Finite Group Databasebeta

← C151×#10024 #50314949

Subgroups — C151×#10024 #50314949

Order 38656.

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

normal subgroups only

This group has 512 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#3140×C151C211yesmaximal, characteristic
2#3113×C151C211yesmaximal, characteristic, complemented
3#2632×C151C211yesmaximal, characteristic
4#1533×C151C211yesmaximal, characteristic
5#1515×C151C211yesmaximal, characteristic, complemented
6#1491×C151C211yesmaximal, characteristic, complemented
7#1288×C151C211yesmaximal, characteristic, complemented
8#533×C151C2211yescharacteristic
9C2×#124×C151C2211yescharacteristic
10C2×C4×Q8×C151C2211yescharacteristic
11#489×C151—21no—
12#489×C151—21no—
13#488×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#419×C151—21no—
22#418×C151—21no—
23C4×M16×C151C2211yescharacteristic
24#399×C151—21no—
25#395×C151—21no—
26#394×C151—21no—
27#393×C151—21no—
28#388×C151—22no—
29#383×C151C2211yescharacteristic
30#329×C151—22no—
31#328×C151—22no—
32Q8⋊C8×C151—22no—
33C22×Q8×C151D411yescharacteristic
34C22×Q8×C151D411yescharacteristic
35C22×D4×C151D411yescharacteristic
36C2×Q16×C151—22no—
37C2×M16×C151—21no—
38C4⋊Q8×C151D411yescharacteristic
39C4⋊Q8×C151D411yescharacteristic
40#125×C151—21no—
41#124×C151—21no—
42#124×C151—21no—
43#124×C151—21no—
44#124×C151—21no—
45C22⋊Q8×C151—21no—
46C22⋊Q8×C151—21no—
47C4×Q8×C151—21no—
48C4×Q8×C151—21no—
49C4×Q8×C151—21no—
50C4×Q8×C151—21no—
51C4×Q8×C151—21no—
52C4×Q8×C151—21no—
53#117×C151—21no—
54C2×C4⋊C4×C151—21no—
55C2×C4⋊C4×C151—22no—
56C2×C4⋊C4×C151D411yescharacteristic
57C2×C22⋊C4×C151—22no—
58C2×C22⋊C4×C151—21no—
59C2×C22⋊C4×C151—21no—
60C2×C22⋊C4×C151—22no—
61C2×C42×C151—21no—
62C2×C42×C151C2311yescharacteristic
63#106×C151—22no—
64C4⋊C8×C151—21no—
65C4⋊C8×C151—21no—
66#103×C151—22no—
67#103×C151—22no—
68#103×C151—22no—
69#103×C151—22no—
70#102×C151—22no—
71#102×C151—22no—
72C22⋊C8×C151—21no—
73C22⋊C8×C151—21no—
74#97×C151—21no—
75#97×C151—21no—
76#97×C151D412yes—
77C4×C8×C151D412yes—
78#95×C151—22no—
79#95×C151—21no—
80#95×C151—21no—
81#95×C151D412yes—
82C24×C151—21no—
83C2×Q8×C151—21no—
84C2×Q8×C151—21no—
85C2×Q8×C151—21no—
86C2×Q8×C151—21no—
87C2×Q8×C151—21no—
88C2×Q8×C151—21no—
89C2×Q8×C151—42no—
90C2×Q8×C151—42no—
91C2×D4×C151—21no—
92C2×D4×C151—21no—
93C2×D4×C151—42no—
94C22×C4×C151—21no—
95C22×C4×C151—22no—
96C22×C4×C151—21no—
97C22×C4×C151—21no—
98C22×C4×C151C2×D411yescharacteristic
99C22×C4×C151C2×D411yescharacteristic
100C22×C4×C151C2×D411yescharacteristic
101Q16×C151—44no—
102M16×C151—42no—
103C2×C8×C151—22no—
104C2×C8×C151—22no—
105C2×C8×C151—41no—
106C4⋊C4×C151—21no—
107C4⋊C4×C151—21no—
108C4⋊C4×C151—21no—
109C4⋊C4×C151—21no—
110C4⋊C4×C151—21no—
111C4⋊C4×C151—21no—
112C4⋊C4×C151—41no—
113C4⋊C4×C151—41no—
114C4⋊C4×C151—41no—
115C4⋊C4×C151—41no—
116C4⋊C4×C151—82no—
117C22⋊C4×C151—44no—
118C22⋊C4×C151—41no—
119C22⋊C4×C151—41no—
120C22⋊C4×C151—41no—
121C22⋊C4×C151—41no—
122C22⋊C4×C151—41no—
123C22⋊C4×C151—82no—
124C42×C151—41no—
125C42×C151—41no—
126C42×C151—41no—
127C42×C151C2×D411yescharacteristic
128C42×C151C2×D411yescharacteristic
129C42×C151C2×D411yescharacteristic
130C42×C151#4111yescharacteristic
131C23×C151—42no—
132C23×C151—42no—
133C23×C151—41no—
134C23×C151—42no—
135C23×C151#12011yescharacteristic
136Q8×C151—22no—
137Q8×C151—22no—
138Q8×C151—41no—
139Q8×C151—41no—
140Q8×C151—42no—
141Q8×C151—42no—
142Q8×C151—81no—
143Q8×C151—81no—
144D4×C151—42no—
145D4×C151—81no—
146C2×C4×C151—22no—
147C2×C4×C151—22no—
148C2×C4×C151—41no—
149C2×C4×C151—41no—
150C2×C4×C151—41no—
151C2×C4×C151—41no—
152C2×C4×C151—42no—
153C2×C4×C151—42no—
154C2×C4×C151—41no—
155C2×C4×C151—41no—
156C2×C4×C151—41no—
157C2×C4×C151—41no—
158C2×C4×C151—42no—
159C2×C4×C151—42no—
160C2×C4×C151—42no—
161C2×C4×C151#12011yescharacteristic
162C2×C4×C151#12011yescharacteristic
163C2×C4×C151#12111yescharacteristic
164C2×C4×C151#12111yescharacteristic
165C2×C4×C151#12111yescharacteristic
166C2×C4×C151#12711yescharacteristic
167C8×C151—42no—
168C8×C151—42no—
169C8×C151—81no—
170C22×C151—21no—
171C22×C151—21no—
172C22×C151—84no—
173C22×C151—81no—
174C22×C151—81no—
175C22×C151—81no—
176C22×C151#39211yescharacteristic
177C22×C151#45512yes—
178C4×C151—21no—
179C4×C151—21no—
180C4×C151—21no—
181C4×C151—21no—
182C4×C151—21no—
183C4×C151—21no—
184C4×C151—42no—
185C4×C151—82no—
186C4×C151—81no—
187C4×C151—81no—
188C4×C151—81no—
189C4×C151—81no—
190C2×C151—22no—
191C2×C151—161no—
192C2×C151#200411yescharacteristic
193C2×C151#200911yescharacteristic
194C2×C151#201011yescharacteristic
195#10024C15111yesmaximal, characteristic, direct product factor, Sylow
196C151#1002411yescharacteristic, direct product factor, Sylow
197#3140C2×C15111yescharacteristic
198#3113C2×C15111yescharacteristic, complemented
199#2632C2×C15111yescharacteristic
200#1533C2×C15111yescharacteristic
201#1515C2×C15111yescharacteristic, complemented
202#1491C2×C15111yescharacteristic, complemented
203#1288C2×C15111yescharacteristic, complemented
204#533C22×C15111yescharacteristic
205C2×#124C22×C15111yescharacteristic
206C2×C4×Q8C22×C15111yescharacteristic
207#489—21no—
208#489—21no—
209#488—22no—
210#483—21no—
211#475—21no—
212#462—21no—
213#451—21no—
214#441—22no—
215#432C22×C15111yescharacteristic
216#432C22×C15111yescharacteristic
217#419—21no—
218#418—21no—
219C4×M16C22×C15111yescharacteristic
220#399—21no—
221#395—21no—
222#394—21no—
223#393—21no—
224#388—22no—
225#383C22×C15111yescharacteristic
226#329—22no—
227#328—22no—
228Q8⋊C8—22no—
229C22×Q8D4×C15111yescharacteristic
230C22×Q8D4×C15111yescharacteristic
231C22×D4D4×C15111yescharacteristic
232C2×Q16—22no—
233C2×M16—21no—
234C4⋊Q8D4×C15111yescharacteristic
235C4⋊Q8D4×C15111yescharacteristic
236#125—21no—
237#124—21no—
238#124—21no—
239#124—21no—
240#124—21no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×Q8—21no—
248C4×Q8—21no—
249#117—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4D4×C15111yescharacteristic
253C2×C22⋊C4—22no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—22no—
257C2×C42—21no—
258C2×C42C23×C15111yescharacteristic
259#106—22no—
260C4⋊C8—21no—
261C4⋊C8—21no—
262#103—22no—
263#103—22no—
264#103—22no—
265#103—22no—
266#102—22no—
267#102—22no—
268C22⋊C8—21no—
269C22⋊C8—21no—
270#97—21no—
271#97—21no—
272#97D4×C15112yes—
273C4×C8D4×C15112yes—
274#95—22no—
275#95—21no—
276#95—21no—
277#95D4×C15112yes—
278C24—21no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—42no—
286C2×Q8—42no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—42no—
290C22×C4—21no—
291C22×C4—22no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4C2×D4×C15111yescharacteristic
295C22×C4C2×D4×C15111yescharacteristic
296C22×C4C2×D4×C15111yescharacteristic
297Q16—44no—
298M16—42no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—41no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—82no—
313C22⋊C4—44no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—82no—
320C42—41no—
321C42—41no—
322C42—41no—
323C42C2×D4×C15111yescharacteristic
324C42C2×D4×C15111yescharacteristic
325C42C2×D4×C15111yescharacteristic
326C42#41×C15111yescharacteristic
327C23—42no—
328C23—42no—
329C23—41no—
330C23—42no—
331C23#120×C15111yescharacteristic
332Q8—22no—
333Q8—22no—
334Q8—41no—
335Q8—41no—
336Q8—42no—
337Q8—42no—
338Q8—81no—
339Q8—81no—
340D4—42no—
341D4—81no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4#120×C15111yescharacteristic
358C2×C4#120×C15111yescharacteristic
359C2×C4#121×C15111yescharacteristic
360C2×C4#121×C15111yescharacteristic
361C2×C4#121×C15111yescharacteristic
362C2×C4#127×C15111yescharacteristic
363C8—42no—
364C8—42no—
365C8—81no—
366C22—21no—
367C22—21no—
368C22—84no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22#392×C15111yescharacteristic
373C22#455×C15112yes—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—42no—
381C4—82no—
382C4—81no—
383C4—81no—
384C4—81no—
385C4—81no—
386C2—22no—
387C2—161no—
388C2#2004×C15111yescharacteristic
389C2#2009×C15111yescharacteristic
390C2#2010×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#392
commutator, Frattini, cosocleC2×C42C23×C151
prime radicalC22×D4×C151D4
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
2. #3113×C151C2semidirect
5. #1515×C151C2semidirect
6. #1491×C151C2semidirect
7. #1288×C151C2semidirect
195. #10024C151direct (N × H)
196. C151#10024direct (N × H)
198. #3113C2×C151semidirect
201. #1515C2×C151semidirect
202. #1491C2×C151semidirect
203. #1288C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3140×C1512
#3113×C1512
#2632×C1512
#1533×C1512
#1515×C1512
#1491×C1512
#1288×C1512
#10024151