Finite Group Databasebeta

← C151×#18434 #50323359

Subgroups — C151×#18434 #50323359

Order 38656.

982 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3560×C151C211yesmaximal, characteristic, complemented
2#3213×C151C211yesmaximal, characteristic, complemented
3#3211×C151C211yesmaximal, characteristic, complemented
4#2662×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#1509×C151C211yesmaximal, characteristic, complemented
14#1502×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×#124×C151C2211yescharacteristic, complemented
36#496×C151—21no—
37#495×C151—21no—
38#489×C151—21no—
39#488×C151—21no—
40#464×C151—21no—
41#463×C151—21no—
42#463×C151—21no—
43#463×C151—21no—
44#451×C151C2211yescharacteristic, complemented
45#450×C151C2211yescharacteristic, complemented
46#448×C151C2211yescharacteristic
47#448×C151C2211yescharacteristic
48#448×C151C2211yescharacteristic, complemented
49#447×C151C2211yescharacteristic
50#447×C151C2211yescharacteristic
51#447×C151C2211yescharacteristic, complemented
52#432×C151C2211yescharacteristic, complemented
53#431×C151C2211yescharacteristic, complemented
54#396×C151—21no—
55#395×C151C2211yescharacteristic, complemented
56#394×C151—21no—
57#394×C151C2211yescharacteristic, complemented
58#393×C151C2211yescharacteristic
59#392×C151C2211yescharacteristic
60#390×C151—21no—
61#388×C151—21no—
62C4×C4⋊C4×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×Q8×C151C2311yescharacteristic
78C22×D4×C151—21no—
79C22×D4×C151—21no—
80C22×D4×C151C2311yescharacteristic
81C2×Q16×C151—21no—
82C2×SD16×C151—21no—
83C2×SD16×C151—21no—
84C2×SD16×C151—21no—
85C2×SD16×C151—21no—
86C2×D8×C151—21no—
87C2×D8×C151—21no—
88C2×D8×C151—21no—
89C4⋊Q8×C151—21no—
90C4⋊Q8×C151D411yescharacteristic, complemented
91#127×C151D411yescharacteristic, complemented
92#126×C151—21no—
93#126×C151—21no—
94#126×C151—21no—
95#126×C151—21no—
96#126×C151—21no—
97#126×C151—21no—
98#126×C151—21no—
99#126×C151—21no—
100#126×C151—21no—
101#125×C151—21no—
102#125×C151—21no—
103#125×C151D411yescharacteristic, complemented
104#124×C151—21no—
105#124×C151—21no—
106#124×C151—21no—
107#124×C151—21no—
108#124×C151—21no—
109#124×C151—21no—
110#124×C151—21no—
111#124×C151—21no—
112#124×C151D411yescharacteristic, complemented
113#123×C151—21no—
114#123×C151—21no—
115#123×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—
125C22⋊Q8×C151—21no—
126C22⋊Q8×C151—21no—
127C22⋊Q8×C151—21no—
128C22⋊Q8×C151—21no—
129C22⋊Q8×C151—21no—
130C22⋊Q8×C151—21no—
131C22⋊Q8×C151—21no—
132C22⋊Q8×C151C2311yescharacteristic
133#121×C151—21no—
134#121×C151—21no—
135#121×C151—21no—
136#121×C151—21no—
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×C151C2311yescharacteristic
146#121×C151C2311yescharacteristic
147#121×C151C2311yescharacteristic
148#120×C151—21no—
149#120×C151—21no—
150#120×C151—21no—
151#120×C151—21no—
152#120×C151—21no—
153C4×Q8×C151D411yescharacteristic, complemented
154C4×D4×C151—21no—
155C4×D4×C151—21no—
156C4×D4×C151—21no—
157C4×D4×C151—21no—
158C4×D4×C151—21no—
159C4×D4×C151—21no—
160C4×D4×C151—21no—
161C4×D4×C151—21no—
162C4×D4×C151D411yescharacteristic, complemented
163C4×D4×C151D411yescharacteristic, complemented
164C4×D4×C151D411yescharacteristic, complemented
165#117×C151—21no—
166#117×C151—21no—
167C2×C4⋊C4×C151—21no—
168C2×C4⋊C4×C151—21no—
169C2×C4⋊C4×C151—21no—
170C2×C4⋊C4×C151D411yescharacteristic
171C2×C4⋊C4×C151D411yescharacteristic
172C2×C4⋊C4×C151C2311yescharacteristic
173C2×C22⋊C4×C151—21no—
174C2×C22⋊C4×C151—21no—
175C2×C22⋊C4×C151—21no—
176C2×C22⋊C4×C151—21no—
177C2×C22⋊C4×C151—21no—
178C2×C22⋊C4×C151—21no—
179C2×C22⋊C4×C151—21no—
180C2×C22⋊C4×C151—21no—
181C2×C22⋊C4×C151D411yescharacteristic
182C2×C22⋊C4×C151D411yescharacteristic
183C2×C22⋊C4×C151C2311yescharacteristic
184C2×C42×C151—21no—
185C2×C42×C151C2311yescharacteristic
186C4⋊C8×C151—21no—
187C4⋊C8×C151—21no—
188#103×C151—21no—
189#103×C151—21no—
190#103×C151—21no—
191#103×C151—21no—
192#102×C151—21no—
193#102×C151—21no—
194#102×C151—21no—
195#102×C151—21no—
196C22⋊C8×C151C2311yescharacteristic
197C22⋊C8×C151C2311yescharacteristic
198C22⋊C8×C151C2311yescharacteristic
199C22⋊C8×C151C2311yescharacteristic
200#97×C151—21no—
201C4×C8×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×C151—21no—
216C2×Q8×C151—21no—
217C2×Q8×C151—81no—
218C2×Q8×C151C2×D411yescharacteristic
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—21no—
231C2×D4×C151—21no—
232C2×D4×C151—21no—
233C2×D4×C151—42no—
234C2×D4×C151—81no—
235C2×D4×C151—81no—
236C2×D4×C151—81no—
237C2×D4×C151—81no—
238C2×D4×C151—81no—
239C2×D4×C151C2×D411yescharacteristic
240C2×D4×C151C2×D411yescharacteristic
241C2×D4×C151C2×D411yescharacteristic
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×C151C2×D411yescharacteristic
254C22×C4×C151C2×D411yescharacteristic
255C22×C4×C151C2×D411yescharacteristic
256C22×C4×C151C2×D411yescharacteristic
257C22×C4×C151C2×D411yescharacteristic
258C22×C4×C151C2411yescharacteristic
259Q16×C151—81no—
260SD16×C151—81no—
261SD16×C151—81no—
262SD16×C151—81no—
263SD16×C151—81no—
264D8×C151—81no—
265D8×C151—81no—
266D8×C151—81no—
267C2×C8×C151—21no—
268C2×C8×C151—21no—
269C2×C8×C151—21no—
270C2×C8×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—21no—
288C4⋊C4×C151—42no—
289C4⋊C4×C151—81no—
290C4⋊C4×C151C2×D411yescharacteristic
291C4⋊C4×C151C2×D411yescharacteristic
292C4⋊C4×C151C2×D411yescharacteristic
293C4⋊C4×C151C2×D411yescharacteristic
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—21no—
318C22⋊C4×C151—21no—
319C22⋊C4×C151—42no—
320C22⋊C4×C151—41no—
321C22⋊C4×C151—41no—
322C22⋊C4×C151—41no—
323C22⋊C4×C151—41no—
324C22⋊C4×C151—81no—
325C22⋊C4×C151—81no—
326C22⋊C4×C151—81no—
327C42×C151—21no—
328C42×C151—21no—
329C42×C151—21no—
330C42×C151—81no—
331C42×C151C2×D411yescharacteristic
332C42×C151C2×D411yescharacteristic
333C42×C151C2×D411yescharacteristic
334C42×C151C2×D411yescharacteristic
335C23×C151—21no—
336C23×C151—21no—
337C23×C151—21no—
338C23×C151—21no—
339C23×C151—21no—
340C23×C151—21no—
341C23×C151—41no—
342C23×C151—41no—
343C23×C151—41no—
344C23×C151—41no—
345C23×C151—41no—
346C23×C151—41no—
347C23×C151—41no—
348C23×C151—41no—
349C23×C151—41no—
350C23×C151—81no—
351C23×C151—81no—
352C23×C151—81no—
353C23×C151C22×D411yescharacteristic
354Q8×C151—41no—
355Q8×C151—41no—
356Q8×C151—41no—
357Q8×C151—41no—
358Q8×C151—41no—
359Q8×C151—81no—
360Q8×C151—81no—
361D4×C151—41no—
362D4×C151—41no—
363D4×C151—41no—
364D4×C151—41no—
365D4×C151—41no—
366D4×C151—41no—
367D4×C151—41no—
368D4×C151—41no—
369D4×C151—41no—
370D4×C151—41no—
371D4×C151—41no—
372D4×C151—41no—
373D4×C151—41no—
374D4×C151—81no—
375D4×C151—81no—
376D4×C151—81no—
377D4×C151—81no—
378D4×C151—81no—
379D4×C151—81no—
380D4×C151—81no—
381D4×C151—81no—
382D4×C151—81no—
383D4×C151—84no—
384C2×C4×C151—21no—
385C2×C4×C151—21no—
386C2×C4×C151—22no—
387C2×C4×C151—21no—
388C2×C4×C151—21no—
389C2×C4×C151—21no—
390C2×C4×C151—21no—
391C2×C4×C151—21no—
392C2×C4×C151—21no—
393C2×C4×C151—21no—
394C2×C4×C151—21no—
395C2×C4×C151—21no—
396C2×C4×C151—21no—
397C2×C4×C151—41no—
398C2×C4×C151—41no—
399C2×C4×C151—41no—
400C2×C4×C151—41no—
401C2×C4×C151—41no—
402C2×C4×C151—41no—
403C2×C4×C151—41no—
404C2×C4×C151—41no—
405C2×C4×C151—41no—
406C2×C4×C151—41no—
407C2×C4×C151—41no—
408C2×C4×C151—41no—
409C2×C4×C151—81no—
410C2×C4×C151—81no—
411C2×C4×C151—81no—
412C2×C4×C151—81no—
413C2×C4×C151—81no—
414C2×C4×C151—81no—
415C2×C4×C151—81no—
416C2×C4×C151—81no—
417C2×C4×C151#12011yescharacteristic
418C2×C4×C151#12011yescharacteristic
419C2×C4×C151#12011yescharacteristic
420C2×C4×C151#12011yescharacteristic
421C2×C4×C151C22×D411yescharacteristic
422C2×C4×C151C22×D411yescharacteristic
423C8×C151—41no—
424C8×C151—41no—
425C8×C151—41no—
426C8×C151—41no—
427C22×C151—21no—
428C22×C151—21no—
429C22×C151—41no—
430C22×C151—41no—
431C22×C151—41no—
432C22×C151—41no—
433C22×C151—41no—
434C22×C151—41no—
435C22×C151—41no—
436C22×C151—41no—
437C22×C151—41no—
438C22×C151—41no—
439C22×C151—41no—
440C22×C151—41no—
441C22×C151—81no—
442C22×C151—81no—
443C22×C151—81no—
444C22×C151—81no—
445C22×C151—81no—
446C22×C151—81no—
447C22×C151—81no—
448C22×C151—81no—
449C22×C151—81no—
450C22×C151—162no—
451C22×C151C2×#12011yescharacteristic
452C22×C151#57611yescharacteristic
453C22×C151#57711yescharacteristic
454C4×C151—21no—
455C4×C151—21no—
456C4×C151—21no—
457C4×C151—21no—
458C4×C151—21no—
459C4×C151—21no—
460C4×C151—42no—
461C4×C151—41no—
462C4×C151—41no—
463C4×C151—41no—
464C4×C151—41no—
465C4×C151—41no—
466C4×C151—41no—
467C4×C151—41no—
468C4×C151—41no—
469C4×C151—81no—
470C4×C151—81no—
471C2×C151—21no—
472C2×C151—21no—
473C2×C151—81no—
474C2×C151—81no—
475C2×C151—81no—
476C2×C151—81no—
477C2×C151—161no—
478C2×C151#301211yescharacteristic
479C2×C151#301811yescharacteristic
480C2×C151#302711yescharacteristic
481#18434C15111yesmaximal, characteristic, direct product factor, Sylow
482C151#1843411yescharacteristic, direct product factor, Sylow
483#3560C2×C15111yescharacteristic, complemented
484#3213C2×C15111yescharacteristic, complemented
485#3211C2×C15111yescharacteristic, complemented
486#2662C2×C15111yescharacteristic, complemented
487#1606C2×C15111yescharacteristic, complemented
488#1604C2×C15111yescharacteristic, complemented
489#1603C2×C15111yescharacteristic, complemented
490#1601C2×C15111yescharacteristic, complemented
491#1600C2×C15111yescharacteristic, complemented
492#1598C2×C15111yescharacteristic, complemented
493#1597C2×C15111yescharacteristic, complemented
494#1595C2×C15111yescharacteristic, complemented
495#1509C2×C15111yescharacteristic, complemented
496#1502C2×C15111yescharacteristic, complemented
497#1473C2×C15111yescharacteristic, complemented
498#563—21no—
499#560—21no—
500#553—21no—
501#553—21no—
502#551—21no—
503#547—21no—
504#546—21no—
505#546—21no—
506#542—21no—
507#539—21no—
508#539C22×C15111yescharacteristic
509#538—21no—
510#538—21no—
511#538C22×C15111yescharacteristic
512#537C22×C15111yescharacteristic
513#534C22×C15111yescharacteristic
514#532C22×C15111yescharacteristic
515#529C22×C15111yescharacteristic
516C2×#126C22×C15111yescharacteristic
517C2×#124C22×C15111yescharacteristic, complemented
518#496—21no—
519#495—21no—
520#489—21no—
521#488—21no—
522#464—21no—
523#463—21no—
524#463—21no—
525#463—21no—
526#451C22×C15111yescharacteristic, complemented
527#450C22×C15111yescharacteristic, complemented
528#448C22×C15111yescharacteristic
529#448C22×C15111yescharacteristic
530#448C22×C15111yescharacteristic, complemented
531#447C22×C15111yescharacteristic
532#447C22×C15111yescharacteristic
533#447C22×C15111yescharacteristic, complemented
534#432C22×C15111yescharacteristic, complemented
535#431C22×C15111yescharacteristic, complemented
536#396—21no—
537#395C22×C15111yescharacteristic, complemented
538#394—21no—
539#394C22×C15111yescharacteristic, complemented
540#393C22×C15111yescharacteristic
541#392C22×C15111yescharacteristic
542#390—21no—
543#388—21no—
544C4×C4⋊C4C22×C15111yescharacteristic, complemented
545#328C22×C15111yescharacteristic, complemented
546#328C22×C15111yescharacteristic, complemented
547#327C22×C15111yescharacteristic
548#327C22×C15111yescharacteristic
549#327C22×C15111yescharacteristic
550#327C22×C15111yescharacteristic
551#327C22×C15111yescharacteristic, complemented
552#327C22×C15111yescharacteristic, complemented
553#324C22×C15111yescharacteristic, complemented
554#324C22×C15111yescharacteristic, complemented
555#323C22×C15111yescharacteristic
556#323C22×C15111yescharacteristic
557C2×#41—21no—
558C2×#41—21no—
559C22×Q8C23×C15111yescharacteristic
560C22×D4—21no—
561C22×D4—21no—
562C22×D4C23×C15111yescharacteristic
563C2×Q16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×D8—21no—
569C2×D8—21no—
570C2×D8—21no—
571C4⋊Q8—21no—
572C4⋊Q8D4×C15111yescharacteristic, complemented
573#127D4×C15111yescharacteristic, complemented
574#126—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#126—21no—
581#126—21no—
582#126—21no—
583#125—21no—
584#125—21no—
585#125D4×C15111yescharacteristic, complemented
586#124—21no—
587#124—21no—
588#124—21no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—21no—
593#124—21no—
594#124D4×C15111yescharacteristic, complemented
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606#123—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8—21no—
614C22⋊Q8C23×C15111yescharacteristic
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121C23×C15111yescharacteristic
628#121C23×C15111yescharacteristic
629#121C23×C15111yescharacteristic
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635C4×Q8D4×C15111yescharacteristic, complemented
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4D4×C15111yescharacteristic, complemented
645C4×D4D4×C15111yescharacteristic, complemented
646C4×D4D4×C15111yescharacteristic, complemented
647#117—21no—
648#117—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C15111yescharacteristic
653C2×C4⋊C4D4×C15111yescharacteristic
654C2×C4⋊C4C23×C15111yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C15111yescharacteristic
664C2×C22⋊C4D4×C15111yescharacteristic
665C2×C22⋊C4C23×C15111yescharacteristic
666C2×C42—21no—
667C2×C42C23×C15111yescharacteristic
668C4⋊C8—21no—
669C4⋊C8—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#102—21no—
675#102—21no—
676#102—21no—
677#102—21no—
678C22⋊C8C23×C15111yescharacteristic
679C22⋊C8C23×C15111yescharacteristic
680C22⋊C8C23×C15111yescharacteristic
681C22⋊C8C23×C15111yescharacteristic
682#97—21no—
683C4×C8—21no—
684#95—21no—
685#95—21no—
686#95C23×C15111yescharacteristic
687#95C23×C15111yescharacteristic
688C24—21no—
689C24—21no—
690C24C2×D4×C15111yescharacteristic
691#41—81no—
692#41—81no—
693#41—81no—
694#41—81no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—81no—
700C2×Q8C2×D4×C15111yescharacteristic
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—42no—
716C2×D4—81no—
717C2×D4—81no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4C2×D4×C15111yescharacteristic
722C2×D4C2×D4×C15111yescharacteristic
723C2×D4C2×D4×C15111yescharacteristic
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4C2×D4×C15111yescharacteristic
736C22×C4C2×D4×C15111yescharacteristic
737C22×C4C2×D4×C15111yescharacteristic
738C22×C4C2×D4×C15111yescharacteristic
739C22×C4C2×D4×C15111yescharacteristic
740C22×C4C24×C15111yescharacteristic
741Q16—81no—
742SD16—81no—
743SD16—81no—
744SD16—81no—
745SD16—81no—
746D8—81no—
747D8—81no—
748D8—81no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—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—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—42no—
771C4⋊C4—81no—
772C4⋊C4C2×D4×C15111yescharacteristic
773C4⋊C4C2×D4×C15111yescharacteristic
774C4⋊C4C2×D4×C15111yescharacteristic
775C4⋊C4C2×D4×C15111yescharacteristic
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—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C22⋊C4—81no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—81no—
813C42C2×D4×C15111yescharacteristic
814C42C2×D4×C15111yescharacteristic
815C42C2×D4×C15111yescharacteristic
816C42C2×D4×C15111yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C22×D4×C15111yescharacteristic
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—81no—
842Q8—81no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—84no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4#120×C15111yescharacteristic
900C2×C4#120×C15111yescharacteristic
901C2×C4#120×C15111yescharacteristic
902C2×C4#120×C15111yescharacteristic
903C2×C4C22×D4×C15111yescharacteristic
904C2×C4C22×D4×C15111yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C22—21no—
910C22—21no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—162no—
933C22C2×#120×C15111yescharacteristic
934C22#576×C15111yescharacteristic
935C22#577×C15111yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C2—21no—
954C2—21no—
955C2—81no—
956C2—81no—
957C2—81no—
958C2—81no—
959C2—161no—
960C2#3012×C15111yescharacteristic
961C2#3018×C15111yescharacteristic
962C2#3027×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. #3213×C151C2semidirect
3. #3211×C151C2semidirect
4. #2662×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. #1509×C151C2semidirect
14. #1502×C151C2semidirect
15. #1473×C151C2semidirect
35. C2×#124×C151C22semidirect
44. #451×C151C22semidirect
45. #450×C151C22semidirect
48. #448×C151C22semidirect
51. #447×C151C22semidirect
52. #432×C151C22semidirect
53. #431×C151C22semidirect
55. #395×C151C22semidirect
57. #394×C151C22semidirect
62. C4×C4⋊C4×C151C22semidirect
63. #328×C151C22semidirect
64. #328×C151C22semidirect
69. #327×C151C22semidirect
70. #327×C151C22semidirect
71. #324×C151C22semidirect
72. #324×C151C22semidirect
90. C4⋊Q8×C151D4semidirect
91. #127×C151D4semidirect
103. #125×C151D4semidirect
112. #124×C151D4semidirect
153. C4×Q8×C151D4semidirect
162. C4×D4×C151D4semidirect
163. C4×D4×C151D4semidirect
164. C4×D4×C151D4semidirect
481. #18434C151direct (N × H)
482. C151#18434direct (N × H)
483. #3560C2×C151semidirect
484. #3213C2×C151semidirect
485. #3211C2×C151semidirect
486. #2662C2×C151semidirect
487. #1606C2×C151semidirect
488. #1604C2×C151semidirect
489. #1603C2×C151semidirect
490. #1601C2×C151semidirect
491. #1600C2×C151semidirect
492. #1598C2×C151semidirect
493. #1597C2×C151semidirect
494. #1595C2×C151semidirect
495. #1509C2×C151semidirect
496. #1502C2×C151semidirect
497. #1473C2×C151semidirect
517. C2×#124C22×C151semidirect
526. #451C22×C151semidirect
527. #450C22×C151semidirect
530. #448C22×C151semidirect
533. #447C22×C151semidirect
534. #432C22×C151semidirect
535. #431C22×C151semidirect
537. #395C22×C151semidirect
539. #394C22×C151semidirect
544. C4×C4⋊C4C22×C151semidirect
545. #328C22×C151semidirect
546. #328C22×C151semidirect
551. #327C22×C151semidirect
552. #327C22×C151semidirect
553. #324C22×C151semidirect
554. #324C22×C151semidirect
572. C4⋊Q8D4×C151semidirect
573. #127D4×C151semidirect
585. #125D4×C151semidirect
594. #124D4×C151semidirect
635. C4×Q8D4×C151semidirect
644. C4×D4D4×C151semidirect
645. C4×D4D4×C151semidirect
646. 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
#3213×C1512
#3211×C1512
#2662×C1512
#1606×C1512
#1604×C1512
#1603×C1512
#1601×C1512
#1600×C1512
#1598×C1512
#1597×C1512
#1595×C1512
#1509×C1512
#1502×C1512
#1473×C1512
#18434151