Finite Group Databasebeta

← C151×#12782 #50317707

Subgroups — C151×#12782 #50317707

Order 38656.

730 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3544×C151C211yesmaximal, characteristic
2#2133×C151C212yesmaximal, complemented
3C2×#356×C151C211yesmaximal, characteristic, complemented
4#1912×C151C212yesmaximal, complemented
5#1886×C151C211yesmaximal, characteristic, complemented
6#563×C151—21no—
7#563×C151C412yescomplemented
8Q82×C151C411yescharacteristic, complemented
9#555×C151C411yescharacteristic, complemented
10#554×C151—21no—
11#552×C151—22no—
12#547×C151—22no—
13#544×C151—22no—
14#542×C151—22no—
15#536×C151—21no—
16#536×C151C2212yes—
17C2×C4⋊Q8×C151C2211yescharacteristic
18#529×C151—21no—
19#519×C151C2211yescharacteristic
20#421×C151—22no—
21#419×C151—21no—
22C2×#101×C151C2212yes—
23C2×#101×C151C2211yescharacteristic
24#356×C151—21no—
25#356×C151—21no—
26#356×C151—22no—
27#355×C151—22no—
28#339×C151—21no—
29H(3,ℤ/4)×C151—22no—
30C2×#41×C151—21no—
31C2×#41×C151D412yes—
32C22×Q8×C151D411yescharacteristic
33C22×Q8×C151C2311yescharacteristic
34C2×M16×C151—22no—
35C2×M16×C151—21no—
36C4⋊Q8×C151—21no—
37C4⋊Q8×C151—21no—
38C4⋊Q8×C151—22no—
39C4⋊Q8×C151—22no—
40C4⋊Q8×C151C2×C411yescharacteristic
41C4⋊Q8×C151C2×C411yescharacteristic
42C4⋊Q8×C151C2×C412yes—
43C4⋊Q8×C151D411yescharacteristic
44C4⋊Q8×C151D411yescharacteristic
45C4⋊Q8×C151D412yes—
46#126×C151—22no—
47#126×C151—22no—
48#126×C151—22no—
49#125×C151—21no—
50#125×C151—22no—
51#125×C151—22no—
52#125×C151—22no—
53#124×C151—21no—
54#124×C151—21no—
55#124×C151—21no—
56#124×C151C2×C412yes—
57#124×C151D412yes—
58#123×C151—22no—
59#123×C151—22no—
60#123×C151—22no—
61#123×C151—22no—
62#123×C151—22no—
63C22⋊Q8×C151—21no—
64C22⋊Q8×C151—22no—
65C22⋊Q8×C151—22no—
66C22⋊Q8×C151—22no—
67C22⋊Q8×C151—22no—
68C22⋊Q8×C151—22no—
69C22⋊Q8×C151—22no—
70C22⋊Q8×C151—22no—
71#121×C151—21no—
72#121×C151—22no—
73C4×Q8×C151—21no—
74C4×Q8×C151—22no—
75C4×Q8×C151—42no—
76C4×D4×C151—22no—
77C4×D4×C151—22no—
78C4×D4×C151—21no—
79#117×C151—22no—
80#117×C151—21no—
81#117×C151—22no—
82#117×C151—22no—
83#117×C151—21no—
84#117×C151D412yes—
85C2×C4⋊C4×C151—22no—
86C2×C4⋊C4×C151—22no—
87C2×C42×C151D411yescharacteristic
88#104×C151—44no—
89#103×C151—42no—
90#101×C151—22no—
91#101×C151—22no—
92#101×C151—22no—
93#41×C151—42no—
94#41×C151—42no—
95#41×C151—81no—
96#41×C151—81no—
97C2×Q8×C151—21no—
98C2×Q8×C151—21no—
99C2×Q8×C151—21no—
100C2×Q8×C151—41no—
101C2×Q8×C151—41no—
102C2×Q8×C151—41no—
103C2×Q8×C151—41no—
104C2×Q8×C151C22⋊C411yescharacteristic
105C2×Q8×C151C22⋊C412yes—
106C2×Q8×C151C22⋊C411yescharacteristic
107C2×Q8×C151C22×C411yescharacteristic
108C2×Q8×C151C2×D411yescharacteristic
109C2×Q8×C151C2×D412yes—
110C2×D4×C151—21no—
111C2×D4×C151—22no—
112C2×D4×C151—21no—
113C2×D4×C151C22⋊C412yes—
114C22×C4×C151—22no—
115C22×C4×C151—21no—
116C22×C4×C151—21no—
117C22×C4×C151—22no—
118C22×C4×C151—22no—
119C22×C4×C151C2×D411yescharacteristic
120C22×C4×C151C2×D412yes—
121M16×C151—42no—
122M16×C151—41no—
123M16×C151—41no—
124M16×C151—42no—
125C2×C8×C151—41no—
126C2×C8×C151—42no—
127C4⋊C4×C151—21no—
128C4⋊C4×C151—22no—
129C4⋊C4×C151—21no—
130C4⋊C4×C151—22no—
131C4⋊C4×C151—22no—
132C4⋊C4×C151—22no—
133C4⋊C4×C151—22no—
134C4⋊C4×C151—22no—
135C4⋊C4×C151—22no—
136C4⋊C4×C151—22no—
137C4⋊C4×C151—22no—
138C4⋊C4×C151—22no—
139C4⋊C4×C151—22no—
140C4⋊C4×C151—22no—
141C4⋊C4×C151—22no—
142C4⋊C4×C151—22no—
143C4⋊C4×C151—22no—
144C4⋊C4×C151—42no—
145C22⋊C4×C151—22no—
146C22⋊C4×C151—22no—
147C22⋊C4×C151—22no—
148C22⋊C4×C151—22no—
149C22⋊C4×C151—22no—
150C22⋊C4×C151—22no—
151C22⋊C4×C151—22no—
152C22⋊C4×C151—22no—
153C22⋊C4×C151—22no—
154C22⋊C4×C151—41no—
155C42×C151—21no—
156C42×C151—22no—
157C42×C151—21no—
158C42×C151—21no—
159C42×C151—24no—
160C42×C151—41no—
161C42×C151C22⋊C411yescharacteristic
162C42×C151C22⋊C411yescharacteristic
163C42×C151C22⋊C412yes—
164C42×C151C22⋊C412yes—
165C23×C151—22no—
166C23×C151#12011yescharacteristic
167Q8×C151—41no—
168Q8×C151—41no—
169Q8×C151—42no—
170Q8×C151—41no—
171Q8×C151—41no—
172Q8×C151—42no—
173Q8×C151—42no—
174Q8×C151—81no—
175Q8×C151—81no—
176D4×C151—42no—
177D4×C151—42no—
178D4×C151—42no—
179D4×C151—42no—
180D4×C151—81no—
181C2×C4×C151—21no—
182C2×C4×C151—21no—
183C2×C4×C151—22no—
184C2×C4×C151—21no—
185C2×C4×C151—22no—
186C2×C4×C151—21no—
187C2×C4×C151—22no—
188C2×C4×C151—21no—
189C2×C4×C151—22no—
190C2×C4×C151—22no—
191C2×C4×C151—21no—
192C2×C4×C151—42no—
193C2×C4×C151—44no—
194C2×C4×C151—41no—
195C2×C4×C151—41no—
196C2×C4×C151—42no—
197C2×C4×C151—82no—
198C2×C4×C151—82no—
199C2×C4×C151C2×C22⋊C411yescharacteristic
200C2×C4×C151C2×C22⋊C412yes—
201C2×C4×C151#12011yescharacteristic
202C2×C4×C151#12012yes—
203C8×C151—82no—
204C8×C151—81no—
205C22×C151—41no—
206C22×C151—42no—
207C22×C151—42no—
208C22×C151—42no—
209C22×C151#37911yescharacteristic
210C22×C151B(4,𝔽2)11yescharacteristic
211C22×C151#45811yescharacteristic
212C4×C151—22no—
213C4×C151—22no—
214C4×C151—21no—
215C4×C151—22no—
216C4×C151—21no—
217C4×C151—42no—
218C4×C151—41no—
219C4×C151—42no—
220C4×C151—41no—
221C4×C151—41no—
222C4×C151—42no—
223C4×C151—82no—
224C2×C151—21no—
225C2×C151—21no—
226C2×C151—21no—
227C2×C151—82no—
228C2×C151#179011yescharacteristic
229#12782C15111yesmaximal, characteristic, direct product factor, Sylow
230C151#1278211yescharacteristic, direct product factor, Sylow
231#3544C2×C15111yescharacteristic
232#2133C2×C15112yescomplemented
233C2×#356C2×C15111yescharacteristic, complemented
234#1912C2×C15112yescomplemented
235#1886C2×C15111yescharacteristic, complemented
236#563—21no—
237#563C4×C15112yescomplemented
238Q82C4×C15111yescharacteristic, complemented
239#555C4×C15111yescharacteristic, complemented
240#554—21no—
241#552—22no—
242#547—22no—
243#544—22no—
244#542—22no—
245#536—21no—
246#536C22×C15112yes—
247C2×C4⋊Q8C22×C15111yescharacteristic
248#529—21no—
249#519C22×C15111yescharacteristic
250#421—22no—
251#419—21no—
252C2×#101C22×C15112yes—
253C2×#101C22×C15111yescharacteristic
254#356—21no—
255#356—21no—
256#356—22no—
257#355—22no—
258#339—21no—
259H(3,ℤ/4)—22no—
260C2×#41—21no—
261C2×#41D4×C15112yes—
262C22×Q8D4×C15111yescharacteristic
263C22×Q8C23×C15111yescharacteristic
264C2×M16—22no—
265C2×M16—21no—
266C4⋊Q8—21no—
267C4⋊Q8—21no—
268C4⋊Q8—22no—
269C4⋊Q8—22no—
270C4⋊Q8C2×C4×C15111yescharacteristic
271C4⋊Q8C2×C4×C15111yescharacteristic
272C4⋊Q8C2×C4×C15112yes—
273C4⋊Q8D4×C15111yescharacteristic
274C4⋊Q8D4×C15111yescharacteristic
275C4⋊Q8D4×C15112yes—
276#126—22no—
277#126—22no—
278#126—22no—
279#125—21no—
280#125—22no—
281#125—22no—
282#125—22no—
283#124—21no—
284#124—21no—
285#124—21no—
286#124C2×C4×C15112yes—
287#124D4×C15112yes—
288#123—22no—
289#123—22no—
290#123—22no—
291#123—22no—
292#123—22no—
293C22⋊Q8—21no—
294C22⋊Q8—22no—
295C22⋊Q8—22no—
296C22⋊Q8—22no—
297C22⋊Q8—22no—
298C22⋊Q8—22no—
299C22⋊Q8—22no—
300C22⋊Q8—22no—
301#121—21no—
302#121—22no—
303C4×Q8—21no—
304C4×Q8—22no—
305C4×Q8—42no—
306C4×D4—22no—
307C4×D4—22no—
308C4×D4—21no—
309#117—22no—
310#117—21no—
311#117—22no—
312#117—22no—
313#117—21no—
314#117D4×C15112yes—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C42D4×C15111yescharacteristic
318#104—44no—
319#103—42no—
320#101—22no—
321#101—22no—
322#101—22no—
323#41—42no—
324#41—42no—
325#41—81no—
326#41—81no—
327C2×Q8—21no—
328C2×Q8—21no—
329C2×Q8—21no—
330C2×Q8—41no—
331C2×Q8—41no—
332C2×Q8—41no—
333C2×Q8—41no—
334C2×Q8C22⋊C4×C15111yescharacteristic
335C2×Q8C22⋊C4×C15112yes—
336C2×Q8C22⋊C4×C15111yescharacteristic
337C2×Q8C22×C4×C15111yescharacteristic
338C2×Q8C2×D4×C15111yescharacteristic
339C2×Q8C2×D4×C15112yes—
340C2×D4—21no—
341C2×D4—22no—
342C2×D4—21no—
343C2×D4C22⋊C4×C15112yes—
344C22×C4—22no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4C2×D4×C15111yescharacteristic
350C22×C4C2×D4×C15112yes—
351M16—42no—
352M16—41no—
353M16—41no—
354M16—42no—
355C2×C8—41no—
356C2×C8—42no—
357C4⋊C4—21no—
358C4⋊C4—22no—
359C4⋊C4—21no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—42no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C22⋊C4—22no—
379C22⋊C4—22no—
380C22⋊C4—22no—
381C22⋊C4—22no—
382C22⋊C4—22no—
383C22⋊C4—22no—
384C22⋊C4—41no—
385C42—21no—
386C42—22no—
387C42—21no—
388C42—21no—
389C42—24no—
390C42—41no—
391C42C22⋊C4×C15111yescharacteristic
392C42C22⋊C4×C15111yescharacteristic
393C42C22⋊C4×C15112yes—
394C42C22⋊C4×C15112yes—
395C23—22no—
396C23#120×C15111yescharacteristic
397Q8—41no—
398Q8—41no—
399Q8—42no—
400Q8—41no—
401Q8—41no—
402Q8—42no—
403Q8—42no—
404Q8—81no—
405Q8—81no—
406D4—42no—
407D4—42no—
408D4—42no—
409D4—42no—
410D4—81no—
411C2×C4—21no—
412C2×C4—22no—
413C2×C4—21no—
414C2×C4—22no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—21no—
422C2×C4—42no—
423C2×C4—44no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—82no—
428C2×C4—82no—
429C2×C4C2×C22⋊C4×C15111yescharacteristic
430C2×C4C2×C22⋊C4×C15112yes—
431C2×C4#120×C15111yescharacteristic
432C2×C4#120×C15112yes—
433C8—82no—
434C8—81no—
435C22—41no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22#379×C15111yescharacteristic
440C22B(4,𝔽2)×C15111yescharacteristic
441C22#458×C15111yescharacteristic
442C4—22no—
443C4—22no—
444C4—21no—
445C4—22no—
446C4—21no—
447C4—42no—
448C4—41no—
449C4—42no—
450C4—41no—
451C4—41no—
452C4—42no—
453C4—82no—
454C2—21no—
455C2—21no—
456C2—21no—
457C2—82no—
458C2#1790×C15111yescharacteristic
subgroupG/H
center, socleC2×C151#1790
commutatorC2×Q8C22×C4×C151
Frattini, cosocleC22×Q8C23×C151
prime radical#3544×C151C2
LCSG ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C151 ◁ C23×C151 ◁ C22×Q8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2133×C151C2semidirect
3. C2×#356×C151C2semidirect
4. #1912×C151C2semidirect
5. #1886×C151C2semidirect
7. #563×C151C4semidirect
8. Q82×C151C4semidirect
9. #555×C151C4semidirect
229. #12782C151direct (N × H)
230. C151#12782direct (N × H)
232. #2133C2×C151semidirect
233. C2×#356C2×C151semidirect
234. #1912C2×C151semidirect
235. #1886C2×C151semidirect
237. #563C4×C151semidirect
238. Q82C4×C151semidirect
239. #555C4×C151semidirect

Maximal subgroups

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

subgroupindex
#3544×C1512
#2133×C1512
C2×#356×C1512
#1912×C1512
#1886×C1512
#12782151