Finite Group Databasebeta

← C151×#22605 #50327530

Subgroups — C151×#22605 #50327530

Order 38656.

780 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#433×C151C211yesmaximal, characteristic
2C2×#432×C151C211yesmaximal, characteristic
3#2296×C151C211yesmaximal, characteristic
4#1940×C151C211yesmaximal, characteristic, complemented
5#1939×C151C211yesmaximal, characteristic, complemented
6#1917×C151C211yesmaximal, characteristic, complemented
7#1917×C151C211yesmaximal, characteristic, complemented
8#1917×C151C211yesmaximal, characteristic, complemented
9#1916×C151C211yesmaximal, characteristic, complemented
10#1818×C151C211yesmaximal, characteristic
11#1817×C151C211yesmaximal, characteristic
12#1798×C151C211yesmaximal, characteristic
13#1771×C151C211yesmaximal, characteristic, complemented
14#1770×C151C211yesmaximal, characteristic, complemented
15#1750×C151C211yesmaximal, characteristic
16C2×#117×C151C2211yescharacteristic
17C2×#117×C151C2211yescharacteristic
18C22×C42×C151C2211yescharacteristic
19#433×C151—24no—
20#432×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
37#389×C151C411yescharacteristic
38#389×C151C411yescharacteristic
39#389×C151C411yescharacteristic
40#389×C151C411yescharacteristic
41#385×C151C411yescharacteristic
42#385×C151C411yescharacteristic
43#385×C151C411yescharacteristic
44#385×C151C411yescharacteristic
45C4×C4⋊C4×C151C2211yescharacteristic
46C4×C4⋊C4×C151C2211yescharacteristic
47C4×C4⋊C4×C151C2211yescharacteristic
48C4×C4⋊C4×C151C2211yescharacteristic
49#336×C151C2211yescharacteristic
50#336×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
61C23×C4×C151C2×C411yescharacteristic
62C23×C4×C151C2×C411yescharacteristic
63C23×C4×C151C2311yescharacteristic
64C22×C8×C151C2311yescharacteristic
65C22×C8×C151C2311yescharacteristic
66C22×C8×C151C2311yescharacteristic
67C22×C8×C151C2311yescharacteristic
68C22×C8×C151C2311yescharacteristic
69C22×C8×C151C2311yescharacteristic
70C22×C8×C151C2311yescharacteristic
71C22×C8×C151C2311yescharacteristic
72#117×C151—22no—
73#117×C151—22no—
74#117×C151—22no—
75#117×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×C4⋊C4×C151C2×C411yescharacteristic
86C2×C4⋊C4×C151C2×C411yescharacteristic
87C2×C4⋊C4×C151C2×C411yescharacteristic
88C2×C22⋊C4×C151C2×C411yescharacteristic
89C2×C22⋊C4×C151C2×C411yescharacteristic
90C2×C22⋊C4×C151C2×C411yescharacteristic
91C2×C22⋊C4×C151C2×C411yescharacteristic
92C2×C42×C151—22no—
93C2×C42×C151—22no—
94C2×C42×C151C2×C411yescharacteristic
95C2×C42×C151C2×C411yescharacteristic
96C2×C42×C151C2311yescharacteristic
97C2×C42×C151C2311yescharacteristic
98C2×C42×C151C2311yescharacteristic
99C2×C42×C151C2311yescharacteristic
100C2×C42×C151C2311yescharacteristic
101C2×C42×C151C2311yescharacteristic
102C4⋊C8×C151—22no—
103C4⋊C8×C151—22no—
104C4⋊C8×C151—22no—
105C4⋊C8×C151—22no—
106C4⋊C8×C151—22no—
107C4⋊C8×C151—22no—
108C22⋊C8×C151—22no—
109C22⋊C8×C151—22no—
110C22⋊C8×C151—22no—
111C22⋊C8×C151D414yes—
112#97×C151—22no—
113#97×C151—22no—
114#97×C151—22no—
115#97×C151—22no—
116C4×C8×C151—22no—
117C4×C8×C151—22no—
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
126C24×C151C22×C411yescharacteristic
127C22×C4×C151—21no—
128C22×C4×C151—21no—
129C22×C4×C151—21no—
130C22×C4×C151—21no—
131C22×C4×C151—22no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—41no—
135C22×C4×C151—41no—
136C22×C4×C151—41no—
137C22×C4×C151C22×C411yescharacteristic
138C22×C4×C151C22×C411yescharacteristic
139C22×C4×C151C22×C411yescharacteristic
140C22×C4×C151C22×C411yescharacteristic
141C22×C4×C151C22×C411yescharacteristic
142C22×C4×C151C22×C411yescharacteristic
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×C151C2×D412yes—
151C22×C4×C151#4112yes—
152C22×C4×C151C2411yescharacteristic
153C2×C8×C151—21no—
154C2×C8×C151—21no—
155C2×C8×C151—21no—
156C2×C8×C151—21no—
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×C151C2×D412yes—
176C2×C8×C151C2×D412yes—
177C4⋊C4×C151—22no—
178C4⋊C4×C151—22no—
179C4⋊C4×C151—22no—
180C4⋊C4×C151—22no—
181C4⋊C4×C151—22no—
182C4⋊C4×C151—22no—
183C4⋊C4×C151—41no—
184C4⋊C4×C151—41no—
185C4⋊C4×C151—41no—
186C4⋊C4×C151—41no—
187C4⋊C4×C151—41no—
188C4⋊C4×C151—41no—
189C22⋊C4×C151—22no—
190C22⋊C4×C151—22no—
191C22⋊C4×C151—22no—
192C22⋊C4×C151—22no—
193C42×C151—22no—
194C42×C151—22no—
195C42×C151—21no—
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#4112yes—
206C42×C151#4112yes—
207C23×C151—21no—
208C23×C151—21no—
209C23×C151—21no—
210C23×C151—21no—
211C23×C151—21no—
212C23×C151—21no—
213C23×C151C4×D412yes—
214C23×C151C23×C411yescharacteristic
215C2×C4×C151—21no—
216C2×C4×C151—21no—
217C2×C4×C151—21no—
218C2×C4×C151—21no—
219C2×C4×C151—21no—
220C2×C4×C151—21no—
221C2×C4×C151—21no—
222C2×C4×C151—21no—
223C2×C4×C151—22no—
224C2×C4×C151—22no—
225C2×C4×C151—22no—
226C2×C4×C151—22no—
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—21no—
252C2×C4×C151—21no—
253C2×C4×C151—21no—
254C2×C4×C151—44no—
255C2×C4×C151—44no—
256C2×C4×C151#11712yes—
257C2×C4×C151#11712yes—
258C2×C4×C151C4×D412yes—
259C2×C4×C151#13112yes—
260C2×C4×C151C22×D411yescharacteristic
261C2×C4×C151C2×#4111yescharacteristic
262C2×C4×C151C2×#4111yescharacteristic
263C2×C4×C151C2×#4111yescharacteristic
264C2×C4×C1512−1+411yescharacteristic
265C2×C4×C1512−1+411yescharacteristic
266C8×C151—22no—
267C8×C151—22no—
268C8×C151—41no—
269C8×C151—41no—
270C8×C151—41no—
271C8×C151—41no—
272C8×C151—41no—
273C8×C151—41no—
274C22×C151—22no—
275C22×C151—22no—
276C22×C151—22no—
277C22×C151—41no—
278C22×C151—41no—
279C22×C151—41no—
280C22×C151—41no—
281C22×C151C2×#11711yescharacteristic
282C22×C151C2×C4×D411yescharacteristic
283C22×C151#51911yescharacteristic
284C22×C151C2×#13111yescharacteristic
285C22×C151#56811yescharacteristic
286C22×C151#56811yescharacteristic
287C22×C151#56811yescharacteristic
288C4×C151—22no—
289C4×C151—22no—
290C4×C151—22no—
291C4×C151—22no—
292C4×C151—41no—
293C4×C151—41no—
294C4×C151—41no—
295C4×C151—41no—
296C4×C151—41no—
297C4×C151—41no—
298C4×C151—41no—
299C4×C151—41no—
300C4×C151—41no—
301C4×C151#54711yescharacteristic
302C4×C151#54711yescharacteristic
303C4×C151#55211yescharacteristic
304C4×C151#55211yescharacteristic
305C2×C151—42no—
306C2×C151#234411yescharacteristic
307C2×C151#292311yescharacteristic
308C2×C151#292511yescharacteristic
309C2×C151#293011yescharacteristic
310C2×C151#293311yescharacteristic
311C2×C151#298511yescharacteristic
312C2×C151#298711yescharacteristic
313#22605C15111yesmaximal, characteristic, direct product factor, Sylow
314C151#2260511yescharacteristic, direct product factor, Sylow
315C2×#433C2×C15111yescharacteristic
316C2×#432C2×C15111yescharacteristic
317#2296C2×C15111yescharacteristic
318#1940C2×C15111yescharacteristic, complemented
319#1939C2×C15111yescharacteristic, complemented
320#1917C2×C15111yescharacteristic, complemented
321#1917C2×C15111yescharacteristic, complemented
322#1917C2×C15111yescharacteristic, complemented
323#1916C2×C15111yescharacteristic, complemented
324#1818C2×C15111yescharacteristic
325#1817C2×C15111yescharacteristic
326#1798C2×C15111yescharacteristic
327#1771C2×C15111yescharacteristic, complemented
328#1770C2×C15111yescharacteristic, complemented
329#1750C2×C15111yescharacteristic
330C2×#117C22×C15111yescharacteristic
331C2×#117C22×C15111yescharacteristic
332C22×C42C22×C15111yescharacteristic
333#433—24no—
334#432—24no—
335C2×C4⋊C8C22×C15111yescharacteristic
336C2×C4⋊C8C22×C15111yescharacteristic
337C2×C4⋊C8C22×C15111yescharacteristic
338C2×C4⋊C8C22×C15111yescharacteristic
339C2×C4⋊C8C22×C15111yescharacteristic
340C2×C4⋊C8C22×C15111yescharacteristic
341C2×C22⋊C8C22×C15111yescharacteristic
342C2×C22⋊C8C22×C15111yescharacteristic
343C2×C22⋊C8C22×C15111yescharacteristic
344C2×C22⋊C8C22×C15111yescharacteristic
345C2×#97C22×C15111yescharacteristic
346C2×#97C22×C15111yescharacteristic
347C2×#97C22×C15111yescharacteristic
348C2×#97C22×C15111yescharacteristic
349C2×C4×C8C22×C15111yescharacteristic
350C2×C4×C8C22×C15111yescharacteristic
351#389C4×C15111yescharacteristic
352#389C4×C15111yescharacteristic
353#389C4×C15111yescharacteristic
354#389C4×C15111yescharacteristic
355#385C4×C15111yescharacteristic
356#385C4×C15111yescharacteristic
357#385C4×C15111yescharacteristic
358#385C4×C15111yescharacteristic
359C4×C4⋊C4C22×C15111yescharacteristic
360C4×C4⋊C4C22×C15111yescharacteristic
361C4×C4⋊C4C22×C15111yescharacteristic
362C4×C4⋊C4C22×C15111yescharacteristic
363#336C22×C15111yescharacteristic
364#336C22×C15111yescharacteristic
365#336C22×C15111yescharacteristic
366#336C22×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
375C23×C4C2×C4×C15111yescharacteristic
376C23×C4C2×C4×C15111yescharacteristic
377C23×C4C23×C15111yescharacteristic
378C22×C8C23×C15111yescharacteristic
379C22×C8C23×C15111yescharacteristic
380C22×C8C23×C15111yescharacteristic
381C22×C8C23×C15111yescharacteristic
382C22×C8C23×C15111yescharacteristic
383C22×C8C23×C15111yescharacteristic
384C22×C8C23×C15111yescharacteristic
385C22×C8C23×C15111yescharacteristic
386#117—22no—
387#117—22no—
388#117—22no—
389#117—22no—
390C2×C4⋊C4C2×C4×C15111yescharacteristic
391C2×C4⋊C4C2×C4×C15111yescharacteristic
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×C4⋊C4C2×C4×C15111yescharacteristic
402C2×C22⋊C4C2×C4×C15111yescharacteristic
403C2×C22⋊C4C2×C4×C15111yescharacteristic
404C2×C22⋊C4C2×C4×C15111yescharacteristic
405C2×C22⋊C4C2×C4×C15111yescharacteristic
406C2×C42—22no—
407C2×C42—22no—
408C2×C42C2×C4×C15111yescharacteristic
409C2×C42C2×C4×C15111yescharacteristic
410C2×C42C23×C15111yescharacteristic
411C2×C42C23×C15111yescharacteristic
412C2×C42C23×C15111yescharacteristic
413C2×C42C23×C15111yescharacteristic
414C2×C42C23×C15111yescharacteristic
415C2×C42C23×C15111yescharacteristic
416C4⋊C8—22no—
417C4⋊C8—22no—
418C4⋊C8—22no—
419C4⋊C8—22no—
420C4⋊C8—22no—
421C4⋊C8—22no—
422C22⋊C8—22no—
423C22⋊C8—22no—
424C22⋊C8—22no—
425C22⋊C8D4×C15114yes—
426#97—22no—
427#97—22no—
428#97—22no—
429#97—22no—
430C4×C8—22no—
431C4×C8—22no—
432#95C2×C4×C15111yescharacteristic
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
440C24C22×C4×C15111yescharacteristic
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4C22×C4×C15111yescharacteristic
452C22×C4C22×C4×C15111yescharacteristic
453C22×C4C22×C4×C15111yescharacteristic
454C22×C4C22×C4×C15111yescharacteristic
455C22×C4C22×C4×C15111yescharacteristic
456C22×C4C22×C4×C15111yescharacteristic
457C22×C4C22×C4×C15111yescharacteristic
458C22×C4C22×C4×C15111yescharacteristic
459C22×C4C22×C4×C15111yescharacteristic
460C22×C4C22×C4×C15111yescharacteristic
461C22×C4C22×C4×C15111yescharacteristic
462C22×C4C22×C4×C15111yescharacteristic
463C22×C4C22×C4×C15111yescharacteristic
464C22×C4C2×D4×C15112yes—
465C22×C4#41×C15112yes—
466C22×C4C24×C15111yescharacteristic
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
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×C8C2×D4×C15112yes—
490C2×C8C2×D4×C15112yes—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C42—22no—
508C42—22no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42#41×C15112yes—
520C42#41×C15112yes—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23C4×D4×C15112yes—
528C23C23×C4×C15111yescharacteristic
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
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—21no—
568C2×C4—44no—
569C2×C4—44no—
570C2×C4#117×C15112yes—
571C2×C4#117×C15112yes—
572C2×C4C4×D4×C15112yes—
573C2×C4#131×C15112yes—
574C2×C4C22×D4×C15111yescharacteristic
575C2×C4C2×#41×C15111yescharacteristic
576C2×C4C2×#41×C15111yescharacteristic
577C2×C4C2×#41×C15111yescharacteristic
578C2×C42−1+4×C15111yescharacteristic
579C2×C42−1+4×C15111yescharacteristic
580C8—22no—
581C8—22no—
582C8—41no—
583C8—41no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C22—22no—
589C22—22no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22C2×#117×C15111yescharacteristic
596C22C2×C4×D4×C15111yescharacteristic
597C22#519×C15111yescharacteristic
598C22C2×#131×C15111yescharacteristic
599C22#568×C15111yescharacteristic
600C22#568×C15111yescharacteristic
601C22#568×C15111yescharacteristic
602C4—22no—
603C4—22no—
604C4—22no—
605C4—22no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4#547×C15111yescharacteristic
616C4#547×C15111yescharacteristic
617C4#552×C15111yescharacteristic
618C4#552×C15111yescharacteristic
619C2—42no—
620C2#2344×C15111yescharacteristic
621C2#2923×C15111yescharacteristic
622C2#2925×C15111yescharacteristic
623C2#2930×C15111yescharacteristic
624C2#2933×C15111yescharacteristic
625C2#2985×C15111yescharacteristic
626C2#2987×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
4. #1940×C151C2semidirect
5. #1939×C151C2semidirect
6. #1917×C151C2semidirect
7. #1917×C151C2semidirect
8. #1917×C151C2semidirect
9. #1916×C151C2semidirect
13. #1771×C151C2semidirect
14. #1770×C151C2semidirect
313. #22605C151direct (N × H)
314. C151#22605direct (N × H)
318. #1940C2×C151semidirect
319. #1939C2×C151semidirect
320. #1917C2×C151semidirect
321. #1917C2×C151semidirect
322. #1917C2×C151semidirect
323. #1916C2×C151semidirect
327. #1771C2×C151semidirect
328. #1770C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#433×C1512
C2×#432×C1512
#2296×C1512
#1940×C1512
#1939×C1512
#1917×C1512
#1916×C1512
#1818×C1512
#1817×C1512
#1798×C1512
#1771×C1512
#1770×C1512
#1750×C1512
#22605151