Finite Group Databasebeta

← #11895862

Subgroups — #11895862

Order 1152.

850 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596013C211yesmaximal, characteristic, complemented
2#10593904C211yesmaximal, characteristic, complemented
3C3×C4×#213C211yesmaximal, characteristic
4C3×#5007C211yesmaximal, characteristic, complemented
5#10591496C212yesmaximal, complemented
6#10591434C212yesmaximal
7#10590461C212yesmaximal, complemented
8#10590432C212yesmaximal, complemented
9#10590365C211yesmaximal, characteristic, complemented
10#10590296C211yesmaximal, characteristic, complemented
11#10590288C211yesmaximal, characteristic, complemented
12#80993—31nomaximal
13#79571—31nomaximal
14C2×D3×Dic6—21no—
15C32×C4×D4C2211yescharacteristic
16#64145C2212yes—
17#64135—21no—
18#64133—21no—
19#64096C2212yes—
20#64088—22no—
21#64078C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C3×C4×D12C2211yescharacteristic
25C3×#869C2211yescharacteristic
26#63919C2212yes—
27#63899—22no—
28#63898C2212yes—
29#63856—21no—
30C2×#3716C2212yes—
31C3×#832C2211yescharacteristic
32C3×#832C2212yes—
33C3×#809C2211yescharacteristic
34C3×#807C2212yes—
35C3×#807C2211yescharacteristic
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37C3×C4×C3⋊C8C2211yescharacteristic
38#63572C2212yes—
39#63567C2212yes—
40#63567C2212yes—
41#63567C2212yes—
42#63555C2212yes—
43#5727—31no—
44#5542—31no—
45#5542—31no—
46#5542—61no—
47D4×Dic6—31no—
48C3×#474—31no—
49C3×C4×D8—31no—
50#5153—32no—
51#5093—31no—
52#5019—31no—
53C4×#213D311yescharacteristic
54#5007D311yescharacteristic, complemented
55#4889—32no—
56#4875—32no—
57#4875—32no—
58#4841—31no—
59#4831—31no—
60#4787—32no—
61#4765—32no—
62#4765—32no—
63#4757—32no—
64#4681—31no—
65#4679—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#634D411yescharacteristic
69C2×#634C2312yes—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6—21no—
73C2×#627—22no—
74C2×D3×Dic3—22no—
75D3×Dic6—44no—
76C32×C4⋊C4C2311yescharacteristic
77C32×C22⋊C4—21no—
78C32×C42C2311yescharacteristic
79#3757—22no—
80#3757—22no—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)D411yescharacteristic
84#3750—22no—
85#3750D412yes—
86C4×C3⋊Dic3—22no—
87C4×C3⋊Dic3C2312yes—
88C3×#213—22no—
89C3×(C2×D3)⋊C4—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2312yes—
92C3×C4⋊Dic3C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2312yes—
96#3724—22no—
97(C2×D3)⋊Dic3—22no—
98#3716—24no—
99#3367—91noSylow
100C2×D3×Q8—61no—
101C22×Dic6—61no—
102C2×C3×D8—31no—
103C3×C4⋊Q8—31no—
104C3×C4×D4—21no—
105C3×C4×D4—31no—
106C3×C4×D4C2×D311yescharacteristic
107C3×C4×D4C2×D311yescharacteristic
108#946—61no—
109#936—32no—
110#936—32no—
111#936—62no—
112D4×Dic3—32no—
113C2×#214—32no—
114C2×#213C2×D311yescharacteristic
115#926—61no—
116#926—61no—
117#926—62no—
118#924—61no—
119#924—61no—
120#924—61no—
121#924—62no—
122C2×#204—32no—
123#896—62no—
124#893—32no—
125#888—32no—
126#888—32no—
127#887—32no—
128#887—32no—
129#887—62no—
130#879—62no—
131#879—62no—
132#879—64no—
133#878—62no—
134C4×D12C2×D311yescharacteristic
135#869—31no—
136#869—31no—
137#869—61no—
138#869C2×D311yescharacteristic
139C4×Dic6—31no—
140C4×Dic6—31no—
141C4×Dic6—61no—
142C3×#107—31no—
143C3×#107—32no—
144C3×C4⋊C8—31no—
145C3×#102—31no—
146C3×#102—32no—
147C3×#102—31no—
148C3×C4×C8—31no—
149#832C2×D312yes—
150#832C2×D311yescharacteristic
151#816—32no—
152#816—32no—
153#816—32no—
154#815—32no—
155#815—32no—
156Dic3⋊C8—32no—
157Dic3⋊C8—32no—
158#810—32no—
159#810—32no—
160#810—32no—
161#809C2×D311yescharacteristic
162#807C2×D311yescharacteristic
163#807C2×D312yes—
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C4×C3⋊C8C2×D311yescharacteristic
166C23×C32—21no—
167C22×C3×D3—21no—
168C32×D4—21no—
169C32×D4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—42no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3C2×D412yes—
177C2×C3⋊Dic3C2×D412yes—
178#634—22no—
179#634—22no—
180#634—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—21no—
183C3×D12—21no—
184C3×D12#4112yes—
185C3×C4×D3—42no—
186C3×Dic6—42no—
187#627—44no—
188D3×Dic3—44no—
189C3×C3⋊C8—22no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192#556—91no—
193D4×Q8—91no—
194#489—92no—
195#487—91no—
196#477—92no—
197#474—31no—
198#463—92no—
199#461—91no—
200#446—91no—
201#440—92no—
202C4×D8—31no—
203C2×C3×Q8—61no—
204C2×C3×D4—21no—
205C2×C3×D4—31no—
206C2×C3×D4C22×D311yescharacteristic
207C2×C3×D4C22×D311yescharacteristic
208C22×C3×C4—22no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—61no—
212C22×Dic3—62no—
213D3×Q8—124no—
214C2×D12C22×D311yescharacteristic
215C2×C4×D3—21no—
216C2×C4×D3—62no—
217C2×Dic6—21no—
218C2×Dic6—31no—
219C2×Dic6—31no—
220C2×Dic6—32no—
221C2×Dic6—32no—
222C2×Dic6—61no—
223C2×Dic6—62no—
224C2×Dic6—62no—
225C2×Dic6—62no—
226C2×Dic6—124no—
227C3×D8—62no—
228C2×C3×C8—31no—
229C2×C3×C8—32no—
230C2×C3×C8—31no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—31no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—61no—
235C3×C4⋊C4C22×D311yescharacteristic
236C3×C4⋊C4C22×D311yescharacteristic
237C3×C22⋊C4—22no—
238C3×C22⋊C4—21no—
239C3×C22⋊C4—21no—
240C3×C22⋊C4—61no—
241C3×C42—21no—
242C3×C42C22×D311yescharacteristic
243C3×C42C22×D311yescharacteristic
244#217—62no—
245#217—62no—
246#217—62no—
247#217—62no—
248#217—62no—
249#217—64no—
250#217—64no—
251#214—64no—
252#213—22no—
253(C2×D3)⋊C4—21no—
254(C2×D3)⋊C4—62no—
255C4⋊Dic3—21no—
256C4⋊Dic3—31no—
257C4⋊Dic3—31no—
258C4⋊Dic3—61no—
259C4⋊Dic3—62no—
260C4⋊Dic3—62no—
261C4⋊Dic3—61no—
262C4⋊Dic3—61no—
263C4⋊Dic3—61no—
264C4⋊Dic3—61no—
265C4⋊Dic3C22×D312yes—
266C4⋊Dic3C22×D311yescharacteristic
267Dic3⋊C4—32no—
268Dic3⋊C4—32no—
269Dic3⋊C4—62no—
270Dic3⋊C4—62no—
271Dic3⋊C4—62no—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274Dic3⋊C4—64no—
275C4×Dic3—32no—
276C4×Dic3—32no—
277C4×Dic3—62no—
278C4×Dic3—62no—
279C4×Dic3—62no—
280C4×Dic3—64no—
281C2×C3⋊C8C22×D311yescharacteristic
282C2×C3⋊C8C22×D311yescharacteristic
283C2×C3⋊C8C22×D312yes—
284#204—64no—
285C22×C32—41no—
286C22×C32—41no—
287C22×C32—41no—
288C22×C32C22×D411yescharacteristic
289C2×C3×D3—22no—
290C2×C3×D3—41no—
291C2×C3×D3—41no—
292C32×C4—21no—
293C32×C4—41no—
294C32×C4AGL(1,ℤ/8)12yes—
295C32×C4C2×#4111yescharacteristic
296C32×C42−1+411yescharacteristic
297C3⋊Dic3—22no—
298C3⋊Dic3—22no—
299C3⋊Dic3—42no—
300C3×Dic3—42no—
301C3×Dic3—41no—
302C22×Q8—181no—
303C2×SD16—92no—
304C2×D8—31no—
305C4⋊Q8—31no—
306C4⋊Q8—92no—
307C4⋊Q8—91no—
308#126—182no—
309#124—92no—
310C22⋊Q8—182no—
311C22⋊Q8—181no—
312C22⋊Q8—181no—
313C4×Q8—91no—
314C4×Q8—92no—
315C4×D4—31no—
316C4×D4—92no—
317C4×D4D3211yescharacteristic
318#117—181no—
319#107—31no—
320#107—32no—
321C4⋊C8—31no—
322C4⋊C8—92no—
323#103—92no—
324#103—92no—
325#103—92no—
326#102—31no—
327#102—32no—
328#102—31no—
329#97—92no—
330C4×C8—31no—
331C23×C3—22no—
332C23×C3—21no—
333C23×C3—21no—
334C23×C3—61no—
335C22×D3—21no—
336C3×Q8—122no—
337C3×D4—21no—
338C3×D4—21no—
339C3×D4—21no—
340C3×D4—21no—
341C3×D4—32no—
342C3×D4—41no—
343C3×D4—41no—
344C3×D4—61no—
345C2×C3×C4—22no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—44no—
352C2×C3×C4—42no—
353C2×C3×C4—42no—
354C2×C3×C4—61no—
355C2×C3×C4—62no—
356C2×C3×C4—122no—
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4C23×D311yescharacteristic
362C2×C3×C4C23×D311yescharacteristic
363C2×Dic3—21no—
364C2×Dic3—22no—
365C2×Dic3—32no—
366C2×Dic3—32no—
367C2×Dic3—32no—
368C2×Dic3—32no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—64no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—124no—
375D12—21no—
376D12#23512yes—
377C4×D3—42no—
378C4×D3—124no—
379Dic6—42no—
380Dic6—62no—
381Dic6—62no—
382Dic6—62no—
383Dic6—62no—
384Dic6—62no—
385Dic6—62no—
386Dic6—122no—
387Dic6—122no—
388Dic6—122no—
389Dic6—124no—
390Dic6—124no—
391C3×C8—62no—
392C3×C8—61no—
393C3×C8—61no—
394C3⋊C8—21no—
395C3⋊C8—22no—
396C3⋊C8—21no—
397C2×C32—81no—
398C2×C32#54811yescharacteristic
399C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
400C2×C32#57811yescharacteristic
401C3×D3—42no—
402C2×Q8—61no—
403C2×Q8—91no—
404C2×Q8—92no—
405C2×Q8—182no—
406C2×Q8—364no—
407C2×D4—31no—
408C2×D4C2×D3211yescharacteristic
409C22×C4—21no—
410C22×C4—61no—
411C22×C4—182no—
412SD16—184no—
413D8—62no—
414C2×C8—31no—
415C2×C8—31no—
416C2×C8—32no—
417C4⋊C4—31no—
418C4⋊C4—32no—
419C4⋊C4—61no—
420C4⋊C4—91no—
421C4⋊C4—92no—
422C4⋊C4—182no—
423C4⋊C4—182no—
424C4⋊C4—181no—
425C4⋊C4—181no—
426C4⋊C4C2×D3211yescharacteristic
427C22⋊C4—21no—
428C22⋊C4—61no—
429C22⋊C4—182no—
430C22⋊C4—182no—
431C22⋊C4—182no—
432C42—92no—
433C42—182no—
434C42C2×D3211yescharacteristic
435C22×C3—21no—
436C22×C3—42no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—62no—
446C22×C3—121no—
447C22×C3—121no—
448C22×C3C2×D3×D411yescharacteristic
449C22×C3C2×D3×D411yescharacteristic
450C2×D3—22no—
451C2×D3—41no—
452C2×D3—41no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—22no—
458C3×C4—41no—
459C3×C4—42no—
460C3×C4—41no—
461C3×C4—41no—
462C3×C4—121no—
463C3×C4—122no—
464C3×C4#91112yes—
465C3×C4#91112yes—
466C3×C4C2×#23511yescharacteristic
467C3×C4#100711yescharacteristic
468C3×C4D3×#4111yescharacteristic
469C3×C4#101011yescharacteristic
470Dic3—42no—
471Dic3—41no—
472Dic3—62no—
473Dic3—62no—
474Dic3—62no—
475Dic3—62no—
476Dic3—122no—
477Dic3—122no—
478Dic3—124no—
479Dic3—122no—
480Dic3—122no—
481C32#336711yescharacteristic, complemented, Sylow
482C23—21no—
483C23—61no—
484Q8—122no—
485Q8—182no—
486Q8—182no—
487Q8—182no—
488Q8—364no—
489D4—21no—
490D4—21no—
491D4—32no—
492D4—61no—
493C2×C4—21no—
494C2×C4—42no—
495C2×C4—61no—
496C2×C4—62no—
497C2×C4—92no—
498C2×C4—92no—
499C2×C4—122no—
500C2×C4—182no—
501C2×C4—364no—
502C2×C4#381111yescharacteristic
503C2×C4#381111yescharacteristic
504C2×C4C22×D3211yescharacteristic
505C8—61no—
506C8—61no—
507C8—62no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—82no—
512C2×C3—81no—
513C2×C3—81no—
514C2×C3—122no—
515C2×C3#555211yescharacteristic
516C2×C3#563311yescharacteristic
517C2×C3C2×#91111yescharacteristic
518C2×C3C2×#91111yescharacteristic
519C2×C3#577111yescharacteristic
520C2×C3#577911yescharacteristic
521D3—42no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22—62no—
526C22—121no—
527C22—121no—
528C22C2×#381111yescharacteristic
529C4—21no—
530C4—41no—
531C4—121no—
532C4—122no—
533C4—182no—
534C4—182no—
535C4—362no—
536C4#6392712yes—
537C4#6429711yescharacteristic
538C4D3×#23511yescharacteristic
539C3—21no—
540C3#7957111yescharacteristic, complemented
541C3#8099311yescharacteristic, complemented
542C2—81no—
543C2—122no—
544C2#1059491611yescharacteristic
545C2C2×#6392711yescharacteristic
546C2#1059547211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenterC4×D4D32
hypocenterC32#3367
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596013C2semidirect
2. #10593904C2semidirect
4. C3×#5007C2semidirect
5. #10591496C2semidirect
7. #10590461C2semidirect
8. #10590432C2semidirect
9. #10590365C2semidirect
10. #10590296C2semidirect
11. #10590288C2semidirect
54. #5007D3semidirect
481. C32#3367semidirect
540. C3#79571semidirect
541. C3#80993semidirect

Maximal subgroups

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

subgroupindex
#105960132
#105939042
C3×C4×#2132
C3×#50072
#105914962
#105914342
#105904612
#105904322
#105903652
#105902962
#105902882
#809933
#795713