Finite Group Databasebeta

← C151×#23320 #50328245

Subgroups — C151×#23320 #50328245

Order 38656.

758 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#123×C151C211yesmaximal, characteristic
2#1954×C151C211yesmaximal, characteristic
3#1940×C151C211yesmaximal, characteristic, complemented
4#1939×C151C211yesmaximal, characteristic, complemented
5#1924×C151C211yesmaximal, characteristic, complemented
6#1924×C151C211yesmaximal, characteristic, complemented
7#1923×C151C211yesmaximal, characteristic, complemented
8#1923×C151C211yesmaximal, characteristic, complemented
9#1916×C151C211yesmaximal, characteristic, complemented
10#1916×C151C211yesmaximal, characteristic, complemented
11#1870×C151C211yesmaximal, characteristic
12#1851×C151C211yesmaximal, characteristic, complemented
13#1851×C151C211yesmaximal, characteristic, complemented
14#1797×C151C211yesmaximal, characteristic, complemented
15#1797×C151C211yesmaximal, characteristic, complemented
16C22×M16×C151C2211yescharacteristic
17C2×#123×C151C411yescharacteristic
18C2×C4×D4×C151C2211yescharacteristic
19C22×C42×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×C4⋊C8×C151C2211yescharacteristic
27C2×C22⋊C8×C151C2211yescharacteristic
28C2×C22⋊C8×C151C2211yescharacteristic
29C2×C22⋊C8×C151C2211yescharacteristic
30C2×C22⋊C8×C151C2211yescharacteristic
31C2×C22⋊C8×C151C2211yescharacteristic
32C2×C22⋊C8×C151C2211yescharacteristic
33C2×C22⋊C8×C151C2211yescharacteristic
34C2×#97×C151C2211yescharacteristic
35C2×C4×C8×C151C2211yescharacteristic
36C2×C4×C8×C151C2211yescharacteristic
37#388×C151C411yescharacteristic
38#388×C151C411yescharacteristic
39#387×C151C411yescharacteristic
40#387×C151C411yescharacteristic
41#386×C151C411yescharacteristic
42#385×C151C411yescharacteristic
43#381×C151C411yescharacteristic
44C4×C4⋊C4×C151C2211yescharacteristic
45C4×C4⋊C4×C151C2211yescharacteristic
46C4×C22⋊C4×C151C2211yescharacteristic
47C4×C22⋊C4×C151C2211yescharacteristic
48C4×C22⋊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
59C22×D4×C151C2×C411yescharacteristic
60C23×C4×C151C2×C411yescharacteristic
61C23×C4×C151C2×C411yescharacteristic
62C23×C4×C151C2311yescharacteristic
63C23×C4×C151C2311yescharacteristic
64C2×M16×C151—41no—
65C2×M16×C151—41no—
66C2×M16×C151—41no—
67C22×C8×C151C2311yescharacteristic
68C22×C8×C151C2311yescharacteristic
69C22×C8×C151C2311yescharacteristic
70C22×C8×C151C2311yescharacteristic
71C22×C8×C151C2311yescharacteristic
72C22×C8×C151C2311yescharacteristic
73C22×C8×C151C2311yescharacteristic
74C22×C8×C151C2311yescharacteristic
75#123×C151—24no—
76C4×D4×C151—41no—
77C4×D4×C151—41no—
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×C22⋊C4×C151C2×C411yescharacteristic
84C2×C22⋊C4×C151C2×C411yescharacteristic
85C2×C22⋊C4×C151C2×C411yescharacteristic
86C2×C22⋊C4×C151C2×C411yescharacteristic
87C2×C22⋊C4×C151C2×C411yescharacteristic
88C2×C22⋊C4×C151C2×C411yescharacteristic
89C2×C22⋊C4×C151C2×C411yescharacteristic
90C2×C22⋊C4×C151C2×C411yescharacteristic
91C2×C42×C151—41no—
92C2×C42×C151—41no—
93C2×C42×C151C2×C411yescharacteristic
94C2×C42×C151C2×C411yescharacteristic
95C2×C42×C151C2311yescharacteristic
96C2×C42×C151C2311yescharacteristic
97C2×C42×C151C2311yescharacteristic
98C2×C42×C151C2311yescharacteristic
99C2×C42×C151C2311yescharacteristic
100C4⋊C8×C151—41no—
101C4⋊C8×C151—41no—
102C4⋊C8×C151—41no—
103C4⋊C8×C151—41no—
104C4⋊C8×C151—41no—
105C4⋊C8×C151—41no—
106C4⋊C8×C151—41no—
107C22⋊C8×C151—41no—
108C22⋊C8×C151—41no—
109C22⋊C8×C151—41no—
110C22⋊C8×C151—41no—
111C22⋊C8×C151—41no—
112C22⋊C8×C151—41no—
113C22⋊C8×C151—41no—
114#97×C151—41no—
115C4×C8×C151—41no—
116C4×C8×C151—41no—
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
128C24×C151C22×C411yescharacteristic
129C2×D4×C151—22no—
130C2×D4×C151—22no—
131C2×D4×C151—41no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—21no—
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—21no—
143C22×C4×C151—21no—
144C22×C4×C151—21no—
145C22×C4×C151—21no—
146C22×C4×C151—21no—
147C22×C4×C151—41no—
148C22×C4×C151—41no—
149C22×C4×C151—41no—
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×C151C22×C411yescharacteristic
157C22×C4×C151C22×C411yescharacteristic
158C22×C4×C151C22×C411yescharacteristic
159C22×C4×C151C22×C411yescharacteristic
160C22×C4×C151C22×C411yescharacteristic
161C22×C4×C151C22×C411yescharacteristic
162C22×C4×C151C2411yescharacteristic
163M16×C151—44no—
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×C151—21no—
178C2×C8×C151—21no—
179C2×C8×C151—21no—
180C2×C8×C151—21no—
181C2×C8×C151—21no—
182C2×C8×C151—21no—
183C2×C8×C151—21no—
184C2×C8×C151—21no—
185C2×C8×C151—21no—
186C2×C8×C151—21no—
187C2×C8×C151—21no—
188C4⋊C4×C151—22no—
189C4⋊C4×C151—22no—
190C4⋊C4×C151—41no—
191C4⋊C4×C151—41no—
192C4⋊C4×C151M1614yescomplemented
193C22⋊C4×C151—22no—
194C22⋊C4×C151—22no—
195C22⋊C4×C151—22no—
196C22⋊C4×C151—22no—
197C22⋊C4×C151—22no—
198C22⋊C4×C151—41no—
199C22⋊C4×C151—41no—
200C22⋊C4×C151—41no—
201C42×C151—21no—
202C42×C151—21no—
203C42×C151—21no—
204C42×C151—21no—
205C42×C151—21no—
206C42×C151—21no—
207C42×C151—21no—
208C42×C151—21no—
209C42×C151—21no—
210C42×C151—21no—
211C42×C151—41no—
212C42×C151—41no—
213C23×C151—21no—
214C23×C151—21no—
215C23×C151—21no—
216C23×C151—21no—
217C23×C151—21no—
218C23×C151—21no—
219C23×C151—21no—
220C23×C151—21no—
221C23×C151—21no—
222C23×C151—21no—
223C23×C151—21no—
224C23×C151—21no—
225C23×C151—21no—
226C23×C151#13112yes—
227C23×C151C23×C411yescharacteristic
228D4×C151—44no—
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—21no—
255C2×C4×C151—21no—
256C2×C4×C151—21no—
257C2×C4×C151—21no—
258C2×C4×C151—21no—
259C2×C4×C151—21no—
260C2×C4×C151—21no—
261C2×C4×C151—44no—
262C2×C4×C151—44no—
263C2×C4×C151—41no—
264C2×C4×C151—41no—
265C2×C4×C151—41no—
266C2×C4×C151—41no—
267C2×C4×C151—41no—
268C2×C4×C151—41no—
269C2×C4×C151—41no—
270C2×C4×C151—41no—
271C2×C4×C151C2×M1612yes—
272C2×C4×C151C2×M1612yes—
273C2×C4×C151C2×M1612yes—
274C2×C4×C151#13112yes—
275C2×C4×C151H(5,𝔽2)11yescharacteristic
276C2×C4×C151H(5,𝔽2)11yescharacteristic
277C2×C4×C151H(5,𝔽2)11yescharacteristic
278C2×C4×C151H(5,𝔽2)11yescharacteristic
279C2×C4×C1512−1+411yescharacteristic
280C2×C4×C1512−1+411yescharacteristic
281C8×C151—41no—
282C8×C151—41no—
283C8×C151—41no—
284C8×C151—41no—
285C8×C151—41no—
286C8×C151—41no—
287C8×C151—41no—
288C8×C151—41no—
289C22×C151—22no—
290C22×C151—22no—
291C22×C151—22no—
292C22×C151—41no—
293C22×C151—41no—
294C22×C151—41no—
295C22×C151—41no—
296C22×C151—41no—
297C22×C151—41no—
298C22×C151—41no—
299C22×C151—41no—
300C22×C151—41no—
301C22×C151—41no—
302C22×C151—41no—
303C22×C151#51811yescharacteristic
304C22×C151#52011yescharacteristic
305C22×C151#52011yescharacteristic
306C22×C151C22×M1611yescharacteristic
307C22×C151C2×#13111yescharacteristic
308C22×C151C2×#13111yescharacteristic
309C22×C151#56811yescharacteristic
310C4×C151—22no—
311C4×C151—22no—
312C4×C151—22no—
313C4×C151—22no—
314C4×C151—41no—
315C4×C151—41no—
316C4×C151—41no—
317C4×C151—41no—
318C4×C151—41no—
319C4×C151—41no—
320C4×C151—41no—
321C4×C151—41no—
322C4×C151#56011yescharacteristic
323C4×C151#56211yescharacteristic
324C4×C151#56211yescharacteristic
325C4×C151#56311yescharacteristic
326C2×C151—42no—
327C2×C151—81no—
328C2×C151#237611yescharacteristic
329C2×C151#297411yescharacteristic
330C2×C151#297611yescharacteristic
331C2×C151#298911yescharacteristic
332C2×C151#299111yescharacteristic
333C2×C151#299211yescharacteristic
334C2×C151#299411yescharacteristic
335#23320C15111yesmaximal, characteristic, direct product factor, Sylow
336C151#2332011yescharacteristic, direct product factor, Sylow
337C4×#123C2×C15111yescharacteristic
338#1954C2×C15111yescharacteristic
339#1940C2×C15111yescharacteristic, complemented
340#1939C2×C15111yescharacteristic, complemented
341#1924C2×C15111yescharacteristic, complemented
342#1924C2×C15111yescharacteristic, complemented
343#1923C2×C15111yescharacteristic, complemented
344#1923C2×C15111yescharacteristic, complemented
345#1916C2×C15111yescharacteristic, complemented
346#1916C2×C15111yescharacteristic, complemented
347#1870C2×C15111yescharacteristic
348#1851C2×C15111yescharacteristic, complemented
349#1851C2×C15111yescharacteristic, complemented
350#1797C2×C15111yescharacteristic, complemented
351#1797C2×C15111yescharacteristic, complemented
352C22×M16C22×C15111yescharacteristic
353C2×#123C4×C15111yescharacteristic
354C2×C4×D4C22×C15111yescharacteristic
355C22×C42C22×C15111yescharacteristic
356C2×C4⋊C8C22×C15111yescharacteristic
357C2×C4⋊C8C22×C15111yescharacteristic
358C2×C4⋊C8C22×C15111yescharacteristic
359C2×C4⋊C8C22×C15111yescharacteristic
360C2×C4⋊C8C22×C15111yescharacteristic
361C2×C4⋊C8C22×C15111yescharacteristic
362C2×C4⋊C8C22×C15111yescharacteristic
363C2×C22⋊C8C22×C15111yescharacteristic
364C2×C22⋊C8C22×C15111yescharacteristic
365C2×C22⋊C8C22×C15111yescharacteristic
366C2×C22⋊C8C22×C15111yescharacteristic
367C2×C22⋊C8C22×C15111yescharacteristic
368C2×C22⋊C8C22×C15111yescharacteristic
369C2×C22⋊C8C22×C15111yescharacteristic
370C2×#97C22×C15111yescharacteristic
371C2×C4×C8C22×C15111yescharacteristic
372C2×C4×C8C22×C15111yescharacteristic
373#388C4×C15111yescharacteristic
374#388C4×C15111yescharacteristic
375#387C4×C15111yescharacteristic
376#387C4×C15111yescharacteristic
377#386C4×C15111yescharacteristic
378#385C4×C15111yescharacteristic
379#381C4×C15111yescharacteristic
380C4×C4⋊C4C22×C15111yescharacteristic
381C4×C4⋊C4C22×C15111yescharacteristic
382C4×C22⋊C4C22×C15111yescharacteristic
383C4×C22⋊C4C22×C15111yescharacteristic
384C4×C22⋊C4C22×C15111yescharacteristic
385#336C22×C15111yescharacteristic
386#336C22×C15111yescharacteristic
387#336C22×C15111yescharacteristic
388#336C22×C15111yescharacteristic
389#336C22×C15111yescharacteristic
390#336C22×C15111yescharacteristic
391#336C22×C15111yescharacteristic
392#336C22×C15111yescharacteristic
393#336C22×C15111yescharacteristic
394#336C22×C15111yescharacteristic
395C22×D4C2×C4×C15111yescharacteristic
396C23×C4C2×C4×C15111yescharacteristic
397C23×C4C2×C4×C15111yescharacteristic
398C23×C4C23×C15111yescharacteristic
399C23×C4C23×C15111yescharacteristic
400C2×M16—41no—
401C2×M16—41no—
402C2×M16—41no—
403C22×C8C23×C15111yescharacteristic
404C22×C8C23×C15111yescharacteristic
405C22×C8C23×C15111yescharacteristic
406C22×C8C23×C15111yescharacteristic
407C22×C8C23×C15111yescharacteristic
408C22×C8C23×C15111yescharacteristic
409C22×C8C23×C15111yescharacteristic
410C22×C8C23×C15111yescharacteristic
411#123—24no—
412C4×D4—41no—
413C4×D4—41no—
414C2×C4⋊C4C2×C4×C15111yescharacteristic
415C2×C4⋊C4C2×C4×C15111yescharacteristic
416C2×C4⋊C4C2×C4×C15111yescharacteristic
417C2×C4⋊C4C2×C4×C15111yescharacteristic
418C2×C4⋊C4C2×C4×C15111yescharacteristic
419C2×C22⋊C4C2×C4×C15111yescharacteristic
420C2×C22⋊C4C2×C4×C15111yescharacteristic
421C2×C22⋊C4C2×C4×C15111yescharacteristic
422C2×C22⋊C4C2×C4×C15111yescharacteristic
423C2×C22⋊C4C2×C4×C15111yescharacteristic
424C2×C22⋊C4C2×C4×C15111yescharacteristic
425C2×C22⋊C4C2×C4×C15111yescharacteristic
426C2×C22⋊C4C2×C4×C15111yescharacteristic
427C2×C42—41no—
428C2×C42—41no—
429C2×C42C2×C4×C15111yescharacteristic
430C2×C42C2×C4×C15111yescharacteristic
431C2×C42C23×C15111yescharacteristic
432C2×C42C23×C15111yescharacteristic
433C2×C42C23×C15111yescharacteristic
434C2×C42C23×C15111yescharacteristic
435C2×C42C23×C15111yescharacteristic
436C4⋊C8—41no—
437C4⋊C8—41no—
438C4⋊C8—41no—
439C4⋊C8—41no—
440C4⋊C8—41no—
441C4⋊C8—41no—
442C4⋊C8—41no—
443C22⋊C8—41no—
444C22⋊C8—41no—
445C22⋊C8—41no—
446C22⋊C8—41no—
447C22⋊C8—41no—
448C22⋊C8—41no—
449C22⋊C8—41no—
450#97—41no—
451C4×C8—41no—
452C4×C8—41no—
453#95C2×C4×C15111yescharacteristic
454#95C2×C4×C15111yescharacteristic
455#95C2×C4×C15111yescharacteristic
456#95C2×C4×C15111yescharacteristic
457#95C2×C4×C15111yescharacteristic
458#95C2×C4×C15111yescharacteristic
459#95C2×C4×C15111yescharacteristic
460#95C2×C4×C15111yescharacteristic
461#95C2×C4×C15111yescharacteristic
462#95C2×C4×C15111yescharacteristic
463C24C22×C4×C15111yescharacteristic
464C24C22×C4×C15111yescharacteristic
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—41no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4C22×C4×C15111yescharacteristic
487C22×C4C22×C4×C15111yescharacteristic
488C22×C4C22×C4×C15111yescharacteristic
489C22×C4C22×C4×C15111yescharacteristic
490C22×C4C22×C4×C15111yescharacteristic
491C22×C4C22×C4×C15111yescharacteristic
492C22×C4C22×C4×C15111yescharacteristic
493C22×C4C22×C4×C15111yescharacteristic
494C22×C4C22×C4×C15111yescharacteristic
495C22×C4C22×C4×C15111yescharacteristic
496C22×C4C22×C4×C15111yescharacteristic
497C22×C4C22×C4×C15111yescharacteristic
498C22×C4C24×C15111yescharacteristic
499M16—44no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4M16×C15114yescomplemented
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—41no—
535C22⋊C4—41no—
536C22⋊C4—41no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—41no—
548C42—41no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23#131×C15112yes—
563C23C23×C4×C15111yescharacteristic
564D4—44no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—44no—
598C2×C4—44no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4C2×M16×C15112yes—
608C2×C4C2×M16×C15112yes—
609C2×C4C2×M16×C15112yes—
610C2×C4#131×C15112yes—
611C2×C4H(5,𝔽2)×C15111yescharacteristic
612C2×C4H(5,𝔽2)×C15111yescharacteristic
613C2×C4H(5,𝔽2)×C15111yescharacteristic
614C2×C4H(5,𝔽2)×C15111yescharacteristic
615C2×C42−1+4×C15111yescharacteristic
616C2×C42−1+4×C15111yescharacteristic
617C8—41no—
618C8—41no—
619C8—41no—
620C8—41no—
621C8—41no—
622C8—41no—
623C8—41no—
624C8—41no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22#518×C15111yescharacteristic
640C22#520×C15111yescharacteristic
641C22#520×C15111yescharacteristic
642C22C22×M16×C15111yescharacteristic
643C22C2×#131×C15111yescharacteristic
644C22C2×#131×C15111yescharacteristic
645C22#568×C15111yescharacteristic
646C4—22no—
647C4—22no—
648C4—22no—
649C4—22no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4#560×C15111yescharacteristic
659C4#562×C15111yescharacteristic
660C4#562×C15111yescharacteristic
661C4#563×C15111yescharacteristic
662C2—42no—
663C2—81no—
664C2#2376×C15111yescharacteristic
665C2#2974×C15111yescharacteristic
666C2#2976×C15111yescharacteristic
667C2#2989×C15111yescharacteristic
668C2#2991×C15111yescharacteristic
669C2#2992×C15111yescharacteristic
670C2#2994×C15111yescharacteristic
subgroupG/H
centerC22×C4×C151C24
commutatorC23C23×C4×C151
Frattini, cosocleC22×C4C24×C151
socleC23×C151C23×C4
prime radicalC22×D4×C151C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1940×C151C2semidirect
4. #1939×C151C2semidirect
5. #1924×C151C2semidirect
6. #1924×C151C2semidirect
7. #1923×C151C2semidirect
8. #1923×C151C2semidirect
9. #1916×C151C2semidirect
10. #1916×C151C2semidirect
12. #1851×C151C2semidirect
13. #1851×C151C2semidirect
14. #1797×C151C2semidirect
15. #1797×C151C2semidirect
192. C4⋊C4×C151M16semidirect
335. #23320C151direct (N × H)
336. C151#23320direct (N × H)
339. #1940C2×C151semidirect
340. #1939C2×C151semidirect
341. #1924C2×C151semidirect
342. #1924C2×C151semidirect
343. #1923C2×C151semidirect
344. #1923C2×C151semidirect
345. #1916C2×C151semidirect
346. #1916C2×C151semidirect
348. #1851C2×C151semidirect
349. #1851C2×C151semidirect
350. #1797C2×C151semidirect
351. #1797C2×C151semidirect
528. C4⋊C4M16×C151semidirect

Maximal subgroups

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

subgroupindex
C4×#123×C1512
#1954×C1512
#1940×C1512
#1939×C1512
#1924×C1512
#1923×C1512
#1916×C1512
#1870×C1512
#1851×C1512
#1797×C1512
#23320151