Finite Group Databasebeta

← #11864161

Subgroups — #11864161

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×C3×D3×#41C211yesmaximal, characteristic, complemented
2C2×#63939C211yesmaximal, characteristic, complemented
3C2×#63925C211yesmaximal, characteristic, complemented
4D3×#930C211yesmaximal, characteristic, complemented
5#10592937C211yesmaximal, characteristic, complemented
6C3×#5238C211yesmaximal, characteristic, complemented
7#10591584C211yesmaximal, characteristic, complemented
8#10591583C211yesmaximal, characteristic, complemented
9#10591550C211yesmaximal, characteristic, complemented
10#10591448C211yesmaximal, characteristic, complemented
11#10591447C211yesmaximal, characteristic, complemented
12#10591414C211yesmaximal, characteristic, complemented
13#10591163C211yesmaximal, characteristic, complemented
14#10591161C211yesmaximal, characteristic, complemented
15#10591154C211yesmaximal, characteristic, complemented
16#84082—31nomaximal
17#80084—31nomaximal
18C2×C32×#41C2211yescharacteristic, complemented
19C3×D3×#41—24no—
20C3×D3×#41—24no—
21C2×C3×#239C2211yescharacteristic
22C2×C3×D3×Q8C2211yescharacteristic, complemented
23C2×C3×#237—21no—
24C2×C3×#237C2211yescharacteristic
25C2×C3×D3×D4—21no—
26C2×C3×D3×D4C2211yescharacteristic, complemented
27C2×C3×#235—21no—
28C2×C3×#235C2211yescharacteristic, complemented
29C22×C3×C4×D3—21no—
30C22×C3×C4×D3C2211yescharacteristic
31C2×D3×#67—21no—
32C2×D3×D12C2211yescharacteristic, complemented
33C2×#3755C2211yescharacteristic, complemented
34C2×#3753C2211yescharacteristic, complemented
35#64139C2211yescharacteristic, complemented
36C2×C3×#215C2211yescharacteristic, complemented
37C2×C3×#213C2211yescharacteristic, complemented
38C3×#930C2211yescharacteristic, complemented
39#63978—21no—
40#63939—24no—
41#63925—24no—
42D3×(C2×D3)⋊C4—21no—
43#63909C2211yescharacteristic
44#63908C2211yescharacteristic
45#63906—21no—
46D3×C4⋊Dic3C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52C2×#3711C2211yescharacteristic, complemented
53#63662C2211yescharacteristic, complemented
54#63659C2211yescharacteristic, complemented
55#63657C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#832C2211yescharacteristic, complemented
58C3×#830C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C22×C3×#41—31no—
66C2×D3×#41D311yescharacteristic, complemented
67C2×#949—31no—
68C2×#949—31no—
69C2×#930—31no—
70C2×#914—31no—
71C2×#911—31no—
72D3×#121—31no—
73C3×#449—31no—
74#5238—31no—
75#5238—31no—
76#5238—31no—
77#5238—31no—
78#5238—61no—
79#5238D311yescharacteristic, complemented
80#5232—31no—
81#5232—31no—
82#5227—31no—
83#5227—31no—
84#5217—31no—
85#5217—31no—
86#5207—31no—
87#5170—31no—
88#5156—31no—
89#5037—31no—
90#4806—31no—
91#4803—31no—
92#4773—31no—
93#4771—31no—
94#4734—31no—
95#4726—31no—
96C23×C3×D3—21no—
97C23×C3×D3D411yescharacteristic
98C22×D32—21no—
99C32×#41—22no—
100C32×#41—22no—
101C2×C32×Q8C2311yescharacteristic
102C2×C32×D4—21no—
103C2×C32×D4C2311yescharacteristic
104C22×C32×C4—21no—
105C22×C32×C4C2311yescharacteristic
106C2×#638—21no—
107C2×C4⋊(C3⋊D3)C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C2×C3×#67—21no—
112C22×C3×Dic3—21no—
113C22×C3×Dic3D411yescharacteristic
114C3×#239—22no—
115C3×#239D414yescomplemented
116C3×D3×Q8—22no—
117C3×D3×Q8—22no—
118C3×#237—28no—
119C3×#237—22no—
120C3×#237D414yescomplemented
121C3×D3×D4—28no—
122C3×D3×D4—22no—
123C3×D3×D4—22no—
124C3×#235—28no—
125C3×#235—22no—
126C3×#235—22no—
127C2×C3×D12—21no—
128C2×C3×D12C2311yescharacteristic
129C2×C3×D12C2311yescharacteristic
130C2×C3×C4×D3—28no—
131C2×C3×C4×D3—21no—
132C2×C3×C4×D3—21no—
133C2×C3×C4×D3—21no—
134C2×C3×C4×D3—22no—
135C2×C3×C4×D3—22no—
136C2×C3×C4×D3D411yescharacteristic
137C2×C3×C4×D3D411yescharacteristic
138C2×C3×C4×D3C2311yescharacteristic
139C2×C3×C4×D3C2311yescharacteristic
140C2×C3×Dic6—21no—
141C2×C3×Dic6C2311yescharacteristic
142D3×#67—44no—
143C2×#626—21no—
144C2×#626—21no—
145C2×#625—21no—
146C2×D3×Dic3—21no—
147D3×D12—22no—
148D3×D12—22no—
149#3755—22no—
150#3753—22no—
151#3752—21no—
152C4⋊(C3⋊Dic3)C2311yescharacteristic
153C2×C3⋊(C3⋊C8)C2311yescharacteristic
154C2×C3⋊(C3⋊C8)C2311yescharacteristic
155C3×#215—22no—
156C3×#213—22no—
157C3×(C2×D3)⋊C4—21no—
158C3×C4⋊Dic3C2311yescharacteristic
159C2×C3×C3⋊C8C2311yescharacteristic
160C2×C3×C3⋊C8C2311yescharacteristic
161Dic3⋊Dic3—21no—
162#3722—21no—
163(C2×D3)⋊Dic3—21no—
164#3717—22no—
165#3715—22no—
166#3714—22no—
167#3713—22no—
168#3711—22no—
169#3711—22no—
170#3006—91noSylow
171C2×C3×#41—21no—
172C2×C3×#41—31no—
173C2×C3×#41—31no—
174C2×C3×#41—31no—
175C2×C3×#41—61no—
176C2×C3×#41—61no—
177C2×C3×#41—64no—
178C2×C3×#41—64no—
179C2×C3×#41C2×D311yescharacteristic, complemented
180C2×C3×#41C2×D311yescharacteristic, complemented
181C22×C3×Q8—31no—
182C22×C3×D4—31no—
183C22×C3×D4—61no—
184C23×C3×C4—31no—
185C23×C3×C4—61no—
186C22×#67—61no—
187D3×#41—24no—
188D3×#41—24no—
189C2×#239C2×D311yescharacteristic
190C2×D3×Q8C2×D311yescharacteristic, complemented
191C2×#237—21no—
192C2×#237C2×D311yescharacteristic
193C2×D3×D4—21no—
194C2×D3×D4—31no—
195C2×D3×D4—61no—
196C2×D3×D4C2×D311yescharacteristic, complemented
197C2×#235—21no—
198C2×#235C2×D311yescharacteristic, complemented
199C22×D12—31no—
200C22×C4×D3—21no—
201C22×C4×D3C2×D311yescharacteristic
202C2×C3×SD16—31no—
203C2×C3×D8—31no—
204C3×#121—31no—
205#949—64no—
206#949—64no—
207C2×#215—31no—
208C2×#215—31no—
209C2×#215—31no—
210C2×#215—31no—
211C2×#215—61no—
212C2×#215C2×D311yescharacteristic, complemented
213#939—61no—
214#938—31no—
215C2×#214—31no—
216C2×#213—31no—
217C2×#213—31no—
218C2×#213—31no—
219C2×#213—31no—
220C2×#213—31no—
221C2×#213—61no—
222C2×#213C2×D311yescharacteristic, complemented
223#930—31no—
224#930—31no—
225#930—31no—
226#930—31no—
227#930—61no—
228#930—61no—
229#930—61no—
230#930C2×D311yescharacteristic, complemented
231C2×(C2×D3)⋊C4—61no—
232C2×C4⋊Dic3—31no—
233C2×#208—31no—
234C2×#208—31no—
235#914—64no—
236#911—64no—
237C2×D24—31no—
238C2×#204—31no—
239C2×ΓL(1,𝔽25)—31no—
240C2×ΓL(1,𝔽25)—31no—
241#895—31no—
242D3×C4⋊C4—31no—
243#884—61no—
244D3×C22⋊C4—61no—
245C3×#103—31no—
246C3×#102—31no—
247C3×C22⋊C8—31no—
248#835—31no—
249#835—31no—
250#835—31no—
251#835—31no—
252#835—61no—
253#835C2×D311yescharacteristic, complemented
254#832—31no—
255#832—31no—
256#832—31no—
257#832—31no—
258#832—61no—
259#832C2×D311yescharacteristic, complemented
260#830—31no—
261#830—31no—
262#830—31no—
263#830—31no—
264#830—61no—
265#830C2×D311yescharacteristic, complemented
266#821—31no—
267(C2×D3)⋊C8—31no—
268(C2×D3)⋊C8—31no—
269#816—31no—
270#810—31no—
271#809—31no—
272C23×C32—21no—
273C23×C32C2×D411yescharacteristic
274C22×C3⋊D3—21no—
275C22×C3×D3—24no—
276C22×C3×D3—21no—
277C22×C3×D3—22no—
278C22×C3×D3—22no—
279C22×C3×D3—21no—
280C22×C3×D3—41no—
281C22×C3×D3—42no—
282C22×C3×D3—42no—
283C22×C3×D3C2×D411yescharacteristic
284C22×C3×D3C2×D411yescharacteristic
285C2×D32—42no—
286C2×D32—42no—
287C2×D32—42no—
288C32×Q8—21no—
289C32×Q8C2×D412yescomplemented
290C32×D4—24no—
291C32×D4—21no—
292C32×D4C2×D412yescomplemented
293C2×C32×C4—24no—
294C2×C32×C4—21no—
295C2×C32×C4—21no—
296C2×C32×C4—21no—
297C2×C32×C4C2×D411yescharacteristic
298C2×C32×C4C2411yescharacteristic
299#638—42no—
300C2×C3⋊Dic3—21no—
301C4⋊(C3⋊D3)—21no—
302C4⋊(C3⋊D3)—21no—
303C3×#67—24no—
304C3×#67—24no—
305C3×#67—24no—
306C3×#67—42no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—24no—
310C2×C3×Dic3—21no—
311C2×C3×Dic3C2×D411yescharacteristic
312C2×C3×Dic3C2×D411yescharacteristic
313C3×D12—24no—
314C3×D12—21no—
315C3×D12—21no—
316C3×D12—21no—
317C3×D12C2×D412yescomplemented
318C3×C4×D3—24no—
319C3×C4×D3—24no—
320C3×C4×D3—22no—
321C3×C4×D3—21no—
322C3×C4×D3—21no—
323C3×C4×D3—22no—
324C3×C4×D3—24no—
325C3×C4×D3C2×D412yes—
326C3×C4×D3C2×D412yes—
327C3×Dic6—24no—
328C3×Dic6—21no—
329C3×Dic6C2×D412yescomplemented
330#626—42no—
331#626—42no—
332#625—42no—
333D3×Dic3—42no—
334C3⋊(C3⋊C8)—21no—
335C3⋊(C3⋊C8)—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C22×#41—31no—
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—91no—
349#447—91no—
350#417—91no—
351#417—91no—
352#407—91no—
353C24×C3—31no—
354C24×C3—61no—
355C23×D3—21no—
356C23×D3—61no—
357C23×D3—61no—
358C23×D3#6711yescharacteristic
359C3×#41—22no—
360C3×#41—22no—
361C3×#41—22no—
362C3×#41—22no—
363C3×#41—34no—
364C3×#41—34no—
365C3×#41—42no—
366C3×#41—42no—
367C3×#41—62no—
368C3×#41—62no—
369C3×#41—68no—
370C3×#41—62no—
371C3×#41—62no—
372C3×#41—68no—
373C2×C3×Q8—21no—
374C2×C3×Q8—31no—
375C2×C3×Q8—61no—
376C2×C3×Q8—62no—
377C2×C3×Q8—62no—
378C2×C3×Q8C22×D311yescharacteristic
379C2×C3×Q8C22×D311yescharacteristic
380C2×C3×D4—21no—
381C2×C3×D4—21no—
382C2×C3×D4—21no—
383C2×C3×D4—31no—
384C2×C3×D4—31no—
385C2×C3×D4—41no—
386C2×C3×D4—61no—
387C2×C3×D4—61no—
388C2×C3×D4—62no—
389C2×C3×D4—68no—
390C2×C3×D4—61no—
391C2×C3×D4—61no—
392C2×C3×D4—62no—
393C2×C3×D4—61no—
394C2×C3×D4C22×D311yescharacteristic
395C2×C3×D4C22×D311yescharacteristic
396C22×C3×C4—21no—
397C22×C3×C4—21no—
398C22×C3×C4—21no—
399C22×C3×C4—31no—
400C22×C3×C4—31no—
401C22×C3×C4—31no—
402C22×C3×C4—31no—
403C22×C3×C4—31no—
404C22×C3×C4—41no—
405C22×C3×C4—62no—
406C22×C3×C4—62no—
407C22×C3×C4—61no—
408C22×C3×C4—61no—
409C22×C3×C4—68no—
410C22×C3×C4—61no—
411C22×C3×C4—61no—
412C22×C3×C4C22×D311yescharacteristic
413C22×C3×C4C22×D311yescharacteristic
414C2×#67—21no—
415C2×#67—21no—
416C2×#67—21no—
417C2×#67—21no—
418C2×#67—61no—
419C2×#67—61no—
420C2×#67—61no—
421C2×#67—61no—
422C2×#67—61no—
423C2×#67—61no—
424C2×#67—121no—
425C2×#67—124no—
426C22×Dic3—21no—
427C22×Dic3—61no—
428C22×Dic3#6711yescharacteristic
429#239—22no—
430#239#6714yescomplemented
431D3×Q8—22no—
432D3×Q8—22no—
433#237—28no—
434#237—22no—
435#237#6714yescomplemented
436D3×D4—28no—
437D3×D4—22no—
438D3×D4—22no—
439D3×D4—62no—
440D3×D4—62no—
441D3×D4—124no—
442#235—28no—
443#235—22no—
444#235—22no—
445C2×D12—21no—
446C2×D12—31no—
447C2×D12—31no—
448C2×D12—61no—
449C2×D12—62no—
450C2×D12—62no—
451C2×D12—61no—
452C2×D12—61no—
453C2×D12C22×D311yescharacteristic
454C2×D12C22×D311yescharacteristic
455C2×C4×D3—28no—
456C2×C4×D3—21no—
457C2×C4×D3—21no—
458C2×C4×D3—21no—
459C2×C4×D3—22no—
460C2×C4×D3—22no—
461C2×C4×D3—61no—
462C2×C4×D3#6711yescharacteristic
463C2×C4×D3#6711yescharacteristic
464C2×C4×D3C22×D311yescharacteristic
465C2×C4×D3C22×D311yescharacteristic
466C2×Dic6—21no—
467C2×Dic6C22×D311yescharacteristic
468C3×SD16—62no—
469C3×D8—62no—
470C2×C3×C8—31no—
471C2×C3×C8—31no—
472C3×C4⋊C4—31no—
473C3×C22⋊C4—61no—
474#217—61no—
475#215—22no—
476#215—62no—
477#215—62no—
478#215—62no—
479#215—62no—
480#215—122no—
481#214—62no—
482#213—22no—
483#213—62no—
484#213—62no—
485#213—62no—
486#213—62no—
487#213—62no—
488#213—122no—
489(C2×D3)⋊C4—21no—
490(C2×D3)⋊C4—61no—
491(C2×D3)⋊C4—61no—
492(C2×D3)⋊C4—61no—
493(C2×D3)⋊C4—61no—
494(C2×D3)⋊C4—61no—
495(C2×D3)⋊C4—121no—
496C4⋊Dic3—31no—
497C4⋊Dic3—31no—
498C4⋊Dic3—61no—
499C4⋊Dic3—61no—
500C4⋊Dic3C22×D311yescharacteristic
501Dic3⋊C4—61no—
502#208—62no—
503#208—62no—
504C2×C3⋊C8—31no—
505C2×C3⋊C8—31no—
506C2×C3⋊C8—31no—
507C2×C3⋊C8—31no—
508C2×C3⋊C8—61no—
509C2×C3⋊C8—61no—
510C2×C3⋊C8C22×D311yescharacteristic
511C2×C3⋊C8C22×D311yescharacteristic
512D24—62no—
513#204—62no—
514ΓL(1,𝔽25)—62no—
515ΓL(1,𝔽25)—62no—
516C22×C32—21no—
517C22×C32—22no—
518C22×C32—21no—
519C22×C32—21no—
520C22×C32—41no—
521C22×C32—41no—
522C22×C32C22×D411yescharacteristic
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—44no—
532C2×C3×D3—48no—
533C2×C3×D3—41no—
534C2×C3×D3—41no—
535C2×C3×D3—41no—
536C2×C3×D3—41no—
537C2×C3×D3—41no—
538C2×C3×D3#12012yes—
539C2×C3×D3AGL(1,ℤ/8)12yescomplemented
540D32—84no—
541C32×C4—22no—
542C32×C4—21no—
543C32×C4C22×D411yescharacteristic
544C32×C4C22×D411yescharacteristic
545C3⋊Dic3—41no—
546C3×Dic3—21no—
547C3×Dic3—22no—
548C3×Dic3—41no—
549C3×Dic3#12012yes—
550C2×#41—31no—
551C2×#41—31no—
552C2×#41—31no—
553C2×#41—61no—
554C2×#41—61no—
555C2×#41—64no—
556C2×#41—64no—
557C2×#41D3211yescharacteristic, complemented
558C22×Q8—31no—
559C22×D4—31no—
560C22×D4—61no—
561C22×D4—91no—
562C22×D4—181no—
563C23×C4—31no—
564C23×C4—61no—
565AGL(1,ℤ/8)—184no—
566AGL(1,ℤ/8)—184no—
567C2×SD16—31no—
568C2×SD16—91no—
569C2×SD16—91no—
570C2×SD16—91no—
571C2×D8—31no—
572C2×D8—91no—
573C2×D8—91no—
574C2×D8—91no—
575C2×M16—91no—
576C2×M16—91no—
577#121—31no—
578#121—91no—
579#121—91no—
580#121—91no—
581#121—181no—
582#121—181no—
583C2×C4⋊C4—91no—
584C2×C22⋊C4—181no—
585#103—31no—
586#103—91no—
587#103—91no—
588#103—91no—
589#102—31no—
590#102—91no—
591#102—91no—
592#102—91no—
593C22⋊C8—31no—
594C22⋊C8—91no—
595C22⋊C8—91no—
596C22⋊C8—91no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—21no—
600C23×C3—31no—
601C23×C3—31no—
602C23×C3—41no—
603C23×C3—62no—
604C23×C3—62no—
605C23×C3—64no—
606C23×C3—61no—
607C23×C3—61no—
608C23×C3—121no—
609C23×C3—122no—
610C23×C3—122no—
611C23×C3D3×D411yescharacteristic
612C23×C3C2×#6711yescharacteristic
613C22×D3—24no—
614C22×D3—21no—
615C22×D3—22no—
616C22×D3—22no—
617C22×D3—21no—
618C22×D3—41no—
619C22×D3—42no—
620C22×D3—42no—
621C22×D3—61no—
622C22×D3—61no—
623C22×D3—121no—
624C22×D3—122no—
625C22×D3—122no—
626C22×D3—122no—
627C22×D3—122no—
628C22×D3—122no—
629C22×D3—122no—
630C22×D3C2×#6711yescharacteristic
631C22×D3C2×#6711yescharacteristic
632C3×Q8—21no—
633C3×Q8—21no—
634C3×Q8—22no—
635C3×Q8—32no—
636C3×Q8—41no—
637C3×Q8—64no—
638C3×Q8—61no—
639C3×Q8D3×D412yescomplemented
640C3×Q8C2×#6712yescomplemented
641C3×D4—24no—
642C3×D4—24no—
643C3×D4—21no—
644C3×D4—21no—
645C3×D4—22no—
646C3×D4—32no—
647C3×D4—41no—
648C3×D4—44no—
649C3×D4—64no—
650C3×D4—64no—
651C3×D4—64no—
652C3×D4—64no—
653C3×D4—61no—
654C3×D4—61no—
655C3×D4—61no—
656C3×D4—122no—
657C3×D4D3×D412yescomplemented
658C3×D4C2×#6712yescomplemented
659C2×C3×C4—24no—
660C2×C3×C4—24no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—31no—
670C2×C3×C4—32no—
671C2×C3×C4—32no—
672C2×C3×C4—31no—
673C2×C3×C4—41no—
674C2×C3×C4—41no—
675C2×C3×C4—41no—
676C2×C3×C4—44no—
677C2×C3×C4—62no—
678C2×C3×C4—64no—
679C2×C3×C4—62no—
680C2×C3×C4—64no—
681C2×C3×C4—64no—
682C2×C3×C4—62no—
683C2×C3×C4—64no—
684C2×C3×C4—61no—
685C2×C3×C4—61no—
686C2×C3×C4—61no—
687C2×C3×C4—61no—
688C2×C3×C4D3×D411yescharacteristic
689C2×C3×C4C2×#6711yescharacteristic
690C2×C3×C4C23×D311yescharacteristic
691C2×C3×C4C23×D311yescharacteristic
692#67—24no—
693#67—24no—
694#67—24no—
695#67—42no—
696#67—122no—
697#67—122no—
698#67—122no—
699#67—122no—
700#67—122no—
701#67—122no—
702#67—242no—
703C2×Dic3—21no—
704C2×Dic3—22no—
705C2×Dic3—24no—
706C2×Dic3—21no—
707C2×Dic3—61no—
708C2×Dic3—61no—
709C2×Dic3—121no—
710C2×Dic3—122no—
711C2×Dic3C2×#6711yescharacteristic
712C2×Dic3C2×#6711yescharacteristic
713D12—24no—
714D12—21no—
715D12—21no—
716D12—21no—
717D12—61no—
718D12—61no—
719D12—61no—
720D12—61no—
721D12—121no—
722D12—121no—
723D12—122no—
724D12—122no—
725D12C2×#6712yescomplemented
726C4×D3—24no—
727C4×D3—24no—
728C4×D3—22no—
729C4×D3—21no—
730C4×D3—21no—
731C4×D3—22no—
732C4×D3—24no—
733C4×D3—122no—
734C4×D3C2×#6712yes—
735C4×D3C2×#6712yes—
736Dic6—24no—
737Dic6—21no—
738Dic6C2×#6712yescomplemented
739C3×C8—61no—
740C3×C8—61no—
741C3⋊C8—21no—
742C3⋊C8—21no—
743C3⋊C8—61no—
744C3⋊C8—61no—
745C3⋊C8—61no—
746C3⋊C8—61no—
747C3⋊C8—121no—
748C3⋊C8—121no—
749C2×C32—41no—
750C2×C32—42no—
751C2×C32C2×#12011yescharacteristic
752C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
753C2×C32#57511yescharacteristic
754C3⋊D3—81no—
755C3×D3—22no—
756C3×D3—22no—
757C3×D3—42no—
758C3×D3—81no—
759C24—31no—
760C24—61no—
761C24—181no—
762#41—22no—
763#41—22no—
764#41—34no—
765#41—34no—
766#41—62no—
767#41—62no—
768#41—68no—
769#41—62no—
770#41—62no—
771#41—68no—
772C2×Q8—31no—
773C2×Q8—61no—
774C2×Q8—62no—
775C2×Q8—62no—
776C2×Q8C2×D3211yescharacteristic
777C2×D4—21no—
778C2×D4—31no—
779C2×D4—31no—
780C2×D4—61no—
781C2×D4—61no—
782C2×D4—62no—
783C2×D4—68no—
784C2×D4—61no—
785C2×D4—61no—
786C2×D4—62no—
787C2×D4—61no—
788C2×D4—91no—
789C2×D4—182no—
790C2×D4—182no—
791C2×D4—181no—
792C2×D4—181no—
793C2×D4—181no—
794C2×D4—181no—
795C2×D4—364no—
796C2×D4C2×D3211yescharacteristic
797C22×C4—21no—
798C22×C4—31no—
799C22×C4—31no—
800C22×C4—31no—
801C22×C4—31no—
802C22×C4—31no—
803C22×C4—62no—
804C22×C4—62no—
805C22×C4—61no—
806C22×C4—61no—
807C22×C4—68no—
808C22×C4—61no—
809C22×C4—61no—
810C22×C4—181no—
811C22×C4C2×D3211yescharacteristic
812SD16—62no—
813SD16—182no—
814SD16—182no—
815SD16—182no—
816D8—62no—
817D8—182no—
818D8—182no—
819D8—182no—
820M16—182no—
821M16—182no—
822C2×C8—31no—
823C2×C8—31no—
824C2×C8—91no—
825C2×C8—91no—
826C4⋊C4—31no—
827C4⋊C4—91no—
828C4⋊C4—181no—
829C22⋊C4—61no—
830C22⋊C4—181no—
831C22⋊C4—181no—
832C22⋊C4—181no—
833C22×C3—21no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—21no—
838C22×C3—22no—
839C22×C3—21no—
840C22×C3—22no—
841C22×C3—21no—
842C22×C3—32no—
843C22×C3—32no—
844C22×C3—41no—
845C22×C3—42no—
846C22×C3—41no—
847C22×C3—41no—
848C22×C3—41no—
849C22×C3—41no—
850C22×C3—41no—
851C22×C3—41no—
852C22×C3—61no—
853C22×C3—61no—
854C22×C3—61no—
855C22×C3—61no—
856C22×C3—62no—
857C22×C3—81no—
858C22×C3—81no—
859C22×C3—124no—
860C22×C3—128no—
861C22×C3—121no—
862C22×C3—121no—
863C22×C3—121no—
864C22×C3—121no—
865C22×C3—121no—
866C22×C3C2×D3×D411yescharacteristic
867C22×C3C22×#6711yescharacteristic
868C2×D3—21no—
869C2×D3—21no—
870C2×D3—21no—
871C2×D3—21no—
872C2×D3—22no—
873C2×D3—44no—
874C2×D3—48no—
875C2×D3—41no—
876C2×D3—41no—
877C2×D3—41no—
878C2×D3—41no—
879C2×D3—41no—
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#94912yescomplemented
892C2×D3#95312yes—
893C3×C4—22no—
894C3×C4—21no—
895C3×C4—21no—
896C3×C4—22no—
897C3×C4—21no—
898C3×C4—21no—
899C3×C4—32no—
900C3×C4—41no—
901C3×C4—42no—
902C3×C4—61no—
903C3×C4—62no—
904C3×C4—121no—
905C3×C4C2×D3×D411yescharacteristic
906C3×C4C2×D3×D411yescharacteristic
907C3×C4C22×#6711yescharacteristic
908C3×C4C22×#6711yescharacteristic
909Dic3—21no—
910Dic3—22no—
911Dic3—41no—
912Dic3—121no—
913Dic3—121no—
914Dic3—241no—
915Dic3#95312yes—
916C32#300611yescharacteristic, complemented, Sylow
917C23—21no—
918C23—31no—
919C23—31no—
920C23—62no—
921C23—62no—
922C23—64no—
923C23—61no—
924C23—61no—
925C23—121no—
926C23—122no—
927C23—122no—
928C23—181no—
929C23—362no—
930C23—362no—
931C23—362no—
932C23D3×#6711yescharacteristic
933Q8—21no—
934Q8—32no—
935Q8—64no—
936Q8—61no—
937Q8D3×#6712yescomplemented
938D4—24no—
939D4—21no—
940D4—32no—
941D4—64no—
942D4—64no—
943D4—64no—
944D4—64no—
945D4—61no—
946D4—61no—
947D4—61no—
948D4—122no—
949D4—181no—
950D4—181no—
951D4—362no—
952D4—362no—
953D4—362no—
954D4—362no—
955D4D3×#6712yescomplemented
956C2×C4—24no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—31no—
961C2×C4—32no—
962C2×C4—32no—
963C2×C4—31no—
964C2×C4—62no—
965C2×C4—64no—
966C2×C4—62no—
967C2×C4—64no—
968C2×C4—64no—
969C2×C4—62no—
970C2×C4—64no—
971C2×C4—61no—
972C2×C4—61no—
973C2×C4—61no—
974C2×C4—61no—
975C2×C4—181no—
976C2×C4—362no—
977C2×C4D3×#6711yescharacteristic
978C2×C4C22×D3211yescharacteristic
979C8—61no—
980C8—61no—
981C8—181no—
982C8—181no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—41no—
987C2×C3—42no—
988C2×C3—41no—
989C2×C3—42no—
990C2×C3—62no—
991C2×C3—62no—
992C2×C3—81no—
993C2×C3—82no—
994C2×C3—122no—
995C2×C3—241no—
996C2×C3D3×#12011yescharacteristic
997C2×C3#576811yescharacteristic
998C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
999C2×C3C2×#94911yescharacteristic
1000C2×C3#582211yescharacteristic
1001C2×C3C2×#95311yescharacteristic
1002D3—22no—
1003D3—22no—
1004D3—42no—
1005D3—81no—
1006D3—241no—
1007D3—241no—
1008D3—481no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—22no—
1013C22—32no—
1014C22—32no—
1015C22—41no—
1016C22—41no—
1017C22—61no—
1018C22—61no—
1019C22—61no—
1020C22—61no—
1021C22—62no—
1022C22—124no—
1023C22—128no—
1024C22—121no—
1025C22—121no—
1026C22—121no—
1027C22—121no—
1028C22—121no—
1029C22—361no—
1030C22—361no—
1031C22—361no—
1032C22—724no—
1033C22C2×D3×#6711yescharacteristic
1034C4—21no—
1035C4—22no—
1036C4—32no—
1037C4—61no—
1038C4—62no—
1039C4—121no—
1040C4—361no—
1041C4C2×D3×#6711yescharacteristic
1042C4C2×D3×#6711yescharacteristic
1043C3—21no—
1044C3#8008411yescharacteristic, complemented
1045C3#8408211yescharacteristic, complemented
1046C2—41no—
1047C2—42no—
1048C2—62no—
1049C2—62no—
1050C2—122no—
1051C2—241no—
1052C2—721no—
1053C2D3×#94911yescharacteristic
1054C2#1059545311yescharacteristic
1055C2D3×#95311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3006
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×#41C2semidirect
2. C2×#63939C2semidirect
3. C2×#63925C2semidirect
4. D3×#930C2semidirect
5. #10592937C2semidirect
6. C3×#5238C2semidirect
7. #10591584C2semidirect
8. #10591583C2semidirect
9. #10591550C2semidirect
10. #10591448C2semidirect
11. #10591447C2semidirect
12. #10591414C2semidirect
13. #10591163C2semidirect
14. #10591161C2semidirect
15. #10591154C2semidirect
18. C2×C32×#41C22semidirect
22. C2×C3×D3×Q8C22semidirect
26. C2×C3×D3×D4C22semidirect
28. C2×C3×#235C22semidirect
32. C2×D3×D12C22semidirect
33. C2×#3755C22semidirect
34. C2×#3753C22semidirect
35. #64139C22semidirect
36. C2×C3×#215C22semidirect
37. C2×C3×#213C22semidirect
38. C3×#930C22semidirect
46. D3×C4⋊Dic3C22semidirect
47. C2×#3717C22semidirect
48. C2×#3715C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×#3711C22semidirect
52. C2×#3711C22semidirect
53. #63662C22semidirect
54. #63659C22semidirect
55. #63657C22semidirect
56. C3×#835C22semidirect
57. C3×#832C22semidirect
58. C3×#830C22semidirect
59. #63566C22semidirect
60. #63565C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
63. (C2×D3)⋊(C3⋊C8)C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
66. C2×D3×#41D3semidirect
79. #5238D3semidirect
115. C3×#239D4semidirect
120. C3×#237D4semidirect
179. C2×C3×#41C2×D3semidirect
180. C2×C3×#41C2×D3semidirect
190. C2×D3×Q8C2×D3semidirect
196. C2×D3×D4C2×D3semidirect
198. C2×#235C2×D3semidirect
212. C2×#215C2×D3semidirect
222. C2×#213C2×D3semidirect
230. #930C2×D3semidirect
253. #835C2×D3semidirect
259. #832C2×D3semidirect
265. #830C2×D3semidirect
289. C32×Q8C2×D4semidirect
292. C32×D4C2×D4semidirect
317. C3×D12C2×D4semidirect
329. C3×Dic6C2×D4semidirect
430. #239#67semidirect
435. #237#67semidirect
539. C2×C3×D3AGL(1,ℤ/8)semidirect
557. C2×#41D32semidirect
639. C3×Q8D3×D4semidirect
640. C3×Q8C2×#67semidirect
657. C3×D4D3×D4semidirect
658. C3×D4C2×#67semidirect
725. D12C2×#67semidirect
738. Dic6C2×#67semidirect
891. C2×D3#949semidirect
916. C32#3006semidirect
937. Q8D3×#67semidirect
955. D4D3×#67semidirect
1044. C3#80084semidirect
1045. C3#84082semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C2×#639392
C2×#639252
D3×#9302
#105929372
C3×#52382
#105915842
#105915832
#105915502
#105914482
#105914472
#105914142
#105911632
#105911612
#105911542
#840823
#800843