Finite Group Databasebeta

← C151×#18280 #50323205

Subgroups — C151×#18280 #50323205

Order 38656.

1002 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3560×C151C211yesmaximal, characteristic, complemented
2#3114×C151C211yesmaximal, characteristic, complemented
3#3100×C151C211yesmaximal, characteristic, complemented
4#2603×C151C211yesmaximal, characteristic, complemented
5#1612×C151C211yesmaximal, characteristic, complemented
6#1610×C151C211yesmaximal, characteristic, complemented
7#1609×C151C211yesmaximal, characteristic, complemented
8#1607×C151C211yesmaximal, characteristic, complemented
9#1600×C151C211yesmaximal, characteristic, complemented
10#1598×C151C211yesmaximal, characteristic, complemented
11#1597×C151C211yesmaximal, characteristic, complemented
12#1595×C151C211yesmaximal, characteristic, complemented
13#1505×C151C211yesmaximal, characteristic, complemented
14#1500×C151C211yesmaximal, characteristic, complemented
15#1473×C151C211yesmaximal, characteristic, complemented
16#563×C151—21no—
17#560×C151—21no—
18#553×C151—21no—
19#553×C151—21no—
20#551×C151—21no—
21#547×C151—21no—
22#546×C151—21no—
23#546×C151—21no—
24#542×C151—21no—
25#539×C151—21no—
26#539×C151C2211yescharacteristic
27#538×C151—21no—
28#538×C151—21no—
29#538×C151C2211yescharacteristic
30#537×C151C2211yescharacteristic
31#534×C151C2211yescharacteristic
32#532×C151C2211yescharacteristic
33#529×C151C2211yescharacteristic
34C2×#126×C151C2211yescharacteristic
35C2×C4×D4×C151C2211yescharacteristic, complemented
36#483×C151C2211yescharacteristic, complemented
37#480×C151C2211yescharacteristic
38#480×C151C2211yescharacteristic
39#480×C151C2211yescharacteristic, complemented
40#478×C151—21no—
41#474×C151—21no—
42#463×C151—21no—
43#459×C151—21no—
44#450×C151C2211yescharacteristic, complemented
45#447×C151C2211yescharacteristic
46#447×C151C2211yescharacteristic
47#447×C151C2211yescharacteristic, complemented
48#442×C151—21no—
49#440×C151—21no—
50C4×D8×C151—21no—
51C4×D8×C151—21no—
52#432×C151C2211yescharacteristic, complemented
53#431×C151C2211yescharacteristic, complemented
54#398×C151C2211yescharacteristic, complemented
55#397×C151C2211yescharacteristic
56#394×C151C2211yescharacteristic, complemented
57#392×C151C2211yescharacteristic
58#390×C151—21no—
59#388×C151—21no—
60#386×C151—21no—
61#385×C151—21no—
62#376×C151C2211yescharacteristic, complemented
63#328×C151C2211yescharacteristic, complemented
64#328×C151C2211yescharacteristic, complemented
65#327×C151C2211yescharacteristic
66#327×C151C2211yescharacteristic
67#327×C151C2211yescharacteristic
68#327×C151C2211yescharacteristic
69#327×C151C2211yescharacteristic, complemented
70#327×C151C2211yescharacteristic, complemented
71#324×C151C2211yescharacteristic, complemented
72#324×C151C2211yescharacteristic, complemented
73#323×C151C2211yescharacteristic
74#323×C151C2211yescharacteristic
75C2×#41×C151—21no—
76C2×#41×C151—21no—
77C22×D4×C151—21no—
78C22×D4×C151—21no—
79C22×D4×C151C2311yescharacteristic
80C23×C4×C151—21no—
81C2×SD16×C151—21no—
82C2×D8×C151—21no—
83C2×D8×C151—21no—
84C2×D8×C151—21no—
85C4⋊Q8×C151—21no—
86C4⋊Q8×C151D411yescharacteristic, complemented
87#127×C151D411yescharacteristic, complemented
88#126×C151—21no—
89#126×C151—21no—
90#126×C151—21no—
91#126×C151—21no—
92#126×C151—21no—
93#126×C151—21no—
94#126×C151—21no—
95#126×C151—21no—
96#126×C151—21no—
97#125×C151—21no—
98#125×C151—21no—
99#125×C151D411yescharacteristic, complemented
100#124×C151—21no—
101#124×C151—21no—
102#124×C151—21no—
103#124×C151—21no—
104#124×C151D411yescharacteristic, complemented
105#123×C151—21no—
106#123×C151—21no—
107#123×C151—21no—
108#123×C151—21no—
109#123×C151—21no—
110#123×C151—21no—
111#123×C151—21no—
112#123×C151—21no—
113#123×C151—21no—
114#123×C151—21no—
115#123×C151—21no—
116#123×C151—21no—
117C22⋊Q8×C151—21no—
118C22⋊Q8×C151—21no—
119C22⋊Q8×C151—21no—
120C22⋊Q8×C151—21no—
121C22⋊Q8×C151—21no—
122C22⋊Q8×C151—21no—
123C22⋊Q8×C151—21no—
124C22⋊Q8×C151C2311yescharacteristic
125#121×C151—21no—
126#121×C151—21no—
127#121×C151—21no—
128#121×C151—21no—
129#121×C151—21no—
130#121×C151—21no—
131#121×C151—21no—
132#121×C151—21no—
133#121×C151—21no—
134#121×C151—21no—
135#121×C151—21no—
136#121×C151—21no—
137#121×C151C2311yescharacteristic
138#121×C151C2311yescharacteristic
139#121×C151C2311yescharacteristic
140#120×C151—21no—
141#120×C151—21no—
142#120×C151—21no—
143#120×C151—21no—
144#120×C151—21no—
145C4×Q8×C151D411yescharacteristic, complemented
146C4×D4×C151—21no—
147C4×D4×C151—21no—
148C4×D4×C151—21no—
149C4×D4×C151—21no—
150C4×D4×C151—21no—
151C4×D4×C151—21no—
152C4×D4×C151—21no—
153C4×D4×C151—21no—
154C4×D4×C151—21no—
155C4×D4×C151—21no—
156C4×D4×C151—21no—
157C4×D4×C151—21no—
158C4×D4×C151D411yescharacteristic, complemented
159C4×D4×C151D411yescharacteristic, complemented
160C4×D4×C151D411yescharacteristic, complemented
161#117×C151—21no—
162#117×C151—21no—
163C2×C4⋊C4×C151—21no—
164C2×C4⋊C4×C151—21no—
165C2×C4⋊C4×C151D411yescharacteristic
166C2×C4⋊C4×C151D411yescharacteristic
167C2×C4⋊C4×C151C2311yescharacteristic
168C2×C4⋊C4×C151C2311yescharacteristic
169C2×C22⋊C4×C151—21no—
170C2×C22⋊C4×C151—21no—
171C2×C22⋊C4×C151—21no—
172C2×C22⋊C4×C151—21no—
173C2×C22⋊C4×C151—21no—
174C2×C22⋊C4×C151—21no—
175C2×C22⋊C4×C151—21no—
176C2×C22⋊C4×C151D411yescharacteristic
177C2×C22⋊C4×C151D411yescharacteristic
178C2×C22⋊C4×C151C2311yescharacteristic
179C2×C42×C151—21no—
180C2×C42×C151C2311yescharacteristic
181#107×C151—21no—
182#107×C151—21no—
183#107×C151—21no—
184#106×C151—21no—
185C4⋊C8×C151—21no—
186C4⋊C8×C151—21no—
187#103×C151—21no—
188#102×C151—21no—
189#102×C151—21no—
190#102×C151—21no—
191#102×C151—21no—
192#102×C151—21no—
193#102×C151—21no—
194#102×C151—21no—
195C22⋊C8×C151C2311yescharacteristic
196C22⋊C8×C151C2311yescharacteristic
197C22⋊C8×C151C2311yescharacteristic
198C22⋊C8×C151C2311yescharacteristic
199#97×C151—21no—
200C4×C8×C151—21no—
201#95×C151—21no—
202#95×C151—21no—
203#95×C151—21no—
204#95×C151C2311yescharacteristic
205#95×C151C2311yescharacteristic
206C24×C151—21no—
207C24×C151—21no—
208C24×C151C2×D411yescharacteristic
209#41×C151—81no—
210#41×C151—81no—
211#41×C151—81no—
212#41×C151—81no—
213C2×Q8×C151—21no—
214C2×Q8×C151—21no—
215C2×Q8×C151C2×D411yescharacteristic
216C2×D4×C151—21no—
217C2×D4×C151—21no—
218C2×D4×C151—21no—
219C2×D4×C151—21no—
220C2×D4×C151—21no—
221C2×D4×C151—21no—
222C2×D4×C151—21no—
223C2×D4×C151—21no—
224C2×D4×C151—21no—
225C2×D4×C151—21no—
226C2×D4×C151—21no—
227C2×D4×C151—21no—
228C2×D4×C151—21no—
229C2×D4×C151—21no—
230C2×D4×C151—42no—
231C2×D4×C151—42no—
232C2×D4×C151—42no—
233C2×D4×C151—81no—
234C2×D4×C151—81no—
235C2×D4×C151—81no—
236C2×D4×C151C2×D411yescharacteristic
237C2×D4×C151C2×D411yescharacteristic
238C2×D4×C151C2×D411yescharacteristic
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—41no—
251C22×C4×C151—41no—
252C22×C4×C151—81no—
253C22×C4×C151—81no—
254C22×C4×C151C2×D411yescharacteristic
255C22×C4×C151C2×D411yescharacteristic
256C22×C4×C151C2×D411yescharacteristic
257C22×C4×C151C2×D411yescharacteristic
258C22×C4×C151C2×D411yescharacteristic
259C22×C4×C151C2411yescharacteristic
260SD16×C151—42no—
261D8×C151—42no—
262D8×C151—42no—
263D8×C151—42no—
264C2×C8×C151—21no—
265C2×C8×C151—21no—
266C2×C8×C151—21no—
267C2×C8×C151—21no—
268C4⋊C4×C151—21no—
269C4⋊C4×C151—21no—
270C4⋊C4×C151—21no—
271C4⋊C4×C151—21no—
272C4⋊C4×C151—21no—
273C4⋊C4×C151—21no—
274C4⋊C4×C151—21no—
275C4⋊C4×C151—21no—
276C4⋊C4×C151—21no—
277C4⋊C4×C151—21no—
278C4⋊C4×C151—21no—
279C4⋊C4×C151—21no—
280C4⋊C4×C151—21no—
281C4⋊C4×C151—21no—
282C4⋊C4×C151—21no—
283C4⋊C4×C151—21no—
284C4⋊C4×C151—21no—
285C4⋊C4×C151—21no—
286C4⋊C4×C151—21no—
287C4⋊C4×C151—81no—
288C4⋊C4×C151C2×D411yescharacteristic
289C4⋊C4×C151C2×D411yescharacteristic
290C4⋊C4×C151C2×D411yescharacteristic
291C4⋊C4×C151C2×D411yescharacteristic
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—21no—
299C22⋊C4×C151—21no—
300C22⋊C4×C151—21no—
301C22⋊C4×C151—21no—
302C22⋊C4×C151—21no—
303C22⋊C4×C151—21no—
304C22⋊C4×C151—21no—
305C22⋊C4×C151—21no—
306C22⋊C4×C151—21no—
307C22⋊C4×C151—21no—
308C22⋊C4×C151—21no—
309C22⋊C4×C151—21no—
310C22⋊C4×C151—21no—
311C22⋊C4×C151—21no—
312C22⋊C4×C151—21no—
313C22⋊C4×C151—21no—
314C22⋊C4×C151—21no—
315C22⋊C4×C151—21no—
316C22⋊C4×C151—21no—
317C22⋊C4×C151—42no—
318C22⋊C4×C151—42no—
319C22⋊C4×C151—41no—
320C22⋊C4×C151—41no—
321C22⋊C4×C151—81no—
322C22⋊C4×C151—81no—
323C42×C151—21no—
324C42×C151—21no—
325C42×C151—21no—
326C42×C151—42no—
327C42×C151C2×D411yescharacteristic
328C42×C151C2×D411yescharacteristic
329C42×C151C2×D411yescharacteristic
330C42×C151C2×D411yescharacteristic
331C23×C151—22no—
332C23×C151—21no—
333C23×C151—21no—
334C23×C151—21no—
335C23×C151—21no—
336C23×C151—21no—
337C23×C151—21no—
338C23×C151—41no—
339C23×C151—41no—
340C23×C151—41no—
341C23×C151—41no—
342C23×C151—41no—
343C23×C151—41no—
344C23×C151—41no—
345C23×C151—41no—
346C23×C151—81no—
347C23×C151—81no—
348C23×C151—81no—
349C23×C151C22×D411yescharacteristic
350Q8×C151—41no—
351Q8×C151—81no—
352Q8×C151—81no—
353D4×C151—22no—
354D4×C151—22no—
355D4×C151—41no—
356D4×C151—41no—
357D4×C151—41no—
358D4×C151—41no—
359D4×C151—41no—
360D4×C151—41no—
361D4×C151—41no—
362D4×C151—41no—
363D4×C151—41no—
364D4×C151—41no—
365D4×C151—41no—
366D4×C151—81no—
367D4×C151—81no—
368D4×C151—81no—
369D4×C151—81no—
370D4×C151—81no—
371D4×C151—81no—
372D4×C151—81no—
373D4×C151—81no—
374D4×C151—81no—
375D4×C151—84no—
376C2×C4×C151—21no—
377C2×C4×C151—21no—
378C2×C4×C151—22no—
379C2×C4×C151—21no—
380C2×C4×C151—21no—
381C2×C4×C151—21no—
382C2×C4×C151—21no—
383C2×C4×C151—21no—
384C2×C4×C151—21no—
385C2×C4×C151—21no—
386C2×C4×C151—21no—
387C2×C4×C151—21no—
388C2×C4×C151—21no—
389C2×C4×C151—41no—
390C2×C4×C151—41no—
391C2×C4×C151—41no—
392C2×C4×C151—41no—
393C2×C4×C151—41no—
394C2×C4×C151—41no—
395C2×C4×C151—41no—
396C2×C4×C151—41no—
397C2×C4×C151—41no—
398C2×C4×C151—41no—
399C2×C4×C151—41no—
400C2×C4×C151—41no—
401C2×C4×C151—81no—
402C2×C4×C151—81no—
403C2×C4×C151—81no—
404C2×C4×C151—82no—
405C2×C4×C151—82no—
406C2×C4×C151—81no—
407C2×C4×C151—81no—
408C2×C4×C151—81no—
409C2×C4×C151—81no—
410C2×C4×C151—81no—
411C2×C4×C151#12011yescharacteristic
412C2×C4×C151#12011yescharacteristic
413C2×C4×C151#12011yescharacteristic
414C2×C4×C151#12011yescharacteristic
415C2×C4×C151C22×D411yescharacteristic
416C2×C4×C151C22×D411yescharacteristic
417C8×C151—41no—
418C8×C151—41no—
419C8×C151—41no—
420C8×C151—41no—
421C22×C151—21no—
422C22×C151—21no—
423C22×C151—42no—
424C22×C151—42no—
425C22×C151—41no—
426C22×C151—41no—
427C22×C151—41no—
428C22×C151—41no—
429C22×C151—41no—
430C22×C151—41no—
431C22×C151—41no—
432C22×C151—41no—
433C22×C151—41no—
434C22×C151—42no—
435C22×C151—41no—
436C22×C151—41no—
437C22×C151—41no—
438C22×C151—81no—
439C22×C151—81no—
440C22×C151—81no—
441C22×C151—81no—
442C22×C151—81no—
443C22×C151—81no—
444C22×C151—162no—
445C22×C151C2×#12011yescharacteristic
446C22×C151#57611yescharacteristic
447C22×C151#57611yescharacteristic
448C4×C151—21no—
449C4×C151—21no—
450C4×C151—21no—
451C4×C151—21no—
452C4×C151—21no—
453C4×C151—21no—
454C4×C151—42no—
455C4×C151—41no—
456C4×C151—41no—
457C4×C151—41no—
458C4×C151—41no—
459C4×C151—41no—
460C4×C151—41no—
461C4×C151—41no—
462C4×C151—41no—
463C4×C151—81no—
464C4×C151—81no—
465C2×C151—21no—
466C2×C151—21no—
467C2×C151—81no—
468C2×C151—82no—
469C2×C151—81no—
470C2×C151—81no—
471C2×C151—81no—
472C2×C151#300811yescharacteristic
473C2×C151#301811yescharacteristic
474C2×C151#302511yescharacteristic
475#18280C15111yesmaximal, characteristic, direct product factor, Sylow
476C151#1828011yescharacteristic, direct product factor, Sylow
477#3560C2×C15111yescharacteristic, complemented
478#3114C2×C15111yescharacteristic, complemented
479#3100C2×C15111yescharacteristic, complemented
480#2603C2×C15111yescharacteristic, complemented
481#1612C2×C15111yescharacteristic, complemented
482#1610C2×C15111yescharacteristic, complemented
483#1609C2×C15111yescharacteristic, complemented
484#1607C2×C15111yescharacteristic, complemented
485#1600C2×C15111yescharacteristic, complemented
486#1598C2×C15111yescharacteristic, complemented
487#1597C2×C15111yescharacteristic, complemented
488#1595C2×C15111yescharacteristic, complemented
489#1505C2×C15111yescharacteristic, complemented
490#1500C2×C15111yescharacteristic, complemented
491#1473C2×C15111yescharacteristic, complemented
492#563—21no—
493#560—21no—
494#553—21no—
495#553—21no—
496#551—21no—
497#547—21no—
498#546—21no—
499#546—21no—
500#542—21no—
501#539—21no—
502#539C22×C15111yescharacteristic
503#538—21no—
504#538—21no—
505#538C22×C15111yescharacteristic
506#537C22×C15111yescharacteristic
507#534C22×C15111yescharacteristic
508#532C22×C15111yescharacteristic
509#529C22×C15111yescharacteristic
510C2×#126C22×C15111yescharacteristic
511C2×C4×D4C22×C15111yescharacteristic, complemented
512#483C22×C15111yescharacteristic, complemented
513#480C22×C15111yescharacteristic
514#480C22×C15111yescharacteristic
515#480C22×C15111yescharacteristic, complemented
516#478—21no—
517#474—21no—
518#463—21no—
519#459—21no—
520#450C22×C15111yescharacteristic, complemented
521#447C22×C15111yescharacteristic
522#447C22×C15111yescharacteristic
523#447C22×C15111yescharacteristic, complemented
524#442—21no—
525#440—21no—
526C4×D8—21no—
527C4×D8—21no—
528#432C22×C15111yescharacteristic, complemented
529#431C22×C15111yescharacteristic, complemented
530#398C22×C15111yescharacteristic, complemented
531#397C22×C15111yescharacteristic
532#394C22×C15111yescharacteristic, complemented
533#392C22×C15111yescharacteristic
534#390—21no—
535#388—21no—
536#386—21no—
537#385—21no—
538#376C22×C15111yescharacteristic, complemented
539#328C22×C15111yescharacteristic, complemented
540#328C22×C15111yescharacteristic, complemented
541#327C22×C15111yescharacteristic
542#327C22×C15111yescharacteristic
543#327C22×C15111yescharacteristic
544#327C22×C15111yescharacteristic
545#327C22×C15111yescharacteristic, complemented
546#327C22×C15111yescharacteristic, complemented
547#324C22×C15111yescharacteristic, complemented
548#324C22×C15111yescharacteristic, complemented
549#323C22×C15111yescharacteristic
550#323C22×C15111yescharacteristic
551C2×#41—21no—
552C2×#41—21no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4C23×C15111yescharacteristic
556C23×C4—21no—
557C2×SD16—21no—
558C2×D8—21no—
559C2×D8—21no—
560C2×D8—21no—
561C4⋊Q8—21no—
562C4⋊Q8D4×C15111yescharacteristic, complemented
563#127D4×C15111yescharacteristic, complemented
564#126—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#126—21no—
573#125—21no—
574#125—21no—
575#125D4×C15111yescharacteristic, complemented
576#124—21no—
577#124—21no—
578#124—21no—
579#124—21no—
580#124D4×C15111yescharacteristic, complemented
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593C22⋊Q8—21no—
594C22⋊Q8—21no—
595C22⋊Q8—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8C23×C15111yescharacteristic
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—21no—
606#121—21no—
607#121—21no—
608#121—21no—
609#121—21no—
610#121—21no—
611#121—21no—
612#121—21no—
613#121C23×C15111yescharacteristic
614#121C23×C15111yescharacteristic
615#121C23×C15111yescharacteristic
616#120—21no—
617#120—21no—
618#120—21no—
619#120—21no—
620#120—21no—
621C4×Q8D4×C15111yescharacteristic, complemented
622C4×D4—21no—
623C4×D4—21no—
624C4×D4—21no—
625C4×D4—21no—
626C4×D4—21no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4D4×C15111yescharacteristic, complemented
635C4×D4D4×C15111yescharacteristic, complemented
636C4×D4D4×C15111yescharacteristic, complemented
637#117—21no—
638#117—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4D4×C15111yescharacteristic
642C2×C4⋊C4D4×C15111yescharacteristic
643C2×C4⋊C4C23×C15111yescharacteristic
644C2×C4⋊C4C23×C15111yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4D4×C15111yescharacteristic
653C2×C22⋊C4D4×C15111yescharacteristic
654C2×C22⋊C4C23×C15111yescharacteristic
655C2×C42—21no—
656C2×C42C23×C15111yescharacteristic
657#107—21no—
658#107—21no—
659#107—21no—
660#106—21no—
661C4⋊C8—21no—
662C4⋊C8—21no—
663#103—21no—
664#102—21no—
665#102—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8C23×C15111yescharacteristic
672C22⋊C8C23×C15111yescharacteristic
673C22⋊C8C23×C15111yescharacteristic
674C22⋊C8C23×C15111yescharacteristic
675#97—21no—
676C4×C8—21no—
677#95—21no—
678#95—21no—
679#95—21no—
680#95C23×C15111yescharacteristic
681#95C23×C15111yescharacteristic
682C24—21no—
683C24—21no—
684C24C2×D4×C15111yescharacteristic
685#41—81no—
686#41—81no—
687#41—81no—
688#41—81no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×Q8C2×D4×C15111yescharacteristic
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—42no—
707C2×D4—42no—
708C2×D4—42no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4—81no—
712C2×D4C2×D4×C15111yescharacteristic
713C2×D4C2×D4×C15111yescharacteristic
714C2×D4C2×D4×C15111yescharacteristic
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—41no—
727C22×C4—41no—
728C22×C4—81no—
729C22×C4—81no—
730C22×C4C2×D4×C15111yescharacteristic
731C22×C4C2×D4×C15111yescharacteristic
732C22×C4C2×D4×C15111yescharacteristic
733C22×C4C2×D4×C15111yescharacteristic
734C22×C4C2×D4×C15111yescharacteristic
735C22×C4C24×C15111yescharacteristic
736SD16—42no—
737D8—42no—
738D8—42no—
739D8—42no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—81no—
764C4⋊C4C2×D4×C15111yescharacteristic
765C4⋊C4C2×D4×C15111yescharacteristic
766C4⋊C4C2×D4×C15111yescharacteristic
767C4⋊C4C2×D4×C15111yescharacteristic
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—42no—
794C22⋊C4—42no—
795C22⋊C4—41no—
796C22⋊C4—41no—
797C22⋊C4—81no—
798C22⋊C4—81no—
799C42—21no—
800C42—21no—
801C42—21no—
802C42—42no—
803C42C2×D4×C15111yescharacteristic
804C42C2×D4×C15111yescharacteristic
805C42C2×D4×C15111yescharacteristic
806C42C2×D4×C15111yescharacteristic
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—81no—
823C23—81no—
824C23—81no—
825C23C22×D4×C15111yescharacteristic
826Q8—41no—
827Q8—81no—
828Q8—81no—
829D4—22no—
830D4—22no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—81no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—84no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—81no—
878C2×C4—81no—
879C2×C4—81no—
880C2×C4—82no—
881C2×C4—82no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4#120×C15111yescharacteristic
888C2×C4#120×C15111yescharacteristic
889C2×C4#120×C15111yescharacteristic
890C2×C4#120×C15111yescharacteristic
891C2×C4C22×D4×C15111yescharacteristic
892C2×C4C22×D4×C15111yescharacteristic
893C8—41no—
894C8—41no—
895C8—41no—
896C8—41no—
897C22—21no—
898C22—21no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—162no—
921C22C2×#120×C15111yescharacteristic
922C22#576×C15111yescharacteristic
923C22#576×C15111yescharacteristic
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—42no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—81no—
940C4—81no—
941C2—21no—
942C2—21no—
943C2—82no—
944C2—81no—
945C2—81no—
946C2—81no—
947C2—81no—
948C2#3008×C15111yescharacteristic
949C2#3018×C15111yescharacteristic
950C2#3025×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3560×C151C2semidirect
2. #3114×C151C2semidirect
3. #3100×C151C2semidirect
4. #2603×C151C2semidirect
5. #1612×C151C2semidirect
6. #1610×C151C2semidirect
7. #1609×C151C2semidirect
8. #1607×C151C2semidirect
9. #1600×C151C2semidirect
10. #1598×C151C2semidirect
11. #1597×C151C2semidirect
12. #1595×C151C2semidirect
13. #1505×C151C2semidirect
14. #1500×C151C2semidirect
15. #1473×C151C2semidirect
35. C2×C4×D4×C151C22semidirect
36. #483×C151C22semidirect
39. #480×C151C22semidirect
44. #450×C151C22semidirect
47. #447×C151C22semidirect
52. #432×C151C22semidirect
53. #431×C151C22semidirect
54. #398×C151C22semidirect
56. #394×C151C22semidirect
62. #376×C151C22semidirect
63. #328×C151C22semidirect
64. #328×C151C22semidirect
69. #327×C151C22semidirect
70. #327×C151C22semidirect
71. #324×C151C22semidirect
72. #324×C151C22semidirect
86. C4⋊Q8×C151D4semidirect
87. #127×C151D4semidirect
99. #125×C151D4semidirect
104. #124×C151D4semidirect
145. C4×Q8×C151D4semidirect
158. C4×D4×C151D4semidirect
159. C4×D4×C151D4semidirect
160. C4×D4×C151D4semidirect
475. #18280C151direct (N × H)
476. C151#18280direct (N × H)
477. #3560C2×C151semidirect
478. #3114C2×C151semidirect
479. #3100C2×C151semidirect
480. #2603C2×C151semidirect
481. #1612C2×C151semidirect
482. #1610C2×C151semidirect
483. #1609C2×C151semidirect
484. #1607C2×C151semidirect
485. #1600C2×C151semidirect
486. #1598C2×C151semidirect
487. #1597C2×C151semidirect
488. #1595C2×C151semidirect
489. #1505C2×C151semidirect
490. #1500C2×C151semidirect
491. #1473C2×C151semidirect
511. C2×C4×D4C22×C151semidirect
512. #483C22×C151semidirect
515. #480C22×C151semidirect
520. #450C22×C151semidirect
523. #447C22×C151semidirect
528. #432C22×C151semidirect
529. #431C22×C151semidirect
530. #398C22×C151semidirect
532. #394C22×C151semidirect
538. #376C22×C151semidirect
539. #328C22×C151semidirect
540. #328C22×C151semidirect
545. #327C22×C151semidirect
546. #327C22×C151semidirect
547. #324C22×C151semidirect
548. #324C22×C151semidirect
562. C4⋊Q8D4×C151semidirect
563. #127D4×C151semidirect
575. #125D4×C151semidirect
580. #124D4×C151semidirect
621. C4×Q8D4×C151semidirect
634. C4×D4D4×C151semidirect
635. C4×D4D4×C151semidirect
636. C4×D4D4×C151semidirect

Maximal subgroups

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

subgroupindex
#3560×C1512
#3114×C1512
#3100×C1512
#2603×C1512
#1612×C1512
#1610×C1512
#1609×C1512
#1607×C1512
#1600×C1512
#1598×C1512
#1597×C1512
#1595×C1512
#1505×C1512
#1500×C1512
#1473×C1512
#18280151