Finite Group Databasebeta

← C151×#18415 #50323340

Subgroups — C151×#18415 #50323340

Order 38656.

992 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3534×C151C211yesmaximal, characteristic
2#3196×C151C211yesmaximal, characteristic, complemented
3#3187×C151C211yesmaximal, characteristic, complemented
4#2663×C151C211yesmaximal, characteristic, complemented
5#1618×C151C211yesmaximal, characteristic, complemented
6#1616×C151C211yesmaximal, characteristic, complemented
7#1615×C151C211yesmaximal, characteristic, complemented
8#1613×C151C211yesmaximal, characteristic, complemented
9#1606×C151C211yesmaximal, characteristic, complemented
10#1604×C151C211yesmaximal, characteristic, complemented
11#1603×C151C211yesmaximal, characteristic, complemented
12#1601×C151C211yesmaximal, characteristic, complemented
13#1507×C151C211yesmaximal, characteristic, complemented
14#1501×C151C211yesmaximal, characteristic, complemented
15#1468×C151C211yesmaximal, characteristic, complemented
16#562×C151—21no—
17#560×C151—21no—
18#553×C151—21no—
19#551×C151—21no—
20#546×C151—21no—
21#546×C151—21no—
22#546×C151—21no—
23D42×C151—21no—
24#540×C151—21no—
25#539×C151—21no—
26#539×C151C2211yescharacteristic
27#538×C151—21no—
28#538×C151C2211yescharacteristic
29#537×C151C2211yescharacteristic
30#534×C151—21no—
31#534×C151C2211yescharacteristic
32#525×C151C2211yescharacteristic
33C2×#123×C151C2211yescharacteristic
34C2×C22⋊Q8×C151C2211yescharacteristic, complemented
35C2×#121×C151C2211yescharacteristic
36#485×C151—21no—
37#484×C151C2211yescharacteristic, complemented
38#483×C151—21no—
39#481×C151C2211yescharacteristic
40#481×C151C2211yescharacteristic, complemented
41#481×C151C2211yescharacteristic, complemented
42#470×C151—21no—
43#468×C151—21no—
44#465×C151—21no—
45#465×C151—21no—
46#452×C151—21no—
47#451×C151C2211yescharacteristic, complemented
48#450×C151—21no—
49#448×C151C2211yescharacteristic
50#448×C151C2211yescharacteristic, complemented
51#448×C151C2211yescharacteristic, complemented
52#407×C151C2211yescharacteristic, complemented
53C2×C22⋊C8×C151C2211yescharacteristic, complemented
54#400×C151C2211yescharacteristic, complemented
55#399×C151C2211yescharacteristic, complemented
56#397×C151—21no—
57#395×C151C2211yescharacteristic, complemented
58#394×C151—21no—
59#393×C151C2211yescharacteristic, complemented
60#389×C151—21no—
61#388×C151—21no—
62C4×C22⋊C4×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×C151D411yescharacteristic
77C22×Q8×C151C2311yescharacteristic
78C22×D4×C151—21no—
79C22×D4×C151—21no—
80C22×D4×C151—21no—
81C22×D4×C151D411yescharacteristic
82C22×D4×C151D411yescharacteristic
83C23×C4×C151C2311yescharacteristic
84C2×Q16×C151—21no—
85C2×SD16×C151—21no—
86C2×SD16×C151—21no—
87C2×SD16×C151—21no—
88C2×M16×C151—21no—
89C22×C8×C151—21no—
90#127×C151—21no—
91#126×C151—21no—
92#126×C151—21no—
93#126×C151—21no—
94#126×C151—21no—
95#125×C151—21no—
96#125×C151—21no—
97#124×C151—21no—
98#124×C151—21no—
99#124×C151—21no—
100#123×C151—21no—
101#123×C151—21no—
102#123×C151—21no—
103#123×C151—21no—
104#123×C151—21no—
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—
114C22⋊Q8×C151—21no—
115C22⋊Q8×C151—21no—
116C22⋊Q8×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×C151D411yescharacteristic
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×C151—21no—
138#121×C151—21no—
139#121×C151—21no—
140#121×C151D411yescharacteristic
141#121×C151D411yescharacteristic
142#121×C151D411yescharacteristic
143#121×C151C2311yescharacteristic
144#121×C151C2311yescharacteristic
145#121×C151C2311yescharacteristic
146#120×C151—21no—
147#120×C151—21no—
148#120×C151—21no—
149#120×C151—21no—
150#120×C151—21no—
151#120×C151—21no—
152#120×C151—21no—
153#120×C151—21no—
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—
162#117×C151—21no—
163#117×C151D411yescharacteristic
164C2×C4⋊C4×C151—21no—
165C2×C4⋊C4×C151—21no—
166C2×C4⋊C4×C151—21no—
167C2×C4⋊C4×C151D411yescharacteristic
168C2×C4⋊C4×C151D411yescharacteristic
169C2×C4⋊C4×C151C2311yescharacteristic
170C2×C4⋊C4×C151C2311yescharacteristic
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×C151—21no—
177C2×C22⋊C4×C151—21no—
178C2×C22⋊C4×C151D411yescharacteristic
179C2×C22⋊C4×C151D411yescharacteristic
180C2×C22⋊C4×C151C2311yescharacteristic
181C2×C42×C151—21no—
182#107×C151—21no—
183#106×C151—21no—
184#106×C151—21no—
185#106×C151—21no—
186#103×C151—21no—
187#103×C151—21no—
188#103×C151—21no—
189#103×C151—21no—
190#103×C151—21no—
191#102×C151—21no—
192#102×C151—21no—
193#102×C151—21no—
194C22⋊C8×C151—21no—
195C22⋊C8×C151—21no—
196C22⋊C8×C151C2311yescharacteristic
197C22⋊C8×C151C2311yescharacteristic
198C22⋊C8×C151C2311yescharacteristic
199C22⋊C8×C151C2311yescharacteristic
200#95×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
209C24×C151C2×D411yescharacteristic
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—81no—
217C2×Q8×C151C2×D411yescharacteristic
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—21no—
231C2×D4×C151—21no—
232C2×D4×C151—21no—
233C2×D4×C151—21no—
234C2×D4×C151—21no—
235C2×D4×C151—81no—
236C2×D4×C151—81no—
237C2×D4×C151—81no—
238C2×D4×C151—81no—
239C2×D4×C151—81no—
240C2×D4×C151—81no—
241C2×D4×C151—82no—
242C2×D4×C151C2×D411yescharacteristic
243C2×D4×C151C2×D411yescharacteristic
244C2×D4×C151C2×D411yescharacteristic
245C22×C4×C151—21no—
246C22×C4×C151—21no—
247C22×C4×C151—21no—
248C22×C4×C151—21no—
249C22×C4×C151—21no—
250C22×C4×C151—21no—
251C22×C4×C151—21no—
252C22×C4×C151—21no—
253C22×C4×C151—21no—
254C22×C4×C151—21no—
255C22×C4×C151—21no—
256C22×C4×C151—81no—
257C22×C4×C151C2×D411yescharacteristic
258C22×C4×C151C2×D411yescharacteristic
259C22×C4×C151C2×D411yescharacteristic
260C22×C4×C151C2×D411yescharacteristic
261C22×C4×C151C2×D411yescharacteristic
262C22×C4×C151C2×D411yescharacteristic
263C22×C4×C151C2×D411yescharacteristic
264C22×C4×C151C2×D411yescharacteristic
265C22×C4×C151C2411yescharacteristic
266Q16×C151—81no—
267SD16×C151—81no—
268SD16×C151—81no—
269SD16×C151—81no—
270M16×C151—81no—
271C2×C8×C151—21no—
272C2×C8×C151—21no—
273C2×C8×C151—21no—
274C2×C8×C151—21no—
275C2×C8×C151—81no—
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—21no—
289C4⋊C4×C151—21no—
290C4⋊C4×C151—21no—
291C4⋊C4×C151—42no—
292C4⋊C4×C151—41no—
293C4⋊C4×C151—41no—
294C4⋊C4×C151—81no—
295C4⋊C4×C151C2×D411yescharacteristic
296C4⋊C4×C151C2×D411yescharacteristic
297C4⋊C4×C151C2×D411yescharacteristic
298C4⋊C4×C151C2×D411yescharacteristic
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—21no—
320C22⋊C4×C151—21no—
321C22⋊C4×C151—21no—
322C22⋊C4×C151—21no—
323C22⋊C4×C151—21no—
324C22⋊C4×C151—42no—
325C22⋊C4×C151—42no—
326C22⋊C4×C151—41no—
327C22⋊C4×C151—41no—
328C22⋊C4×C151—81no—
329C42×C151—21no—
330C42×C151—21no—
331C42×C151—21no—
332C42×C151—81no—
333C23×C151—21no—
334C23×C151—21no—
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—42no—
344C23×C151—41no—
345C23×C151—41no—
346C23×C151—81no—
347C23×C151—81no—
348C23×C151—81no—
349C23×C151—81no—
350C23×C151—81no—
351C23×C151#12011yescharacteristic
352C23×C151#12011yescharacteristic
353C23×C151C22×D411yescharacteristic
354Q8×C151—41no—
355Q8×C151—41no—
356Q8×C151—41no—
357Q8×C151—41no—
358Q8×C151—41no—
359Q8×C151—81no—
360D4×C151—41no—
361D4×C151—41no—
362D4×C151—41no—
363D4×C151—42no—
364D4×C151—42no—
365D4×C151—41no—
366D4×C151—41no—
367D4×C151—41no—
368D4×C151—41no—
369D4×C151—41no—
370D4×C151—41no—
371D4×C151—81no—
372D4×C151—81no—
373D4×C151—81no—
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—
383C2×C4×C151—22no—
384C2×C4×C151—21no—
385C2×C4×C151—21no—
386C2×C4×C151—21no—
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—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—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—41no—
410C2×C4×C151—41no—
411C2×C4×C151—41no—
412C2×C4×C151—41no—
413C2×C4×C151—81no—
414C2×C4×C151—81no—
415C2×C4×C151—81no—
416C2×C4×C151—81no—
417C2×C4×C151—81no—
418C2×C4×C151—81no—
419C2×C4×C151—81no—
420C2×C4×C151#12011yescharacteristic
421C2×C4×C151#12011yescharacteristic
422C2×C4×C151C22×D411yescharacteristic
423C2×C4×C151C22×D411yescharacteristic
424C8×C151—41no—
425C8×C151—41no—
426C8×C151—41no—
427C8×C151—41no—
428C22×C151—21no—
429C22×C151—21no—
430C22×C151—21no—
431C22×C151—21no—
432C22×C151—21no—
433C22×C151—21no—
434C22×C151—21no—
435C22×C151—21no—
436C22×C151—41no—
437C22×C151—41no—
438C22×C151—41no—
439C22×C151—41no—
440C22×C151—41no—
441C22×C151—41no—
442C22×C151—41no—
443C22×C151—41no—
444C22×C151—41no—
445C22×C151—41no—
446C22×C151—41no—
447C22×C151—41no—
448C22×C151—81no—
449C22×C151—81no—
450C22×C151—81no—
451C22×C151—81no—
452C22×C151—162no—
453C22×C151—162no—
454C22×C151C2×#12011yescharacteristic
455C22×C151#57711yescharacteristic
456C22×C151#57711yescharacteristic
457C4×C151—21no—
458C4×C151—21no—
459C4×C151—21no—
460C4×C151—21no—
461C4×C151—42no—
462C4×C151—41no—
463C4×C151—41no—
464C4×C151—41no—
465C4×C151—41no—
466C4×C151—41no—
467C4×C151—41no—
468C4×C151—41no—
469C4×C151—41no—
470C4×C151—81no—
471C4×C151—81no—
472C4×C151—81no—
473C2×C151—21no—
474C2×C151—21no—
475C2×C151—41no—
476C2×C151—41no—
477C2×C151—81no—
478C2×C151—81no—
479C2×C151—81no—
480C2×C151—81no—
481C2×C151#300911yescharacteristic
482C2×C151#301811yescharacteristic
483C2×C151#302611yescharacteristic
484#18415C15111yesmaximal, characteristic, direct product factor, Sylow
485C151#1841511yescharacteristic, direct product factor, Sylow
486#3534C2×C15111yescharacteristic
487#3196C2×C15111yescharacteristic, complemented
488#3187C2×C15111yescharacteristic, complemented
489#2663C2×C15111yescharacteristic, complemented
490#1618C2×C15111yescharacteristic, complemented
491#1616C2×C15111yescharacteristic, complemented
492#1615C2×C15111yescharacteristic, complemented
493#1613C2×C15111yescharacteristic, complemented
494#1606C2×C15111yescharacteristic, complemented
495#1604C2×C15111yescharacteristic, complemented
496#1603C2×C15111yescharacteristic, complemented
497#1601C2×C15111yescharacteristic, complemented
498#1507C2×C15111yescharacteristic, complemented
499#1501C2×C15111yescharacteristic, complemented
500#1468C2×C15111yescharacteristic, complemented
501#562—21no—
502#560—21no—
503#553—21no—
504#551—21no—
505#546—21no—
506#546—21no—
507#546—21no—
508D42—21no—
509#540—21no—
510#539—21no—
511#539C22×C15111yescharacteristic
512#538—21no—
513#538C22×C15111yescharacteristic
514#537C22×C15111yescharacteristic
515#534—21no—
516#534C22×C15111yescharacteristic
517#525C22×C15111yescharacteristic
518C2×#123C22×C15111yescharacteristic
519C2×C22⋊Q8C22×C15111yescharacteristic, complemented
520C2×#121C22×C15111yescharacteristic
521#485—21no—
522#484C22×C15111yescharacteristic, complemented
523#483—21no—
524#481C22×C15111yescharacteristic
525#481C22×C15111yescharacteristic, complemented
526#481C22×C15111yescharacteristic, complemented
527#470—21no—
528#468—21no—
529#465—21no—
530#465—21no—
531#452—21no—
532#451C22×C15111yescharacteristic, complemented
533#450—21no—
534#448C22×C15111yescharacteristic
535#448C22×C15111yescharacteristic, complemented
536#448C22×C15111yescharacteristic, complemented
537#407C22×C15111yescharacteristic, complemented
538C2×C22⋊C8C22×C15111yescharacteristic, complemented
539#400C22×C15111yescharacteristic, complemented
540#399C22×C15111yescharacteristic, complemented
541#397—21no—
542#395C22×C15111yescharacteristic, complemented
543#394—21no—
544#393C22×C15111yescharacteristic, complemented
545#389—21no—
546#388—21no—
547C4×C22⋊C4C22×C15111yescharacteristic, complemented
548#328C22×C15111yescharacteristic, complemented
549#328C22×C15111yescharacteristic, complemented
550#327C22×C15111yescharacteristic
551#327C22×C15111yescharacteristic
552#327C22×C15111yescharacteristic, complemented
553#327C22×C15111yescharacteristic, complemented
554#327C22×C15111yescharacteristic, complemented
555#327C22×C15111yescharacteristic, complemented
556#324C22×C15111yescharacteristic, complemented
557#324C22×C15111yescharacteristic, complemented
558#323C22×C15111yescharacteristic, complemented
559#323C22×C15111yescharacteristic, complemented
560C2×#41—21no—
561C2×#41D4×C15111yescharacteristic
562C22×Q8C23×C15111yescharacteristic
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4D4×C15111yescharacteristic
567C22×D4D4×C15111yescharacteristic
568C23×C4C23×C15111yescharacteristic
569C2×Q16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×M16—21no—
574C22×C8—21no—
575#127—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#125—21no—
581#125—21no—
582#124—21no—
583#124—21no—
584#124—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—
593#123—21no—
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8D4×C15111yescharacteristic
609C22⋊Q8C23×C15111yescharacteristic
610#121—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
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#121D4×C15111yescharacteristic
626#121D4×C15111yescharacteristic
627#121D4×C15111yescharacteristic
628#121C23×C15111yescharacteristic
629#121C23×C15111yescharacteristic
630#121C23×C15111yescharacteristic
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635#120—21no—
636#120—21no—
637#120—21no—
638#120—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—21no—
646C4×D4—21no—
647#117—21no—
648#117D4×C15111yescharacteristic
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×C4⋊C4C23×C15111yescharacteristic
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—
667#107—21no—
668#106—21no—
669#106—21no—
670#106—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#103—21no—
675#103—21no—
676#102—21no—
677#102—21no—
678#102—21no—
679C22⋊C8—21no—
680C22⋊C8—21no—
681C22⋊C8C23×C15111yescharacteristic
682C22⋊C8C23×C15111yescharacteristic
683C22⋊C8C23×C15111yescharacteristic
684C22⋊C8C23×C15111yescharacteristic
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95C23×C15111yescharacteristic
690#95C23×C15111yescharacteristic
691C24—21no—
692C24—21no—
693C24C2×D4×C15111yescharacteristic
694C24C2×D4×C15111yescharacteristic
695#41—81no—
696#41—81no—
697#41—81no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—81no—
702C2×Q8C2×D4×C15111yescharacteristic
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—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—81no—
721C2×D4—81no—
722C2×D4—81no—
723C2×D4—81no—
724C2×D4—81no—
725C2×D4—81no—
726C2×D4—82no—
727C2×D4C2×D4×C15111yescharacteristic
728C2×D4C2×D4×C15111yescharacteristic
729C2×D4C2×D4×C15111yescharacteristic
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—81no—
742C22×C4C2×D4×C15111yescharacteristic
743C22×C4C2×D4×C15111yescharacteristic
744C22×C4C2×D4×C15111yescharacteristic
745C22×C4C2×D4×C15111yescharacteristic
746C22×C4C2×D4×C15111yescharacteristic
747C22×C4C2×D4×C15111yescharacteristic
748C22×C4C2×D4×C15111yescharacteristic
749C22×C4C2×D4×C15111yescharacteristic
750C22×C4C24×C15111yescharacteristic
751Q16—81no—
752SD16—81no—
753SD16—81no—
754SD16—81no—
755M16—81no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
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—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—42no—
777C4⋊C4—41no—
778C4⋊C4—41no—
779C4⋊C4—81no—
780C4⋊C4C2×D4×C15111yescharacteristic
781C4⋊C4C2×D4×C15111yescharacteristic
782C4⋊C4C2×D4×C15111yescharacteristic
783C4⋊C4C2×D4×C15111yescharacteristic
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—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—42no—
810C22⋊C4—42no—
811C22⋊C4—41no—
812C22⋊C4—41no—
813C22⋊C4—81no—
814C42—21no—
815C42—21no—
816C42—21no—
817C42—81no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23#120×C15111yescharacteristic
837C23#120×C15111yescharacteristic
838C23C22×D4×C15111yescharacteristic
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—42no—
849D4—42no—
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—81no—
866D4—81no—
867D4—81no—
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—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4#120×C15111yescharacteristic
906C2×C4#120×C15111yescharacteristic
907C2×C4C22×D4×C15111yescharacteristic
908C2×C4C22×D4×C15111yescharacteristic
909C8—41no—
910C8—41no—
911C8—41no—
912C8—41no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×#120×C15111yescharacteristic
940C22#577×C15111yescharacteristic
941C22#577×C15111yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—42no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—41no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2#3009×C15111yescharacteristic
967C2#3018×C15111yescharacteristic
968C2#3026×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3534×C151C2
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
2. #3196×C151C2semidirect
3. #3187×C151C2semidirect
4. #2663×C151C2semidirect
5. #1618×C151C2semidirect
6. #1616×C151C2semidirect
7. #1615×C151C2semidirect
8. #1613×C151C2semidirect
9. #1606×C151C2semidirect
10. #1604×C151C2semidirect
11. #1603×C151C2semidirect
12. #1601×C151C2semidirect
13. #1507×C151C2semidirect
14. #1501×C151C2semidirect
15. #1468×C151C2semidirect
34. C2×C22⋊Q8×C151C22semidirect
37. #484×C151C22semidirect
40. #481×C151C22semidirect
41. #481×C151C22semidirect
47. #451×C151C22semidirect
50. #448×C151C22semidirect
51. #448×C151C22semidirect
52. #407×C151C22semidirect
53. C2×C22⋊C8×C151C22semidirect
54. #400×C151C22semidirect
55. #399×C151C22semidirect
57. #395×C151C22semidirect
59. #393×C151C22semidirect
62. C4×C22⋊C4×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
484. #18415C151direct (N × H)
485. C151#18415direct (N × H)
487. #3196C2×C151semidirect
488. #3187C2×C151semidirect
489. #2663C2×C151semidirect
490. #1618C2×C151semidirect
491. #1616C2×C151semidirect
492. #1615C2×C151semidirect
493. #1613C2×C151semidirect
494. #1606C2×C151semidirect
495. #1604C2×C151semidirect
496. #1603C2×C151semidirect
497. #1601C2×C151semidirect
498. #1507C2×C151semidirect
499. #1501C2×C151semidirect
500. #1468C2×C151semidirect
519. C2×C22⋊Q8C22×C151semidirect
522. #484C22×C151semidirect
525. #481C22×C151semidirect
526. #481C22×C151semidirect
532. #451C22×C151semidirect
535. #448C22×C151semidirect
536. #448C22×C151semidirect
537. #407C22×C151semidirect
538. C2×C22⋊C8C22×C151semidirect
539. #400C22×C151semidirect
540. #399C22×C151semidirect
542. #395C22×C151semidirect
544. #393C22×C151semidirect
547. C4×C22⋊C4C22×C151semidirect
548. #328C22×C151semidirect
549. #328C22×C151semidirect
552. #327C22×C151semidirect
553. #327C22×C151semidirect
554. #327C22×C151semidirect
555. #327C22×C151semidirect
556. #324C22×C151semidirect
557. #324C22×C151semidirect
558. #323C22×C151semidirect
559. #323C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3534×C1512
#3196×C1512
#3187×C1512
#2663×C1512
#1618×C1512
#1616×C1512
#1615×C1512
#1613×C1512
#1606×C1512
#1604×C1512
#1603×C1512
#1601×C1512
#1507×C1512
#1501×C1512
#1468×C1512
#18415151