Finite Group Databasebeta

← C151×#10019 #50314944

Subgroups — C151×#10019 #50314944

Order 38656.

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

normal subgroups only

This group has 540 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#3142×C151C211yesmaximal, characteristic, complemented
2#3109×C151C211yesmaximal, characteristic
3#2633×C151C211yesmaximal, characteristic, complemented
4#1534×C151C211yesmaximal, characteristic, complemented
5#1514×C151C211yesmaximal, characteristic, complemented
6#1490×C151C211yesmaximal, characteristic, complemented
7#1288×C151C211yesmaximal, characteristic, complemented
8#532×C151C2211yescharacteristic
9C2×#125×C151C2211yescharacteristic
10C2×C4×D4×C151C2211yescharacteristic
11#491×C151—21no—
12#490×C151—21no—
13#488×C151—22no—
14#481×C151—21no—
15#476×C151—21no—
16#459×C151—21no—
17#447×C151—21no—
18#442×C151—22no—
19#432×C151C2211yescharacteristic
20#432×C151C2211yescharacteristic
21#417×C151—21no—
22#417×C151—21no—
23C4×M16×C151C2211yescharacteristic
24#399×C151—21no—
25#398×C151—21no—
26#397×C151—21no—
27#394×C151—21no—
28#385×C151—22no—
29#383×C151C2211yescharacteristic
30#330×C151—22no—
31#327×C151—22no—
32D4⋊C8×C151—22no—
33C2×#41×C151—21no—
34C22×D4×C151D411yescharacteristic
35C23×C4×C151—21no—
36C2×D8×C151—22no—
37C2×M16×C151—21no—
38C4⋊Q8×C151D411yescharacteristic
39#127×C151D411yescharacteristic
40#125×C151—21no—
41#125×C151—21no—
42#125×C151—21no—
43#125×C151—21no—
44#124×C151—21no—
45#121×C151—21no—
46#121×C151—21no—
47C4×D4×C151—21no—
48C4×D4×C151—21no—
49C4×D4×C151—21no—
50C4×D4×C151—21no—
51C4×D4×C151—21no—
52C4×D4×C151—21no—
53C2×C4⋊C4×C151—21no—
54C2×C4⋊C4×C151—21no—
55C2×C4⋊C4×C151—22no—
56C2×C4⋊C4×C151D411yescharacteristic
57C2×C4⋊C4×C151D411yescharacteristic
58C2×C4⋊C4×C151D411yescharacteristic
59C2×C22⋊C4×C151—22no—
60C2×C22⋊C4×C151—21no—
61C2×C22⋊C4×C151—22no—
62C2×C42×C151C2311yescharacteristic
63#106×C151—22no—
64C4⋊C8×C151—21no—
65C4⋊C8×C151—21no—
66#103×C151—22no—
67#103×C151—22no—
68#102×C151—22no—
69#102×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—
83#41×C151—44no—
84C2×Q8×C151—21no—
85C2×D4×C151—21no—
86C2×D4×C151—21no—
87C2×D4×C151—21no—
88C2×D4×C151—21no—
89C2×D4×C151—21no—
90C2×D4×C151—42no—
91C2×D4×C151—41no—
92C22×C4×C151—22no—
93C22×C4×C151—21no—
94C22×C4×C151—21no—
95C22×C4×C151—21no—
96C22×C4×C151—41no—
97C22×C4×C151—41no—
98C22×C4×C151—41no—
99C22×C4×C151—82no—
100C22×C4×C151C2×D411yescharacteristic
101C22×C4×C151C2×D411yescharacteristic
102C22×C4×C151C2×D411yescharacteristic
103D8×C151—44no—
104M16×C151—42no—
105C2×C8×C151—22no—
106C2×C8×C151—22no—
107C2×C8×C151—41no—
108C4⋊C4×C151—21no—
109C4⋊C4×C151—21no—
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—41no—
117C4⋊C4×C151—41no—
118C4⋊C4×C151—41no—
119C4⋊C4×C151—41no—
120C4⋊C4×C151—82no—
121C22⋊C4×C151—44no—
122C22⋊C4×C151—41no—
123C22⋊C4×C151—41no—
124C22⋊C4×C151—41no—
125C22⋊C4×C151—41no—
126C22⋊C4×C151—82no—
127C42×C151C2×D411yescharacteristic
128C42×C151C2×D411yescharacteristic
129C42×C151C2×D411yescharacteristic
130C42×C151#4111yescharacteristic
131C23×C151—22no—
132C23×C151—42no—
133C23×C151—41no—
134C23×C151—41no—
135C23×C151—42no—
136C23×C151—41no—
137C23×C151#12011yescharacteristic
138Q8×C151—42no—
139D4×C151—22no—
140D4×C151—22no—
141D4×C151—41no—
142D4×C151—41no—
143D4×C151—42no—
144D4×C151—42no—
145D4×C151—81no—
146D4×C151—82no—
147C2×C4×C151—22no—
148C2×C4×C151—41no—
149C2×C4×C151—41no—
150C2×C4×C151—42no—
151C2×C4×C151—42no—
152C2×C4×C151—41no—
153C2×C4×C151—42no—
154C2×C4×C151—41no—
155C2×C4×C151—42no—
156C2×C4×C151—41no—
157C2×C4×C151—41no—
158C2×C4×C151—41no—
159C2×C4×C151—41no—
160C2×C4×C151—42no—
161C2×C4×C151—82no—
162C2×C4×C151—82no—
163C2×C4×C151—82no—
164C2×C4×C151#12011yescharacteristic
165C2×C4×C151#12011yescharacteristic
166C2×C4×C151#12111yescharacteristic
167C2×C4×C151#12111yescharacteristic
168C2×C4×C151#12111yescharacteristic
169C2×C4×C151#12711yescharacteristic
170C8×C151—42no—
171C8×C151—42no—
172C8×C151—81no—
173C22×C151—21no—
174C22×C151—21no—
175C22×C151—44no—
176C22×C151—42no—
177C22×C151—82no—
178C22×C151—81no—
179C22×C151—81no—
180C22×C151—81no—
181C22×C151—81no—
182C22×C151—81no—
183C22×C151#39211yescharacteristic
184C22×C151#45412yes—
185C4×C151—21no—
186C4×C151—21no—
187C4×C151—21no—
188C4×C151—21no—
189C4×C151—21no—
190C4×C151—21no—
191C4×C151—82no—
192C4×C151—81no—
193C4×C151—81no—
194C4×C151—81no—
195C4×C151—81no—
196C2×C151—22no—
197C2×C151—82no—
198C2×C151—161no—
199C2×C151#200311yescharacteristic
200C2×C151#200811yescharacteristic
201C2×C151#201011yescharacteristic
202#10019C15111yesmaximal, characteristic, direct product factor, Sylow
203C151#1001911yescharacteristic, direct product factor, Sylow
204#3142C2×C15111yescharacteristic, complemented
205#3109C2×C15111yescharacteristic
206#2633C2×C15111yescharacteristic, complemented
207#1534C2×C15111yescharacteristic, complemented
208#1514C2×C15111yescharacteristic, complemented
209#1490C2×C15111yescharacteristic, complemented
210#1288C2×C15111yescharacteristic, complemented
211#532C22×C15111yescharacteristic
212C2×#125C22×C15111yescharacteristic
213C2×C4×D4C22×C15111yescharacteristic
214#491—21no—
215#490—21no—
216#488—22no—
217#481—21no—
218#476—21no—
219#459—21no—
220#447—21no—
221#442—22no—
222#432C22×C15111yescharacteristic
223#432C22×C15111yescharacteristic
224#417—21no—
225#417—21no—
226C4×M16C22×C15111yescharacteristic
227#399—21no—
228#398—21no—
229#397—21no—
230#394—21no—
231#385—22no—
232#383C22×C15111yescharacteristic
233#330—22no—
234#327—22no—
235D4⋊C8—22no—
236C2×#41—21no—
237C22×D4D4×C15111yescharacteristic
238C23×C4—21no—
239C2×D8—22no—
240C2×M16—21no—
241C4⋊Q8D4×C15111yescharacteristic
242#127D4×C15111yescharacteristic
243#125—21no—
244#125—21no—
245#125—21no—
246#125—21no—
247#124—21no—
248#121—21no—
249#121—21no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—21no—
255C4×D4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4D4×C15111yescharacteristic
260C2×C4⋊C4D4×C15111yescharacteristic
261C2×C4⋊C4D4×C15111yescharacteristic
262C2×C22⋊C4—22no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—22no—
265C2×C42C23×C15111yescharacteristic
266#106—22no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269#103—22no—
270#103—22no—
271#102—22no—
272#102—22no—
273#102—22no—
274#102—22no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277#97—21no—
278#97—21no—
279#97D4×C15112yes—
280C4×C8D4×C15112yes—
281#95—22no—
282#95—21no—
283#95—21no—
284#95D4×C15112yes—
285C24—21no—
286#41—44no—
287C2×Q8—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—42no—
294C2×D4—41no—
295C22×C4—22no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—82no—
303C22×C4C2×D4×C15111yescharacteristic
304C22×C4C2×D4×C15111yescharacteristic
305C22×C4C2×D4×C15111yescharacteristic
306D8—44no—
307M16—42no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—41no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—82no—
324C22⋊C4—44no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—82no—
330C42C2×D4×C15111yescharacteristic
331C42C2×D4×C15111yescharacteristic
332C42C2×D4×C15111yescharacteristic
333C42#41×C15111yescharacteristic
334C23—22no—
335C23—42no—
336C23—41no—
337C23—41no—
338C23—42no—
339C23—41no—
340C23#120×C15111yescharacteristic
341Q8—42no—
342D4—22no—
343D4—22no—
344D4—41no—
345D4—41no—
346D4—42no—
347D4—42no—
348D4—81no—
349D4—82no—
350C2×C4—22no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4—82no—
367C2×C4#120×C15111yescharacteristic
368C2×C4#120×C15111yescharacteristic
369C2×C4#121×C15111yescharacteristic
370C2×C4#121×C15111yescharacteristic
371C2×C4#121×C15111yescharacteristic
372C2×C4#127×C15111yescharacteristic
373C8—42no—
374C8—42no—
375C8—81no—
376C22—21no—
377C22—21no—
378C22—44no—
379C22—42no—
380C22—82no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22#392×C15111yescharacteristic
387C22#454×C15112yes—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—82no—
395C4—81no—
396C4—81no—
397C4—81no—
398C4—81no—
399C2—22no—
400C2—82no—
401C2—161no—
402C2#2003×C15111yescharacteristic
403C2#2008×C15111yescharacteristic
404C2#2010×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. #3142×C151C2semidirect
3. #2633×C151C2semidirect
4. #1534×C151C2semidirect
5. #1514×C151C2semidirect
6. #1490×C151C2semidirect
7. #1288×C151C2semidirect
202. #10019C151direct (N × H)
203. C151#10019direct (N × H)
204. #3142C2×C151semidirect
206. #2633C2×C151semidirect
207. #1534C2×C151semidirect
208. #1514C2×C151semidirect
209. #1490C2×C151semidirect
210. #1288C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3142×C1512
#3109×C1512
#2633×C1512
#1534×C1512
#1514×C1512
#1490×C1512
#1288×C1512
#10019151