Finite Group Databasebeta

← #11864129

Subgroups — #11864129

Order 1152.

1693 conjugacy classes of subgroups.

The subgroup lattice has 1057 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#237C211yesmaximal, characteristic, complemented
2C2×#63925C211yesmaximal, characteristic, complemented
3C2×#63795C211yesmaximal, characteristic, complemented
4D3×#895C211yesmaximal, characteristic, complemented
5#10592480C211yesmaximal, characteristic, complemented
6C3×#4773C211yesmaximal, characteristic, complemented
7C3×#4771C211yesmaximal, characteristic, complemented
8#10591457C211yesmaximal, characteristic, complemented
9#10591448C211yesmaximal, characteristic, complemented
10#10590963C211yesmaximal, characteristic, complemented
11#10590951C211yesmaximal, characteristic, complemented
12#10590936C211yesmaximal, characteristic, complemented
13#10590617C211yesmaximal, characteristic, complemented
14#10590607C211yesmaximal, characteristic, complemented
15#10590603C211yesmaximal, characteristic, complemented
16#80003—31nomaximal
17#78884—31nomaximal
18C2×#3830C2211yescharacteristic, complemented
19C2×C3×#237C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic, complemented
21C2×D3×#67—21no—
22C2×#3805—21no—
23C2×#3804—21no—
24C22×D3×Dic3—21no—
25D3×#237—24no—
26D3×#237—24no—
27C2×D3×D12—21no—
28C2×D3×D12C2211yescharacteristic, complemented
29C2×C4×D32C2211yescharacteristic
30C2×#3796C2211yescharacteristic, complemented
31C2×#3795C2211yescharacteristic
32C2×D3×Dic6C2211yescharacteristic, complemented
33C2×#3753C2211yescharacteristic, complemented
34C2×#3744C2211yescharacteristic, complemented
35#64104C2211yescharacteristic, complemented
36C2×C3×#213C2211yescharacteristic, complemented
37C2×C3×D24C2211yescharacteristic, complemented
38C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
39C3×#895C2211yescharacteristic
40C3×D3×C4⋊C4C2211yescharacteristic, complemented
41#63925—24no—
42D3×(C2×D3)⋊C4—21no—
43#63916C2211yescharacteristic, complemented
44#63910—21no—
45#63909C2211yescharacteristic
46#63886—21no—
47C2×#3717C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52#63795—24no—
53C32×#102C2211yescharacteristic, complemented
54#63647C2211yescharacteristic, complemented
55#63637C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#237—31no—
67C2×#949—31no—
68C2×#911—31no—
69C2×#911—31no—
70C2×#908—31no—
71D3×#121—31no—
72C2×#895—31no—
73C3×#447—31no—
74C3×#417—31no—
75#5217—31no—
76#5158—31no—
77#5158—31no—
78#5126—31no—
79#5040—31no—
80#4966—31no—
81#4810—31no—
82#4810—31no—
83#4806—31no—
84#4806—31no—
85#4781—31no—
86#4781—31no—
87#4781—31no—
88#4781—31no—
89#4781—61no—
90#4773—31no—
91#4773D311yescharacteristic, complemented
92#4771—31no—
93#4771D311yescharacteristic, complemented
94#4738—31no—
95#4726—31no—
96C23×C3×D3—21no—
97C22×D32—21no—
98C22×D32D411yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C2×#638—21no—
101C22×C3⋊Dic3—21no—
102#3830—22no—
103#3830—22no—
104C2×C4⋊(C3⋊D3)—21no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C22×C3×Dic3—21no—
111C3×#237—22no—
112C3×#237D414yescomplemented
113C3×D3×D4—22no—
114C3×D3×D4—22no—
115C2×C3×D12—21no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3—21no—
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122D3×#67—28no—
123C2×#627—21no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#625—21no—
129C2×#624D411yescharacteristic
130#3805—28no—
131#3804—28no—
132C2×D3×Dic3—28no—
133C2×D3×Dic3—21no—
134C2×D3×Dic3—21no—
135C2×D3×Dic3—21no—
136C2×D3×Dic3D411yescharacteristic
137C2×D3×Dic3D411yescharacteristic
138D3×D12—22no—
139D3×D12—22no—
140D3×D12—44no—
141C4×D32—22no—
142C4×D32—22no—
143#3796—22no—
144#3796—22no—
145#3795—22no—
146#3795D414yescomplemented
147D3×Dic6—22no—
148D3×Dic6—22no—
149C2×C32×C8C2311yescharacteristic
150C32×C4⋊C4C2311yescharacteristic
151#3753—22no—
152#3752—21no—
153C2×C3⋊(C3⋊C8)C2311yescharacteristic
154#3744—22no—
155C3×#213—22no—
156C3×(C2×D3)⋊C4—21no—
157C3×C4⋊Dic3C2311yescharacteristic
158C3×Dic3⋊C4—21no—
159C2×C3×C3⋊C8C2311yescharacteristic
160C2×C3×C3⋊C8C2311yescharacteristic
161C3×D24—22no—
162C3×ΓL(1,𝔽25)—22no—
163#3722—21no—
164(C2×D3)⋊Dic3—21no—
165#3717—22no—
166#3716—22no—
167#3715—22no—
168#3714—22no—
169#3711—22no—
170#3006—91noSylow
171C2×C3×#41—31no—
172C22×C3×D4—31no—
173C22×#67—61no—
174C23×Dic3—61no—
175D3×#41—64no—
176D3×#41—64no—
177C2×#239—31no—
178C2×D3×Q8—31no—
179C2×#237—31no—
180C2×#237—31no—
181C2×#237—31no—
182C2×#237—31no—
183C2×#237—61no—
184C2×#237—61no—
185C2×#237—61no—
186C2×#237—64no—
187C2×#237—61no—
188C2×#237—64no—
189C2×#237C2×D311yescharacteristic
190C2×D3×D4—31no—
191C2×D3×D4—61no—
192C2×D3×D4—61no—
193C2×D3×D4C2×D311yescharacteristic, complemented
194C2×#235—31no—
195C2×#235—61no—
196C22×D12—31no—
197C22×D12—61no—
198C22×C4×D3—31no—
199C22×C4×D3—31no—
200C22×C4×D3—61no—
201C22×Dic6—31no—
202C2×C3×D8—31no—
203C2×C3×D8—31no—
204C2×C3×M16—31no—
205C3×#121—31no—
206C2×C3×C4⋊C4—31no—
207#949—64no—
208C2×#215—31no—
209C2×#215—31no—
210#939—61no—
211#938—31no—
212C2×#214—31no—
213C2×#214—31no—
214C2×#213—31no—
215C2×#213—31no—
216C2×#213—31no—
217C2×#213—61no—
218C2×#213C2×D311yescharacteristic, complemented
219#930—31no—
220C2×(C2×D3)⋊C4—61no—
221C2×#208—31no—
222#911—64no—
223#911—64no—
224#908—64no—
225C2×D24—31no—
226C2×D24C2×D311yescharacteristic, complemented
227C2×#204—31no—
228C2×#204—31no—
229C2×#204—31no—
230C2×#204—31no—
231C2×#204—61no—
232C2×ΓL(1,𝔽25)—31no—
233C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
234#895—31no—
235#895—31no—
236#895—31no—
237#895—31no—
238#895—61no—
239#895—61no—
240#895—61no—
241#895C2×D311yescharacteristic
242D3×C4⋊C4C2×D311yescharacteristic, complemented
243#884—61no—
244D3×C22⋊C4—61no—
245C3×#103—31no—
246C3×#103—31no—
247C3×#102—21no—
248C3×#102—31no—
249C3×#102—31no—
250C3×#102C2×D311yescharacteristic, complemented
251C3×#102C2×D311yescharacteristic, complemented
252C3×C22⋊C8—31no—
253#832—31no—
254#832C2×D311yescharacteristic, complemented
255#830—31no—
256(C2×D3)⋊C8—31no—
257(C2×D3)⋊C8—31no—
258(C2×D3)⋊C8—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—61no—
262(C2×D3)⋊C8C2×D311yescharacteristic, complemented
263#816—31no—
264#816C2×D311yescharacteristic, complemented
265#810—31no—
266#810—31no—
267#810—31no—
268#810—61no—
269#810C2×D311yescharacteristic, complemented
270#809—31no—
271#809C2×D311yescharacteristic, complemented
272C23×C32—21no—
273C22×C3⋊D3—21no—
274C22×C3⋊D3C2×D411yescharacteristic
275C22×C3×D3—24no—
276C22×C3×D3—21no—
277C22×C3×D3—21no—
278C22×C3×D3—42no—
279C22×C3×D3—42no—
280C22×C3×D3C2×D411yescharacteristic
281C22×C3×D3C2×D411yescharacteristic
282C2×D32—22no—
283C2×D32—22no—
284C2×D32—41no—
285C2×D32—42no—
286C2×D32—42no—
287C2×D32—42no—
288C32×D4—21no—
289C32×D4C2×D412yescomplemented
290C2×C32×C4—21no—
291C2×C32×C4C2411yescharacteristic
292#638—24no—
293C2×C3⋊Dic3—24no—
294C2×C3⋊Dic3—21no—
295C2×C3⋊Dic3C2×D411yescharacteristic
296C4⋊(C3⋊D3)—21no—
297C4⋊(C3⋊D3)—21no—
298C4⋊(C3⋊D3)—42no—
299C4×C3⋊D3—21no—
300C4×C3⋊D3—21no—
301#634—21no—
302#634C2×D412yescomplemented
303C3×#67—24no—
304C3×#67—24no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—24no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3C2×D411yescharacteristic
309C2×C3×Dic3C2×D411yescharacteristic
310C3×D12—21no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12—42no—
314C3×D12C2×D412yescomplemented
315C3×C4×D3—21no—
316C3×C4×D3—21no—
317C3×C4×D3—42no—
318C3×C4×D3C2×D412yes—
319C3×C4×D3C2×D412yes—
320C3×Dic6—21no—
321C3×Dic6C2×D412yescomplemented
322#627—24no—
323#626—24no—
324#626—42no—
325#626—42no—
326#626—42no—
327#625—24no—
328#624—22no—
329D3×Dic3—24no—
330D3×Dic3—24no—
331D3×Dic3—22no—
332D3×Dic3—24no—
333D3×Dic3—22no—
334C32×C8—21no—
335C3⋊(C3⋊C8)—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C22×#41—91no—
339C2×AGL(1,ℤ/8)—91no—
340C2×AGL(1,ℤ/8)—91no—
341C2×#121—91no—
342#449—91no—
343#449—91no—
344#449—91no—
345#449—91no—
346#448—91no—
347#448—91no—
348#447—31no—
349#447—91no—
350#417—31no—
351#417—91no—
352#407—91no—
353C24×C3—61no—
354C23×D3—21no—
355C23×D3—31no—
356C23×D3—31no—
357C23×D3—61no—
358C23×D3—61no—
359C3×#41—34no—
360C3×#41—62no—
361C2×C3×Q8—31no—
362C2×C3×D4—21no—
363C2×C3×D4—31no—
364C2×C3×D4—31no—
365C2×C3×D4—61no—
366C2×C3×D4—61no—
367C2×C3×D4—62no—
368C2×C3×D4—61no—
369C2×C3×D4—62no—
370C2×C3×D4C22×D311yescharacteristic
371C2×C3×D4C22×D311yescharacteristic
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—61no—
375C22×C3×C4—61no—
376C2×#67—21no—
377C2×#67—21no—
378C2×#67—61no—
379C2×#67—61no—
380C2×#67—61no—
381C2×#67—68no—
382C2×#67—61no—
383C2×#67—61no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—61no—
387C2×#67—121no—
388C22×Dic3—21no—
389C22×Dic3—31no—
390C22×Dic3—31no—
391C22×Dic3—61no—
392C22×Dic3—61no—
393C22×Dic3—68no—
394C22×Dic3—61no—
395C22×Dic3—61no—
396C22×Dic3—61no—
397C22×Dic3—121no—
398#239—62no—
399#239—62no—
400D3×Q8—62no—
401D3×Q8—62no—
402#237—22no—
403#237—34no—
404#237—62no—
405#237—62no—
406#237—62no—
407#237—68no—
408#237—68no—
409#237—68no—
410#237—62no—
411#237—62no—
412#237—62no—
413#237—62no—
414#237—122no—
415#237—122no—
416#237D1214yescomplemented
417D3×D4—22no—
418D3×D4—22no—
419D3×D4—68no—
420D3×D4—62no—
421D3×D4—62no—
422D3×D4—124no—
423#235—34no—
424#235—62no—
425#235—68no—
426C2×D12—21no—
427C2×D12—31no—
428C2×D12—31no—
429C2×D12—61no—
430C2×D12—62no—
431C2×D12—62no—
432C2×D12—61no—
433C2×D12—61no—
434C2×D12—61no—
435C2×D12—61no—
436C2×D12—61no—
437C2×D12—61no—
438C2×D12—121no—
439C2×D12—124no—
440C2×D12C22×D311yescharacteristic
441C2×D12C22×D311yescharacteristic
442C2×C4×D3—21no—
443C2×C4×D3—31no—
444C2×C4×D3—31no—
445C2×C4×D3—31no—
446C2×C4×D3—31no—
447C2×C4×D3—31no—
448C2×C4×D3—31no—
449C2×C4×D3—61no—
450C2×C4×D3—62no—
451C2×C4×D3—62no—
452C2×C4×D3—61no—
453C2×C4×D3—61no—
454C2×C4×D3—68no—
455C2×C4×D3—61no—
456C2×C4×D3—62no—
457C2×C4×D3—62no—
458C2×C4×D3C22×D311yescharacteristic
459C2×C4×D3C22×D311yescharacteristic
460C2×Dic6—31no—
461C2×Dic6—31no—
462C2×Dic6—61no—
463C2×Dic6—62no—
464C2×Dic6—61no—
465C2×Dic6—61no—
466C2×Dic6—62no—
467C2×Dic6C22×D311yescharacteristic
468C3×D8—62no—
469C3×D8—62no—
470C3×M16—62no—
471C2×C3×C8—21no—
472C2×C3×C8—31no—
473C2×C3×C8—31no—
474C2×C3×C8C22×D311yescharacteristic
475C2×C3×C8C22×D311yescharacteristic
476C3×C4⋊C4—21no—
477C3×C4⋊C4—31no—
478C3×C4⋊C4—61no—
479C3×C4⋊C4C22×D311yescharacteristic
480C3×C4⋊C4C22×D311yescharacteristic
481C3×C22⋊C4—61no—
482#217—61no—
483#215—62no—
484#215—62no—
485#214—62no—
486#214—62no—
487#213—22no—
488#213—62no—
489#213—62no—
490#213—62no—
491#213—122no—
492(C2×D3)⋊C4—21no—
493(C2×D3)⋊C4—61no—
494(C2×D3)⋊C4—61no—
495(C2×D3)⋊C4—61no—
496(C2×D3)⋊C4—61no—
497(C2×D3)⋊C4—61no—
498(C2×D3)⋊C4—121no—
499C4⋊Dic3C22×D311yescharacteristic
500Dic3⋊C4—21no—
501#208—62no—
502C2×C3⋊C8—31no—
503C2×C3⋊C8—31no—
504C2×C3⋊C8—61no—
505C2×C3⋊C8C22×D311yescharacteristic
506C2×C3⋊C8C22×D311yescharacteristic
507D24—22no—
508D24—62no—
509#204—62no—
510#204—62no—
511#204—62no—
512#204—62no—
513#204—122no—
514ΓL(1,𝔽25)—22no—
515ΓL(1,𝔽25)—62no—
516C22×C32—22no—
517C22×C32—41no—
518C22×C32—41no—
519C22×C32C22×D411yescharacteristic
520C2×C3⋊D3—21no—
521C2×C3⋊D3—21no—
522C2×C3⋊D3—21no—
523C2×C3⋊D3—41no—
524C2×C3⋊D3—41no—
525C2×C3⋊D3—41no—
526C2×C3×D3—21no—
527C2×C3×D3—21no—
528C2×C3×D3—21no—
529C2×C3×D3—21no—
530C2×C3×D3—22no—
531C2×C3×D3—48no—
532C2×C3×D3—41no—
533C2×C3×D3—41no—
534C2×C3×D3—41no—
535C2×C3×D3—41no—
536C2×C3×D3—41no—
537C2×C3×D3#12012yes—
538C2×C3×D3AGL(1,ℤ/8)12yescomplemented
539D32—44no—
540D32—84no—
541C32×C4—41no—
542C32×C4C22×D411yescharacteristic
543C32×C4C22×D411yescharacteristic
544C3⋊Dic3—21no—
545C3⋊Dic3—22no—
546C3×Dic3—22no—
547C3×Dic3—21no—
548C3×Dic3—41no—
549C3×Dic3#12012yes—
550C2×#41—31no—
551C2×#41—91no—
552C2×#41—91no—
553C2×#41—91no—
554C2×#41—181no—
555C2×#41—181no—
556C2×#41—184no—
557C2×#41—184no—
558C22×Q8—91no—
559C22×D4—31no—
560C22×D4—91no—
561C22×D4—181no—
562C22×D4—181no—
563C23×C4—91no—
564C23×C4—181no—
565AGL(1,ℤ/8)—184no—
566AGL(1,ℤ/8)—184no—
567C2×SD16—91no—
568C2×SD16—91no—
569C2×SD16—91no—
570C2×SD16—91no—
571C2×D8—31no—
572C2×D8—31no—
573C2×D8—91no—
574C2×D8—91no—
575C2×M16—31no—
576C2×M16—91no—
577#121—31no—
578#121—91no—
579#121—91no—
580#121—91no—
581#121—181no—
582#121—181no—
583C2×C4⋊C4—31no—
584C2×C22⋊C4—181no—
585#103—31no—
586#103—31no—
587#103—91no—
588#103—91no—
589#102—31no—
590#102—31no—
591#102—91no—
592#102D3211yescharacteristic, complemented
593C22⋊C8—31no—
594C22⋊C8—91no—
595C22⋊C8—91no—
596C22⋊C8—91no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—31no—
600C23×C3—31no—
601C23×C3—41no—
602C23×C3—64no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3—122no—
606C23×C3—122no—
607C22×D3—24no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—31no—
611C22×D3—31no—
612C22×D3—42no—
613C22×D3—42no—
614C22×D3—61no—
615C22×D3—62no—
616C22×D3—62no—
617C22×D3—62no—
618C22×D3—62no—
619C22×D3—61no—
620C22×D3—61no—
621C22×D3—121no—
622C22×D3—121no—
623C22×D3—121no—
624C22×D3—122no—
625C22×D3—122no—
626C22×D3—122no—
627C22×D3—122no—
628C22×D3—122no—
629C22×D3—122no—
630C22×D3D3×D411yescharacteristic
631C22×D3D3×D411yescharacteristic
632C3×Q8—32no—
633C3×Q8—61no—
634C3×D4—21no—
635C3×D4—21no—
636C3×D4—22no—
637C3×D4—32no—
638C3×D4—41no—
639C3×D4—64no—
640C3×D4—64no—
641C3×D4—61no—
642C3×D4—61no—
643C3×D4—61no—
644C3×D4—122no—
645C3×D4C2×D1212yescomplemented
646C3×D4D3×D412yescomplemented
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—31no—
651C2×C3×C4—32no—
652C2×C3×C4—32no—
653C2×C3×C4—31no—
654C2×C3×C4—41no—
655C2×C3×C4—64no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4—122no—
661C2×C3×C4C23×D311yescharacteristic
662C2×C3×C4C23×D311yescharacteristic
663#67—24no—
664#67—24no—
665#67—64no—
666#67—64no—
667#67—64no—
668#67—64no—
669#67—64no—
670#67—124no—
671#67—122no—
672#67—122no—
673#67—122no—
674C2×Dic3—21no—
675C2×Dic3—24no—
676C2×Dic3—21no—
677C2×Dic3—31no—
678C2×Dic3—31no—
679C2×Dic3—61no—
680C2×Dic3—62no—
681C2×Dic3—64no—
682C2×Dic3—64no—
683C2×Dic3—64no—
684C2×Dic3—64no—
685C2×Dic3—61no—
686C2×Dic3—61no—
687C2×Dic3—62no—
688C2×Dic3—64no—
689C2×Dic3—121no—
690C2×Dic3—124no—
691C2×Dic3D3×D411yescharacteristic
692C2×Dic3D3×D411yescharacteristic
693D12—21no—
694D12—21no—
695D12—21no—
696D12—42no—
697D12—64no—
698D12—61no—
699D12—61no—
700D12—61no—
701D12—61no—
702D12—121no—
703D12—121no—
704D12—122no—
705D12—122no—
706D12—122no—
707D12—122no—
708D12—122no—
709D12—242no—
710D12D3×D412yescomplemented
711C4×D3—21no—
712C4×D3—21no—
713C4×D3—42no—
714C4×D3—62no—
715C4×D3—62no—
716C4×D3—64no—
717C4×D3—64no—
718C4×D3—64no—
719C4×D3—62no—
720C4×D3—61no—
721C4×D3—61no—
722C4×D3—61no—
723C4×D3—61no—
724C4×D3—62no—
725C4×D3—121no—
726C4×D3—121no—
727C4×D3C2×D1212yes—
728C4×D3D3×D412yes—
729Dic6—21no—
730Dic6—32no—
731Dic6—32no—
732Dic6—62no—
733Dic6—64no—
734Dic6—64no—
735Dic6—61no—
736Dic6—61no—
737Dic6—121no—
738Dic6C2×D1212yescomplemented
739C3×C8—21no—
740C3×C8—21no—
741C3×C8—41no—
742C3×C8—61no—
743C3×C8—61no—
744C3⋊C8—21no—
745C3⋊C8—21no—
746C3⋊C8—61no—
747C3⋊C8—61no—
748C3⋊C8—121no—
749C2×C32—42no—
750C2×C32C2×#12011yescharacteristic
751C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
752C2×C32#57511yescharacteristic
753C3⋊D3—41no—
754C3⋊D3—81no—
755C3×D3—22no—
756C3×D3—22no—
757C3×D3—42no—
758C3×D3—81no—
759C24—61no—
760C24—91no—
761C24—181no—
762#41—34no—
763#41—62no—
764#41—94no—
765#41—182no—
766#41—188no—
767#41—182no—
768#41—182no—
769#41—188no—
770#41—182no—
771#41—182no—
772C2×Q8—31no—
773C2×Q8—91no—
774C2×Q8—181no—
775C2×Q8—182no—
776C2×Q8—182no—
777C2×D4—31no—
778C2×D4—31no—
779C2×D4—61no—
780C2×D4—61no—
781C2×D4—62no—
782C2×D4—61no—
783C2×D4—62no—
784C2×D4—91no—
785C2×D4—181no—
786C2×D4—182no—
787C2×D4—182no—
788C2×D4—181no—
789C2×D4—181no—
790C2×D4—181no—
791C2×D4—181no—
792C2×D4—188no—
793C2×D4—181no—
794C2×D4—181no—
795C2×D4—364no—
796C2×D4C2×D3211yescharacteristic
797C22×C4—31no—
798C22×C4—31no—
799C22×C4—61no—
800C22×C4—61no—
801C22×C4—91no—
802C22×C4—91no—
803C22×C4—91no—
804C22×C4—91no—
805C22×C4—182no—
806C22×C4—182no—
807C22×C4—181no—
808C22×C4—181no—
809C22×C4—181no—
810C22×C4—188no—
811C22×C4—181no—
812SD16—182no—
813SD16—182no—
814SD16—182no—
815SD16—182no—
816D8—62no—
817D8—62no—
818D8—182no—
819D8—182no—
820M16—62no—
821M16—182no—
822C2×C8—31no—
823C2×C8—31no—
824C2×C8—91no—
825C2×C8C2×D3211yescharacteristic
826C4⋊C4—31no—
827C4⋊C4—61no—
828C4⋊C4C2×D3211yescharacteristic
829C22⋊C4—61no—
830C22⋊C4—181no—
831C22⋊C4—181no—
832C22⋊C4—181no—
833C22×C3—22no—
834C22×C3—22no—
835C22×C3—21no—
836C22×C3—32no—
837C22×C3—32no—
838C22×C3—42no—
839C22×C3—41no—
840C22×C3—41no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—61no—
844C22×C3—61no—
845C22×C3—61no—
846C22×C3—61no—
847C22×C3—62no—
848C22×C3—81no—
849C22×C3—81no—
850C22×C3—128no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3—121no—
854C22×C3—121no—
855C22×C3—121no—
856C22×C3C2×D3×D411yescharacteristic
857C22×C3C2×D3×D411yescharacteristic
858C2×D3—21no—
859C2×D3—21no—
860C2×D3—21no—
861C2×D3—21no—
862C2×D3—22no—
863C2×D3—48no—
864C2×D3—41no—
865C2×D3—41no—
866C2×D3—41no—
867C2×D3—41no—
868C2×D3—41no—
869C2×D3—61no—
870C2×D3—61no—
871C2×D3—61no—
872C2×D3—61no—
873C2×D3—61no—
874C2×D3—61no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—121no—
878C2×D3—124no—
879C2×D3—124no—
880C2×D3—121no—
881C2×D3—121no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—121no—
885C2×D3—121no—
886C2×D3—241no—
887C2×D3—241no—
888C2×D3—241no—
889C2×D3—244no—
890C2×D3—244no—
891C2×D3#88212yes—
892C2×D3#91112yescomplemented
893C3×C4—21no—
894C3×C4—21no—
895C3×C4—32no—
896C3×C4—41no—
897C3×C4—41no—
898C3×C4—61no—
899C3×C4—62no—
900C3×C4—81no—
901C3×C4—121no—
902C3×C4C22×D1211yescharacteristic
903C3×C4C2×D3×D411yescharacteristic
904C3×C4C2×D3×D411yescharacteristic
905C3×C4C2×D3×D411yescharacteristic
906Dic3—22no—
907Dic3—21no—
908Dic3—41no—
909Dic3—62no—
910Dic3—61no—
911Dic3—62no—
912Dic3—61no—
913Dic3—122no—
914Dic3—121no—
915Dic3#88212yes—
916C32#300611yescharacteristic, complemented, Sylow
917C23—21no—
918C23—31no—
919C23—31no—
920C23—64no—
921C23—61no—
922C23—61no—
923C23—91no—
924C23—122no—
925C23—122no—
926C23—182no—
927C23—182no—
928C23—181no—
929C23—362no—
930C23—361no—
931C23—362no—
932C23—362no—
933Q8—32no—
934Q8—61no—
935Q8—92no—
936Q8—184no—
937Q8—181no—
938D4—21no—
939D4—32no—
940D4—64no—
941D4—64no—
942D4—61no—
943D4—61no—
944D4—61no—
945D4—122no—
946D4—184no—
947D4—184no—
948D4—184no—
949D4—181no—
950D4—181no—
951D4—362no—
952D4—362no—
953D4—362no—
954D4—362no—
955D4D3×D1212yescomplemented
956C2×C4—21no—
957C2×C4—31no—
958C2×C4—32no—
959C2×C4—32no—
960C2×C4—31no—
961C2×C4—64no—
962C2×C4—61no—
963C2×C4—61no—
964C2×C4—61no—
965C2×C4—61no—
966C2×C4—91no—
967C2×C4—122no—
968C2×C4—182no—
969C2×C4—182no—
970C2×C4—184no—
971C2×C4—182no—
972C2×C4—184no—
973C2×C4—184no—
974C2×C4—184no—
975C2×C4—181no—
976C2×C4—181no—
977C2×C4—181no—
978C2×C4C22×D3211yescharacteristic
979C8—21no—
980C8—61no—
981C8—61no—
982C8—181no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—42no—
987C2×C3—42no—
988C2×C3—62no—
989C2×C3—62no—
990C2×C3—82no—
991C2×C3—122no—
992C2×C3—241no—
993C2×C3C2×#88211yescharacteristic
994C2×C3D3×#12011yescharacteristic
995C2×C3C2×#91111yescharacteristic
996C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
997C2×C3#577311yescharacteristic
998C2×C3#577711yescharacteristic
999D3—22no—
1000D3—22no—
1001D3—42no—
1002D3—81no—
1003D3—121no—
1004D3—121no—
1005D3—241no—
1006D3—241no—
1007D3—241no—
1008D3—481no—
1009C22—22no—
1010C22—32no—
1011C22—32no—
1012C22—41no—
1013C22—41no—
1014C22—61no—
1015C22—61no—
1016C22—61no—
1017C22—61no—
1018C22—62no—
1019C22—128no—
1020C22—121no—
1021C22—121no—
1022C22—121no—
1023C22—121no—
1024C22—121no—
1025C22—181no—
1026C22—181no—
1027C22—181no—
1028C22—364no—
1029C22—361no—
1030C22—361no—
1031C22—361no—
1032C22—724no—
1033C22D32×D411yescharacteristic
1034C4—32no—
1035C4—41no—
1036C4—61no—
1037C4—62no—
1038C4—121no—
1039C4—181no—
1040C4—182no—
1041C4C2×D3×D1211yescharacteristic
1042C4D32×D411yescharacteristic
1043C3—21no—
1044C3#7888411yescharacteristic, complemented
1045C3#8000311yescharacteristic, complemented
1046C2—42no—
1047C2—62no—
1048C2—62no—
1049C2—122no—
1050C2—241no—
1051C2—361no—
1052C2—721no—
1053C2D3×#88211yescharacteristic
1054C2D3×#91111yescharacteristic
1055C2#1059474411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3006
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. C2×D3×#237C2semidirect
2. C2×#63925C2semidirect
3. C2×#63795C2semidirect
4. D3×#895C2semidirect
5. #10592480C2semidirect
6. C3×#4773C2semidirect
7. C3×#4771C2semidirect
8. #10591457C2semidirect
9. #10591448C2semidirect
10. #10590963C2semidirect
11. #10590951C2semidirect
12. #10590936C2semidirect
13. #10590617C2semidirect
14. #10590607C2semidirect
15. #10590603C2semidirect
18. C2×#3830C22semidirect
20. C2×C3×D3×D4C22semidirect
28. C2×D3×D12C22semidirect
30. C2×#3796C22semidirect
32. C2×D3×Dic6C22semidirect
33. C2×#3753C22semidirect
34. C2×#3744C22semidirect
35. #64104C22semidirect
36. C2×C3×#213C22semidirect
37. C2×C3×D24C22semidirect
38. C2×C3×ΓL(1,𝔽25)C22semidirect
40. C3×D3×C4⋊C4C22semidirect
43. #63916C22semidirect
47. C2×#3717C22semidirect
48. C2×#3716C22semidirect
49. C2×#3715C22semidirect
50. C2×#3714C22semidirect
51. C2×#3711C22semidirect
53. C32×#102C22semidirect
54. #63647C22semidirect
55. #63637C22semidirect
56. C3×#832C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. C3×#810C22semidirect
60. C3×#809C22semidirect
61. #63567C22semidirect
62. #63562C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
91. #4773D3semidirect
93. #4771D3semidirect
112. C3×#237D4semidirect
146. #3795D4semidirect
193. C2×D3×D4C2×D3semidirect
218. C2×#213C2×D3semidirect
226. C2×D24C2×D3semidirect
233. C2×ΓL(1,𝔽25)C2×D3semidirect
242. D3×C4⋊C4C2×D3semidirect
250. C3×#102C2×D3semidirect
251. C3×#102C2×D3semidirect
254. #832C2×D3semidirect
262. (C2×D3)⋊C8C2×D3semidirect
264. #816C2×D3semidirect
269. #810C2×D3semidirect
271. #809C2×D3semidirect
289. C32×D4C2×D4semidirect
302. #634C2×D4semidirect
314. C3×D12C2×D4semidirect
321. C3×Dic6C2×D4semidirect
416. #237D12semidirect
538. C2×C3×D3AGL(1,ℤ/8)semidirect
592. #102D32semidirect
645. C3×D4C2×D12semidirect
646. C3×D4D3×D4semidirect
710. D12D3×D4semidirect
738. Dic6C2×D12semidirect
892. C2×D3#911semidirect
916. C32#3006semidirect
955. D4D3×D12semidirect
1044. C3#78884semidirect
1045. C3#80003semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2372
C2×#639252
C2×#637952
D3×#8952
#105924802
C3×#47732
C3×#47712
#105914572
#105914482
#105909632
#105909512
#105909362
#105906172
#105906072
#105906032
#800033
#788843