Finite Group Databasebeta

← C151×#23052 #50327977

Subgroups — C151×#23052 #50327977

Order 38656.

824 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#446×C151C211yesmaximal, characteristic, complemented
2C2×#431×C151C211yesmaximal, characteristic
3C4×C22⋊Q8×C151C211yesmaximal, characteristic
4#1985×C151C211yesmaximal, characteristic, complemented
5#1940×C151C211yesmaximal, characteristic, complemented
6#1924×C151C211yesmaximal, characteristic
7#1924×C151C211yesmaximal, characteristic
8#1923×C151C211yesmaximal, characteristic
9#1923×C151C211yesmaximal, characteristic
10#1916×C151C211yesmaximal, characteristic, complemented
11#1916×C151C211yesmaximal, characteristic, complemented
12#1771×C151C211yesmaximal, characteristic, complemented
13#1771×C151C211yesmaximal, characteristic, complemented
14C8×C4⋊C4×C151C211yesmaximal, characteristic, complemented
15#1749×C151C211yesmaximal, characteristic
16C2×C22⋊Q8×C151C411yescharacteristic
17C2×C4×Q8×C151C2211yescharacteristic
18C22×C42×C151C2211yescharacteristic
19#446×C151—24no—
20#431×C151—24no—
21C2×C4⋊C8×C151C2211yescharacteristic
22C2×C4⋊C8×C151C2211yescharacteristic
23C2×C4⋊C8×C151C2211yescharacteristic
24C2×C4⋊C8×C151C2211yescharacteristic
25C2×C4⋊C8×C151C2211yescharacteristic
26C2×C4⋊C8×C151C2211yescharacteristic
27C2×C22⋊C8×C151C2211yescharacteristic
28C2×C22⋊C8×C151C2211yescharacteristic
29C2×C22⋊C8×C151C2211yescharacteristic
30C2×C22⋊C8×C151C2211yescharacteristic
31C2×#97×C151C2211yescharacteristic
32C2×#97×C151C2211yescharacteristic
33C2×#97×C151C2211yescharacteristic
34C2×#97×C151C2211yescharacteristic
35C2×C4×C8×C151C2211yescharacteristic
36C2×C4×C8×C151C2211yescharacteristic
37C2×C4×C8×C151C2211yescharacteristic
38C2×C4×C8×C151C2211yescharacteristic
39#391×C151C411yescharacteristic
40#389×C151C411yescharacteristic
41#387×C151C411yescharacteristic
42#387×C151C411yescharacteristic
43#385×C151C411yescharacteristic
44#385×C151C411yescharacteristic
45#380×C151C411yescharacteristic
46C4×C4⋊C4×C151C2211yescharacteristic
47C4×C4⋊C4×C151C2211yescharacteristic
48C4×C4⋊C4×C151C2211yescharacteristic
49C4×C22⋊C4×C151C2211yescharacteristic
50C4×C22⋊C4×C151C2211yescharacteristic
51#336×C151C2211yescharacteristic
52#336×C151C2211yescharacteristic
53#336×C151C2211yescharacteristic
54#336×C151C2211yescharacteristic
55#336×C151C2211yescharacteristic
56#336×C151C2211yescharacteristic
57#336×C151C2211yescharacteristic
58#336×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61C22×Q8×C151C2×C411yescharacteristic
62C23×C4×C151C2×C411yescharacteristic
63C23×C4×C151C2×C411yescharacteristic
64C23×C4×C151C2311yescharacteristic
65C22×C8×C151C2311yescharacteristic
66C22×C8×C151C2311yescharacteristic
67C22×C8×C151C2311yescharacteristic
68C22×C8×C151C2311yescharacteristic
69C22×C8×C151C2311yescharacteristic
70C22×C8×C151C2311yescharacteristic
71C22×C8×C151C2311yescharacteristic
72C22×C8×C151C2311yescharacteristic
73C22⋊Q8×C151—24no—
74C4×Q8×C151—22no—
75C4×Q8×C151—22no—
76C2×C4⋊C4×C151C2×C411yescharacteristic
77C2×C4⋊C4×C151C2×C411yescharacteristic
78C2×C4⋊C4×C151C2×C411yescharacteristic
79C2×C4⋊C4×C151C2×C411yescharacteristic
80C2×C4⋊C4×C151C2×C411yescharacteristic
81C2×C4⋊C4×C151C2×C411yescharacteristic
82C2×C4⋊C4×C151C2×C411yescharacteristic
83C2×C4⋊C4×C151C2×C411yescharacteristic
84C2×C4⋊C4×C151C2×C411yescharacteristic
85C2×C22⋊C4×C151C2×C411yescharacteristic
86C2×C22⋊C4×C151C2×C411yescharacteristic
87C2×C22⋊C4×C151C2×C411yescharacteristic
88C2×C22⋊C4×C151C2×C411yescharacteristic
89C2×C42×C151—22no—
90C2×C42×C151—22no—
91C2×C42×C151C2×C411yescharacteristic
92C2×C42×C151C2×C411yescharacteristic
93C2×C42×C151C2311yescharacteristic
94C2×C42×C151C2311yescharacteristic
95C2×C42×C151C2311yescharacteristic
96C2×C42×C151C2311yescharacteristic
97C2×C42×C151C2311yescharacteristic
98C2×C42×C151C2311yescharacteristic
99C4⋊C8×C151—22no—
100C4⋊C8×C151—22no—
101C4⋊C8×C151—22no—
102C4⋊C8×C151—22no—
103C4⋊C8×C151—22no—
104C4⋊C8×C151D414yes—
105C22⋊C8×C151—22no—
106C22⋊C8×C151—22no—
107C22⋊C8×C151—22no—
108C22⋊C8×C151—22no—
109#97×C151—22no—
110#97×C151—22no—
111#97×C151—22no—
112#97×C151—22no—
113C4×C8×C151—22no—
114C4×C8×C151—22no—
115C4×C8×C151—22no—
116C4×C8×C151—22no—
117#95×C151C2×C411yescharacteristic
118#95×C151C2×C411yescharacteristic
119#95×C151C2×C411yescharacteristic
120#95×C151C2×C411yescharacteristic
121#95×C151C2×C411yescharacteristic
122#95×C151C2×C411yescharacteristic
123#95×C151C2×C411yescharacteristic
124#95×C151C2×C411yescharacteristic
125#95×C151C2×C411yescharacteristic
126#95×C151C2×C411yescharacteristic
127C24×C151C22×C411yescharacteristic
128C2×Q8×C151—22no—
129C2×Q8×C151—22no—
130C2×Q8×C151—41no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—22no—
136C22×C4×C151—21no—
137C22×C4×C151—21no—
138C22×C4×C151—21no—
139C22×C4×C151—21no—
140C22×C4×C151—21no—
141C22×C4×C151—21no—
142C22×C4×C151—41no—
143C22×C4×C151C22×C411yescharacteristic
144C22×C4×C151C22×C411yescharacteristic
145C22×C4×C151C22×C411yescharacteristic
146C22×C4×C151C22×C411yescharacteristic
147C22×C4×C151C22×C411yescharacteristic
148C22×C4×C151C22×C411yescharacteristic
149C22×C4×C151C22×C411yescharacteristic
150C22×C4×C151C22×C411yescharacteristic
151C22×C4×C151C22×C411yescharacteristic
152C22×C4×C151C22×C411yescharacteristic
153C22×C4×C151C22×C411yescharacteristic
154C22×C4×C151C22×C411yescharacteristic
155C22×C4×C151C22×C411yescharacteristic
156C22×C4×C151C2411yescharacteristic
157C2×C8×C151—21no—
158C2×C8×C151—21no—
159C2×C8×C151—21no—
160C2×C8×C151—21no—
161C2×C8×C151—21no—
162C2×C8×C151—21no—
163C2×C8×C151—21no—
164C2×C8×C151—21no—
165C2×C8×C151—21no—
166C2×C8×C151—21no—
167C2×C8×C151—21no—
168C2×C8×C151—21no—
169C2×C8×C151—21no—
170C2×C8×C151—21no—
171C2×C8×C151—21no—
172C2×C8×C151—21no—
173C2×C8×C151—21no—
174C2×C8×C151—21no—
175C2×C8×C151—21no—
176C2×C8×C151—21no—
177C2×C8×C151C2×D412yes—
178C2×C8×C151C2×D412yes—
179C2×C8×C151#4112yes—
180C2×C8×C151#4112yes—
181C4⋊C4×C151—22no—
182C4⋊C4×C151—22no—
183C4⋊C4×C151—22no—
184C4⋊C4×C151—22no—
185C4⋊C4×C151—22no—
186C4⋊C4×C151—22no—
187C4⋊C4×C151—22no—
188C4⋊C4×C151—41no—
189C4⋊C4×C151M1614yes—
190C22⋊C4×C151—22no—
191C22⋊C4×C151—22no—
192C22⋊C4×C151—22no—
193C22⋊C4×C151—22no—
194C42×C151—22no—
195C42×C151—22no—
196C42×C151—21no—
197C42×C151—21no—
198C42×C151—21no—
199C42×C151—21no—
200C42×C151—21no—
201C42×C151—21no—
202C42×C151—21no—
203C42×C151—21no—
204C42×C151—21no—
205C42×C151—21no—
206C42×C151C2×D412yes—
207C42×C151#4112yes—
208C23×C151—21no—
209C23×C151—21no—
210C23×C151—21no—
211C23×C151—21no—
212C23×C151—21no—
213C23×C151—21no—
214C23×C151#13112yes—
215C23×C151C23×C411yescharacteristic
216Q8×C151—44no—
217C2×C4×C151—28no—
218C2×C4×C151—21no—
219C2×C4×C151—21no—
220C2×C4×C151—21no—
221C2×C4×C151—21no—
222C2×C4×C151—21no—
223C2×C4×C151—21no—
224C2×C4×C151—21no—
225C2×C4×C151—21no—
226C2×C4×C151—21no—
227C2×C4×C151—21no—
228C2×C4×C151—21no—
229C2×C4×C151—21no—
230C2×C4×C151—21no—
231C2×C4×C151—21no—
232C2×C4×C151—21no—
233C2×C4×C151—21no—
234C2×C4×C151—21no—
235C2×C4×C151—21no—
236C2×C4×C151—21no—
237C2×C4×C151—21no—
238C2×C4×C151—21no—
239C2×C4×C151—21no—
240C2×C4×C151—21no—
241C2×C4×C151—21no—
242C2×C4×C151—21no—
243C2×C4×C151—21no—
244C2×C4×C151—21no—
245C2×C4×C151—21no—
246C2×C4×C151—21no—
247C2×C4×C151—21no—
248C2×C4×C151—21no—
249C2×C4×C151—21no—
250C2×C4×C151—21no—
251C2×C4×C151—44no—
252C2×C4×C151—41no—
253C2×C4×C151—41no—
254C2×C4×C151—41no—
255C2×C4×C151—41no—
256C2×C4×C151C4×D412yes—
257C2×C4×C151C4×D412yes—
258C2×C4×C151C2×M1612yes—
259C2×C4×C151C2×M1612yes—
260C2×C4×C151C2×M1612yes—
261C2×C4×C151#13112yes—
262C2×C4×C151C22×D411yescharacteristic
263C2×C4×C151C2×#4111yescharacteristic
264C2×C4×C151C2×#4111yescharacteristic
265C2×C4×C151C2×#4111yescharacteristic
266C2×C4×C1512−1+411yescharacteristic
267C2×C4×C1512−1+411yescharacteristic
268C8×C151—22no—
269C8×C151—22no—
270C8×C151—22no—
271C8×C151—22no—
272C8×C151—41no—
273C8×C151—41no—
274C8×C151—41no—
275C8×C151—41no—
276C22×C151—22no—
277C22×C151—22no—
278C22×C151—22no—
279C22×C151—41no—
280C22×C151—41no—
281C22×C151—41no—
282C22×C151—41no—
283C22×C151C2×C4×D411yescharacteristic
284C22×C151C4×#4111yescharacteristic
285C22×C151#51911yescharacteristic
286C22×C151C22×M1611yescharacteristic
287C22×C151C2×#13111yescharacteristic
288C22×C151C2×#13111yescharacteristic
289C22×C151#56811yescharacteristic
290C4×C151—22no—
291C4×C151—22no—
292C4×C151—22no—
293C4×C151—22no—
294C4×C151—22no—
295C4×C151—22no—
296C4×C151—41no—
297C4×C151—41no—
298C4×C151—41no—
299C4×C151—41no—
300C4×C151—41no—
301C4×C151—41no—
302C4×C151—41no—
303C4×C151#54711yescharacteristic
304C4×C151#54811yescharacteristic
305C4×C151#55211yescharacteristic
306C4×C151#55611yescharacteristic
307C2×C151—42no—
308C2×C151#236211yescharacteristic
309C2×C151#292911yescharacteristic
310C2×C151D4×M1611yescharacteristic
311C2×C151#296511yescharacteristic
312C2×C151#296811yescharacteristic
313C2×C151#298411yescharacteristic
314C2×C151#298511yescharacteristic
315#23052C15111yesmaximal, characteristic, direct product factor, Sylow
316C151#2305211yescharacteristic, direct product factor, Sylow
317C2×#446C2×C15111yescharacteristic, complemented
318C2×#431C2×C15111yescharacteristic
319C4×C22⋊Q8C2×C15111yescharacteristic
320#1985C2×C15111yescharacteristic, complemented
321#1940C2×C15111yescharacteristic, complemented
322#1924C2×C15111yescharacteristic
323#1924C2×C15111yescharacteristic
324#1923C2×C15111yescharacteristic
325#1923C2×C15111yescharacteristic
326#1916C2×C15111yescharacteristic, complemented
327#1916C2×C15111yescharacteristic, complemented
328#1771C2×C15111yescharacteristic, complemented
329#1771C2×C15111yescharacteristic, complemented
330C8×C4⋊C4C2×C15111yescharacteristic, complemented
331#1749C2×C15111yescharacteristic
332C2×C22⋊Q8C4×C15111yescharacteristic
333C2×C4×Q8C22×C15111yescharacteristic
334C22×C42C22×C15111yescharacteristic
335#446—24no—
336#431—24no—
337C2×C4⋊C8C22×C15111yescharacteristic
338C2×C4⋊C8C22×C15111yescharacteristic
339C2×C4⋊C8C22×C15111yescharacteristic
340C2×C4⋊C8C22×C15111yescharacteristic
341C2×C4⋊C8C22×C15111yescharacteristic
342C2×C4⋊C8C22×C15111yescharacteristic
343C2×C22⋊C8C22×C15111yescharacteristic
344C2×C22⋊C8C22×C15111yescharacteristic
345C2×C22⋊C8C22×C15111yescharacteristic
346C2×C22⋊C8C22×C15111yescharacteristic
347C2×#97C22×C15111yescharacteristic
348C2×#97C22×C15111yescharacteristic
349C2×#97C22×C15111yescharacteristic
350C2×#97C22×C15111yescharacteristic
351C2×C4×C8C22×C15111yescharacteristic
352C2×C4×C8C22×C15111yescharacteristic
353C2×C4×C8C22×C15111yescharacteristic
354C2×C4×C8C22×C15111yescharacteristic
355#391C4×C15111yescharacteristic
356#389C4×C15111yescharacteristic
357#387C4×C15111yescharacteristic
358#387C4×C15111yescharacteristic
359#385C4×C15111yescharacteristic
360#385C4×C15111yescharacteristic
361#380C4×C15111yescharacteristic
362C4×C4⋊C4C22×C15111yescharacteristic
363C4×C4⋊C4C22×C15111yescharacteristic
364C4×C4⋊C4C22×C15111yescharacteristic
365C4×C22⋊C4C22×C15111yescharacteristic
366C4×C22⋊C4C22×C15111yescharacteristic
367#336C22×C15111yescharacteristic
368#336C22×C15111yescharacteristic
369#336C22×C15111yescharacteristic
370#336C22×C15111yescharacteristic
371#336C22×C15111yescharacteristic
372#336C22×C15111yescharacteristic
373#336C22×C15111yescharacteristic
374#336C22×C15111yescharacteristic
375#336C22×C15111yescharacteristic
376#336C22×C15111yescharacteristic
377C22×Q8C2×C4×C15111yescharacteristic
378C23×C4C2×C4×C15111yescharacteristic
379C23×C4C2×C4×C15111yescharacteristic
380C23×C4C23×C15111yescharacteristic
381C22×C8C23×C15111yescharacteristic
382C22×C8C23×C15111yescharacteristic
383C22×C8C23×C15111yescharacteristic
384C22×C8C23×C15111yescharacteristic
385C22×C8C23×C15111yescharacteristic
386C22×C8C23×C15111yescharacteristic
387C22×C8C23×C15111yescharacteristic
388C22×C8C23×C15111yescharacteristic
389C22⋊Q8—24no—
390C4×Q8—22no—
391C4×Q8—22no—
392C2×C4⋊C4C2×C4×C15111yescharacteristic
393C2×C4⋊C4C2×C4×C15111yescharacteristic
394C2×C4⋊C4C2×C4×C15111yescharacteristic
395C2×C4⋊C4C2×C4×C15111yescharacteristic
396C2×C4⋊C4C2×C4×C15111yescharacteristic
397C2×C4⋊C4C2×C4×C15111yescharacteristic
398C2×C4⋊C4C2×C4×C15111yescharacteristic
399C2×C4⋊C4C2×C4×C15111yescharacteristic
400C2×C4⋊C4C2×C4×C15111yescharacteristic
401C2×C22⋊C4C2×C4×C15111yescharacteristic
402C2×C22⋊C4C2×C4×C15111yescharacteristic
403C2×C22⋊C4C2×C4×C15111yescharacteristic
404C2×C22⋊C4C2×C4×C15111yescharacteristic
405C2×C42—22no—
406C2×C42—22no—
407C2×C42C2×C4×C15111yescharacteristic
408C2×C42C2×C4×C15111yescharacteristic
409C2×C42C23×C15111yescharacteristic
410C2×C42C23×C15111yescharacteristic
411C2×C42C23×C15111yescharacteristic
412C2×C42C23×C15111yescharacteristic
413C2×C42C23×C15111yescharacteristic
414C2×C42C23×C15111yescharacteristic
415C4⋊C8—22no—
416C4⋊C8—22no—
417C4⋊C8—22no—
418C4⋊C8—22no—
419C4⋊C8—22no—
420C4⋊C8D4×C15114yes—
421C22⋊C8—22no—
422C22⋊C8—22no—
423C22⋊C8—22no—
424C22⋊C8—22no—
425#97—22no—
426#97—22no—
427#97—22no—
428#97—22no—
429C4×C8—22no—
430C4×C8—22no—
431C4×C8—22no—
432C4×C8—22no—
433#95C2×C4×C15111yescharacteristic
434#95C2×C4×C15111yescharacteristic
435#95C2×C4×C15111yescharacteristic
436#95C2×C4×C15111yescharacteristic
437#95C2×C4×C15111yescharacteristic
438#95C2×C4×C15111yescharacteristic
439#95C2×C4×C15111yescharacteristic
440#95C2×C4×C15111yescharacteristic
441#95C2×C4×C15111yescharacteristic
442#95C2×C4×C15111yescharacteristic
443C24C22×C4×C15111yescharacteristic
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—41no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—41no—
459C22×C4C22×C4×C15111yescharacteristic
460C22×C4C22×C4×C15111yescharacteristic
461C22×C4C22×C4×C15111yescharacteristic
462C22×C4C22×C4×C15111yescharacteristic
463C22×C4C22×C4×C15111yescharacteristic
464C22×C4C22×C4×C15111yescharacteristic
465C22×C4C22×C4×C15111yescharacteristic
466C22×C4C22×C4×C15111yescharacteristic
467C22×C4C22×C4×C15111yescharacteristic
468C22×C4C22×C4×C15111yescharacteristic
469C22×C4C22×C4×C15111yescharacteristic
470C22×C4C22×C4×C15111yescharacteristic
471C22×C4C22×C4×C15111yescharacteristic
472C22×C4C24×C15111yescharacteristic
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8C2×D4×C15112yes—
494C2×C8C2×D4×C15112yes—
495C2×C8#41×C15112yes—
496C2×C8#41×C15112yes—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—41no—
505C4⋊C4M16×C15114yes—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C42—22no—
511C42—22no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42C2×D4×C15112yes—
523C42#41×C15112yes—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23#131×C15112yes—
531C23C23×C4×C15111yescharacteristic
532Q8—44no—
533C2×C4—28no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—44no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4C4×D4×C15112yes—
573C2×C4C4×D4×C15112yes—
574C2×C4C2×M16×C15112yes—
575C2×C4C2×M16×C15112yes—
576C2×C4C2×M16×C15112yes—
577C2×C4#131×C15112yes—
578C2×C4C22×D4×C15111yescharacteristic
579C2×C4C2×#41×C15111yescharacteristic
580C2×C4C2×#41×C15111yescharacteristic
581C2×C4C2×#41×C15111yescharacteristic
582C2×C42−1+4×C15111yescharacteristic
583C2×C42−1+4×C15111yescharacteristic
584C8—22no—
585C8—22no—
586C8—22no—
587C8—22no—
588C8—41no—
589C8—41no—
590C8—41no—
591C8—41no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22C2×C4×D4×C15111yescharacteristic
600C22C4×#41×C15111yescharacteristic
601C22#519×C15111yescharacteristic
602C22C22×M16×C15111yescharacteristic
603C22C2×#131×C15111yescharacteristic
604C22C2×#131×C15111yescharacteristic
605C22#568×C15111yescharacteristic
606C4—22no—
607C4—22no—
608C4—22no—
609C4—22no—
610C4—22no—
611C4—22no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—41no—
617C4—41no—
618C4—41no—
619C4#547×C15111yescharacteristic
620C4#548×C15111yescharacteristic
621C4#552×C15111yescharacteristic
622C4#556×C15111yescharacteristic
623C2—42no—
624C2#2362×C15111yescharacteristic
625C2#2929×C15111yescharacteristic
626C2D4×M16×C15111yescharacteristic
627C2#2965×C15111yescharacteristic
628C2#2968×C15111yescharacteristic
629C2#2984×C15111yescharacteristic
630C2#2985×C15111yescharacteristic
subgroupG/H
centerC22×C4×C151C24
commutatorC23C23×C4×C151
Frattini, cosocleC22×C4C24×C151
socleC23×C151C23×C4
prime radicalC24×C151C22×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#446×C151C2semidirect
4. #1985×C151C2semidirect
5. #1940×C151C2semidirect
10. #1916×C151C2semidirect
11. #1916×C151C2semidirect
12. #1771×C151C2semidirect
13. #1771×C151C2semidirect
14. C8×C4⋊C4×C151C2semidirect
315. #23052C151direct (N × H)
316. C151#23052direct (N × H)
317. C2×#446C2×C151semidirect
320. #1985C2×C151semidirect
321. #1940C2×C151semidirect
326. #1916C2×C151semidirect
327. #1916C2×C151semidirect
328. #1771C2×C151semidirect
329. #1771C2×C151semidirect
330. C8×C4⋊C4C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#446×C1512
C2×#431×C1512
C4×C22⋊Q8×C1512
#1985×C1512
#1940×C1512
#1924×C1512
#1923×C1512
#1916×C1512
#1771×C1512
C8×C4⋊C4×C1512
#1749×C1512
#23052151