Finite Group Databasebeta

← C151×#10039 #50314964

Subgroups — C151×#10039 #50314964

Order 38656.

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

normal subgroups only

This group has 510 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#3216×C151C211yesmaximal, characteristic, complemented
2#3109×C151C211yesmaximal, characteristic
3#3101×C151C211yesmaximal, characteristic, complemented
4#1537×C151C211yesmaximal, characteristic, complemented
5#1496×C151C211yesmaximal, characteristic, complemented
6#1466×C151C211yesmaximal, characteristic, complemented
7#1287×C151C211yesmaximal, characteristic, complemented
8#533×C151C2211yescharacteristic
9#532×C151C2211yescharacteristic
10C2×C4×D4×C151C2211yescharacteristic
11#497×C151—21no—
12#489×C151—21no—
13#483×C151—21no—
14#481×C151—21no—
15#476×C151—21no—
16#476×C151—21no—
17#462×C151—21no—
18#461×C151—21no—
19#460×C151—21no—
20#459×C151—21no—
21#452×C151—22no—
22#450×C151—21no—
23#447×C151—21no—
24#442×C151—22no—
25C4×SD16×C151—22no—
26#432×C151C2211yescharacteristic
27#432×C151C2211yescharacteristic
28#432×C151C2211yescharacteristic
29#431×C151C2211yescharacteristic
30#330×C151—22no—
31D4⋊C8×C151—22no—
32#323×C151—22no—
33C2×#41×C151—21no—
34C22×D4×C151D411yescharacteristic
35C23×C4×C151—21no—
36C2×Q16×C151—22no—
37C2×SD16×C151—22no—
38C2×SD16×C151—22no—
39C2×D8×C151—22no—
40C4⋊Q8×C151D411yescharacteristic
41C4⋊Q8×C151D411yescharacteristic
42C4⋊Q8×C151D411yescharacteristic
43#127×C151D411yescharacteristic
44#125×C151—21no—
45#124×C151—21no—
46C22⋊Q8×C151—21no—
47C22⋊Q8×C151—21no—
48#121×C151—21no—
49#121×C151—21no—
50C4×Q8×C151—21no—
51C4×Q8×C151—21no—
52C4×D4×C151—21no—
53C4×D4×C151—21no—
54C4×D4×C151—21no—
55C4×D4×C151—21no—
56C4×D4×C151—21no—
57C4×D4×C151—21no—
58#117×C151—21no—
59C2×C4⋊C4×C151D411yescharacteristic
60C2×C22⋊C4×C151—21no—
61C2×C42×C151C2311yescharacteristic
62#106×C151—22no—
63#106×C151—22no—
64C4⋊C8×C151—21no—
65C4⋊C8×C151—21no—
66C4⋊C8×C151—21no—
67C4⋊C8×C151—21no—
68#103×C151—22no—
69#103×C151—22no—
70#102×C151—22no—
71#102×C151—22no—
72#102×C151—22no—
73#102×C151—22no—
74C22⋊C8×C151—21no—
75C22⋊C8×C151—21no—
76C22⋊C8×C151—21no—
77C22⋊C8×C151D412yes—
78#97×C151—21no—
79#97×C151—21no—
80#97×C151D412yes—
81C4×C8×C151D412yes—
82C24×C151—21no—
83#41×C151—82no—
84C2×Q8×C151—21no—
85C2×Q8×C151—21no—
86C2×Q8×C151—21no—
87C2×D4×C151—21no—
88C2×D4×C151—21no—
89C2×D4×C151—21no—
90C2×D4×C151—21no—
91C2×D4×C151—21no—
92C2×D4×C151—42no—
93C2×D4×C151—41no—
94C22×C4×C151—21no—
95C22×C4×C151—41no—
96C22×C4×C151—41no—
97C22×C4×C151—41no—
98C22×C4×C151—82no—
99C22×C4×C151C2×D411yescharacteristic
100C22×C4×C151C2×D411yescharacteristic
101C22×C4×C151#4111yescharacteristic
102Q16×C151—82no—
103SD16×C151—44no—
104SD16×C151—82no—
105D8×C151—44no—
106C2×C8×C151—22no—
107C2×C8×C151—22no—
108C2×C8×C151—22no—
109C2×C8×C151—41no—
110C4⋊C4×C151—21no—
111C4⋊C4×C151—21no—
112C4⋊C4×C151—21no—
113C4⋊C4×C151—21no—
114C4⋊C4×C151—21no—
115C4⋊C4×C151—21no—
116C4⋊C4×C151—21no—
117C4⋊C4×C151—21no—
118C4⋊C4×C151—41no—
119C4⋊C4×C151—41no—
120C22⋊C4×C151—41no—
121C22⋊C4×C151—41no—
122C22⋊C4×C151—41no—
123C22⋊C4×C151—41no—
124C22⋊C4×C151—41no—
125C42×C151—41no—
126C42×C151C2×D411yescharacteristic
127C42×C151C2×D411yescharacteristic
128C42×C151C2×D411yescharacteristic
129C42×C151C2×D411yescharacteristic
130C23×C151—22no—
131C23×C151—41no—
132C23×C151—41no—
133C23×C151—41no—
134C23×C151—81no—
135C23×C151—81no—
136C23×C151#12111yescharacteristic
137Q8×C151—42no—
138Q8×C151—42no—
139Q8×C151—41no—
140Q8×C151—41no—
141D4×C151—22no—
142D4×C151—22no—
143D4×C151—41no—
144D4×C151—41no—
145D4×C151—42no—
146D4×C151—42no—
147D4×C151—42no—
148D4×C151—82no—
149C2×C4×C151—22no—
150C2×C4×C151—41no—
151C2×C4×C151—41no—
152C2×C4×C151—41no—
153C2×C4×C151—41no—
154C2×C4×C151—41no—
155C2×C4×C151—41no—
156C2×C4×C151—82no—
157C2×C4×C151—82no—
158C2×C4×C151—82no—
159C2×C4×C151—81no—
160C2×C4×C151#12011yescharacteristic
161C2×C4×C151#12011yescharacteristic
162C2×C4×C151#12011yescharacteristic
163C2×C4×C151#12111yescharacteristic
164C2×C4×C151#12111yescharacteristic
165C2×C4×C151#12711yescharacteristic
166C8×C151—42no—
167C8×C151—42no—
168C8×C151—42no—
169C8×C151—81no—
170C22×C151—21no—
171C22×C151—21no—
172C22×C151—21no—
173C22×C151—42no—
174C22×C151—82no—
175C22×C151—82no—
176C22×C151—81no—
177C22×C151—81no—
178C22×C151—81no—
179C22×C151—81no—
180C22×C151—81no—
181C22×C151#39211yescharacteristic
182C4×C151—21no—
183C4×C151—21no—
184C4×C151—21no—
185C4×C151—21no—
186C4×C151—21no—
187C4×C151—81no—
188C4×C151—81no—
189C4×C151—81no—
190C4×C151—81no—
191C4×C151#47112yes—
192C2×C151—41no—
193C2×C151—82no—
194C2×C151—161no—
195C2×C151#200811yescharacteristic
196C2×C151#201011yescharacteristic
197C2×C151#201911yescharacteristic
198#10039C15111yesmaximal, characteristic, direct product factor, Sylow
199C151#1003911yescharacteristic, direct product factor, Sylow
200#3216C2×C15111yescharacteristic, complemented
201#3109C2×C15111yescharacteristic
202#3101C2×C15111yescharacteristic, complemented
203#1537C2×C15111yescharacteristic, complemented
204#1496C2×C15111yescharacteristic, complemented
205#1466C2×C15111yescharacteristic, complemented
206#1287C2×C15111yescharacteristic, complemented
207#533C22×C15111yescharacteristic
208#532C22×C15111yescharacteristic
209C2×C4×D4C22×C15111yescharacteristic
210#497—21no—
211#489—21no—
212#483—21no—
213#481—21no—
214#476—21no—
215#476—21no—
216#462—21no—
217#461—21no—
218#460—21no—
219#459—21no—
220#452—22no—
221#450—21no—
222#447—21no—
223#442—22no—
224C4×SD16—22no—
225#432C22×C15111yescharacteristic
226#432C22×C15111yescharacteristic
227#432C22×C15111yescharacteristic
228#431C22×C15111yescharacteristic
229#330—22no—
230D4⋊C8—22no—
231#323—22no—
232C2×#41—21no—
233C22×D4D4×C15111yescharacteristic
234C23×C4—21no—
235C2×Q16—22no—
236C2×SD16—22no—
237C2×SD16—22no—
238C2×D8—22no—
239C4⋊Q8D4×C15111yescharacteristic
240C4⋊Q8D4×C15111yescharacteristic
241C4⋊Q8D4×C15111yescharacteristic
242#127D4×C15111yescharacteristic
243#125—21no—
244#124—21no—
245C22⋊Q8—21no—
246C22⋊Q8—21no—
247#121—21no—
248#121—21no—
249C4×Q8—21no—
250C4×Q8—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4—21no—
256C4×D4—21no—
257#117—21no—
258C2×C4⋊C4D4×C15111yescharacteristic
259C2×C22⋊C4—21no—
260C2×C42C23×C15111yescharacteristic
261#106—22no—
262#106—22no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267#103—22no—
268#103—22no—
269#102—22no—
270#102—22no—
271#102—22no—
272#102—22no—
273C22⋊C8—21no—
274C22⋊C8—21no—
275C22⋊C8—21no—
276C22⋊C8D4×C15112yes—
277#97—21no—
278#97—21no—
279#97D4×C15112yes—
280C4×C8D4×C15112yes—
281C24—21no—
282#41—82no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—42no—
292C2×D4—41no—
293C22×C4—21no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—82no—
298C22×C4C2×D4×C15111yescharacteristic
299C22×C4C2×D4×C15111yescharacteristic
300C22×C4#41×C15111yescharacteristic
301Q16—82no—
302SD16—44no—
303SD16—82no—
304D8—44no—
305C2×C8—22no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—41no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C42—41no—
325C42C2×D4×C15111yescharacteristic
326C42C2×D4×C15111yescharacteristic
327C42C2×D4×C15111yescharacteristic
328C42C2×D4×C15111yescharacteristic
329C23—22no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—81no—
334C23—81no—
335C23#121×C15111yescharacteristic
336Q8—42no—
337Q8—41no—
338Q8—41no—
339Q8—42no—
340D4—22no—
341D4—22no—
342D4—41no—
343D4—41no—
344D4—42no—
345D4—42no—
346D4—42no—
347D4—82no—
348C2×C4—22no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—82no—
356C2×C4—82no—
357C2×C4—82no—
358C2×C4—81no—
359C2×C4#120×C15111yescharacteristic
360C2×C4#120×C15111yescharacteristic
361C2×C4#120×C15111yescharacteristic
362C2×C4#121×C15111yescharacteristic
363C2×C4#121×C15111yescharacteristic
364C2×C4#127×C15111yescharacteristic
365C8—42no—
366C8—42no—
367C8—42no—
368C8—81no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—42no—
373C22—82no—
374C22—82no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22#392×C15111yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—81no—
387C4—81no—
388C4—81no—
389C4—81no—
390C4#471×C15112yes—
391C2—41no—
392C2—82no—
393C2—161no—
394C2#2008×C15111yescharacteristic
395C2#2010×C15111yescharacteristic
396C2#2019×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#392
commutator, Frattini, cosocleC2×C42C23×C151
prime radical#3109×C151C2
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
1. #3216×C151C2semidirect
3. #3101×C151C2semidirect
4. #1537×C151C2semidirect
5. #1496×C151C2semidirect
6. #1466×C151C2semidirect
7. #1287×C151C2semidirect
198. #10039C151direct (N × H)
199. C151#10039direct (N × H)
200. #3216C2×C151semidirect
202. #3101C2×C151semidirect
203. #1537C2×C151semidirect
204. #1496C2×C151semidirect
205. #1466C2×C151semidirect
206. #1287C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3216×C1512
#3109×C1512
#3101×C1512
#1537×C1512
#1496×C1512
#1466×C1512
#1287×C1512
#10039151