Finite Group Databasebeta

← C151×#22631 #50327556

Subgroups — C151×#22631 #50327556

Order 38656.

724 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2296×C151C211yesmaximal, characteristic
2#1940×C151C211yesmaximal, characteristic, complemented
3#1939×C151C211yesmaximal, characteristic, complemented
4#1917×C151C211yesmaximal, characteristic, complemented
5#1917×C151C211yesmaximal, characteristic, complemented
6#1917×C151C211yesmaximal, characteristic, complemented
7#1916×C151C211yesmaximal, characteristic, complemented
8#1798×C151C211yesmaximal, characteristic
9#1798×C151C211yesmaximal, characteristic
10#1797×C151C211yesmaximal, characteristic
11#1771×C151C211yesmaximal, characteristic, complemented
12#1770×C151C211yesmaximal, characteristic, complemented
13#1750×C151C211yesmaximal, characteristic
14#1750×C151C211yesmaximal, characteristic
15#1749×C151C211yesmaximal, characteristic
16C2×#117×C151C2211yescharacteristic
17C2×#117×C151C2211yescharacteristic
18C22×C42×C151C2211yescharacteristic
19C2×C4⋊C8×C151C2211yescharacteristic
20C2×C4⋊C8×C151C2211yescharacteristic
21C2×C4⋊C8×C151C2211yescharacteristic
22C2×C4⋊C8×C151C2211yescharacteristic
23C2×C4⋊C8×C151C2211yescharacteristic
24C2×C4⋊C8×C151C2211yescharacteristic
25C2×C22⋊C8×C151C2211yescharacteristic
26C2×C22⋊C8×C151C2211yescharacteristic
27C2×C22⋊C8×C151C2211yescharacteristic
28C2×C22⋊C8×C151C2211yescharacteristic
29C2×#97×C151C2211yescharacteristic
30C2×#97×C151C2211yescharacteristic
31C2×#97×C151C2211yescharacteristic
32C2×#97×C151C2211yescharacteristic
33C2×C4×C8×C151C2211yescharacteristic
34C2×C4×C8×C151C2211yescharacteristic
35#389×C151C411yescharacteristic
36#389×C151C411yescharacteristic
37#389×C151C411yescharacteristic
38#389×C151C411yescharacteristic
39#385×C151C411yescharacteristic
40#385×C151C411yescharacteristic
41#385×C151C411yescharacteristic
42#385×C151C411yescharacteristic
43C4×C4⋊C4×C151C2211yescharacteristic
44C4×C4⋊C4×C151C2211yescharacteristic
45C4×C4⋊C4×C151C2211yescharacteristic
46C4×C4⋊C4×C151C2211yescharacteristic
47#336×C151C2211yescharacteristic
48#336×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
59C23×C4×C151C2×C411yescharacteristic
60C23×C4×C151C2×C411yescharacteristic
61C23×C4×C151C2311yescharacteristic
62C22×C8×C151C2311yescharacteristic
63C22×C8×C151C2311yescharacteristic
64C22×C8×C151C2311yescharacteristic
65C22×C8×C151C2311yescharacteristic
66C22×C8×C151C2311yescharacteristic
67C22×C8×C151C2311yescharacteristic
68C22×C8×C151C2311yescharacteristic
69C22×C8×C151C2311yescharacteristic
70#117×C151—22no—
71#117×C151—22no—
72#117×C151—41no—
73#117×C151—41no—
74C2×C4⋊C4×C151C2×C411yescharacteristic
75C2×C4⋊C4×C151C2×C411yescharacteristic
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×C22⋊C4×C151C2×C411yescharacteristic
87C2×C22⋊C4×C151C2×C411yescharacteristic
88C2×C22⋊C4×C151C2×C411yescharacteristic
89C2×C22⋊C4×C151C2×C411yescharacteristic
90C2×C42×C151—41no—
91C2×C42×C151—41no—
92C2×C42×C151C2×C411yescharacteristic
93C2×C42×C151C2×C411yescharacteristic
94C2×C42×C151C2311yescharacteristic
95C2×C42×C151C2311yescharacteristic
96C2×C42×C151C2311yescharacteristic
97C2×C42×C151C2311yescharacteristic
98C2×C42×C151C2311yescharacteristic
99C2×C42×C151C2311yescharacteristic
100C4⋊C8×C151—22no—
101C4⋊C8×C151—22no—
102C4⋊C8×C151—41no—
103C4⋊C8×C151—41no—
104C4⋊C8×C151—41no—
105C4⋊C8×C151—41no—
106C22⋊C8×C151—22no—
107C22⋊C8×C151—22no—
108C22⋊C8×C151—22no—
109C22⋊C8×C151Q814yes—
110#97×C151—22no—
111#97×C151—41no—
112#97×C151—41no—
113#97×C151—41no—
114C4×C8×C151—22no—
115C4×C8×C151—41no—
116#95×C151C2×C411yescharacteristic
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
124C24×C151C22×C411yescharacteristic
125C22×C4×C151—21no—
126C22×C4×C151—21no—
127C22×C4×C151—21no—
128C22×C4×C151—21no—
129C22×C4×C151—22no—
130C22×C4×C151—41no—
131C22×C4×C151—41no—
132C22×C4×C151—41no—
133C22×C4×C151—41no—
134C22×C4×C151—41no—
135C22×C4×C151C22×C411yescharacteristic
136C22×C4×C151C22×C411yescharacteristic
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×C151C2×Q812yes—
149C22×C4×C151#4112yes—
150C22×C4×C151C2411yescharacteristic
151C2×C8×C151—21no—
152C2×C8×C151—21no—
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×C151C2×Q812yes—
174C2×C8×C151C2×Q812yes—
175C4⋊C4×C151—22no—
176C4⋊C4×C151—22no—
177C4⋊C4×C151—22no—
178C4⋊C4×C151—22no—
179C4⋊C4×C151—41no—
180C4⋊C4×C151—41no—
181C4⋊C4×C151—41no—
182C4⋊C4×C151—41no—
183C4⋊C4×C151—41no—
184C4⋊C4×C151—41no—
185C4⋊C4×C151—41no—
186C4⋊C4×C151—41no—
187C22⋊C4×C151—22no—
188C22⋊C4×C151—22no—
189C22⋊C4×C151—41no—
190C22⋊C4×C151—41no—
191C42×C151—21no—
192C42×C151—21no—
193C42×C151—21no—
194C42×C151—21no—
195C42×C151—21no—
196C42×C151—21no—
197C42×C151—21no—
198C42×C151—21no—
199C42×C151—21no—
200C42×C151—21no—
201C42×C151—41no—
202C42×C151—41no—
203C42×C151#4112yes—
204C42×C151#4112yes—
205C23×C151—21no—
206C23×C151—21no—
207C23×C151—21no—
208C23×C151—21no—
209C23×C151—21no—
210C23×C151—21no—
211C23×C151C4×Q812yes—
212C23×C151C23×C411yescharacteristic
213C2×C4×C151—21no—
214C2×C4×C151—21no—
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—22no—
222C2×C4×C151—22no—
223C2×C4×C151—22no—
224C2×C4×C151—22no—
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—21no—
252C2×C4×C151—44no—
253C2×C4×C151—44no—
254C2×C4×C151#11712yes—
255C2×C4×C151#11712yes—
256C2×C4×C151C4×Q812yes—
257C2×C4×C151#13112yes—
258C2×C4×C151C22×Q811yescharacteristic
259C2×C4×C151C2×#4111yescharacteristic
260C2×C4×C151C2×#4111yescharacteristic
261C2×C4×C151C2×#4111yescharacteristic
262C2×C4×C151H(5,𝔽2)11yescharacteristic
263C2×C4×C151H(5,𝔽2)11yescharacteristic
264C8×C151—22no—
265C8×C151—22no—
266C8×C151—41no—
267C8×C151—41no—
268C8×C151—41no—
269C8×C151—41no—
270C8×C151—41no—
271C8×C151—41no—
272C22×C151—22no—
273C22×C151—22no—
274C22×C151—22no—
275C22×C151—41no—
276C22×C151—41no—
277C22×C151—41no—
278C22×C151—41no—
279C22×C151C2×#11711yescharacteristic
280C22×C151C2×C4×Q811yescharacteristic
281C22×C151#51811yescharacteristic
282C22×C151C2×#13111yescharacteristic
283C22×C151#56811yescharacteristic
284C22×C151#56811yescharacteristic
285C22×C151#56811yescharacteristic
286C4×C151—22no—
287C4×C151—22no—
288C4×C151—22no—
289C4×C151—22no—
290C4×C151—41no—
291C4×C151—41no—
292C4×C151—41no—
293C4×C151—41no—
294C4×C151—41no—
295C4×C151—41no—
296C4×C151—41no—
297C4×C151—41no—
298C4×C151—41no—
299C4×C151#55311yescharacteristic
300C4×C151#55311yescharacteristic
301C4×C151#55411yescharacteristic
302C4×C151#55411yescharacteristic
303C2×C151—42no—
304C2×C151#234511yescharacteristic
305C2×C151#292311yescharacteristic
306C2×C151#292511yescharacteristic
307C2×C151#296111yescharacteristic
308C2×C151#296211yescharacteristic
309C2×C151#297611yescharacteristic
310C2×C151#297811yescharacteristic
311#22631C15111yesmaximal, characteristic, direct product factor, Sylow
312C151#2263111yescharacteristic, direct product factor, Sylow
313#2296C2×C15111yescharacteristic
314#1940C2×C15111yescharacteristic, complemented
315#1939C2×C15111yescharacteristic, complemented
316#1917C2×C15111yescharacteristic, complemented
317#1917C2×C15111yescharacteristic, complemented
318#1917C2×C15111yescharacteristic, complemented
319#1916C2×C15111yescharacteristic, complemented
320#1798C2×C15111yescharacteristic
321#1798C2×C15111yescharacteristic
322#1797C2×C15111yescharacteristic
323#1771C2×C15111yescharacteristic, complemented
324#1770C2×C15111yescharacteristic, complemented
325#1750C2×C15111yescharacteristic
326#1750C2×C15111yescharacteristic
327#1749C2×C15111yescharacteristic
328C2×#117C22×C15111yescharacteristic
329C2×#117C22×C15111yescharacteristic
330C22×C42C22×C15111yescharacteristic
331C2×C4⋊C8C22×C15111yescharacteristic
332C2×C4⋊C8C22×C15111yescharacteristic
333C2×C4⋊C8C22×C15111yescharacteristic
334C2×C4⋊C8C22×C15111yescharacteristic
335C2×C4⋊C8C22×C15111yescharacteristic
336C2×C4⋊C8C22×C15111yescharacteristic
337C2×C22⋊C8C22×C15111yescharacteristic
338C2×C22⋊C8C22×C15111yescharacteristic
339C2×C22⋊C8C22×C15111yescharacteristic
340C2×C22⋊C8C22×C15111yescharacteristic
341C2×#97C22×C15111yescharacteristic
342C2×#97C22×C15111yescharacteristic
343C2×#97C22×C15111yescharacteristic
344C2×#97C22×C15111yescharacteristic
345C2×C4×C8C22×C15111yescharacteristic
346C2×C4×C8C22×C15111yescharacteristic
347#389C4×C15111yescharacteristic
348#389C4×C15111yescharacteristic
349#389C4×C15111yescharacteristic
350#389C4×C15111yescharacteristic
351#385C4×C15111yescharacteristic
352#385C4×C15111yescharacteristic
353#385C4×C15111yescharacteristic
354#385C4×C15111yescharacteristic
355C4×C4⋊C4C22×C15111yescharacteristic
356C4×C4⋊C4C22×C15111yescharacteristic
357C4×C4⋊C4C22×C15111yescharacteristic
358C4×C4⋊C4C22×C15111yescharacteristic
359#336C22×C15111yescharacteristic
360#336C22×C15111yescharacteristic
361#336C22×C15111yescharacteristic
362#336C22×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
371C23×C4C2×C4×C15111yescharacteristic
372C23×C4C2×C4×C15111yescharacteristic
373C23×C4C23×C15111yescharacteristic
374C22×C8C23×C15111yescharacteristic
375C22×C8C23×C15111yescharacteristic
376C22×C8C23×C15111yescharacteristic
377C22×C8C23×C15111yescharacteristic
378C22×C8C23×C15111yescharacteristic
379C22×C8C23×C15111yescharacteristic
380C22×C8C23×C15111yescharacteristic
381C22×C8C23×C15111yescharacteristic
382#117—22no—
383#117—22no—
384#117—41no—
385#117—41no—
386C2×C4⋊C4C2×C4×C15111yescharacteristic
387C2×C4⋊C4C2×C4×C15111yescharacteristic
388C2×C4⋊C4C2×C4×C15111yescharacteristic
389C2×C4⋊C4C2×C4×C15111yescharacteristic
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×C22⋊C4C2×C4×C15111yescharacteristic
399C2×C22⋊C4C2×C4×C15111yescharacteristic
400C2×C22⋊C4C2×C4×C15111yescharacteristic
401C2×C22⋊C4C2×C4×C15111yescharacteristic
402C2×C42—41no—
403C2×C42—41no—
404C2×C42C2×C4×C15111yescharacteristic
405C2×C42C2×C4×C15111yescharacteristic
406C2×C42C23×C15111yescharacteristic
407C2×C42C23×C15111yescharacteristic
408C2×C42C23×C15111yescharacteristic
409C2×C42C23×C15111yescharacteristic
410C2×C42C23×C15111yescharacteristic
411C2×C42C23×C15111yescharacteristic
412C4⋊C8—22no—
413C4⋊C8—22no—
414C4⋊C8—41no—
415C4⋊C8—41no—
416C4⋊C8—41no—
417C4⋊C8—41no—
418C22⋊C8—22no—
419C22⋊C8—22no—
420C22⋊C8—22no—
421C22⋊C8Q8×C15114yes—
422#97—22no—
423#97—41no—
424#97—41no—
425#97—41no—
426C4×C8—22no—
427C4×C8—41no—
428#95C2×C4×C15111yescharacteristic
429#95C2×C4×C15111yescharacteristic
430#95C2×C4×C15111yescharacteristic
431#95C2×C4×C15111yescharacteristic
432#95C2×C4×C15111yescharacteristic
433#95C2×C4×C15111yescharacteristic
434#95C2×C4×C15111yescharacteristic
435#95C2×C4×C15111yescharacteristic
436C24C22×C4×C15111yescharacteristic
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4C22×C4×C15111yescharacteristic
448C22×C4C22×C4×C15111yescharacteristic
449C22×C4C22×C4×C15111yescharacteristic
450C22×C4C22×C4×C15111yescharacteristic
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×C4C2×Q8×C15112yes—
461C22×C4#41×C15112yes—
462C22×C4C24×C15111yescharacteristic
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
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×C8C2×Q8×C15112yes—
486C2×C8C2×Q8×C15112yes—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—41no—
514C42—41no—
515C42#41×C15112yes—
516C42#41×C15112yes—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23C4×Q8×C15112yes—
524C23C23×C4×C15111yescharacteristic
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
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—44no—
565C2×C4—44no—
566C2×C4#117×C15112yes—
567C2×C4#117×C15112yes—
568C2×C4C4×Q8×C15112yes—
569C2×C4#131×C15112yes—
570C2×C4C22×Q8×C15111yescharacteristic
571C2×C4C2×#41×C15111yescharacteristic
572C2×C4C2×#41×C15111yescharacteristic
573C2×C4C2×#41×C15111yescharacteristic
574C2×C4H(5,𝔽2)×C15111yescharacteristic
575C2×C4H(5,𝔽2)×C15111yescharacteristic
576C8—22no—
577C8—22no—
578C8—41no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8—41no—
583C8—41no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22C2×#117×C15111yescharacteristic
592C22C2×C4×Q8×C15111yescharacteristic
593C22#518×C15111yescharacteristic
594C22C2×#131×C15111yescharacteristic
595C22#568×C15111yescharacteristic
596C22#568×C15111yescharacteristic
597C22#568×C15111yescharacteristic
598C4—22no—
599C4—22no—
600C4—22no—
601C4—22no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4#553×C15111yescharacteristic
612C4#553×C15111yescharacteristic
613C4#554×C15111yescharacteristic
614C4#554×C15111yescharacteristic
615C2—42no—
616C2#2345×C15111yescharacteristic
617C2#2923×C15111yescharacteristic
618C2#2925×C15111yescharacteristic
619C2#2961×C15111yescharacteristic
620C2#2962×C15111yescharacteristic
621C2#2976×C15111yescharacteristic
622C2#2978×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
2. #1940×C151C2semidirect
3. #1939×C151C2semidirect
4. #1917×C151C2semidirect
5. #1917×C151C2semidirect
6. #1917×C151C2semidirect
7. #1916×C151C2semidirect
11. #1771×C151C2semidirect
12. #1770×C151C2semidirect
311. #22631C151direct (N × H)
312. C151#22631direct (N × H)
314. #1940C2×C151semidirect
315. #1939C2×C151semidirect
316. #1917C2×C151semidirect
317. #1917C2×C151semidirect
318. #1917C2×C151semidirect
319. #1916C2×C151semidirect
323. #1771C2×C151semidirect
324. #1770C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2296×C1512
#1940×C1512
#1939×C1512
#1917×C1512
#1916×C1512
#1798×C1512
#1797×C1512
#1771×C1512
#1770×C1512
#1750×C1512
#1749×C1512
#22631151