Finite Group Databasebeta

← #11787746

Subgroups — #11787746

Order 1152.

887 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595975C211yesmaximal, characteristic, complemented
2C2×#63830C211yesmaximal, characteristic
3C3×#4988C211yesmaximal, characteristic, complemented
4C2×#63570C211yesmaximal, characteristic, complemented
5#10591086C211yesmaximal, characteristic, complemented
6C3×#4530C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#69663—31nomaximal
9#69005—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C4×#638—22no—
14#64135C2211yescharacteristic
15#64102—21no—
16#64101—21no—
17C4⋊C4×C3⋊D3—21no—
18#64096—21no—
19C2×C3×(C2×D3)⋊C4—22no—
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23#63830—22no—
24#63830C414yescomplemented
25C2×#3716—21no—
26C2×#3714—21no—
27#63570—22no—
28#63563—21no—
29#63563—21no—
30C2×#932—31no—
31C2×#908—31no—
32#5504—31no—
33#5504—31no—
34#5504—61no—
35C3×#390—31no—
36#5215—31no—
37C2×#825—31no—
38#5131—31no—
39#4988D311yescharacteristic, complemented
40C2×#805—31no—
41C3×#343—31no—
42#4555—31no—
43#4530D311yescharacteristic, complemented
44#4523—31no—
45C23×C3×D3—21no—
46C22×C32×C4D412yes—
47C22×C32×C4C2311yescharacteristic
48C2×#638—21no—
49#3828—21no—
50#3828—21no—
51#3828C2×C412yes—
52#3828D412yes—
53C2×C4⋊(C3⋊D3)D411yescharacteristic
54C2×C4×C3⋊D3—21no—
55C2×C4×C3⋊D3—22no—
56C2×#634D411yescharacteristic
57C22×C3×Dic3—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12—21no—
62C2×C3×D12—21no—
63C2×C3×D12C2×C412yescomplemented
64C32×C4⋊C4—21no—
65C32×C4⋊C4—21no—
66#3757—21no—
67#3752—22no—
68C4⋊(C3⋊Dic3)D411yescharacteristic
69C4⋊(C3⋊Dic3)D411yescharacteristic
70#3750—22no—
71C4×C3⋊Dic3—22no—
72C4×C3⋊Dic3—21no—
73C3×(C2×D3)⋊C4—44no—
74C3×C4×Dic3—21no—
75C3×C4×Dic3—21no—
76C3×#208—21no—
77C3×#208—21no—
78C3×#208—21no—
79C3×#208C2×C412yescomplemented
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8—21no—
82#3716—24no—
83#3714—24no—
84#1883—91noSylow
85C22×C3×D4—31no—
86C2×#235—31no—
87C2×#235—31no—
88C2×#235—61no—
89C22×D12C2×D311yescharacteristic
90C2×C3×M16—31no—
91C2×C3×M16—31no—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4C2×D311yescharacteristic
94C2×C3×C4⋊C4C2×D311yescharacteristic
95C2×C3×C22⋊C4—62no—
96C2×C3×C42—31no—
97C2×#214—61no—
98#932—34no—
99#932—62no—
100C2×#213—61no—
101C4×#67—64no—
102C4×#67—62no—
103C4×#67—62no—
104C2×(C2×D3)⋊C4—22no—
105#926—31no—
106#926—31no—
107#926—61no—
108C2×C4×Dic3C2×D311yescharacteristic
109C2×#208C2×D311yescharacteristic
110C2×#208C2×D311yescharacteristic
111#908—34no—
112#908—62no—
113C2×D24—61no—
114C2×#204—61no—
115#893—61no—
116#893—61no—
117#893—62no—
118#892—61no—
119#892—61no—
120#892—62no—
121D3×C4⋊C4—61no—
122D3×C4⋊C4—61no—
123D3×C4⋊C4—62no—
124#887—61no—
125#887—61no—
126#887—62no—
127#832—61no—
128#832—61no—
129#825—62no—
130#821—61no—
131#821—61no—
132#805—62no—
133C23×C32C2×D411yescharacteristic
134C22×C3⋊D3—21no—
135C22×C3×D3—22no—
136C22×C3×D3—42no—
137C22×C3×D3—42no—
138C22×C3×D3—41no—
139C22×C3×D3—41no—
140C2×C32×C4—22no—
141C2×C32×C4—42no—
142C2×C32×C4C22×C411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4#4111yescharacteristic
147C2×C32×C4#4111yescharacteristic
148#638—22no—
149#638—22no—
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3—21no—
152C2×C3⋊Dic3—21no—
153C4⋊(C3⋊D3)—21no—
154C4⋊(C3⋊D3)C22⋊C412yescomplemented
155C4×C3⋊D3—22no—
156C4×C3⋊D3—22no—
157C4×C3⋊D3—82no—
158#634—21no—
159#634C22⋊C412yescomplemented
160C2×C3×Dic3—22no—
161C2×C3×Dic3—41no—
162C2×C3×Dic3—41no—
163C3×D12—22no—
164C3×D12—22no—
165C3×D12—41no—
166C3×D12—41no—
167C3×C3⋊C8—22no—
168C3×C3⋊C8—41no—
169C2×AGL(1,ℤ/8)—91no—
170#520—91no—
171C2×#104—91no—
172#418—91no—
173#390—31no—
174#343—31no—
175#339—91no—
176C24×C3—61no—
177C23×D3—21no—
178C2×C3×D4—32no—
179C2×C3×D4—61no—
180C2×C3×D4—61no—
181C2×C3×D4—61no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C22×C3×C4—22no—
185C22×C3×C4—21no—
186C22×C3×C4—61no—
187C22×C3×C4D1212yes—
188C22×C3×C4#6712yes—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C2×#67—62no—
192C2×#67—61no—
193C2×#67—61no—
194C22×Dic3—21no—
195#235—32no—
196#235—32no—
197#235—32no—
198#235—32no—
199#235—62no—
200#235—62no—
201#235—62no—
202#235—62no—
203#235—61no—
204#235—61no—
205#235—61no—
206#235—61no—
207C2×D12—21no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12—21no—
212C2×D12—31no—
213C2×D12—31no—
214C2×D12—61no—
215C2×D12C4×D312yescomplemented
216C2×C4×D3—62no—
217C2×C4×D3—61no—
218C2×C4×D3—61no—
219C2×C4×D3—64no—
220C2×C4×D3—62no—
221C2×C4×D3—62no—
222C2×Dic6—31no—
223C2×Dic6—31no—
224C2×Dic6—61no—
225C3×M16—32no—
226C3×M16—61no—
227C3×M16—61no—
228C3×M16—61no—
229C2×C3×C8—61no—
230C2×C3×C8—61no—
231C3×C4⋊C4—22no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C22⋊C4—124no—
238C3×C42—61no—
239C3×C42—61no—
240#217—62no—
241#217—61no—
242#217—61no—
243#214—64no—
244#213—64no—
245(C2×D3)⋊C4—44no—
246(C2×D3)⋊C4—64no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—62no—
249C4⋊Dic3—31no—
250C4⋊Dic3—31no—
251C4⋊Dic3—31no—
252C4⋊Dic3—31no—
253C4⋊Dic3—61no—
254C4⋊Dic3—61no—
255Dic3⋊C4—64no—
256Dic3⋊C4—62no—
257Dic3⋊C4—62no—
258C4×Dic3—21no—
259C4×Dic3—21no—
260C4×Dic3—64no—
261C4×Dic3—62no—
262C4×Dic3—62no—
263C4×Dic3—62no—
264C4×Dic3—61no—
265C4×Dic3—61no—
266#208—21no—
267#208—21no—
268#208—21no—
269#208C4×D312yescomplemented
270C2×C3⋊C8—21no—
271C2×C3⋊C8—21no—
272D24—64no—
273#204—64no—
274C22×C32—21no—
275C22×C32—21no—
276C22×C32C4×D411yescharacteristic
277C22×C32#12011yescharacteristic
278C22×C32#12111yescharacteristic
279C2×C3⋊D3—22no—
280C2×C3⋊D3—41no—
281C2×C3⋊D3—41no—
282C2×C3×D3—44no—
283C2×C3×D3—42no—
284C2×C3×D3—82no—
285C2×C3×D3—81no—
286C2×C3×D3—81no—
287C32×C4—42no—
288C32×C4C2×C22⋊C411yescharacteristic
289C32×C4C4×D411yescharacteristic
290C32×C4#12111yescharacteristic
291C32×C4#12311yescharacteristic
292C3⋊Dic3—22no—
293C3⋊Dic3—41no—
294C3⋊Dic3—41no—
295C3×Dic3—42no—
296C2×#41—91no—
297C22×D4—31no—
298AGL(1,ℤ/8)—94no—
299AGL(1,ℤ/8)—182no—
300C2×SD16—181no—
301C2×D8—181no—
302C2×M16—31no—
303C2×M16—31no—
304C4×Q8—181no—
305C4×D4—181no—
306C4×D4—182no—
307#117—91no—
308#117—181no—
309C2×C4⋊C4—181no—
310C2×C4⋊C4D3211yescharacteristic
311C2×C22⋊C4—62no—
312C2×C42—31no—
313#104—182no—
314#102—181no—
315#102—181no—
316C23×C3—21no—
317C23×C3—62no—
318C23×C3—122no—
319C23×C3—122no—
320C23×C3—121no—
321C23×C3—121no—
322C23×C3C2×D1211yescharacteristic
323C23×C3C2×#6711yescharacteristic
324C22×D3—22no—
325C22×D3—42no—
326C22×D3—42no—
327C22×D3—41no—
328C22×D3—41no—
329C22×D3—62no—
330C22×D3—61no—
331C22×D3—61no—
332C3×D4—62no—
333C3×D4—62no—
334C3×D4—121no—
335C3×D4—121no—
336C2×C3×C4—24no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—42no—
346C2×C3×C4—42no—
347C2×C3×C4—62no—
348C2×C3×C4—82no—
349C2×C3×C4—121no—
350C2×C3×C4—121no—
351C2×C3×C4C2×C4×D311yescharacteristic
352C2×C3×C4C2×C4×D311yescharacteristic
353C2×C3×C4#23511yescharacteristic
354C2×C3×C4#23511yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4#23711yescharacteristic
362C2×C3×C4#23911yescharacteristic
363#67—64no—
364#67—64no—
365#67—62no—
366#67—62no—
367#67—62no—
368#67—62no—
369C2×Dic3—22no—
370C2×Dic3—41no—
371C2×Dic3—41no—
372C2×Dic3—62no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381D12—22no—
382D12—22no—
383D12—32no—
384D12—32no—
385D12—41no—
386D12—41no—
387D12—62no—
388D12—62no—
389D12—61no—
390D12—61no—
391C4×D3—64no—
392C4×D3—64no—
393C4×D3—62no—
394C4×D3—62no—
395C4×D3—62no—
396C4×D3—62no—
397C4×D3—244no—
398C4×D3—242no—
399C4×D3—242no—
400Dic6—32no—
401Dic6—32no—
402Dic6—62no—
403Dic6—62no—
404Dic6—61no—
405Dic6—61no—
406C3×C8—62no—
407C3×C8—121no—
408C3⋊C8—22no—
409C3⋊C8—41no—
410C2×C32—21no—
411C2×C32—21no—
412C2×C32#38611yescharacteristic
413C2×C32#45311yescharacteristic
414C2×C32#45411yescharacteristic
415C3⋊D3—42no—
416C3×D3—82no—
417C24—61no—
418#41—92no—
419#41—92no—
420#41—181no—
421#41—181no—
422C2×Q8—91no—
423C2×D4—32no—
424C2×D4—61no—
425C2×D4—61no—
426C2×D4—61no—
427C2×D4—61no—
428C2×D4—61no—
429C2×D4—91no—
430C2×D4—181no—
431C22×C4—61no—
432C22×C4—182no—
433C22×C4—181no—
434C22×C4#62612yes—
435C22×C4C2×D3211yescharacteristic
436SD16—184no—
437D8—184no—
438M16—32no—
439M16—61no—
440M16—61no—
441M16—61no—
442C2×C8—61no—
443C2×C8—61no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—91no—
447C4⋊C4—91no—
448C4⋊C4—182no—
449C22⋊C4—124no—
450C22⋊C4—182no—
451C22⋊C4—181no—
452C42—61no—
453C42—61no—
454C42—182no—
455C42—181no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—41no—
464C22×C3—41no—
465C22×C3—124no—
466C22×C3—122no—
467C22×C3—242no—
468C22×C3—241no—
469C22×C3—241no—
470C22×C3C4×D1211yescharacteristic
471C22×C3#88211yescharacteristic
472C22×C3#89511yescharacteristic
473C22×C3C4×#6711yescharacteristic
474C22×C3#93711yescharacteristic
475C22×C3#93811yescharacteristic
476C2×D3—44no—
477C2×D3—42no—
478C2×D3—64no—
479C2×D3—62no—
480C2×D3—62no—
481C2×D3—82no—
482C2×D3—81no—
483C2×D3—81no—
484C2×D3—122no—
485C2×D3—122no—
486C2×D3—121no—
487C2×D3—121no—
488C2×D3—121no—
489C2×D3—121no—
490C3×C4—21no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—44no—
495C3×C4—42no—
496C3×C4—42no—
497C3×C4—122no—
498C3×C4D3×C22⋊C411yescharacteristic
499C3×C4D3×C22⋊C411yescharacteristic
500C3×C4#67⋊C411yescharacteristic
501C3×C4#88311yescharacteristic
502C3×C4#88411yescharacteristic
503C3×C4#88411yescharacteristic
504C3×C4#89311yescharacteristic
505C3×C4#89411yescharacteristic
506Dic3—42no—
507Dic3—64no—
508Dic3—62no—
509Dic3—62no—
510Dic3—122no—
511Dic3—122no—
512Dic3—121no—
513Dic3—121no—
514Dic3—121no—
515Dic3—121no—
516C32#188311yescharacteristic, complemented, Sylow
517C23—62no—
518C23—122no—
519C23—122no—
520C23—121no—
521C23—121no—
522C23—181no—
523C23C2×#62611yescharacteristic
524Q8—92no—
525Q8—181no—
526D4—62no—
527D4—62no—
528D4—92no—
529D4—121no—
530D4—121no—
531D4—182no—
532D4—182no—
533D4—181no—
534C2×C4—22no—
535C2×C4—42no—
536C2×C4—62no—
537C2×C4—121no—
538C2×C4—121no—
539C2×C4—181no—
540C2×C4—182no—
541C2×C4—182no—
542C2×C4—181no—
543C2×C4—181no—
544C2×C4—722no—
545C2×C4#379611yescharacteristic
546C2×C4#379811yescharacteristic
547C2×C4C4×D3211yescharacteristic
548C2×C4#380211yescharacteristic
549C2×C4#381111yescharacteristic
550C2×C4#381111yescharacteristic
551C8—62no—
552C8—121no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—41no—
561C2×C3—41no—
562C2×C3—242no—
563C2×C3#466511yescharacteristic
564C2×C3#474711yescharacteristic
565C2×C3#475311yescharacteristic
566C2×C3#495611yescharacteristic
567C2×C3#506211yescharacteristic
568C2×C3#507711yescharacteristic
569D3—82no—
570D3—124no—
571D3—122no—
572D3—122no—
573C22—21no—
574C22—21no—
575C22—124no—
576C22—122no—
577C22—182no—
578C22—242no—
579C22—241no—
580C22—241no—
581C22—361no—
582C22—361no—
583C22C4×#62611yescharacteristic
584C22#6391611yescharacteristic
585C22#6398111yescharacteristic
586C4—42no—
587C4—122no—
588C4—182no—
589C4—361no—
590C4—361no—
591C4#6385311yescharacteristic
592C4#6388111yescharacteristic
593C4#6391211yescharacteristic
594C4#6392111yescharacteristic
595C3—21no—
596C3#6900511yescharacteristic, complemented
597C3#6966311yescharacteristic, complemented
598C2—21no—
599C2—21no—
600C2—242no—
601C2—362no—
602C2#1059138711yescharacteristic
603C2#1059151111yescharacteristic
604C2#1059164711yescharacteristic
subgroupG/H
centerC22#63981
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC2×#63830C2
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1883
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595975C2semidirect
3. C3×#4988C2semidirect
4. C2×#63570C2semidirect
5. #10591086C2semidirect
6. C3×#4530C2semidirect
7. #10589162C2semidirect
24. #63830C4semidirect
39. #4988D3semidirect
43. #4530D3semidirect
63. C2×C3×D12C2×C4semidirect
79. C3×#208C2×C4semidirect
154. C4⋊(C3⋊D3)C22⋊C4semidirect
159. #634C22⋊C4semidirect
215. C2×D12C4×D3semidirect
269. #208C4×D3semidirect
516. C32#1883semidirect
596. C3#69005semidirect
597. C3#69663semidirect

Maximal subgroups

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

subgroupindex
#105959752
C2×#638302
C3×#49882
C2×#635702
#105910862
C3×#45302
#105891622
#696633
#690053