Finite Group Databasebeta

← C151×#18197 #50323122

Subgroups — C151×#18197 #50323122

Order 38656.

1174 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3501×C151C211yesmaximal, characteristic
2C2×#451×C151C212yesmaximal, complemented
3#2409×C151C211yesmaximal, characteristic
4#1605×C151C214yesmaximal, complemented
5#1602×C151C214yesmaximal, complemented
6#1520×C151C212yesmaximal, complemented
7#1459×C151C211yesmaximal, characteristic
8C23×Q8×C151C2211yescharacteristic
9C22×Q16×C151—22no—
10#554×C151—24no—
11#554×C151—22no—
12D4×Q8×C151—22no—
13#544×C151C2212yes—
14#543×C151—21no—
15#543×C151C2212yes—
16#533×C151—21no—
17C2×C22⋊Q8×C151—21no—
18C2×C22⋊Q8×C151—21no—
19C2×C22⋊Q8×C151C2212yes—
20#518×C151—21no—
21C2×C4×D4×C151C2211yescharacteristic
22#451×C151—24no—
23#451×C151C2218yes—
24C2×#103×C151—22no—
25C2×C22⋊C8×C151C2212yes—
26#395×C151C2212yes—
27#393×C151C2212yes—
28#391×C151—21no—
29#386×C151—21no—
30#385×C151—21no—
31#380×C151C2211yescharacteristic
32#328×C151C2218yes—
33#324×C151C2212yes—
34#323×C151C2212yes—
35C22×Q8×C151—22no—
36C22×Q8×C151—21no—
37C22×Q8×C151—21no—
38C22×Q8×C151—22no—
39C22×Q8×C151—44no—
40C22×Q8×C151D412yes—
41C22×Q8×C151C2312yes—
42C22×D4×C151D411yescharacteristic
43C23×C4×C151—21no—
44C23×C4×C151D411yescharacteristic
45C23×C4×C151C2311yescharacteristic
46C2×Q16×C151—28no—
47C2×Q16×C151—48no—
48C22×C8×C151—22no—
49C4⋊Q8×C151—21no—
50C4⋊Q8×C151—21no—
51C4⋊Q8×C151—24no—
52#125×C151—22no—
53#125×C151—24no—
54C22⋊Q8×C151—22no—
55C22⋊Q8×C151—22no—
56C22⋊Q8×C151—24no—
57C22⋊Q8×C151—24no—
58C22⋊Q8×C151—22no—
59C22⋊Q8×C151—22no—
60C22⋊Q8×C151—22no—
61C22⋊Q8×C151—22no—
62C22⋊Q8×C151—24no—
63C22⋊Q8×C151—24no—
64C22⋊Q8×C151—44no—
65C22⋊Q8×C151D414yes—
66C22⋊Q8×C151C2314yes—
67C4×Q8×C151—22no—
68C4×Q8×C151—22no—
69C4×D4×C151—24no—
70C4×D4×C151—24no—
71C4×D4×C151—22no—
72C4×D4×C151—22no—
73#117×C151—22no—
74C2×C4⋊C4×C151—21no—
75C2×C4⋊C4×C151—22no—
76C2×C4⋊C4×C151—22no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—22no—
79C2×C4⋊C4×C151D412yes—
80C2×C4⋊C4×C151C2311yescharacteristic
81C2×C22⋊C4×C151—22no—
82C2×C22⋊C4×C151—22no—
83C2×C22⋊C4×C151—21no—
84C2×C22⋊C4×C151—22no—
85C2×C22⋊C4×C151D411yescharacteristic
86C2×C22⋊C4×C151C2311yescharacteristic
87C2×C42×C151D411yescharacteristic
88#103×C151—28no—
89C22⋊C8×C151—22no—
90C22⋊C8×C151C2314yes—
91#95×C151—22no—
92#95×C151—22no—
93#95×C151C2312yes—
94C24×C151C2×D411yescharacteristic
95C24×C151C2×D411yescharacteristic
96C2×Q8×C151—24no—
97C2×Q8×C151—22no—
98C2×Q8×C151—22no—
99C2×Q8×C151—22no—
100C2×Q8×C151—28no—
101C2×Q8×C151—24no—
102C2×Q8×C151—44no—
103C2×Q8×C151—44no—
104C2×Q8×C151—42no—
105C2×Q8×C151—44no—
106C2×Q8×C151—48no—
107C2×Q8×C151—41no—
108C2×Q8×C151—41no—
109C2×Q8×C151—82no—
110C2×Q8×C151C2×D414yes—
111C2×D4×C151—22no—
112C2×D4×C151—22no—
113C2×D4×C151Q1614yescomplemented
114C22×C4×C151—22no—
115C22×C4×C151—22no—
116C22×C4×C151—22no—
117C22×C4×C151—22no—
118C22×C4×C151—22no—
119C22×C4×C151—21no—
120C22×C4×C151—21no—
121C22×C4×C151—22no—
122C22×C4×C151—42no—
123C22×C4×C151—44no—
124C22×C4×C151—42no—
125C22×C4×C151—42no—
126C22×C4×C151C2×D411yescharacteristic
127C22×C4×C151C2×D412yes—
128C22×C4×C151C2×D411yescharacteristic
129C22×C4×C151C2×D411yescharacteristic
130C22×C4×C151C2×D411yescharacteristic
131C22×C4×C151C2×D412yes—
132C22×C4×C151C2411yescharacteristic
133Q16×C151—416no—
134C2×C8×C151—24no—
135C2×C8×C151—44no—
136C4⋊C4×C151—22no—
137C4⋊C4×C151—24no—
138C4⋊C4×C151—22no—
139C4⋊C4×C151—22no—
140C4⋊C4×C151—24no—
141C4⋊C4×C151—22no—
142C4⋊C4×C151—24no—
143C4⋊C4×C151—22no—
144C4⋊C4×C151—24no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—42no—
147C4⋊C4×C151—44no—
148C4⋊C4×C151C2×D414yes—
149C22⋊C4×C151—24no—
150C22⋊C4×C151—24no—
151C22⋊C4×C151—22no—
152C22⋊C4×C151—24no—
153C22⋊C4×C151—22no—
154C22⋊C4×C151—44no—
155C22⋊C4×C151—42no—
156C42×C151—24no—
157C42×C151—21no—
158C42×C151—21no—
159C23×C151—21no—
160C23×C151—21no—
161C23×C151—41no—
162C23×C151—41no—
163C23×C151—41no—
164C23×C151—41no—
165C23×C151#12012yes—
166C23×C151C2×Q1612yes—
167C23×C151C2×Q1612yescomplemented
168C23×C151#13712yes—
169C23×C151C22×D411yescharacteristic
170Q8×C151—28no—
171Q8×C151—44no—
172Q8×C151—44no—
173Q8×C151—44no—
174Q8×C151—44no—
175Q8×C151—44no—
176Q8×C151—82no—
177Q8×C151—82no—
178D4×C151—28no—
179C2×C4×C151—21no—
180C2×C4×C151—21no—
181C2×C4×C151—24no—
182C2×C4×C151—22no—
183C2×C4×C151—24no—
184C2×C4×C151—24no—
185C2×C4×C151—21no—
186C2×C4×C151—21no—
187C2×C4×C151—24no—
188C2×C4×C151—42no—
189C2×C4×C151—41no—
190C2×C4×C151—48no—
191C2×C4×C151—42no—
192C2×C4×C151—42no—
193C2×C4×C151—42no—
194C2×C4×C151—41no—
195C2×C4×C151—41no—
196C2×C4×C151—42no—
197C2×C4×C151—42no—
198C2×C4×C151—42no—
199C2×C4×C151—81no—
200C2×C4×C151—82no—
201C2×C4×C151—82no—
202C2×C4×C151—82no—
203C2×C4×C151—82no—
204C2×C4×C151#12011yescharacteristic
205C2×C4×C151#12011yescharacteristic
206C2×C4×C151C2×Q1612yescomplemented
207C2×C4×C151C22×D412yes—
208C8×C151—44no—
209C22×C151—21no—
210C22×C151—22no—
211C22×C151—21no—
212C22×C151—22no—
213C22×C151—22no—
214C22×C151—42no—
215C22×C151—42no—
216C22×C151—42no—
217C22×C151—41no—
218C22×C151—41no—
219C22×C151—81no—
220C22×C151#45114yes—
221C22×C151C2×#12011yescharacteristic
222C22×C151C22×Q1611yescharacteristic
223C22×C151C2×#13711yescharacteristic
224C4×C151—22no—
225C4×C151—22no—
226C4×C151—21no—
227C4×C151—41no—
228C4×C151—44no—
229C4×C151—44no—
230C4×C151—41no—
231C4×C151—44no—
232C4×C151—82no—
233C4×C151B(4,𝔽2)12yes—
234C2×C151—21no—
235C2×C151—21no—
236C2×C151—24no—
237C2×C151—42no—
238C2×C151C2×#45111yescharacteristic
239C2×C151#302211yescharacteristic
240C2×C151C2×B(4,𝔽2)11yescharacteristic
241#18197C15111yesmaximal, characteristic, direct product factor, Sylow
242C151#1819711yescharacteristic, direct product factor, Sylow
243#3501C2×C15111yescharacteristic
244C2×#451C2×C15112yescomplemented
245#2409C2×C15111yescharacteristic
246#1605C2×C15114yescomplemented
247#1602C2×C15114yescomplemented
248#1520C2×C15112yescomplemented
249#1459C2×C15111yescharacteristic
250C23×Q8C22×C15111yescharacteristic
251C22×Q16—22no—
252#554—24no—
253#554—22no—
254D4×Q8—22no—
255#544C22×C15112yes—
256#543—21no—
257#543C22×C15112yes—
258#533—21no—
259C2×C22⋊Q8—21no—
260C2×C22⋊Q8—21no—
261C2×C22⋊Q8C22×C15112yes—
262#518—21no—
263C2×C4×D4C22×C15111yescharacteristic
264#451—24no—
265#451C22×C15118yes—
266C2×#103—22no—
267C2×C22⋊C8C22×C15112yes—
268#395C22×C15112yes—
269#393C22×C15112yes—
270#391—21no—
271#386—21no—
272#385—21no—
273#380C22×C15111yescharacteristic
274#328C22×C15118yes—
275#324C22×C15112yes—
276#323C22×C15112yes—
277C22×Q8—21no—
278C22×Q8—21no—
279C22×Q8—22no—
280C22×Q8—22no—
281C22×Q8—44no—
282C22×Q8D4×C15112yes—
283C22×Q8C23×C15112yes—
284C22×D4D4×C15111yescharacteristic
285C23×C4—21no—
286C23×C4D4×C15111yescharacteristic
287C23×C4C23×C15111yescharacteristic
288C2×Q16—28no—
289C2×Q16—48no—
290C22×C8—22no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8—24no—
294#125—22no—
295#125—24no—
296C22⋊Q8—22no—
297C22⋊Q8—22no—
298C22⋊Q8—24no—
299C22⋊Q8—24no—
300C22⋊Q8—24no—
301C22⋊Q8—22no—
302C22⋊Q8—22no—
303C22⋊Q8—22no—
304C22⋊Q8—22no—
305C22⋊Q8—24no—
306C22⋊Q8—44no—
307C22⋊Q8D4×C15114yes—
308C22⋊Q8C23×C15114yes—
309C4×Q8—22no—
310C4×Q8—22no—
311C4×D4—24no—
312C4×D4—24no—
313C4×D4—22no—
314C4×D4—22no—
315#117—22no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4D4×C15112yes—
322C2×C4⋊C4C23×C15111yescharacteristic
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4D4×C15111yescharacteristic
328C2×C22⋊C4C23×C15111yescharacteristic
329C2×C42D4×C15111yescharacteristic
330#103—28no—
331C22⋊C8—22no—
332C22⋊C8C23×C15114yes—
333#95—22no—
334#95—22no—
335#95C23×C15112yes—
336C24C2×D4×C15111yescharacteristic
337C24C2×D4×C15111yescharacteristic
338C2×Q8—24no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—28no—
343C2×Q8—24no—
344C2×Q8—44no—
345C2×Q8—42no—
346C2×Q8—44no—
347C2×Q8—44no—
348C2×Q8—48no—
349C2×Q8—41no—
350C2×Q8—41no—
351C2×Q8—82no—
352C2×Q8C2×D4×C15114yes—
353C2×D4—22no—
354C2×D4—22no—
355C2×D4Q16×C15114yescomplemented
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—42no—
365C22×C4—44no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4C2×D4×C15111yescharacteristic
369C22×C4C2×D4×C15112yes—
370C22×C4C2×D4×C15111yescharacteristic
371C22×C4C2×D4×C15111yescharacteristic
372C22×C4C2×D4×C15111yescharacteristic
373C22×C4C2×D4×C15112yes—
374C22×C4C24×C15111yescharacteristic
375Q16—416no—
376C2×C8—24no—
377C2×C8—44no—
378C4⋊C4—22no—
379C4⋊C4—24no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—24no—
383C4⋊C4—22no—
384C4⋊C4—24no—
385C4⋊C4—22no—
386C4⋊C4—24no—
387C4⋊C4—22no—
388C4⋊C4—42no—
389C4⋊C4—44no—
390C4⋊C4C2×D4×C15114yes—
391C22⋊C4—24no—
392C22⋊C4—24no—
393C22⋊C4—22no—
394C22⋊C4—24no—
395C22⋊C4—22no—
396C22⋊C4—44no—
397C22⋊C4—42no—
398C42—24no—
399C42—21no—
400C42—21no—
401C23—21no—
402C23—21no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23#120×C15112yes—
408C23C2×Q16×C15112yes—
409C23C2×Q16×C15112yescomplemented
410C23#137×C15112yes—
411C23C22×D4×C15111yescharacteristic
412Q8—28no—
413Q8—44no—
414Q8—44no—
415Q8—44no—
416Q8—44no—
417Q8—44no—
418Q8—82no—
419Q8—82no—
420D4—28no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—22no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—21no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—21no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—48no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—81no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4—82no—
445C2×C4—82no—
446C2×C4#120×C15111yescharacteristic
447C2×C4#120×C15111yescharacteristic
448C2×C4C2×Q16×C15112yescomplemented
449C2×C4C22×D4×C15112yes—
450C8—44no—
451C22—21no—
452C22—22no—
453C22—21no—
454C22—22no—
455C22—22no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—41no—
460C22—41no—
461C22—81no—
462C22#451×C15114yes—
463C22C2×#120×C15111yescharacteristic
464C22C22×Q16×C15111yescharacteristic
465C22C2×#137×C15111yescharacteristic
466C4—22no—
467C4—22no—
468C4—21no—
469C4—41no—
470C4—44no—
471C4—44no—
472C4—41no—
473C4—44no—
474C4—82no—
475C4B(4,𝔽2)×C15112yes—
476C2—21no—
477C2—21no—
478C2—24no—
479C2—42no—
480C2C2×#451×C15111yescharacteristic
481C2#3022×C15111yescharacteristic
482C2C2×B(4,𝔽2)×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#451×C151C2semidirect
4. #1605×C151C2semidirect
5. #1602×C151C2semidirect
6. #1520×C151C2semidirect
113. C2×D4×C151Q16semidirect
167. C23×C151C2×Q16semidirect
206. C2×C4×C151C2×Q16semidirect
241. #18197C151direct (N × H)
242. C151#18197direct (N × H)
244. C2×#451C2×C151semidirect
246. #1605C2×C151semidirect
247. #1602C2×C151semidirect
248. #1520C2×C151semidirect
355. C2×D4Q16×C151semidirect
409. C23C2×Q16×C151semidirect
448. C2×C4C2×Q16×C151semidirect

Maximal subgroups

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

subgroupindex
#3501×C1512
C2×#451×C1512
#2409×C1512
#1605×C1512
#1602×C1512
#1520×C1512
#1459×C1512
#18197151