Finite Group Databasebeta

← C151×#23124 #50328049

Subgroups — C151×#23124 #50328049

Order 38656.

922 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#435×C151C211yesmaximal, characteristic, complemented
2C2×#435×C151C211yesmaximal, characteristic, complemented
3#2392×C151C211yesmaximal, characteristic
4#1924×C151C211yesmaximal, characteristic, complemented
5#1923×C151C211yesmaximal, characteristic, complemented
6#1917×C151C211yesmaximal, characteristic, complemented
7#1917×C151C211yesmaximal, characteristic, complemented
8#1870×C151C211yesmaximal, characteristic, complemented
9#1870×C151C211yesmaximal, characteristic, complemented
10#1869×C151C211yesmaximal, characteristic, complemented
11#1869×C151C211yesmaximal, characteristic, complemented
12#1753×C151C211yesmaximal, characteristic, complemented
13#1752×C151C211yesmaximal, characteristic, complemented
14#1750×C151C211yesmaximal, characteristic, complemented
15#1729×C151C211yesmaximal, characteristic, complemented
16C22×M16×C151C2211yescharacteristic
17C22×M16×C151C2211yescharacteristic
18C23×C8×C151C2211yescharacteristic
19C23×C8×C151C2211yescharacteristic
20C2×C4×D4×C151C2211yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23C2×#117×C151C2211yescharacteristic
24#435×C151—24no—
25#435×C151—24no—
26C2×C4⋊C8×C151C2211yescharacteristic
27C2×C4⋊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×C22⋊C8×C151C2211yescharacteristic
35C2×C22⋊C8×C151C2211yescharacteristic
36C2×#97×C151C2211yescharacteristic
37C2×#97×C151C2211yescharacteristic
38C2×#97×C151C2211yescharacteristic
39C2×C4×C8×C151C2211yescharacteristic
40#398×C151C411yescharacteristic
41#397×C151C411yescharacteristic
42#396×C151C411yescharacteristic
43#396×C151C411yescharacteristic
44#394×C151C411yescharacteristic
45#394×C151C411yescharacteristic
46#394×C151C411yescharacteristic
47#392×C151C411yescharacteristic
48C4×C4⋊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
62C22×D4×C151C2×C411yescharacteristic
63C22×D4×C151C2×C411yescharacteristic
64C23×C4×C151C2311yescharacteristic
65C23×C4×C151C2311yescharacteristic
66C23×C4×C151C2311yescharacteristic
67C2×M16×C151—22no—
68C2×M16×C151—22no—
69C2×M16×C151—22no—
70C2×M16×C151—22no—
71C2×M16×C151—41no—
72C2×M16×C151—41no—
73C22×C8×C151—22no—
74C22×C8×C151—22no—
75C22×C8×C151—22no—
76C22×C8×C151—22no—
77C22×C8×C151—41no—
78C22×C8×C151—41no—
79C22×C8×C151C2311yescharacteristic
80C22×C8×C151C2311yescharacteristic
81C22×C8×C151C2311yescharacteristic
82C22×C8×C151C2311yescharacteristic
83C22×C8×C151C2311yescharacteristic
84C22×C8×C151C2311yescharacteristic
85C22×C8×C151C2311yescharacteristic
86C22×C8×C151C2311yescharacteristic
87C4×D4×C151—22no—
88C4×D4×C151—22no—
89C4×D4×C151—22no—
90C4×D4×C151—22no—
91C4×D4×C151—41no—
92C4×D4×C151—41no—
93#117×C151—41no—
94#117×C151—41no—
95C2×C4⋊C4×C151C2×C411yescharacteristic
96C2×C4⋊C4×C151C2×C411yescharacteristic
97C2×C4⋊C4×C151C2×C411yescharacteristic
98C2×C4⋊C4×C151C2×C411yescharacteristic
99C2×C4⋊C4×C151C2×C411yescharacteristic
100C2×C4⋊C4×C151C2×C411yescharacteristic
101C2×C4⋊C4×C151C2×C411yescharacteristic
102C2×C22⋊C4×C151C2×C411yescharacteristic
103C2×C22⋊C4×C151C2×C411yescharacteristic
104C2×C22⋊C4×C151C2×C411yescharacteristic
105C2×C22⋊C4×C151C2×C411yescharacteristic
106C2×C22⋊C4×C151C2×C411yescharacteristic
107C2×C22⋊C4×C151C2×C411yescharacteristic
108C2×C22⋊C4×C151C2×C411yescharacteristic
109C2×C22⋊C4×C151C2×C411yescharacteristic
110C2×C22⋊C4×C151C2×C411yescharacteristic
111C2×C22⋊C4×C151C2×C411yescharacteristic
112C2×C22⋊C4×C151C2×C411yescharacteristic
113C2×C22⋊C4×C151C2×C411yescharacteristic
114C2×C42×C151C2311yescharacteristic
115C2×C42×C151C2311yescharacteristic
116C2×C42×C151C2311yescharacteristic
117C2×C42×C151C2311yescharacteristic
118C4⋊C8×C151—22no—
119C4⋊C8×C151—22no—
120C22⋊C8×C151—22no—
121C22⋊C8×C151—22no—
122C22⋊C8×C151—22no—
123C22⋊C8×C151—22no—
124C22⋊C8×C151—22no—
125C22⋊C8×C151—41no—
126C22⋊C8×C151—41no—
127C22⋊C8×C151D414yescomplemented
128#97×C151—22no—
129#97×C151—22no—
130#97×C151—41no—
131C4×C8×C151—41no—
132#95×C151C2×C411yescharacteristic
133#95×C151C2×C411yescharacteristic
134#95×C151C2×C411yescharacteristic
135#95×C151C2×C411yescharacteristic
136#95×C151C2×C411yescharacteristic
137#95×C151C2×C411yescharacteristic
138C24×C151C22×C411yescharacteristic
139C24×C151C22×C411yescharacteristic
140C24×C151C22×C411yescharacteristic
141C2×D4×C151—22no—
142C2×D4×C151—22no—
143C2×D4×C151—22no—
144C2×D4×C151—22no—
145C2×D4×C151—41no—
146C2×D4×C151—41no—
147C2×D4×C151—41no—
148C2×D4×C151—41no—
149C2×D4×C151—41no—
150C22×C4×C151—21no—
151C22×C4×C151—21no—
152C22×C4×C151—21no—
153C22×C4×C151—21no—
154C22×C4×C151—21no—
155C22×C4×C151—21no—
156C22×C4×C151—21no—
157C22×C4×C151—21no—
158C22×C4×C151—21no—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—21no—
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151—21no—
165C22×C4×C151—21no—
166C22×C4×C151C22×C411yescharacteristic
167C22×C4×C151C22×C411yescharacteristic
168C22×C4×C151C22×C411yescharacteristic
169C22×C4×C151C22×C411yescharacteristic
170C22×C4×C151C22×C411yescharacteristic
171C22×C4×C151C22×C411yescharacteristic
172C22×C4×C151C22×C411yescharacteristic
173C22×C4×C151C22×C411yescharacteristic
174C22×C4×C151C22×C411yescharacteristic
175C22×C4×C151C22×C411yescharacteristic
176C22×C4×C151C22×C411yescharacteristic
177C22×C4×C151C2×D412yes—
178C22×C4×C151#4112yes—
179C22×C4×C151C2411yescharacteristic
180M16×C151—44no—
181M16×C151—44no—
182C2×C8×C151—21no—
183C2×C8×C151—21no—
184C2×C8×C151—21no—
185C2×C8×C151—21no—
186C2×C8×C151—21no—
187C2×C8×C151—21no—
188C2×C8×C151—21no—
189C2×C8×C151—21no—
190C2×C8×C151—21no—
191C2×C8×C151—21no—
192C2×C8×C151—21no—
193C2×C8×C151—21no—
194C2×C8×C151—21no—
195C2×C8×C151—21no—
196C2×C8×C151—21no—
197C2×C8×C151—21no—
198C2×C8×C151—21no—
199C2×C8×C151—21no—
200C2×C8×C151—21no—
201C2×C8×C151—21no—
202C2×C8×C151—44no—
203C2×C8×C151—44no—
204C2×C8×C151C2×D412yes—
205C2×C8×C151C2×D412yes—
206C2×C8×C151#4112yes—
207C2×C8×C151#4112yes—
208C4⋊C4×C151—22no—
209C4⋊C4×C151—22no—
210C4⋊C4×C151—41no—
211C4⋊C4×C151—41no—
212C4⋊C4×C151—41no—
213C4⋊C4×C151—41no—
214C4⋊C4×C151—41no—
215C22⋊C4×C151—22no—
216C22⋊C4×C151—22no—
217C22⋊C4×C151—22no—
218C22⋊C4×C151—22no—
219C22⋊C4×C151—22no—
220C22⋊C4×C151—41no—
221C22⋊C4×C151—41no—
222C22⋊C4×C151—41no—
223C22⋊C4×C151—41no—
224C22⋊C4×C151—41no—
225C22⋊C4×C151—41no—
226C22⋊C4×C151—41no—
227C42×C151—21no—
228C42×C151—21no—
229C42×C151—21no—
230C42×C151—21no—
231C42×C151—21no—
232C42×C151—21no—
233C42×C151—21no—
234C42×C151—21no—
235C23×C151—21no—
236C23×C151—21no—
237C23×C151—21no—
238C23×C151—21no—
239C23×C151—21no—
240C23×C151—21no—
241C23×C151—21no—
242C23×C151—21no—
243C23×C151—21no—
244C23×C151—21no—
245C23×C151—21no—
246C23×C151—21no—
247C23×C151—21no—
248C23×C151—21no—
249C23×C151—21no—
250C23×C151—21no—
251C23×C151—21no—
252C23×C151—21no—
253C23×C151—21no—
254C23×C151C4×D412yes—
255C23×C151#13112yes—
256C23×C151C23×C411yescharacteristic
257D4×C151—44no—
258D4×C151—44no—
259D4×C151—44no—
260C2×C4×C151—21no—
261C2×C4×C151—21no—
262C2×C4×C151—22no—
263C2×C4×C151—22no—
264C2×C4×C151—22no—
265C2×C4×C151—22no—
266C2×C4×C151—21no—
267C2×C4×C151—21no—
268C2×C4×C151—21no—
269C2×C4×C151—21no—
270C2×C4×C151—21no—
271C2×C4×C151—21no—
272C2×C4×C151—21no—
273C2×C4×C151—21no—
274C2×C4×C151—21no—
275C2×C4×C151—21no—
276C2×C4×C151—21no—
277C2×C4×C151—21no—
278C2×C4×C151—21no—
279C2×C4×C151—21no—
280C2×C4×C151—21no—
281C2×C4×C151—21no—
282C2×C4×C151—21no—
283C2×C4×C151—21no—
284C2×C4×C151—21no—
285C2×C4×C151—21no—
286C2×C4×C151—21no—
287C2×C4×C151—21no—
288C2×C4×C151—21no—
289C2×C4×C151—21no—
290C2×C4×C151—21no—
291C2×C4×C151—21no—
292C2×C4×C151—21no—
293C2×C4×C151—21no—
294C2×C4×C151—21no—
295C2×C4×C151—21no—
296C2×C4×C151—41no—
297C2×C4×C151—41no—
298C2×C4×C151—41no—
299C2×C4×C151—41no—
300C2×C4×C151—41no—
301C2×C4×C151—41no—
302C2×C4×C151—41no—
303C2×C4×C151—41no—
304C2×C4×C151C4×D412yes—
305C2×C4×C151C22×D411yescharacteristic
306C2×C4×C151C2×#4111yescharacteristic
307C2×C4×C151C2×#4111yescharacteristic
308C2×C4×C151C2×#4111yescharacteristic
309C2×C4×C151H(5,𝔽2)11yescharacteristic
310C2×C4×C151H(5,𝔽2)11yescharacteristic
311C8×C151—22no—
312C8×C151—22no—
313C8×C151—22no—
314C8×C151—22no—
315C8×C151—41no—
316C8×C151—41no—
317C8×C151—41no—
318C8×C151—41no—
319C22×C151—22no—
320C22×C151—22no—
321C22×C151—22no—
322C22×C151—22no—
323C22×C151—22no—
324C22×C151—22no—
325C22×C151—41no—
326C22×C151—41no—
327C22×C151—41no—
328C22×C151—41no—
329C22×C151—41no—
330C22×C151—41no—
331C22×C151—41no—
332C22×C151—41no—
333C22×C151—41no—
334C22×C151—41no—
335C22×C151—41no—
336C22×C151—41no—
337C22×C151—41no—
338C22×C151—41no—
339C22×C151—41no—
340C22×C151C2×C4×D411yescharacteristic
341C22×C151C4×#4111yescharacteristic
342C22×C151#51811yescharacteristic
343C22×C151C2×#13111yescharacteristic
344C22×C151#56811yescharacteristic
345C22×C151#56811yescharacteristic
346C22×C151#56811yescharacteristic
347C4×C151—22no—
348C4×C151—41no—
349C4×C151—41no—
350C4×C151—41no—
351C4×C151—41no—
352C4×C151—41no—
353C4×C151—41no—
354C4×C151—41no—
355C4×C151—41no—
356C4×C151—41no—
357C4×C151—41no—
358C4×C151#54611yescharacteristic
359C4×C151#54611yescharacteristic
360C4×C151#55311yescharacteristic
361C4×C151#55311yescharacteristic
362C2×C151—42no—
363C2×C151—42no—
364C2×C151—81no—
365C2×C151#236411yescharacteristic
366C2×C151#293011yescharacteristic
367C2×C151#293311yescharacteristic
368C2×C151#296711yescharacteristic
369C2×C151#296811yescharacteristic
370C2×C151#297611yescharacteristic
371C2×C151#298011yescharacteristic
372#23124C15111yesmaximal, characteristic, direct product factor, Sylow
373C151#2312411yescharacteristic, direct product factor, Sylow
374C2×#435C2×C15111yescharacteristic, complemented
375C2×#435C2×C15111yescharacteristic, complemented
376#2392C2×C15111yescharacteristic
377#1924C2×C15111yescharacteristic, complemented
378#1923C2×C15111yescharacteristic, complemented
379#1917C2×C15111yescharacteristic, complemented
380#1917C2×C15111yescharacteristic, complemented
381#1870C2×C15111yescharacteristic, complemented
382#1870C2×C15111yescharacteristic, complemented
383#1869C2×C15111yescharacteristic, complemented
384#1869C2×C15111yescharacteristic, complemented
385#1753C2×C15111yescharacteristic, complemented
386#1752C2×C15111yescharacteristic, complemented
387#1750C2×C15111yescharacteristic, complemented
388#1729C2×C15111yescharacteristic, complemented
389C22×M16C22×C15111yescharacteristic
390C22×M16C22×C15111yescharacteristic
391C23×C8C22×C15111yescharacteristic
392C23×C8C22×C15111yescharacteristic
393C2×C4×D4C22×C15111yescharacteristic
394C2×C4×D4C22×C15111yescharacteristic
395C2×C4×D4C22×C15111yescharacteristic
396C2×#117C22×C15111yescharacteristic
397#435—24no—
398#435—24no—
399C2×C4⋊C8C22×C15111yescharacteristic
400C2×C4⋊C8C22×C15111yescharacteristic
401C2×C22⋊C8C22×C15111yescharacteristic
402C2×C22⋊C8C22×C15111yescharacteristic
403C2×C22⋊C8C22×C15111yescharacteristic
404C2×C22⋊C8C22×C15111yescharacteristic
405C2×C22⋊C8C22×C15111yescharacteristic
406C2×C22⋊C8C22×C15111yescharacteristic
407C2×C22⋊C8C22×C15111yescharacteristic
408C2×C22⋊C8C22×C15111yescharacteristic
409C2×#97C22×C15111yescharacteristic
410C2×#97C22×C15111yescharacteristic
411C2×#97C22×C15111yescharacteristic
412C2×C4×C8C22×C15111yescharacteristic
413#398C4×C15111yescharacteristic
414#397C4×C15111yescharacteristic
415#396C4×C15111yescharacteristic
416#396C4×C15111yescharacteristic
417#394C4×C15111yescharacteristic
418#394C4×C15111yescharacteristic
419#394C4×C15111yescharacteristic
420#392C4×C15111yescharacteristic
421C4×C4⋊C4C22×C15111yescharacteristic
422C4×C22⋊C4C22×C15111yescharacteristic
423C4×C22⋊C4C22×C15111yescharacteristic
424#336C22×C15111yescharacteristic
425#336C22×C15111yescharacteristic
426#336C22×C15111yescharacteristic
427#336C22×C15111yescharacteristic
428#336C22×C15111yescharacteristic
429#336C22×C15111yescharacteristic
430#336C22×C15111yescharacteristic
431#336C22×C15111yescharacteristic
432#336C22×C15111yescharacteristic
433#336C22×C15111yescharacteristic
434C22×D4C2×C4×C15111yescharacteristic
435C22×D4C2×C4×C15111yescharacteristic
436C22×D4C2×C4×C15111yescharacteristic
437C23×C4C23×C15111yescharacteristic
438C23×C4C23×C15111yescharacteristic
439C23×C4C23×C15111yescharacteristic
440C2×M16—22no—
441C2×M16—22no—
442C2×M16—22no—
443C2×M16—22no—
444C2×M16—41no—
445C2×M16—41no—
446C22×C8—22no—
447C22×C8—22no—
448C22×C8—22no—
449C22×C8—22no—
450C22×C8—41no—
451C22×C8—41no—
452C22×C8C23×C15111yescharacteristic
453C22×C8C23×C15111yescharacteristic
454C22×C8C23×C15111yescharacteristic
455C22×C8C23×C15111yescharacteristic
456C22×C8C23×C15111yescharacteristic
457C22×C8C23×C15111yescharacteristic
458C22×C8C23×C15111yescharacteristic
459C22×C8C23×C15111yescharacteristic
460C4×D4—22no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—22no—
464C4×D4—41no—
465C4×D4—41no—
466#117—41no—
467#117—41no—
468C2×C4⋊C4C2×C4×C15111yescharacteristic
469C2×C4⋊C4C2×C4×C15111yescharacteristic
470C2×C4⋊C4C2×C4×C15111yescharacteristic
471C2×C4⋊C4C2×C4×C15111yescharacteristic
472C2×C4⋊C4C2×C4×C15111yescharacteristic
473C2×C4⋊C4C2×C4×C15111yescharacteristic
474C2×C4⋊C4C2×C4×C15111yescharacteristic
475C2×C22⋊C4C2×C4×C15111yescharacteristic
476C2×C22⋊C4C2×C4×C15111yescharacteristic
477C2×C22⋊C4C2×C4×C15111yescharacteristic
478C2×C22⋊C4C2×C4×C15111yescharacteristic
479C2×C22⋊C4C2×C4×C15111yescharacteristic
480C2×C22⋊C4C2×C4×C15111yescharacteristic
481C2×C22⋊C4C2×C4×C15111yescharacteristic
482C2×C22⋊C4C2×C4×C15111yescharacteristic
483C2×C22⋊C4C2×C4×C15111yescharacteristic
484C2×C22⋊C4C2×C4×C15111yescharacteristic
485C2×C22⋊C4C2×C4×C15111yescharacteristic
486C2×C22⋊C4C2×C4×C15111yescharacteristic
487C2×C42C23×C15111yescharacteristic
488C2×C42C23×C15111yescharacteristic
489C2×C42C23×C15111yescharacteristic
490C2×C42C23×C15111yescharacteristic
491C4⋊C8—22no—
492C4⋊C8—22no—
493C22⋊C8—22no—
494C22⋊C8—22no—
495C22⋊C8—22no—
496C22⋊C8—22no—
497C22⋊C8—22no—
498C22⋊C8—41no—
499C22⋊C8—41no—
500C22⋊C8D4×C15114yescomplemented
501#97—22no—
502#97—22no—
503#97—41no—
504C4×C8—41no—
505#95C2×C4×C15111yescharacteristic
506#95C2×C4×C15111yescharacteristic
507#95C2×C4×C15111yescharacteristic
508#95C2×C4×C15111yescharacteristic
509#95C2×C4×C15111yescharacteristic
510#95C2×C4×C15111yescharacteristic
511C24C22×C4×C15111yescharacteristic
512C24C22×C4×C15111yescharacteristic
513C24C22×C4×C15111yescharacteristic
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4—41no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4C22×C4×C15111yescharacteristic
540C22×C4C22×C4×C15111yescharacteristic
541C22×C4C22×C4×C15111yescharacteristic
542C22×C4C22×C4×C15111yescharacteristic
543C22×C4C22×C4×C15111yescharacteristic
544C22×C4C22×C4×C15111yescharacteristic
545C22×C4C22×C4×C15111yescharacteristic
546C22×C4C22×C4×C15111yescharacteristic
547C22×C4C22×C4×C15111yescharacteristic
548C22×C4C22×C4×C15111yescharacteristic
549C22×C4C22×C4×C15111yescharacteristic
550C22×C4C2×D4×C15112yes—
551C22×C4#41×C15112yes—
552C22×C4C24×C15111yescharacteristic
553M16—44no—
554M16—44no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—44no—
576C2×C8—44no—
577C2×C8C2×D4×C15112yes—
578C2×C8C2×D4×C15112yes—
579C2×C8#41×C15112yes—
580C2×C8#41×C15112yes—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—41no—
584C4⋊C4—41no—
585C4⋊C4—41no—
586C4⋊C4—41no—
587C4⋊C4—41no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—22no—
591C22⋊C4—22no—
592C22⋊C4—22no—
593C22⋊C4—41no—
594C22⋊C4—41no—
595C22⋊C4—41no—
596C22⋊C4—41no—
597C22⋊C4—41no—
598C22⋊C4—41no—
599C22⋊C4—41no—
600C42—21no—
601C42—21no—
602C42—21no—
603C42—21no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23C4×D4×C15112yes—
628C23#131×C15112yes—
629C23C23×C4×C15111yescharacteristic
630D4—44no—
631D4—44no—
632D4—44no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4C4×D4×C15112yes—
678C2×C4C22×D4×C15111yescharacteristic
679C2×C4C2×#41×C15111yescharacteristic
680C2×C4C2×#41×C15111yescharacteristic
681C2×C4C2×#41×C15111yescharacteristic
682C2×C4H(5,𝔽2)×C15111yescharacteristic
683C2×C4H(5,𝔽2)×C15111yescharacteristic
684C8—22no—
685C8—22no—
686C8—22no—
687C8—22no—
688C8—41no—
689C8—41no—
690C8—41no—
691C8—41no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22C2×C4×D4×C15111yescharacteristic
714C22C4×#41×C15111yescharacteristic
715C22#518×C15111yescharacteristic
716C22C2×#131×C15111yescharacteristic
717C22#568×C15111yescharacteristic
718C22#568×C15111yescharacteristic
719C22#568×C15111yescharacteristic
720C4—22no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4—41no—
730C4—41no—
731C4#546×C15111yescharacteristic
732C4#546×C15111yescharacteristic
733C4#553×C15111yescharacteristic
734C4#553×C15111yescharacteristic
735C2—42no—
736C2—42no—
737C2—81no—
738C2#2364×C15111yescharacteristic
739C2#2930×C15111yescharacteristic
740C2#2933×C15111yescharacteristic
741C2#2967×C15111yescharacteristic
742C2#2968×C15111yescharacteristic
743C2#2976×C15111yescharacteristic
744C2#2980×C15111yescharacteristic
subgroupG/H
centerC22×C4×C151C24
commutatorC23C23×C4×C151
Frattini, cosocleC22×C4C24×C151
socleC23×C151C23×C4
prime radical#392×C151C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#435×C151C2semidirect
2. C2×#435×C151C2semidirect
4. #1924×C151C2semidirect
5. #1923×C151C2semidirect
6. #1917×C151C2semidirect
7. #1917×C151C2semidirect
8. #1870×C151C2semidirect
9. #1870×C151C2semidirect
10. #1869×C151C2semidirect
11. #1869×C151C2semidirect
12. #1753×C151C2semidirect
13. #1752×C151C2semidirect
14. #1750×C151C2semidirect
15. #1729×C151C2semidirect
127. C22⋊C8×C151D4semidirect
372. #23124C151direct (N × H)
373. C151#23124direct (N × H)
374. C2×#435C2×C151semidirect
375. C2×#435C2×C151semidirect
377. #1924C2×C151semidirect
378. #1923C2×C151semidirect
379. #1917C2×C151semidirect
380. #1917C2×C151semidirect
381. #1870C2×C151semidirect
382. #1870C2×C151semidirect
383. #1869C2×C151semidirect
384. #1869C2×C151semidirect
385. #1753C2×C151semidirect
386. #1752C2×C151semidirect
387. #1750C2×C151semidirect
388. #1729C2×C151semidirect
500. C22⋊C8D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#435×C1512
#2392×C1512
#1924×C1512
#1923×C1512
#1917×C1512
#1870×C1512
#1869×C1512
#1753×C1512
#1752×C1512
#1750×C1512
#1729×C1512
#23124151