Finite Group Databasebeta

← #72258712

Subgroups — #72258712

Order 1536.

1228 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 1228 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊(#126⋊C3)C211yesmaximal, characteristic, complemented
2C2×#2852⋊C3C211yesmaximal, characteristic, complemented
3C2×#2852⋊C3C211yesmaximal, characteristic, complemented
4C2×C4×#126⋊C3C211yesmaximal, characteristic, complemented
5#14711⋊C3C211yesmaximal, characteristic, complemented
6#14710⋊C3C211yesmaximal, characteristic, complemented
7C22⋊C4×C42⋊C3C211yesmaximal, characteristic, complemented
8#616821C311yesmaximal, characteristic, complemented, Sylow
9C22×#126⋊C3C2211yescharacteristic
10C22×#126⋊C3C2211yescharacteristic
11A4×#121—41nomaximal
12C23×C42⋊C3C2211yescharacteristic
13C4⋊(#126⋊C3)—22no—
14#2852⋊C3—22no—
15#2852⋊C3—22no—
16C4×#126⋊C3—22no—
17C2×#383⋊C3C2211yescharacteristic
18C2×#383⋊C3C2211yescharacteristic
19C2×C4×C42⋊C3C2211yescharacteristic
20C2×C4×C42⋊C3C2211yescharacteristic
21C2×#2860C2×C311yescharacteristic, complemented
22C2×#2852C2×C311yescharacteristic, complemented
23C2×#2852C2×C311yescharacteristic, complemented
24C2×C4×#126C2×C311yescharacteristic, complemented
25#14976—31no—
26#14967—31no—
27#14756—31no—
28#14755—31no—
29#14711C2×C311yescharacteristic, complemented
30#14710C2×C311yescharacteristic, complemented
31#14209—31no—
32#14206—31no—
33#14112—31no—
34#14100—31no—
35C42×C22⋊C4C2×C311yescharacteristic, complemented
36C2×D4×A4—41no—
37C2×D4×A4—41no—
38C2×D4×A4—41no—
39C22×C4×A4—41no—
40C2×#126⋊C3—21no—
41C2×#126⋊C3—21no—
42C2×#126⋊C3—21no—
43C2×#126⋊C3—21no—
44C2×#126⋊C3—21no—
45C2×#126⋊C3D412yescomplemented
46A4×C4⋊C4—41no—
47A4×C22⋊C4—41no—
48A4×C22⋊C4—41no—
49C22×C42⋊C3—21no—
50C22×C42⋊C3—21no—
51C22×C42⋊C3—21no—
52C22×C42⋊C3C2311yescharacteristic
53#383⋊C3—21no—
54#383⋊C3D412yescomplemented
55C4×C42⋊C3—21no—
56C4×C42⋊C3—21no—
57C22×#126C22×C311yescharacteristic
58C22×#126C22×C311yescharacteristic
59C22×#121A411yescharacteristic
60C23×C42C22×C311yescharacteristic
61#2860—22no—
62#2860—62no—
63#2852—22no—
64#2852—22no—
65#2852—62no—
66#2852—62no—
67C2×#397—31no—
68C2×#396—31no—
69C4×#126—22no—
70C4×#126—62no—
71C2×#390—31no—
72C2×#389—31no—
73C2×#388—31no—
74C2×#388—31no—
75C2×#388—31no—
76C2×#388—31no—
77C2×#388—31no—
78C2×#388—31no—
79C2×#387—31no—
80C2×#387—31no—
81C2×#387—31no—
82C2×#386—31no—
83C2×#386—31no—
84C2×#385—31no—
85C2×#385—31no—
86C2×#383C22×C311yescharacteristic
87C2×#383C22×C311yescharacteristic
88C2×C4×C4⋊C4—31no—
89C2×C4×C22⋊C4—31no—
90C2×C4×C22⋊C4—31no—
91C2×C4×C22⋊C4—31no—
92C2×C43C22×C311yescharacteristic
93C2×C43C22×C311yescharacteristic
94#1444—31no—
95#1443—31no—
96#1443—31no—
97#1442—31no—
98#1441—31no—
99#1441—31no—
100#1441—31no—
101#1440—31no—
102#1439—31no—
103#1439—31no—
104#1439—31no—
105#1438—31no—
106#1438—31no—
107#1438—31no—
108#1437—31no—
109#1437—31no—
110#1437—31no—
111#1436—31no—
112#1436—31no—
113#1436—31no—
114#1436—31no—
115#1436—31no—
116#1436—31no—
117#1436—31no—
118C4⋊#95—31no—
119C22⋊#95—31no—
120C4×#95—31no—
121C4×#95—31no—
122C23×A4—41no—
123C23×A4—41no—
124C23×A4—41no—
125D4×A4—82no—
126D4×A4—82no—
127D4×A4—82no—
128C2×C4×A4—41no—
129C2×C4×A4—41no—
130C2×C4×A4—41no—
131C2×C4×A4—41no—
132C2×C4×A4—82no—
133C3×#121—161no—
134#126⋊C3—22no—
135#126⋊C3—41no—
136C2×C42⋊C3—41no—
137C2×C42⋊C3C2×D411yescharacteristic
138C2×C42⋊C3C2×D411yescharacteristic
139C2×C42⋊C3#4111yescharacteristic
140C23×D4C2×A411yescharacteristic
141C23×D4C2×A411yescharacteristic
142C23×D4C2×A411yescharacteristic
143C24×C4—31no—
144C24×C4C2×A411yescharacteristic
145C2×#126—21no—
146C2×#126—21no—
147C2×#126—21no—
148C2×#126—21no—
149C2×#126—21no—
150C2×#126—32no—
151C2×#126—61no—
152C2×#126—61no—
153C2×#126—61no—
154C2×#126—61no—
155C2×#126—61no—
156C2×#126C3×D412yescomplemented
157C2×#121—61no—
158C2×#121—61no—
159C2×#121—61no—
160C2×#121—61no—
161C22×C4⋊C4—31no—
162C22×C4⋊C4—31no—
163C22×C4⋊C4—31no—
164C22×C4⋊C4—31no—
165C22×C4⋊C4—31no—
166C22×C4⋊C4—31no—
167C22×C4⋊C4—31no—
168C22×C4⋊C4C2×A411yescharacteristic
169C22×C22⋊C4—31no—
170C22×C22⋊C4—31no—
171C22×C22⋊C4—31no—
172C22×C22⋊C4—31no—
173C22×C22⋊C4—31no—
174C22×C22⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4—31no—
178C22×C22⋊C4—31no—
179C22×C22⋊C4—31no—
180C22×C22⋊C4C2×A411yescharacteristic
181C22×C22⋊C4C2×A411yescharacteristic
182C22×C42—21no—
183C22×C42—21no—
184C22×C42—21no—
185C22×C42—31no—
186C22×C42—31no—
187C22×C42—31no—
188C22×C42—31no—
189C22×C42—31no—
190C22×C42—31no—
191C22×C42—61no—
192C22×C42—61no—
193C22×C42—61no—
194C22×C42C23×C311yescharacteristic
195#397—64no—
196#396—64no—
197#390—62no—
198#390—62no—
199#389—62no—
200#389—62no—
201#388—62no—
202#388—62no—
203#388—62no—
204#388—62no—
205#388—61no—
206#388—61no—
207#388—61no—
208#388—61no—
209#388—62no—
210#388—62no—
211#388—62no—
212#388—62no—
213#388—62no—
214#388—62no—
215#387—62no—
216#387—62no—
217#387—62no—
218#387—62no—
219#387—62no—
220#387—62no—
221#386—62no—
222#386—62no—
223#386—62no—
224#386—62no—
225#385—62no—
226#385—62no—
227#385—62no—
228#385—62no—
229#383—21no—
230#383—32no—
231#383—61no—
232#383C3×D412yescomplemented
233C4×C4⋊C4—62no—
234C4×C4⋊C4—62no—
235C4×C22⋊C4—62no—
236C4×C22⋊C4—62no—
237C4×C22⋊C4—64no—
238C4×C22⋊C4—61no—
239C4×C22⋊C4—61no—
240C4×C22⋊C4—61no—
241C4×C22⋊C4—61no—
242C2×#95—31no—
243C2×#95—31no—
244C2×#95—31no—
245C2×#95—31no—
246C2×#95—31no—
247C2×#95—31no—
248C2×#95—31no—
249C2×#95—31no—
250C2×#95—31no—
251C2×#95—31no—
252C2×#95—31no—
253C2×#95—31no—
254C2×#95—31no—
255C2×#95—31no—
256C2×#95—31no—
257C2×#95—31no—
258C2×#95—31no—
259C2×#95—31no—
260C2×#95—31no—
261C2×#95—31no—
262C2×#95—31no—
263C2×#95—31no—
264C2×#95—31no—
265C2×#95—31no—
266C43—21no—
267C43—21no—
268C43—61no—
269C43—61no—
270C22×A4—42no—
271C22×A4—41no—
272C22×A4—81no—
273C22×A4—81no—
274C22×A4—81no—
275C22×A4—81no—
276C22×A4—81no—
277C22×A4—81no—
278C22×A4—81no—
279C22×A4—81no—
280C2×C3×D4—161no—
281C2×C3×D4—161no—
282C2×C3×D4—161no—
283C22×C3×C4—161no—
284C4×A4—42no—
285C4×A4—81no—
286C4×A4—81no—
287C4×A4—81no—
288C3×C4⋊C4—161no—
289C3×C22⋊C4—161no—
290C3×C22⋊C4—161no—
291C42⋊C3#12111yescharacteristic, complemented
292C25C22×A411yescharacteristic
293C25C22×A411yescharacteristic
294C25C22×A411yescharacteristic
295C22×D4—22no—
296C22×D4—22no—
297C22×D4—22no—
298C22×D4—61no—
299C22×D4—61no—
300C22×D4—61no—
301C22×D4—61no—
302C22×D4—61no—
303C22×D4—61no—
304C22×D4—121no—
305C22×D4—121no—
306C22×D4—121no—
307C23×C4—22no—
308C23×C4—31no—
309C23×C4—31no—
310C23×C4—31no—
311C23×C4—31no—
312C23×C4—31no—
313C23×C4—31no—
314C23×C4—31no—
315C23×C4—31no—
316C23×C4—61no—
317C23×C4—61no—
318C23×C4—61no—
319C23×C4—62no—
320C23×C4—61no—
321C23×C4—61no—
322C23×C4—61no—
323C23×C4—61no—
324C23×C4—61no—
325C23×C4—61no—
326C23×C4—61no—
327C23×C4—121no—
328C23×C4—121no—
329C23×C4—121no—
330C23×C4C22×A411yescharacteristic
331C23×C4C22×A411yescharacteristic
332C23×C4C22×A411yescharacteristic
333C23×C4C22×A411yescharacteristic
334#126—22no—
335#126—41no—
336#126—64no—
337#126—62no—
338#126—62no—
339#126—62no—
340#126—122no—
341#126—121no—
342#126—121no—
343#126—121no—
344#121—41no—
345#121—121no—
346#121—121no—
347#121—121no—
348#121—122no—
349C2×C4⋊C4—32no—
350C2×C4⋊C4—32no—
351C2×C4⋊C4—61no—
352C2×C4⋊C4—61no—
353C2×C4⋊C4—61no—
354C2×C4⋊C4—61no—
355C2×C4⋊C4—61no—
356C2×C4⋊C4—62no—
357C2×C4⋊C4—61no—
358C2×C4⋊C4—61no—
359C2×C4⋊C4—61no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—62no—
364C2×C4⋊C4—62no—
365C2×C4⋊C4—62no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4—61no—
368C2×C4⋊C4—62no—
369C2×C4⋊C4—62no—
370C2×C4⋊C4—62no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4—62no—
373C2×C4⋊C4—121no—
374C2×C4⋊C4—121no—
375C2×C4⋊C4—121no—
376C2×C4⋊C4—121no—
377C2×C4⋊C4—121no—
378C2×C4⋊C4—121no—
379C2×C22⋊C4—31no—
380C2×C22⋊C4—31no—
381C2×C22⋊C4—31no—
382C2×C22⋊C4—31no—
383C2×C22⋊C4—32no—
384C2×C22⋊C4—32no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C22⋊C4—61no—
388C2×C22⋊C4—61no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4—62no—
391C2×C22⋊C4—62no—
392C2×C22⋊C4—61no—
393C2×C22⋊C4—61no—
394C2×C22⋊C4—61no—
395C2×C22⋊C4—61no—
396C2×C22⋊C4—61no—
397C2×C22⋊C4—61no—
398C2×C22⋊C4—61no—
399C2×C22⋊C4—61no—
400C2×C22⋊C4—62no—
401C2×C22⋊C4—62no—
402C2×C22⋊C4—62no—
403C2×C22⋊C4—62no—
404C2×C22⋊C4—62no—
405C2×C22⋊C4—62no—
406C2×C22⋊C4—62no—
407C2×C22⋊C4—62no—
408C2×C22⋊C4—62no—
409C2×C22⋊C4—62no—
410C2×C22⋊C4—61no—
411C2×C22⋊C4—61no—
412C2×C22⋊C4—61no—
413C2×C22⋊C4—61no—
414C2×C22⋊C4—62no—
415C2×C22⋊C4—62no—
416C2×C22⋊C4—61no—
417C2×C22⋊C4—62no—
418C2×C22⋊C4—121no—
419C2×C22⋊C4—121no—
420C2×C22⋊C4—121no—
421C2×C22⋊C4—121no—
422C2×C22⋊C4—121no—
423C2×C22⋊C4—121no—
424C2×C22⋊C4—121no—
425C2×C22⋊C4—121no—
426C2×C22⋊C4—121no—
427C2×C42—31no—
428C2×C42—31no—
429C2×C42—31no—
430C2×C42—41no—
431C2×C42—61no—
432C2×C42—61no—
433C2×C42—61no—
434C2×C42—61no—
435C2×C42—62no—
436C2×C42—61no—
437C2×C42—61no—
438C2×C42—61no—
439C2×C42—61no—
440C2×C42—61no—
441C2×C42—61no—
442C2×C42—61no—
443C2×C42—61no—
444C2×C42—61no—
445C2×C42—61no—
446C2×C42—61no—
447C2×C42—61no—
448C2×C42—61no—
449C2×C42—61no—
450C2×C42—62no—
451C2×C42—62no—
452C2×C42—61no—
453C2×C42—61no—
454C2×C42—122no—
455C2×C42—121no—
456C2×C42—121no—
457C2×C42—121no—
458C2×C42—121no—
459C2×C42—121no—
460C2×C42—121no—
461C2×C42—121no—
462C2×C42—121no—
463C2×C42C2×C3×D411yescharacteristic
464C2×C42C2×C3×D411yescharacteristic
465C2×C42C3×#4111yescharacteristic
466#95—32no—
467#95—34no—
468#95—32no—
469#95—32no—
470#95—32no—
471#95—61no—
472#95—61no—
473#95—62no—
474#95—61no—
475#95—61no—
476#95—61no—
477#95—61no—
478#95—61no—
479#95—61no—
480#95—62no—
481#95—62no—
482#95—62no—
483#95—62no—
484#95—61no—
485#95—61no—
486#95—61no—
487#95—61no—
488#95—62no—
489#95—62no—
490#95—62no—
491#95—62no—
492#95—62no—
493#95—62no—
494#95—121no—
495#95—121no—
496#95—121no—
497#95—121no—
498C23×C3—161no—
499C23×C3—161no—
500C23×C3—161no—
501C2×A4—41no—
502C2×A4—41no—
503C2×A4—41no—
504C2×A4—82no—
505C2×A4—161no—
506C2×A4—161no—
507C3×D4—322no—
508C3×D4—322no—
509C3×D4—322no—
510C2×C3×C4—161no—
511C2×C3×C4—161no—
512C2×C3×C4—161no—
513C2×C3×C4—161no—
514C2×C3×C4—322no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—31no—
524C24—31no—
525C24—61no—
526C24—61no—
527C24—61no—
528C24—61no—
529C24—61no—
530C24—61no—
531C24—61no—
532C24—61no—
533C24—61no—
534C24—61no—
535C24—61no—
536C24D4×A412yes—
537C24C23×A411yescharacteristic
538C2×D4—41no—
539C2×D4—41no—
540C2×D4—41no—
541C2×D4—121no—
542C2×D4—121no—
543C2×D4—121no—
544C2×D4—122no—
545C2×D4—122no—
546C2×D4—122no—
547C2×D4—122no—
548C2×D4—122no—
549C2×D4—122no—
550C2×D4—241no—
551C2×D4—241no—
552C2×D4—241no—
553C2×D4—241no—
554C2×D4—241no—
555C2×D4—241no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—32no—
570C22×C4—32no—
571C22×C4—32no—
572C22×C4—32no—
573C22×C4—32no—
574C22×C4—41no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—62no—
607C22×C4—62no—
608C22×C4—62no—
609C22×C4—62no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—61no—
625C22×C4—61no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—61no—
629C22×C4—61no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—121no—
634C22×C4—121no—
635C22×C4—121no—
636C22×C4—121no—
637C22×C4—121no—
638C22×C4—122no—
639C22×C4—122no—
640C22×C4—122no—
641C22×C4—122no—
642C22×C4—122no—
643C22×C4—122no—
644C22×C4—121no—
645C22×C4—121no—
646C22×C4—121no—
647C22×C4—121no—
648C22×C4—121no—
649C22×C4—121no—
650C22×C4—121no—
651C22×C4—121no—
652C22×C4—122no—
653C22×C4—122no—
654C22×C4—241no—
655C22×C4—241no—
656C22×C4D4×A412yes—
657C4⋊C4—41no—
658C4⋊C4—62no—
659C4⋊C4—62no—
660C4⋊C4—62no—
661C4⋊C4—62no—
662C4⋊C4—121no—
663C4⋊C4—121no—
664C4⋊C4—121no—
665C4⋊C4—121no—
666C4⋊C4—121no—
667C4⋊C4—122no—
668C4⋊C4—122no—
669C4⋊C4—124no—
670C4⋊C4—124no—
671C4⋊C4—124no—
672C4⋊C4—242no—
673C22⋊C4—32no—
674C22⋊C4—31no—
675C22⋊C4—31no—
676C22⋊C4—31no—
677C22⋊C4—41no—
678C22⋊C4—62no—
679C22⋊C4—62no—
680C22⋊C4—62no—
681C22⋊C4—62no—
682C22⋊C4—64no—
683C22⋊C4—64no—
684C22⋊C4—121no—
685C22⋊C4—121no—
686C22⋊C4—121no—
687C22⋊C4—121no—
688C22⋊C4—121no—
689C22⋊C4—124no—
690C22⋊C4—124no—
691C22⋊C4—124no—
692C22⋊C4—124no—
693C22⋊C4—122no—
694C22⋊C4—122no—
695C22⋊C4—122no—
696C22⋊C4—122no—
697C22⋊C4—124no—
698C22⋊C4—242no—
699C22⋊C4#126⋊C311yescharacteristic, complemented
700C42—31no—
701C42—31no—
702C42—31no—
703C42—32no—
704C42—121no—
705C42—121no—
706C42—121no—
707C42—121no—
708C42—121no—
709C42—121no—
710C42—122no—
711C42—121no—
712C42—121no—
713C42—121no—
714C42—121no—
715C42—121no—
716C42—121no—
717C42—122no—
718C42—122no—
719C42—122no—
720C42—122no—
721C42—122no—
722C42C3×#12111yescharacteristic, complemented
723C22×C3—162no—
724C22×C3—161no—
725C22×C3—321no—
726C22×C3—321no—
727C22×C3—321no—
728C22×C3—321no—
729C22×C3—321no—
730C22×C3—321no—
731C22×C3—321no—
732C22×C3—321no—
733A4—41no—
734C3×C4—162no—
735C3×C4—321no—
736C3×C4—321no—
737C3×C4—321no—
738C23—22no—
739C23—31no—
740C23—31no—
741C23—31no—
742C23—31no—
743C23—31no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—61no—
749C23—61no—
750C23—61no—
751C23—61no—
752C23—61no—
753C23—61no—
754C23—62no—
755C23—61no—
756C23—61no—
757C23—61no—
758C23—61no—
759C23—61no—
760C23—61no—
761C23—62no—
762C23—121no—
763C23—121no—
764C23—121no—
765C23—121no—
766C23—121no—
767C23—121no—
768C23—121no—
769C23—121no—
770C23—121no—
771C23—121no—
772C23—121no—
773C23—121no—
774C23—121no—
775C23—121no—
776C23—121no—
777C23—121no—
778C23—121no—
779C23—121no—
780C23—121no—
781C23—121no—
782C23—121no—
783C23—121no—
784C23—121no—
785C23—121no—
786C23—121no—
787C23C2×#126⋊C311yescharacteristic
788C23C2×D4×A411yescharacteristic
789C23C2×D4×A411yescharacteristic
790C23A4×#4111yescharacteristic
791D4—82no—
792D4—82no—
793D4—82no—
794D4—242no—
795D4—242no—
796D4—242no—
797C2×C4—31no—
798C2×C4—31no—
799C2×C4—31no—
800C2×C4—31no—
801C2×C4—31no—
802C2×C4—31no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—62no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—61no—
826C2×C4—62no—
827C2×C4—62no—
828C2×C4—62no—
829C2×C4—62no—
830C2×C4—62no—
831C2×C4—62no—
832C2×C4—62no—
833C2×C4—62no—
834C2×C4—62no—
835C2×C4—62no—
836C2×C4—62no—
837C2×C4—62no—
838C2×C4—62no—
839C2×C4—62no—
840C2×C4—62no—
841C2×C4—82no—
842C2×C4—121no—
843C2×C4—122no—
844C2×C4—122no—
845C2×C4—122no—
846C2×C4—122no—
847C2×C4—122no—
848C2×C4—122no—
849C2×C4—122no—
850C2×C4—122no—
851C2×C4—121no—
852C2×C4—121no—
853C2×C4—121no—
854C2×C4—121no—
855C2×C4—121no—
856C2×C4—121no—
857C2×C4—121no—
858C2×C4—121no—
859C2×C4—121no—
860C2×C4—121no—
861C2×C4—121no—
862C2×C4—121no—
863C2×C4—121no—
864C2×C4—121no—
865C2×C4—121no—
866C2×C4—121no—
867C2×C4—121no—
868C2×C4—121no—
869C2×C4—121no—
870C2×C4—121no—
871C2×C4—121no—
872C2×C4—121no—
873C2×C4—121no—
874C2×C4—121no—
875C2×C4—121no—
876C2×C4—121no—
877C2×C4—121no—
878C2×C4—121no—
879C2×C4—121no—
880C2×C4—121no—
881C2×C4—121no—
882C2×C4—121no—
883C2×C4—121no—
884C2×C4—121no—
885C2×C4—121no—
886C2×C4—121no—
887C2×C4—242no—
888C2×C4C2×#126⋊C311yescharacteristic
889C2×C4C2×#126⋊C311yescharacteristic
890C2×C3—161no—
891C2×C3—161no—
892C2×C3—161no—
893C2×C3—322no—
894C2×C3—641no—
895C2×C3—641no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—31no—
900C22—31no—
901C22—31no—
902C22—31no—
903C22—31no—
904C22—31no—
905C22—31no—
906C22—31no—
907C22—31no—
908C22—31no—
909C22—31no—
910C22—42no—
911C22—61no—
912C22—61no—
913C22—61no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—121no—
920C22—121no—
921C22—121no—
922C22—121no—
923C22—122no—
924C22—122no—
925C22—121no—
926C22—121no—
927C22—121no—
928C22—121no—
929C22—241no—
930C22—241no—
931C22—241no—
932C22—241no—
933C22—241no—
934C22—241no—
935C22A4×#12111yescharacteristic
936C22C22×#126⋊C311yescharacteristic
937C4—21no—
938C4—21no—
939C4—42no—
940C4—61no—
941C4—61no—
942C4—61no—
943C4—61no—
944C4—61no—
945C4—61no—
946C4—81no—
947C4—122no—
948C4—122no—
949C4—122no—
950C4—122no—
951C4—122no—
952C4—241no—
953C4—241no—
954C3—161noSylow
955C2—31no—
956C2—31no—
957C2—31no—
958C2—31no—
959C2—41no—
960C2—82no—
961C2—121no—
962C2—161no—
963C2D4×#126⋊C311yescharacteristic
964C2D4×#126⋊C311yescharacteristic
965C2#36641⋊C311yescharacteristic
subgroupG/H
centerC22C22×#126⋊C3
commutator, cosocleC22×C42C23×C3
Frattini, socleC24C23×A4
Fitting#616821C3
hypercenterC22⋊C4#126⋊C3
hypocenterC42C3×#121
LCSG ▷ C22×C42 ▷ C42
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊(#126⋊C3)C2semidirect
2. C2×#2852⋊C3C2semidirect
3. C2×#2852⋊C3C2semidirect
4. C2×C4×#126⋊C3C2semidirect
5. #14711⋊C3C2semidirect
6. #14710⋊C3C2semidirect
7. C22⋊C4×C42⋊C3C2semidirect
8. #616821C3semidirect
21. C2×#2860C2×C3semidirect
22. C2×#2852C2×C3semidirect
23. C2×#2852C2×C3semidirect
24. C2×C4×#126C2×C3semidirect
29. #14711C2×C3semidirect
30. #14710C2×C3semidirect
35. C42×C22⋊C4C2×C3semidirect
45. C2×#126⋊C3D4semidirect
54. #383⋊C3D4semidirect
156. C2×#126C3×D4semidirect
232. #383C3×D4semidirect
291. C42⋊C3#121semidirect
699. C22⋊C4#126⋊C3semidirect
722. C42C3×#121semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊(#126⋊C3)2
C2×#2852⋊C32
C2×C4×#126⋊C32
#14711⋊C32
#14710⋊C32
C22⋊C4×C42⋊C32
#6168213
A4×#1214