Finite Group Databasebeta

← C151×#14816 #50319741

Subgroups — C151×#14816 #50319741

Order 38656.

1510 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#398×C151C211yesmaximal, characteristic
2C2×#395×C151C211yesmaximal, characteristic
3C2×#395×C151C211yesmaximal, characteristic
4C2×#391×C151C211yesmaximal, characteristic
5C2×#389×C151C211yesmaximal, characteristic
6C2×C4×C4⋊C4×C151C211yesmaximal, characteristic
7#1444×C151C211yesmaximal, characteristic
8#1444×C151C211yesmaximal, characteristic
9#1441×C151C211yesmaximal, characteristic
10#1441×C151C211yesmaximal, characteristic
11#1441×C151C211yesmaximal, characteristic
12#1436×C151C211yesmaximal, characteristic
13#1436×C151C211yesmaximal, characteristic
14C4⋊#95×C151C211yesmaximal, characteristic
15#1434×C151C211yesmaximal, characteristic
16C23×Q8×C151C2211yescharacteristic
17C22×C4⋊C4×C151C2211yescharacteristic
18C22×C4⋊C4×C151C2211yescharacteristic
19C22×C4⋊C4×C151C2211yescharacteristic
20C22×C4⋊C4×C151C2211yescharacteristic
21C22×C4⋊C4×C151C2211yescharacteristic
22C22×C4⋊C4×C151C2211yescharacteristic
23C22×C4⋊C4×C151C2211yescharacteristic
24C22×C4⋊C4×C151C2211yescharacteristic
25C22×C4⋊C4×C151C2211yescharacteristic
26C22×C4⋊C4×C151C2211yescharacteristic
27C22×C4⋊C4×C151C2211yescharacteristic
28C22×C42×C151C2211yescharacteristic
29C22×C42×C151C2211yescharacteristic
30C22×C42×C151C2211yescharacteristic
31#398×C151—24no—
32#395×C151—24no—
33#395×C151—24no—
34#391×C151—24no—
35#389×C151—24no—
36C4×C4⋊C4×C151—24no—
37C2×#95×C151C2211yescharacteristic
38C2×#95×C151C2211yescharacteristic
39C2×#95×C151C2211yescharacteristic
40C2×#95×C151C2211yescharacteristic
41C2×#95×C151C2211yescharacteristic
42C2×#95×C151C2211yescharacteristic
43C2×#95×C151C2211yescharacteristic
44C2×#95×C151C2211yescharacteristic
45C2×#95×C151C2211yescharacteristic
46C2×#95×C151C2211yescharacteristic
47C2×#95×C151C2211yescharacteristic
48C2×#95×C151C2211yescharacteristic
49C2×#95×C151C2211yescharacteristic
50C2×#95×C151C2211yescharacteristic
51C2×#95×C151C2211yescharacteristic
52C2×#95×C151C2211yescharacteristic
53C2×#95×C151C2211yescharacteristic
54C2×#95×C151C2211yescharacteristic
55C2×#95×C151C2211yescharacteristic
56C2×#95×C151C2211yescharacteristic
57C22×Q8×C151—22no—
58C22×Q8×C151—22no—
59C22×Q8×C151—22no—
60C22×Q8×C151—22no—
61C22×Q8×C151—22no—
62C22×Q8×C151—41no—
63C22×Q8×C151—41no—
64C23×C4×C151C2311yescharacteristic
65C23×C4×C151C2311yescharacteristic
66C23×C4×C151C2311yescharacteristic
67C23×C4×C151C2311yescharacteristic
68C23×C4×C151C2311yescharacteristic
69C23×C4×C151C2311yescharacteristic
70C23×C4×C151C2311yescharacteristic
71C23×C4×C151C2311yescharacteristic
72C23×C4×C151C2311yescharacteristic
73C23×C4×C151C2311yescharacteristic
74C23×C4×C151C2311yescharacteristic
75C23×C4×C151C2311yescharacteristic
76C23×C4×C151C2311yescharacteristic
77C23×C4×C151C2311yescharacteristic
78C23×C4×C151C2311yescharacteristic
79C2×C4⋊C4×C151—22no—
80C2×C4⋊C4×C151—22no—
81C2×C4⋊C4×C151—22no—
82C2×C4⋊C4×C151—22no—
83C2×C4⋊C4×C151—22no—
84C2×C4⋊C4×C151—22no—
85C2×C4⋊C4×C151—22no—
86C2×C4⋊C4×C151—22no—
87C2×C4⋊C4×C151—22no—
88C2×C4⋊C4×C151—22no—
89C2×C4⋊C4×C151—22no—
90C2×C4⋊C4×C151—22no—
91C2×C4⋊C4×C151—22no—
92C2×C4⋊C4×C151—22no—
93C2×C4⋊C4×C151—22no—
94C2×C4⋊C4×C151—22no—
95C2×C4⋊C4×C151—22no—
96C2×C4⋊C4×C151—22no—
97C2×C4⋊C4×C151—22no—
98C2×C4⋊C4×C151—22no—
99C2×C4⋊C4×C151—22no—
100C2×C4⋊C4×C151—22no—
101C2×C4⋊C4×C151—22no—
102C2×C4⋊C4×C151—22no—
103C2×C4⋊C4×C151—41no—
104C2×C4⋊C4×C151—41no—
105C2×C4⋊C4×C151—41no—
106C2×C4⋊C4×C151—41no—
107C2×C4⋊C4×C151—41no—
108C2×C4⋊C4×C151—41no—
109C2×C4⋊C4×C151—41no—
110C2×C4⋊C4×C151D414yes—
111C2×C4⋊C4×C151Q814yescomplemented
112C2×C42×C151—22no—
113C2×C42×C151—22no—
114C2×C42×C151—22no—
115C2×C42×C151—22no—
116C2×C42×C151—22no—
117C2×C42×C151—22no—
118C2×C42×C151—41no—
119C2×C42×C151—41no—
120C2×C42×C151Q814yescomplemented
121#95×C151—22no—
122#95×C151—22no—
123#95×C151—22no—
124#95×C151—22no—
125#95×C151—22no—
126#95×C151—22no—
127#95×C151—22no—
128#95×C151—22no—
129#95×C151—22no—
130#95×C151—22no—
131#95×C151—22no—
132#95×C151—22no—
133#95×C151—22no—
134#95×C151—22no—
135#95×C151—22no—
136#95×C151—22no—
137#95×C151—41no—
138#95×C151D414yes—
139#95×C151D414yes—
140#95×C151Q814yescomplemented
141C24×C151C2411yescharacteristic
142C2×Q8×C151—28no—
143C2×Q8×C151—44no—
144C2×Q8×C151—44no—
145C2×Q8×C151—44no—
146C2×Q8×C151—44no—
147C2×Q8×C151—44no—
148C2×Q8×C151—44no—
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—21no—
167C22×C4×C151—21no—
168C22×C4×C151—21no—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—21no—
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—21no—
188C22×C4×C151—21no—
189C22×C4×C151—21no—
190C22×C4×C151—21no—
191C22×C4×C151—21no—
192C22×C4×C151—21no—
193C22×C4×C151—21no—
194C22×C4×C151—21no—
195C22×C4×C151—21no—
196C22×C4×C151—21no—
197C22×C4×C151—21no—
198C22×C4×C151—21no—
199C22×C4×C151—21no—
200C22×C4×C151—21no—
201C22×C4×C151—21no—
202C22×C4×C151—21no—
203C22×C4×C151—21no—
204C22×C4×C151—21no—
205C22×C4×C151—21no—
206C22×C4×C151—21no—
207C22×C4×C151—21no—
208C22×C4×C151—21no—
209C22×C4×C151—21no—
210C22×C4×C151—21no—
211C22×C4×C151—21no—
212C22×C4×C151—21no—
213C22×C4×C151—21no—
214C22×C4×C151—21no—
215C22×C4×C151—21no—
216C22×C4×C151—21no—
217C22×C4×C151—21no—
218C22×C4×C151—21no—
219C22×C4×C151—21no—
220C22×C4×C151—21no—
221C22×C4×C151—21no—
222C22×C4×C151—21no—
223C22×C4×C151—21no—
224C22×C4×C151—21no—
225C22×C4×C151—21no—
226C22×C4×C151—21no—
227C22×C4×C151—21no—
228C22×C4×C151—21no—
229C22×C4×C151—21no—
230C22×C4×C151—21no—
231C22×C4×C151C2×D412yes—
232C22×C4×C151C2×D412yes—
233C22×C4×C151C2×D412yes—
234C22×C4×C151C2×D412yes—
235C22×C4×C151C2×D412yes—
236C22×C4×C151C2×D412yes—
237C22×C4×C151C2×D412yes—
238C22×C4×C151C2×D412yes—
239C22×C4×C151C2×D412yes—
240C22×C4×C151C2×Q812yes—
241C22×C4×C151C2×Q812yes—
242C22×C4×C151C2×Q812yes—
243C22×C4×C151C2×Q812yes—
244C22×C4×C151C2×Q812yes—
245C22×C4×C151C2×Q812yes—
246C22×C4×C151C2×Q812yes—
247C22×C4×C151C2×Q812yes—
248C22×C4×C151C2×Q812yes—
249C22×C4×C151#4112yes—
250C22×C4×C151#4112yes—
251C22×C4×C151#4112yes—
252C22×C4×C151#4112yes—
253C22×C4×C151#4112yes—
254C4⋊C4×C151—28no—
255C4⋊C4×C151—28no—
256C4⋊C4×C151—28no—
257C4⋊C4×C151—44no—
258C4⋊C4×C151—44no—
259C4⋊C4×C151—44no—
260C4⋊C4×C151—44no—
261C4⋊C4×C151—44no—
262C4⋊C4×C151—44no—
263C4⋊C4×C151—44no—
264C4⋊C4×C151—44no—
265C42×C151—28no—
266C42×C151—44no—
267C42×C151—44no—
268C23×C151C22×D411yescharacteristic
269C23×C151C22×D411yescharacteristic
270C23×C151C22×D411yescharacteristic
271C23×C151C22×Q811yescharacteristic
272C23×C151C22×Q811yescharacteristic
273C23×C151C22×Q811yescharacteristic
274C23×C151C2×#4111yescharacteristic
275C23×C151C2×#4111yescharacteristic
276C23×C151C2×#4111yescharacteristic
277C23×C151C2×#4111yescharacteristic
278C23×C151C2×#4111yescharacteristic
279C23×C151H(5,𝔽2)11yescharacteristic
280C23×C151H(5,𝔽2)11yescharacteristic
281C23×C1512−1+411yescharacteristic
282C23×C1512−1+411yescharacteristic
283Q8×C151—416no—
284C2×C4×C151—22no—
285C2×C4×C151—22no—
286C2×C4×C151—22no—
287C2×C4×C151—22no—
288C2×C4×C151—22no—
289C2×C4×C151—22no—
290C2×C4×C151—22no—
291C2×C4×C151—22no—
292C2×C4×C151—22no—
293C2×C4×C151—22no—
294C2×C4×C151—22no—
295C2×C4×C151—22no—
296C2×C4×C151—22no—
297C2×C4×C151—22no—
298C2×C4×C151—22no—
299C2×C4×C151—22no—
300C2×C4×C151—22no—
301C2×C4×C151—22no—
302C2×C4×C151—22no—
303C2×C4×C151—22no—
304C2×C4×C151—22no—
305C2×C4×C151—22no—
306C2×C4×C151—22no—
307C2×C4×C151—22no—
308C2×C4×C151—22no—
309C2×C4×C151—22no—
310C2×C4×C151—22no—
311C2×C4×C151—22no—
312C2×C4×C151—22no—
313C2×C4×C151—22no—
314C2×C4×C151—22no—
315C2×C4×C151—22no—
316C2×C4×C151—22no—
317C2×C4×C151—22no—
318C2×C4×C151—22no—
319C2×C4×C151—22no—
320C2×C4×C151—22no—
321C2×C4×C151—22no—
322C2×C4×C151—22no—
323C2×C4×C151—22no—
324C2×C4×C151—22no—
325C2×C4×C151—22no—
326C2×C4×C151—22no—
327C2×C4×C151—22no—
328C2×C4×C151—22no—
329C2×C4×C151—22no—
330C2×C4×C151—22no—
331C2×C4×C151—22no—
332C2×C4×C151—22no—
333C2×C4×C151—22no—
334C2×C4×C151—22no—
335C2×C4×C151—22no—
336C2×C4×C151—22no—
337C2×C4×C151—22no—
338C2×C4×C151—41no—
339C2×C4×C151—41no—
340C2×C4×C151—41no—
341C2×C4×C151—41no—
342C2×C4×C151—41no—
343C2×C4×C151—41no—
344C2×C4×C151—41no—
345C2×C4×C151—41no—
346C2×C4×C151—41no—
347C2×C4×C151—41no—
348C2×C4×C151—41no—
349C2×C4×C151—41no—
350C2×C4×C151—41no—
351C2×C4×C151—41no—
352C2×C4×C151—41no—
353C2×C4×C151—41no—
354C2×C4×C151—41no—
355C2×C4×C151—41no—
356C2×C4×C151—41no—
357C2×C4×C151—41no—
358C2×C4×C151—41no—
359C2×C4×C151—41no—
360C2×C4×C151—41no—
361C2×C4×C151—41no—
362C2×C4×C151—41no—
363C2×C4×C151—41no—
364C2×C4×C151—41no—
365C2×C4×C151—41no—
366C2×C4×C151—41no—
367C2×C4×C151—41no—
368C2×C4×C151—41no—
369C2×C4×C151—41no—
370C2×C4×C151—41no—
371C2×C4×C151—41no—
372C2×C4×C151—41no—
373C2×C4×C151—41no—
374C2×C4×C151—41no—
375C2×C4×C151—41no—
376C2×C4×C151—41no—
377C2×C4×C151—41no—
378C2×C4×C151—41no—
379C2×C4×C151—41no—
380C2×C4×C151—41no—
381C2×C4×C151—41no—
382C2×C4×C151—41no—
383C2×C4×C151—41no—
384C2×C4×C151#12114yes—
385C2×C4×C151C22⋊Q814yes—
386C2×C4×C151C22⋊Q814yes—
387C2×C4×C151C4⋊Q814yes—
388C2×C4×C151C4⋊Q814yes—
389C22×C151C2×#12111yescharacteristic
390C22×C151C2×C22⋊Q811yescharacteristic
391C22×C151C2×C22⋊Q811yescharacteristic
392C22×C151#52511yescharacteristic
393C22×C151#52511yescharacteristic
394C22×C151C2×C4⋊Q811yescharacteristic
395C22×C151C2×C4⋊Q811yescharacteristic
396C22×C151#53211yescharacteristic
397C22×C151#53311yescharacteristic
398C22×C151#53311yescharacteristic
399C22×C151#53311yescharacteristic
400C22×C151#53311yescharacteristic
401C22×C151#53311yescharacteristic
402C22×C151#53811yescharacteristic
403C22×C151#53911yescharacteristic
404C22×C151#54111yescharacteristic
405C22×C151#54211yescharacteristic
406C22×C151#54411yescharacteristic
407C22×C151#54411yescharacteristic
408C22×C151D4211yescharacteristic
409C22×C151D4211yescharacteristic
410C22×C151#54611yescharacteristic
411C22×C151#54611yescharacteristic
412C22×C151#54711yescharacteristic
413C22×C151#54711yescharacteristic
414C22×C151#54811yescharacteristic
415C22×C151D4×Q811yescharacteristic
416C22×C151D4×Q811yescharacteristic
417C22×C151D4×Q811yescharacteristic
418C22×C151#55111yescharacteristic
419C22×C151#55211yescharacteristic
420C22×C151#55411yescharacteristic
421C22×C151#55411yescharacteristic
422C22×C151#55711yescharacteristic
423C22×C151Q8211yescharacteristic
424C4×C151—24no—
425C4×C151—24no—
426C4×C151—24no—
427C4×C151—24no—
428C4×C151—24no—
429C4×C151—42no—
430C4×C151—42no—
431C4×C151—42no—
432C4×C151—42no—
433C4×C151—42no—
434C4×C151—42no—
435C4×C151—42no—
436C4×C151—42no—
437C4×C151—81no—
438C4×C151—81no—
439C2×C151#239911yescharacteristic
440C2×C151#242411yescharacteristic
441C2×C151#242911yescharacteristic
442C2×C151#243811yescharacteristic
443C2×C151#244011yescharacteristic
444C2×C151#244911yescharacteristic
445C2×C151#245111yescharacteristic
446C2×C151#246111yescharacteristic
447C2×C151#246211yescharacteristic
448C2×C151#255011yescharacteristic
449C2×C151#255111yescharacteristic
450C2×C151#255611yescharacteristic
451C2×C151#258611yescharacteristic
452C2×C151#266611yescharacteristic
453C2×C151#285711yescharacteristic
454#14816C15111yesmaximal, characteristic, direct product factor, Sylow
455C151#1481611yescharacteristic, direct product factor, Sylow
456C2×#398C2×C15111yescharacteristic
457C2×#395C2×C15111yescharacteristic
458C2×#395C2×C15111yescharacteristic
459C2×#391C2×C15111yescharacteristic
460C2×#389C2×C15111yescharacteristic
461C2×C4×C4⋊C4C2×C15111yescharacteristic
462#1444C2×C15111yescharacteristic
463#1444C2×C15111yescharacteristic
464#1441C2×C15111yescharacteristic
465#1441C2×C15111yescharacteristic
466#1441C2×C15111yescharacteristic
467#1436C2×C15111yescharacteristic
468#1436C2×C15111yescharacteristic
469C4⋊#95C2×C15111yescharacteristic
470#1434C2×C15111yescharacteristic
471C23×Q8C22×C15111yescharacteristic
472C22×C4⋊C4C22×C15111yescharacteristic
473C22×C4⋊C4C22×C15111yescharacteristic
474C22×C4⋊C4C22×C15111yescharacteristic
475C22×C4⋊C4C22×C15111yescharacteristic
476C22×C4⋊C4C22×C15111yescharacteristic
477C22×C4⋊C4C22×C15111yescharacteristic
478C22×C4⋊C4C22×C15111yescharacteristic
479C22×C4⋊C4C22×C15111yescharacteristic
480C22×C4⋊C4C22×C15111yescharacteristic
481C22×C4⋊C4C22×C15111yescharacteristic
482C22×C4⋊C4C22×C15111yescharacteristic
483C22×C42C22×C15111yescharacteristic
484C22×C42C22×C15111yescharacteristic
485C22×C42C22×C15111yescharacteristic
486#398—24no—
487#395—24no—
488#395—24no—
489#391—24no—
490#389—24no—
491C4×C4⋊C4—24no—
492C2×#95C22×C15111yescharacteristic
493C2×#95C22×C15111yescharacteristic
494C2×#95C22×C15111yescharacteristic
495C2×#95C22×C15111yescharacteristic
496C2×#95C22×C15111yescharacteristic
497C2×#95C22×C15111yescharacteristic
498C2×#95C22×C15111yescharacteristic
499C2×#95C22×C15111yescharacteristic
500C2×#95C22×C15111yescharacteristic
501C2×#95C22×C15111yescharacteristic
502C2×#95C22×C15111yescharacteristic
503C2×#95C22×C15111yescharacteristic
504C2×#95C22×C15111yescharacteristic
505C2×#95C22×C15111yescharacteristic
506C2×#95C22×C15111yescharacteristic
507C2×#95C22×C15111yescharacteristic
508C2×#95C22×C15111yescharacteristic
509C2×#95C22×C15111yescharacteristic
510C2×#95C22×C15111yescharacteristic
511C2×#95C22×C15111yescharacteristic
512C22×Q8—22no—
513C22×Q8—22no—
514C22×Q8—22no—
515C22×Q8—22no—
516C22×Q8—22no—
517C22×Q8—41no—
518C22×Q8—41no—
519C23×C4C23×C15111yescharacteristic
520C23×C4C23×C15111yescharacteristic
521C23×C4C23×C15111yescharacteristic
522C23×C4C23×C15111yescharacteristic
523C23×C4C23×C15111yescharacteristic
524C23×C4C23×C15111yescharacteristic
525C23×C4C23×C15111yescharacteristic
526C23×C4C23×C15111yescharacteristic
527C23×C4C23×C15111yescharacteristic
528C23×C4C23×C15111yescharacteristic
529C23×C4C23×C15111yescharacteristic
530C23×C4C23×C15111yescharacteristic
531C23×C4C23×C15111yescharacteristic
532C23×C4C23×C15111yescharacteristic
533C23×C4C23×C15111yescharacteristic
534C2×C4⋊C4—22no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—22no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—22no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—22no—
543C2×C4⋊C4—22no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—22no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—22no—
552C2×C4⋊C4—22no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—41no—
559C2×C4⋊C4—41no—
560C2×C4⋊C4—41no—
561C2×C4⋊C4—41no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4D4×C15114yes—
566C2×C4⋊C4Q8×C15114yescomplemented
567C2×C42—22no—
568C2×C42—22no—
569C2×C42—22no—
570C2×C42—22no—
571C2×C42—22no—
572C2×C42—22no—
573C2×C42—41no—
574C2×C42—41no—
575C2×C42Q8×C15114yescomplemented
576#95—22no—
577#95—22no—
578#95—22no—
579#95—22no—
580#95—22no—
581#95—22no—
582#95—22no—
583#95—22no—
584#95—22no—
585#95—22no—
586#95—22no—
587#95—22no—
588#95—22no—
589#95—22no—
590#95—22no—
591#95—22no—
592#95—41no—
593#95D4×C15114yes—
594#95D4×C15114yes—
595#95Q8×C15114yescomplemented
596C24C24×C15111yescharacteristic
597C2×Q8—28no—
598C2×Q8—44no—
599C2×Q8—44no—
600C2×Q8—44no—
601C2×Q8—44no—
602C2×Q8—44no—
603C2×Q8—44no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4C2×D4×C15112yes—
687C22×C4C2×D4×C15112yes—
688C22×C4C2×D4×C15112yes—
689C22×C4C2×D4×C15112yes—
690C22×C4C2×D4×C15112yes—
691C22×C4C2×D4×C15112yes—
692C22×C4C2×D4×C15112yes—
693C22×C4C2×D4×C15112yes—
694C22×C4C2×D4×C15112yes—
695C22×C4C2×Q8×C15112yes—
696C22×C4C2×Q8×C15112yes—
697C22×C4C2×Q8×C15112yes—
698C22×C4C2×Q8×C15112yes—
699C22×C4C2×Q8×C15112yes—
700C22×C4C2×Q8×C15112yes—
701C22×C4C2×Q8×C15112yes—
702C22×C4C2×Q8×C15112yes—
703C22×C4C2×Q8×C15112yes—
704C22×C4#41×C15112yes—
705C22×C4#41×C15112yes—
706C22×C4#41×C15112yes—
707C22×C4#41×C15112yes—
708C22×C4#41×C15112yes—
709C4⋊C4—28no—
710C4⋊C4—28no—
711C4⋊C4—28no—
712C4⋊C4—44no—
713C4⋊C4—44no—
714C4⋊C4—44no—
715C4⋊C4—44no—
716C4⋊C4—44no—
717C4⋊C4—44no—
718C4⋊C4—44no—
719C4⋊C4—44no—
720C42—28no—
721C42—44no—
722C42—44no—
723C23C22×D4×C15111yescharacteristic
724C23C22×D4×C15111yescharacteristic
725C23C22×D4×C15111yescharacteristic
726C23C22×Q8×C15111yescharacteristic
727C23C22×Q8×C15111yescharacteristic
728C23C22×Q8×C15111yescharacteristic
729C23C2×#41×C15111yescharacteristic
730C23C2×#41×C15111yescharacteristic
731C23C2×#41×C15111yescharacteristic
732C23C2×#41×C15111yescharacteristic
733C23C2×#41×C15111yescharacteristic
734C23H(5,𝔽2)×C15111yescharacteristic
735C23H(5,𝔽2)×C15111yescharacteristic
736C232−1+4×C15111yescharacteristic
737C232−1+4×C15111yescharacteristic
738Q8—416no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4#121×C15114yes—
840C2×C4C22⋊Q8×C15114yes—
841C2×C4C22⋊Q8×C15114yes—
842C2×C4C4⋊Q8×C15114yes—
843C2×C4C4⋊Q8×C15114yes—
844C22C2×#121×C15111yescharacteristic
845C22C2×C22⋊Q8×C15111yescharacteristic
846C22C2×C22⋊Q8×C15111yescharacteristic
847C22#525×C15111yescharacteristic
848C22#525×C15111yescharacteristic
849C22C2×C4⋊Q8×C15111yescharacteristic
850C22C2×C4⋊Q8×C15111yescharacteristic
851C22#532×C15111yescharacteristic
852C22#533×C15111yescharacteristic
853C22#533×C15111yescharacteristic
854C22#533×C15111yescharacteristic
855C22#533×C15111yescharacteristic
856C22#533×C15111yescharacteristic
857C22#538×C15111yescharacteristic
858C22#539×C15111yescharacteristic
859C22#541×C15111yescharacteristic
860C22#542×C15111yescharacteristic
861C22#544×C15111yescharacteristic
862C22#544×C15111yescharacteristic
863C22D42×C15111yescharacteristic
864C22D42×C15111yescharacteristic
865C22#546×C15111yescharacteristic
866C22#546×C15111yescharacteristic
867C22#547×C15111yescharacteristic
868C22#547×C15111yescharacteristic
869C22#548×C15111yescharacteristic
870C22D4×Q8×C15111yescharacteristic
871C22D4×Q8×C15111yescharacteristic
872C22D4×Q8×C15111yescharacteristic
873C22#551×C15111yescharacteristic
874C22#552×C15111yescharacteristic
875C22#554×C15111yescharacteristic
876C22#554×C15111yescharacteristic
877C22#557×C15111yescharacteristic
878C22Q82×C15111yescharacteristic
879C4—24no—
880C4—24no—
881C4—24no—
882C4—24no—
883C4—24no—
884C4—42no—
885C4—42no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—42no—
891C4—42no—
892C4—81no—
893C4—81no—
894C2#2399×C15111yescharacteristic
895C2#2424×C15111yescharacteristic
896C2#2429×C15111yescharacteristic
897C2#2438×C15111yescharacteristic
898C2#2440×C15111yescharacteristic
899C2#2449×C15111yescharacteristic
900C2#2451×C15111yescharacteristic
901C2#2461×C15111yescharacteristic
902C2#2462×C15111yescharacteristic
903C2#2550×C15111yescharacteristic
904C2#2551×C15111yescharacteristic
905C2#2556×C15111yescharacteristic
906C2#2586×C15111yescharacteristic
907C2#2666×C15111yescharacteristic
908C2#2857×C15111yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C151C24
commutator, Frattini, cosocleC24C24×C151
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
111. C2×C4⋊C4×C151Q8semidirect
120. C2×C42×C151Q8semidirect
140. #95×C151Q8semidirect
454. #14816C151direct (N × H)
455. C151#14816direct (N × H)
566. C2×C4⋊C4Q8×C151semidirect
575. C2×C42Q8×C151semidirect
595. #95Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#398×C1512
C2×#395×C1512
C2×#391×C1512
C2×#389×C1512
C2×C4×C4⋊C4×C1512
#1444×C1512
#1441×C1512
#1436×C1512
C4⋊#95×C1512
#1434×C1512
#14816151