×C151#213311yescharacteristic
188#11805C15111yesmaximal, characteristic, direct product factor, Sylow
189C151#1180511yescharacteristic, direct product factor, Sylow
190#2618C2×C15111yescharacteristic
191#1821C2×C15111yescharacteristic, complemented
192#1463C2×C15111yescharacteristic, complemented
193#1346C2×C15112yescomplemented
194#1345C2×C15112yescomplemented
195C2×#123—21no—
196C2×#121C4×C15111yescharacteristic
197C22×C4⋊C4C22×C15111yescharacteristic
198#407—21no—
199#407—21no—
200#398C4×C15111yescharacteristic
201#398C22×C15111yescharacteristic
202#396—21no—
203#396—21no—
204#394C4×C15111yescharacteristic
205#394C22×C15111yescharacteristic
206#386—21no—
207#380C4×C15111yescharacteristic
208#343—21no—
209#343C22×C15112yes—
210#324—21no—
211#324C22×C15112yes—
212C22×D4—21no—
213C22×D4C2×C4×C15111yescharacteristic
214C23×C4C2×C4×C15111yescharacteristic
215C23×C4D4×C15111yescharacteristic
216C23×C4D4×C15111yescharacteristic
217C2×M16—22no—
218C2×M16—41no—
219#123—44no—
220#121—41no—
221#121—41no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—41no—
226C2×C4⋊C4—41no—
227C2×C4⋊C4C2×C4×C15111yescharacteristic
228C2×C4⋊C4C2×C4×C15111yescharacteristic
229C2×C4⋊C4D4×C15111yescharacteristic
230C2×C4⋊C4D4×C15111yescharacteristic
231C2×C4⋊C4C23×C15111yescharacteristic
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C22⋊C8—22no—
239C22⋊C8—41no—
240C22⋊C8—41no—
241C22⋊C8—41no—
242#95—21no—
243#95—21no—
244#95C2×C4×C15111yescharacteristic
245#95C2×C4×C15111yescharacteristic
246C24—21no—
247C24C22⋊C4×C15111yescharacteristic
248C2×D4—41no—
249C2×D4—42no—
250C2×D4—42no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—81no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—41no—
265C22×C4—81no—
266C22×C4—81no—
267C22×C4C22⋊C4×C15111yescharacteristic
268C22×C4C22⋊C4×C15111yescharacteristic
269C22×C4C22⋊C4×C15111yescharacteristic
270C22×C4C22×C4×C15111yescharacteristic
271C22×C4C2×D4×C15111yescharacteristic
272C22×C4C2×D4×C15111yescharacteristic
273M16—42no—
274M16—42no—
275M16—82no—
276C2×C8—42no—
277C2×C8—42no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—42no—
284C4⋊C4—42no—
285C4⋊C4—81no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C22⋊C4—81no—
291C22⋊C4—81no—
292C23—21no—
293C23—21no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23#99×C15111yescharacteristic
304C23#99×C15111yescharacteristic
305C23C2×C22⋊C4×C15111yescharacteristic
306D4—82no—
307D4—82no—
308D4—82no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4AGL(1,ℤ/8)×C15112yes—
338C8—82no—
339C8—82no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—42no—
349C22—42no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22C2×#99×C15111yescharacteristic
358C22#418×C15111yescharacteristic
359C22#421×C15111yescharacteristic
360C4—22no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—81no—
367C4—81no—
368C4—81no—
369C2—21no—
370C2—21no—
371C2—41no—
372C2—41no—
373C2—161no—
374C2#1510×C15111yescharacteristic
375C2#2121×C15111yescharacteristic
376C2#2133×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#99
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C4⋊C4C23×C151
prime radicalC2×#121×C151C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C24×C151 ◁ C22×C4⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1821×C151C2semidirect
3. #1463×C151C2semidirect
4. #1346×C151C2semidirect
5. #1345×C151C2semidirect
188. #11805C151direct (N × H)
189. C151#11805direct (N × H)
191. #1821C2×C151semidirect
192. #1463C2×C151semidirect
193. #1346C2×C151semidirect
194. #1345C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2618×C1512
#1821×C1512
#1463×C1512
#1346×C1512
#1345×C1512
#11805151