Finite Group Databasebeta

← #11884031

Subgroups — #11884031

Order 1152.

1159 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595237C211yesmaximal, characteristic, complemented
2C2×#63925C211yesmaximal, characteristic, complemented
3C2×#63796C211yesmaximal, characteristic, complemented
4#10594621C211yesmaximal, characteristic, complemented
5#10592474C211yesmaximal, characteristic, complemented
6C3×#4787C211yesmaximal, characteristic, complemented
7C3×#4781C211yesmaximal, characteristic, complemented
8#10591516C211yesmaximal, characteristic, complemented
9#10591483C211yesmaximal, characteristic, complemented
10#10590942C211yesmaximal, characteristic, complemented
11#10590799C211yesmaximal, characteristic, complemented
12#10590737C211yesmaximal, characteristic, complemented
13#10590606C211yesmaximal, characteristic, complemented
14#10590515C211yesmaximal, characteristic, complemented
15#10590478C211yesmaximal, characteristic, complemented
16#80553—31nomaximal
17#80121—31nomaximal
18C2×C3×#237C2211yescharacteristic, complemented
19C2×#3802C2211yescharacteristic
20C2×D3×D12—21no—
21C2×D3×D12C2211yescharacteristic
22C2×#3797C2211yescharacteristic, complemented
23#64147C2211yescharacteristic, complemented
24C2×#3753C2211yescharacteristic, complemented
25C2×C8×C3⋊D3C2211yescharacteristic, complemented
26#64104C2211yescharacteristic
27C3×#936C2211yescharacteristic, complemented
28C2×C3×#213C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic, complemented
30C2×C3×#204C2211yescharacteristic
31C2×C3×#204C2211yescharacteristic, complemented
32C3×#895C2211yescharacteristic
33C3×#893C2211yescharacteristic
34#63964—21no—
35#63959—21no—
36#63958—21no—
37#63952—21no—
38#63925—24no—
39#63923—21no—
40#63922—21no—
41#63911C2211yescharacteristic
42#63906—21no—
43C4×#626C2211yescharacteristic
44#63856C2211yescharacteristic, complemented
45Dic3×Dic6C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic, complemented
48C2×#3715C2211yescharacteristic
49C2×#3715C2211yescharacteristic, complemented
50C2×#3711C2211yescharacteristic, complemented
51#63796—24no—
52C32×#102C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54#63634C2211yescharacteristic, complemented
55C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#810C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic, complemented
61#63557C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63#5831—31no—
64C2×#949—31no—
65C2×D3×SD16—31no—
66C2×D3×SD16—31no—
67C2×#911—31no—
68#5677—31no—
69#5609—31no—
70D4×D12—31no—
71C3×#463—31no—
72C3×#449—31no—
73#5169—31no—
74#5163—31no—
75#5156—31no—
76#5156—31no—
77#5154—31no—
78#5058—31no—
79#5042—31no—
80#5018—31no—
81#4848—31no—
82#4836—31no—
83#4817—31no—
84#4812—31no—
85#4806—31no—
86#4806—31no—
87#4787D311yescharacteristic, complemented
88#4781D311yescharacteristic, complemented
89#4775—31no—
90#4775—31no—
91#4775—61no—
92#4731—31no—
93#4728—31no—
94C22×D32—21no—
95C22×D32—21no—
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98C2×C4⋊(C3⋊D3)—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3C2311yescharacteristic
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C3×#237—22no—
104C3×#237—41no—
105C2×C3×D12—21no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×#627—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#626D411yescharacteristic
117C2×#625—21no—
118C2×#624—21no—
119#3802—22no—
120#3802—41no—
121D3×D12—22no—
122D3×D12—44no—
123D3×D12—41no—
124#3797—22no—
125#3797—41no—
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4C2311yescharacteristic
128#3757—21no—
129#3753—22no—
130#3752—21no—
131C4⋊(C3⋊Dic3)C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C8×C3⋊D3—22no—
134C3×#217—21no—
135C3×#217—21no—
136C3×#213—22no—
137C3×#213—41no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×C4×Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C3×#204—22no—
144C3×#204—22no—
145#3724—21no—
146Dic3⋊Dic3—21no—
147Dic3⋊Dic3D411yescharacteristic
148#3722D411yescharacteristic
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3D411yescharacteristic
151Dic32—21no—
152#3717—22no—
153#3717—41no—
154#3715—22no—
155#3715D414yescomplemented
156#3711—22no—
157#3265—91noSylow
158C2×C3×#41—31no—
159C2×D3×Q8—31no—
160C2×D3×Q8—31no—
161C2×#237C2×D311yescharacteristic, complemented
162C2×D3×D4—31no—
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C2×D3×D4—61no—
166C22×D12—31no—
167C22×D12—61no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C2×C3×D8—31no—
171C2×C3×D8—31no—
172C3×#124—31no—
173C3×#121—31no—
174C3×C4×D4—31no—
175#949—64no—
176#946—31no—
177Q8×Dic3—31no—
178C2×#215—31no—
179C2×#215—31no—
180C2×#215—31no—
181C2×#215—31no—
182#940—31no—
183#938—31no—
184#938—31no—
185#938—61no—
186#938—61no—
187#937—61no—
188#936—61no—
189#936C2×D311yescharacteristic, complemented
190C2×#214—31no—
191C2×#214—31no—
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—61no—
195C2×#213C2×D311yescharacteristic
196C2×#213C2×D311yescharacteristic, complemented
197#930—61no—
198C4×#67—31no—
199C4×#67—61no—
200#924—31no—
201#924—61no—
202C2×#208—31no—
203D3×SD16—64no—
204D3×SD16—64no—
205#911—64no—
206C2×#204—31no—
207C2×#204—31no—
208C2×#204C2×D311yescharacteristic
209C2×#204C2×D311yescharacteristic, complemented
210C2×ΓL(1,𝔽25)—31no—
211C2×D3×C8—31no—
212C2×D3×C8—31no—
213C2×D3×C8—61no—
214#895—31no—
215#895—31no—
216#895—61no—
217#895C2×D311yescharacteristic
218#893C2×D311yescharacteristic
219#885—61no—
220#884—61no—
221#884—61no—
222#882—61no—
223#882—61no—
224#882—61no—
225#67⋊C4—61no—
226#878—61no—
227#874—31no—
228C4×D12—31no—
229C4×Dic6—31no—
230C3×C4⋊C8—31no—
231C3×#103—31no—
232C3×#103—31no—
233C3×#102—21no—
234C3×#102C2×D311yescharacteristic, complemented
235C3×#102C2×D311yescharacteristic, complemented
236C3×C22⋊C8—31no—
237#832—31no—
238#832—31no—
239#821—31no—
240#821—31no—
241#821—31no—
242#821—31no—
243#821—61no—
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8—31no—
246(C2×D3)⋊C8C2×D311yescharacteristic, complemented
247#815—31no—
248Dic3⋊C8C2×D311yescharacteristic, complemented
249#810C2×D311yescharacteristic, complemented
250#810C2×D311yescharacteristic, complemented
251#807—31no—
252#807—31no—
253#807—61no—
254#803—31no—
255C23×C32—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3C2×D411yescharacteristic
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3C2×D411yescharacteristic
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—42no—
264C2×D32—42no—
265C2×D32—81no—
266C2×D32—81no—
267C32×D4—21no—
268C32×D4—21no—
269C2×C32×C4—21no—
270C2×C32×C4C2411yescharacteristic
271#638—42no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3C2×D411yescharacteristic
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—42no—
277C4×C3⋊D3—21no—
278C4×C3⋊D3—21no—
279C3×#67—42no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—42no—
283C2×C3×Dic3C2×D411yescharacteristic
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—42no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297C3×Dic6C2×D412yescomplemented
298#627—42no—
299#626—22no—
300#626—42no—
301#626—42no—
302#626—81no—
303#625—42no—
304#624—42no—
305C32×C8—21no—
306C3⋊(C3⋊C8)C2×D412yescomplemented
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—91no—
311#548—91no—
312D42—91no—
313#496—91no—
314#468—91no—
315#466—91no—
316#463—31no—
317#460—91no—
318#450—91no—
319#449—31no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—91no—
324C23×D3—61no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—61no—
328C3×#41—62no—
329C3×#41—121no—
330C2×C3×Q8—31no—
331C2×C3×Q8—31no—
332C2×C3×D4—21no—
333C2×C3×D4—31no—
334C2×C3×D4—31no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C2×C3×D4C22×D311yescharacteristic
338C2×C3×D4C22×D311yescharacteristic
339C22×C3×C4—31no—
340C22×C3×C4—61no—
341C22×C3×C4—61no—
342C2×#67—21no—
343C2×#67—31no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—121no—
352C22×Dic3—21no—
353D3×Q8—62no—
354D3×Q8—62no—
355D3×Q8—121no—
356D3×Q8—121no—
357#237—22no—
358#237—41no—
359D3×D4—62no—
360D3×D4—62no—
361D3×D4—62no—
362D3×D4—121no—
363D3×D4—124no—
364D3×D4—121no—
365D3×D4—121no—
366C2×D12—21no—
367C2×D12—31no—
368C2×D12—31no—
369C2×D12—31no—
370C2×D12—61no—
371C2×D12—62no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—121no—
378C2×D12—121no—
379C2×D12—124no—
380C2×D12C22×D311yescharacteristic
381C2×D12C22×D311yescharacteristic
382C2×C4×D3—21no—
383C2×C4×D3—31no—
384C2×C4×D3—31no—
385C2×C4×D3—61no—
386C2×C4×D3—61no—
387C2×C4×D3—61no—
388C2×C4×D3C22×D311yescharacteristic
389C2×Dic6—61no—
390C2×Dic6—61no—
391C2×Dic6C22×D311yescharacteristic
392C2×Dic6C22×D311yescharacteristic
393C3×SD16—62no—
394C3×SD16—62no—
395C3×D8—62no—
396C3×D8—121no—
397C2×C3×C8—21no—
398C2×C3×C8—31no—
399C2×C3×C8—31no—
400C2×C3×C8C22×D311yescharacteristic
401C2×C3×C8C22×D311yescharacteristic
402C3×C4⋊C4—21no—
403C3×C4⋊C4C22×D311yescharacteristic
404C3×C4⋊C4C22×D311yescharacteristic
405C3×C22⋊C4—61no—
406C3×C22⋊C4—61no—
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C42—31no—
410#217—21no—
411#217—21no—
412#217—31no—
413#217—61no—
414#217—61no—
415#217—61no—
416#217—121no—
417#215—34no—
418#215—62no—
419#215—62no—
420#215—121no—
421#214—34no—
422#214—62no—
423#213—22no—
424#213—41no—
425#213—62no—
426#213—62no—
427#213—122no—
428(C2×D3)⋊C4—21no—
429(C2×D3)⋊C4—21no—
430(C2×D3)⋊C4—31no—
431(C2×D3)⋊C4—31no—
432(C2×D3)⋊C4—31no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—121no—
437C4⋊Dic3—31no—
438C4⋊Dic3—31no—
439C4⋊Dic3—31no—
440C4⋊Dic3—61no—
441C4⋊Dic3—61no—
442Dic3⋊C4—31no—
443Dic3⋊C4—61no—
444Dic3⋊C4—61no—
445Dic3⋊C4—61no—
446C4×Dic3—61no—
447C4×Dic3—61no—
448C4×Dic3C22×D311yescharacteristic
449#208—62no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—61no—
453C2×C3⋊C8C22×D311yescharacteristic
454C2×C3⋊C8C22×D311yescharacteristic
455#204—22no—
456#204—22no—
457#204—62no—
458#204—121no—
459ΓL(1,𝔽25)—62no—
460D3×C8—62no—
461D3×C8—62no—
462D3×C8—122no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32—41no—
466C22×C32C22×D411yescharacteristic
467C2×C3⋊D3—21no—
468C2×C3⋊D3—21no—
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
473C2×C3×D3—22no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482D32—84no—
483D32—84no—
484C32×C4—41no—
485C32×C4C22×D411yescharacteristic
486C32×C4H(5,𝔽2)11yescharacteristic
487C3⋊Dic3—21no—
488C3⋊Dic3—41no—
489C3×Dic3—22no—
490C3×Dic3—21no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—41no—
494C2×#41—31no—
495C22×Q8—91no—
496C22×D4—91no—
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—31no—
509C2×D8—91no—
510C2×M16—91no—
511C22×C8—91no—
512#127—91no—
513#124—31no—
514#124—181no—
515C22⋊Q8—91no—
516C22⋊Q8—181no—
517#121—31no—
518#121—91no—
519#121—91no—
520#121—181no—
521#121—181no—
522#120—181no—
523#120—181no—
524C4×Q8—91no—
525C4×D4—31no—
526C4×D4—91no—
527C4×D4—181no—
528#107—91no—
529C4⋊C8—31no—
530#103—31no—
531#103—31no—
532#102—91no—
533#102—91no—
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—41no—
543C23×C3—61no—
544C23×C3—61no—
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—31no—
548C22×D3—31no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—121no—
553C22×D3—122no—
554C22×D3—122no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—241no—
562C22×D3—241no—
563C22×D3—241no—
564C22×D3—241no—
565C22×D3D3×D411yescharacteristic
566C3×Q8—32no—
567C3×Q8—61no—
568C3×Q8—61no—
569C3×Q8—61no—
570C3×D4—21no—
571C3×D4—21no—
572C3×D4—21no—
573C3×D4—21no—
574C3×D4—32no—
575C3×D4—41no—
576C3×D4—41no—
577C3×D4—61no—
578C3×D4—61no—
579C3×D4—61no—
580C3×D4—122no—
581C3×D4—122no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—31no—
586C2×C3×C4—31no—
587C2×C3×C4—31no—
588C2×C3×C4—41no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—122no—
594C2×C3×C4—122no—
595C2×C3×C4C23×D311yescharacteristic
596C2×C3×C4C23×D311yescharacteristic
597#67—42no—
598#67—62no—
599#67—122no—
600#67—122no—
601#67—122no—
602#67—122no—
603#67—122no—
604#67—122no—
605#67—242no—
606#67—241no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—31no—
610C2×Dic3—31no—
611C2×Dic3—42no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—121no—
616C2×Dic3D3×D411yescharacteristic
617C2×Dic3D3×D411yescharacteristic
618C2×Dic3D3×D411yescharacteristic
619D12—21no—
620D12—21no—
621D12—21no—
622D12—42no—
623D12—62no—
624D12—61no—
625D12—61no—
626D12—61no—
627D12—61no—
628D12—121no—
629D12—121no—
630D12—122no—
631D12—122no—
632D12—122no—
633D12—122no—
634D12—242no—
635D12—241no—
636D12D3×D412yes—
637C4×D3—21no—
638C4×D3—21no—
639C4×D3—42no—
640C4×D3—61no—
641C4×D3—61no—
642C4×D3—61no—
643C4×D3—61no—
644C4×D3—121no—
645C4×D3—121no—
646C4×D3—122no—
647C4×D3—122no—
648Dic6—21no—
649Dic6—21no—
650Dic6—21no—
651Dic6—122no—
652Dic6—122no—
653Dic6D3×D412yescomplemented
654C3×C8—21no—
655C3×C8—21no—
656C3×C8—41no—
657C3×C8—61no—
658C3×C8—61no—
659C3⋊C8—21no—
660C3⋊C8—21no—
661C3⋊C8—32no—
662C3⋊C8—32no—
663C3⋊C8—62no—
664C2×C32—81no—
665C2×C32D4211yescharacteristic
666C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
667C2×C32#57711yescharacteristic
668C3⋊D3—22no—
669C3⋊D3—81no—
670C3×D3—41no—
671C3×D3—42no—
672C3×D3—81no—
673C24—181no—
674C24—181no—
675#41—62no—
676#41—121no—
677C2×Q8—31no—
678C2×Q8—31no—
679C2×Q8—181no—
680C2×Q8—182no—
681C2×Q8—361no—
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—91no—
687C2×D4—91no—
688C2×D4—181no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4—181no—
692C2×D4—182no—
693C2×D4—181no—
694C2×D4—182no—
695C2×D4—181no—
696C2×D4—361no—
697C2×D4—364no—
698C2×D4—361no—
699C2×D4C2×D3211yescharacteristic
700C22×C4—31no—
701C22×C4—61no—
702C22×C4—61no—
703C22×C4—91no—
704C22×C4—181no—
705SD16—62no—
706SD16—62no—
707SD16—94no—
708SD16—182no—
709SD16—182no—
710SD16—361no—
711D8—62no—
712D8—121no—
713D8—182no—
714M16—182no—
715C2×C8—31no—
716C2×C8—31no—
717C2×C8—91no—
718C2×C8—182no—
719C2×C8C2×D3211yescharacteristic
720C4⋊C4—91no—
721C4⋊C4—91no—
722C4⋊C4—181no—
723C4⋊C4—181no—
724C4⋊C4C2×D3211yescharacteristic
725C22⋊C4—61no—
726C22⋊C4—61no—
727C22⋊C4—61no—
728C22⋊C4—61no—
729C22⋊C4—91no—
730C22⋊C4—91no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C22⋊C4—181no—
734C42—31no—
735C42—181no—
736C22×C3—21no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—61no—
744C22×C3—61no—
745C22×C3—62no—
746C22×C3—61no—
747C22×C3—81no—
748C22×C3—81no—
749C22×C3—81no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3C2×D3×D411yescharacteristic
756C22×C3C2×D3×D411yescharacteristic
757C2×D3—21no—
758C2×D3—21no—
759C2×D3—21no—
760C2×D3—22no—
761C2×D3—32no—
762C2×D3—32no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—62no—
769C2×D3—61no—
770C2×D3—61no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—121no—
781C2×D3—241no—
782C2×D3—241no—
783C2×D3—241no—
784C2×D3—244no—
785C2×D3—244no—
786C2×D3—244no—
787C2×D3—244no—
788C3×C4—21no—
789C3×C4—21no—
790C3×C4—41no—
791C3×C4—41no—
792C3×C4—61no—
793C3×C4—61no—
794C3×C4—62no—
795C3×C4—61no—
796C3×C4—81no—
797C3×C4—121no—
798C3×C4C2×D3×D411yescharacteristic
799C3×C4C2×D3×D411yescharacteristic
800C3×C4#100411yescharacteristic
801C3×C4#100911yescharacteristic
802Dic3—21no—
803Dic3—21no—
804Dic3—22no—
805Dic3—21no—
806Dic3—41no—
807Dic3—61no—
808Dic3—61no—
809Dic3—121no—
810Dic3—121no—
811Dic3—121no—
812Dic3—241no—
813C32#326511yescharacteristic, complemented, Sylow
814C23—21no—
815C23—31no—
816C23—61no—
817C23—61no—
818C23—91no—
819C23—181no—
820C23—362no—
821C23—362no—
822C23—362no—
823C23—362no—
824C23—721no—
825C23—721no—
826Q8—32no—
827Q8—61no—
828Q8—61no—
829Q8—61no—
830Q8—362no—
831D4—21no—
832D4—21no—
833D4—32no—
834D4—61no—
835D4—61no—
836D4—61no—
837D4—122no—
838D4—122no—
839D4—182no—
840D4—181no—
841D4—181no—
842D4—362no—
843D4—362no—
844D4—362no—
845D4—362no—
846D4—362no—
847D4—721no—
848C2×C4—21no—
849C2×C4—31no—
850C2×C4—31no—
851C2×C4—31no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—91no—
857C2×C4—122no—
858C2×C4—122no—
859C2×C4—181no—
860C2×C4—181no—
861C2×C4—181no—
862C2×C4—362no—
863C2×C4C22×D3211yescharacteristic
864C8—21no—
865C8—61no—
866C8—61no—
867C8—92no—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—81no—
872C2×C3—81no—
873C2×C3—121no—
874C2×C3—122no—
875C2×C3—161no—
876C2×C3—241no—
877C2×C3#559011yescharacteristic
878C2×C3#560911yescharacteristic
879C2×C3#577011yescharacteristic
880C2×C3#577011yescharacteristic
881C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
882C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
883D3—42no—
884D3—41no—
885D3—62no—
886D3—62no—
887D3—81no—
888D3—122no—
889D3—241no—
890D3—241no—
891D3—481no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—61no—
896C22—61no—
897C22—61no—
898C22—62no—
899C22—92no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—121no—
905C22—181no—
906C22—181no—
907C22—361no—
908C22—361no—
909C22—361no—
910C22—724no—
911C22—724no—
912C22D32×D411yescharacteristic
913C4—41no—
914C4—61no—
915C4—61no—
916C4—61no—
917C4—62no—
918C4—121no—
919C4—181no—
920C4—361no—
921C4#6430711yescharacteristic
922C4D32×D411yescharacteristic
923C3—21no—
924C3#8012111yescharacteristic, complemented
925C3#8055311yescharacteristic, complemented
926C2—81no—
927C2—121no—
928C2—122no—
929C2—182no—
930C2—241no—
931C2—721no—
932C2#1059427511yescharacteristic
933C2#1059472611yescharacteristic
934C2#1059475711yescharacteristic
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. #10595237C2semidirect
2. C2×#63925C2semidirect
3. C2×#63796C2semidirect
4. #10594621C2semidirect
5. #10592474C2semidirect
6. C3×#4787C2semidirect
7. C3×#4781C2semidirect
8. #10591516C2semidirect
9. #10591483C2semidirect
10. #10590942C2semidirect
11. #10590799C2semidirect
12. #10590737C2semidirect
13. #10590606C2semidirect
14. #10590515C2semidirect
15. #10590478C2semidirect
18. C2×C3×#237C22semidirect
22. C2×#3797C22semidirect
23. #64147C22semidirect
24. C2×#3753C22semidirect
25. C2×C8×C3⋊D3C22semidirect
27. C3×#936C22semidirect
29. C2×C3×#213C22semidirect
31. C2×C3×#204C22semidirect
44. #63856C22semidirect
45. Dic3×Dic6C22semidirect
46. C2×#3717C22semidirect
47. C2×#3717C22semidirect
49. C2×#3715C22semidirect
50. C2×#3711C22semidirect
52. C32×#102C22semidirect
53. #63648C22semidirect
54. #63634C22semidirect
55. C3×(C2×D3)⋊C8C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#810C22semidirect
58. C3×#810C22semidirect
60. #63563C22semidirect
61. #63557C22semidirect
62. #63554C22semidirect
87. #4787D3semidirect
88. #4781D3semidirect
155. #3715D4semidirect
161. C2×#237C2×D3semidirect
189. #936C2×D3semidirect
196. C2×#213C2×D3semidirect
209. C2×#204C2×D3semidirect
234. C3×#102C2×D3semidirect
235. C3×#102C2×D3semidirect
246. (C2×D3)⋊C8C2×D3semidirect
248. Dic3⋊C8C2×D3semidirect
249. #810C2×D3semidirect
250. #810C2×D3semidirect
297. C3×Dic6C2×D4semidirect
306. C3⋊(C3⋊C8)C2×D4semidirect
472. C2×C3⋊D3AGL(1,ℤ/8)semidirect
535. #102D32semidirect
653. Dic6D3×D4semidirect
813. C32#3265semidirect
924. C3#80121semidirect
925. C3#80553semidirect

Maximal subgroups

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

subgroupindex
#105952372
C2×#639252
C2×#637962
#105946212
#105924742
C3×#47872
C3×#47812
#105915162
#105914832
#105909422
#105907992
#105907372
#105906062
#105905152
#105904782
#805533
#801213