Finite Group Databasebeta

← #11884243

Subgroups — #11884243

Order 1152.

1500 conjugacy classes of subgroups.

The subgroup lattice has 627 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64128C211yesmaximal, characteristic, complemented
2C2×#64117C211yesmaximal, characteristic, complemented
3#10596102C211yesmaximal, characteristic, complemented
4#10596101C211yesmaximal, characteristic, complemented
5C32×#470C211yesmaximal, characteristic, complemented
6#10592889C211yesmaximal, characteristic, complemented
7#10592826C211yesmaximal, characteristic, complemented
8#10592746C211yesmaximal, characteristic, complemented
9#10592745C211yesmaximal, characteristic, complemented
10#10592568C211yesmaximal, characteristic, complemented
11#10592563C211yesmaximal, characteristic, complemented
12#10592518C211yesmaximal, characteristic, complemented
13#10592517C211yesmaximal, characteristic, complemented
14#10592509C211yesmaximal, characteristic, complemented
15#10592507C211yesmaximal, characteristic, complemented
16#80921—34nomaximal
17C2×#3832C2211yescharacteristic
18C2×#3832C2211yescharacteristic, complemented
19C2×#3828C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C32×Q16C2211yescharacteristic, complemented
22C2×C32×M16C2211yescharacteristic
23C32×C22⋊Q8C2211yescharacteristic
24C32×C22⋊Q8C2211yescharacteristic
25#64156C2211yescharacteristic
26#64153C2211yescharacteristic, complemented
27C2×#3756C2211yescharacteristic, complemented
28C2×#3755C2211yescharacteristic
29C2×#3755C2211yescharacteristic
30C2×#3755C2211yescharacteristic, complemented
31C4×#638C2211yescharacteristic
32#64128—24no—
33#64117—24no—
34C2×#3745C2211yescharacteristic
35C2×#3745C2211yescharacteristic
36C2×#3744C2211yescharacteristic
37C2×#3744C2211yescharacteristic
38C2×C8×C3⋊D3C2211yescharacteristic, complemented
39#64106C2211yescharacteristic, complemented
40#64104—21no—
41#64104C2211yescharacteristic
42#64103—21no—
43#64103—21no—
44#64102C2211yescharacteristic
45#64102C2211yescharacteristic, complemented
46C4⋊C4×C3⋊D3—21no—
47#64093—21no—
48#64092—21no—
49#64091—21no—
50C22⋊C4×C3⋊D3—21no—
51C32×#106C2211yescharacteristic, complemented
52C32×#103C2211yescharacteristic, complemented
53C32×#103C2211yescharacteristic, complemented
54#63657C2211yescharacteristic
55#63647C2211yescharacteristic, complemented
56#63642C2211yescharacteristic, complemented
57#63641C2211yescharacteristic, complemented
58#63637C2211yescharacteristic, complemented
59#63636C2211yescharacteristic
60#63636C2211yescharacteristic
61#63636C2211yescharacteristic, complemented
62C2×#919—34no—
63C2×#908—34no—
64#5631—34no—
65#5630—34no—
66C3×#470D314yescomplemented
67#5190—34no—
68#5127—34no—
69#5047—34no—
70#5046—34no—
71#4869—34no—
72#4864—34no—
73#4819—34no—
74#4818—34no—
75#4810—34no—
76#4808—34no—
77C23×C3⋊D3—21no—
78C2×C32×Q8C2311yescharacteristic
79C2×C32×Q8C2311yescharacteristic
80C22×C32×C4C2311yescharacteristic
81C2×#638—21no—
82C2×#638D411yescharacteristic
83#3832—22no—
84#3832—22no—
85#3832—41no—
86#3832—41no—
87#3828—22no—
88#3828—41no—
89C2×C4⋊(C3⋊D3)—22no—
90C2×C4⋊(C3⋊D3)—21no—
91C2×C4⋊(C3⋊D3)—21no—
92C2×C4⋊(C3⋊D3)—21no—
93C2×C4⋊(C3⋊D3)—21no—
94C2×C4⋊(C3⋊D3)—41no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×#634C2311yescharacteristic
105C32×Q16—22no—
106C32×M16—22no—
107C2×C32×C8C2311yescharacteristic
108C2×C32×C8C2311yescharacteristic
109C32×C4⋊C4—21no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C32×C22⋊C4—21no—
115#3757D411yescharacteristic
116#3756—41no—
117#3755—22no—
118#3755—22no—
119#3755—41no—
120#3752—21no—
121#3752—21no—
122#3752—21no—
123#3752—21no—
124#3752—21no—
125#3752—21no—
126#3752D411yescharacteristic
127C4⋊(C3⋊Dic3)—21no—
128#3750—21no—
129#3750—21no—
130#3750D411yescharacteristic
131C4×C3⋊Dic3C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134#3745—22no—
135#3745D414yescomplemented
136#3744—22no—
137#3744—22no—
138C8×C3⋊D3—22no—
139#3267—91noSylow
140C2×#239—34no—
141C2×#239—34no—
142C2×#235—34no—
143C22×D12—34no—
144C2×C3×Q16C2×D314yescomplemented
145C2×C3×M16C2×D314yes—
146C3×C22⋊Q8C2×D314yes—
147C3×C22⋊Q8C2×D314yes—
148#947—34no—
149#944—34no—
150C2×#216—34no—
151C2×#215—34no—
152C2×#215—34no—
153C2×#215—34no—
154C4×#67—34no—
155#919—616no—
156#908—616no—
157C2×D24—34no—
158C2×D24—34no—
159C2×#204—34no—
160C2×#204—34no—
161C2×D3×C8—34no—
162#897—34no—
163#895—34no—
164#895—64no—
165#894—64no—
166#894—64no—
167#893—34no—
168#893—34no—
169D3×C4⋊C4—64no—
170#884—64no—
171#883—64no—
172#882—64no—
173D3×C22⋊C4—64no—
174C3×#106C2×D314yescomplemented
175C3×#103C2×D314yescomplemented
176C3×#103C2×D314yescomplemented
177#830—34no—
178(C2×D3)⋊C8—34no—
179#815—34no—
180Dic3⋊C8—34no—
181#810—34no—
182#809—34no—
183#809—34no—
184#809—34no—
185C23×C32C2×D411yescharacteristic
186C22×C3⋊D3—21no—
187C22×C3⋊D3—21no—
188C22×C3⋊D3—21no—
189C22×C3⋊D3—42no—
190C22×C3⋊D3—42no—
191C22×C3⋊D3—81no—
192C22×C3⋊D3C2×D411yescharacteristic
193C32×Q8—21no—
194C32×Q8—21no—
195C32×Q8—21no—
196C32×Q8—21no—
197C2×C32×C4—21no—
198C2×C32×C4—21no—
199C2×C32×C4—21no—
200C2×C32×C4—21no—
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4C2×D411yescharacteristic
204C2×C32×C4C2411yescharacteristic
205#638—41no—
206#638—42no—
207C2×C3⋊Dic3—21no—
208C2×C3⋊Dic3C2×D411yescharacteristic
209C2×C3⋊Dic3C2×D411yescharacteristic
210C2×C3⋊Dic3C2×D411yescharacteristic
211C4⋊(C3⋊D3)—21no—
212C4⋊(C3⋊D3)—21no—
213C4⋊(C3⋊D3)—21no—
214C4⋊(C3⋊D3)—21no—
215C4⋊(C3⋊D3)—42no—
216C4⋊(C3⋊D3)—42no—
217C4⋊(C3⋊D3)—42no—
218C4⋊(C3⋊D3)—81no—
219C4⋊(C3⋊D3)C2×D412yes—
220C4⋊(C3⋊D3)C2×D412yes—
221C4×C3⋊D3—21no—
222C4×C3⋊D3—21no—
223C4×C3⋊D3—42no—
224C4×C3⋊D3—42no—
225C4×C3⋊D3—42no—
226C4×C3⋊D3—42no—
227C4×C3⋊D3—81no—
228#634—21no—
229#634—21no—
230C32×C8—21no—
231C32×C8C2×D412yes—
232C3⋊(C3⋊C8)—21no—
233C3⋊(C3⋊C8)—21no—
234C2×AGL(1,ℤ/8)—91no—
235C2×#135—91no—
236#547—91no—
237#546—91no—
238#497—91no—
239#470C3⋊D311yescharacteristic, complemented
240#465—91no—
241#463—91no—
242#461—91no—
243#452—91no—
244#452—91no—
245#450—91no—
246#449—91no—
247#442—91no—
248#435—91no—
249C23×D3—64no—
250C2×C3×Q8C22×D314yes—
251C2×C3×Q8C22×D314yes—
252C22×C3×C4C22×D314yes—
253C2×#67—34no—
254C2×#67—64no—
255#239—68no—
256#239—68no—
257#239—124no—
258#239—124no—
259#235—68no—
260#235—124no—
261C2×D12—34no—
262C2×D12—34no—
263C2×D12—34no—
264C2×D12—68no—
265C2×D12—64no—
266C2×D12—64no—
267C2×D12—64no—
268C2×D12—64no—
269C2×D12—124no—
270C2×C4×D3—34no—
271C2×C4×D3—64no—
272C2×C4×D3—64no—
273C2×C4×D3—64no—
274C2×C4×D3—64no—
275C2×C4×D3—64no—
276C2×Dic6—34no—
277C3×Q16—28no—
278C3×M16—28no—
279C2×C3×C8C22×D314yes—
280C2×C3×C8C22×D314yes—
281C3×C4⋊C4—24no—
282C3×C4⋊C4—24no—
283C3×C4⋊C4C22×D314yes—
284C3×C4⋊C4C22×D314yes—
285C3×C22⋊C4—24no—
286C3×C22⋊C4—24no—
287#217—34no—
288#216—124no—
289#215—68no—
290#215—68no—
291#215—124no—
292(C2×D3)⋊C4—34no—
293(C2×D3)⋊C4—64no—
294(C2×D3)⋊C4—64no—
295(C2×D3)⋊C4—64no—
296(C2×D3)⋊C4—64no—
297(C2×D3)⋊C4—64no—
298(C2×D3)⋊C4—64no—
299C4⋊Dic3—64no—
300Dic3⋊C4—34no—
301Dic3⋊C4—64no—
302Dic3⋊C4—64no—
303C4×Dic3—34no—
304C2×C3⋊C8—34no—
305C2×C3⋊C8—34no—
306D24—316no—
307D24—68no—
308#204—68no—
309#204—68no—
310D3×C8—68no—
311C22×C32—21no—
312C22×C32—21no—
313C22×C32—21no—
314C22×C32C22×D411yescharacteristic
315C2×C3⋊D3—21no—
316C2×C3⋊D3—22no—
317C2×C3⋊D3—22no—
318C2×C3⋊D3—21no—
319C2×C3⋊D3—21no—
320C2×C3⋊D3—41no—
321C2×C3⋊D3—41no—
322C2×C3⋊D3—41no—
323C2×C3⋊D3—41no—
324C2×C3⋊D3—41no—
325C2×C3⋊D3—41no—
326C2×C3⋊D3—41no—
327C2×C3⋊D3—84no—
328C32×C4—21no—
329C32×C4—41no—
330C32×C4—41no—
331C32×C4—41no—
332C32×C4—41no—
333C32×C4C22×D411yescharacteristic
334C32×C4H(5,𝔽2)11yescharacteristic
335C3⋊Dic3—21no—
336C3⋊Dic3—21no—
337C3⋊Dic3—21no—
338C3⋊Dic3—41no—
339C2×#41—91no—
340C2×#41—91no—
341C2×#41—91no—
342C22×D4—91no—
343AGL(1,ℤ/8)—184no—
344#135—184no—
345C2×Q16—91no—
346C2×Q16C2×C3⋊D311yescharacteristic, complemented
347C2×SD16—91no—
348C2×SD16—91no—
349C2×SD16—91no—
350C2×SD16—91no—
351C2×SD16—91no—
352C2×D8—91no—
353C2×D8—91no—
354C2×M16C2×C3⋊D311yescharacteristic
355C22×C8—91no—
356C4⋊Q8—91no—
357#124—91no—
358#123—181no—
359#123—181no—
360#123—181no—
361C22⋊Q8—91no—
362C22⋊Q8C2×C3⋊D311yescharacteristic
363C22⋊Q8C2×C3⋊D311yescharacteristic
364#121—91no—
365#121—181no—
366#121—181no—
367#120—181no—
368C4×D4—91no—
369C4×D4—91no—
370C4×D4—91no—
371C2×C4⋊C4—181no—
372C2×C22⋊C4—181no—
373#106C2×C3⋊D311yescharacteristic, complemented
374C4⋊C8—91no—
375#103—91no—
376#103C2×C3⋊D311yescharacteristic, complemented
377#103C2×C3⋊D311yescharacteristic, complemented
378#102—91no—
379#102—91no—
380#102—91no—
381C22⋊C8—91no—
382C22⋊C8—91no—
383#97—91no—
384C23×C3D3×D414yes—
385C22×D3—34no—
386C22×D3—64no—
387C22×D3—64no—
388C22×D3—64no—
389C22×D3—128no—
390C22×D3—128no—
391C22×D3—244no—
392C3×Q8—24no—
393C3×Q8—24no—
394C3×Q8—24no—
395C3×Q8—24no—
396C2×C3×C4—24no—
397C2×C3×C4—24no—
398C2×C3×C4—24no—
399C2×C3×C4—24no—
400C2×C3×C4—24no—
401C2×C3×C4—24no—
402C2×C3×C4D3×D414yes—
403C2×C3×C4C23×D314yes—
404#67—124no—
405#67—128no—
406C2×Dic3—34no—
407C2×Dic3—34no—
408C2×Dic3—34no—
409C2×Dic3—64no—
410D12—38no—
411D12—38no—
412D12—64no—
413D12—64no—
414D12—64no—
415D12—64no—
416D12—128no—
417D12—128no—
418D12—128no—
419D12—244no—
420C4×D3—64no—
421C4×D3—64no—
422C4×D3—128no—
423C4×D3—128no—
424C4×D3—128no—
425C4×D3—128no—
426C4×D3—244no—
427Dic6—64no—
428Dic6—64no—
429C3×C8—24no—
430C3×C8D3×D418yes—
431C3⋊C8—64no—
432C3⋊C8—64no—
433C2×C32—41no—
434C2×C32D4211yescharacteristic
435C2×C32#57511yescharacteristic
436C2×C32#57711yescharacteristic
437C3⋊D3—41no—
438C3⋊D3—42no—
439C3⋊D3—42no—
440C3⋊D3—81no—
441C24—181no—
442#41—182no—
443#41—182no—
444#41—182no—
445#41—361no—
446#41—361no—
447#41—361no—
448C2×Q8—91no—
449C2×Q8C22×C3⋊D311yescharacteristic
450C2×Q8C22×C3⋊D311yescharacteristic
451C2×D4—91no—
452C2×D4—91no—
453C2×D4—91no—
454C2×D4—91no—
455C2×D4—182no—
456C2×D4—181no—
457C2×D4—181no—
458C2×D4—181no—
459C2×D4—181no—
460C2×D4—181no—
461C2×D4—361no—
462C22×C4—91no—
463C22×C4—181no—
464C22×C4—181no—
465C22×C4—181no—
466C22×C4—181no—
467C22×C4—181no—
468C22×C4C22×C3⋊D311yescharacteristic
469Q16—22no—
470Q16—361no—
471SD16—182no—
472SD16—182no—
473SD16—182no—
474SD16—182no—
475SD16—361no—
476D8—94no—
477D8—182no—
478M16—22no—
479C2×C8—91no—
480C2×C8—91no—
481C2×C8—182no—
482C2×C8C22×C3⋊D311yescharacteristic
483C2×C8C22×C3⋊D311yescharacteristic
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—91no—
487C4⋊C4—181no—
488C4⋊C4—181no—
489C4⋊C4—181no—
490C4⋊C4C22×C3⋊D311yescharacteristic
491C4⋊C4C22×C3⋊D311yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—91no—
495C22⋊C4—91no—
496C22⋊C4—181no—
497C22⋊C4—181no—
498C22⋊C4—181no—
499C22⋊C4—181no—
500C22⋊C4—181no—
501C22⋊C4—181no—
502C42—91no—
503C22×C3—24no—
504C22×C3—24no—
505C22×C3—24no—
506C22×C3C2×D3×D414yes—
507C2×D3—64no—
508C2×D3—64no—
509C2×D3—64no—
510C2×D3—68no—
511C2×D3—68no—
512C2×D3—124no—
513C2×D3—124no—
514C2×D3—124no—
515C2×D3—124no—
516C2×D3—124no—
517C2×D3—124no—
518C2×D3—124no—
519C2×D3—2416no—
520C3×C4—24no—
521C3×C4—44no—
522C3×C4—44no—
523C3×C4—44no—
524C3×C4—44no—
525C3×C4C2×D3×D414yes—
526C3×C4#100914yes—
527Dic3—64no—
528Dic3—64no—
529Dic3—64no—
530Dic3—124no—
531C32#326711yescharacteristic, complemented, Sylow
532C23—91no—
533C23—181no—
534C23—181no—
535C23—181no—
536C23—362no—
537C23—362no—
538C23—721no—
539C23D4×C3⋊D311yescharacteristic
540Q8—21no—
541Q8—21no—
542Q8—21no—
543Q8—21no—
544Q8—181no—
545Q8—181no—
546D4—92no—
547D4—92no—
548D4—181no—
549D4—181no—
550D4—181no—
551D4—181no—
552D4—362no—
553D4—362no—
554D4—362no—
555D4—361no—
556D4—362no—
557D4—721no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—91no—
565C2×C4—91no—
566C2×C4—91no—
567C2×C4—181no—
568C2×C4—181no—
569C2×C4—181no—
570C2×C4—362no—
571C2×C4—362no—
572C2×C4—362no—
573C2×C4—362no—
574C2×C4—721no—
575C2×C4D4×C3⋊D311yescharacteristic
576C2×C4C23×C3⋊D311yescharacteristic
577C8—21no—
578C8—181no—
579C8—181no—
580C8D4×C3⋊D312yes—
581C2×C3—44no—
582C2×C3#560914yes—
583C2×C3#577714yes—
584C2×C3#577814yes—
585D3—124no—
586D3—128no—
587D3—128no—
588D3—244no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—181no—
593C22—181no—
594C22—181no—
595C22—182no—
596C22—182no—
597C22—361no—
598C22—361no—
599C22—361no—
600C22—361no—
601C22—361no—
602C22—361no—
603C22—361no—
604C22—724no—
605C22C2×D4×C3⋊D311yescharacteristic
606C4—21no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—181no—
612C4—181no—
613C4—181no—
614C4—361no—
615C4C2×D4×C3⋊D311yescharacteristic
616C4#6436611yescharacteristic
617C3#8092114yescomplemented
618C2—41no—
619C2—361no—
620C2—362no—
621C2—362no—
622C2—721no—
623C2#1059608011yescharacteristic
624C2#1059624811yescharacteristic
625C2#1059624911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#470C2
socleC22×C32C22×D4
hypercenter#470C3⋊D3
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. C2×#64128C2semidirect
2. C2×#64117C2semidirect
3. #10596102C2semidirect
4. #10596101C2semidirect
5. C32×#470C2semidirect
6. #10592889C2semidirect
7. #10592826C2semidirect
8. #10592746C2semidirect
9. #10592745C2semidirect
10. #10592568C2semidirect
11. #10592563C2semidirect
12. #10592518C2semidirect
13. #10592517C2semidirect
14. #10592509C2semidirect
15. #10592507C2semidirect
18. C2×#3832C22semidirect
21. C2×C32×Q16C22semidirect
26. #64153C22semidirect
27. C2×#3756C22semidirect
30. C2×#3755C22semidirect
38. C2×C8×C3⋊D3C22semidirect
39. #64106C22semidirect
45. #64102C22semidirect
51. C32×#106C22semidirect
52. C32×#103C22semidirect
53. C32×#103C22semidirect
55. #63647C22semidirect
56. #63642C22semidirect
57. #63641C22semidirect
58. #63637C22semidirect
61. #63636C22semidirect
66. C3×#470D3semidirect
135. #3745D4semidirect
144. C2×C3×Q16C2×D3semidirect
174. C3×#106C2×D3semidirect
175. C3×#103C2×D3semidirect
176. C3×#103C2×D3semidirect
239. #470C3⋊D3semidirect
346. C2×Q16C2×C3⋊D3semidirect
373. #106C2×C3⋊D3semidirect
376. #103C2×C3⋊D3semidirect
377. #103C2×C3⋊D3semidirect
531. C32#3267semidirect
617. C3#80921semidirect

Maximal subgroups

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

subgroupindex
C2×#641282
C2×#641172
#105961022
#105961012
C32×#4702
#105928892
#105928262
#105927462
#105927452
#105925682
#105925632
#105925182
#105925172
#105925092
#105925072
#809213