Finite Group Databasebeta

← C151×#22292 #50327217

Subgroups — C151×#22292 #50327217

Order 38656.

702 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2396×C151C211yesmaximal, characteristic
2#1985×C151C211yesmaximal, characteristic, complemented
3#1984×C151C211yesmaximal, characteristic, complemented
4#1940×C151C211yesmaximal, characteristic, complemented
5#1939×C151C211yesmaximal, characteristic, complemented
6#1917×C151C211yesmaximal, characteristic, complemented
7#1917×C151C211yesmaximal, characteristic, complemented
8#1916×C151C211yesmaximal, characteristic, complemented
9#1916×C151C211yesmaximal, characteristic, complemented
10#1851×C151C211yesmaximal, characteristic
11#1851×C151C211yesmaximal, characteristic
12#1798×C151C211yesmaximal, characteristic
13#1752×C151C211yesmaximal, characteristic
14C8×C22⋊C4×C151C211yesmaximal, characteristic
15#1729×C151C211yesmaximal, characteristic
16C22×M16×C151C2211yescharacteristic
17C23×C8×C151C2211yescharacteristic
18C2×C4×Q8×C151C2211yescharacteristic
19C2×#117×C151C2211yescharacteristic
20C2×C4⋊C8×C151C2211yescharacteristic
21C2×C4⋊C8×C151C2211yescharacteristic
22C2×C4⋊C8×C151C2211yescharacteristic
23C2×C4⋊C8×C151C2211yescharacteristic
24C2×C4⋊C8×C151C2211yescharacteristic
25C2×C4⋊C8×C151C2211yescharacteristic
26C2×C22⋊C8×C151C2211yescharacteristic
27C2×C22⋊C8×C151C2211yescharacteristic
28C2×#97×C151C2211yescharacteristic
29C2×#97×C151C2211yescharacteristic
30C2×C4×C8×C151C2211yescharacteristic
31C2×C4×C8×C151C2211yescharacteristic
32#400×C151C411yescharacteristic
33#399×C151C411yescharacteristic
34#398×C151C411yescharacteristic
35#398×C151C411yescharacteristic
36#396×C151C411yescharacteristic
37#396×C151C411yescharacteristic
38#395×C151C411yescharacteristic
39#393×C151C411yescharacteristic
40C4×C4⋊C4×C151C2211yescharacteristic
41C4×C4⋊C4×C151C2211yescharacteristic
42C4×C4⋊C4×C151C2211yescharacteristic
43C4×C22⋊C4×C151C2211yescharacteristic
44C4×C22⋊C4×C151C2211yescharacteristic
45#336×C151C2211yescharacteristic
46#336×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
59C22×Q8×C151C2×C411yescharacteristic
60C23×C4×C151C2311yescharacteristic
61C2×M16×C151—22no—
62C2×M16×C151—41no—
63C2×M16×C151—41no—
64C22×C8×C151—41no—
65C22×C8×C151—41no—
66C22×C8×C151Q814yescomplemented
67C22×C8×C151C2311yescharacteristic
68C22×C8×C151C2311yescharacteristic
69C22×C8×C151C2311yescharacteristic
70C22×C8×C151C2311yescharacteristic
71C22×C8×C151C2311yescharacteristic
72C22×C8×C151C2311yescharacteristic
73C22×C8×C151C2311yescharacteristic
74C22×C8×C151C2311yescharacteristic
75C4×Q8×C151—41no—
76C4×Q8×C151—41no—
77#117×C151—41no—
78#117×C151—41no—
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×C4⋊C4×C151C2×C411yescharacteristic
89C2×C4⋊C4×C151C2×C411yescharacteristic
90C2×C22⋊C4×C151C2×C411yescharacteristic
91C2×C22⋊C4×C151C2×C411yescharacteristic
92C2×C22⋊C4×C151C2×C411yescharacteristic
93C2×C22⋊C4×C151C2×C411yescharacteristic
94C2×C22⋊C4×C151C2×C411yescharacteristic
95C2×C22⋊C4×C151C2×C411yescharacteristic
96C2×C42×C151C2311yescharacteristic
97C2×C42×C151C2311yescharacteristic
98C2×C42×C151C2311yescharacteristic
99C2×C42×C151C2311yescharacteristic
100C2×C42×C151C2311yescharacteristic
101C2×C42×C151C2311yescharacteristic
102C4⋊C8×C151—41no—
103C4⋊C8×C151—41no—
104C4⋊C8×C151—41no—
105C4⋊C8×C151—41no—
106C4⋊C8×C151—41no—
107C4⋊C8×C151—41no—
108C22⋊C8×C151—22no—
109C22⋊C8×C151—22no—
110#97×C151—41no—
111#97×C151—41no—
112C4×C8×C151—41no—
113C4×C8×C151—41no—
114#95×C151C2×C411yescharacteristic
115#95×C151C2×C411yescharacteristic
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
125C2×Q8×C151—22no—
126C2×Q8×C151—41no—
127C2×Q8×C151—41no—
128C22×C4×C151—21no—
129C22×C4×C151—21no—
130C22×C4×C151—21no—
131C22×C4×C151—21no—
132C22×C4×C151C22×C411yescharacteristic
133C22×C4×C151C22×C411yescharacteristic
134C22×C4×C151C22×C411yescharacteristic
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×C151C2×Q812yes—
146C22×C4×C151#4112yes—
147C22×C4×C151C2411yescharacteristic
148M16×C151—44no—
149C2×C8×C151—21no—
150C2×C8×C151—21no—
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—44no—
172C2×C8×C151C2×Q812yes—
173C2×C8×C151C2×Q812yes—
174C4⋊C4×C151—22no—
175C4⋊C4×C151—22no—
176C4⋊C4×C151—22no—
177C4⋊C4×C151—41no—
178C4⋊C4×C151—41no—
179C4⋊C4×C151—41no—
180C4⋊C4×C151—41no—
181C4⋊C4×C151—41no—
182C4⋊C4×C151—41no—
183C4⋊C4×C151—41no—
184C4⋊C4×C151—41no—
185C22⋊C4×C151—22no—
186C22⋊C4×C151—22no—
187C22⋊C4×C151—41no—
188C22⋊C4×C151—41no—
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—21no—
202C42×C151—21no—
203C23×C151—21no—
204C23×C151—21no—
205C23×C151—21no—
206C23×C151—21no—
207C23×C151—21no—
208C23×C151—21no—
209C23×C151C4×Q812yes—
210C23×C151C23×C411yescharacteristic
211Q8×C151—44no—
212C2×C4×C151—21no—
213C2×C4×C151—21no—
214C2×C4×C151—21no—
215C2×C4×C151—21no—
216C2×C4×C151—21no—
217C2×C4×C151—21no—
218C2×C4×C151—22no—
219C2×C4×C151—22no—
220C2×C4×C151—22no—
221C2×C4×C151—22no—
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—21no—
252C2×C4×C151C4×Q812yes—
253C2×C4×C151#13112yes—
254C2×C4×C151#13112yes—
255C2×C4×C151C22×Q811yescharacteristic
256C2×C4×C151C2×#4111yescharacteristic
257C2×C4×C151H(5,𝔽2)11yescharacteristic
258C2×C4×C151H(5,𝔽2)11yescharacteristic
259C2×C4×C151H(5,𝔽2)11yescharacteristic
260C2×C4×C1512−1+411yescharacteristic
261C8×C151—22no—
262C8×C151—22no—
263C8×C151—41no—
264C8×C151—41no—
265C8×C151—41no—
266C8×C151—41no—
267C8×C151—41no—
268C8×C151—41no—
269C22×C151—22no—
270C22×C151—22no—
271C22×C151—22no—
272C22×C151—41no—
273C22×C151—41no—
274C22×C151—41no—
275C22×C151—41no—
276C22×C151C2×C4×Q811yescharacteristic
277C22×C151#51811yescharacteristic
278C22×C151#52011yescharacteristic
279C22×C151C2×#13111yescharacteristic
280C22×C151C2×#13111yescharacteristic
281C22×C151#56811yescharacteristic
282C22×C151#56811yescharacteristic
283C4×C151—22no—
284C4×C151—22no—
285C4×C151—22no—
286C4×C151—41no—
287C4×C151—41no—
288C4×C151—41no—
289C4×C151—41no—
290C4×C151—41no—
291C4×C151—41no—
292C4×C151—41no—
293C4×C151—41no—
294C4×C151—41no—
295C4×C151—41no—
296C4×C151#53811yescharacteristic
297C4×C151#53911yescharacteristic
298C4×C151#54311yescharacteristic
299C4×C151#54411yescharacteristic
300C2×C151—42no—
301C2×C151#232911yescharacteristic
302C2×C151#296011yescharacteristic
303C2×C151#296111yescharacteristic
304C2×C151#297611yescharacteristic
305C2×C151#298111yescharacteristic
306C2×C151#299211yescharacteristic
307C2×C151#299311yescharacteristic
308#22292C15111yesmaximal, characteristic, direct product factor, Sylow
309C151#2229211yescharacteristic, direct product factor, Sylow
310#2396C2×C15111yescharacteristic
311#1985C2×C15111yescharacteristic, complemented
312#1984C2×C15111yescharacteristic, complemented
313#1940C2×C15111yescharacteristic, complemented
314#1939C2×C15111yescharacteristic, complemented
315#1917C2×C15111yescharacteristic, complemented
316#1917C2×C15111yescharacteristic, complemented
317#1916C2×C15111yescharacteristic, complemented
318#1916C2×C15111yescharacteristic, complemented
319#1851C2×C15111yescharacteristic
320#1851C2×C15111yescharacteristic
321#1798C2×C15111yescharacteristic
322#1752C2×C15111yescharacteristic
323C8×C22⋊C4C2×C15111yescharacteristic
324#1729C2×C15111yescharacteristic
325C22×M16C22×C15111yescharacteristic
326C23×C8C22×C15111yescharacteristic
327C2×C4×Q8C22×C15111yescharacteristic
328C2×#117C22×C15111yescharacteristic
329C2×C4⋊C8C22×C15111yescharacteristic
330C2×C4⋊C8C22×C15111yescharacteristic
331C2×C4⋊C8C22×C15111yescharacteristic
332C2×C4⋊C8C22×C15111yescharacteristic
333C2×C4⋊C8C22×C15111yescharacteristic
334C2×C4⋊C8C22×C15111yescharacteristic
335C2×C22⋊C8C22×C15111yescharacteristic
336C2×C22⋊C8C22×C15111yescharacteristic
337C2×#97C22×C15111yescharacteristic
338C2×#97C22×C15111yescharacteristic
339C2×C4×C8C22×C15111yescharacteristic
340C2×C4×C8C22×C15111yescharacteristic
341#400C4×C15111yescharacteristic
342#399C4×C15111yescharacteristic
343#398C4×C15111yescharacteristic
344#398C4×C15111yescharacteristic
345#396C4×C15111yescharacteristic
346#396C4×C15111yescharacteristic
347#395C4×C15111yescharacteristic
348#393C4×C15111yescharacteristic
349C4×C4⋊C4C22×C15111yescharacteristic
350C4×C4⋊C4C22×C15111yescharacteristic
351C4×C4⋊C4C22×C15111yescharacteristic
352C4×C22⋊C4C22×C15111yescharacteristic
353C4×C22⋊C4C22×C15111yescharacteristic
354#336C22×C15111yescharacteristic
355#336C22×C15111yescharacteristic
356#336C22×C15111yescharacteristic
357#336C22×C15111yescharacteristic
358#336C22×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
368C22×Q8C2×C4×C15111yescharacteristic
369C23×C4C23×C15111yescharacteristic
370C2×M16—22no—
371C2×M16—41no—
372C2×M16—41no—
373C22×C8—41no—
374C22×C8—41no—
375C22×C8Q8×C15114yescomplemented
376C22×C8C23×C15111yescharacteristic
377C22×C8C23×C15111yescharacteristic
378C22×C8C23×C15111yescharacteristic
379C22×C8C23×C15111yescharacteristic
380C22×C8C23×C15111yescharacteristic
381C22×C8C23×C15111yescharacteristic
382C22×C8C23×C15111yescharacteristic
383C22×C8C23×C15111yescharacteristic
384C4×Q8—41no—
385C4×Q8—41no—
386#117—41no—
387#117—41no—
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×C4⋊C4C2×C4×C15111yescharacteristic
399C2×C22⋊C4C2×C4×C15111yescharacteristic
400C2×C22⋊C4C2×C4×C15111yescharacteristic
401C2×C22⋊C4C2×C4×C15111yescharacteristic
402C2×C22⋊C4C2×C4×C15111yescharacteristic
403C2×C22⋊C4C2×C4×C15111yescharacteristic
404C2×C22⋊C4C2×C4×C15111yescharacteristic
405C2×C42C23×C15111yescharacteristic
406C2×C42C23×C15111yescharacteristic
407C2×C42C23×C15111yescharacteristic
408C2×C42C23×C15111yescharacteristic
409C2×C42C23×C15111yescharacteristic
410C2×C42C23×C15111yescharacteristic
411C4⋊C8—41no—
412C4⋊C8—41no—
413C4⋊C8—41no—
414C4⋊C8—41no—
415C4⋊C8—41no—
416C4⋊C8—41no—
417C22⋊C8—22no—
418C22⋊C8—22no—
419#97—41no—
420#97—41no—
421C4×C8—41no—
422C4×C8—41no—
423#95C2×C4×C15111yescharacteristic
424#95C2×C4×C15111yescharacteristic
425#95C2×C4×C15111yescharacteristic
426#95C2×C4×C15111yescharacteristic
427#95C2×C4×C15111yescharacteristic
428#95C2×C4×C15111yescharacteristic
429#95C2×C4×C15111yescharacteristic
430#95C2×C4×C15111yescharacteristic
431#95C2×C4×C15111yescharacteristic
432#95C2×C4×C15111yescharacteristic
433C24C22×C4×C15111yescharacteristic
434C2×Q8—22no—
435C2×Q8—41no—
436C2×Q8—41no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4C22×C4×C15111yescharacteristic
442C22×C4C22×C4×C15111yescharacteristic
443C22×C4C22×C4×C15111yescharacteristic
444C22×C4C22×C4×C15111yescharacteristic
445C22×C4C22×C4×C15111yescharacteristic
446C22×C4C22×C4×C15111yescharacteristic
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×C4C2×Q8×C15112yes—
455C22×C4#41×C15112yes—
456C22×C4C24×C15111yescharacteristic
457M16—44no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
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—44no—
481C2×C8C2×Q8×C15112yes—
482C2×C8C2×Q8×C15112yes—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23C4×Q8×C15112yes—
519C23C23×C4×C15111yescharacteristic
520Q8—44no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
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×C4C4×Q8×C15112yes—
562C2×C4#131×C15112yes—
563C2×C4#131×C15112yes—
564C2×C4C22×Q8×C15111yescharacteristic
565C2×C4C2×#41×C15111yescharacteristic
566C2×C4H(5,𝔽2)×C15111yescharacteristic
567C2×C4H(5,𝔽2)×C15111yescharacteristic
568C2×C4H(5,𝔽2)×C15111yescharacteristic
569C2×C42−1+4×C15111yescharacteristic
570C8—22no—
571C8—22no—
572C8—41no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22C2×C4×Q8×C15111yescharacteristic
586C22#518×C15111yescharacteristic
587C22#520×C15111yescharacteristic
588C22C2×#131×C15111yescharacteristic
589C22C2×#131×C15111yescharacteristic
590C22#568×C15111yescharacteristic
591C22#568×C15111yescharacteristic
592C4—22no—
593C4—22no—
594C4—22no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4#538×C15111yescharacteristic
606C4#539×C15111yescharacteristic
607C4#543×C15111yescharacteristic
608C4#544×C15111yescharacteristic
609C2—42no—
610C2#2329×C15111yescharacteristic
611C2#2960×C15111yescharacteristic
612C2#2961×C15111yescharacteristic
613C2#2976×C15111yescharacteristic
614C2#2981×C15111yescharacteristic
615C2#2992×C15111yescharacteristic
616C2#2993×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. #1985×C151C2semidirect
3. #1984×C151C2semidirect
4. #1940×C151C2semidirect
5. #1939×C151C2semidirect
6. #1917×C151C2semidirect
7. #1917×C151C2semidirect
8. #1916×C151C2semidirect
9. #1916×C151C2semidirect
66. C22×C8×C151Q8semidirect
308. #22292C151direct (N × H)
309. C151#22292direct (N × H)
311. #1985C2×C151semidirect
312. #1984C2×C151semidirect
313. #1940C2×C151semidirect
314. #1939C2×C151semidirect
315. #1917C2×C151semidirect
316. #1917C2×C151semidirect
317. #1916C2×C151semidirect
318. #1916C2×C151semidirect
375. C22×C8Q8×C151semidirect

Maximal subgroups

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

subgroupindex
#2396×C1512
#1985×C1512
#1984×C1512
#1940×C1512
#1939×C1512
#1917×C1512
#1916×C1512
#1851×C1512
#1798×C1512
#1752×C1512
C8×C22⋊C4×C1512
#1729×C1512
#22292151