Finite Group Databasebeta

← #11884030

Subgroups — #11884030

Order 1152.

1156 conjugacy classes of subgroups.

The subgroup lattice has 933 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595288C211yesmaximal, characteristic, complemented
2C2×#63932C211yesmaximal, characteristic, complemented
3C2×D3×#204C211yesmaximal, characteristic, complemented
4#10594525C211yesmaximal, characteristic, complemented
5#10592461C211yesmaximal, characteristic, complemented
6C3×#4776C211yesmaximal, characteristic, complemented
7C3×#4775C211yesmaximal, characteristic, complemented
8#10591517C211yesmaximal, characteristic, complemented
9#10591475C211yesmaximal, characteristic, complemented
10#10590968C211yesmaximal, characteristic, complemented
11#10590750C211yesmaximal, characteristic, complemented
12#10590723C211yesmaximal, characteristic, complemented
13#10590595C211yesmaximal, characteristic, complemented
14#10590585C211yesmaximal, characteristic, complemented
15#10590461C211yesmaximal, characteristic, complemented
16#80727—31nomaximal
17#80156—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×D12C2211yescharacteristic
21C2×#3795C2211yescharacteristic, complemented
22C2×D3×Dic6C2211yescharacteristic, complemented
23#64149C2211yescharacteristic
24C2×#3754C2211yescharacteristic, complemented
25C2×#3744C2211yescharacteristic, complemented
26#64096C2211yescharacteristic, complemented
27C3×#938C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic, complemented
30C2×C3×#204C2211yescharacteristic
31C2×C3×D3×C8C2211yescharacteristic, complemented
32C3×#897C2211yescharacteristic, complemented
33C3×#895C2211yescharacteristic, complemented
34#63983—21no—
35#63977—21no—
36#63971—21no—
37#63932—24no—
38#63915—21no—
39#63909C2211yescharacteristic
40C4×#625C2211yescharacteristic
41#63899—21no—
42#63898—21no—
43#63898C2211yescharacteristic
44#63885—21no—
45#63863C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic
48C2×#3714C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic
50C2×#3711C2211yescharacteristic, complemented
51D3×#204—24no—
52C32×#102C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54#63636C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#807C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63555C2211yescharacteristic, complemented
63D4×#67—31no—
64C2×#932—31no—
65C2×D3×SD16—31no—
66C2×#911—31no—
67C22×#204—31no—
68#5633—31no—
69#5609—31no—
70#5598—31no—
71C3×#466—31no—
72C3×#450—31no—
73#5176—31no—
74#5170—31no—
75#5165—31no—
76#5154—31no—
77#5111—31no—
78#5049—31no—
79#5040—31no—
80#5036—31no—
81#4889—31no—
82#4886—31no—
83#4787—31no—
84#4781—31no—
85#4776D311yescharacteristic, complemented
86#4775D311yescharacteristic, complemented
87#4773—31no—
88#4762—31no—
89#4762—31no—
90#4762—61no—
91#4757—31no—
92#4734—31no—
93#4728—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98C2×#638—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×#634C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C3×D3×D4—22no—
104C3×D3×D4—41no—
105C2×C3×D12—21no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111D3×#67—44no—
112C2×#627—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#625—21no—
116C2×#625D411yescharacteristic
117C2×D3×Dic3—21no—
118C2×D3×Dic3—21no—
119C2×D3×Dic3—21no—
120D3×D12—22no—
121D3×D12—41no—
122#3795—22no—
123#3795—41no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4C2311yescharacteristic
128#3754—22no—
129#3750—21no—
130C4×C3⋊Dic3—21no—
131C4×C3⋊Dic3C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133#3744—22no—
134C3×#217—21no—
135C3×#214—41no—
136C3×#213—22no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×C4⋊Dic3—21no—
140C3×C4⋊Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×#204—22no—
144C3×D3×C8—22no—
145#3724D411yescharacteristic
146#3722—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3D411yescharacteristic
151(C2×D3)⋊Dic3D411yescharacteristic
152#3717—22no—
153#3716D414yescomplemented
154#3714—41no—
155#3713—22no—
156#3711—22no—
157#3265—91noSylow
158C22×C3×D4—31no—
159C22×#67—61no—
160C2×D3×Q8—31no—
161C2×#237—31no—
162C2×D3×D4—31no—
163C2×D3×D4—61no—
164C2×D3×D4C2×D311yescharacteristic
165C2×#235—31no—
166C22×D12—31no—
167C22×Dic6—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×D8—31no—
171C22×C3×C8—31no—
172C3×C22⋊Q8—31no—
173C3×#121—31no—
174C3×#121—31no—
175#953—61no—
176#947—31no—
177C2×#215—31no—
178#940—31no—
179#940—31no—
180#940—61no—
181#939—61no—
182#939—61no—
183#938C2×D311yescharacteristic
184#937—61no—
185#937—61no—
186#936—31no—
187D4×Dic3—31no—
188D4×Dic3—61no—
189C2×#214—31no—
190C2×#214—31no—
191C2×#214—31no—
192C2×#214—61no—
193C2×#214C2×D311yescharacteristic, complemented
194#932—64no—
195C2×#213—31no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213C2×D311yescharacteristic, complemented
199#930—31no—
200C4×#67—31no—
201C4×#67—31no—
202C2×#208—31no—
203D3×SD16—64no—
204#911—64no—
205C2×D24—31no—
206C2×#204—31no—
207C2×#204—31no—
208C2×#204—31no—
209C2×#204—31no—
210C2×#204—61no—
211C2×#204—64no—
212C2×#204C2×D311yescharacteristic
213C2×ΓL(1,𝔽25)—31no—
214C2×D3×C8C2×D311yescharacteristic, complemented
215#897C2×D311yescharacteristic, complemented
216#896—61no—
217#895—31no—
218#895C2×D311yescharacteristic, complemented
219#893—31no—
220#893—61no—
221#887—31no—
222#887—31no—
223#887—61no—
224#885—61no—
225#885—61no—
226#884—61no—
227#884—61no—
228#882—61no—
229#878—61no—
230C3×#107—31no—
231C3×#102—21no—
232C3×#102—31no—
233C3×#102—31no—
234C3×#102C2×D311yescharacteristic, complemented
235C3×#102C2×D311yescharacteristic, complemented
236C3×C22⋊C8—31no—
237#835—31no—
238#830—31no—
239#821C2×D311yescharacteristic, complemented
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8C2×D311yescharacteristic, complemented
242#816—31no—
243#815—31no—
244#815—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—31no—
247Dic3⋊C8—61no—
248#810—31no—
249#810—31no—
250#809—31no—
251#809—31no—
252#809—61no—
253#809C2×D311yescharacteristic
254#807C2×D311yescharacteristic, complemented
255C23×C32—21no—
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—81no—
262C22×C3×D3C2×D411yescharacteristic
263C22×C3×D3C2×D411yescharacteristic
264C2×D32—42no—
265C2×D32—42no—
266C2×D32—81no—
267C32×D4—21no—
268C32×D4—21no—
269C2×C32×C4—21no—
270C2×C32×C4C2411yescharacteristic
271#638—42no—
272#638—81no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3C2×D411yescharacteristic
275C2×C3⋊Dic3C2×D411yescharacteristic
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)—21no—
278#634—21no—
279#634C2×D412yescomplemented
280C3×#67—42no—
281C3×#67—42no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—42no—
290C3×D12C2×D412yes—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—21no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297#627—42no—
298#626—42no—
299#626—42no—
300#625—22no—
301#625—42no—
302D3×Dic3—42no—
303D3×Dic3—42no—
304D3×Dic3—42no—
305C32×C8—21no—
306C3⋊(C3⋊C8)—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8C2×D412yescomplemented
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—91no—
311#548—91no—
312D42—91no—
313#496—91no—
314#468—91no—
315#466—31no—
316#463—91no—
317#460—91no—
318#450—31no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—91no—
324C24×C3—61no—
325C23×D3—21no—
326C23×D3—61no—
327C23×D3—61no—
328C2×C3×Q8—31no—
329C2×C3×D4—21no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C2×C3×D4—62no—
335C2×C3×D4—61no—
336C2×C3×D4—121no—
337C2×C3×D4C22×D311yescharacteristic
338C2×C3×D4C22×D311yescharacteristic
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C2×#67—21no—
342C2×#67—21no—
343C2×#67—31no—
344C2×#67—31no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—121no—
354C2×#67—121no—
355C2×#67—124no—
356C22×Dic3—61no—
357C22×Dic3—61no—
358C22×Dic3—61no—
359D3×Q8—62no—
360D3×Q8—121no—
361#237—62no—
362#237—121no—
363D3×D4—22no—
364D3×D4—41no—
365D3×D4—62no—
366D3×D4—121no—
367D3×D4—124no—
368#235—62no—
369#235—121no—
370C2×D12—21no—
371C2×D12—31no—
372C2×D12—31no—
373C2×D12—61no—
374C2×D12—62no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—121no—
378C2×D12C22×D311yescharacteristic
379C2×D12C22×D311yescharacteristic
380C2×C4×D3—61no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3C22×D311yescharacteristic
384C2×C4×D3C22×D311yescharacteristic
385C2×Dic6—31no—
386C2×Dic6—31no—
387C2×Dic6—61no—
388C2×Dic6—62no—
389C2×Dic6—61no—
390C2×Dic6—61no—
391C2×Dic6—121no—
392C2×Dic6C22×D311yescharacteristic
393C3×SD16—62no—
394C3×SD16—121no—
395C3×D8—62no—
396C2×C3×C8—21no—
397C2×C3×C8—31no—
398C2×C3×C8—31no—
399C2×C3×C8—62no—
400C2×C3×C8C22×D311yescharacteristic
401C2×C3×C8C22×D311yescharacteristic
402C3×C4⋊C4—21no—
403C3×C4⋊C4—31no—
404C3×C4⋊C4—61no—
405C3×C4⋊C4C22×D311yescharacteristic
406C3×C4⋊C4C22×D311yescharacteristic
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C22⋊C4—61no—
410#217—21no—
411#217—31no—
412#217—31no—
413#217—61no—
414#217—61no—
415#217—61no—
416#215—62no—
417#214—34no—
418#214—41no—
419#214—62no—
420#214—62no—
421#214—122no—
422#213—22no—
423#213—62no—
424#213—62no—
425#213—121no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—21no—
428(C2×D3)⋊C4—31no—
429(C2×D3)⋊C4—31no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435C4⋊Dic3—21no—
436C4⋊Dic3C22×D311yescharacteristic
437Dic3⋊C4—31no—
438Dic3⋊C4—31no—
439Dic3⋊C4—61no—
440Dic3⋊C4—61no—
441Dic3⋊C4—121no—
442C4×Dic3—31no—
443C4×Dic3—31no—
444C4×Dic3—61no—
445C4×Dic3—61no—
446C4×Dic3—61no—
447C4×Dic3—121no—
448#208—62no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—61no—
452C2×C3⋊C8C22×D311yescharacteristic
453C2×C3⋊C8C22×D311yescharacteristic
454D24—121no—
455#204—22no—
456#204—34no—
457#204—62no—
458#204—62no—
459#204—62no—
460#204—122no—
461ΓL(1,𝔽25)—62no—
462D3×C8—22no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32C22×D411yescharacteristic
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—22no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—84no—
482C2×C3×D3AGL(1,ℤ/8)12yescomplemented
483D32—84no—
484C32×C4—41no—
485C32×C4C22×D411yescharacteristic
486C32×C4H(5,𝔽2)11yescharacteristic
487C3⋊Dic3—21no—
488C3⋊Dic3—22no—
489C3⋊Dic3—21no—
490C3×Dic3—21no—
491C3×Dic3—21no—
492C3×Dic3—41no—
493C3×Dic3—41no—
494C2×#41—91no—
495C22×Q8—91no—
496C22×D4—31no—
497C22×D4—91no—
498C22×D4—181no—
499AGL(1,ℤ/8)—184no—
500C2×SD16—31no—
501C2×SD16—31no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—184no—
507C2×D8—31no—
508C2×D8—91no—
509C2×D8—91no—
510C2×M16—91no—
511C22×C8—31no—
512#127—91no—
513#124—91no—
514#124—181no—
515C22⋊Q8—31no—
516C22⋊Q8—181no—
517#121—31no—
518#121—31no—
519#121—91no—
520#121—181no—
521#121—181no—
522#120—181no—
523#120—181no—
524C4×Q8—91no—
525C4×D4—91no—
526C4×D4—91no—
527C4×D4—181no—
528#107—31no—
529C4⋊C8—91no—
530#103—91no—
531#103—91no—
532#102—31no—
533#102—31no—
534#102—91no—
535#102D3211yescharacteristic, complemented
536C22⋊C8—31no—
537C22⋊C8—91no—
538#97—91no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—31no—
542C23×C3—31no—
543C23×C3—41no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—122no—
547C23×C3—122no—
548C23×C3—241no—
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—42no—
552C22×D3—42no—
553C22×D3—61no—
554C22×D3—61no—
555C22×D3—81no—
556C22×D3—121no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—241no—
562C22×D3—241no—
563C22×D3D3×D411yescharacteristic
564C22×D3D3×D411yescharacteristic
565C3×Q8—61no—
566C3×Q8—61no—
567C3×D4—21no—
568C3×D4—21no—
569C3×D4—21no—
570C3×D4—21no—
571C3×D4—32no—
572C3×D4—41no—
573C3×D4—41no—
574C3×D4—61no—
575C3×D4—61no—
576C3×D4—61no—
577C3×D4—122no—
578C3×D4—122no—
579C3×D4—122no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—31no—
584C2×C3×C4—31no—
585C2×C3×C4—41no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4C23×D311yescharacteristic
593C2×C3×C4C23×D311yescharacteristic
594#67—42no—
595#67—42no—
596#67—62no—
597#67—62no—
598#67—122no—
599#67—122no—
600#67—122no—
601#67—122no—
602#67—122no—
603#67—122no—
604#67—242no—
605#67—241no—
606#67—241no—
607#67—242no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—31no—
611C2×Dic3—31no—
612C2×Dic3—31no—
613C2×Dic3—31no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—61no—
618C2×Dic3—121no—
619C2×Dic3—122no—
620C2×Dic3—122no—
621C2×Dic3—122no—
622C2×Dic3D3×D411yescharacteristic
623C2×Dic3D3×D411yescharacteristic
624D12—21no—
625D12—21no—
626D12—21no—
627D12—42no—
628D12—61no—
629D12—61no—
630D12—61no—
631D12—61no—
632D12—121no—
633D12—121no—
634D12—122no—
635D12—122no—
636D12D3×D412yes—
637C4×D3—21no—
638C4×D3—21no—
639C4×D3—21no—
640C4×D3—21no—
641C4×D3—122no—
642C4×D3—122no—
643C4×D3—122no—
644Dic6—21no—
645Dic6—21no—
646Dic6—32no—
647Dic6—32no—
648Dic6—62no—
649Dic6—61no—
650Dic6—61no—
651Dic6—121no—
652Dic6—122no—
653Dic6—122no—
654C3×C8—21no—
655C3×C8—21no—
656C3×C8—32no—
657C3×C8—41no—
658C3×C8—61no—
659C3⋊C8—21no—
660C3⋊C8—61no—
661C3⋊C8—61no—
662C3⋊C8—121no—
663C3⋊C8D3×D412yescomplemented
664C2×C32—81no—
665C2×C32D4211yescharacteristic
666C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
667C2×C32#57711yescharacteristic
668C3⋊D3—81no—
669C3×D3—22no—
670C3×D3—42no—
671C3×D3—41no—
672C3×D3—81no—
673C24—61no—
674C24—181no—
675#41—182no—
676#41—361no—
677C2×Q8—31no—
678C2×Q8—91no—
679C2×Q8—181no—
680C2×Q8—182no—
681C2×Q8—361no—
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—62no—
687C2×D4—61no—
688C2×D4—91no—
689C2×D4—91no—
690C2×D4—121no—
691C2×D4—181no—
692C2×D4—182no—
693C2×D4—181no—
694C2×D4—181no—
695C2×D4—181no—
696C2×D4—181no—
697C2×D4—361no—
698C2×D4—364no—
699C2×D4C2×D3211yescharacteristic
700C22×C4—31no—
701C22×C4—31no—
702C22×C4—181no—
703C22×C4—181no—
704C22×C4—181no—
705SD16—62no—
706SD16—94no—
707SD16—121no—
708SD16—182no—
709SD16—182no—
710SD16—182no—
711D8—62no—
712D8—182no—
713D8—361no—
714M16—182no—
715C2×C8—31no—
716C2×C8—31no—
717C2×C8—62no—
718C2×C8—91no—
719C2×C8C2×D3211yescharacteristic
720C4⋊C4—31no—
721C4⋊C4—61no—
722C4⋊C4—91no—
723C4⋊C4—181no—
724C4⋊C4C2×D3211yescharacteristic
725C22⋊C4—61no—
726C22⋊C4—61no—
727C22⋊C4—61no—
728C22⋊C4—91no—
729C22⋊C4—91no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C22⋊C4—181no—
734C42—91no—
735C42—181no—
736C22×C3—21no—
737C22×C3—32no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—61no—
745C22×C3—61no—
746C22×C3—61no—
747C22×C3—61no—
748C22×C3—61no—
749C22×C3—62no—
750C22×C3—81no—
751C22×C3—81no—
752C22×C3—81no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3—244no—
759C22×C3C2×D3×D411yescharacteristic
760C22×C3C2×D3×D411yescharacteristic
761C2×D3—21no—
762C2×D3—21no—
763C2×D3—21no—
764C2×D3—21no—
765C2×D3—21no—
766C2×D3—22no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—41no—
772C2×D3—84no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—241no—
780C2×D3—241no—
781C2×D3—241no—
782C2×D3—244no—
783C2×D3—244no—
784C2×D3#91112yescomplemented
785C3×C4—21no—
786C3×C4—21no—
787C3×C4—41no—
788C3×C4—41no—
789C3×C4—61no—
790C3×C4—61no—
791C3×C4—81no—
792C3×C4—121no—
793C3×C4—121no—
794C3×C4C2×D3×D411yescharacteristic
795C3×C4C2×D3×D411yescharacteristic
796C3×C4#100411yescharacteristic
797C3×C4#100911yescharacteristic
798Dic3—21no—
799Dic3—21no—
800Dic3—41no—
801Dic3—41no—
802Dic3—62no—
803Dic3—61no—
804Dic3—61no—
805Dic3—61no—
806Dic3—61no—
807Dic3—62no—
808Dic3—62no—
809Dic3—122no—
810Dic3—121no—
811C32#326511yescharacteristic, complemented, Sylow
812C23—21no—
813C23—31no—
814C23—31no—
815C23—61no—
816C23—61no—
817C23—122no—
818C23—122no—
819C23—181no—
820C23—241no—
821C23—362no—
822C23—362no—
823C23—721no—
824Q8—61no—
825Q8—61no—
826Q8—92no—
827Q8—181no—
828Q8—362no—
829D4—21no—
830D4—21no—
831D4—32no—
832D4—61no—
833D4—61no—
834D4—61no—
835D4—122no—
836D4—122no—
837D4—122no—
838D4—182no—
839D4—181no—
840D4—181no—
841D4—362no—
842D4—362no—
843D4—362no—
844D4—362no—
845D4—721no—
846C2×C4—21no—
847C2×C4—31no—
848C2×C4—31no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—91no—
856C2×C4—91no—
857C2×C4—181no—
858C2×C4—362no—
859C2×C4—362no—
860C2×C4—362no—
861C2×C4C22×D3211yescharacteristic
862C8—21no—
863C8—32no—
864C8—61no—
865C8—181no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—62no—
870C2×C3—81no—
871C2×C3—81no—
872C2×C3—122no—
873C2×C3—121no—
874C2×C3—161no—
875C2×C3—241no—
876C2×C3#559011yescharacteristic
877C2×C3#560911yescharacteristic
878C2×C3C2×#91111yescharacteristic
879C2×C3#576211yescharacteristic
880C2×C3#577011yescharacteristic
881C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
882D3—22no—
883D3—41no—
884D3—42no—
885D3—81no—
886D3—241no—
887D3—241no—
888D3—481no—
889C22—32no—
890C22—41no—
891C22—41no—
892C22—41no—
893C22—61no—
894C22—61no—
895C22—61no—
896C22—61no—
897C22—61no—
898C22—62no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—244no—
905C22—361no—
906C22—361no—
907C22—361no—
908C22—724no—
909C22D32×D411yescharacteristic
910C4—41no—
911C4—61no—
912C4—61no—
913C4—121no—
914C4—121no—
915C4—181no—
916C4—181no—
917C4—182no—
918C4#6430711yescharacteristic
919C4D32×D411yescharacteristic
920C3—21no—
921C3#8015611yescharacteristic, complemented
922C3#8072711yescharacteristic, complemented
923C2—62no—
924C2—81no—
925C2—121no—
926C2—122no—
927C2—241no—
928C2—721no—
929C2#1059427511yescharacteristic
930C2D3×#91111yescharacteristic
931C2#1059475311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3265
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. #10595288C2semidirect
2. C2×#63932C2semidirect
3. C2×D3×#204C2semidirect
4. #10594525C2semidirect
5. #10592461C2semidirect
6. C3×#4776C2semidirect
7. C3×#4775C2semidirect
8. #10591517C2semidirect
9. #10591475C2semidirect
10. #10590968C2semidirect
11. #10590750C2semidirect
12. #10590723C2semidirect
13. #10590595C2semidirect
14. #10590585C2semidirect
15. #10590461C2semidirect
21. C2×#3795C22semidirect
22. C2×D3×Dic6C22semidirect
24. C2×#3754C22semidirect
25. C2×#3744C22semidirect
26. #64096C22semidirect
28. C2×C3×#214C22semidirect
29. C2×C3×#213C22semidirect
31. C2×C3×D3×C8C22semidirect
32. C3×#897C22semidirect
33. C3×#895C22semidirect
45. #63863C22semidirect
46. C2×#3717C22semidirect
48. C2×#3714C22semidirect
50. C2×#3711C22semidirect
52. C32×#102C22semidirect
53. #63641C22semidirect
54. #63636C22semidirect
55. C3×#821C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
58. C3×#807C22semidirect
59. #63567C22semidirect
60. #63565C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63555C22semidirect
85. #4776D3semidirect
86. #4775D3semidirect
153. #3716D4semidirect
193. C2×#214C2×D3semidirect
198. C2×#213C2×D3semidirect
214. C2×D3×C8C2×D3semidirect
215. #897C2×D3semidirect
218. #895C2×D3semidirect
234. C3×#102C2×D3semidirect
235. C3×#102C2×D3semidirect
239. #821C2×D3semidirect
241. (C2×D3)⋊C8C2×D3semidirect
254. #807C2×D3semidirect
279. #634C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
482. C2×C3×D3AGL(1,ℤ/8)semidirect
535. #102D32semidirect
663. C3⋊C8D3×D4semidirect
784. C2×D3#911semidirect
811. C32#3265semidirect
921. C3#80156semidirect
922. C3#80727semidirect

Maximal subgroups

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

subgroupindex
#105952882
C2×#639322
C2×D3×#2042
#105945252
#105924612
C3×#47762
C3×#47752
#105915172
#105914752
#105909682
#105907502
#105907232
#105905952
#105905852
#105904612
#807273
#801563