Finite Group Databasebeta

← #11864128

Subgroups — #11864128

Order 1152.

1693 conjugacy classes of subgroups.

The subgroup lattice has 1051 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#237C211yesmaximal, characteristic, complemented
2C2×#63927C211yesmaximal, characteristic, complemented
3C2×#63798C211yesmaximal, characteristic, complemented
4#10594612C211yesmaximal, characteristic, complemented
5#10592470C211yesmaximal, characteristic, complemented
6C3×#4781C211yesmaximal, characteristic, complemented
7C3×#4773C211yesmaximal, characteristic, complemented
8#10591450C211yesmaximal, characteristic, complemented
9#10591447C211yesmaximal, characteristic, complemented
10#10590962C211yesmaximal, characteristic, complemented
11#10590937C211yesmaximal, characteristic, complemented
12#10590822C211yesmaximal, characteristic, complemented
13#10590613C211yesmaximal, characteristic, complemented
14#10590612C211yesmaximal, characteristic, complemented
15#10590603C211yesmaximal, characteristic, complemented
16#80084—31nomaximal
17#80003—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic, complemented
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×#3802—21no—
28C2×#3802C2211yescharacteristic, complemented
29C2×C4×D32C2211yescharacteristic
30C2×#3796C2211yescharacteristic
31C2×#3795C2211yescharacteristic, complemented
32C2×D3×Dic6C2211yescharacteristic, complemented
33C2×#3743C2211yescharacteristic, complemented
34C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
35C2×C3×#213C2211yescharacteristic, complemented
36C2×C3×#213C2211yescharacteristic, complemented
37C2×C3×D24C2211yescharacteristic, complemented
38C2×C3×#204C2211yescharacteristic, complemented
39C3×#895C2211yescharacteristic
40C3×#895C2211yescharacteristic, complemented
41#63927—24no—
42#63921—21no—
43#63908C2211yescharacteristic
44#63908C2211yescharacteristic, complemented
45#63885—21no—
46#63885—21no—
47C2×#3716C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×#3712C2211yescharacteristic, complemented
52#63798—24no—
53C32×#102C2211yescharacteristic, complemented
54#63659C2211yescharacteristic, complemented
55#63643C2211yescharacteristic, complemented
56#63637C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×#810C2211yescharacteristic, complemented
60C3×#809C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#237—31no—
67C2×#914—31no—
68C2×#911—31no—
69C2×#911—31no—
70C2×#911—31no—
71D3×#121—31no—
72D3×#121—31no—
73C3×#449—31no—
74C3×#447—31no—
75#5238—31no—
76#5217—31no—
77#5170—31no—
78#5158—31no—
79#5158—31no—
80#5156—31no—
81#5040—31no—
82#5037—31no—
83#4806—31no—
84#4803—31no—
85#4781—31no—
86#4781D311yescharacteristic, complemented
87#4773D311yescharacteristic, complemented
88#4771—31no—
89#4771—31no—
90#4771—31no—
91#4771—61no—
92#4738—31no—
93#4734—31no—
94#4726—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#3830D414yescomplemented
104C2×C4×C3⋊D3—21no—
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×#634C2311yescharacteristic
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C22×C3×Dic3—21no—
110C3×#237—22no—
111C3×#237—22no—
112C3×D3×D4—22no—
113C3×D3×D4—22no—
114C2×C3×D12—21no—
115C2×C3×D12—21no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×D12C2311yescharacteristic
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122D3×#67—28no—
123C2×#627—21no—
124C2×#626—21no—
125C2×#625—21no—
126C2×#625—21no—
127C2×#625—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
138#3802—22no—
139#3802—22no—
140#3802—44no—
141C4×D32—22no—
142C4×D32—22no—
143#3796—22no—
144#3796D414yescomplemented
145#3795—22no—
146#3795—22no—
147D3×Dic6—22no—
148D3×Dic6—22no—
149C2×C32×C8C2311yescharacteristic
150C32×C4⋊C4C2311yescharacteristic
151C4⋊(C3⋊Dic3)C2311yescharacteristic
152#3750—21no—
153C2×C3⋊(C3⋊C8)C2311yescharacteristic
154#3743—22no—
155C3×#213—22no—
156C3×#213—22no—
157C3×(C2×D3)⋊C4—21no—
158C3×(C2×D3)⋊C4—21no—
159C2×C3×C3⋊C8C2311yescharacteristic
160C2×C3×C3⋊C8C2311yescharacteristic
161C3×D24—22no—
162C3×#204—22no—
163(C2×D3)⋊Dic3—21no—
164(C2×D3)⋊Dic3—21no—
165#3716—22no—
166#3716—22no—
167#3715—22no—
168#3713—22no—
169#3712—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—64no—
188C2×#237—61no—
189C2×#237C2×D311yescharacteristic, complemented
190C2×D3×D4—31no—
191C2×D3×D4—31no—
192C2×D3×D4—61no—
193C2×D3×D4—61no—
194C2×D3×D4—61no—
195C2×D3×D4C2×D311yescharacteristic, complemented
196C2×#235—31no—
197C2×#235—61no—
198C22×C4×D3—31no—
199C22×C4×D3—31no—
200C22×C4×D3—61no—
201C22×Dic6—31no—
202C2×C3×SD16—31no—
203C2×C3×D8—31no—
204C2×C3×D8—31no—
205C2×C3×D8—31no—
206C3×#121—31no—
207C3×#121—31no—
208C2×#215—31no—
209#939—61no—
210#939—61no—
211#938—31no—
212#938—31no—
213C2×#214—31no—
214C2×#214—31no—
215C2×#214—31no—
216C2×#213—31no—
217C2×#213—31no—
218C2×#213C2×D311yescharacteristic, complemented
219C2×#213C2×D311yescharacteristic, complemented
220#930—31no—
221#930—31no—
222#914—64no—
223#911—64no—
224#911—64no—
225#911—64no—
226C2×D24C2×D311yescharacteristic, complemented
227C2×#204—31no—
228C2×#204—31no—
229C2×#204C2×D311yescharacteristic, complemented
230C2×ΓL(1,𝔽25)—31no—
231C2×ΓL(1,𝔽25)—31no—
232C2×ΓL(1,𝔽25)—31no—
233C2×ΓL(1,𝔽25)—31no—
234C2×ΓL(1,𝔽25)—61no—
235#895C2×D311yescharacteristic
236#895C2×D311yescharacteristic, complemented
237D3×C4⋊C4—31no—
238D3×C4⋊C4—31no—
239D3×C4⋊C4—61no—
240#884—61no—
241#884—61no—
242D3×C22⋊C4—61no—
243D3×C22⋊C4—61no—
244C3×#103—31no—
245C3×#102—21no—
246C3×#102—31no—
247C3×#102C2×D311yescharacteristic, complemented
248C3×#102C2×D311yescharacteristic, complemented
249C3×C22⋊C8—31no—
250C3×C22⋊C8—31no—
251#835—31no—
252#832—31no—
253#832—31no—
254#832—31no—
255#832—61no—
256#830—31no—
257#830—31no—
258#821—31no—
259(C2×D3)⋊C8—31no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8C2×D311yescharacteristic, complemented
262(C2×D3)⋊C8C2×D311yescharacteristic, complemented
263#816—31no—
264#816—31no—
265#816—31no—
266#816—61no—
267#810—31no—
268#810—31no—
269#810—61no—
270#810C2×D311yescharacteristic, complemented
271#809C2×D311yescharacteristic, complemented
272C23×C32—21no—
273C22×C3⋊D3C2×D411yescharacteristic
274C22×C3×D3—24no—
275C22×C3×D3—21no—
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—21no—
294C2×C3⋊Dic3—24no—
295C2×C3⋊Dic3—21no—
296C2×C3⋊Dic3C2×D411yescharacteristic
297C4×C3⋊D3—42no—
298C4×C3⋊D3C2×D412yes—
299C4×C3⋊D3C2×D412yes—
300#634—21no—
301#634C2×D412yescomplemented
302C3×#67—24no—
303C3×#67—24no—
304C2×C3×Dic3—24no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3C2×D411yescharacteristic
307C2×C3×Dic3C2×D411yescharacteristic
308C3×D12—21no—
309C3×D12—21no—
310C3×D12—21no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12—42no—
314C3×D12—42no—
315C3×D12C2×D412yescomplemented
316C3×C4×D3—21no—
317C3×C4×D3—21no—
318C3×C4×D3—21no—
319C3×C4×D3—21no—
320C3×Dic6—21no—
321C3×Dic6C2×D412yescomplemented
322#627—24no—
323#626—24no—
324#625—24no—
325#625—42no—
326#625—42no—
327#625—42no—
328#624—22no—
329D3×Dic3—24no—
330D3×Dic3—24no—
331D3×Dic3—24no—
332D3×Dic3—22no—
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—31no—
343#449—91no—
344#449—91no—
345#449—91no—
346#448—91no—
347#448—91no—
348#447—31no—
349#447—91no—
350#417—91no—
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—62no—
360C3×#41—62no—
361C2×C3×Q8—31no—
362C2×C3×D4—21no—
363C2×C3×D4—31no—
364C2×C3×D4—31no—
365C2×C3×D4—31no—
366C2×C3×D4—61no—
367C2×C3×D4—61no—
368C2×C3×D4—61no—
369C2×C3×D4—62no—
370C2×C3×D4—61no—
371C2×C3×D4—62no—
372C2×C3×D4C22×D311yescharacteristic
373C2×C3×D4C22×D311yescharacteristic
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—61no—
377C2×#67—21no—
378C2×#67—21no—
379C2×#67—61no—
380C2×#67—61no—
381C2×#67—61no—
382C2×#67—68no—
383C2×#67—61no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—61no—
387C2×#67—61no—
388C2×#67—61no—
389C2×#67—61no—
390C2×#67—61no—
391C2×#67—121no—
392C22×Dic3—21no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—61no—
396C22×Dic3—61no—
397C22×Dic3—68no—
398C22×Dic3—61no—
399C22×Dic3—61no—
400C22×Dic3—61no—
401C22×Dic3—121no—
402#239—34no—
403#239—62no—
404D3×Q8—62no—
405D3×Q8—62no—
406#237—22no—
407#237—22no—
408#237—34no—
409#237—34no—
410#237—34no—
411#237—64no—
412#237—62no—
413#237—62no—
414#237—62no—
415#237—62no—
416#237—62no—
417#237—68no—
418#237—68no—
419#237—68no—
420#237—122no—
421D3×D4—22no—
422D3×D4—22no—
423D3×D4—62no—
424D3×D4—62no—
425D3×D4—62no—
426D3×D4—62no—
427D3×D4—68no—
428D3×D4—124no—
429D3×D4—124no—
430#235—62no—
431#235—68no—
432#235—62no—
433C2×D12—21no—
434C2×D12—21no—
435C2×D12—61no—
436C2×D12C22×D311yescharacteristic
437C2×D12C22×D311yescharacteristic
438C2×D12C22×D311yescharacteristic
439C2×C4×D3—31no—
440C2×C4×D3—31no—
441C2×C4×D3—31no—
442C2×C4×D3—31no—
443C2×C4×D3—31no—
444C2×C4×D3—31no—
445C2×C4×D3—61no—
446C2×C4×D3—62no—
447C2×C4×D3—62no—
448C2×C4×D3—62no—
449C2×C4×D3—62no—
450C2×C4×D3—61no—
451C2×C4×D3—61no—
452C2×C4×D3—68no—
453C2×C4×D3—61no—
454C2×C4×D3—61no—
455C2×C4×D3—61no—
456C2×C4×D3—121no—
457C2×C4×D3C22×D311yescharacteristic
458C2×C4×D3C22×D311yescharacteristic
459C2×Dic6—31no—
460C2×Dic6—31no—
461C2×Dic6—61no—
462C2×Dic6—62no—
463C2×Dic6—61no—
464C2×Dic6—61no—
465C2×Dic6—62no—
466C2×Dic6C22×D311yescharacteristic
467C3×SD16—62no—
468C3×D8—62no—
469C3×D8—62no—
470C3×D8—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⋊C4C22×D311yescharacteristic
478C3×C4⋊C4C22×D311yescharacteristic
479C3×C22⋊C4—61no—
480C3×C22⋊C4—61no—
481#217—61no—
482#217—61no—
483#215—62no—
484#214—62no—
485#214—62no—
486#214—62no—
487#213—22no—
488#213—22no—
489#213—62no—
490#213—62no—
491(C2×D3)⋊C4—21no—
492(C2×D3)⋊C4—21no—
493(C2×D3)⋊C4—61no—
494(C2×D3)⋊C4—61no—
495C4⋊Dic3—31no—
496C4⋊Dic3—31no—
497C4⋊Dic3—61no—
498Dic3⋊C4—61no—
499Dic3⋊C4—61no—
500Dic3⋊C4—121no—
501C2×C3⋊C8—31no—
502C2×C3⋊C8—31no—
503C2×C3⋊C8—61no—
504C2×C3⋊C8C22×D311yescharacteristic
505C2×C3⋊C8C22×D311yescharacteristic
506D24—22no—
507#204—22no—
508#204—62no—
509#204—62no—
510ΓL(1,𝔽25)—62no—
511ΓL(1,𝔽25)—62no—
512ΓL(1,𝔽25)—62no—
513ΓL(1,𝔽25)—62no—
514ΓL(1,𝔽25)—122no—
515C22×C32—22no—
516C22×C32—41no—
517C22×C32—41no—
518C22×C32C22×D411yescharacteristic
519C2×C3⋊D3—21no—
520C2×C3⋊D3—21no—
521C2×C3⋊D3#12012yes—
522C2×C3×D3—21no—
523C2×C3×D3—21no—
524C2×C3×D3—22no—
525C2×C3×D3—21no—
526C2×C3×D3—21no—
527C2×C3×D3—21no—
528C2×C3×D3—48no—
529C2×C3×D3—41no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533C2×C3×D3—41no—
534C2×C3×D3—41no—
535C2×C3×D3—41no—
536C2×C3×D3—41no—
537C2×C3×D3AGL(1,ℤ/8)12yescomplemented
538D32—44no—
539D32—84no—
540C32×C4—41no—
541C32×C4C22×D411yescharacteristic
542C32×C4C22×D411yescharacteristic
543C3⋊Dic3—22no—
544C3⋊Dic3—41no—
545C3⋊Dic3#12012yes—
546C3×Dic3—21no—
547C3×Dic3—22no—
548C3×Dic3—21no—
549C2×#41—31no—
550C2×#41—91no—
551C2×#41—91no—
552C2×#41—91no—
553C2×#41—181no—
554C2×#41—181no—
555C2×#41—184no—
556C2×#41—184no—
557C22×Q8—91no—
558C22×D4—31no—
559C22×D4—91no—
560C22×D4—181no—
561C22×D4—181no—
562C23×C4—91no—
563C23×C4—181no—
564AGL(1,ℤ/8)—184no—
565AGL(1,ℤ/8)—184no—
566C2×SD16—31no—
567C2×SD16—91no—
568C2×SD16—91no—
569C2×SD16—91no—
570C2×D8—31no—
571C2×D8—31no—
572C2×D8—31no—
573C2×D8—91no—
574C2×M16—91no—
575C2×M16—91no—
576#121—31no—
577#121—31no—
578#121—91no—
579#121—91no—
580#121—181no—
581#121—181no—
582C2×C4⋊C4—91no—
583C2×C22⋊C4—181no—
584#103—31no—
585#103—91no—
586#103—91no—
587#103—91no—
588#102—31no—
589#102—91no—
590#102—91no—
591#102D3211yescharacteristic, complemented
592C22⋊C8—31no—
593C22⋊C8—31no—
594C22⋊C8—91no—
595C22⋊C8—91no—
596C23×C3—21no—
597C23×C3—21no—
598C23×C3—31no—
599C23×C3—31no—
600C23×C3—41no—
601C23×C3—64no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3—122no—
606C23×C3—122no—
607C22×D3—24no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—31no—
612C22×D3—31no—
613C22×D3—42no—
614C22×D3—42no—
615C22×D3—61no—
616C22×D3—62no—
617C22×D3—62no—
618C22×D3—62no—
619C22×D3—62no—
620C22×D3—121no—
621C22×D3—121no—
622C22×D3—122no—
623C22×D3—122no—
624C22×D3—122no—
625C22×D3—122no—
626C22×D3—122no—
627C22×D3—122no—
628C22×D3D3×D411yescharacteristic
629C22×D3D3×D411yescharacteristic
630C3×Q8—32no—
631C3×Q8—61no—
632C3×D4—21no—
633C3×D4—21no—
634C3×D4—22no—
635C3×D4—32no—
636C3×D4—41no—
637C3×D4—64no—
638C3×D4—64no—
639C3×D4—61no—
640C3×D4—61no—
641C3×D4—61no—
642C3×D4—61no—
643C3×D4—61no—
644C3×D4—122no—
645C3×D4—122no—
646C3×D4D3×D412yescomplemented
647C3×D4D3×D412yescomplemented
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—31no—
652C2×C3×C4—31no—
653C2×C3×C4—41no—
654C2×C3×C4—64no—
655C2×C3×C4—61no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4C23×D311yescharacteristic
661C2×C3×C4C23×D311yescharacteristic
662#67—24no—
663#67—24no—
664#67—64no—
665#67—64no—
666#67—64no—
667#67—64no—
668#67—64no—
669#67—124no—
670#67—122no—
671#67—122no—
672#67—122no—
673#67—122no—
674#67—122no—
675#67—122no—
676C2×Dic3—24no—
677C2×Dic3—21no—
678C2×Dic3—31no—
679C2×Dic3—31no—
680C2×Dic3—61no—
681C2×Dic3—62no—
682C2×Dic3—62no—
683C2×Dic3—64no—
684C2×Dic3—64no—
685C2×Dic3—64no—
686C2×Dic3—64no—
687C2×Dic3—64no—
688C2×Dic3—61no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—61no—
692C2×Dic3—124no—
693C2×Dic3—121no—
694C2×Dic3—121no—
695C2×Dic3D3×D411yescharacteristic
696C2×Dic3D3×D411yescharacteristic
697D12—21no—
698D12—21no—
699D12—21no—
700D12—21no—
701D12—21no—
702D12—42no—
703D12—42no—
704D12—64no—
705D12D3×D412yescomplemented
706C4×D3—21no—
707C4×D3—21no—
708C4×D3—21no—
709C4×D3—21no—
710C4×D3—32no—
711C4×D3—32no—
712C4×D3—32no—
713C4×D3—32no—
714C4×D3—62no—
715C4×D3—62no—
716C4×D3—62no—
717C4×D3—62no—
718C4×D3—62no—
719C4×D3—62no—
720C4×D3—64no—
721C4×D3—64no—
722C4×D3—64no—
723C4×D3—122no—
724C4×D3—122no—
725C4×D3—242no—
726Dic6—21no—
727Dic6—32no—
728Dic6—32no—
729Dic6—62no—
730Dic6—64no—
731Dic6—64no—
732Dic6—61no—
733Dic6—61no—
734Dic6—121no—
735Dic6D3×D412yescomplemented
736C3×C8—21no—
737C3×C8—21no—
738C3×C8—41no—
739C3×C8—61no—
740C3×C8—61no—
741C3⋊C8—21no—
742C3⋊C8—21no—
743C3⋊C8—61no—
744C3⋊C8—61no—
745C3⋊C8—121no—
746C2×C32—42no—
747C2×C32C2×#12011yescharacteristic
748C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
749C2×C32#57511yescharacteristic
750C3⋊D3—22no—
751C3×D3—22no—
752C3×D3—41no—
753C3×D3—42no—
754C3×D3—81no—
755C3×D3—81no—
756C24—61no—
757C24—91no—
758C24—181no—
759#41—62no—
760#41—62no—
761#41—94no—
762#41—94no—
763#41—182no—
764#41—182no—
765#41—188no—
766#41—182no—
767#41—182no—
768#41—188no—
769C2×Q8—31no—
770C2×Q8—91no—
771C2×Q8—181no—
772C2×Q8—182no—
773C2×Q8—182no—
774C2×D4—31no—
775C2×D4—31no—
776C2×D4—31no—
777C2×D4—61no—
778C2×D4—61no—
779C2×D4—61no—
780C2×D4—62no—
781C2×D4—61no—
782C2×D4—62no—
783C2×D4—181no—
784C2×D4—182no—
785C2×D4—182no—
786C2×D4—181no—
787C2×D4—188no—
788C2×D4—181no—
789C2×D4—181no—
790C2×D4—181no—
791C2×D4—181no—
792C2×D4—364no—
793C2×D4C2×D3211yescharacteristic
794C22×C4—31no—
795C22×C4—31no—
796C22×C4—61no—
797C22×C4—91no—
798C22×C4—91no—
799C22×C4—91no—
800C22×C4—91no—
801C22×C4—181no—
802C22×C4—181no—
803C22×C4—182no—
804C22×C4—182no—
805C22×C4—181no—
806C22×C4—181no—
807C22×C4—188no—
808C22×C4—181no—
809SD16—62no—
810SD16—182no—
811SD16—182no—
812SD16—182no—
813D8—62no—
814D8—62no—
815D8—62no—
816D8—182no—
817M16—182no—
818M16—182no—
819C2×C8—31no—
820C2×C8—31no—
821C2×C8—91no—
822C2×C8C2×D3211yescharacteristic
823C4⋊C4—91no—
824C4⋊C4—181no—
825C4⋊C4C2×D3211yescharacteristic
826C22⋊C4—61no—
827C22⋊C4—61no—
828C22⋊C4—181no—
829C22⋊C4—181no—
830C22×C3—22no—
831C22×C3—22no—
832C22×C3—21no—
833C22×C3—32no—
834C22×C3—42no—
835C22×C3—41no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—41no—
839C22×C3—61no—
840C22×C3—61no—
841C22×C3—61no—
842C22×C3—61no—
843C22×C3—62no—
844C22×C3—61no—
845C22×C3—81no—
846C22×C3—81no—
847C22×C3—128no—
848C22×C3—121no—
849C22×C3—121no—
850C22×C3—121no—
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—21no—
863C2×D3—22no—
864C2×D3—32no—
865C2×D3—32no—
866C2×D3—48no—
867C2×D3—41no—
868C2×D3—41no—
869C2×D3—41no—
870C2×D3—41no—
871C2×D3—41no—
872C2×D3—41no—
873C2×D3—41no—
874C2×D3—41no—
875C2×D3—62no—
876C2×D3—61no—
877C2×D3—61no—
878C2×D3—61no—
879C2×D3—61no—
880C2×D3—121no—
881C2×D3—121no—
882C2×D3—124no—
883C2×D3—124no—
884C2×D3—244no—
885C2×D3—244no—
886C2×D3#91112yescomplemented
887C3×C4—21no—
888C3×C4—21no—
889C3×C4—41no—
890C3×C4—41no—
891C3×C4—61no—
892C3×C4—62no—
893C3×C4—61no—
894C3×C4—81no—
895C3×C4C2×D3×D411yescharacteristic
896C3×C4C2×D3×D411yescharacteristic
897C3×C4C2×D3×D411yescharacteristic
898C3×C4C2×D3×D411yescharacteristic
899Dic3—22no—
900Dic3—21no—
901Dic3—21no—
902Dic3—32no—
903Dic3—32no—
904Dic3—62no—
905Dic3—62no—
906Dic3—62no—
907Dic3—122no—
908Dic3—121no—
909Dic3—121no—
910Dic3—241no—
911C32#300611yescharacteristic, complemented, Sylow
912C23—21no—
913C23—31no—
914C23—31no—
915C23—64no—
916C23—61no—
917C23—61no—
918C23—61no—
919C23—91no—
920C23—122no—
921C23—122no—
922C23—182no—
923C23—182no—
924C23—361no—
925C23—362no—
926C23—362no—
927C23—362no—
928Q8—32no—
929Q8—61no—
930Q8—92no—
931Q8—184no—
932Q8—181no—
933D4—21no—
934D4—32no—
935D4—64no—
936D4—64no—
937D4—61no—
938D4—61no—
939D4—61no—
940D4—61no—
941D4—61no—
942D4—122no—
943D4—122no—
944D4—184no—
945D4—184no—
946D4—184no—
947D4—362no—
948D4—362no—
949D4—362no—
950D4#380212yescomplemented
951C2×C4—21no—
952C2×C4—31no—
953C2×C4—31no—
954C2×C4—64no—
955C2×C4—61no—
956C2×C4—61no—
957C2×C4—61no—
958C2×C4—61no—
959C2×C4—61no—
960C2×C4—91no—
961C2×C4—92no—
962C2×C4—92no—
963C2×C4—182no—
964C2×C4—182no—
965C2×C4—182no—
966C2×C4—184no—
967C2×C4—184no—
968C2×C4—184no—
969C2×C4—184no—
970C2×C4—181no—
971C2×C4—181no—
972C2×C4—362no—
973C2×C4C22×D3211yescharacteristic
974C8—21no—
975C8—61no—
976C8—61no—
977C8—181no—
978C2×C3—21no—
979C2×C3—21no—
980C2×C3—21no—
981C2×C3—42no—
982C2×C3—42no—
983C2×C3—62no—
984C2×C3—82no—
985C2×C3—121no—
986C2×C3—122no—
987C2×C3—241no—
988C2×C3—241no—
989C2×C3D3×#12011yescharacteristic
990C2×C3D3×#12011yescharacteristic
991C2×C3C2×#91111yescharacteristic
992C2×C3#576811yescharacteristic
993C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
994C2×C3#577311yescharacteristic
995D3—22no—
996D3—42no—
997D3—41no—
998D3—62no—
999D3—62no—
1000D3—81no—
1001D3—81no—
1002D3—122no—
1003C22—22no—
1004C22—32no—
1005C22—41no—
1006C22—41no—
1007C22—61no—
1008C22—61no—
1009C22—61no—
1010C22—61no—
1011C22—61no—
1012C22—62no—
1013C22—92no—
1014C22—128no—
1015C22—121no—
1016C22—121no—
1017C22—121no—
1018C22—121no—
1019C22—121no—
1020C22—121no—
1021C22—121no—
1022C22—121no—
1023C22—181no—
1024C22—181no—
1025C22—364no—
1026C22—724no—
1027C22D32×D411yescharacteristic
1028C4—41no—
1029C4—61no—
1030C4—61no—
1031C4—62no—
1032C4—92no—
1033C4—182no—
1034C4—361no—
1035C4C2×#380211yescharacteristic
1036C4D32×D411yescharacteristic
1037C3—21no—
1038C3#8000311yescharacteristic, complemented
1039C3#8008411yescharacteristic, complemented
1040C2—42no—
1041C2—62no—
1042C2—121no—
1043C2—122no—
1044C2—182no—
1045C2—241no—
1046C2—241no—
1047C2#1059425811yescharacteristic
1048C2D3×#91111yescharacteristic
1049C2#1059474511yescharacteristic
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×#63927C2semidirect
3. C2×#63798C2semidirect
4. #10594612C2semidirect
5. #10592470C2semidirect
6. C3×#4781C2semidirect
7. C3×#4773C2semidirect
8. #10591450C2semidirect
9. #10591447C2semidirect
10. #10590962C2semidirect
11. #10590937C2semidirect
12. #10590822C2semidirect
13. #10590613C2semidirect
14. #10590612C2semidirect
15. #10590603C2semidirect
19. C2×C3×#237C22semidirect
20. C2×C3×D3×D4C22semidirect
28. C2×#3802C22semidirect
31. C2×#3795C22semidirect
32. C2×D3×Dic6C22semidirect
33. C2×#3743C22semidirect
34. C4⋊C4×C3⋊D3C22semidirect
35. C2×C3×#213C22semidirect
36. C2×C3×#213C22semidirect
37. C2×C3×D24C22semidirect
38. C2×C3×#204C22semidirect
40. C3×#895C22semidirect
44. #63908C22semidirect
47. C2×#3716C22semidirect
48. C2×#3716C22semidirect
49. C2×#3715C22semidirect
50. C2×#3713C22semidirect
51. C2×#3712C22semidirect
53. C32×#102C22semidirect
54. #63659C22semidirect
55. #63643C22semidirect
56. #63637C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×#810C22semidirect
60. C3×#809C22semidirect
61. #63566C22semidirect
62. #63563C22semidirect
63. (C2×D3)⋊(C3⋊C8)C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
86. #4781D3semidirect
87. #4773D3semidirect
103. #3830D4semidirect
144. #3796D4semidirect
189. C2×#237C2×D3semidirect
195. C2×D3×D4C2×D3semidirect
218. C2×#213C2×D3semidirect
219. C2×#213C2×D3semidirect
226. C2×D24C2×D3semidirect
229. C2×#204C2×D3semidirect
236. #895C2×D3semidirect
247. C3×#102C2×D3semidirect
248. C3×#102C2×D3semidirect
261. (C2×D3)⋊C8C2×D3semidirect
262. (C2×D3)⋊C8C2×D3semidirect
270. #810C2×D3semidirect
271. #809C2×D3semidirect
289. C32×D4C2×D4semidirect
301. #634C2×D4semidirect
315. C3×D12C2×D4semidirect
321. C3×Dic6C2×D4semidirect
537. C2×C3×D3AGL(1,ℤ/8)semidirect
591. #102D32semidirect
646. C3×D4D3×D4semidirect
647. C3×D4D3×D4semidirect
705. D12D3×D4semidirect
735. Dic6D3×D4semidirect
886. C2×D3#911semidirect
911. C32#3006semidirect
950. D4#3802semidirect
1038. C3#80003semidirect
1039. C3#80084semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2372
C2×#639272
C2×#637982
#105946122
#105924702
C3×#47812
C3×#47732
#105914502
#105914472
#105909622
#105909372
#105908222
#105906132
#105906122
#105906032
#800843
#800033