Finite Group Databasebeta

← C151×#15280 #50320205

Subgroups — C151×#15280 #50320205

Order 38656.

2142 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Q8×C151C211yesmaximal, characteristic, complemented
2C2×#396×C151C211yesmaximal, characteristic, complemented
3C2×#393×C151C211yesmaximal, characteristic, complemented
4C2×#391×C151C211yesmaximal, characteristic, complemented
5C2×#390×C151C211yesmaximal, characteristic
6C2×#386×C151C211yesmaximal, characteristic
7#1444×C151C211yesmaximal, characteristic, complemented
8#1441×C151C211yesmaximal, characteristic, complemented
9#1439×C151C211yesmaximal, characteristic, complemented
10#1439×C151C211yesmaximal, characteristic, complemented
11#1439×C151C211yesmaximal, characteristic, complemented
12#1439×C151C211yesmaximal, characteristic, complemented
13#1438×C151C211yesmaximal, characteristic
14#1436×C151C211yesmaximal, characteristic, complemented
15C22⋊#95×C151C211yesmaximal, characteristic, complemented
16C23×Q8×C151C2211yescharacteristic
17C23×D4×C151C2211yescharacteristic
18C24×C4×C151C2211yescharacteristic
19C2×C22⋊Q8×C151—24no—
20C2×C22⋊Q8×C151—24no—
21C2×C22⋊Q8×C151—24no—
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×C22⋊C4×C151C2211yescharacteristic
29C22×C22⋊C4×C151C2211yescharacteristic
30C22×C22⋊C4×C151C2211yescharacteristic
31C22×C22⋊C4×C151C2211yescharacteristic
32C22×C22⋊C4×C151C2211yescharacteristic
33C22×C22⋊C4×C151C2211yescharacteristic
34C22×C22⋊C4×C151C2211yescharacteristic
35C22×C22⋊C4×C151C2211yescharacteristic
36C22×C22⋊C4×C151C2211yescharacteristic
37C22×C22⋊C4×C151C2211yescharacteristic
38C22×C22⋊C4×C151C2211yescharacteristic
39C22×C42×C151C2211yescharacteristic
40#396×C151—24no—
41#393×C151—24no—
42#391×C151—24no—
43#390×C151—24no—
44#386×C151—24no—
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
57C2×#95×C151C2211yescharacteristic
58C2×#95×C151C2211yescharacteristic
59C25×C151C2311yescharacteristic
60C25×C151C2311yescharacteristic
61C22×Q8×C151—22no—
62C22×Q8×C151—22no—
63C22×Q8×C151—22no—
64C22×Q8×C151—22no—
65C22×Q8×C151—41no—
66C22×Q8×C151—41no—
67C22×Q8×C151D414yescomplemented
68C22×D4×C151—22no—
69C22×D4×C151—22no—
70C22×D4×C151—22no—
71C22×D4×C151—22no—
72C22×D4×C151—41no—
73C22×D4×C151—41no—
74C22×D4×C151Q814yescomplemented
75C23×C4×C151—22no—
76C23×C4×C151—22no—
77C23×C4×C151—22no—
78C23×C4×C151—22no—
79C23×C4×C151—22no—
80C23×C4×C151—41no—
81C23×C4×C151—41no—
82C23×C4×C151C2311yescharacteristic
83C23×C4×C151C2311yescharacteristic
84C23×C4×C151C2311yescharacteristic
85C23×C4×C151C2311yescharacteristic
86C23×C4×C151C2311yescharacteristic
87C23×C4×C151C2311yescharacteristic
88C23×C4×C151C2311yescharacteristic
89C23×C4×C151C2311yescharacteristic
90C23×C4×C151C2311yescharacteristic
91C23×C4×C151C2311yescharacteristic
92C23×C4×C151C2311yescharacteristic
93C23×C4×C151C2311yescharacteristic
94C23×C4×C151C2311yescharacteristic
95C22⋊Q8×C151—232no—
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—22no—
104C2×C4⋊C4×C151—22no—
105C2×C4⋊C4×C151—22no—
106C2×C4⋊C4×C151—22no—
107C2×C4⋊C4×C151—22no—
108C2×C4⋊C4×C151—22no—
109C2×C4⋊C4×C151—41no—
110C2×C4⋊C4×C151—41no—
111C2×C4⋊C4×C151—41no—
112C2×C4⋊C4×C151—41no—
113C2×C4⋊C4×C151D414yescomplemented
114C2×C22⋊C4×C151—22no—
115C2×C22⋊C4×C151—22no—
116C2×C22⋊C4×C151—22no—
117C2×C22⋊C4×C151—22no—
118C2×C22⋊C4×C151—22no—
119C2×C22⋊C4×C151—22no—
120C2×C22⋊C4×C151—22no—
121C2×C22⋊C4×C151—22no—
122C2×C22⋊C4×C151—22no—
123C2×C22⋊C4×C151—22no—
124C2×C22⋊C4×C151—22no—
125C2×C22⋊C4×C151—22no—
126C2×C22⋊C4×C151—22no—
127C2×C22⋊C4×C151—22no—
128C2×C22⋊C4×C151—22no—
129C2×C22⋊C4×C151—22no—
130C2×C22⋊C4×C151—22no—
131C2×C22⋊C4×C151—22no—
132C2×C22⋊C4×C151—22no—
133C2×C22⋊C4×C151—22no—
134C2×C22⋊C4×C151—22no—
135C2×C22⋊C4×C151—22no—
136C2×C22⋊C4×C151—41no—
137C2×C22⋊C4×C151—41no—
138C2×C22⋊C4×C151—41no—
139C2×C22⋊C4×C151—41no—
140C2×C22⋊C4×C151—41no—
141C2×C22⋊C4×C151—41no—
142C2×C22⋊C4×C151—41no—
143C2×C22⋊C4×C151—41no—
144C2×C22⋊C4×C151—41no—
145C2×C22⋊C4×C151—41no—
146C2×C22⋊C4×C151D414yes—
147C2×C42×C151—22no—
148C2×C42×C151—22no—
149C2×C42×C151—41no—
150#95×C151—22no—
151#95×C151—22no—
152#95×C151—22no—
153#95×C151—22no—
154#95×C151—22no—
155#95×C151—22no—
156#95×C151—22no—
157#95×C151—22no—
158#95×C151—22no—
159#95×C151—22no—
160#95×C151—41no—
161#95×C151—41no—
162#95×C151—41no—
163#95×C151D414yes—
164C24×C151—21no—
165C24×C151—21no—
166C24×C151—21no—
167C24×C151—21no—
168C24×C151—21no—
169C24×C151—21no—
170C24×C151—21no—
171C24×C151—21no—
172C24×C151—21no—
173C24×C151—21no—
174C24×C151—21no—
175C24×C151—21no—
176C24×C151—21no—
177C24×C151—21no—
178C24×C151—21no—
179C24×C151—21no—
180C24×C151—21no—
181C24×C151—21no—
182C24×C151—21no—
183C24×C151—21no—
184C24×C151—21no—
185C24×C151—21no—
186C24×C151—21no—
187C24×C151—21no—
188C24×C151—21no—
189C24×C151—21no—
190C24×C151C2×D412yes—
191C24×C151C2×Q812yes—
192C24×C151C2×Q812yes—
193C24×C151#4112yes—
194C24×C151C2411yescharacteristic
195C2×Q8×C151—28no—
196C2×Q8×C151—28no—
197C2×Q8×C151—44no—
198C2×Q8×C151—44no—
199C2×Q8×C151—44no—
200C2×Q8×C151—44no—
201C2×Q8×C151—44no—
202C2×D4×C151—28no—
203C2×D4×C151—28no—
204C2×D4×C151—44no—
205C2×D4×C151—44no—
206C2×D4×C151—44no—
207C2×D4×C151—44no—
208C2×D4×C151—44no—
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—28no—
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×C151—21no—
232C22×C4×C151—21no—
233C22×C4×C151—21no—
234C22×C4×C151—21no—
235C22×C4×C151—21no—
236C22×C4×C151—21no—
237C22×C4×C151—21no—
238C22×C4×C151—21no—
239C22×C4×C151—21no—
240C22×C4×C151—21no—
241C22×C4×C151—21no—
242C22×C4×C151—21no—
243C22×C4×C151—21no—
244C22×C4×C151—21no—
245C22×C4×C151—21no—
246C22×C4×C151—21no—
247C22×C4×C151—21no—
248C22×C4×C151—21no—
249C22×C4×C151—21no—
250C22×C4×C151—21no—
251C22×C4×C151—21no—
252C22×C4×C151—21no—
253C22×C4×C151—21no—
254C22×C4×C151—21no—
255C22×C4×C151—21no—
256C22×C4×C151—21no—
257C22×C4×C151—21no—
258C22×C4×C151—21no—
259C22×C4×C151—21no—
260C22×C4×C151—21no—
261C22×C4×C151—21no—
262C22×C4×C151—21no—
263C22×C4×C151—21no—
264C22×C4×C151—21no—
265C22×C4×C151—21no—
266C22×C4×C151—21no—
267C22×C4×C151—21no—
268C22×C4×C151—21no—
269C22×C4×C151—21no—
270C22×C4×C151—21no—
271C22×C4×C151—21no—
272C22×C4×C151—21no—
273C22×C4×C151—21no—
274C22×C4×C151—21no—
275C22×C4×C151—21no—
276C22×C4×C151—21no—
277C22×C4×C151—21no—
278C22×C4×C151—21no—
279C22×C4×C151—21no—
280C22×C4×C151—21no—
281C22×C4×C151—21no—
282C22×C4×C151—21no—
283C22×C4×C151—21no—
284C22×C4×C151—21no—
285C22×C4×C151—21no—
286C22×C4×C151—44no—
287C22×C4×C151—44no—
288C22×C4×C151—44no—
289C22×C4×C151—44no—
290C22×C4×C151—44no—
291C22×C4×C151—44no—
292C22×C4×C151C2×D412yes—
293C22×C4×C151C2×D412yes—
294C22×C4×C151C2×D412yes—
295C22×C4×C151C2×D412yes—
296C22×C4×C151C2×D412yes—
297C22×C4×C151C2×D412yes—
298C22×C4×C151C2×D412yes—
299C22×C4×C151C2×D412yes—
300C22×C4×C151C2×D412yes—
301C22×C4×C151C2×D412yes—
302C22×C4×C151C2×D412yes—
303C22×C4×C151C2×Q812yes—
304C22×C4×C151#4112yes—
305C22×C4×C151#4112yes—
306C22×C4×C151#4112yes—
307C4⋊C4×C151—28no—
308C4⋊C4×C151—28no—
309C4⋊C4×C151—28no—
310C4⋊C4×C151—44no—
311C4⋊C4×C151—44no—
312C4⋊C4×C151—44no—
313C22⋊C4×C151—28no—
314C22⋊C4×C151—28no—
315C22⋊C4×C151—44no—
316C22⋊C4×C151—44no—
317C22⋊C4×C151—44no—
318C22⋊C4×C151—44no—
319C22⋊C4×C151—44no—
320C22⋊C4×C151—44no—
321C22⋊C4×C151—44no—
322C22⋊C4×C151—44no—
323C22⋊C4×C151—44no—
324C42×C151—44no—
325C23×C151—22no—
326C23×C151—22no—
327C23×C151—22no—
328C23×C151—22no—
329C23×C151—22no—
330C23×C151—22no—
331C23×C151—22no—
332C23×C151—22no—
333C23×C151—22no—
334C23×C151—22no—
335C23×C151—22no—
336C23×C151—22no—
337C23×C151—22no—
338C23×C151—22no—
339C23×C151—22no—
340C23×C151—22no—
341C23×C151—22no—
342C23×C151—22no—
343C23×C151—22no—
344C23×C151—22no—
345C23×C151—22no—
346C23×C151—22no—
347C23×C151—22no—
348C23×C151—22no—
349C23×C151—22no—
350C23×C151—41no—
351C23×C151—41no—
352C23×C151—41no—
353C23×C151—41no—
354C23×C151—41no—
355C23×C151—41no—
356C23×C151—41no—
357C23×C151—41no—
358C23×C151—41no—
359C23×C151—41no—
360C23×C151—41no—
361C23×C151—41no—
362C23×C151—41no—
363C23×C151—41no—
364C23×C151—41no—
365C23×C151—41no—
366C23×C151—41no—
367C23×C151—41no—
368C23×C151—41no—
369C23×C151—41no—
370C23×C151—41no—
371C23×C151—41no—
372C23×C151—41no—
373C23×C151—41no—
374C23×C151—41no—
375C23×C151—41no—
376C23×C151—41no—
377C23×C151—41no—
378C23×C151—41no—
379C23×C151—41no—
380C23×C151—41no—
381C23×C151—41no—
382C23×C151—41no—
383C23×C151—41no—
384C23×C151—41no—
385C23×C151—41no—
386C23×C151—41no—
387C23×C151—41no—
388C23×C151—41no—
389C23×C151—41no—
390C23×C151—41no—
391C23×C151—41no—
392C23×C151—41no—
393C23×C151—41no—
394C23×C151C22⋊Q814yes—
395C23×C151C22×D411yescharacteristic
396C23×C151C22×D411yescharacteristic
397C23×C151C22×D411yescharacteristic
398C23×C151C22×D411yescharacteristic
399C23×C151C22×Q811yescharacteristic
400C23×C151C2×#4111yescharacteristic
401C23×C151C2×#4111yescharacteristic
402C23×C151C2×#4111yescharacteristic
403C23×C151C2×#4111yescharacteristic
404C23×C151H(5,𝔽2)11yescharacteristic
405C23×C151H(5,𝔽2)11yescharacteristic
406C23×C151H(5,𝔽2)11yescharacteristic
407C23×C151H(5,𝔽2)11yescharacteristic
408C23×C1512−1+411yescharacteristic
409C23×C1512−1+411yescharacteristic
410Q8×C151—416no—
411D4×C151—416no—
412C2×C4×C151—22no—
413C2×C4×C151—22no—
414C2×C4×C151—22no—
415C2×C4×C151—22no—
416C2×C4×C151—22no—
417C2×C4×C151—22no—
418C2×C4×C151—22no—
419C2×C4×C151—22no—
420C2×C4×C151—22no—
421C2×C4×C151—22no—
422C2×C4×C151—22no—
423C2×C4×C151—22no—
424C2×C4×C151—22no—
425C2×C4×C151—22no—
426C2×C4×C151—22no—
427C2×C4×C151—22no—
428C2×C4×C151—22no—
429C2×C4×C151—22no—
430C2×C4×C151—22no—
431C2×C4×C151—22no—
432C2×C4×C151—22no—
433C2×C4×C151—22no—
434C2×C4×C151—22no—
435C2×C4×C151—22no—
436C2×C4×C151—22no—
437C2×C4×C151—22no—
438C2×C4×C151—22no—
439C2×C4×C151—22no—
440C2×C4×C151—22no—
441C2×C4×C151—22no—
442C2×C4×C151—22no—
443C2×C4×C151—22no—
444C2×C4×C151—22no—
445C2×C4×C151—22no—
446C2×C4×C151—22no—
447C2×C4×C151—22no—
448C2×C4×C151—416no—
449C2×C4×C151—41no—
450C2×C4×C151—41no—
451C2×C4×C151—41no—
452C2×C4×C151—41no—
453C2×C4×C151—41no—
454C2×C4×C151—41no—
455C2×C4×C151—41no—
456C2×C4×C151—41no—
457C2×C4×C151—41no—
458C2×C4×C151—41no—
459C2×C4×C151—41no—
460C2×C4×C151—41no—
461C2×C4×C151—41no—
462C2×C4×C151—41no—
463C2×C4×C151—41no—
464C2×C4×C151—41no—
465C2×C4×C151—41no—
466C2×C4×C151—41no—
467C2×C4×C151—41no—
468C2×C4×C151—41no—
469C2×C4×C151—41no—
470C2×C4×C151—41no—
471C2×C4×C151—41no—
472C2×C4×C151—41no—
473C2×C4×C151—41no—
474C2×C4×C151—41no—
475C2×C4×C151—41no—
476C2×C4×C151—41no—
477C2×C4×C151—41no—
478C2×C4×C151—41no—
479C2×C4×C151—41no—
480C2×C4×C151—41no—
481C2×C4×C151—41no—
482C2×C4×C151—41no—
483C2×C4×C151—41no—
484C2×C4×C151—41no—
485C2×C4×C151—41no—
486C2×C4×C151—41no—
487C2×C4×C151—41no—
488C2×C4×C151—41no—
489C2×C4×C151—41no—
490C2×C4×C151—41no—
491C2×C4×C151—41no—
492C2×C4×C151—41no—
493C2×C4×C151—41no—
494C2×C4×C151—41no—
495C2×C4×C151—41no—
496C2×C4×C151—41no—
497C2×C4×C151—41no—
498C2×C4×C151—41no—
499C2×C4×C151—41no—
500C2×C4×C151—41no—
501C2×C4×C151#12014yes—
502C2×C4×C151#12114yes—
503C2×C4×C151C22⋊Q814yescomplemented
504C22×C151—24no—
505C22×C151—24no—
506C22×C151—24no—
507C22×C151—42no—
508C22×C151—42no—
509C22×C151—42no—
510C22×C151—42no—
511C22×C151—42no—
512C22×C151—42no—
513C22×C151—42no—
514C22×C151—42no—
515C22×C151—42no—
516C22×C151—42no—
517C22×C151—42no—
518C22×C151—42no—
519C22×C151—42no—
520C22×C151—42no—
521C22×C151—42no—
522C22×C151—42no—
523C22×C151—42no—
524C22×C151—42no—
525C22×C151—42no—
526C22×C151—81no—
527C22×C151—81no—
528C22×C151—81no—
529C22×C151—81no—
530C22×C151—81no—
531C22×C151—81no—
532C22×C151—81no—
533C22×C151—81no—
534C22×C151C2×#12011yescharacteristic
535C22×C151C2×#12111yescharacteristic
536C22×C151C2×C22⋊Q811yescharacteristic
537C22×C151C2×C22⋊Q811yescharacteristic
538C22×C151#52911yescharacteristic
539C22×C151#53211yescharacteristic
540C22×C151#53411yescharacteristic
541C22×C151#53511yescharacteristic
542C22×C151#53611yescharacteristic
543C22×C151#53711yescharacteristic
544C22×C151#53811yescharacteristic
545C22×C151#53911yescharacteristic
546C22×C151#54211yescharacteristic
547C22×C151#54211yescharacteristic
548C22×C151#54311yescharacteristic
549C22×C151D4211yescharacteristic
550C22×C151D4211yescharacteristic
551C22×C151#54611yescharacteristic
552C22×C151#54611yescharacteristic
553C22×C151#54611yescharacteristic
554C22×C151#54611yescharacteristic
555C22×C151#54611yescharacteristic
556C22×C151#54811yescharacteristic
557C22×C151#54811yescharacteristic
558C22×C151#54811yescharacteristic
559C22×C151D4×Q811yescharacteristic
560C22×C151D4×Q811yescharacteristic
561C22×C151#55011yescharacteristic
562C22×C151#55011yescharacteristic
563C22×C151#55111yescharacteristic
564C22×C151#55411yescharacteristic
565C22×C151#55411yescharacteristic
566C22×C151#55611yescharacteristic
567C22×C151#56211yescharacteristic
568C22×C151#56211yescharacteristic
569C4×C151—24no—
570C4×C151—24no—
571C4×C151—24no—
572C4×C151—42no—
573C4×C151—42no—
574C4×C151—42no—
575C4×C151—42no—
576C4×C151—42no—
577C4×C151—42no—
578C4×C151—81no—
579C4×C151—81no—
580C4×C151—81no—
581C4×C151—81no—
582C2×C151—44no—
583C2×C151—82no—
584C2×C151#240911yescharacteristic
585C2×C151#241011yescharacteristic
586C2×C151#242611yescharacteristic
587C2×C151#243111yescharacteristic
588C2×C151#243711yescharacteristic
589C2×C151#245011yescharacteristic
590C2×C151#245211yescharacteristic
591C2×C151#253811yescharacteristic
592C2×C151#256011yescharacteristic
593C2×C151#267611yescharacteristic
594C2×C151#268111yescharacteristic
595C2×C151#269211yescharacteristic
596C2×C151#270011yescharacteristic
597C2×C151#273011yescharacteristic
598C2×C151#273211yescharacteristic
599#15280C15111yesmaximal, characteristic, direct product factor, Sylow
600C151#1528011yescharacteristic, direct product factor, Sylow
601C22×C22⋊Q8C2×C15111yescharacteristic, complemented
602C2×#396C2×C15111yescharacteristic, complemented
603C2×#393C2×C15111yescharacteristic, complemented
604C2×#391C2×C15111yescharacteristic, complemented
605C2×#390C2×C15111yescharacteristic
606C2×#386C2×C15111yescharacteristic
607#1444C2×C15111yescharacteristic, complemented
608#1441C2×C15111yescharacteristic, complemented
609#1439C2×C15111yescharacteristic, complemented
610#1439C2×C15111yescharacteristic, complemented
611#1439C2×C15111yescharacteristic, complemented
612#1439C2×C15111yescharacteristic, complemented
613#1438C2×C15111yescharacteristic
614#1436C2×C15111yescharacteristic, complemented
615C22⋊#95C2×C15111yescharacteristic, complemented
616C23×Q8C22×C15111yescharacteristic
617C23×D4C22×C15111yescharacteristic
618C24×C4C22×C15111yescharacteristic
619C2×C22⋊Q8—24no—
620C2×C22⋊Q8—24no—
621C2×C22⋊Q8—24no—
622C22×C4⋊C4C22×C15111yescharacteristic
623C22×C4⋊C4C22×C15111yescharacteristic
624C22×C4⋊C4C22×C15111yescharacteristic
625C22×C4⋊C4C22×C15111yescharacteristic
626C22×C4⋊C4C22×C15111yescharacteristic
627C22×C4⋊C4C22×C15111yescharacteristic
628C22×C22⋊C4C22×C15111yescharacteristic
629C22×C22⋊C4C22×C15111yescharacteristic
630C22×C22⋊C4C22×C15111yescharacteristic
631C22×C22⋊C4C22×C15111yescharacteristic
632C22×C22⋊C4C22×C15111yescharacteristic
633C22×C22⋊C4C22×C15111yescharacteristic
634C22×C22⋊C4C22×C15111yescharacteristic
635C22×C22⋊C4C22×C15111yescharacteristic
636C22×C22⋊C4C22×C15111yescharacteristic
637C22×C22⋊C4C22×C15111yescharacteristic
638C22×C22⋊C4C22×C15111yescharacteristic
639C22×C42C22×C15111yescharacteristic
640#396—24no—
641#393—24no—
642#391—24no—
643#390—24no—
644#386—24no—
645C2×#95C22×C15111yescharacteristic
646C2×#95C22×C15111yescharacteristic
647C2×#95C22×C15111yescharacteristic
648C2×#95C22×C15111yescharacteristic
649C2×#95C22×C15111yescharacteristic
650C2×#95C22×C15111yescharacteristic
651C2×#95C22×C15111yescharacteristic
652C2×#95C22×C15111yescharacteristic
653C2×#95C22×C15111yescharacteristic
654C2×#95C22×C15111yescharacteristic
655C2×#95C22×C15111yescharacteristic
656C2×#95C22×C15111yescharacteristic
657C2×#95C22×C15111yescharacteristic
658C2×#95C22×C15111yescharacteristic
659C25C23×C15111yescharacteristic
660C25C23×C15111yescharacteristic
661C22×Q8—22no—
662C22×Q8—22no—
663C22×Q8—22no—
664C22×Q8—22no—
665C22×Q8—41no—
666C22×Q8—41no—
667C22×Q8D4×C15114yescomplemented
668C22×D4—22no—
669C22×D4—22no—
670C22×D4—22no—
671C22×D4—22no—
672C22×D4—41no—
673C22×D4—41no—
674C22×D4Q8×C15114yescomplemented
675C23×C4—22no—
676C23×C4—22no—
677C23×C4—22no—
678C23×C4—22no—
679C23×C4—22no—
680C23×C4—41no—
681C23×C4—41no—
682C23×C4C23×C15111yescharacteristic
683C23×C4C23×C15111yescharacteristic
684C23×C4C23×C15111yescharacteristic
685C23×C4C23×C15111yescharacteristic
686C23×C4C23×C15111yescharacteristic
687C23×C4C23×C15111yescharacteristic
688C23×C4C23×C15111yescharacteristic
689C23×C4C23×C15111yescharacteristic
690C23×C4C23×C15111yescharacteristic
691C23×C4C23×C15111yescharacteristic
692C23×C4C23×C15111yescharacteristic
693C23×C4C23×C15111yescharacteristic
694C23×C4C23×C15111yescharacteristic
695C22⋊Q8—232no—
696C2×C4⋊C4—22no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—22no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4—22no—
704C2×C4⋊C4—22no—
705C2×C4⋊C4—22no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4—22no—
708C2×C4⋊C4—22no—
709C2×C4⋊C4—41no—
710C2×C4⋊C4—41no—
711C2×C4⋊C4—41no—
712C2×C4⋊C4—41no—
713C2×C4⋊C4D4×C15114yescomplemented
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—22no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—41no—
737C2×C22⋊C4—41no—
738C2×C22⋊C4—41no—
739C2×C22⋊C4—41no—
740C2×C22⋊C4—41no—
741C2×C22⋊C4—41no—
742C2×C22⋊C4—41no—
743C2×C22⋊C4—41no—
744C2×C22⋊C4—41no—
745C2×C22⋊C4—41no—
746C2×C22⋊C4D4×C15114yes—
747C2×C42—22no—
748C2×C42—22no—
749C2×C42—41no—
750#95—22no—
751#95—22no—
752#95—22no—
753#95—22no—
754#95—22no—
755#95—22no—
756#95—22no—
757#95—22no—
758#95—22no—
759#95—22no—
760#95—41no—
761#95—41no—
762#95—41no—
763#95D4×C15114yes—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24C2×D4×C15112yes—
791C24C2×Q8×C15112yes—
792C24C2×Q8×C15112yes—
793C24#41×C15112yes—
794C24C24×C15111yescharacteristic
795C2×Q8—28no—
796C2×Q8—28no—
797C2×Q8—44no—
798C2×Q8—44no—
799C2×Q8—44no—
800C2×Q8—44no—
801C2×Q8—44no—
802C2×D4—28no—
803C2×D4—28no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—44no—
808C2×D4—44no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—28no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4C2×D4×C15112yes—
893C22×C4C2×D4×C15112yes—
894C22×C4C2×D4×C15112yes—
895C22×C4C2×D4×C15112yes—
896C22×C4C2×D4×C15112yes—
897C22×C4C2×D4×C15112yes—
898C22×C4C2×D4×C15112yes—
899C22×C4C2×D4×C15112yes—
900C22×C4C2×D4×C15112yes—
901C22×C4C2×D4×C15112yes—
902C22×C4C2×D4×C15112yes—
903C22×C4C2×Q8×C15112yes—
904C22×C4#41×C15112yes—
905C22×C4#41×C15112yes—
906C22×C4#41×C15112yes—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—28no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C42—44no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23C22⋊Q8×C15114yes—
995C23C22×D4×C15111yescharacteristic
996C23C22×D4×C15111yescharacteristic
997C23C22×D4×C15111yescharacteristic
998C23C22×D4×C15111yescharacteristic
999C23C22×Q8×C15111yescharacteristic
1000C23C2×#41×C15111yescharacteristic
1001C23C2×#41×C15111yescharacteristic
1002C23C2×#41×C15111yescharacteristic
1003C23C2×#41×C15111yescharacteristic
1004C23H(5,𝔽2)×C15111yescharacteristic
1005C23H(5,𝔽2)×C15111yescharacteristic
1006C23H(5,𝔽2)×C15111yescharacteristic
1007C23H(5,𝔽2)×C15111yescharacteristic
1008C232−1+4×C15111yescharacteristic
1009C232−1+4×C15111yescharacteristic
1010Q8—416no—
1011D4—416no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—416no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4#120×C15114yes—
1102C2×C4#121×C15114yes—
1103C2×C4C22⋊Q8×C15114yescomplemented
1104C22—24no—
1105C22—24no—
1106C22—24no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—81no—
1127C22—81no—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22—81no—
1132C22—81no—
1133C22—81no—
1134C22C2×#120×C15111yescharacteristic
1135C22C2×#121×C15111yescharacteristic
1136C22C2×C22⋊Q8×C15111yescharacteristic
1137C22C2×C22⋊Q8×C15111yescharacteristic
1138C22#529×C15111yescharacteristic
1139C22#532×C15111yescharacteristic
1140C22#534×C15111yescharacteristic
1141C22#535×C15111yescharacteristic
1142C22#536×C15111yescharacteristic
1143C22#537×C15111yescharacteristic
1144C22#538×C15111yescharacteristic
1145C22#539×C15111yescharacteristic
1146C22#542×C15111yescharacteristic
1147C22#542×C15111yescharacteristic
1148C22#543×C15111yescharacteristic
1149C22D42×C15111yescharacteristic
1150C22D42×C15111yescharacteristic
1151C22#546×C15111yescharacteristic
1152C22#546×C15111yescharacteristic
1153C22#546×C15111yescharacteristic
1154C22#546×C15111yescharacteristic
1155C22#546×C15111yescharacteristic
1156C22#548×C15111yescharacteristic
1157C22#548×C15111yescharacteristic
1158C22#548×C15111yescharacteristic
1159C22D4×Q8×C15111yescharacteristic
1160C22D4×Q8×C15111yescharacteristic
1161C22#550×C15111yescharacteristic
1162C22#550×C15111yescharacteristic
1163C22#551×C15111yescharacteristic
1164C22#554×C15111yescharacteristic
1165C22#554×C15111yescharacteristic
1166C22#556×C15111yescharacteristic
1167C22#562×C15111yescharacteristic
1168C22#562×C15111yescharacteristic
1169C4—24no—
1170C4—24no—
1171C4—24no—
1172C4—42no—
1173C4—42no—
1174C4—42no—
1175C4—42no—
1176C4—42no—
1177C4—42no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C2—44no—
1183C2—82no—
1184C2#2409×C15111yescharacteristic
1185C2#2410×C15111yescharacteristic
1186C2#2426×C15111yescharacteristic
1187C2#2431×C15111yescharacteristic
1188C2#2437×C15111yescharacteristic
1189C2#2450×C15111yescharacteristic
1190C2#2452×C15111yescharacteristic
1191C2#2538×C15111yescharacteristic
1192C2#2560×C15111yescharacteristic
1193C2#2676×C15111yescharacteristic
1194C2#2681×C15111yescharacteristic
1195C2#2692×C15111yescharacteristic
1196C2#2700×C15111yescharacteristic
1197C2#2730×C15111yescharacteristic
1198C2#2732×C15111yescharacteristic
subgroupG/H
center, socleC24×C151C24
commutator, Frattini, cosocleC24C24×C151
prime radicalC23×D4×C151C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊Q8×C151C2semidirect
2. C2×#396×C151C2semidirect
3. C2×#393×C151C2semidirect
4. C2×#391×C151C2semidirect
7. #1444×C151C2semidirect
8. #1441×C151C2semidirect
9. #1439×C151C2semidirect
10. #1439×C151C2semidirect
11. #1439×C151C2semidirect
12. #1439×C151C2semidirect
14. #1436×C151C2semidirect
15. C22⋊#95×C151C2semidirect
67. C22×Q8×C151D4semidirect
74. C22×D4×C151Q8semidirect
113. C2×C4⋊C4×C151D4semidirect
503. C2×C4×C151C22⋊Q8semidirect
599. #15280C151direct (N × H)
600. C151#15280direct (N × H)
601. C22×C22⋊Q8C2×C151semidirect
602. C2×#396C2×C151semidirect
603. C2×#393C2×C151semidirect
604. C2×#391C2×C151semidirect
607. #1444C2×C151semidirect
608. #1441C2×C151semidirect
609. #1439C2×C151semidirect
610. #1439C2×C151semidirect
611. #1439C2×C151semidirect
612. #1439C2×C151semidirect
614. #1436C2×C151semidirect
615. C22⋊#95C2×C151semidirect
667. C22×Q8D4×C151semidirect
674. C22×D4Q8×C151semidirect
713. C2×C4⋊C4D4×C151semidirect
1103. C2×C4C22⋊Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Q8×C1512
C2×#396×C1512
C2×#393×C1512
C2×#391×C1512
C2×#390×C1512
C2×#386×C1512
#1444×C1512
#1441×C1512
#1439×C1512
#1438×C1512
#1436×C1512
C22⋊#95×C1512
#15280151