Finite Group Databasebeta

← C151×#21568 #50326493

Subgroups — C151×#21568 #50326493

Order 38656.

878 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#435×C151C211yesmaximal, characteristic
2C2×#405×C151C211yesmaximal, characteristic, complemented
3#2395×C151C211yesmaximal, characteristic
4#1924×C151C211yesmaximal, characteristic, complemented
5#1923×C151C211yesmaximal, characteristic, complemented
6#1917×C151C211yesmaximal, characteristic, complemented
7#1916×C151C211yesmaximal, characteristic, complemented
8#1869×C151C211yesmaximal, characteristic
9#1850×C151C211yesmaximal, characteristic, complemented
10#1818×C151C211yesmaximal, characteristic, complemented
11#1771×C151C211yesmaximal, characteristic, complemented
12#1770×C151C211yesmaximal, characteristic, complemented
13#1753×C151C211yesmaximal, characteristic, complemented
14#1752×C151C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C151C211yesmaximal, characteristic, complemented
16C22×M16×C151C2211yescharacteristic
17C23×C8×C151C2211yescharacteristic
18C23×C8×C151C2211yescharacteristic
19C2×C4×D4×C151C2211yescharacteristic
20C2×#117×C151C2211yescharacteristic
21#435×C151—24no—
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×C22⋊C8×C151C2211yescharacteristic
30#405×C151—24no—
31C2×#97×C151C2211yescharacteristic
32C2×#97×C151C2211yescharacteristic
33C2×#97×C151C2211yescharacteristic
34C2×#97×C151C2211yescharacteristic
35C2×C4×C8×C151C2211yescharacteristic
36C2×C4×C8×C151C2211yescharacteristic
37C2×C4×C8×C151C2211yescharacteristic
38#400×C151C411yescharacteristic
39#399×C151C411yescharacteristic
40#398×C151C411yescharacteristic
41#397×C151C411yescharacteristic
42#397×C151C411yescharacteristic
43#397×C151C411yescharacteristic
44#394×C151C411yescharacteristic
45#394×C151C411yescharacteristic
46C4×C4⋊C4×C151C2211yescharacteristic
47C4×C4⋊C4×C151C2211yescharacteristic
48C4×C22⋊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×D4×C151C2×C411yescharacteristic
62C23×C4×C151C2311yescharacteristic
63C23×C4×C151C2311yescharacteristic
64C2×M16×C151—22no—
65C2×M16×C151—22no—
66C2×M16×C151D414yes—
67C22×C8×C151—22no—
68C22×C8×C151—22no—
69C22×C8×C151—22no—
70C22×C8×C151—22no—
71C22×C8×C151—22no—
72C22×C8×C151—22no—
73C22×C8×C151C2311yescharacteristic
74C22×C8×C151C2311yescharacteristic
75C22×C8×C151C2311yescharacteristic
76C22×C8×C151C2311yescharacteristic
77C22×C8×C151C2311yescharacteristic
78C22×C8×C151C2311yescharacteristic
79C22×C8×C151C2311yescharacteristic
80C22×C8×C151C2311yescharacteristic
81C4×D4×C151—22no—
82C4×D4×C151—22no—
83#117×C151—22no—
84#117×C151—22no—
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×C4⋊C4×C151C2×C411yescharacteristic
91C2×C4⋊C4×C151C2×C411yescharacteristic
92C2×C22⋊C4×C151C2×C411yescharacteristic
93C2×C22⋊C4×C151C2×C411yescharacteristic
94C2×C22⋊C4×C151C2×C411yescharacteristic
95C2×C22⋊C4×C151C2×C411yescharacteristic
96C2×C22⋊C4×C151C2×C411yescharacteristic
97C2×C22⋊C4×C151C2×C411yescharacteristic
98C2×C22⋊C4×C151C2×C411yescharacteristic
99C2×C22⋊C4×C151C2×C411yescharacteristic
100C2×C22⋊C4×C151C2×C411yescharacteristic
101C2×C22⋊C4×C151C2×C411yescharacteristic
102C2×C42×C151C2311yescharacteristic
103C2×C42×C151C2311yescharacteristic
104C2×C42×C151C2311yescharacteristic
105C2×C42×C151C2311yescharacteristic
106C2×C42×C151C2311yescharacteristic
107C4⋊C8×C151—22no—
108C4⋊C8×C151—22no—
109C4⋊C8×C151—22no—
110C22⋊C8×C151—22no—
111C22⋊C8×C151—22no—
112C22⋊C8×C151—22no—
113C22⋊C8×C151—22no—
114C22⋊C8×C151—22no—
115#97×C151—22no—
116#97×C151—22no—
117#97×C151—22no—
118#97×C151—22no—
119C4×C8×C151—22no—
120C4×C8×C151—22no—
121C4×C8×C151—22no—
122#95×C151C2×C411yescharacteristic
123#95×C151C2×C411yescharacteristic
124#95×C151C2×C411yescharacteristic
125#95×C151C2×C411yescharacteristic
126#95×C151C2×C411yescharacteristic
127#95×C151C2×C411yescharacteristic
128#95×C151C2×C411yescharacteristic
129#95×C151C2×C411yescharacteristic
130#95×C151C2×C411yescharacteristic
131#95×C151C2×C411yescharacteristic
132C24×C151C22×C411yescharacteristic
133C24×C151C22×C411yescharacteristic
134C2×D4×C151—22no—
135C2×D4×C151—22no—
136C2×D4×C151—41no—
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×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×C151C22×C411yescharacteristic
157C22×C4×C151C22×C411yescharacteristic
158C22×C4×C151C22×C411yescharacteristic
159C22×C4×C151C2×D412yes—
160C22×C4×C151#4112yes—
161C22×C4×C151C2411yescharacteristic
162M16×C151—28no—
163C2×C8×C151—28no—
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—44no—
183C2×C8×C151C2×D412yes—
184C2×C8×C151C2×D412yes—
185C2×C8×C151#4112yes—
186C2×C8×C151#4112yes—
187C2×C8×C151#4112yes—
188C2×C8×C151#4112yes—
189C4⋊C4×C151—22no—
190C4⋊C4×C151—22no—
191C4⋊C4×C151—22no—
192C4⋊C4×C151—22no—
193C4⋊C4×C151—41no—
194C4⋊C4×C151—41no—
195C4⋊C4×C151—41no—
196C22⋊C4×C151—22no—
197C22⋊C4×C151—22no—
198C22⋊C4×C151—22no—
199C22⋊C4×C151—22no—
200C22⋊C4×C151—22no—
201C22⋊C4×C151—22no—
202C22⋊C4×C151—22no—
203C22⋊C4×C151—22no—
204C22⋊C4×C151—41no—
205C22⋊C4×C151—41no—
206C42×C151—21no—
207C42×C151—21no—
208C42×C151—21no—
209C42×C151—21no—
210C42×C151—21no—
211C42×C151—21no—
212C42×C151—21no—
213C42×C151—21no—
214C42×C151—21no—
215C42×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—21no—
227C23×C151—21no—
228C23×C151C4×D412yes—
229C23×C151#13112yes—
230C23×C151C23×C411yescharacteristic
231D4×C151—44no—
232C2×C4×C151—21no—
233C2×C4×C151—21no—
234C2×C4×C151—21no—
235C2×C4×C151—21no—
236C2×C4×C151—22no—
237C2×C4×C151—22no—
238C2×C4×C151—22no—
239C2×C4×C151—22no—
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—21no—
262C2×C4×C151—21no—
263C2×C4×C151—21no—
264C2×C4×C151—21no—
265C2×C4×C151—21no—
266C2×C4×C151—21no—
267C2×C4×C151—21no—
268C2×C4×C151—21no—
269C2×C4×C151—21no—
270C2×C4×C151—41no—
271C2×C4×C151—41no—
272C2×C4×C151—41no—
273C2×C4×C151—41no—
274C2×C4×C151C4×D412yes—
275C2×C4×C151#13112yes—
276C2×C4×C151C22×D411yescharacteristic
277C2×C4×C151C2×#4111yescharacteristic
278C2×C4×C151C2×#4111yescharacteristic
279C2×C4×C151C2×#4111yescharacteristic
280C2×C4×C151C2×#4111yescharacteristic
281C2×C4×C151C2×#4111yescharacteristic
282C8×C151—22no—
283C8×C151—22no—
284C8×C151—22no—
285C8×C151—41no—
286C8×C151—41no—
287C8×C151—41no—
288C8×C151—41no—
289C8×C151#12314yes—
290C22×C151—22no—
291C22×C151—22no—
292C22×C151—22no—
293C22×C151—22no—
294C22×C151—22no—
295C22×C151—22no—
296C22×C151—41no—
297C22×C151—41no—
298C22×C151—41no—
299C22×C151—41no—
300C22×C151—41no—
301C22×C151—41no—
302C22×C151—41no—
303C22×C151—41no—
304C22×C151C2×C4×D411yescharacteristic
305C22×C151C4×#4111yescharacteristic
306C22×C151C4×#4111yescharacteristic
307C22×C151C2×#13111yescharacteristic
308C22×C151C2×#13111yescharacteristic
309C22×C151#56811yescharacteristic
310C22×C151#56811yescharacteristic
311C4×C151—22no—
312C4×C151—22no—
313C4×C151—41no—
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—41no—
323C4×C151C2×#12311yescharacteristic
324C4×C151#52511yescharacteristic
325C4×C151#52911yescharacteristic
326C4×C151#52911yescharacteristic
327C2×C151—42no—
328C2×C151—42no—
329C2×C151C4×#12311yescharacteristic
330C2×C151#293311yescharacteristic
331C2×C151#293511yescharacteristic
332C2×C151#296611yescharacteristic
333C2×C151#296711yescharacteristic
334C2×C151#296811yescharacteristic
335C2×C151#296811yescharacteristic
336#21568C15111yesmaximal, characteristic, direct product factor, Sylow
337C151#2156811yescharacteristic, direct product factor, Sylow
338C2×#435C2×C15111yescharacteristic
339C2×#405C2×C15111yescharacteristic, complemented
340#2395C2×C15111yescharacteristic
341#1924C2×C15111yescharacteristic, complemented
342#1923C2×C15111yescharacteristic, complemented
343#1917C2×C15111yescharacteristic, complemented
344#1916C2×C15111yescharacteristic, complemented
345#1869C2×C15111yescharacteristic
346#1850C2×C15111yescharacteristic, complemented
347#1818C2×C15111yescharacteristic, complemented
348#1771C2×C15111yescharacteristic, complemented
349#1770C2×C15111yescharacteristic, complemented
350#1753C2×C15111yescharacteristic, complemented
351#1752C2×C15111yescharacteristic, complemented
352C8×C22⋊C4C2×C15111yescharacteristic, complemented
353C22×M16C22×C15111yescharacteristic
354C23×C8C22×C15111yescharacteristic
355C23×C8C22×C15111yescharacteristic
356C2×C4×D4C22×C15111yescharacteristic
357C2×#117C22×C15111yescharacteristic
358#435—24no—
359C2×C4⋊C8C22×C15111yescharacteristic
360C2×C4⋊C8C22×C15111yescharacteristic
361C2×C4⋊C8C22×C15111yescharacteristic
362C2×C22⋊C8C22×C15111yescharacteristic
363C2×C22⋊C8C22×C15111yescharacteristic
364C2×C22⋊C8C22×C15111yescharacteristic
365C2×C22⋊C8C22×C15111yescharacteristic
366C2×C22⋊C8C22×C15111yescharacteristic
367#405—24no—
368C2×#97C22×C15111yescharacteristic
369C2×#97C22×C15111yescharacteristic
370C2×#97C22×C15111yescharacteristic
371C2×#97C22×C15111yescharacteristic
372C2×C4×C8C22×C15111yescharacteristic
373C2×C4×C8C22×C15111yescharacteristic
374C2×C4×C8C22×C15111yescharacteristic
375#400C4×C15111yescharacteristic
376#399C4×C15111yescharacteristic
377#398C4×C15111yescharacteristic
378#397C4×C15111yescharacteristic
379#397C4×C15111yescharacteristic
380#397C4×C15111yescharacteristic
381#394C4×C15111yescharacteristic
382#394C4×C15111yescharacteristic
383C4×C4⋊C4C22×C15111yescharacteristic
384C4×C4⋊C4C22×C15111yescharacteristic
385C4×C22⋊C4C22×C15111yescharacteristic
386C4×C22⋊C4C22×C15111yescharacteristic
387C4×C22⋊C4C22×C15111yescharacteristic
388#336C22×C15111yescharacteristic
389#336C22×C15111yescharacteristic
390#336C22×C15111yescharacteristic
391#336C22×C15111yescharacteristic
392#336C22×C15111yescharacteristic
393#336C22×C15111yescharacteristic
394#336C22×C15111yescharacteristic
395#336C22×C15111yescharacteristic
396#336C22×C15111yescharacteristic
397#336C22×C15111yescharacteristic
398C22×D4C2×C4×C15111yescharacteristic
399C23×C4C23×C15111yescharacteristic
400C23×C4C23×C15111yescharacteristic
401C2×M16—22no—
402C2×M16—22no—
403C2×M16D4×C15114yes—
404C22×C8—22no—
405C22×C8—22no—
406C22×C8—22no—
407C22×C8—22no—
408C22×C8—22no—
409C22×C8—22no—
410C22×C8C23×C15111yescharacteristic
411C22×C8C23×C15111yescharacteristic
412C22×C8C23×C15111yescharacteristic
413C22×C8C23×C15111yescharacteristic
414C22×C8C23×C15111yescharacteristic
415C22×C8C23×C15111yescharacteristic
416C22×C8C23×C15111yescharacteristic
417C22×C8C23×C15111yescharacteristic
418C4×D4—22no—
419C4×D4—22no—
420#117—22no—
421#117—22no—
422C2×C4⋊C4C2×C4×C15111yescharacteristic
423C2×C4⋊C4C2×C4×C15111yescharacteristic
424C2×C4⋊C4C2×C4×C15111yescharacteristic
425C2×C4⋊C4C2×C4×C15111yescharacteristic
426C2×C4⋊C4C2×C4×C15111yescharacteristic
427C2×C4⋊C4C2×C4×C15111yescharacteristic
428C2×C4⋊C4C2×C4×C15111yescharacteristic
429C2×C22⋊C4C2×C4×C15111yescharacteristic
430C2×C22⋊C4C2×C4×C15111yescharacteristic
431C2×C22⋊C4C2×C4×C15111yescharacteristic
432C2×C22⋊C4C2×C4×C15111yescharacteristic
433C2×C22⋊C4C2×C4×C15111yescharacteristic
434C2×C22⋊C4C2×C4×C15111yescharacteristic
435C2×C22⋊C4C2×C4×C15111yescharacteristic
436C2×C22⋊C4C2×C4×C15111yescharacteristic
437C2×C22⋊C4C2×C4×C15111yescharacteristic
438C2×C22⋊C4C2×C4×C15111yescharacteristic
439C2×C42C23×C15111yescharacteristic
440C2×C42C23×C15111yescharacteristic
441C2×C42C23×C15111yescharacteristic
442C2×C42C23×C15111yescharacteristic
443C2×C42C23×C15111yescharacteristic
444C4⋊C8—22no—
445C4⋊C8—22no—
446C4⋊C8—22no—
447C22⋊C8—22no—
448C22⋊C8—22no—
449C22⋊C8—22no—
450C22⋊C8—22no—
451C22⋊C8—22no—
452#97—22no—
453#97—22no—
454#97—22no—
455#97—22no—
456C4×C8—22no—
457C4×C8—22no—
458C4×C8—22no—
459#95C2×C4×C15111yescharacteristic
460#95C2×C4×C15111yescharacteristic
461#95C2×C4×C15111yescharacteristic
462#95C2×C4×C15111yescharacteristic
463#95C2×C4×C15111yescharacteristic
464#95C2×C4×C15111yescharacteristic
465#95C2×C4×C15111yescharacteristic
466#95C2×C4×C15111yescharacteristic
467#95C2×C4×C15111yescharacteristic
468#95C2×C4×C15111yescharacteristic
469C24C22×C4×C15111yescharacteristic
470C24C22×C4×C15111yescharacteristic
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—41no—
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—21no—
484C22×C4C22×C4×C15111yescharacteristic
485C22×C4C22×C4×C15111yescharacteristic
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×C4C2×D4×C15112yes—
497C22×C4#41×C15112yes—
498C22×C4C24×C15111yescharacteristic
499M16—28no—
500C2×C8—28no—
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—44no—
520C2×C8C2×D4×C15112yes—
521C2×C8C2×D4×C15112yes—
522C2×C8#41×C15112yes—
523C2×C8#41×C15112yes—
524C2×C8#41×C15112yes—
525C2×C8#41×C15112yes—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—41no—
542C22⋊C4—41no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23C4×D4×C15112yes—
566C23#131×C15112yes—
567C23C23×C4×C15111yescharacteristic
568D4—44no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
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—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4C4×D4×C15112yes—
612C2×C4#131×C15112yes—
613C2×C4C22×D4×C15111yescharacteristic
614C2×C4C2×#41×C15111yescharacteristic
615C2×C4C2×#41×C15111yescharacteristic
616C2×C4C2×#41×C15111yescharacteristic
617C2×C4C2×#41×C15111yescharacteristic
618C2×C4C2×#41×C15111yescharacteristic
619C8—22no—
620C8—22no—
621C8—22no—
622C8—41no—
623C8—41no—
624C8—41no—
625C8—41no—
626C8#123×C15114yes—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22C2×C4×D4×C15111yescharacteristic
642C22C4×#41×C15111yescharacteristic
643C22C4×#41×C15111yescharacteristic
644C22C2×#131×C15111yescharacteristic
645C22C2×#131×C15111yescharacteristic
646C22#568×C15111yescharacteristic
647C22#568×C15111yescharacteristic
648C4—22no—
649C4—22no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4—41no—
659C4—41no—
660C4C2×#123×C15111yescharacteristic
661C4#525×C15111yescharacteristic
662C4#529×C15111yescharacteristic
663C4#529×C15111yescharacteristic
664C2—42no—
665C2—42no—
666C2C4×#123×C15111yescharacteristic
667C2#2933×C15111yescharacteristic
668C2#2935×C15111yescharacteristic
669C2#2966×C15111yescharacteristic
670C2#2967×C15111yescharacteristic
671C2#2968×C15111yescharacteristic
672C2#2968×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
2. C2×#405×C151C2semidirect
4. #1924×C151C2semidirect
5. #1923×C151C2semidirect
6. #1917×C151C2semidirect
7. #1916×C151C2semidirect
9. #1850×C151C2semidirect
10. #1818×C151C2semidirect
11. #1771×C151C2semidirect
12. #1770×C151C2semidirect
13. #1753×C151C2semidirect
14. #1752×C151C2semidirect
15. C8×C22⋊C4×C151C2semidirect
336. #21568C151direct (N × H)
337. C151#21568direct (N × H)
339. C2×#405C2×C151semidirect
341. #1924C2×C151semidirect
342. #1923C2×C151semidirect
343. #1917C2×C151semidirect
344. #1916C2×C151semidirect
346. #1850C2×C151semidirect
347. #1818C2×C151semidirect
348. #1771C2×C151semidirect
349. #1770C2×C151semidirect
350. #1753C2×C151semidirect
351. #1752C2×C151semidirect
352. C8×C22⋊C4C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#435×C1512
C2×#405×C1512
#2395×C1512
#1924×C1512
#1923×C1512
#1917×C1512
#1916×C1512
#1869×C1512
#1850×C1512
#1818×C1512
#1771×C1512
#1770×C1512
#1753×C1512
#1752×C1512
C8×C22⋊C4×C1512
#21568151