Finite Group Databasebeta

← C151×#18737 #50323662

Subgroups — C151×#18737 #50323662

Order 38656.

820 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3556×C151C211yesmaximal, characteristic
2#3229×C151C211yesmaximal, characteristic
3#3209×C151C211yesmaximal, characteristic
4#3165×C151C211yesmaximal, characteristic
5#1653×C151C214yesmaximal, complemented
6#1648×C151C214yesmaximal, complemented
7#1544×C151C211yesmaximal, characteristic
8#1485×C151C211yesmaximal, characteristic
9#1485×C151C211yesmaximal, characteristic
10#564×C151—22no—
11#557×C151—21no—
12#557×C151—21no—
13#557×C151—21no—
14#557×C151—21no—
15#557×C151C2212yes—
16#557×C151C2212yes—
17#541×C151—22no—
18#541×C151—22no—
19#541×C151—22no—
20#533×C151C2211yescharacteristic
21#533×C151C2211yescharacteristic
22#533×C151C2211yescharacteristic
23C2×C4⋊Q8×C151C2211yescharacteristic
24#501×C151—22no—
25#500×C151C2212yes—
26#498×C151—21no—
27#498×C151C2212yes—
28#494×C151—21no—
29#487×C151—21no—
30#487×C151—21no—
31#483×C151—22no—
32#475×C151C2214yes—
33#462×C151C2214yes—
34#451×C151—22no—
35#431×C151C2211yescharacteristic
36#431×C151C2211yescharacteristic
37#428×C151—22no—
38C4×M16×C151C2211yescharacteristic
39#332×C151C2212yes—
40#332×C151C2212yes—
41Q8⋊C8×C151C2214yes—
42Q8⋊C8×C151C2214yes—
43C22×Q8×C151—21no—
44C2×Q16×C151—24no—
45C2×M16×C151—21no—
46C4⋊Q8×C151—22no—
47C4⋊Q8×C151—21no—
48C4⋊Q8×C151—22no—
49C4⋊Q8×C151—22no—
50C4⋊Q8×C151—21no—
51C4⋊Q8×C151—21no—
52C4⋊Q8×C151D411yescharacteristic
53C4⋊Q8×C151D411yescharacteristic
54C4⋊Q8×C151D411yescharacteristic
55C4⋊Q8×C151D411yescharacteristic
56C4⋊Q8×C151C2312yes—
57C4⋊Q8×C151C2311yescharacteristic
58C4⋊Q8×C151C2311yescharacteristic
59#126×C151—24no—
60#126×C151—24no—
61#125×C151—22no—
62#125×C151—24no—
63#125×C151—24no—
64#125×C151—24no—
65#125×C151—24no—
66#125×C151—22no—
67#125×C151—22no—
68#125×C151—24no—
69#125×C151—24no—
70#125×C151—21no—
71#125×C151—21no—
72#125×C151D412yes—
73C22⋊Q8×C151—21no—
74C22⋊Q8×C151—21no—
75C22⋊Q8×C151—21no—
76C22⋊Q8×C151—21no—
77C22⋊Q8×C151D412yes—
78C22⋊Q8×C151D412yes—
79C4×Q8×C151—22no—
80C4×Q8×C151—22no—
81C4×Q8×C151—22no—
82C4×Q8×C151—22no—
83C4×Q8×C151—21no—
84C4×Q8×C151—21no—
85C4×Q8×C151—21no—
86C4×Q8×C151—21no—
87C4×Q8×C151—22no—
88C4×Q8×C151—22no—
89C4×Q8×C151C2312yes—
90C4×Q8×C151C2312yes—
91#117×C151—21no—
92#117×C151—21no—
93#117×C151D412yes—
94C2×C4⋊C4×C151—21no—
95C2×C4⋊C4×C151—21no—
96C2×C42×C151C2311yescharacteristic
97#107×C151—24no—
98#106×C151—24no—
99#106×C151—24no—
100C4⋊C8×C151C2312yes—
101C4⋊C8×C151C2312yes—
102#103×C151—24no—
103#103×C151—24no—
104C22⋊C8×C151—21no—
105C22⋊C8×C151—21no—
106#97×C151—21no—
107C4×C8×C151—21no—
108C4×C8×C151—21no—
109C4×C8×C151C2312yes—
110C2×Q8×C151—21no—
111C2×Q8×C151—21no—
112C2×Q8×C151—21no—
113C2×Q8×C151—21no—
114C2×Q8×C151—22no—
115C2×Q8×C151—41no—
116C2×Q8×C151—82no—
117C2×Q8×C151C2×D412yes—
118C2×Q8×C151C2×D412yes—
119C22×C4×C151—41no—
120C22×C4×C151C2×D411yescharacteristic
121C22×C4×C151C2×D411yescharacteristic
122C22×C4×C151C2×D411yescharacteristic
123Q16×C151—84no—
124M16×C151—24no—
125C2×C8×C151—22no—
126C2×C8×C151—22no—
127C2×C8×C151—22no—
128C4⋊C4×C151—24no—
129C4⋊C4×C151—24no—
130C4⋊C4×C151—24no—
131C4⋊C4×C151—24no—
132C4⋊C4×C151—24no—
133C4⋊C4×C151—24no—
134C4⋊C4×C151—21no—
135C4⋊C4×C151—21no—
136C4⋊C4×C151—21no—
137C4⋊C4×C151—21no—
138C4⋊C4×C151—21no—
139C4⋊C4×C151—21no—
140C4⋊C4×C151—22no—
141C4⋊C4×C151—22no—
142C4⋊C4×C151—22no—
143C4⋊C4×C151—22no—
144C4⋊C4×C151—21no—
145C4⋊C4×C151—21no—
146C4⋊C4×C151—22no—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—22no—
149C4⋊C4×C151—22no—
150C4⋊C4×C151—41no—
151C4⋊C4×C151—41no—
152C4⋊C4×C151C2×D412yes—
153C4⋊C4×C151C2×D412yes—
154C4⋊C4×C151C2×D412yes—
155C4⋊C4×C151C2×D412yes—
156C22⋊C4×C151—22no—
157C22⋊C4×C151—22no—
158C22⋊C4×C151—22no—
159C42×C151—24no—
160C42×C151—24no—
161C42×C151—22no—
162C42×C151—22no—
163C42×C151—22no—
164C42×C151C2×D411yescharacteristic
165C42×C151C2×D411yescharacteristic
166C42×C151C2×D411yescharacteristic
167C42×C151C2411yescharacteristic
168C23×C151#12011yescharacteristic
169Q8×C151—24no—
170Q8×C151—24no—
171Q8×C151—42no—
172Q8×C151—42no—
173Q8×C151—42no—
174Q8×C151—42no—
175Q8×C151—44no—
176Q8×C151—82no—
177C2×C4×C151—22no—
178C2×C4×C151—22no—
179C2×C4×C151—22no—
180C2×C4×C151—22no—
181C2×C4×C151—22no—
182C2×C4×C151—22no—
183C2×C4×C151—22no—
184C2×C4×C151—22no—
185C2×C4×C151—22no—
186C2×C4×C151—42no—
187C2×C4×C151—82no—
188C2×C4×C151#12011yescharacteristic
189C2×C4×C151#12011yescharacteristic
190C2×C4×C151#12011yescharacteristic
191C2×C4×C151C22×D411yescharacteristic
192C2×C4×C151C22×D411yescharacteristic
193C2×C4×C151C22×D411yescharacteristic
194C8×C151—24no—
195C8×C151—42no—
196C8×C151—42no—
197C22×C151—21no—
198C22×C151—21no—
199C22×C151—21no—
200C22×C151C2×#12011yescharacteristic
201C4×C151—21no—
202C4×C151—21no—
203C4×C151—21no—
204C4×C151—42no—
205C4×C151—42no—
206C4×C151—42no—
207C4×C151—42no—
208C4×C151—42no—
209C4×C151—42no—
210C4×C151—82no—
211C4×C151#45612yes—
212C4×C151#57712yes—
213C4×C151#57812yes—
214C2×C151—41no—
215C2×C151#301011yescharacteristic
216C2×C151#301111yescharacteristic
217C2×C151C2×#45611yescharacteristic
218#18737C15111yesmaximal, characteristic, direct product factor, Sylow
219C151#1873711yescharacteristic, direct product factor, Sylow
220#3556C2×C15111yescharacteristic
221#3229C2×C15111yescharacteristic
222#3209C2×C15111yescharacteristic
223#3165C2×C15111yescharacteristic
224#1653C2×C15114yescomplemented
225#1648C2×C15114yescomplemented
226#1544C2×C15111yescharacteristic
227#1485C2×C15111yescharacteristic
228#1485C2×C15111yescharacteristic
229#564—22no—
230#557—21no—
231#557—21no—
232#557—21no—
233#557—21no—
234#557C22×C15112yes—
235#557C22×C15112yes—
236#541—22no—
237#541—22no—
238#541—22no—
239#533C22×C15111yescharacteristic
240#533C22×C15111yescharacteristic
241#533C22×C15111yescharacteristic
242C2×C4⋊Q8C22×C15111yescharacteristic
243#501—22no—
244#500C22×C15112yes—
245#498—21no—
246#498C22×C15112yes—
247#494—21no—
248#487—21no—
249#487—21no—
250#483—22no—
251#475C22×C15114yes—
252#462C22×C15114yes—
253#451—22no—
254#431C22×C15111yescharacteristic
255#431C22×C15111yescharacteristic
256#428—22no—
257C4×M16C22×C15111yescharacteristic
258#332C22×C15112yes—
259#332C22×C15112yes—
260Q8⋊C8C22×C15114yes—
261Q8⋊C8C22×C15114yes—
262C22×Q8—21no—
263C2×Q16—24no—
264C2×M16—21no—
265C4⋊Q8—22no—
266C4⋊Q8—22no—
267C4⋊Q8—22no—
268C4⋊Q8—21no—
269C4⋊Q8—21no—
270C4⋊Q8—21no—
271C4⋊Q8D4×C15111yescharacteristic
272C4⋊Q8D4×C15111yescharacteristic
273C4⋊Q8D4×C15111yescharacteristic
274C4⋊Q8D4×C15111yescharacteristic
275C4⋊Q8C23×C15112yes—
276C4⋊Q8C23×C15111yescharacteristic
277C4⋊Q8C23×C15111yescharacteristic
278#126—24no—
279#126—24no—
280#125—22no—
281#125—24no—
282#125—24no—
283#125—24no—
284#125—24no—
285#125—22no—
286#125—22no—
287#125—24no—
288#125—24no—
289#125—21no—
290#125—21no—
291#125D4×C15112yes—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8D4×C15112yes—
297C22⋊Q8D4×C15112yes—
298C4×Q8—22no—
299C4×Q8—22no—
300C4×Q8—22no—
301C4×Q8—22no—
302C4×Q8—22no—
303C4×Q8—22no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8—21no—
307C4×Q8—21no—
308C4×Q8C23×C15112yes—
309C4×Q8C23×C15112yes—
310#117—21no—
311#117—21no—
312#117D4×C15112yes—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C42C23×C15111yescharacteristic
316#107—24no—
317#106—24no—
318#106—24no—
319C4⋊C8C23×C15112yes—
320C4⋊C8C23×C15112yes—
321#103—24no—
322#103—24no—
323C22⋊C8—21no—
324C22⋊C8—21no—
325#97—21no—
326C4×C8—21no—
327C4×C8—21no—
328C4×C8C23×C15112yes—
329C2×Q8—21no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—22no—
334C2×Q8—41no—
335C2×Q8—82no—
336C2×Q8C2×D4×C15112yes—
337C2×Q8C2×D4×C15112yes—
338C22×C4—41no—
339C22×C4C2×D4×C15111yescharacteristic
340C22×C4C2×D4×C15111yescharacteristic
341C22×C4C2×D4×C15111yescharacteristic
342Q16—84no—
343M16—24no—
344C2×C8—22no—
345C2×C8—22no—
346C2×C8—22no—
347C4⋊C4—24no—
348C4⋊C4—24no—
349C4⋊C4—24no—
350C4⋊C4—24no—
351C4⋊C4—24no—
352C4⋊C4—24no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4C2×D4×C15112yes—
372C4⋊C4C2×D4×C15112yes—
373C4⋊C4C2×D4×C15112yes—
374C4⋊C4C2×D4×C15112yes—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C42—24no—
379C42—24no—
380C42—22no—
381C42—22no—
382C42—22no—
383C42C2×D4×C15111yescharacteristic
384C42C2×D4×C15111yescharacteristic
385C42C2×D4×C15111yescharacteristic
386C42C24×C15111yescharacteristic
387C23#120×C15111yescharacteristic
388Q8—24no—
389Q8—24no—
390Q8—42no—
391Q8—42no—
392Q8—42no—
393Q8—42no—
394Q8—44no—
395Q8—82no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—42no—
406C2×C4—82no—
407C2×C4#120×C15111yescharacteristic
408C2×C4#120×C15111yescharacteristic
409C2×C4#120×C15111yescharacteristic
410C2×C4C22×D4×C15111yescharacteristic
411C2×C4C22×D4×C15111yescharacteristic
412C2×C4C22×D4×C15111yescharacteristic
413C8—24no—
414C8—42no—
415C8—42no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22C2×#120×C15111yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—42no—
424C4—42no—
425C4—42no—
426C4—42no—
427C4—42no—
428C4—42no—
429C4—82no—
430C4#456×C15112yes—
431C4#577×C15112yes—
432C4#578×C15112yes—
433C2—41no—
434C2#3010×C15111yescharacteristic
435C2#3011×C15111yescharacteristic
436C2C2×#456×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radicalC23×C151#120
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
5. #1653×C151C2semidirect
6. #1648×C151C2semidirect
218. #18737C151direct (N × H)
219. C151#18737direct (N × H)
224. #1653C2×C151semidirect
225. #1648C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3556×C1512
#3229×C1512
#3209×C1512
#3165×C1512
#1653×C1512
#1648×C1512
#1544×C1512
#1485×C1512
#18737151