Finite Group Databasebeta

← C151×#24471 #50329396

Subgroups — C151×#24471 #50329396

Order 38656.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3488×C151C211yesmaximal, characteristic
2#3056×C151C211yesmaximal, characteristic, complemented
3C2×#455×C151C211yesmaximal, characteristic, complemented
4#3007×C151C211yesmaximal, characteristic, complemented
5C2×#421×C151C211yesmaximal, characteristic, complemented
6#2620×C151C211yesmaximal, characteristic, complemented
7#2039×C151C211yesmaximal, characteristic, complemented
8#2037×C151C211yesmaximal, characteristic, complemented
9#2007×C151C211yesmaximal, characteristic, complemented
10#2004×C151C211yesmaximal, characteristic, complemented
11#1900×C151C211yesmaximal, characteristic, complemented
12#1897×C151C211yesmaximal, characteristic, complemented
13#1882×C151C211yesmaximal, characteristic, complemented
14#1859×C151C211yesmaximal, characteristic, complemented
15#1792×C151C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C151C2211yescharacteristic
17C22×#41×C151C2211yescharacteristic
18C2×#137×C151C2211yescharacteristic
19C2×#137×C151C2211yescharacteristic, complemented
20C2×#137×C151C2211yescharacteristic, complemented
21C22×M16×C151C2211yescharacteristic, complemented
22#550×C151—21no—
23#548×C151—21no—
24#546×C151—21no—
25#546×C151—22no—
26D42×C151—22no—
27D42×C151—21no—
28#537×C151—21no—
29#537×C151C2211yescharacteristic
30#535×C151—21no—
31#535×C151C2211yescharacteristic
32C2×#124×C151C2211yescharacteristic, complemented
33#525×C151—21no—
34#525×C151C2211yescharacteristic
35C2×C22⋊Q8×C151C2211yescharacteristic, complemented
36C2×#121×C151—21no—
37C2×#121×C151C2211yescharacteristic
38#520×C151C2211yescharacteristic
39C2×#117×C151C2211yescharacteristic, complemented
40#470×C151—21no—
41#468×C151—21no—
42#467×C151—21no—
43#465×C151—21no—
44#455×C151—24no—
45#452×C151—21no—
46#452×C151—21no—
47#451×C151—21no—
48#450×C151—21no—
49#428×C151C2211yescharacteristic, complemented
50#421×C151—24no—
51C2×#104×C151C2211yescharacteristic
52C2×#104×C151C2211yescharacteristic
53C2×#104×C151C2211yescharacteristic, complemented
54C2×#104×C151C2211yescharacteristic, complemented
55C2×#104×C151C2211yescharacteristic, complemented
56C2×#104×C151C2211yescharacteristic, complemented
57#419×C151C2211yescharacteristic, complemented
58#417×C151C2211yescharacteristic
59#417×C151C2211yescharacteristic, complemented
60#417×C151C2211yescharacteristic, complemented
61C2×#100×C151C2211yescharacteristic, complemented
62C2×#100×C151C2211yescharacteristic, complemented
63#407×C151C2211yescharacteristic, complemented
64#396×C151—22no—
65#394×C151—22no—
66#391×C151C2211yescharacteristic, complemented
67#390×C151C2211yescharacteristic, complemented
68#384×C151C2211yescharacteristic, complemented
69#343×C151C2211yescharacteristic, complemented
70#343×C151C2211yescharacteristic, complemented
71#339×C151C2211yescharacteristic, complemented
72#339×C151C2211yescharacteristic, complemented
73H(5,𝔽2)×C151—22no—
74H(5,𝔽2)×C151—22no—
75H(5,𝔽2)×C151—41no—
76H(5,𝔽2)×C151—41no—
77C2×#41×C151—22no—
78C2×#41×C151—22no—
79C2×#41×C151—21no—
80C2×#41×C151—21no—
81C2×#41×C151—21no—
82C2×#41×C151—21no—
83C2×#41×C151—41no—
84C2×#41×C151—41no—
85C2×#41×C151D411yescharacteristic
86C2×#41×C151D411yescharacteristic
87C2×#41×C151C2311yescharacteristic
88C2×#41×C151C2311yescharacteristic
89C2×#41×C151C2311yescharacteristic
90C22×Q8×C151D411yescharacteristic
91C22×Q8×C151C2311yescharacteristic
92C22×D4×C151—22no—
93C22×D4×C151—21no—
94C22×D4×C151—21no—
95C22×D4×C151—21no—
96C22×D4×C151—22no—
97C22×D4×C151D411yescharacteristic
98C22×D4×C151D412yes—
99C22×D4×C151C2311yescharacteristic
100C23×C4×C151—21no—
101C23×C4×C151C2311yescharacteristic
102#137×C151—22no—
103#137×C151—22no—
104#137×C151—22no—
105#137×C151—41no—
106#137×C151—41no—
107#137×C151—41no—
108C2×Q16×C151—21no—
109C2×Q16×C151—21no—
110C2×Q16×C151—21no—
111C2×SD16×C151—21no—
112C2×SD16×C151—21no—
113C2×SD16×C151—21no—
114C2×M16×C151—21no—
115C2×M16×C151—22no—
116C2×M16×C151—41no—
117C2×M16×C151C2311yescharacteristic
118C2×M16×C151C2311yescharacteristic
119C2×M16×C151C2311yescharacteristic
120C2×M16×C151C2311yescharacteristic
121C22×C8×C151—21no—
122#127×C151—22no—
123#127×C151—21no—
124#124×C151—22no—
125#124×C151—22no—
126#124×C151—21no—
127#124×C151—41no—
128#123×C151—22no—
129#123×C151—21no—
130C22⋊Q8×C151—22no—
131C22⋊Q8×C151—21no—
132C22⋊Q8×C151—21no—
133C22⋊Q8×C151—21no—
134C22⋊Q8×C151—21no—
135C22⋊Q8×C151—21no—
136C22⋊Q8×C151—21no—
137C22⋊Q8×C151D411yescharacteristic
138C22⋊Q8×C151D411yescharacteristic
139#121×C151—22no—
140#121×C151—22no—
141#121×C151—22no—
142#121×C151—22no—
143#121×C151—22no—
144#121×C151—21no—
145#121×C151—21no—
146#121×C151—21no—
147#121×C151—21no—
148#121×C151—21no—
149#121×C151—21no—
150#121×C151—22no—
151#121×C151—21no—
152#121×C151—21no—
153#121×C151D411yescharacteristic
154#121×C151D411yescharacteristic
155#120×C151—22no—
156#120×C151—22no—
157#120×C151—22no—
158#120×C151—21no—
159#120×C151—22no—
160C4×Q8×C151—21no—
161C4×D4×C151—22no—
162C4×D4×C151—22no—
163C4×D4×C151—21no—
164C4×D4×C151—22no—
165C4×D4×C151—21no—
166C4×D4×C151—21no—
167#117×C151—21no—
168#117×C151—22no—
169#117×C151—41no—
170#117×C151C2311yescharacteristic
171C2×C4⋊C4×C151—21no—
172C2×C4⋊C4×C151—21no—
173C2×C4⋊C4×C151—21no—
174C2×C4⋊C4×C151—22no—
175C2×C4⋊C4×C151C2311yescharacteristic
176C2×C4⋊C4×C151C2311yescharacteristic
177C2×C22⋊C4×C151—22no—
178C2×C22⋊C4×C151—21no—
179C2×C22⋊C4×C151—21no—
180C2×C22⋊C4×C151—22no—
181C2×C22⋊C4×C151—22no—
182C2×C22⋊C4×C151D412yes—
183C2×C42×C151C2311yescharacteristic
184C2×C42×C151C2311yescharacteristic
185#107×C151—21no—
186#106×C151—21no—
187#104×C151—22no—
188#104×C151—22no—
189#104×C151—22no—
190#104×C151—22no—
191#104×C151—41no—
192#104×C151D414yescomplemented
193#103×C151—21no—
194#103×C151—21no—
195#103×C151—21no—
196#103×C151—21no—
197#103×C151—21no—
198#102×C151—21no—
199#102×C151—21no—
200#102×C151—21no—
201#100×C151—22no—
202#100×C151—41no—
203C22⋊C8×C151—21no—
204C22⋊C8×C151—21no—
205#95×C151—22no—
206C24×C151—22no—
207C24×C151—21no—
208C24×C151C2×D412yes—
209C24×C151C2×D411yescharacteristic
210#41×C151—21no—
211#41×C151—21no—
212#41×C151—22no—
213#41×C151—22no—
214#41×C151—21no—
215#41×C151—21no—
216#41×C151—21no—
217#41×C151—21no—
218#41×C151—21no—
219#41×C151—21no—
220#41×C151—21no—
221#41×C151—21no—
222#41×C151—42no—
223#41×C151—42no—
224#41×C151—41no—
225#41×C151—41no—
226#41×C151—42no—
227#41×C151—42no—
228#41×C151—42no—
229#41×C151—42no—
230#41×C151—42no—
231#41×C151—42no—
232#41×C151C2×D412yes—
233#41×C151#4112yes—
234C2×Q8×C151—21no—
235C2×Q8×C151—22no—
236C2×Q8×C151—21no—
237C2×Q8×C151—21no—
238C2×Q8×C151—21no—
239C2×Q8×C151—21no—
240C2×Q8×C151—21no—
241C2×Q8×C151—21no—
242C2×Q8×C151—41no—
243C2×Q8×C151C2×D411yescharacteristic
244C2×Q8×C151C2×D411yescharacteristic
245C2×Q8×C151C2×D411yescharacteristic
246C2×D4×C151—21no—
247C2×D4×C151—22no—
248C2×D4×C151—22no—
249C2×D4×C151—22no—
250C2×D4×C151—22no—
251C2×D4×C151—21no—
252C2×D4×C151—21no—
253C2×D4×C151—21no—
254C2×D4×C151—21no—
255C2×D4×C151—21no—
256C2×D4×C151—22no—
257C2×D4×C151—22no—
258C2×D4×C151—22no—
259C2×D4×C151—21no—
260C2×D4×C151—22no—
261C2×D4×C151—21no—
262C2×D4×C151—21no—
263C2×D4×C151—21no—
264C2×D4×C151—21no—
265C2×D4×C151—21no—
266C2×D4×C151—21no—
267C2×D4×C151—21no—
268C2×D4×C151—41no—
269C2×D4×C151—42no—
270C2×D4×C151—42no—
271C2×D4×C151—42no—
272C2×D4×C151—42no—
273C2×D4×C151—44no—
274C2×D4×C151—44no—
275C2×D4×C151—42no—
276C2×D4×C151—42no—
277C2×D4×C151—82no—
278C2×D4×C151—84no—
279C2×D4×C151C2×D411yescharacteristic
280C2×D4×C151C2×D411yescharacteristic
281C2×D4×C151C2×D411yescharacteristic
282C22×C4×C151—21no—
283C22×C4×C151—21no—
284C22×C4×C151—21no—
285C22×C4×C151—21no—
286C22×C4×C151—21no—
287C22×C4×C151—22no—
288C22×C4×C151—21no—
289C22×C4×C151—21no—
290C22×C4×C151—22no—
291C22×C4×C151—21no—
292C22×C4×C151—21no—
293C22×C4×C151—21no—
294C22×C4×C151—21no—
295C22×C4×C151—21no—
296C22×C4×C151—21no—
297C22×C4×C151—21no—
298C22×C4×C151—42no—
299C22×C4×C151—42no—
300C22×C4×C151C2×D411yescharacteristic
301C22×C4×C151C2×D411yescharacteristic
302C22×C4×C151C2×D411yescharacteristic
303C22×C4×C151C2×D411yescharacteristic
304C22×C4×C151C2×D411yescharacteristic
305C22×C4×C151C2×D412yes—
306C22×C4×C151C2411yescharacteristic
307Q16×C151—42no—
308Q16×C151—42no—
309Q16×C151—42no—
310SD16×C151—42no—
311SD16×C151—42no—
312SD16×C151—42no—
313M16×C151—21no—
314M16×C151—21no—
315M16×C151—21no—
316M16×C151—21no—
317M16×C151—21no—
318M16×C151—21no—
319M16×C151—21no—
320M16×C151—42no—
321M16×C151C2×D412yescomplemented
322C2×C8×C151—21no—
323C2×C8×C151—21no—
324C2×C8×C151—21no—
325C2×C8×C151—21no—
326C2×C8×C151—42no—
327C4⋊C4×C151—22no—
328C4⋊C4×C151—22no—
329C4⋊C4×C151—21no—
330C4⋊C4×C151—21no—
331C4⋊C4×C151—21no—
332C4⋊C4×C151—21no—
333C4⋊C4×C151—21no—
334C4⋊C4×C151—21no—
335C4⋊C4×C151—42no—
336C4⋊C4×C151—41no—
337C4⋊C4×C151—41no—
338C4⋊C4×C151—82no—
339C4⋊C4×C151C2×D411yescharacteristic
340C4⋊C4×C151C2×D411yescharacteristic
341C22⋊C4×C151—22no—
342C22⋊C4×C151—22no—
343C22⋊C4×C151—22no—
344C22⋊C4×C151—22no—
345C22⋊C4×C151—22no—
346C22⋊C4×C151—21no—
347C22⋊C4×C151—21no—
348C22⋊C4×C151—21no—
349C22⋊C4×C151—21no—
350C22⋊C4×C151—22no—
351C22⋊C4×C151—22no—
352C22⋊C4×C151—21no—
353C22⋊C4×C151—42no—
354C22⋊C4×C151—44no—
355C22⋊C4×C151—41no—
356C22⋊C4×C151—41no—
357C22⋊C4×C151—82no—
358C42×C151—22no—
359C42×C151—21no—
360C42×C151—21no—
361C42×C151—21no—
362C42×C151—21no—
363C42×C151C2×D412yescomplemented
364C23×C151—21no—
365C23×C151—21no—
366C23×C151—21no—
367C23×C151—21no—
368C23×C151—22no—
369C23×C151—21no—
370C23×C151—22no—
371C23×C151—22no—
372C23×C151—41no—
373C23×C151—41no—
374C23×C151—42no—
375C23×C151—42no—
376C23×C151—44no—
377C23×C151—42no—
378C23×C151—42no—
379C23×C151—81no—
380C23×C151—82no—
381C23×C151—82no—
382C23×C151#12011yescharacteristic
383C23×C151#12011yescharacteristic
384C23×C151C22×D411yescharacteristic
385Q8×C151—21no—
386Q8×C151—21no—
387Q8×C151—21no—
388Q8×C151—21no—
389Q8×C151—21no—
390Q8×C151—42no—
391Q8×C151—41no—
392Q8×C151—41no—
393Q8×C151—41no—
394Q8×C151—41no—
395Q8×C151#12112yes—
396D4×C151—22no—
397D4×C151—22no—
398D4×C151—21no—
399D4×C151—21no—
400D4×C151—21no—
401D4×C151—21no—
402D4×C151—21no—
403D4×C151—42no—
404D4×C151—42no—
405D4×C151—44no—
406D4×C151—42no—
407D4×C151—44no—
408D4×C151—44no—
409D4×C151—42no—
410D4×C151—41no—
411D4×C151—41no—
412D4×C151—41no—
413D4×C151—41no—
414D4×C151—41no—
415D4×C151—41no—
416D4×C151—41no—
417D4×C151—41no—
418D4×C151—81no—
419D4×C151—82no—
420D4×C151—82no—
421D4×C151—82no—
422D4×C151—82no—
423D4×C151#12112yes—
424C2×C4×C151—21no—
425C2×C4×C151—21no—
426C2×C4×C151—21no—
427C2×C4×C151—21no—
428C2×C4×C151—21no—
429C2×C4×C151—21no—
430C2×C4×C151—21no—
431C2×C4×C151—22no—
432C2×C4×C151—21no—
433C2×C4×C151—21no—
434C2×C4×C151—22no—
435C2×C4×C151—21no—
436C2×C4×C151—21no—
437C2×C4×C151—21no—
438C2×C4×C151—21no—
439C2×C4×C151—21no—
440C2×C4×C151—22no—
441C2×C4×C151—21no—
442C2×C4×C151—22no—
443C2×C4×C151—42no—
444C2×C4×C151—42no—
445C2×C4×C151—42no—
446C2×C4×C151—44no—
447C2×C4×C151—41no—
448C2×C4×C151—41no—
449C2×C4×C151—41no—
450C2×C4×C151—41no—
451C2×C4×C151—41no—
452C2×C4×C151—41no—
453C2×C4×C151—42no—
454C2×C4×C151—41no—
455C2×C4×C151—42no—
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—82no—
463C2×C4×C151#12011yescharacteristic
464C2×C4×C151#12011yescharacteristic
465C2×C4×C151C22×D411yescharacteristic
466C2×C4×C151C22×D411yescharacteristic
467C2×C4×C151C22×D411yescharacteristic
468C2×C4×C151C2×#4111yescharacteristic
469C2×C4×C151H(5,𝔽2)11yescharacteristic
470C2×C4×C151H(5,𝔽2)11yescharacteristic
471C8×C151—22no—
472C8×C151—41no—
473C8×C151—41no—
474C8×C151—41no—
475C22×C151—21no—
476C22×C151—21no—
477C22×C151—21no—
478C22×C151—21no—
479C22×C151—22no—
480C22×C151—21no—
481C22×C151—21no—
482C22×C151—21no—
483C22×C151—21no—
484C22×C151—41no—
485C22×C151—41no—
486C22×C151—41no—
487C22×C151—41no—
488C22×C151—42no—
489C22×C151—42no—
490C22×C151—41no—
491C22×C151—41no—
492C22×C151—41no—
493C22×C151—42no—
494C22×C151—41no—
495C22×C151—81no—
496C22×C151—81no—
497C22×C151—82no—
498C22×C151—82no—
499C22×C151—84no—
500C22×C151—164no—
501C22×C151C2×#12011yescharacteristic
502C22×C151D4211yescharacteristic
503C22×C151#54611yescharacteristic
504C4×C151—21no—
505C4×C151—21no—
506C4×C151—22no—
507C4×C151—42no—
508C4×C151—41no—
509C4×C151—41no—
510C4×C151—42no—
511C4×C151—41no—
512C4×C151—41no—
513C4×C151—81no—
514C4×C151—81no—
515C4×C151—81no—
516C4×C151C2×#12111yescharacteristic
517C4×C151#53411yescharacteristic
518C4×C151D4211yescharacteristic
519C4×C151#54611yescharacteristic
520C2×C151—21no—
521C2×C151—21no—
522C2×C151—41no—
523C2×C151—41no—
524C2×C151—42no—
525C2×C151—81no—
526C2×C151—82no—
527C2×C151—81no—
528C2×C151#241011yescharacteristic
529C2×C151#301911yescharacteristic
530C2×C151#302211yescharacteristic
531#24471C15111yesmaximal, characteristic, direct product factor, Sylow
532C151#2447111yescharacteristic, direct product factor, Sylow
533#3488C2×C15111yescharacteristic
534#3056C2×C15111yescharacteristic, complemented
535C2×#455C2×C15111yescharacteristic, complemented
536#3007C2×C15111yescharacteristic, complemented
537C2×#421C2×C15111yescharacteristic, complemented
538#2620C2×C15111yescharacteristic, complemented
539#2039C2×C15111yescharacteristic, complemented
540#2037C2×C15111yescharacteristic, complemented
541#2007C2×C15111yescharacteristic, complemented
542#2004C2×C15111yescharacteristic, complemented
543#1900C2×C15111yescharacteristic, complemented
544#1897C2×C15111yescharacteristic, complemented
545#1882C2×C15111yescharacteristic, complemented
546#1859C2×C15111yescharacteristic, complemented
547#1792C2×C15111yescharacteristic, complemented
548C2×H(5,𝔽2)C22×C15111yescharacteristic
549C22×#41C22×C15111yescharacteristic
550C2×#137C22×C15111yescharacteristic
551C2×#137C22×C15111yescharacteristic, complemented
552C2×#137C22×C15111yescharacteristic, complemented
553C22×M16C22×C15111yescharacteristic, complemented
554#550—21no—
555#548—21no—
556#546—21no—
557#546—22no—
558D42—22no—
559D42—21no—
560#537—21no—
561#537C22×C15111yescharacteristic
562#535—21no—
563#535C22×C15111yescharacteristic
564C2×#124C22×C15111yescharacteristic, complemented
565#525—21no—
566#525C22×C15111yescharacteristic
567C2×C22⋊Q8C22×C15111yescharacteristic, complemented
568C2×#121—21no—
569C2×#121C22×C15111yescharacteristic
570#520C22×C15111yescharacteristic
571C2×#117C22×C15111yescharacteristic, complemented
572#470—21no—
573#468—21no—
574#467—21no—
575#465—21no—
576#455—24no—
577#452—21no—
578#452—21no—
579#451—21no—
580#450—21no—
581#428C22×C15111yescharacteristic, complemented
582#421—24no—
583C2×#104C22×C15111yescharacteristic
584C2×#104C22×C15111yescharacteristic
585C2×#104C22×C15111yescharacteristic, complemented
586C2×#104C22×C15111yescharacteristic, complemented
587C2×#104C22×C15111yescharacteristic, complemented
588C2×#104C22×C15111yescharacteristic, complemented
589#419C22×C15111yescharacteristic, complemented
590#417C22×C15111yescharacteristic
591#417C22×C15111yescharacteristic, complemented
592#417C22×C15111yescharacteristic, complemented
593C2×#100C22×C15111yescharacteristic, complemented
594C2×#100C22×C15111yescharacteristic, complemented
595#407C22×C15111yescharacteristic, complemented
596#396—22no—
597#394—22no—
598#391C22×C15111yescharacteristic, complemented
599#390C22×C15111yescharacteristic, complemented
600#384C22×C15111yescharacteristic, complemented
601#343C22×C15111yescharacteristic, complemented
602#343C22×C15111yescharacteristic, complemented
603#339C22×C15111yescharacteristic, complemented
604#339C22×C15111yescharacteristic, complemented
605H(5,𝔽2)—22no—
606H(5,𝔽2)—22no—
607H(5,𝔽2)—41no—
608H(5,𝔽2)—41no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—41no—
616C2×#41—41no—
617C2×#41D4×C15111yescharacteristic
618C2×#41D4×C15111yescharacteristic
619C2×#41C23×C15111yescharacteristic
620C2×#41C23×C15111yescharacteristic
621C2×#41C23×C15111yescharacteristic
622C22×Q8D4×C15111yescharacteristic
623C22×Q8C23×C15111yescharacteristic
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—21no—
628C22×D4—21no—
629C22×D4D4×C15111yescharacteristic
630C22×D4D4×C15112yes—
631C22×D4C23×C15111yescharacteristic
632C23×C4—21no—
633C23×C4C23×C15111yescharacteristic
634#137—22no—
635#137—22no—
636#137—22no—
637#137—41no—
638#137—41no—
639#137—41no—
640C2×Q16—21no—
641C2×Q16—21no—
642C2×Q16—21no—
643C2×SD16—21no—
644C2×SD16—21no—
645C2×SD16—21no—
646C2×M16—21no—
647C2×M16—22no—
648C2×M16—41no—
649C2×M16C23×C15111yescharacteristic
650C2×M16C23×C15111yescharacteristic
651C2×M16C23×C15111yescharacteristic
652C2×M16C23×C15111yescharacteristic
653C22×C8—21no—
654#127—22no—
655#127—21no—
656#124—22no—
657#124—21no—
658#124—22no—
659#124—41no—
660#123—22no—
661#123—21no—
662C22⋊Q8—22no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8D4×C15111yescharacteristic
670C22⋊Q8D4×C15111yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—22no—
675#121—22no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—22no—
683#121—21no—
684#121—21no—
685#121D4×C15111yescharacteristic
686#121D4×C15111yescharacteristic
687#120—22no—
688#120—22no—
689#120—22no—
690#120—21no—
691#120—22no—
692C4×Q8—21no—
693C4×D4—22no—
694C4×D4—22no—
695C4×D4—21no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—21no—
699#117—21no—
700#117—22no—
701#117—41no—
702#117C23×C15111yescharacteristic
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4C23×C15111yescharacteristic
708C2×C4⋊C4C23×C15111yescharacteristic
709C2×C22⋊C4—22no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4D4×C15112yes—
715C2×C42C23×C15111yescharacteristic
716C2×C42C23×C15111yescharacteristic
717#107—21no—
718#106—21no—
719#104—22no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—41no—
724#104D4×C15114yescomplemented
725#103—21no—
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#102—21no—
731#102—21no—
732#102—21no—
733#100—22no—
734#100—41no—
735C22⋊C8—21no—
736C22⋊C8—21no—
737#95—22no—
738C24—22no—
739C24—21no—
740C24C2×D4×C15112yes—
741C24C2×D4×C15111yescharacteristic
742#41—21no—
743#41—21no—
744#41—22no—
745#41—22no—
746#41—21no—
747#41—21no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—42no—
755#41—42no—
756#41—41no—
757#41—41no—
758#41—42no—
759#41—42no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41C2×D4×C15112yes—
765#41#41×C15112yes—
766C2×Q8—21no—
767C2×Q8—22no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—41no—
775C2×Q8C2×D4×C15111yescharacteristic
776C2×Q8C2×D4×C15111yescharacteristic
777C2×Q8C2×D4×C15111yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—41no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—82no—
810C2×D4—84no—
811C2×D4C2×D4×C15111yescharacteristic
812C2×D4C2×D4×C15111yescharacteristic
813C2×D4C2×D4×C15111yescharacteristic
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4C2×D4×C15111yescharacteristic
833C22×C4C2×D4×C15111yescharacteristic
834C22×C4C2×D4×C15111yescharacteristic
835C22×C4C2×D4×C15111yescharacteristic
836C22×C4C2×D4×C15111yescharacteristic
837C22×C4C2×D4×C15112yes—
838C22×C4C24×C15111yescharacteristic
839Q16—42no—
840Q16—42no—
841Q16—42no—
842SD16—42no—
843SD16—42no—
844SD16—42no—
845M16—21no—
846M16—21no—
847M16—21no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—42no—
853M16C2×D4×C15112yescomplemented
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—42no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—82no—
871C4⋊C4C2×D4×C15111yescharacteristic
872C4⋊C4C2×D4×C15111yescharacteristic
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—21no—
885C22⋊C4—42no—
886C22⋊C4—44no—
887C22⋊C4—41no—
888C22⋊C4—41no—
889C22⋊C4—82no—
890C42—22no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42C2×D4×C15112yescomplemented
896C23—21no—
897C23—21no—
898C23—21no—
899C23—22no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—41no—
905C23—41no—
906C23—42no—
907C23—42no—
908C23—44no—
909C23—42no—
910C23—42no—
911C23—81no—
912C23—82no—
913C23—82no—
914C23#120×C15111yescharacteristic
915C23#120×C15111yescharacteristic
916C23C22×D4×C15111yescharacteristic
917Q8—21no—
918Q8—21no—
919Q8—21no—
920Q8—21no—
921Q8—21no—
922Q8—42no—
923Q8—41no—
924Q8—41no—
925Q8—41no—
926Q8—41no—
927Q8#121×C15112yes—
928D4—22no—
929D4—22no—
930D4—21no—
931D4—21no—
932D4—21no—
933D4—21no—
934D4—21no—
935D4—42no—
936D4—42no—
937D4—44no—
938D4—42no—
939D4—44no—
940D4—44no—
941D4—42no—
942D4—41no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—82no—
951D4—81no—
952D4—82no—
953D4—82no—
954D4—82no—
955D4#121×C15112yes—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—44no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—42no—
986C2×C4—41no—
987C2×C4—42no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—82no—
995C2×C4#120×C15111yescharacteristic
996C2×C4#120×C15111yescharacteristic
997C2×C4C22×D4×C15111yescharacteristic
998C2×C4C22×D4×C15111yescharacteristic
999C2×C4C22×D4×C15111yescharacteristic
1000C2×C4C2×#41×C15111yescharacteristic
1001C2×C4H(5,𝔽2)×C15111yescharacteristic
1002C2×C4H(5,𝔽2)×C15111yescharacteristic
1003C8—22no—
1004C8—41no—
1005C8—41no—
1006C8—41no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—22no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—42no—
1021C22—42no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—42no—
1026C22—41no—
1027C22—81no—
1028C22—81no—
1029C22—82no—
1030C22—82no—
1031C22—84no—
1032C22—164no—
1033C22C2×#120×C15111yescharacteristic
1034C22D42×C15111yescharacteristic
1035C22#546×C15111yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—22no—
1039C4—42no—
1040C4—41no—
1041C4—41no—
1042C4—42no—
1043C4—41no—
1044C4—41no—
1045C4—81no—
1046C4—81no—
1047C4—81no—
1048C4C2×#121×C15111yescharacteristic
1049C4#534×C15111yescharacteristic
1050C4D42×C15111yescharacteristic
1051C4#546×C15111yescharacteristic
1052C2—21no—
1053C2—21no—
1054C2—41no—
1055C2—41no—
1056C2—42no—
1057C2—81no—
1058C2—82no—
1059C2—81no—
1060C2#2410×C15111yescharacteristic
1061C2#3019×C15111yescharacteristic
1062C2#3022×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3488×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3056×C151C2semidirect
3. C2×#455×C151C2semidirect
4. #3007×C151C2semidirect
5. C2×#421×C151C2semidirect
6. #2620×C151C2semidirect
7. #2039×C151C2semidirect
8. #2037×C151C2semidirect
9. #2007×C151C2semidirect
10. #2004×C151C2semidirect
11. #1900×C151C2semidirect
12. #1897×C151C2semidirect
13. #1882×C151C2semidirect
14. #1859×C151C2semidirect
15. #1792×C151C2semidirect
19. C2×#137×C151C22semidirect
20. C2×#137×C151C22semidirect
21. C22×M16×C151C22semidirect
32. C2×#124×C151C22semidirect
35. C2×C22⋊Q8×C151C22semidirect
39. C2×#117×C151C22semidirect
49. #428×C151C22semidirect
53. C2×#104×C151C22semidirect
54. C2×#104×C151C22semidirect
55. C2×#104×C151C22semidirect
56. C2×#104×C151C22semidirect
57. #419×C151C22semidirect
59. #417×C151C22semidirect
60. #417×C151C22semidirect
61. C2×#100×C151C22semidirect
62. C2×#100×C151C22semidirect
63. #407×C151C22semidirect
66. #391×C151C22semidirect
67. #390×C151C22semidirect
68. #384×C151C22semidirect
69. #343×C151C22semidirect
70. #343×C151C22semidirect
71. #339×C151C22semidirect
72. #339×C151C22semidirect
192. #104×C151D4semidirect
321. M16×C151C2×D4semidirect
363. C42×C151C2×D4semidirect
531. #24471C151direct (N × H)
532. C151#24471direct (N × H)
534. #3056C2×C151semidirect
535. C2×#455C2×C151semidirect
536. #3007C2×C151semidirect
537. C2×#421C2×C151semidirect
538. #2620C2×C151semidirect
539. #2039C2×C151semidirect
540. #2037C2×C151semidirect
541. #2007C2×C151semidirect
542. #2004C2×C151semidirect
543. #1900C2×C151semidirect
544. #1897C2×C151semidirect
545. #1882C2×C151semidirect
546. #1859C2×C151semidirect
547. #1792C2×C151semidirect
551. C2×#137C22×C151semidirect
552. C2×#137C22×C151semidirect
553. C22×M16C22×C151semidirect
564. C2×#124C22×C151semidirect
567. C2×C22⋊Q8C22×C151semidirect
571. C2×#117C22×C151semidirect
581. #428C22×C151semidirect
585. C2×#104C22×C151semidirect
586. C2×#104C22×C151semidirect
587. C2×#104C22×C151semidirect
588. C2×#104C22×C151semidirect
589. #419C22×C151semidirect
591. #417C22×C151semidirect
592. #417C22×C151semidirect
593. C2×#100C22×C151semidirect
594. C2×#100C22×C151semidirect
595. #407C22×C151semidirect
598. #391C22×C151semidirect
599. #390C22×C151semidirect
600. #384C22×C151semidirect
601. #343C22×C151semidirect
602. #343C22×C151semidirect
603. #339C22×C151semidirect
604. #339C22×C151semidirect
724. #104D4×C151semidirect
853. M16C2×D4×C151semidirect
895. C42C2×D4×C151semidirect

Maximal subgroups

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

subgroupindex
#3488×C1512
#3056×C1512
C2×#455×C1512
#3007×C1512
C2×#421×C1512
#2620×C1512
#2039×C1512
#2037×C1512
#2007×C1512
#2004×C1512
#1900×C1512
#1897×C1512
#1882×C1512
#1859×C1512
#1792×C1512
#24471151