Finite Group Databasebeta

← C151×#10025 #50314950

Subgroups — C151×#10025 #50314950

Order 38656.

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

normal subgroups only

This group has 470 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#3166×C151C211yesmaximal, characteristic
2#3113×C151C211yesmaximal, characteristic
3#2634×C151C211yesmaximal, characteristic
4#1534×C151C211yesmaximal, characteristic
5#1515×C151C211yesmaximal, characteristic
6#1491×C151C211yesmaximal, characteristic
7#1288×C151C211yesmaximal, characteristic
8#533×C151C2211yescharacteristic
9C2×#125×C151C2211yescharacteristic
10C2×C4×Q8×C151C2211yescharacteristic
11#501×C151—21no—
12#501×C151—21no—
13#499×C151—22no—
14#483×C151—21no—
15#475×C151—21no—
16#462×C151—21no—
17#451×C151—21no—
18#441×C151—22no—
19#432×C151C2211yescharacteristic
20#432×C151C2211yescharacteristic
21#428×C151—21no—
22#428×C151—21no—
23C4×M16×C151C2211yescharacteristic
24#400×C151—21no—
25#400×C151—21no—
26#398×C151—21no—
27#395×C151—21no—
28#387×C151—22no—
29#383×C151C2211yescharacteristic
30#330×C151—22no—
31#328×C151—22no—
32Q8⋊C8×C151—22no—
33C22×Q8×C151D411yescharacteristic
34C2×Q16×C151—22no—
35C2×M16×C151—21no—
36C4⋊Q8×C151D411yescharacteristic
37C4⋊Q8×C151D411yescharacteristic
38#125×C151—21no—
39#125×C151—21no—
40#125×C151—21no—
41#125×C151—21no—
42#125×C151—21no—
43C22⋊Q8×C151—21no—
44C22⋊Q8×C151—21no—
45C4×Q8×C151—21no—
46C4×Q8×C151—21no—
47C4×Q8×C151—21no—
48C4×Q8×C151—21no—
49C4×Q8×C151—21no—
50C4×Q8×C151—21no—
51#117×C151—21no—
52C2×C4⋊C4×C151—22no—
53C2×C4⋊C4×C151—21no—
54C2×C4⋊C4×C151—21no—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151D411yescharacteristic
57C2×C4⋊C4×C151D411yescharacteristic
58C2×C4⋊C4×C151D411yescharacteristic
59C2×C42×C151—21no—
60C2×C42×C151C2311yescharacteristic
61#107×C151—22no—
62#107×C151—22no—
63#106×C151—22no—
64#106×C151—22no—
65#106×C151—22no—
66C4⋊C8×C151—21no—
67C4⋊C8×C151—21no—
68#103×C151—22no—
69#103×C151—22no—
70C22⋊C8×C151—21no—
71C22⋊C8×C151—21no—
72#97×C151—21no—
73#97×C151—21no—
74#97×C151D412yes—
75C4×C8×C151D412yes—
76#95×C151—22no—
77#95×C151—22no—
78#95×C151—22no—
79#95×C151—21no—
80#95×C151—21no—
81#95×C151D412yes—
82C2×Q8×C151—21no—
83C2×Q8×C151—21no—
84C2×Q8×C151—21no—
85C2×Q8×C151—21no—
86C2×Q8×C151—42no—
87C22×C4×C151—21no—
88C22×C4×C151—22no—
89C22×C4×C151—21no—
90C22×C4×C151—21no—
91C22×C4×C151—21no—
92C22×C4×C151C2×D411yescharacteristic
93C22×C4×C151C2×D411yescharacteristic
94C22×C4×C151C2×D411yescharacteristic
95Q16×C151—44no—
96M16×C151—24no—
97C2×C8×C151—22no—
98C2×C8×C151—22no—
99C2×C8×C151—41no—
100C4⋊C4×C151—21no—
101C4⋊C4×C151—21no—
102C4⋊C4×C151—21no—
103C4⋊C4×C151—21no—
104C4⋊C4×C151—21no—
105C4⋊C4×C151—21no—
106C4⋊C4×C151—21no—
107C4⋊C4×C151—21no—
108C4⋊C4×C151—21no—
109C4⋊C4×C151—21no—
110C4⋊C4×C151—44no—
111C4⋊C4×C151—41no—
112C4⋊C4×C151—41no—
113C4⋊C4×C151—41no—
114C4⋊C4×C151—41no—
115C4⋊C4×C151—41no—
116C4⋊C4×C151—41no—
117C4⋊C4×C151—41no—
118C4⋊C4×C151—41no—
119C22⋊C4×C151—41no—
120C42×C151—41no—
121C42×C151—41no—
122C42×C151—41no—
123C42×C151C2×D411yescharacteristic
124C42×C151C2×D411yescharacteristic
125C42×C151C2×D411yescharacteristic
126C42×C151#4111yescharacteristic
127C23×C151#12011yescharacteristic
128Q8×C151—22no—
129Q8×C151—22no—
130Q8×C151—41no—
131Q8×C151—41no—
132Q8×C151—42no—
133Q8×C151—81no—
134C2×C4×C151—22no—
135C2×C4×C151—22no—
136C2×C4×C151—41no—
137C2×C4×C151—41no—
138C2×C4×C151—41no—
139C2×C4×C151—41no—
140C2×C4×C151—42no—
141C2×C4×C151—42no—
142C2×C4×C151—42no—
143C2×C4×C151—42no—
144C2×C4×C151—41no—
145C2×C4×C151—41no—
146C2×C4×C151—41no—
147C2×C4×C151—41no—
148C2×C4×C151—41no—
149C2×C4×C151—42no—
150C2×C4×C151—42no—
151C2×C4×C151#12011yescharacteristic
152C2×C4×C151#12011yescharacteristic
153C2×C4×C151#12111yescharacteristic
154C2×C4×C151#12111yescharacteristic
155C2×C4×C151#12111yescharacteristic
156C2×C4×C151#12711yescharacteristic
157C8×C151—24no—
158C8×C151—42no—
159C8×C151—81no—
160C22×C151—21no—
161C22×C151—21no—
162C22×C151#39211yescharacteristic
163C22×C151#45612yes—
164C4×C151—21no—
165C4×C151—21no—
166C4×C151—21no—
167C4×C151—21no—
168C4×C151—21no—
169C4×C151—21no—
170C4×C151—42no—
171C4×C151—82no—
172C4×C151—81no—
173C4×C151—81no—
174C4×C151—81no—
175C4×C151—81no—
176C4×C151—81no—
177C2×C151—22no—
178C2×C151#200511yescharacteristic
179C2×C151#200911yescharacteristic
180C2×C151#201011yescharacteristic
181#10025C15111yesmaximal, characteristic, direct product factor, Sylow
182C151#1002511yescharacteristic, direct product factor, Sylow
183#3166C2×C15111yescharacteristic
184#3113C2×C15111yescharacteristic
185#2634C2×C15111yescharacteristic
186#1534C2×C15111yescharacteristic
187#1515C2×C15111yescharacteristic
188#1491C2×C15111yescharacteristic
189#1288C2×C15111yescharacteristic
190#533C22×C15111yescharacteristic
191C2×#125C22×C15111yescharacteristic
192C2×C4×Q8C22×C15111yescharacteristic
193#501—21no—
194#501—21no—
195#499—22no—
196#483—21no—
197#475—21no—
198#462—21no—
199#451—21no—
200#441—22no—
201#432C22×C15111yescharacteristic
202#432C22×C15111yescharacteristic
203#428—21no—
204#428—21no—
205C4×M16C22×C15111yescharacteristic
206#400—21no—
207#400—21no—
208#398—21no—
209#395—21no—
210#387—22no—
211#383C22×C15111yescharacteristic
212#330—22no—
213#328—22no—
214Q8⋊C8—22no—
215C22×Q8D4×C15111yescharacteristic
216C2×Q16—22no—
217C2×M16—21no—
218C4⋊Q8D4×C15111yescharacteristic
219C4⋊Q8D4×C15111yescharacteristic
220#125—21no—
221#125—21no—
222#125—21no—
223#125—21no—
224#125—21no—
225C22⋊Q8—21no—
226C22⋊Q8—21no—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×Q8—21no—
231C4×Q8—21no—
232C4×Q8—21no—
233#117—21no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4D4×C15111yescharacteristic
239C2×C4⋊C4D4×C15111yescharacteristic
240C2×C4⋊C4D4×C15111yescharacteristic
241C2×C42—21no—
242C2×C42C23×C15111yescharacteristic
243#107—22no—
244#107—22no—
245#106—22no—
246#106—22no—
247#106—22no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250#103—22no—
251#103—22no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254#97—21no—
255#97—21no—
256#97D4×C15112yes—
257C4×C8D4×C15112yes—
258#95—22no—
259#95—22no—
260#95—22no—
261#95—21no—
262#95—21no—
263#95D4×C15112yes—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—21no—
268C2×Q8—42no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4C2×D4×C15111yescharacteristic
275C22×C4C2×D4×C15111yescharacteristic
276C22×C4C2×D4×C15111yescharacteristic
277Q16—44no—
278M16—24no—
279C2×C8—22no—
280C2×C8—22no—
281C2×C8—41no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—44no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C22⋊C4—41no—
302C42—41no—
303C42—41no—
304C42—41no—
305C42C2×D4×C15111yescharacteristic
306C42C2×D4×C15111yescharacteristic
307C42C2×D4×C15111yescharacteristic
308C42#41×C15111yescharacteristic
309C23#120×C15111yescharacteristic
310Q8—22no—
311Q8—22no—
312Q8—41no—
313Q8—41no—
314Q8—42no—
315Q8—81no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4#120×C15111yescharacteristic
334C2×C4#120×C15111yescharacteristic
335C2×C4#121×C15111yescharacteristic
336C2×C4#121×C15111yescharacteristic
337C2×C4#121×C15111yescharacteristic
338C2×C4#127×C15111yescharacteristic
339C8—24no—
340C8—42no—
341C8—81no—
342C22—21no—
343C22—21no—
344C22#392×C15111yescharacteristic
345C22#456×C15112yes—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—42no—
353C4—82no—
354C4—81no—
355C4—81no—
356C4—81no—
357C4—81no—
358C4—81no—
359C2—22no—
360C2#2005×C15111yescharacteristic
361C2#2009×C15111yescharacteristic
362C2#2010×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#392
commutator, Frattini, cosocleC2×C42C23×C151
prime radicalC23×C151#120
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
181. #10025C151direct (N × H)
182. C151#10025direct (N × H)

Maximal subgroups

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

subgroupindex
#3166×C1512
#3113×C1512
#2634×C1512
#1534×C1512
#1515×C1512
#1491×C1512
#1288×C1512
#10025151