Finite Group Databasebeta

← C151×#19561 #50324486

Subgroups — C151×#19561 #50324486

Order 38656.

612 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3253×C151C211yesmaximal, characteristic
2#3227×C151C211yesmaximal, characteristic, complemented
3#3226×C151C211yesmaximal, characteristic, complemented
4#2979×C151C211yesmaximal, characteristic, complemented
5#1697×C151C212yesmaximal, complemented
6#1695×C151C212yesmaximal, complemented
7#1677×C151C212yesmaximal, complemented
8#1675×C151C212yesmaximal, complemented
9#1574×C151C211yesmaximal, characteristic, complemented
10#1548×C151C211yesmaximal, characteristic, complemented
11#1543×C151C211yesmaximal, characteristic, complemented
12#532×C151C2211yescharacteristic
13#532×C151C2211yescharacteristic
14C2×C4⋊Q8×C151C2211yescharacteristic
15#500×C151C2212yes—
16#498×C151—21no—
17#486×C151—21no—
18#486×C151C2212yes—
19#481×C151—22no—
20#480×C151—22no—
21#476×C151—21no—
22#476×C151C2212yes—
23#476×C151C2212yes—
24#476×C151C2212yes—
25#474×C151—21no—
26#474×C151—21no—
27#469×C151—22no—
28#459×C151—21no—
29#459×C151C2212yes—
30#436×C151—21no—
31#436×C151C2212yes—
32C8×D4×C151—21no—
33C8×D4×C151C2212yes—
34#431×C151C2211yescharacteristic
35#431×C151C2211yescharacteristic
36#431×C151C2211yescharacteristic
37#423×C151C2211yescharacteristic
38#408×C151—22no—
39#335×C151C2212yes—
40#334×C151C2212yes—
41#333×C151C2211yescharacteristic
42#333×C151C2212yes—
43#333×C151C2211yescharacteristic
44#333×C151C2212yes—
45#331×C151C2211yescharacteristic
46#331×C151C2211yescharacteristic
47C2×#41×C151—21no—
48C2×#41×C151—21no—
49C22×Q8×C151—21no—
50C2×D8×C151—22no—
51C2×M16×C151—21no—
52C2×M16×C151—22no—
53C22×C8×C151—22no—
54C4⋊Q8×C151—21no—
55C4⋊Q8×C151—21no—
56C4⋊Q8×C151—21no—
57C4⋊Q8×C151D411yescharacteristic
58C4⋊Q8×C151C2312yes—
59C4⋊Q8×C151C2311yescharacteristic
60#127×C151D411yescharacteristic
61#127×C151C2311yescharacteristic
62#124×C151—21no—
63#124×C151—21no—
64#121×C151—21no—
65#121×C151—21no—
66#121×C151—21no—
67#121×C151D412yes—
68C4×D4×C151—21no—
69C4×D4×C151—21no—
70C4×D4×C151—21no—
71C4×D4×C151C2312yes—
72C2×C4⋊C4×C151—21no—
73C2×C4⋊C4×C151—21no—
74C2×C42×C151C2311yescharacteristic
75#107×C151—22no—
76#107×C151—22no—
77#106×C151—22no—
78#106×C151—22no—
79#106×C151—22no—
80C4⋊C8×C151—21no—
81C4⋊C8×C151D411yescharacteristic
82C4⋊C8×C151D411yescharacteristic
83C4⋊C8×C151C2312yes—
84C4⋊C8×C151C2311yescharacteristic
85C4⋊C8×C151C2311yescharacteristic
86C4⋊C8×C151C2311yescharacteristic
87C4⋊C8×C151C2311yescharacteristic
88#102×C151—22no—
89#102×C151—22no—
90#102×C151—22no—
91#102×C151—22no—
92#102×C151—22no—
93#102×C151—22no—
94C22⋊C8×C151—21no—
95C22⋊C8×C151—21no—
96C22⋊C8×C151—22no—
97C22⋊C8×C151—22no—
98C22⋊C8×C151D412yes—
99C4×C8×C151—21no—
100C4×C8×C151—21no—
101C4×C8×C151C2312yes—
102#41×C151—81no—
103#41×C151—81no—
104#41×C151—82no—
105C2×Q8×C151—21no—
106C2×Q8×C151—21no—
107C2×Q8×C151—22no—
108C2×Q8×C151—41no—
109C2×Q8×C151—82no—
110C2×D4×C151—22no—
111C2×D4×C151—21no—
112C2×D4×C151—21no—
113C2×D4×C151—21no—
114C2×D4×C151—21no—
115C2×D4×C151—21no—
116C2×D4×C151—41no—
117C2×D4×C151C2×D412yes—
118C22×C4×C151—22no—
119C22×C4×C151—41no—
120C22×C4×C151—41no—
121C22×C4×C151C2×D411yescharacteristic
122C22×C4×C151C2×D411yescharacteristic
123C22×C4×C151#4111yescharacteristic
124D8×C151—82no—
125M16×C151—82no—
126M16×C151—81no—
127C2×C8×C151—21no—
128C2×C8×C151—21no—
129C2×C8×C151—21no—
130C2×C8×C151—21no—
131C2×C8×C151—22no—
132C2×C8×C151—82no—
133C2×C8×C151C2×D412yes—
134C2×C8×C151C2×D412yes—
135C4⋊C4×C151—21no—
136C4⋊C4×C151—22no—
137C4⋊C4×C151—21no—
138C4⋊C4×C151—22no—
139C4⋊C4×C151—21no—
140C4⋊C4×C151—41no—
141C4⋊C4×C151—41no—
142C4⋊C4×C151C2×D412yes—
143C22⋊C4×C151—22no—
144C22⋊C4×C151—22no—
145C22⋊C4×C151—41no—
146C22⋊C4×C151—41no—
147C42×C151C2×D411yescharacteristic
148C42×C151C2×D411yescharacteristic
149C42×C151#4111yescharacteristic
150C42×C151C2411yescharacteristic
151C23×C151—22no—
152C23×C151—41no—
153C23×C151#12111yescharacteristic
154Q8×C151—81no—
155Q8×C151—82no—
156Q8×C151—81no—
157Q8×C151—82no—
158D4×C151—22no—
159D4×C151—22no—
160D4×C151—41no—
161D4×C151—41no—
162D4×C151—41no—
163D4×C151—41no—
164D4×C151—42no—
165D4×C151—81no—
166D4×C151—81no—
167D4×C151—82no—
168D4×C151—82no—
169C2×C4×C151—21no—
170C2×C4×C151—21no—
171C2×C4×C151—21no—
172C2×C4×C151—21no—
173C2×C4×C151—22no—
174C2×C4×C151—22no—
175C2×C4×C151—42no—
176C2×C4×C151—42no—
177C2×C4×C151—42no—
178C2×C4×C151—41no—
179C2×C4×C151—82no—
180C2×C4×C151—82no—
181C2×C4×C151#12111yescharacteristic
182C2×C4×C151#12111yescharacteristic
183C2×C4×C151#12111yescharacteristic
184C2×C4×C151C22×D411yescharacteristic
185C2×C4×C151C22×D411yescharacteristic
186C2×C4×C151C2×#4111yescharacteristic
187C8×C151—22no—
188C8×C151—22no—
189C8×C151—41no—
190C8×C151—41no—
191C8×C151—41no—
192C8×C151—42no—
193C8×C151—41no—
194C22×C151—21no—
195C22×C151—21no—
196C22×C151—21no—
197C22×C151—42no—
198C22×C151—42no—
199C22×C151—42no—
200C22×C151—81no—
201C22×C151—81no—
202C22×C151—81no—
203C22×C151C2×#12111yescharacteristic
204C4×C151—21no—
205C4×C151—21no—
206C4×C151—21no—
207C4×C151—42no—
208C4×C151—81no—
209C4×C151—82no—
210C4×C151#47212yes—
211C4×C151#57711yescharacteristic
212C4×C151#57711yescharacteristic
213C4×C151#57711yescharacteristic
214C4×C151#57811yescharacteristic
215C2×C151—41no—
216C2×C151—82no—
217C2×C151—161no—
218C2×C151#304211yescharacteristic
219C2×C151#306311yescharacteristic
220C2×C151C2×#47211yescharacteristic
221#19561C15111yesmaximal, characteristic, direct product factor, Sylow
222C151#1956111yescharacteristic, direct product factor, Sylow
223#3253C2×C15111yescharacteristic
224#3227C2×C15111yescharacteristic, complemented
225#3226C2×C15111yescharacteristic, complemented
226#2979C2×C15111yescharacteristic, complemented
227#1697C2×C15112yescomplemented
228#1695C2×C15112yescomplemented
229#1677C2×C15112yescomplemented
230#1675C2×C15112yescomplemented
231#1574C2×C15111yescharacteristic, complemented
232#1548C2×C15111yescharacteristic, complemented
233#1543C2×C15111yescharacteristic, complemented
234#532C22×C15111yescharacteristic
235#532C22×C15111yescharacteristic
236C2×C4⋊Q8C22×C15111yescharacteristic
237#500C22×C15112yes—
238#498—21no—
239#486—21no—
240#486C22×C15112yes—
241#481—22no—
242#480—22no—
243#476—21no—
244#476C22×C15112yes—
245#476C22×C15112yes—
246#476C22×C15112yes—
247#474—21no—
248#474—21no—
249#469—22no—
250#459—21no—
251#459C22×C15112yes—
252#436—21no—
253#436C22×C15112yes—
254C8×D4—21no—
255C8×D4C22×C15112yes—
256#431C22×C15111yescharacteristic
257#431C22×C15111yescharacteristic
258#431C22×C15111yescharacteristic
259#423C22×C15111yescharacteristic
260#408—22no—
261#335C22×C15112yes—
262#334C22×C15112yes—
263#333C22×C15111yescharacteristic
264#333C22×C15111yescharacteristic
265#333C22×C15112yes—
266#333C22×C15112yes—
267#331C22×C15111yescharacteristic
268#331C22×C15111yescharacteristic
269C2×#41—21no—
270C2×#41—21no—
271C22×Q8—21no—
272C2×D8—22no—
273C2×M16—21no—
274C2×M16—22no—
275C22×C8—22no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8—21no—
279C4⋊Q8D4×C15111yescharacteristic
280C4⋊Q8C23×C15112yes—
281C4⋊Q8C23×C15111yescharacteristic
282#127D4×C15111yescharacteristic
283#127C23×C15111yescharacteristic
284#124—21no—
285#124—21no—
286#121—21no—
287#121—21no—
288#121—21no—
289#121D4×C15112yes—
290C4×D4—21no—
291C4×D4—21no—
292C4×D4—21no—
293C4×D4C23×C15112yes—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C42C23×C15111yescharacteristic
297#107—22no—
298#107—22no—
299#106—22no—
300#106—22no—
301#106—22no—
302C4⋊C8—21no—
303C4⋊C8D4×C15111yescharacteristic
304C4⋊C8D4×C15111yescharacteristic
305C4⋊C8C23×C15111yescharacteristic
306C4⋊C8C23×C15111yescharacteristic
307C4⋊C8C23×C15111yescharacteristic
308C4⋊C8C23×C15111yescharacteristic
309C4⋊C8C23×C15112yes—
310#102—22no—
311#102—22no—
312#102—22no—
313#102—22no—
314#102—22no—
315#102—22no—
316C22⋊C8—21no—
317C22⋊C8—21no—
318C22⋊C8—22no—
319C22⋊C8—22no—
320C22⋊C8D4×C15112yes—
321C4×C8—21no—
322C4×C8—21no—
323C4×C8C23×C15112yes—
324#41—81no—
325#41—81no—
326#41—82no—
327C2×Q8—21no—
328C2×Q8—21no—
329C2×Q8—22no—
330C2×Q8—41no—
331C2×Q8—82no—
332C2×D4—22no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—41no—
339C2×D4C2×D4×C15112yes—
340C22×C4—22no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4C2×D4×C15111yescharacteristic
344C22×C4C2×D4×C15111yescharacteristic
345C22×C4#41×C15111yescharacteristic
346D8—82no—
347M16—82no—
348M16—81no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—22no—
354C2×C8—82no—
355C2×C8C2×D4×C15112yes—
356C2×C8C2×D4×C15112yes—
357C4⋊C4—21no—
358C4⋊C4—22no—
359C4⋊C4—21no—
360C4⋊C4—22no—
361C4⋊C4—21no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4C2×D4×C15112yes—
365C22⋊C4—22no—
366C22⋊C4—22no—
367C22⋊C4—41no—
368C22⋊C4—41no—
369C42C2×D4×C15111yescharacteristic
370C42C2×D4×C15111yescharacteristic
371C42#41×C15111yescharacteristic
372C42C24×C15111yescharacteristic
373C23—22no—
374C23—41no—
375C23#121×C15111yescharacteristic
376Q8—81no—
377Q8—82no—
378Q8—81no—
379Q8—82no—
380D4—22no—
381D4—22no—
382D4—42no—
383D4—41no—
384D4—41no—
385D4—41no—
386D4—41no—
387D4—81no—
388D4—81no—
389D4—82no—
390D4—82no—
391C2×C4—22no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—22no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—82no—
402C2×C4—82no—
403C2×C4#121×C15111yescharacteristic
404C2×C4#121×C15111yescharacteristic
405C2×C4#121×C15111yescharacteristic
406C2×C4C22×D4×C15111yescharacteristic
407C2×C4C22×D4×C15111yescharacteristic
408C2×C4C2×#41×C15111yescharacteristic
409C8—22no—
410C8—22no—
411C8—41no—
412C8—41no—
413C8—42no—
414C8—41no—
415C8—41no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22C2×#121×C15111yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—42no—
430C4—81no—
431C4—82no—
432C4#472×C15112yes—
433C4#577×C15111yescharacteristic
434C4#577×C15111yescharacteristic
435C4#577×C15111yescharacteristic
436C4#578×C15111yescharacteristic
437C2—41no—
438C2—82no—
439C2—161no—
440C2#3042×C15111yescharacteristic
441C2#3063×C15111yescharacteristic
442C2C2×#472×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#3253×C151C2
LCSG ▷ 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. #3227×C151C2semidirect
3. #3226×C151C2semidirect
4. #2979×C151C2semidirect
5. #1697×C151C2semidirect
6. #1695×C151C2semidirect
7. #1677×C151C2semidirect
8. #1675×C151C2semidirect
9. #1574×C151C2semidirect
10. #1548×C151C2semidirect
11. #1543×C151C2semidirect
221. #19561C151direct (N × H)
222. C151#19561direct (N × H)
224. #3227C2×C151semidirect
225. #3226C2×C151semidirect
226. #2979C2×C151semidirect
227. #1697C2×C151semidirect
228. #1695C2×C151semidirect
229. #1677C2×C151semidirect
230. #1675C2×C151semidirect
231. #1574C2×C151semidirect
232. #1548C2×C151semidirect
233. #1543C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3253×C1512
#3227×C1512
#3226×C1512
#2979×C1512
#1697×C1512
#1695×C1512
#1677×C1512
#1675×C1512
#1574×C1512
#1548×C1512
#1543×C1512
#19561151