Finite Group Databasebeta

← C151×#24319 #50329244

Subgroups — C151×#24319 #50329244

Order 38656.

930 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3502×C151C211yesmaximal, characteristic
2#3078×C151C212yesmaximal
3#2327×C151C211yesmaximal, characteristic
4#2061×C151C212yesmaximal
5#2028×C151C212yesmaximal
6#1995×C151C212yesmaximal
7#1886×C151C212yesmaximal
8#1857×C151C212yesmaximal
9#1801×C151C211yesmaximal, characteristic
10Q82×C151—22no—
11#557×C151—22no—
12#557×C151—24no—
13#544×C151—22no—
14#544×C151C2212yes—
15#533×C151—22no—
16#533×C151C2212yes—
17C2×C4⋊Q8×C151C2211yescharacteristic
18#519×C151C2212yes—
19C2×C4×Q8×C151C2211yescharacteristic
20C2×C4×Q8×C151C2211yescharacteristic
21#479×C151—24no—
22#477×C151—22no—
23#475×C151—22no—
24#428×C151C2214yes—
25#423×C151C2212yes—
26#419×C151C2214yes—
27C2×#101×C151C2212yes—
28#391×C151C2211yescharacteristic
29#391×C151C2211yescharacteristic
30#387×C151—22no—
31#387×C151—22no—
32#382×C151C2211yescharacteristic
33#376×C151C2211yescharacteristic
34#343×C151C2212yes—
35#339×C151C2214yes—
36#339×C151C2214yes—
37C22×Q8×C151C2311yescharacteristic
38C22×Q8×C151C2311yescharacteristic
39C2×M16×C151C2314yes—
40C4⋊Q8×C151—22no—
41C4⋊Q8×C151—22no—
42C4⋊Q8×C151—28no—
43C4⋊Q8×C151—24no—
44C4⋊Q8×C151—22no—
45C4⋊Q8×C151D412yes—
46C4⋊Q8×C151D412yes—
47C4⋊Q8×C151Q814yescomplemented
48#125×C151—24no—
49#125×C151—28no—
50#125×C151—24no—
51#125×C151D414yes—
52C22⋊Q8×C151—22no—
53C22⋊Q8×C151—24no—
54C22⋊Q8×C151—22no—
55C4×Q8×C151—24no—
56C4×Q8×C151—24no—
57C4×Q8×C151—24no—
58C4×Q8×C151—24no—
59C4×Q8×C151—22no—
60C4×Q8×C151—22no—
61C4×Q8×C151—22no—
62C4×Q8×C151—22no—
63C4×Q8×C151—22no—
64C4×Q8×C151—22no—
65#117×C151—24no—
66#117×C151C2314yes—
67C2×C4⋊C4×C151—22no—
68C2×C4⋊C4×C151—21no—
69C2×C4⋊C4×C151D412yes—
70C2×C4⋊C4×C151C2311yescharacteristic
71C2×C4⋊C4×C151C2311yescharacteristic
72C2×C42×C151—21no—
73C2×C42×C151D412yes—
74C2×C42×C151C2311yescharacteristic
75C2×C42×C151C2311yescharacteristic
76C2×C42×C151C2311yescharacteristic
77#107×C151—24no—
78#106×C151—24no—
79C4⋊C8×C151—22no—
80C4⋊C8×C151—22no—
81#103×C151—24no—
82#103×C151—24no—
83#101×C151—24no—
84#95×C151—21no—
85#95×C151—21no—
86#95×C151—22no—
87#95×C151—22no—
88#95×C151—22no—
89C2×Q8×C151—24no—
90C2×Q8×C151—22no—
91C2×Q8×C151—22no—
92C2×Q8×C151—22no—
93C2×Q8×C151—21no—
94C2×Q8×C151—22no—
95C2×Q8×C151—22no—
96C2×Q8×C151—22no—
97C2×Q8×C151C2×Q812yes—
98C2×Q8×C151C2×Q812yes—
99C2×Q8×C151#4112yes—
100C22×C4×C151—21no—
101C22×C4×C151—21no—
102C22×C4×C151—21no—
103C22×C4×C151—21no—
104C22×C4×C151C2×D412yes—
105C22×C4×C151C2×D412yes—
106C22×C4×C151C2×D411yescharacteristic
107C22×C4×C151C2×D411yescharacteristic
108C22×C4×C151C2411yescharacteristic
109M16×C151—24no—
110M16×C151—24no—
111C2×C8×C151—24no—
112C4⋊C4×C151—24no—
113C4⋊C4×C151—24no—
114C4⋊C4×C151—24no—
115C4⋊C4×C151—28no—
116C4⋊C4×C151—24no—
117C4⋊C4×C151—24no—
118C4⋊C4×C151—22no—
119C4⋊C4×C151—22no—
120C4⋊C4×C151—24no—
121C4⋊C4×C151—28no—
122C4⋊C4×C151—22no—
123C4⋊C4×C151—22no—
124C4⋊C4×C151—41no—
125C4⋊C4×C151—41no—
126C4⋊C4×C151C2×D414yes—
127C4⋊C4×C151C2×D414yes—
128C22⋊C4×C151—24no—
129C42×C151—28no—
130C42×C151—22no—
131C42×C151—22no—
132C42×C151—24no—
133C42×C151—21no—
134C42×C151—22no—
135C42×C151—42no—
136C42×C151C2×D412yes—
137C42×C151C2×D412yes—
138C42×C151C2×Q812yes—
139C23×C151C22×D411yescharacteristic
140Q8×C151—24no—
141Q8×C151—24no—
142Q8×C151—24no—
143Q8×C151—44no—
144Q8×C151—42no—
145Q8×C151—82no—
146Q8×C151—84no—
147C2×C4×C151—22no—
148C2×C4×C151—22no—
149C2×C4×C151—24no—
150C2×C4×C151—22no—
151C2×C4×C151—24no—
152C2×C4×C151—22no—
153C2×C4×C151—22no—
154C2×C4×C151—41no—
155C2×C4×C151—41no—
156C2×C4×C151—41no—
157C2×C4×C151—41no—
158C2×C4×C151—41no—
159C2×C4×C151—41no—
160C2×C4×C151—42no—
161C2×C4×C151—41no—
162C2×C4×C151—41no—
163C2×C4×C151—42no—
164C2×C4×C151—41no—
165C2×C4×C151—41no—
166C2×C4×C151#12011yescharacteristic
167C2×C4×C151#12012yes—
168C2×C4×C151#12011yescharacteristic
169C2×C4×C151C22⋊Q814yes—
170C2×C4×C151C22×D412yes—
171C2×C4×C151C22×Q811yescharacteristic
172C2×C4×C151C2×#4111yescharacteristic
173C2×C4×C1512−1+412yes—
174C8×C151—44no—
175C22×C151—21no—
176C22×C151—21no—
177C22×C151C2×#12011yescharacteristic
178C22×C151C2×C22⋊Q811yescharacteristic
179C22×C151#53611yescharacteristic
180C4×C151—24no—
181C4×C151—21no—
182C4×C151—21no—
183C4×C151—22no—
184C4×C151—42no—
185C4×C151—42no—
186C4×C151—44no—
187C4×C151—42no—
188C4×C151—44no—
189C4×C151—81no—
190C4×C151—81no—
191C4×C151#54812yes—
192C4×C151D4×Q812yes—
193C2×C151—21no—
194C2×C151—21no—
195C2×C151#240911yescharacteristic
196C2×C151#302011yescharacteristic
197C2×C151#302211yescharacteristic
198#24319C15111yesmaximal, characteristic, direct product factor, Sylow
199C151#2431911yescharacteristic, direct product factor, Sylow
200#3502C2×C15111yescharacteristic
201#3078C2×C15112yes—
202#2327C2×C15111yescharacteristic
203#2061C2×C15112yes—
204#2028C2×C15112yes—
205#1995C2×C15112yes—
206#1886C2×C15112yes—
207#1857C2×C15112yes—
208#1801C2×C15111yescharacteristic
209Q82—22no—
210#557—22no—
211#557—24no—
212#544—22no—
213#544C22×C15112yes—
214#533—22no—
215#533C22×C15112yes—
216C2×C4⋊Q8C22×C15111yescharacteristic
217#519C22×C15112yes—
218C2×C4×Q8C22×C15111yescharacteristic
219C2×C4×Q8C22×C15111yescharacteristic
220#479—24no—
221#477—22no—
222#475—22no—
223#428C22×C15114yes—
224#423C22×C15112yes—
225#419C22×C15114yes—
226C2×#101C22×C15112yes—
227#391C22×C15111yescharacteristic
228#391C22×C15111yescharacteristic
229#387—22no—
230#387—22no—
231#382C22×C15111yescharacteristic
232#376C22×C15111yescharacteristic
233#343C22×C15112yes—
234#339C22×C15114yes—
235#339C22×C15114yes—
236C22×Q8C23×C15111yescharacteristic
237C22×Q8C23×C15111yescharacteristic
238C2×M16C23×C15114yes—
239C4⋊Q8—22no—
240C4⋊Q8—22no—
241C4⋊Q8—28no—
242C4⋊Q8—22no—
243C4⋊Q8—24no—
244C4⋊Q8D4×C15112yes—
245C4⋊Q8D4×C15112yes—
246C4⋊Q8Q8×C15114yescomplemented
247#125—24no—
248#125—28no—
249#125—24no—
250#125D4×C15114yes—
251C22⋊Q8—22no—
252C22⋊Q8—24no—
253C22⋊Q8—22no—
254C4×Q8—24no—
255C4×Q8—24no—
256C4×Q8—24no—
257C4×Q8—24no—
258C4×Q8—22no—
259C4×Q8—22no—
260C4×Q8—22no—
261C4×Q8—22no—
262C4×Q8—22no—
263C4×Q8—22no—
264#117—24no—
265#117C23×C15114yes—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4D4×C15112yes—
269C2×C4⋊C4C23×C15111yescharacteristic
270C2×C4⋊C4C23×C15111yescharacteristic
271C2×C42—21no—
272C2×C42D4×C15112yes—
273C2×C42C23×C15111yescharacteristic
274C2×C42C23×C15111yescharacteristic
275C2×C42C23×C15111yescharacteristic
276#107—24no—
277#106—24no—
278C4⋊C8—22no—
279C4⋊C8—22no—
280#103—24no—
281#103—24no—
282#101—24no—
283#95—21no—
284#95—21no—
285#95—22no—
286#95—22no—
287#95—22no—
288C2×Q8—24no—
289C2×Q8—22no—
290C2×Q8—22no—
291C2×Q8—22no—
292C2×Q8—21no—
293C2×Q8—22no—
294C2×Q8—22no—
295C2×Q8—22no—
296C2×Q8C2×Q8×C15112yes—
297C2×Q8C2×Q8×C15112yes—
298C2×Q8#41×C15112yes—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4C2×D4×C15112yes—
304C22×C4C2×D4×C15112yes—
305C22×C4C2×D4×C15111yescharacteristic
306C22×C4C2×D4×C15111yescharacteristic
307C22×C4C24×C15111yescharacteristic
308M16—24no—
309M16—24no—
310C2×C8—24no—
311C4⋊C4—24no—
312C4⋊C4—24no—
313C4⋊C4—24no—
314C4⋊C4—28no—
315C4⋊C4—24no—
316C4⋊C4—24no—
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—24no—
320C4⋊C4—28no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4C2×D4×C15114yes—
326C4⋊C4C2×D4×C15114yes—
327C22⋊C4—24no—
328C42—28no—
329C42—22no—
330C42—22no—
331C42—24no—
332C42—21no—
333C42—22no—
334C42—42no—
335C42C2×D4×C15112yes—
336C42C2×D4×C15112yes—
337C42C2×Q8×C15112yes—
338C23C22×D4×C15111yescharacteristic
339Q8—24no—
340Q8—24no—
341Q8—24no—
342Q8—44no—
343Q8—42no—
344Q8—82no—
345Q8—84no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—24no—
349C2×C4—24no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4#120×C15111yescharacteristic
366C2×C4#120×C15111yescharacteristic
367C2×C4#120×C15112yes—
368C2×C4C22⋊Q8×C15114yes—
369C2×C4C22×D4×C15112yes—
370C2×C4C22×Q8×C15111yescharacteristic
371C2×C4C2×#41×C15111yescharacteristic
372C2×C42−1+4×C15112yes—
373C8—44no—
374C22—21no—
375C22—21no—
376C22C2×#120×C15111yescharacteristic
377C22C2×C22⋊Q8×C15111yescharacteristic
378C22#536×C15111yescharacteristic
379C4—24no—
380C4—21no—
381C4—21no—
382C4—22no—
383C4—42no—
384C4—42no—
385C4—44no—
386C4—42no—
387C4—44no—
388C4—81no—
389C4—81no—
390C4#548×C15112yes—
391C4D4×Q8×C15112yes—
392C2—21no—
393C2—21no—
394C2#2409×C15111yescharacteristic
395C2#3020×C15111yescharacteristic
396C2#3022×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC23×C151C22×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
47. C4⋊Q8×C151Q8semidirect
198. #24319C151direct (N × H)
199. C151#24319direct (N × H)
246. C4⋊Q8Q8×C151semidirect

Maximal subgroups

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

subgroupindex
#3502×C1512
#3078×C1512
#2327×C1512
#2061×C1512
#2028×C1512
#1995×C1512
#1886×C1512
#1857×C1512
#1801×C1512
#24319151