Finite Group Databasebeta

← C151×#21855 #50326780

Subgroups — C151×#21855 #50326780

Order 38656.

1128 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#529×C151C211yesmaximal, characteristic
2C2×#433×C151C211yesmaximal, characteristic, complemented
3C2×#424×C151C211yesmaximal, characteristic, complemented
4#1985×C151C211yesmaximal, characteristic, complemented
5#1984×C151C211yesmaximal, characteristic, complemented
6#1955×C151C211yesmaximal, characteristic, complemented
7#1954×C151C211yesmaximal, characteristic, complemented
8#1870×C151C211yesmaximal, characteristic, complemented
9#1870×C151C211yesmaximal, characteristic, complemented
10#1869×C151C211yesmaximal, characteristic, complemented
11#1869×C151C211yesmaximal, characteristic, complemented
12#1798×C151C211yesmaximal, characteristic, complemented
13#1798×C151C211yesmaximal, characteristic, complemented
14#1797×C151C211yesmaximal, characteristic, complemented
15#1797×C151C211yesmaximal, characteristic, complemented
16C22×M16×C151C2211yescharacteristic
17C23×C8×C151C2211yescharacteristic
18#529×C151—24no—
19#529×C151—24no—
20C2×#126×C151C411yescharacteristic
21C2×#126×C151C411yescharacteristic
22C2×#125×C151C411yescharacteristic
23C2×#124×C151C411yescharacteristic
24C2×#123×C151C411yescharacteristic
25C2×#123×C151C411yescharacteristic
26C2×C22⋊Q8×C151C411yescharacteristic
27C2×#121×C151C411yescharacteristic
28C2×C4×Q8×C151C2211yescharacteristic
29C2×C4×D4×C151C2211yescharacteristic
30C2×C4×D4×C151C2211yescharacteristic
31C2×C4×D4×C151C2211yescharacteristic
32C2×#117×C151C2211yescharacteristic
33C2×#117×C151C2211yescharacteristic
34C22×C42×C151C2211yescharacteristic
35#433×C151—24no—
36#424×C151—24no—
37C2×C4⋊C8×C151C2211yescharacteristic
38C2×C4⋊C8×C151C2211yescharacteristic
39C2×C4⋊C8×C151C2211yescharacteristic
40C2×C4⋊C8×C151C2211yescharacteristic
41C2×C4⋊C8×C151C2211yescharacteristic
42C2×C4⋊C8×C151C2211yescharacteristic
43C2×C22⋊C8×C151C2211yescharacteristic
44C2×C22⋊C8×C151C2211yescharacteristic
45C2×C22⋊C8×C151C2211yescharacteristic
46C2×C22⋊C8×C151C2211yescharacteristic
47C2×C22⋊C8×C151C2211yescharacteristic
48C2×C22⋊C8×C151C2211yescharacteristic
49C2×C22⋊C8×C151C2211yescharacteristic
50C2×C22⋊C8×C151C2211yescharacteristic
51C2×C22⋊C8×C151C2211yescharacteristic
52C2×C22⋊C8×C151C2211yescharacteristic
53C2×#97×C151C2211yescharacteristic
54C2×C4×C8×C151C2211yescharacteristic
55#336×C151C2211yescharacteristic
56#336×C151C2211yescharacteristic
57#336×C151C2211yescharacteristic
58#336×C151C2211yescharacteristic
59#336×C151C2211yescharacteristic
60#336×C151C2211yescharacteristic
61#336×C151C2211yescharacteristic
62#336×C151C2211yescharacteristic
63C22×Q8×C151C2×C411yescharacteristic
64C22×D4×C151C2×C411yescharacteristic
65C22×D4×C151C2×C411yescharacteristic
66C22×D4×C151C2×C411yescharacteristic
67C23×C4×C151C2×C411yescharacteristic
68C23×C4×C151C2×C411yescharacteristic
69C23×C4×C151C2311yescharacteristic
70C23×C4×C151C2311yescharacteristic
71C23×C4×C151C2311yescharacteristic
72C2×M16×C151—22no—
73C2×M16×C151—41no—
74C2×M16×C151—41no—
75C22×C8×C151—22no—
76C22×C8×C151—41no—
77C22×C8×C151—41no—
78C22×C8×C151C2311yescharacteristic
79C22×C8×C151C2311yescharacteristic
80C22×C8×C151C2311yescharacteristic
81C22×C8×C151C2311yescharacteristic
82C22×C8×C151C2311yescharacteristic
83C22×C8×C151C2311yescharacteristic
84C22×C8×C151C2311yescharacteristic
85C22×C8×C151C2311yescharacteristic
86#126×C151—24no—
87#126×C151—24no—
88#125×C151—24no—
89#124×C151—24no—
90#123×C151—24no—
91#123×C151—24no—
92C22⋊Q8×C151—24no—
93#121×C151—24no—
94C4×Q8×C151—22no—
95C4×Q8×C151—22no—
96C4×D4×C151—22no—
97C4×D4×C151—22no—
98C4×D4×C151—22no—
99C4×D4×C151—22no—
100C4×D4×C151—22no—
101C4×D4×C151—22no—
102#117×C151—22no—
103#117×C151—22no—
104#117×C151D414yes—
105#117×C151D414yes—
106C2×C4⋊C4×C151C2×C411yescharacteristic
107C2×C4⋊C4×C151C2×C411yescharacteristic
108C2×C4⋊C4×C151C2×C411yescharacteristic
109C2×C4⋊C4×C151C2×C411yescharacteristic
110C2×C4⋊C4×C151C2×C411yescharacteristic
111C2×C4⋊C4×C151C2×C411yescharacteristic
112C2×C4⋊C4×C151C2×C411yescharacteristic
113C2×C4⋊C4×C151C2×C411yescharacteristic
114C2×C4⋊C4×C151C2×C411yescharacteristic
115C2×C4⋊C4×C151C2×C411yescharacteristic
116C2×C22⋊C4×C151C2×C411yescharacteristic
117C2×C22⋊C4×C151C2×C411yescharacteristic
118C2×C22⋊C4×C151C2×C411yescharacteristic
119C2×C22⋊C4×C151C2×C411yescharacteristic
120C2×C22⋊C4×C151C2×C411yescharacteristic
121C2×C22⋊C4×C151C2×C411yescharacteristic
122C2×C22⋊C4×C151C2×C411yescharacteristic
123C2×C22⋊C4×C151C2×C411yescharacteristic
124C2×C22⋊C4×C151C2×C411yescharacteristic
125C2×C22⋊C4×C151C2×C411yescharacteristic
126C2×C42×C151—22no—
127C2×C42×C151—22no—
128C2×C42×C151C2×C411yescharacteristic
129C2×C42×C151C2×C411yescharacteristic
130C2×C42×C151C2311yescharacteristic
131C2×C42×C151C2311yescharacteristic
132C2×C42×C151C2311yescharacteristic
133C2×C42×C151C2311yescharacteristic
134C4⋊C8×C151—22no—
135C4⋊C8×C151—22no—
136C4⋊C8×C151—22no—
137C4⋊C8×C151—22no—
138C4⋊C8×C151—22no—
139C4⋊C8×C151—22no—
140C22⋊C8×C151—22no—
141C22⋊C8×C151—22no—
142C22⋊C8×C151—41no—
143C22⋊C8×C151—41no—
144C22⋊C8×C151—41no—
145C22⋊C8×C151—41no—
146C22⋊C8×C151—41no—
147C22⋊C8×C151—41no—
148C22⋊C8×C151—41no—
149C22⋊C8×C151—41no—
150#97×C151—22no—
151C4×C8×C151—22no—
152C24×C151C22×C411yescharacteristic
153C24×C151C22×C411yescharacteristic
154C24×C151C22×C411yescharacteristic
155C2×Q8×C151—22no—
156C2×Q8×C151—22no—
157C2×Q8×C151—41no—
158C2×D4×C151—22no—
159C2×D4×C151—22no—
160C2×D4×C151—22no—
161C2×D4×C151—22no—
162C2×D4×C151—22no—
163C2×D4×C151—22no—
164C2×D4×C151—41no—
165C2×D4×C151—41no—
166C2×D4×C151—41no—
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—22no—
172C22×C4×C151—22no—
173C22×C4×C151—22no—
174C22×C4×C151—22no—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—21no—
178C22×C4×C151—21no—
179C22×C4×C151—21no—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151—21no—
183C22×C4×C151—21no—
184C22×C4×C151—21no—
185C22×C4×C151—21no—
186C22×C4×C151—21no—
187C22×C4×C151—41no—
188C22×C4×C151—41no—
189C22×C4×C151C22×C411yescharacteristic
190C22×C4×C151C22×C411yescharacteristic
191C22×C4×C151C22×C411yescharacteristic
192C22×C4×C151C22×C411yescharacteristic
193C22×C4×C151C22×C411yescharacteristic
194C22×C4×C151C22×C411yescharacteristic
195C22×C4×C151C22×C411yescharacteristic
196C22×C4×C151C22×C411yescharacteristic
197C22×C4×C151C22×C411yescharacteristic
198C22×C4×C151C22×C411yescharacteristic
199C22×C4×C151C22×C411yescharacteristic
200C22×C4×C151C2×D412yes—
201C22×C4×C151C2×D412yes—
202C22×C4×C151C2411yescharacteristic
203M16×C151—44no—
204C2×C8×C151—21no—
205C2×C8×C151—21no—
206C2×C8×C151—21no—
207C2×C8×C151—21no—
208C2×C8×C151—21no—
209C2×C8×C151—21no—
210C2×C8×C151—21no—
211C2×C8×C151—21no—
212C2×C8×C151—21no—
213C2×C8×C151—21no—
214C2×C8×C151—21no—
215C2×C8×C151—21no—
216C2×C8×C151—21no—
217C2×C8×C151—21no—
218C2×C8×C151—21no—
219C2×C8×C151—21no—
220C2×C8×C151—21no—
221C2×C8×C151—21no—
222C2×C8×C151—21no—
223C2×C8×C151—21no—
224C2×C8×C151—21no—
225C2×C8×C151—21no—
226C2×C8×C151—21no—
227C2×C8×C151—21no—
228C2×C8×C151—44no—
229C4⋊C4×C151—22no—
230C4⋊C4×C151—22no—
231C4⋊C4×C151—22no—
232C4⋊C4×C151—22no—
233C4⋊C4×C151—22no—
234C4⋊C4×C151—22no—
235C4⋊C4×C151—22no—
236C4⋊C4×C151—22no—
237C4⋊C4×C151C22⋊C414yes—
238C4⋊C4×C151C22⋊C414yes—
239C22⋊C4×C151—22no—
240C22⋊C4×C151—22no—
241C22⋊C4×C151—22no—
242C22⋊C4×C151—22no—
243C22⋊C4×C151—22no—
244C22⋊C4×C151—22no—
245C22⋊C4×C151—22no—
246C22⋊C4×C151—22no—
247C22⋊C4×C151C22⋊C414yes—
248C22⋊C4×C151C22⋊C414yes—
249C42×C151—22no—
250C42×C151—22no—
251C42×C151—21no—
252C42×C151—21no—
253C42×C151—21no—
254C42×C151—21no—
255C42×C151C2×D412yes—
256C42×C151C2×D412yes—
257C42×C151C2×D412yes—
258C42×C151C2×D412yes—
259C23×C151—21no—
260C23×C151—21no—
261C23×C151—21no—
262C23×C151—21no—
263C23×C151—21no—
264C23×C151—21no—
265C23×C151—21no—
266C23×C151—21no—
267C23×C151—21no—
268C23×C151—21no—
269C23×C151—21no—
270C23×C151—21no—
271C23×C151—21no—
272C23×C151—21no—
273C23×C151—21no—
274C23×C151—21no—
275C23×C151—21no—
276C23×C151—21no—
277C23×C151—21no—
278C23×C151C2×C22⋊C412yes—
279C23×C151#13112yes—
280C23×C151C23×C411yescharacteristic
281Q8×C151—44no—
282D4×C151—44no—
283D4×C151—44no—
284D4×C151—44no—
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—21no—
297C2×C4×C151—22no—
298C2×C4×C151—22no—
299C2×C4×C151—22no—
300C2×C4×C151—22no—
301C2×C4×C151—21no—
302C2×C4×C151—21no—
303C2×C4×C151—21no—
304C2×C4×C151—21no—
305C2×C4×C151—21no—
306C2×C4×C151—21no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—21no—
310C2×C4×C151—21no—
311C2×C4×C151—21no—
312C2×C4×C151—21no—
313C2×C4×C151—21no—
314C2×C4×C151—21no—
315C2×C4×C151—21no—
316C2×C4×C151—44no—
317C2×C4×C151—44no—
318C2×C4×C151—41no—
319C2×C4×C151—41no—
320C2×C4×C151—41no—
321C2×C4×C151—41no—
322C2×C4×C151—41no—
323C2×C4×C151—41no—
324C2×C4×C151—41no—
325C2×C4×C151—41no—
326C2×C4×C151C2×C22⋊C412yes—
327C2×C4×C151C2×C22⋊C412yes—
328C2×C4×C151C2×C22⋊C412yes—
329C2×C4×C151C2×C22⋊C412yes—
330C2×C4×C151C2×C22⋊C412yes—
331C2×C4×C151#13112yes—
332C2×C4×C151C22×D411yescharacteristic
333C2×C4×C151C22×D411yescharacteristic
334C2×C4×C151H(5,𝔽2)11yescharacteristic
335C2×C4×C151H(5,𝔽2)11yescharacteristic
336C2×C4×C1512−1+411yescharacteristic
337C2×C4×C1512−1+411yescharacteristic
338C8×C151—41no—
339C8×C151—41no—
340C8×C151—41no—
341C8×C151—41no—
342C8×C151—41no—
343C8×C151—41no—
344C8×C151—41no—
345C8×C151—41no—
346C22×C151—22no—
347C22×C151—22no—
348C22×C151—22no—
349C22×C151—22no—
350C22×C151—22no—
351C22×C151—22no—
352C22×C151—41no—
353C22×C151—41no—
354C22×C151—41no—
355C22×C151—41no—
356C22×C151—41no—
357C22×C151—41no—
358C22×C151—41no—
359C22×C151—41no—
360C22×C151—41no—
361C22×C151—41no—
362C22×C151—41no—
363C22×C151—41no—
364C22×C151—41no—
365C22×C151—41no—
366C22×C151—41no—
367C22×C151C22×C22⋊C411yescharacteristic
368C22×C151#52011yescharacteristic
369C22×C151#52011yescharacteristic
370C22×C151C2×#13111yescharacteristic
371C22×C151C2×#13111yescharacteristic
372C22×C151#56811yescharacteristic
373C22×C151#56811yescharacteristic
374C4×C151—22no—
375C4×C151—22no—
376C4×C151—22no—
377C4×C151—22no—
378C4×C151—22no—
379C4×C151—22no—
380C4×C151—41no—
381C4×C151—41no—
382C4×C151—41no—
383C4×C151—41no—
384C4×C151—41no—
385C4×C151#53511yescharacteristic
386C4×C151#53611yescharacteristic
387C4×C151#53711yescharacteristic
388C4×C151#53711yescharacteristic
389C2×C151—42no—
390C2×C151—42no—
391C2×C151—81no—
392C2×C151#231111yescharacteristic
393C2×C151#288011yescharacteristic
394C2×C151#288011yescharacteristic
395C2×C151#299211yescharacteristic
396C2×C151#299311yescharacteristic
397C2×C151#299411yescharacteristic
398C2×C151#299511yescharacteristic
399#21855C15111yesmaximal, characteristic, direct product factor, Sylow
400C151#2185511yescharacteristic, direct product factor, Sylow
401C2×#529C2×C15111yescharacteristic
402C2×#433C2×C15111yescharacteristic, complemented
403C2×#424C2×C15111yescharacteristic, complemented
404#1985C2×C15111yescharacteristic, complemented
405#1984C2×C15111yescharacteristic, complemented
406#1955C2×C15111yescharacteristic, complemented
407#1954C2×C15111yescharacteristic, complemented
408#1870C2×C15111yescharacteristic, complemented
409#1870C2×C15111yescharacteristic, complemented
410#1869C2×C15111yescharacteristic, complemented
411#1869C2×C15111yescharacteristic, complemented
412#1798C2×C15111yescharacteristic, complemented
413#1798C2×C15111yescharacteristic, complemented
414#1797C2×C15111yescharacteristic, complemented
415#1797C2×C15111yescharacteristic, complemented
416C22×M16C22×C15111yescharacteristic
417C23×C8C22×C15111yescharacteristic
418#529—24no—
419#529—24no—
420C2×#126C4×C15111yescharacteristic
421C2×#126C4×C15111yescharacteristic
422C2×#125C4×C15111yescharacteristic
423C2×#124C4×C15111yescharacteristic
424C2×#123C4×C15111yescharacteristic
425C2×#123C4×C15111yescharacteristic
426C2×C22⋊Q8C4×C15111yescharacteristic
427C2×#121C4×C15111yescharacteristic
428C2×C4×Q8C22×C15111yescharacteristic
429C2×C4×D4C22×C15111yescharacteristic
430C2×C4×D4C22×C15111yescharacteristic
431C2×C4×D4C22×C15111yescharacteristic
432C2×#117C22×C15111yescharacteristic
433C2×#117C22×C15111yescharacteristic
434C22×C42C22×C15111yescharacteristic
435#433—24no—
436#424—24no—
437C2×C4⋊C8C22×C15111yescharacteristic
438C2×C4⋊C8C22×C15111yescharacteristic
439C2×C4⋊C8C22×C15111yescharacteristic
440C2×C4⋊C8C22×C15111yescharacteristic
441C2×C4⋊C8C22×C15111yescharacteristic
442C2×C4⋊C8C22×C15111yescharacteristic
443C2×C22⋊C8C22×C15111yescharacteristic
444C2×C22⋊C8C22×C15111yescharacteristic
445C2×C22⋊C8C22×C15111yescharacteristic
446C2×C22⋊C8C22×C15111yescharacteristic
447C2×C22⋊C8C22×C15111yescharacteristic
448C2×C22⋊C8C22×C15111yescharacteristic
449C2×C22⋊C8C22×C15111yescharacteristic
450C2×C22⋊C8C22×C15111yescharacteristic
451C2×C22⋊C8C22×C15111yescharacteristic
452C2×C22⋊C8C22×C15111yescharacteristic
453C2×#97C22×C15111yescharacteristic
454C2×C4×C8C22×C15111yescharacteristic
455#336C22×C15111yescharacteristic
456#336C22×C15111yescharacteristic
457#336C22×C15111yescharacteristic
458#336C22×C15111yescharacteristic
459#336C22×C15111yescharacteristic
460#336C22×C15111yescharacteristic
461#336C22×C15111yescharacteristic
462#336C22×C15111yescharacteristic
463C22×Q8C2×C4×C15111yescharacteristic
464C22×D4C2×C4×C15111yescharacteristic
465C22×D4C2×C4×C15111yescharacteristic
466C22×D4C2×C4×C15111yescharacteristic
467C23×C4C2×C4×C15111yescharacteristic
468C23×C4C2×C4×C15111yescharacteristic
469C23×C4C23×C15111yescharacteristic
470C23×C4C23×C15111yescharacteristic
471C23×C4C23×C15111yescharacteristic
472C2×M16—22no—
473C2×M16—41no—
474C2×M16—41no—
475C22×C8—22no—
476C22×C8—41no—
477C22×C8—41no—
478C22×C8C23×C15111yescharacteristic
479C22×C8C23×C15111yescharacteristic
480C22×C8C23×C15111yescharacteristic
481C22×C8C23×C15111yescharacteristic
482C22×C8C23×C15111yescharacteristic
483C22×C8C23×C15111yescharacteristic
484C22×C8C23×C15111yescharacteristic
485C22×C8C23×C15111yescharacteristic
486#126—24no—
487#126—24no—
488#125—24no—
489#124—24no—
490#123—24no—
491#123—24no—
492C22⋊Q8—24no—
493#121—24no—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—22no—
503#117—22no—
504#117D4×C15114yes—
505#117D4×C15114yes—
506C2×C4⋊C4C2×C4×C15111yescharacteristic
507C2×C4⋊C4C2×C4×C15111yescharacteristic
508C2×C4⋊C4C2×C4×C15111yescharacteristic
509C2×C4⋊C4C2×C4×C15111yescharacteristic
510C2×C4⋊C4C2×C4×C15111yescharacteristic
511C2×C4⋊C4C2×C4×C15111yescharacteristic
512C2×C4⋊C4C2×C4×C15111yescharacteristic
513C2×C4⋊C4C2×C4×C15111yescharacteristic
514C2×C4⋊C4C2×C4×C15111yescharacteristic
515C2×C4⋊C4C2×C4×C15111yescharacteristic
516C2×C22⋊C4C2×C4×C15111yescharacteristic
517C2×C22⋊C4C2×C4×C15111yescharacteristic
518C2×C22⋊C4C2×C4×C15111yescharacteristic
519C2×C22⋊C4C2×C4×C15111yescharacteristic
520C2×C22⋊C4C2×C4×C15111yescharacteristic
521C2×C22⋊C4C2×C4×C15111yescharacteristic
522C2×C22⋊C4C2×C4×C15111yescharacteristic
523C2×C22⋊C4C2×C4×C15111yescharacteristic
524C2×C22⋊C4C2×C4×C15111yescharacteristic
525C2×C22⋊C4C2×C4×C15111yescharacteristic
526C2×C42—22no—
527C2×C42—22no—
528C2×C42C2×C4×C15111yescharacteristic
529C2×C42C2×C4×C15111yescharacteristic
530C2×C42C23×C15111yescharacteristic
531C2×C42C23×C15111yescharacteristic
532C2×C42C23×C15111yescharacteristic
533C2×C42C23×C15111yescharacteristic
534C4⋊C8—22no—
535C4⋊C8—22no—
536C4⋊C8—22no—
537C4⋊C8—22no—
538C4⋊C8—22no—
539C4⋊C8—22no—
540C22⋊C8—22no—
541C22⋊C8—22no—
542C22⋊C8—41no—
543C22⋊C8—41no—
544C22⋊C8—41no—
545C22⋊C8—41no—
546C22⋊C8—41no—
547C22⋊C8—41no—
548C22⋊C8—41no—
549C22⋊C8—41no—
550#97—22no—
551C4×C8—22no—
552C24C22×C4×C15111yescharacteristic
553C24C22×C4×C15111yescharacteristic
554C24C22×C4×C15111yescharacteristic
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—41no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4C22×C4×C15111yescharacteristic
590C22×C4C22×C4×C15111yescharacteristic
591C22×C4C22×C4×C15111yescharacteristic
592C22×C4C22×C4×C15111yescharacteristic
593C22×C4C22×C4×C15111yescharacteristic
594C22×C4C22×C4×C15111yescharacteristic
595C22×C4C22×C4×C15111yescharacteristic
596C22×C4C22×C4×C15111yescharacteristic
597C22×C4C22×C4×C15111yescharacteristic
598C22×C4C22×C4×C15111yescharacteristic
599C22×C4C22×C4×C15111yescharacteristic
600C22×C4C2×D4×C15112yes—
601C22×C4C2×D4×C15112yes—
602C22×C4C24×C15111yescharacteristic
603M16—44no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—44no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4C22⋊C4×C15114yes—
638C4⋊C4C22⋊C4×C15114yes—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4C22⋊C4×C15114yes—
648C22⋊C4C22⋊C4×C15114yes—
649C42—22no—
650C42—22no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42—21no—
655C42C2×D4×C15112yes—
656C42C2×D4×C15112yes—
657C42C2×D4×C15112yes—
658C42C2×D4×C15112yes—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23C2×C22⋊C4×C15112yes—
679C23#131×C15112yes—
680C23C23×C4×C15111yescharacteristic
681Q8—44no—
682D4—44no—
683D4—44no—
684D4—44no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4C2×C22⋊C4×C15112yes—
727C2×C4C2×C22⋊C4×C15112yes—
728C2×C4C2×C22⋊C4×C15112yes—
729C2×C4C2×C22⋊C4×C15112yes—
730C2×C4C2×C22⋊C4×C15112yes—
731C2×C4#131×C15112yes—
732C2×C4C22×D4×C15111yescharacteristic
733C2×C4C22×D4×C15111yescharacteristic
734C2×C4H(5,𝔽2)×C15111yescharacteristic
735C2×C4H(5,𝔽2)×C15111yescharacteristic
736C2×C42−1+4×C15111yescharacteristic
737C2×C42−1+4×C15111yescharacteristic
738C8—41no—
739C8—41no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22C22×C22⋊C4×C15111yescharacteristic
768C22#520×C15111yescharacteristic
769C22#520×C15111yescharacteristic
770C22C2×#131×C15111yescharacteristic
771C22C2×#131×C15111yescharacteristic
772C22#568×C15111yescharacteristic
773C22#568×C15111yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—22no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4#535×C15111yescharacteristic
786C4#536×C15111yescharacteristic
787C4#537×C15111yescharacteristic
788C4#537×C15111yescharacteristic
789C2—42no—
790C2—42no—
791C2—81no—
792C2#2311×C15111yescharacteristic
793C2#2880×C15111yescharacteristic
794C2#2880×C15111yescharacteristic
795C2#2992×C15111yescharacteristic
796C2#2993×C15111yescharacteristic
797C2#2994×C15111yescharacteristic
798C2#2995×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. C2×#433×C151C2semidirect
3. C2×#424×C151C2semidirect
4. #1985×C151C2semidirect
5. #1984×C151C2semidirect
6. #1955×C151C2semidirect
7. #1954×C151C2semidirect
8. #1870×C151C2semidirect
9. #1870×C151C2semidirect
10. #1869×C151C2semidirect
11. #1869×C151C2semidirect
12. #1798×C151C2semidirect
13. #1798×C151C2semidirect
14. #1797×C151C2semidirect
15. #1797×C151C2semidirect
399. #21855C151direct (N × H)
400. C151#21855direct (N × H)
402. C2×#433C2×C151semidirect
403. C2×#424C2×C151semidirect
404. #1985C2×C151semidirect
405. #1984C2×C151semidirect
406. #1955C2×C151semidirect
407. #1954C2×C151semidirect
408. #1870C2×C151semidirect
409. #1870C2×C151semidirect
410. #1869C2×C151semidirect
411. #1869C2×C151semidirect
412. #1798C2×C151semidirect
413. #1798C2×C151semidirect
414. #1797C2×C151semidirect
415. #1797C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#529×C1512
C2×#433×C1512
C2×#424×C1512
#1985×C1512
#1984×C1512
#1955×C1512
#1954×C1512
#1870×C1512
#1869×C1512
#1798×C1512
#1797×C1512
#21855151