Finite Group Databasebeta

← C151×#23335 #50328260

Subgroups — C151×#23335 #50328260

Order 38656.

776 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2392×C151C211yesmaximal, characteristic
2#1955×C151C211yesmaximal, characteristic, complemented
3#1955×C151C211yesmaximal, characteristic, complemented
4#1924×C151C211yesmaximal, characteristic, complemented
5#1924×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#1851×C151C211yesmaximal, characteristic, complemented
13#1850×C151C211yesmaximal, characteristic, complemented
14#1818×C151C211yesmaximal, characteristic, complemented
15#1798×C151C211yesmaximal, characteristic, complemented
16C22×M16×C151C2211yescharacteristic
17C23×C8×C151C2211yescharacteristic
18C2×C4×D4×C151C2211yescharacteristic
19C2×C4×D4×C151C2211yescharacteristic
20C2×C4×D4×C151C2211yescharacteristic
21C2×#117×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×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
38#398×C151C411yescharacteristic
39#397×C151C411yescharacteristic
40#396×C151C411yescharacteristic
41#396×C151C411yescharacteristic
42#394×C151C411yescharacteristic
43#394×C151C411yescharacteristic
44#394×C151C411yescharacteristic
45#392×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×C151C2311yescharacteristic
63C23×C4×C151C2311yescharacteristic
64C23×C4×C151C2311yescharacteristic
65C2×M16×C151—41no—
66C2×M16×C151—41no—
67C2×M16×C151—41no—
68C22×C8×C151—41no—
69C22×C8×C151—41no—
70C22×C8×C151—41no—
71C22×C8×C151C2311yescharacteristic
72C22×C8×C151C2311yescharacteristic
73C22×C8×C151C2311yescharacteristic
74C22×C8×C151C2311yescharacteristic
75C22×C8×C151C2311yescharacteristic
76C22×C8×C151C2311yescharacteristic
77C22×C8×C151C2311yescharacteristic
78C22×C8×C151C2311yescharacteristic
79C4×D4×C151—41no—
80C4×D4×C151—41no—
81C4×D4×C151—41no—
82C4×D4×C151—41no—
83C4×D4×C151—41no—
84C4×D4×C151—41no—
85#117×C151—41no—
86#117×C151—41no—
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×C4⋊C4×C151C2×C411yescharacteristic
93C2×C4⋊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×C22⋊C4×C151C2×C411yescharacteristic
104C2×C22⋊C4×C151C2×C411yescharacteristic
105C2×C22⋊C4×C151C2×C411yescharacteristic
106C2×C42×C151C2311yescharacteristic
107C2×C42×C151C2311yescharacteristic
108C2×C42×C151C2311yescharacteristic
109C2×C42×C151C2311yescharacteristic
110C4⋊C8×C151—41no—
111C4⋊C8×C151—41no—
112C4⋊C8×C151—41no—
113C4⋊C8×C151—41no—
114C22⋊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—
124#97×C151—41no—
125#97×C151—41no—
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
134C24×C151C22×C411yescharacteristic
135C2×D4×C151—22no—
136C2×D4×C151—22no—
137C2×D4×C151—41no—
138C2×D4×C151—41no—
139C2×D4×C151—41no—
140C2×D4×C151—41no—
141C2×D4×C151—41no—
142C2×D4×C151—41no—
143C2×D4×C151—41no—
144C22×C4×C151—21no—
145C22×C4×C151—21no—
146C22×C4×C151—21no—
147C22×C4×C151—21no—
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×C151C22×C411yescharacteristic
163C22×C4×C151C22×C411yescharacteristic
164C22×C4×C151C22×C411yescharacteristic
165C22×C4×C151C22×C411yescharacteristic
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×C151C2411yescharacteristic
174M16×C151—44no—
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—
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—44no—
200C4⋊C4×C151—41no—
201C4⋊C4×C151—41no—
202C4⋊C4×C151—41no—
203C4⋊C4×C151—41no—
204C4⋊C4×C151—41no—
205C4⋊C4×C151—41no—
206C4⋊C4×C151—41no—
207C22⋊C4×C151—22no—
208C22⋊C4×C151—41no—
209C22⋊C4×C151—41no—
210C22⋊C4×C151—41no—
211C22⋊C4×C151—41no—
212C22⋊C4×C151—41no—
213C22⋊C4×C151—41no—
214C22⋊C4×C151—41no—
215C22⋊C4×C151—41no—
216C22⋊C4×C151—41no—
217C22⋊C4×C151—41no—
218C22⋊C4×C151—41no—
219C42×C151—21no—
220C42×C151—21no—
221C42×C151—21no—
222C42×C151—21no—
223C42×C151—21no—
224C42×C151—21no—
225C42×C151—21no—
226C42×C151—21no—
227C23×C151—21no—
228C23×C151—21no—
229C23×C151—21no—
230C23×C151—21no—
231C23×C151—21no—
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#13112yes—
248C23×C151C23×C411yescharacteristic
249D4×C151—44no—
250D4×C151—44no—
251D4×C151—44no—
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—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—41no—
286C2×C4×C151—41no—
287C2×C4×C151—41no—
288C2×C4×C151—41no—
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×C151H(5,𝔽2)11yescharacteristic
298C2×C4×C151H(5,𝔽2)11yescharacteristic
299C2×C4×C151H(5,𝔽2)11yescharacteristic
300C2×C4×C151H(5,𝔽2)11yescharacteristic
301C2×C4×C151H(5,𝔽2)11yescharacteristic
302C2×C4×C1512−1+411yescharacteristic
303C8×C151—41no—
304C8×C151—41no—
305C8×C151—41no—
306C8×C151—41no—
307C8×C151—41no—
308C8×C151—41no—
309C8×C151—41no—
310C8×C151—41no—
311C22×C151—22no—
312C22×C151—22no—
313C22×C151—22no—
314C22×C151—41no—
315C22×C151—41no—
316C22×C151—41no—
317C22×C151—41no—
318C22×C151—41no—
319C22×C151—41no—
320C22×C151—41no—
321C22×C151—41no—
322C22×C151—41no—
323C22×C151—41no—
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#51811yescharacteristic
333C22×C151#51811yescharacteristic
334C22×C151#52011yescharacteristic
335C22×C151C2×#13111yescharacteristic
336C22×C151#56811yescharacteristic
337C22×C151#56811yescharacteristic
338C22×C151#56811yescharacteristic
339C4×C151—41no—
340C4×C151—41no—
341C4×C151—41no—
342C4×C151—41no—
343C4×C151—41no—
344C4×C151—41no—
345C4×C151—41no—
346C4×C151—41no—
347C4×C151—41no—
348C4×C151—41no—
349C4×C151—41no—
350C4×C151#56011yescharacteristic
351C4×C151#56011yescharacteristic
352C4×C151#56211yescharacteristic
353C4×C151#56211yescharacteristic
354C2×C151—42no—
355C2×C151—81no—
356C2×C151—81no—
357C2×C151#237711yescharacteristic
358C2×C151#297611yescharacteristic
359C2×C151#297611yescharacteristic
360C2×C151#297811yescharacteristic
361C2×C151#298011yescharacteristic
362C2×C151#299211yescharacteristic
363C2×C151#299511yescharacteristic
364#23335C15111yesmaximal, characteristic, direct product factor, Sylow
365C151#2333511yescharacteristic, direct product factor, Sylow
366#2392C2×C15111yescharacteristic
367#1955C2×C15111yescharacteristic, complemented
368#1955C2×C15111yescharacteristic, complemented
369#1924C2×C15111yescharacteristic, complemented
370#1924C2×C15111yescharacteristic, complemented
371#1917C2×C15111yescharacteristic, complemented
372#1917C2×C15111yescharacteristic, complemented
373#1870C2×C15111yescharacteristic, complemented
374#1870C2×C15111yescharacteristic, complemented
375#1869C2×C15111yescharacteristic, complemented
376#1869C2×C15111yescharacteristic, complemented
377#1851C2×C15111yescharacteristic, complemented
378#1850C2×C15111yescharacteristic, complemented
379#1818C2×C15111yescharacteristic, complemented
380#1798C2×C15111yescharacteristic, complemented
381C22×M16C22×C15111yescharacteristic
382C23×C8C22×C15111yescharacteristic
383C2×C4×D4C22×C15111yescharacteristic
384C2×C4×D4C22×C15111yescharacteristic
385C2×C4×D4C22×C15111yescharacteristic
386C2×#117C22×C15111yescharacteristic
387C2×C4⋊C8C22×C15111yescharacteristic
388C2×C4⋊C8C22×C15111yescharacteristic
389C2×C4⋊C8C22×C15111yescharacteristic
390C2×C4⋊C8C22×C15111yescharacteristic
391C2×C22⋊C8C22×C15111yescharacteristic
392C2×C22⋊C8C22×C15111yescharacteristic
393C2×C22⋊C8C22×C15111yescharacteristic
394C2×C22⋊C8C22×C15111yescharacteristic
395C2×C22⋊C8C22×C15111yescharacteristic
396C2×C22⋊C8C22×C15111yescharacteristic
397C2×C22⋊C8C22×C15111yescharacteristic
398C2×C22⋊C8C22×C15111yescharacteristic
399C2×C22⋊C8C22×C15111yescharacteristic
400C2×C22⋊C8C22×C15111yescharacteristic
401C2×#97C22×C15111yescharacteristic
402C2×#97C22×C15111yescharacteristic
403#398C4×C15111yescharacteristic
404#397C4×C15111yescharacteristic
405#396C4×C15111yescharacteristic
406#396C4×C15111yescharacteristic
407#394C4×C15111yescharacteristic
408#394C4×C15111yescharacteristic
409#394C4×C15111yescharacteristic
410#392C4×C15111yescharacteristic
411C4×C4⋊C4C22×C15111yescharacteristic
412C4×C22⋊C4C22×C15111yescharacteristic
413C4×C22⋊C4C22×C15111yescharacteristic
414#336C22×C15111yescharacteristic
415#336C22×C15111yescharacteristic
416#336C22×C15111yescharacteristic
417#336C22×C15111yescharacteristic
418#336C22×C15111yescharacteristic
419#336C22×C15111yescharacteristic
420#336C22×C15111yescharacteristic
421#336C22×C15111yescharacteristic
422#336C22×C15111yescharacteristic
423#336C22×C15111yescharacteristic
424C22×D4C2×C4×C15111yescharacteristic
425C22×D4C2×C4×C15111yescharacteristic
426C22×D4C2×C4×C15111yescharacteristic
427C23×C4C23×C15111yescharacteristic
428C23×C4C23×C15111yescharacteristic
429C23×C4C23×C15111yescharacteristic
430C2×M16—41no—
431C2×M16—41no—
432C2×M16—41no—
433C22×C8—41no—
434C22×C8—41no—
435C22×C8—41no—
436C22×C8C23×C15111yescharacteristic
437C22×C8C23×C15111yescharacteristic
438C22×C8C23×C15111yescharacteristic
439C22×C8C23×C15111yescharacteristic
440C22×C8C23×C15111yescharacteristic
441C22×C8C23×C15111yescharacteristic
442C22×C8C23×C15111yescharacteristic
443C22×C8C23×C15111yescharacteristic
444C4×D4—41no—
445C4×D4—41no—
446C4×D4—41no—
447C4×D4—41no—
448C4×D4—41no—
449C4×D4—41no—
450#117—41no—
451#117—41no—
452C2×C4⋊C4C2×C4×C15111yescharacteristic
453C2×C4⋊C4C2×C4×C15111yescharacteristic
454C2×C4⋊C4C2×C4×C15111yescharacteristic
455C2×C4⋊C4C2×C4×C15111yescharacteristic
456C2×C4⋊C4C2×C4×C15111yescharacteristic
457C2×C4⋊C4C2×C4×C15111yescharacteristic
458C2×C4⋊C4C2×C4×C15111yescharacteristic
459C2×C22⋊C4C2×C4×C15111yescharacteristic
460C2×C22⋊C4C2×C4×C15111yescharacteristic
461C2×C22⋊C4C2×C4×C15111yescharacteristic
462C2×C22⋊C4C2×C4×C15111yescharacteristic
463C2×C22⋊C4C2×C4×C15111yescharacteristic
464C2×C22⋊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×C42C23×C15111yescharacteristic
472C2×C42C23×C15111yescharacteristic
473C2×C42C23×C15111yescharacteristic
474C2×C42C23×C15111yescharacteristic
475C4⋊C8—41no—
476C4⋊C8—41no—
477C4⋊C8—41no—
478C4⋊C8—41no—
479C22⋊C8—41no—
480C22⋊C8—41no—
481C22⋊C8—41no—
482C22⋊C8—41no—
483C22⋊C8—41no—
484C22⋊C8—41no—
485C22⋊C8—41no—
486C22⋊C8—41no—
487C22⋊C8—41no—
488C22⋊C8—41no—
489#97—41no—
490#97—41no—
491#95C2×C4×C15111yescharacteristic
492#95C2×C4×C15111yescharacteristic
493#95C2×C4×C15111yescharacteristic
494#95C2×C4×C15111yescharacteristic
495#95C2×C4×C15111yescharacteristic
496#95C2×C4×C15111yescharacteristic
497C24C22×C4×C15111yescharacteristic
498C24C22×C4×C15111yescharacteristic
499C24C22×C4×C15111yescharacteristic
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—41no—
503C2×D4—41no—
504C2×D4—41no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4—41no—
508C2×D4—41no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4C22×C4×C15111yescharacteristic
528C22×C4C22×C4×C15111yescharacteristic
529C22×C4C22×C4×C15111yescharacteristic
530C22×C4C22×C4×C15111yescharacteristic
531C22×C4C22×C4×C15111yescharacteristic
532C22×C4C22×C4×C15111yescharacteristic
533C22×C4C22×C4×C15111yescharacteristic
534C22×C4C22×C4×C15111yescharacteristic
535C22×C4C22×C4×C15111yescharacteristic
536C22×C4C22×C4×C15111yescharacteristic
537C22×C4C22×C4×C15111yescharacteristic
538C22×C4C24×C15111yescharacteristic
539M16—44no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
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—44no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C22⋊C4—22no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—41no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C22⋊C4—41no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23#131×C15112yes—
613C23C23×C4×C15111yescharacteristic
614D4—44no—
615D4—44no—
616D4—44no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
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—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4H(5,𝔽2)×C15111yescharacteristic
663C2×C4H(5,𝔽2)×C15111yescharacteristic
664C2×C4H(5,𝔽2)×C15111yescharacteristic
665C2×C4H(5,𝔽2)×C15111yescharacteristic
666C2×C4H(5,𝔽2)×C15111yescharacteristic
667C2×C42−1+4×C15111yescharacteristic
668C8—41no—
669C8—41no—
670C8—41no—
671C8—41no—
672C8—41no—
673C8—41no—
674C8—41no—
675C8—41no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22#518×C15111yescharacteristic
698C22#518×C15111yescharacteristic
699C22#520×C15111yescharacteristic
700C22C2×#131×C15111yescharacteristic
701C22#568×C15111yescharacteristic
702C22#568×C15111yescharacteristic
703C22#568×C15111yescharacteristic
704C4—41no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—41no—
709C4—41no—
710C4—41no—
711C4—41no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4#560×C15111yescharacteristic
716C4#560×C15111yescharacteristic
717C4#562×C15111yescharacteristic
718C4#562×C15111yescharacteristic
719C2—42no—
720C2—81no—
721C2—81no—
722C2#2377×C15111yescharacteristic
723C2#2976×C15111yescharacteristic
724C2#2976×C15111yescharacteristic
725C2#2978×C15111yescharacteristic
726C2#2980×C15111yescharacteristic
727C2#2992×C15111yescharacteristic
728C2#2995×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
2. #1955×C151C2semidirect
3. #1955×C151C2semidirect
4. #1924×C151C2semidirect
5. #1924×C151C2semidirect
6. #1917×C151C2semidirect
7. #1917×C151C2semidirect
8. #1870×C151C2semidirect
9. #1870×C151C2semidirect
10. #1869×C151C2semidirect
11. #1869×C151C2semidirect
12. #1851×C151C2semidirect
13. #1850×C151C2semidirect
14. #1818×C151C2semidirect
15. #1798×C151C2semidirect
364. #23335C151direct (N × H)
365. C151#23335direct (N × H)
367. #1955C2×C151semidirect
368. #1955C2×C151semidirect
369. #1924C2×C151semidirect
370. #1924C2×C151semidirect
371. #1917C2×C151semidirect
372. #1917C2×C151semidirect
373. #1870C2×C151semidirect
374. #1870C2×C151semidirect
375. #1869C2×C151semidirect
376. #1869C2×C151semidirect
377. #1851C2×C151semidirect
378. #1850C2×C151semidirect
379. #1818C2×C151semidirect
380. #1798C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2392×C1512
#1955×C1512
#1924×C1512
#1917×C1512
#1870×C1512
#1869×C1512
#1851×C1512
#1850×C1512
#1818×C1512
#1798×C1512
#23335151