Finite Group Databasebeta

← C151×#23331 #50328256

Subgroups — C151×#23331 #50328256

Order 38656.

854 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#121×C151C211yesmaximal, characteristic
2#1955×C151C211yesmaximal, characteristic, complemented
3#1954×C151C211yesmaximal, characteristic, complemented
4#1924×C151C211yesmaximal, characteristic, complemented
5#1923×C151C211yesmaximal, characteristic, complemented
6#1917×C151C211yesmaximal, characteristic, complemented
7#1916×C151C211yesmaximal, characteristic, complemented
8#1870×C151C211yesmaximal, characteristic, complemented
9#1870×C151C211yesmaximal, characteristic, complemented
10#1869×C151C211yesmaximal, characteristic, complemented
11#1869×C151C211yesmaximal, characteristic, complemented
12#1851×C151C211yesmaximal, characteristic, complemented
13#1850×C151C211yesmaximal, characteristic, complemented
14#1817×C151C211yesmaximal, characteristic, complemented
15#1797×C151C211yesmaximal, characteristic, complemented
16C22×M16×C151C2211yescharacteristic
17C23×C8×C151C2211yescharacteristic
18C2×#121×C151C411yescharacteristic
19C2×C4×D4×C151C2211yescharacteristic
20C2×C4×D4×C151C2211yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22C22×C42×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×C22⋊C8×C151C2211yescharacteristic
35C2×C22⋊C8×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2211yescharacteristic
37C2×#97×C151C2211yescharacteristic
38C2×C4×C8×C151C2211yescharacteristic
39#390×C151C411yescharacteristic
40#389×C151C411yescharacteristic
41#388×C151C411yescharacteristic
42#388×C151C411yescharacteristic
43#386×C151C411yescharacteristic
44#386×C151C411yescharacteristic
45#380×C151C411yescharacteristic
46C4×C4⋊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
60C22×D4×C151C2×C411yescharacteristic
61C22×D4×C151C2×C411yescharacteristic
62C23×C4×C151C2×C411yescharacteristic
63C23×C4×C151C2×C411yescharacteristic
64C23×C4×C151C2311yescharacteristic
65C23×C4×C151C2311yescharacteristic
66C23×C4×C151C2311yescharacteristic
67C2×M16×C151—41no—
68C2×M16×C151—41no—
69C2×M16×C151—41no—
70C22×C8×C151—41no—
71C22×C8×C151—41no—
72C22×C8×C151—41no—
73C22×C8×C151C2311yescharacteristic
74C22×C8×C151C2311yescharacteristic
75C22×C8×C151C2311yescharacteristic
76C22×C8×C151C2311yescharacteristic
77C22×C8×C151C2311yescharacteristic
78C22×C8×C151C2311yescharacteristic
79C22×C8×C151C2311yescharacteristic
80C22×C8×C151C2311yescharacteristic
81#121×C151—24no—
82C4×D4×C151—41no—
83C4×D4×C151—41no—
84C4×D4×C151—41no—
85C4×D4×C151—41no—
86C4×D4×C151—41no—
87C4×D4×C151—41no—
88C2×C4⋊C4×C151C2×C411yescharacteristic
89C2×C4⋊C4×C151C2×C411yescharacteristic
90C2×C4⋊C4×C151C2×C411yescharacteristic
91C2×C4⋊C4×C151C2×C411yescharacteristic
92C2×C4⋊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×C22⋊C4×C151C2×C411yescharacteristic
103C2×C42×C151—41no—
104C2×C42×C151—41no—
105C2×C42×C151C2×C411yescharacteristic
106C2×C42×C151C2×C411yescharacteristic
107C2×C42×C151C2311yescharacteristic
108C2×C42×C151C2311yescharacteristic
109C2×C42×C151C2311yescharacteristic
110C2×C42×C151C2311yescharacteristic
111C4⋊C8×C151—41no—
112C4⋊C8×C151—41no—
113C4⋊C8×C151—41no—
114C4⋊C8×C151—41no—
115C22⋊C8×C151—41no—
116C22⋊C8×C151—41no—
117C22⋊C8×C151—41no—
118C22⋊C8×C151—41no—
119C22⋊C8×C151—41no—
120C22⋊C8×C151—41no—
121C22⋊C8×C151—41no—
122C22⋊C8×C151—41no—
123C22⋊C8×C151—41no—
124C22⋊C8×C151—41no—
125#97×C151—41no—
126C4×C8×C151—41no—
127#95×C151C2×C411yescharacteristic
128#95×C151C2×C411yescharacteristic
129#95×C151C2×C411yescharacteristic
130#95×C151C2×C411yescharacteristic
131#95×C151C2×C411yescharacteristic
132#95×C151C2×C411yescharacteristic
133C24×C151C22×C411yescharacteristic
134C24×C151C22×C411yescharacteristic
135C24×C151C22×C411yescharacteristic
136C2×D4×C151—22no—
137C2×D4×C151—22no—
138C2×D4×C151—22no—
139C2×D4×C151—41no—
140C2×D4×C151—41no—
141C2×D4×C151—41no—
142C2×D4×C151—41no—
143C2×D4×C151—41no—
144C2×D4×C151M1614yescomplemented
145C22×C4×C151—22no—
146C22×C4×C151—22no—
147C22×C4×C151—22no—
148C22×C4×C151—21no—
149C22×C4×C151—21no—
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×C151—41no—
167C22×C4×C151—41no—
168C22×C4×C151—41no—
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×C151C22×C411yescharacteristic
178C22×C4×C151C22×C411yescharacteristic
179C22×C4×C151C22×C411yescharacteristic
180C22×C4×C151C2411yescharacteristic
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—21no—
203C2×C8×C151—21no—
204C2×C8×C151—21no—
205C2×C8×C151—21no—
206C2×C8×C151—44no—
207C4⋊C4×C151—22no—
208C4⋊C4×C151—22no—
209C4⋊C4×C151—41no—
210C4⋊C4×C151—41no—
211C4⋊C4×C151—41no—
212C22⋊C4×C151—22no—
213C22⋊C4×C151—22no—
214C22⋊C4×C151—22no—
215C22⋊C4×C151—22no—
216C22⋊C4×C151—41no—
217C22⋊C4×C151—41no—
218C22⋊C4×C151—41no—
219C22⋊C4×C151—41no—
220C22⋊C4×C151—41no—
221C22⋊C4×C151—41no—
222C42×C151—21no—
223C42×C151—21no—
224C42×C151—21no—
225C42×C151—21no—
226C42×C151—21no—
227C42×C151—21no—
228C42×C151—21no—
229C42×C151—21no—
230C42×C151—41no—
231C42×C151—41no—
232C23×C151—21no—
233C23×C151—21no—
234C23×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×C151C2×M1612yes—
252C23×C151C2×M1612yes—
253C23×C151C23×C411yescharacteristic
254D4×C151—44no—
255D4×C151—44no—
256D4×C151—44no—
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—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—44no—
288C2×C4×C151—44no—
289C2×C4×C151—41no—
290C2×C4×C151—41no—
291C2×C4×C151—41no—
292C2×C4×C151—41no—
293C2×C4×C151—41no—
294C2×C4×C151—41no—
295C2×C4×C151—41no—
296C2×C4×C151—41no—
297C2×C4×C151—41no—
298C2×C4×C151—41no—
299C2×C4×C151—41no—
300C2×C4×C151—41no—
301C2×C4×C151C2×M1612yes—
302C2×C4×C151#13112yes—
303C2×C4×C151#13112yes—
304C2×C4×C151H(5,𝔽2)11yescharacteristic
305C2×C4×C151H(5,𝔽2)11yescharacteristic
306C2×C4×C151H(5,𝔽2)11yescharacteristic
307C2×C4×C151H(5,𝔽2)11yescharacteristic
308C2×C4×C151H(5,𝔽2)11yescharacteristic
309C2×C4×C1512−1+411yescharacteristic
310C8×C151—41no—
311C8×C151—41no—
312C8×C151—41no—
313C8×C151—41no—
314C8×C151—41no—
315C8×C151—41no—
316C8×C151—41no—
317C8×C151—41no—
318C22×C151—22no—
319C22×C151—22no—
320C22×C151—22no—
321C22×C151—22no—
322C22×C151—22no—
323C22×C151—22no—
324C22×C151—41no—
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#51811yescharacteristic
340C22×C151#51811yescharacteristic
341C22×C151#52011yescharacteristic
342C22×C151C22×M1611yescharacteristic
343C22×C151C2×#13111yescharacteristic
344C22×C151C2×#13111yescharacteristic
345C22×C151#56811yescharacteristic
346C4×C151—22no—
347C4×C151—22no—
348C4×C151—22no—
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#56011yescharacteristic
358C4×C151#56011yescharacteristic
359C4×C151#56211yescharacteristic
360C4×C151#56211yescharacteristic
361C2×C151—42no—
362C2×C151—42no—
363C2×C151—81no—
364C2×C151#237711yescharacteristic
365C2×C151#297311yescharacteristic
366C2×C151#297411yescharacteristic
367C2×C151#297611yescharacteristic
368C2×C151#297911yescharacteristic
369C2×C151#299011yescharacteristic
370C2×C151#299311yescharacteristic
371#23331C15111yesmaximal, characteristic, direct product factor, Sylow
372C151#2333111yescharacteristic, direct product factor, Sylow
373C4×#121C2×C15111yescharacteristic
374#1955C2×C15111yescharacteristic, complemented
375#1954C2×C15111yescharacteristic, complemented
376#1924C2×C15111yescharacteristic, complemented
377#1923C2×C15111yescharacteristic, complemented
378#1917C2×C15111yescharacteristic, complemented
379#1916C2×C15111yescharacteristic, complemented
380#1870C2×C15111yescharacteristic, complemented
381#1870C2×C15111yescharacteristic, complemented
382#1869C2×C15111yescharacteristic, complemented
383#1869C2×C15111yescharacteristic, complemented
384#1851C2×C15111yescharacteristic, complemented
385#1850C2×C15111yescharacteristic, complemented
386#1817C2×C15111yescharacteristic, complemented
387#1797C2×C15111yescharacteristic, complemented
388C22×M16C22×C15111yescharacteristic
389C23×C8C22×C15111yescharacteristic
390C2×#121C4×C15111yescharacteristic
391C2×C4×D4C22×C15111yescharacteristic
392C2×C4×D4C22×C15111yescharacteristic
393C2×C4×D4C22×C15111yescharacteristic
394C22×C42C22×C15111yescharacteristic
395C2×C4⋊C8C22×C15111yescharacteristic
396C2×C4⋊C8C22×C15111yescharacteristic
397C2×C4⋊C8C22×C15111yescharacteristic
398C2×C4⋊C8C22×C15111yescharacteristic
399C2×C22⋊C8C22×C15111yescharacteristic
400C2×C22⋊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×C4×C8C22×C15111yescharacteristic
411#390C4×C15111yescharacteristic
412#389C4×C15111yescharacteristic
413#388C4×C15111yescharacteristic
414#388C4×C15111yescharacteristic
415#386C4×C15111yescharacteristic
416#386C4×C15111yescharacteristic
417#380C4×C15111yescharacteristic
418C4×C4⋊C4C22×C15111yescharacteristic
419C4×C22⋊C4C22×C15111yescharacteristic
420C4×C22⋊C4C22×C15111yescharacteristic
421#336C22×C15111yescharacteristic
422#336C22×C15111yescharacteristic
423#336C22×C15111yescharacteristic
424#336C22×C15111yescharacteristic
425#336C22×C15111yescharacteristic
426#336C22×C15111yescharacteristic
427#336C22×C15111yescharacteristic
428#336C22×C15111yescharacteristic
429#336C22×C15111yescharacteristic
430#336C22×C15111yescharacteristic
431C22×D4C2×C4×C15111yescharacteristic
432C22×D4C2×C4×C15111yescharacteristic
433C22×D4C2×C4×C15111yescharacteristic
434C23×C4C2×C4×C15111yescharacteristic
435C23×C4C2×C4×C15111yescharacteristic
436C23×C4C23×C15111yescharacteristic
437C23×C4C23×C15111yescharacteristic
438C23×C4C23×C15111yescharacteristic
439C2×M16—41no—
440C2×M16—41no—
441C2×M16—41no—
442C22×C8—41no—
443C22×C8—41no—
444C22×C8—41no—
445C22×C8C23×C15111yescharacteristic
446C22×C8C23×C15111yescharacteristic
447C22×C8C23×C15111yescharacteristic
448C22×C8C23×C15111yescharacteristic
449C22×C8C23×C15111yescharacteristic
450C22×C8C23×C15111yescharacteristic
451C22×C8C23×C15111yescharacteristic
452C22×C8C23×C15111yescharacteristic
453#121—24no—
454C4×D4—41no—
455C4×D4—41no—
456C4×D4—41no—
457C4×D4—41no—
458C4×D4—41no—
459C4×D4—41no—
460C2×C4⋊C4C2×C4×C15111yescharacteristic
461C2×C4⋊C4C2×C4×C15111yescharacteristic
462C2×C4⋊C4C2×C4×C15111yescharacteristic
463C2×C4⋊C4C2×C4×C15111yescharacteristic
464C2×C4⋊C4C2×C4×C15111yescharacteristic
465C2×C22⋊C4C2×C4×C15111yescharacteristic
466C2×C22⋊C4C2×C4×C15111yescharacteristic
467C2×C22⋊C4C2×C4×C15111yescharacteristic
468C2×C22⋊C4C2×C4×C15111yescharacteristic
469C2×C22⋊C4C2×C4×C15111yescharacteristic
470C2×C22⋊C4C2×C4×C15111yescharacteristic
471C2×C22⋊C4C2×C4×C15111yescharacteristic
472C2×C22⋊C4C2×C4×C15111yescharacteristic
473C2×C22⋊C4C2×C4×C15111yescharacteristic
474C2×C22⋊C4C2×C4×C15111yescharacteristic
475C2×C42—41no—
476C2×C42—41no—
477C2×C42C2×C4×C15111yescharacteristic
478C2×C42C2×C4×C15111yescharacteristic
479C2×C42C23×C15111yescharacteristic
480C2×C42C23×C15111yescharacteristic
481C2×C42C23×C15111yescharacteristic
482C2×C42C23×C15111yescharacteristic
483C4⋊C8—41no—
484C4⋊C8—41no—
485C4⋊C8—41no—
486C4⋊C8—41no—
487C22⋊C8—41no—
488C22⋊C8—41no—
489C22⋊C8—41no—
490C22⋊C8—41no—
491C22⋊C8—41no—
492C22⋊C8—41no—
493C22⋊C8—41no—
494C22⋊C8—41no—
495C22⋊C8—41no—
496C22⋊C8—41no—
497#97—41no—
498C4×C8—41no—
499#95C2×C4×C15111yescharacteristic
500#95C2×C4×C15111yescharacteristic
501#95C2×C4×C15111yescharacteristic
502#95C2×C4×C15111yescharacteristic
503#95C2×C4×C15111yescharacteristic
504#95C2×C4×C15111yescharacteristic
505C24C22×C4×C15111yescharacteristic
506C24C22×C4×C15111yescharacteristic
507C24C22×C4×C15111yescharacteristic
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—41no—
512C2×D4—41no—
513C2×D4—41no—
514C2×D4—41no—
515C2×D4—41no—
516C2×D4M16×C15114yescomplemented
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
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—41no—
539C22×C4—41no—
540C22×C4—41no—
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×C4C22×C4×C15111yescharacteristic
551C22×C4C22×C4×C15111yescharacteristic
552C22×C4C24×C15111yescharacteristic
553M16—44no—
554C2×C8—21no—
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—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—44no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—41no—
589C22⋊C4—41no—
590C22⋊C4—41no—
591C22⋊C4—41no—
592C22⋊C4—41no—
593C22⋊C4—41no—
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—21no—
602C42—41no—
603C42—41no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—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—
623C23C2×M16×C15112yes—
624C23C2×M16×C15112yes—
625C23C23×C4×C15111yescharacteristic
626D4—44no—
627D4—44no—
628D4—44no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
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—44no—
660C2×C4—44no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4C2×M16×C15112yes—
674C2×C4#131×C15112yes—
675C2×C4#131×C15112yes—
676C2×C4H(5,𝔽2)×C15111yescharacteristic
677C2×C4H(5,𝔽2)×C15111yescharacteristic
678C2×C4H(5,𝔽2)×C15111yescharacteristic
679C2×C4H(5,𝔽2)×C15111yescharacteristic
680C2×C4H(5,𝔽2)×C15111yescharacteristic
681C2×C42−1+4×C15111yescharacteristic
682C8—41no—
683C8—41no—
684C8—41no—
685C8—41no—
686C8—41no—
687C8—41no—
688C8—41no—
689C8—41no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
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#518×C15111yescharacteristic
712C22#518×C15111yescharacteristic
713C22#520×C15111yescharacteristic
714C22C22×M16×C15111yescharacteristic
715C22C2×#131×C15111yescharacteristic
716C22C2×#131×C15111yescharacteristic
717C22#568×C15111yescharacteristic
718C4—22no—
719C4—22no—
720C4—22no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4#560×C15111yescharacteristic
730C4#560×C15111yescharacteristic
731C4#562×C15111yescharacteristic
732C4#562×C15111yescharacteristic
733C2—42no—
734C2—42no—
735C2—81no—
736C2#2377×C15111yescharacteristic
737C2#2973×C15111yescharacteristic
738C2#2974×C15111yescharacteristic
739C2#2976×C15111yescharacteristic
740C2#2979×C15111yescharacteristic
741C2#2990×C15111yescharacteristic
742C2#2993×C15111yescharacteristic
subgroupG/H
centerC22×C4×C151C24
commutatorC23C23×C4×C151
Frattini, cosocleC22×C4C24×C151
socleC23×C151C23×C4
prime radicalC2×#121×C151C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1955×C151C2semidirect
3. #1954×C151C2semidirect
4. #1924×C151C2semidirect
5. #1923×C151C2semidirect
6. #1917×C151C2semidirect
7. #1916×C151C2semidirect
8. #1870×C151C2semidirect
9. #1870×C151C2semidirect
10. #1869×C151C2semidirect
11. #1869×C151C2semidirect
12. #1851×C151C2semidirect
13. #1850×C151C2semidirect
14. #1817×C151C2semidirect
15. #1797×C151C2semidirect
144. C2×D4×C151M16semidirect
371. #23331C151direct (N × H)
372. C151#23331direct (N × H)
374. #1955C2×C151semidirect
375. #1954C2×C151semidirect
376. #1924C2×C151semidirect
377. #1923C2×C151semidirect
378. #1917C2×C151semidirect
379. #1916C2×C151semidirect
380. #1870C2×C151semidirect
381. #1870C2×C151semidirect
382. #1869C2×C151semidirect
383. #1869C2×C151semidirect
384. #1851C2×C151semidirect
385. #1850C2×C151semidirect
386. #1817C2×C151semidirect
387. #1797C2×C151semidirect
516. C2×D4M16×C151semidirect

Maximal subgroups

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

subgroupindex
C4×#121×C1512
#1955×C1512
#1954×C1512
#1924×C1512
#1923×C1512
#1917×C1512
#1916×C1512
#1870×C1512
#1869×C1512
#1851×C1512
#1850×C1512
#1817×C1512
#1797×C1512
#23331151