Finite Group Databasebeta

← C151×#18252 #50323177

Subgroups — C151×#18252 #50323177

Order 38656.

1260 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#3534×C151C211yesmaximal, characteristic, complemented
2#3006×C151C211yesmaximal, characteristic, complemented
3#3002×C151C211yesmaximal, characteristic, complemented
4#2430×C151C211yesmaximal, characteristic, complemented
5#1606×C151C211yesmaximal, characteristic, complemented
6#1604×C151C211yesmaximal, characteristic, complemented
7#1603×C151C211yesmaximal, characteristic, complemented
8#1601×C151C211yesmaximal, characteristic, complemented
9#1600×C151C211yesmaximal, characteristic, complemented
10#1598×C151C211yesmaximal, characteristic, complemented
11#1597×C151C211yesmaximal, characteristic, complemented
12#1595×C151C211yesmaximal, characteristic, complemented
13#1504×C151C211yesmaximal, characteristic, complemented
14C2×#327×C151C211yesmaximal, characteristic, complemented
15#1468×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic, complemented
17C2×AGL(1,ℤ/8)×C151—21no—
18C2×#135×C151—21no—
19#562×C151—21no—
20#560×C151—21no—
21#553×C151—21no—
22#551×C151—21no—
23#546×C151—21no—
24#546×C151—21no—
25#546×C151—21no—
26D42×C151—21no—
27#540×C151—21no—
28#539×C151—21no—
29#539×C151C2211yescharacteristic
30#538×C151—21no—
31#538×C151C2211yescharacteristic
32#537×C151C2211yescharacteristic
33#534×C151—21no—
34#534×C151C2211yescharacteristic
35#525×C151C2211yescharacteristic
36C2×#123×C151C2211yescharacteristic
37C2×#121×C151—21no—
38C2×#121×C151C2211yescharacteristic
39#452×C151—21no—
40#451×C151C2211yescharacteristic, complemented
41#450×C151C2211yescharacteristic, complemented
42#449×C151—21no—
43#449×C151—21no—
44#449×C151—21no—
45#448×C151C2211yescharacteristic
46#448×C151C2211yescharacteristic, complemented
47#448×C151C2211yescharacteristic, complemented
48#447×C151C2211yescharacteristic
49#447×C151C2211yescharacteristic, complemented
50#447×C151C2211yescharacteristic, complemented
51#417×C151—21no—
52#416×C151—21no—
53#407×C151C2211yescharacteristic, complemented
54C2×C22⋊C8×C151C2211yescharacteristic, complemented
55#395×C151C2211yescharacteristic, complemented
56#394×C151C2211yescharacteristic, complemented
57#393×C151C2211yescharacteristic, complemented
58#392×C151C2211yescharacteristic, complemented
59#386×C151—21no—
60#386×C151—21no—
61#385×C151—21no—
62C2×#95×C151C2211yescharacteristic, complemented
63#328×C151C2211yescharacteristic, complemented
64#328×C151C2211yescharacteristic, complemented
65#327×C151C2211yescharacteristic
66#327×C151C2211yescharacteristic
67#327×C151C2211yescharacteristic, complemented
68#327×C151C2211yescharacteristic, complemented
69#327×C151C2211yescharacteristic, complemented
70#327×C151C2211yescharacteristic, complemented
71#324×C151C2211yescharacteristic, complemented
72#324×C151C2211yescharacteristic, complemented
73#323×C151C2211yescharacteristic, complemented
74#323×C151C2211yescharacteristic, complemented
75C2×#41×C151—21no—
76C2×#41×C151—21no—
77C2×#41×C151—21no—
78C2×#41×C151—21no—
79C2×#41×C151—21no—
80C2×#41×C151—44no—
81C2×#41×C151D411yescharacteristic, complemented
82C22×Q8×C151C2311yescharacteristic
83C22×D4×C151—21no—
84C22×D4×C151—21no—
85C22×D4×C151—21no—
86C22×D4×C151—21no—
87C22×D4×C151—21no—
88C22×D4×C151D411yescharacteristic
89C22×D4×C151D411yescharacteristic, complemented
90C22×D4×C151C2311yescharacteristic
91C23×C4×C151—21no—
92C23×C4×C151—21no—
93C23×C4×C151C2311yescharacteristic
94AGL(1,ℤ/8)×C151—44no—
95#135×C151—44no—
96C2×Q16×C151—21no—
97C2×SD16×C151—21no—
98C2×SD16×C151—21no—
99C2×SD16×C151—21no—
100C2×SD16×C151—21no—
101C2×D8×C151—21no—
102C2×D8×C151—21no—
103C2×D8×C151—21no—
104C2×M16×C151—21no—
105C22×C8×C151—21no—
106#127×C151—21no—
107#126×C151—21no—
108#126×C151—21no—
109#126×C151—21no—
110#126×C151—21no—
111#125×C151—21no—
112#125×C151—21no—
113#124×C151—21no—
114#124×C151—21no—
115#124×C151—21no—
116#123×C151—21no—
117#123×C151—21no—
118#123×C151—21no—
119#123×C151—21no—
120#123×C151—21no—
121#123×C151—21no—
122#123×C151—21no—
123#123×C151—21no—
124#123×C151—21no—
125#123×C151—21no—
126#123×C151—21no—
127#123×C151—21no—
128#123×C151—21no—
129#123×C151—21no—
130C22⋊Q8×C151—21no—
131C22⋊Q8×C151—21no—
132C22⋊Q8×C151—21no—
133C22⋊Q8×C151—21no—
134C22⋊Q8×C151—21no—
135C22⋊Q8×C151D411yescharacteristic, complemented
136C22⋊Q8×C151C2311yescharacteristic
137#121×C151—21no—
138#121×C151—21no—
139#121×C151—21no—
140#121×C151—21no—
141#121×C151—21no—
142#121×C151—21no—
143#121×C151—21no—
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—21no—
151#121×C151—21no—
152#121×C151—44no—
153#121×C151D411yescharacteristic, complemented
154#121×C151D411yescharacteristic, complemented
155#121×C151D411yescharacteristic, complemented
156#121×C151C2311yescharacteristic
157#121×C151C2311yescharacteristic
158#121×C151C2311yescharacteristic
159#120×C151—21no—
160#120×C151—21no—
161#120×C151—21no—
162#120×C151—21no—
163#120×C151—21no—
164#120×C151—21no—
165#120×C151—21no—
166#120×C151—21no—
167C4×D4×C151—21no—
168C4×D4×C151—21no—
169C4×D4×C151—21no—
170C4×D4×C151—21no—
171C4×D4×C151—21no—
172C4×D4×C151—21no—
173C4×D4×C151—21no—
174C4×D4×C151—21no—
175#117×C151—21no—
176#117×C151D411yescharacteristic, complemented
177C2×C4⋊C4×C151—21no—
178C2×C4⋊C4×C151D411yescharacteristic
179C2×C4⋊C4×C151D411yescharacteristic, complemented
180C2×C4⋊C4×C151C2311yescharacteristic
181C2×C22⋊C4×C151—21no—
182C2×C22⋊C4×C151—21no—
183C2×C22⋊C4×C151—21no—
184C2×C22⋊C4×C151—21no—
185C2×C22⋊C4×C151—21no—
186C2×C22⋊C4×C151—21no—
187C2×C22⋊C4×C151—21no—
188C2×C22⋊C4×C151D411yescharacteristic
189C2×C22⋊C4×C151D411yescharacteristic
190C2×C22⋊C4×C151C2311yescharacteristic
191#103×C151—21no—
192#103×C151—21no—
193#103×C151—21no—
194#103×C151—21no—
195#102×C151—21no—
196#102×C151—21no—
197#102×C151—21no—
198#102×C151—21no—
199C22⋊C8×C151—21no—
200C22⋊C8×C151—21no—
201C22⋊C8×C151C2311yescharacteristic
202C22⋊C8×C151C2311yescharacteristic
203C22⋊C8×C151C2311yescharacteristic
204C22⋊C8×C151C2311yescharacteristic
205#95×C151—21no—
206#95×C151—21no—
207#95×C151—21no—
208#95×C151C2311yescharacteristic
209#95×C151C2311yescharacteristic
210C24×C151—21no—
211C24×C151—21no—
212C24×C151—21no—
213C24×C151C2×D411yescharacteristic
214C24×C151C2×D411yescharacteristic
215#41×C151—24no—
216#41×C151—24no—
217#41×C151—42no—
218#41×C151—42no—
219#41×C151—42no—
220#41×C151—42no—
221#41×C151—42no—
222#41×C151—42no—
223#41×C151—42no—
224#41×C151—81no—
225#41×C151—81no—
226C2×Q8×C151—21no—
227C2×Q8×C151—21no—
228C2×Q8×C151—21no—
229C2×Q8×C151—42no—
230C2×Q8×C151C2×D411yescharacteristic
231C2×D4×C151—24no—
232C2×D4×C151—21no—
233C2×D4×C151—21no—
234C2×D4×C151—21no—
235C2×D4×C151—21no—
236C2×D4×C151—21no—
237C2×D4×C151—21no—
238C2×D4×C151—21no—
239C2×D4×C151—21no—
240C2×D4×C151—21no—
241C2×D4×C151—21no—
242C2×D4×C151—21no—
243C2×D4×C151—21no—
244C2×D4×C151—21no—
245C2×D4×C151—21no—
246C2×D4×C151—21no—
247C2×D4×C151—21no—
248C2×D4×C151—21no—
249C2×D4×C151—21no—
250C2×D4×C151—21no—
251C2×D4×C151—42no—
252C2×D4×C151—42no—
253C2×D4×C151—42no—
254C2×D4×C151—42no—
255C2×D4×C151—41no—
256C2×D4×C151—41no—
257C2×D4×C151—42no—
258C2×D4×C151—42no—
259C2×D4×C151—81no—
260C2×D4×C151—81no—
261C2×D4×C151—81no—
262C2×D4×C151—81no—
263C2×D4×C151—81no—
264C2×D4×C151—82no—
265C2×D4×C151C2×D411yescharacteristic
266C2×D4×C151C2×D411yescharacteristic
267C2×D4×C151C2×D411yescharacteristic
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—42no—
279C22×C4×C151—42no—
280C22×C4×C151—42no—
281C22×C4×C151—42no—
282C22×C4×C151—41no—
283C22×C4×C151—41no—
284C22×C4×C151—42no—
285C22×C4×C151—81no—
286C22×C4×C151C2×D411yescharacteristic
287C22×C4×C151C2×D411yescharacteristic
288C22×C4×C151C2×D411yescharacteristic
289C22×C4×C151C2×D411yescharacteristic
290C22×C4×C151C2×D411yescharacteristic
291C22×C4×C151C2×D411yescharacteristic
292C22×C4×C151C2×D411yescharacteristic
293C22×C4×C151C2×D411yescharacteristic
294C22×C4×C151C2411yescharacteristic
295Q16×C151—42no—
296SD16×C151—42no—
297SD16×C151—42no—
298SD16×C151—42no—
299SD16×C151—42no—
300D8×C151—42no—
301D8×C151—42no—
302D8×C151—42no—
303M16×C151—42no—
304C2×C8×C151—21no—
305C2×C8×C151—21no—
306C2×C8×C151—21no—
307C2×C8×C151—21no—
308C2×C8×C151—42no—
309C4⋊C4×C151—21no—
310C4⋊C4×C151—21no—
311C4⋊C4×C151—21no—
312C4⋊C4×C151—21no—
313C4⋊C4×C151—21no—
314C4⋊C4×C151—21no—
315C4⋊C4×C151—21no—
316C4⋊C4×C151—21no—
317C4⋊C4×C151—21no—
318C4⋊C4×C151—21no—
319C4⋊C4×C151—21no—
320C4⋊C4×C151—21no—
321C4⋊C4×C151—21no—
322C4⋊C4×C151—42no—
323C4⋊C4×C151C2×D411yescharacteristic
324C4⋊C4×C151C2×D411yescharacteristic
325C4⋊C4×C151C2×D411yescharacteristic
326C4⋊C4×C151C2×D411yescharacteristic
327C22⋊C4×C151—21no—
328C22⋊C4×C151—21no—
329C22⋊C4×C151—21no—
330C22⋊C4×C151—21no—
331C22⋊C4×C151—21no—
332C22⋊C4×C151—21no—
333C22⋊C4×C151—21no—
334C22⋊C4×C151—21no—
335C22⋊C4×C151—21no—
336C22⋊C4×C151—21no—
337C22⋊C4×C151—21no—
338C22⋊C4×C151—21no—
339C22⋊C4×C151—21no—
340C22⋊C4×C151—21no—
341C22⋊C4×C151—21no—
342C22⋊C4×C151—21no—
343C22⋊C4×C151—21no—
344C22⋊C4×C151—21no—
345C22⋊C4×C151—21no—
346C22⋊C4×C151—21no—
347C22⋊C4×C151—21no—
348C22⋊C4×C151—21no—
349C22⋊C4×C151—21no—
350C22⋊C4×C151—21no—
351C22⋊C4×C151—21no—
352C22⋊C4×C151—42no—
353C22⋊C4×C151—42no—
354C22⋊C4×C151—42no—
355C22⋊C4×C151—81no—
356C42×C151—21no—
357C42×C151—21no—
358C42×C151—21no—
359C23×C151—21no—
360C23×C151—21no—
361C23×C151—22no—
362C23×C151—22no—
363C23×C151—21no—
364C23×C151—21no—
365C23×C151—21no—
366C23×C151—21no—
367C23×C151—21no—
368C23×C151—21no—
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—42no—
379C23×C151—81no—
380C23×C151—81no—
381C23×C151—81no—
382C23×C151—81no—
383C23×C151—81no—
384C23×C151#12011yescharacteristic
385C23×C151#12011yescharacteristic
386C23×C151C22×D411yescharacteristic
387Q8×C151—22no—
388Q8×C151—22no—
389Q8×C151—41no—
390Q8×C151—41no—
391Q8×C151—41no—
392Q8×C151—81no—
393D4×C151—22no—
394D4×C151—22no—
395D4×C151—41no—
396D4×C151—41no—
397D4×C151—41no—
398D4×C151—41no—
399D4×C151—41no—
400D4×C151—44no—
401D4×C151—41no—
402D4×C151—41no—
403D4×C151—41no—
404D4×C151—41no—
405D4×C151—41no—
406D4×C151—41no—
407D4×C151—44no—
408D4×C151—42no—
409D4×C151—42no—
410D4×C151—81no—
411D4×C151—81no—
412D4×C151—81no—
413D4×C151—81no—
414D4×C151—81no—
415D4×C151—81no—
416D4×C151—81no—
417D4×C151—81no—
418D4×C151—81no—
419D4×C151—81no—
420D4×C151—81no—
421D4×C151—81no—
422D4×C151—84no—
423C2×C4×C151—22no—
424C2×C4×C151—22no—
425C2×C4×C151—22no—
426C2×C4×C151—22no—
427C2×C4×C151—21no—
428C2×C4×C151—21no—
429C2×C4×C151—21no—
430C2×C4×C151—21no—
431C2×C4×C151—21no—
432C2×C4×C151—21no—
433C2×C4×C151—21no—
434C2×C4×C151—21no—
435C2×C4×C151—21no—
436C2×C4×C151—21no—
437C2×C4×C151—41no—
438C2×C4×C151—41no—
439C2×C4×C151—41no—
440C2×C4×C151—41no—
441C2×C4×C151—44no—
442C2×C4×C151—44no—
443C2×C4×C151—41no—
444C2×C4×C151—41no—
445C2×C4×C151—41no—
446C2×C4×C151—41no—
447C2×C4×C151—41no—
448C2×C4×C151—41no—
449C2×C4×C151—41no—
450C2×C4×C151—41no—
451C2×C4×C151—41no—
452C2×C4×C151—81no—
453C2×C4×C151—81no—
454C2×C4×C151—81no—
455C2×C4×C151—81no—
456C2×C4×C151—81no—
457C2×C4×C151—81no—
458C2×C4×C151—81no—
459C2×C4×C151—84no—
460C2×C4×C151#12011yescharacteristic
461C2×C4×C151#12011yescharacteristic
462C2×C4×C151C22×D411yescharacteristic
463C2×C4×C151C22×D411yescharacteristic
464C8×C151—41no—
465C8×C151—41no—
466C8×C151—41no—
467C8×C151—41no—
468C22×C151—21no—
469C22×C151—21no—
470C22×C151—21no—
471C22×C151—21no—
472C22×C151—21no—
473C22×C151—21no—
474C22×C151—21no—
475C22×C151—42no—
476C22×C151—42no—
477C22×C151—42no—
478C22×C151—42no—
479C22×C151—41no—
480C22×C151—41no—
481C22×C151—41no—
482C22×C151—41no—
483C22×C151—41no—
484C22×C151—41no—
485C22×C151—41no—
486C22×C151—41no—
487C22×C151—42no—
488C22×C151—41no—
489C22×C151—41no—
490C22×C151—41no—
491C22×C151—41no—
492C22×C151—81no—
493C22×C151—81no—
494C22×C151—81no—
495C22×C151—81no—
496C22×C151—81no—
497C22×C151—81no—
498C22×C151—162no—
499C22×C151—162no—
500C22×C151B(4,𝔽2)12yes—
501C22×C151C2×#12011yescharacteristic
502C22×C151#57611yescharacteristic
503C22×C151#57711yescharacteristic
504C4×C151—21no—
505C4×C151—21no—
506C4×C151—21no—
507C4×C151—21no—
508C4×C151—42no—
509C4×C151—41no—
510C4×C151—41no—
511C4×C151—41no—
512C4×C151—41no—
513C4×C151—41no—
514C4×C151—41no—
515C4×C151—42no—
516C4×C151—41no—
517C4×C151—41no—
518C4×C151—81no—
519C2×C151—21no—
520C2×C151—21no—
521C2×C151—22no—
522C2×C151—41no—
523C2×C151—82no—
524C2×C151—81no—
525C2×C151—81no—
526C2×C151—81no—
527C2×C151—81no—
528C2×C151#301211yescharacteristic
529C2×C151#301811yescharacteristic
530C2×C151C2×B(4,𝔽2)11yescharacteristic
531#18252C15111yesmaximal, characteristic, direct product factor, Sylow
532C151#1825211yescharacteristic, direct product factor, Sylow
533#3534C2×C15111yescharacteristic, complemented
534#3006C2×C15111yescharacteristic, complemented
535#3002C2×C15111yescharacteristic, complemented
536#2430C2×C15111yescharacteristic, complemented
537#1606C2×C15111yescharacteristic, complemented
538#1604C2×C15111yescharacteristic, complemented
539#1603C2×C15111yescharacteristic, complemented
540#1601C2×C15111yescharacteristic, complemented
541#1600C2×C15111yescharacteristic, complemented
542#1598C2×C15111yescharacteristic, complemented
543#1597C2×C15111yescharacteristic, complemented
544#1595C2×C15111yescharacteristic, complemented
545#1504C2×C15111yescharacteristic, complemented
546C2×#327C2×C15111yescharacteristic, complemented
547#1468C2×C15111yescharacteristic, complemented
548C22×#41C22×C15111yescharacteristic, complemented
549C2×AGL(1,ℤ/8)—21no—
550C2×#135—21no—
551#562—21no—
552#560—21no—
553#553—21no—
554#551—21no—
555#546—21no—
556#546—21no—
557#546—21no—
558D42—21no—
559#540—21no—
560#539—21no—
561#539C22×C15111yescharacteristic
562#538—21no—
563#538C22×C15111yescharacteristic
564#537C22×C15111yescharacteristic
565#534—21no—
566#534C22×C15111yescharacteristic
567#525C22×C15111yescharacteristic
568C2×#123C22×C15111yescharacteristic
569C2×#121—21no—
570C2×#121C22×C15111yescharacteristic
571#452—21no—
572#451C22×C15111yescharacteristic, complemented
573#450C22×C15111yescharacteristic, complemented
574#449—21no—
575#449—21no—
576#449—21no—
577#448C22×C15111yescharacteristic
578#448C22×C15111yescharacteristic, complemented
579#448C22×C15111yescharacteristic, complemented
580#447C22×C15111yescharacteristic
581#447C22×C15111yescharacteristic, complemented
582#447C22×C15111yescharacteristic, complemented
583#417—21no—
584#416—21no—
585#407C22×C15111yescharacteristic, complemented
586C2×C22⋊C8C22×C15111yescharacteristic, complemented
587#395C22×C15111yescharacteristic, complemented
588#394C22×C15111yescharacteristic, complemented
589#393C22×C15111yescharacteristic, complemented
590#392C22×C15111yescharacteristic, complemented
591#386—21no—
592#386—21no—
593#385—21no—
594C2×#95C22×C15111yescharacteristic, complemented
595#328C22×C15111yescharacteristic, complemented
596#328C22×C15111yescharacteristic, complemented
597#327C22×C15111yescharacteristic
598#327C22×C15111yescharacteristic
599#327C22×C15111yescharacteristic, complemented
600#327C22×C15111yescharacteristic, complemented
601#327C22×C15111yescharacteristic, complemented
602#327C22×C15111yescharacteristic, complemented
603#324C22×C15111yescharacteristic, complemented
604#324C22×C15111yescharacteristic, complemented
605#323C22×C15111yescharacteristic, complemented
606#323C22×C15111yescharacteristic, complemented
607C2×#41—21no—
608C2×#41—21no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—44no—
613C2×#41D4×C15111yescharacteristic, complemented
614C22×Q8C23×C15111yescharacteristic
615C22×D4—21no—
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4—21no—
620C22×D4D4×C15111yescharacteristic
621C22×D4D4×C15111yescharacteristic, complemented
622C22×D4C23×C15111yescharacteristic
623C23×C4—21no—
624C23×C4—21no—
625C23×C4C23×C15111yescharacteristic
626AGL(1,ℤ/8)—44no—
627#135—44no—
628C2×Q16—21no—
629C2×SD16—21no—
630C2×SD16—21no—
631C2×SD16—21no—
632C2×SD16—21no—
633C2×D8—21no—
634C2×D8—21no—
635C2×D8—21no—
636C2×M16—21no—
637C22×C8—21no—
638#127—21no—
639#126—21no—
640#126—21no—
641#126—21no—
642#126—21no—
643#125—21no—
644#125—21no—
645#124—21no—
646#124—21no—
647#124—21no—
648#123—21no—
649#123—21no—
650#123—21no—
651#123—21no—
652#123—21no—
653#123—21no—
654#123—21no—
655#123—21no—
656#123—21no—
657#123—21no—
658#123—21no—
659#123—21no—
660#123—21no—
661#123—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8D4×C15111yescharacteristic, complemented
668C22⋊Q8C23×C15111yescharacteristic
669#121—21no—
670#121—21no—
671#121—21no—
672#121—21no—
673#121—21no—
674#121—21no—
675#121—21no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—44no—
685#121D4×C15111yescharacteristic, complemented
686#121D4×C15111yescharacteristic, complemented
687#121D4×C15111yescharacteristic, complemented
688#121C23×C15111yescharacteristic
689#121C23×C15111yescharacteristic
690#121C23×C15111yescharacteristic
691#120—21no—
692#120—21no—
693#120—21no—
694#120—21no—
695#120—21no—
696#120—21no—
697#120—21no—
698#120—21no—
699C4×D4—21no—
700C4×D4—21no—
701C4×D4—21no—
702C4×D4—21no—
703C4×D4—21no—
704C4×D4—21no—
705C4×D4—21no—
706C4×D4—21no—
707#117—21no—
708#117D4×C15111yescharacteristic, complemented
709C2×C4⋊C4—21no—
710C2×C4⋊C4D4×C15111yescharacteristic
711C2×C4⋊C4D4×C15111yescharacteristic, complemented
712C2×C4⋊C4C23×C15111yescharacteristic
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4D4×C15111yescharacteristic
721C2×C22⋊C4D4×C15111yescharacteristic
722C2×C22⋊C4C23×C15111yescharacteristic
723#103—21no—
724#103—21no—
725#103—21no—
726#103—21no—
727#102—21no—
728#102—21no—
729#102—21no—
730#102—21no—
731C22⋊C8—21no—
732C22⋊C8—21no—
733C22⋊C8C23×C15111yescharacteristic
734C22⋊C8C23×C15111yescharacteristic
735C22⋊C8C23×C15111yescharacteristic
736C22⋊C8C23×C15111yescharacteristic
737#95—21no—
738#95—21no—
739#95—21no—
740#95C23×C15111yescharacteristic
741#95C23×C15111yescharacteristic
742C24—21no—
743C24—21no—
744C24—21no—
745C24C2×D4×C15111yescharacteristic
746C24C2×D4×C15111yescharacteristic
747#41—24no—
748#41—24no—
749#41—42no—
750#41—42no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—42no—
756#41—81no—
757#41—81no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—42no—
762C2×Q8C2×D4×C15111yescharacteristic
763C2×D4—24no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—81no—
792C2×D4—81no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—82no—
797C2×D4C2×D4×C15111yescharacteristic
798C2×D4C2×D4×C15111yescharacteristic
799C2×D4C2×D4×C15111yescharacteristic
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—42no—
817C22×C4—81no—
818C22×C4C2×D4×C15111yescharacteristic
819C22×C4C2×D4×C15111yescharacteristic
820C22×C4C2×D4×C15111yescharacteristic
821C22×C4C2×D4×C15111yescharacteristic
822C22×C4C2×D4×C15111yescharacteristic
823C22×C4C2×D4×C15111yescharacteristic
824C22×C4C2×D4×C15111yescharacteristic
825C22×C4C2×D4×C15111yescharacteristic
826C22×C4C24×C15111yescharacteristic
827Q16—42no—
828SD16—42no—
829SD16—42no—
830SD16—42no—
831SD16—42no—
832D8—42no—
833D8—42no—
834D8—42no—
835M16—42no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—42no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—42no—
855C4⋊C4C2×D4×C15111yescharacteristic
856C4⋊C4C2×D4×C15111yescharacteristic
857C4⋊C4C2×D4×C15111yescharacteristic
858C4⋊C4C2×D4×C15111yescharacteristic
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—42no—
885C22⋊C4—42no—
886C22⋊C4—42no—
887C22⋊C4—81no—
888C42—21no—
889C42—21no—
890C42—21no—
891C23—22no—
892C23—21no—
893C23—21no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—21no—
900C23—21no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—42no—
911C23—81no—
912C23—81no—
913C23—81no—
914C23—81no—
915C23—81no—
916C23#120×C15111yescharacteristic
917C23#120×C15111yescharacteristic
918C23C22×D4×C15111yescharacteristic
919Q8—22no—
920Q8—22no—
921Q8—41no—
922Q8—41no—
923Q8—41no—
924Q8—81no—
925D4—22no—
926D4—22no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—44no—
933D4—44no—
934D4—42no—
935D4—42no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—41no—
940D4—41no—
941D4—41no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—81no—
951D4—81no—
952D4—81no—
953D4—81no—
954D4—84no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—81no—
985C2×C4—81no—
986C2×C4—81no—
987C2×C4—81no—
988C2×C4—81no—
989C2×C4—81no—
990C2×C4—81no—
991C2×C4—84no—
992C2×C4#120×C15111yescharacteristic
993C2×C4#120×C15111yescharacteristic
994C2×C4C22×D4×C15111yescharacteristic
995C2×C4C22×D4×C15111yescharacteristic
996C8—41no—
997C8—41no—
998C8—41no—
999C8—41no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—81no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—162no—
1031C22—162no—
1032C22B(4,𝔽2)×C15112yes—
1033C22C2×#120×C15111yescharacteristic
1034C22#576×C15111yescharacteristic
1035C22#577×C15111yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C2—21no—
1052C2—21no—
1053C2—22no—
1054C2—41no—
1055C2—82no—
1056C2—81no—
1057C2—81no—
1058C2—81no—
1059C2—81no—
1060C2#3012×C15111yescharacteristic
1061C2#3018×C15111yescharacteristic
1062C2C2×B(4,𝔽2)×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3534×C151C2semidirect
2. #3006×C151C2semidirect
3. #3002×C151C2semidirect
4. #2430×C151C2semidirect
5. #1606×C151C2semidirect
6. #1604×C151C2semidirect
7. #1603×C151C2semidirect
8. #1601×C151C2semidirect
9. #1600×C151C2semidirect
10. #1598×C151C2semidirect
11. #1597×C151C2semidirect
12. #1595×C151C2semidirect
13. #1504×C151C2semidirect
14. C2×#327×C151C2semidirect
15. #1468×C151C2semidirect
16. C22×#41×C151C22semidirect
40. #451×C151C22semidirect
41. #450×C151C22semidirect
46. #448×C151C22semidirect
47. #448×C151C22semidirect
49. #447×C151C22semidirect
50. #447×C151C22semidirect
53. #407×C151C22semidirect
54. C2×C22⋊C8×C151C22semidirect
55. #395×C151C22semidirect
56. #394×C151C22semidirect
57. #393×C151C22semidirect
58. #392×C151C22semidirect
62. C2×#95×C151C22semidirect
63. #328×C151C22semidirect
64. #328×C151C22semidirect
67. #327×C151C22semidirect
68. #327×C151C22semidirect
69. #327×C151C22semidirect
70. #327×C151C22semidirect
71. #324×C151C22semidirect
72. #324×C151C22semidirect
73. #323×C151C22semidirect
74. #323×C151C22semidirect
81. C2×#41×C151D4semidirect
89. C22×D4×C151D4semidirect
135. C22⋊Q8×C151D4semidirect
153. #121×C151D4semidirect
154. #121×C151D4semidirect
155. #121×C151D4semidirect
176. #117×C151D4semidirect
179. C2×C4⋊C4×C151D4semidirect
531. #18252C151direct (N × H)
532. C151#18252direct (N × H)
533. #3534C2×C151semidirect
534. #3006C2×C151semidirect
535. #3002C2×C151semidirect
536. #2430C2×C151semidirect
537. #1606C2×C151semidirect
538. #1604C2×C151semidirect
539. #1603C2×C151semidirect
540. #1601C2×C151semidirect
541. #1600C2×C151semidirect
542. #1598C2×C151semidirect
543. #1597C2×C151semidirect
544. #1595C2×C151semidirect
545. #1504C2×C151semidirect
546. C2×#327C2×C151semidirect
547. #1468C2×C151semidirect
548. C22×#41C22×C151semidirect
572. #451C22×C151semidirect
573. #450C22×C151semidirect
578. #448C22×C151semidirect
579. #448C22×C151semidirect
581. #447C22×C151semidirect
582. #447C22×C151semidirect
585. #407C22×C151semidirect
586. C2×C22⋊C8C22×C151semidirect
587. #395C22×C151semidirect
588. #394C22×C151semidirect
589. #393C22×C151semidirect
590. #392C22×C151semidirect
594. C2×#95C22×C151semidirect
595. #328C22×C151semidirect
596. #328C22×C151semidirect
599. #327C22×C151semidirect
600. #327C22×C151semidirect
601. #327C22×C151semidirect
602. #327C22×C151semidirect
603. #324C22×C151semidirect
604. #324C22×C151semidirect
605. #323C22×C151semidirect
606. #323C22×C151semidirect
613. C2×#41D4×C151semidirect
621. C22×D4D4×C151semidirect
667. C22⋊Q8D4×C151semidirect
685. #121D4×C151semidirect
686. #121D4×C151semidirect
687. #121D4×C151semidirect
708. #117D4×C151semidirect
711. C2×C4⋊C4D4×C151semidirect

Maximal subgroups

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

subgroupindex
#3534×C1512
#3006×C1512
#3002×C1512
#2430×C1512
#1606×C1512
#1604×C1512
#1603×C1512
#1601×C1512
#1600×C1512
#1598×C1512
#1597×C1512
#1595×C1512
#1504×C1512
C2×#327×C1512
#1468×C1512
#18252151