Finite Group Databasebeta

← #11897557

Subgroups — #11897557

Order 1152.

888 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#634C211yesmaximal, characteristic, complemented
2#10593956C211yesmaximal, characteristic, complemented
3C3×C4×#213C211yesmaximal, characteristic
4C3×#5008C211yesmaximal, characteristic, complemented
5#10591479C212yesmaximal, complemented
6#10591436C212yesmaximal
7#10590546C212yesmaximal, complemented
8#10590472C212yesmaximal, complemented
9#10590303C211yesmaximal, characteristic, complemented
10#10590296C211yesmaximal, characteristic, complemented
11#10590272C211yesmaximal, characteristic, complemented
12#81089—31nomaximal
13#79576—31nomaximal
14C22×#634—21no—
15C32×C4×D4C2211yescharacteristic
16D4×C3⋊Dic3C2212yes—
17#64133—21no—
18#64097C2212yes—
19#64087—22no—
20#64078C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C2×C3×#213C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×#869C2211yescharacteristic
25#63898C2212yes—
26D3×C4⋊Dic3—21no—
27#63887—22no—
28#63872C2212yes—
29#63857—21no—
30C3×#832C2212yes—
31C3×#832C2211yescharacteristic
32C3×#809C2211yescharacteristic
33C3×#808C2212yes—
34C3×#807C2211yescharacteristic
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63575C2212yes—
38#63573C2212yes—
39#63573C2212yes—
40#63572C2212yes—
41#63563C2212yes—
42#63555C2212yes—
43#5730—31no—
44#5543—31no—
45D4×Dic6—31no—
46D4×Dic6—31no—
47D4×Dic6—61no—
48C3×#476—31no—
49C3×C4×D8—31no—
50#5152—32no—
51#5080—31no—
52C4×#213D311yescharacteristic
53#5008D311yescharacteristic, complemented
54#5007—31no—
55#4876—32no—
56#4870—32no—
57#4856—32no—
58#4846—31no—
59#4831—31no—
60#4785—32no—
61#4766—32no—
62#4763—32no—
63#4761—32no—
64#4680—31no—
65#4679—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C22×C3⋊Dic3—22no—
69C2×#634—21no—
70C2×#634—22no—
71C2×#634—44no—
72C2×#634D411yescharacteristic
73C2×C3×D12C2311yescharacteristic
74C2×C3×C4×D3—21no—
75C2×C3×Dic6—21no—
76C2×D3×Dic3—22no—
77C32×C4⋊C4C2311yescharacteristic
78C32×C22⋊C4—21no—
79C32×C42C2311yescharacteristic
80#3757—22no—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)D411yescharacteristic
83C4⋊(C3⋊Dic3)C2312yes—
84#3750—22no—
85#3750D412yes—
86C4×C3⋊Dic3C2312yes—
87C3×#213Q814yescomplemented
88C3×(C2×D3)⋊C4—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2312yes—
91C3×C4⋊Dic3C2311yescharacteristic
92C2×C3×C3⋊C8C2312yes—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95Dic3⋊Dic3—22no—
96Dic3⋊Dic3—22no—
97(C2×D3)⋊Dic3—22no—
98#3384—91noSylow
99C22×Dic6—61no—
100C22×Dic6—61no—
101C22×Dic6—62no—
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—62no—
109D4×Dic3—32no—
110D4×Dic3—32no—
111D4×Dic3—32no—
112D4×Dic3—62no—
113C2×#213C2×D311yescharacteristic
114C2×C4⋊Dic3—61no—
115#924—61no—
116#924—61no—
117#924—61no—
118#924—62no—
119#897—61no—
120#893—32no—
121D3×C4⋊C4—61no—
122#890—32no—
123#890—32no—
124#888—32no—
125#888—32no—
126#888—62no—
127#878—62no—
128#878—62no—
129#878—62no—
130#878—64no—
131C4×D12C2×D311yescharacteristic
132#869—31no—
133#869—31no—
134#869—61no—
135#869C2×D311yescharacteristic
136C4×Dic6—31no—
137C4×Dic6—31no—
138C4×Dic6—61no—
139C3×#107—31no—
140C3×#106—32no—
141C3×C4⋊C8—31no—
142C3×#102—31no—
143C3×#102—32no—
144C3×#102—31no—
145C3×C4×C8—31no—
146#832—32no—
147#832C2×D312yes—
148#832C2×D311yescharacteristic
149#821—32no—
150#818—32no—
151#817—32no—
152#817—32no—
153#815—32no—
154#815—32no—
155Dic3⋊C8—32no—
156Dic3⋊C8—32no—
157#809C2×D311yescharacteristic
158#808—32no—
159#808—32no—
160#808C2×D312yes—
161#807—32no—
162#807C2×D311yescharacteristic
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C4×C3⋊C8C2×D311yescharacteristic
165C23×C32—21no—
166C22×C3×D3—21no—
167C32×D4—21no—
168C32×D4C2×Q812yes—
169C2×C32×C4—21no—
170C2×C32×C4—42no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3—22no—
175C2×C3⋊Dic3—44no—
176C2×C3⋊Dic3C2×D412yes—
177C2×C3⋊Dic3C2×D412yes—
178#634—22no—
179#634—44no—
180#634—42no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—21no—
183C3×D12—21no—
184C3×D12C2×Q812yescomplemented
185C3×C4×D3—42no—
186C3×Dic6—81no—
187D3×Dic3—82no—
188C3×C3⋊C8—22no—
189C3×C3⋊C8—21no—
190C3×C3⋊C8C2×Q812yescomplemented
191#554—91no—
192D4×Q8—91no—
193#501—92no—
194#498—91no—
195#478—92no—
196#476—31no—
197#476—92no—
198#474—91no—
199#446—91no—
200#442—92no—
201C4×D8—31no—
202C2×C3×Q8—61no—
203C2×C3×D4—21no—
204C2×C3×D4—31no—
205C2×C3×D4C22×D311yescharacteristic
206C2×C3×D4C22×D311yescharacteristic
207C22×C3×C4—22no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—61no—
211C22×Dic3—62no—
212C22×Dic3—62no—
213C22×Dic3—62no—
214C22×Dic3—64no—
215C2×D12C22×D311yescharacteristic
216C2×C4×D3—21no—
217C2×C4×D3—62no—
218C2×Dic6—21no—
219C2×Dic6—31no—
220C2×Dic6—31no—
221C2×Dic6—61no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C2×Dic6—62no—
225C2×Dic6—64no—
226C2×Dic6—61no—
227C2×Dic6—61no—
228C2×Dic6—128no—
229C2×Dic6—124no—
230C2×Dic6—124no—
231C3×D8—34no—
232C2×C3×C8—31no—
233C2×C3×C8—31no—
234C2×C3×C8—32no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—32no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4C22×D311yescharacteristic
240C3×C4⋊C4C22×D311yescharacteristic
241C3×C22⋊C4—22no—
242C3×C22⋊C4—21no—
243C3×C22⋊C4—21no—
244C3×C22⋊C4—61no—
245C3×C42—21no—
246C3×C42C22×D311yescharacteristic
247C3×C42C22×D311yescharacteristic
248#217—62no—
249#217—62no—
250#217—62no—
251#217—64no—
252#213Dic614yescomplemented
253(C2×D3)⋊C4—21no—
254(C2×D3)⋊C4—62no—
255C4⋊Dic3—21no—
256C4⋊Dic3—31no—
257C4⋊Dic3—31no—
258C4⋊Dic3—32no—
259C4⋊Dic3—32no—
260C4⋊Dic3—61no—
261C4⋊Dic3—62no—
262C4⋊Dic3—62no—
263C4⋊Dic3—62no—
264C4⋊Dic3—62no—
265C4⋊Dic3—61no—
266C4⋊Dic3—61no—
267C4⋊Dic3C22×D311yescharacteristic
268C4⋊Dic3C22×D312yes—
269Dic3⋊C4—32no—
270Dic3⋊C4—32no—
271Dic3⋊C4—62no—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276Dic3⋊C4—64no—
277C4×Dic3—32no—
278C4×Dic3—32no—
279C4×Dic3—62no—
280C2×C3⋊C8C22×D311yescharacteristic
281C2×C3⋊C8C22×D312yes—
282C2×C3⋊C8C22×D311yescharacteristic
283C22×C32—22no—
284C22×C32—41no—
285C22×C32—41no—
286C22×C32C22×D411yescharacteristic
287C2×C3×D3—22no—
288C2×C3×D3—41no—
289C2×C3×D3—41no—
290C32×C4—21no—
291C32×C4—41no—
292C32×C4AGL(1,ℤ/8)12yes—
293C32×C4C22×Q811yescharacteristic
294C32×C42−1+411yescharacteristic
295C3⋊Dic3—22no—
296C3⋊Dic3—22no—
297C3⋊Dic3—42no—
298C3×Dic3—41no—
299C3×Dic3—42no—
300C22×Q8—181no—
301C2×D8—31no—
302C4⋊Q8—31no—
303C4⋊Q8—92no—
304C4⋊Q8—91no—
305#125—92no—
306C22⋊Q8—182no—
307C22⋊Q8—182no—
308C22⋊Q8—181no—
309C22⋊Q8—181no—
310C4×Q8—91no—
311C4×D4—31no—
312C4×D4—92no—
313C4×D4—92no—
314C4×D4D3211yescharacteristic
315C2×C4⋊C4—181no—
316#107—31no—
317#107—92no—
318#106—32no—
319#106—92no—
320#106—92no—
321C4⋊C8—31no—
322C4⋊C8—92no—
323#102—31no—
324#102—32no—
325#102—31no—
326#102—92no—
327#97—92no—
328C4×C8—31no—
329C23×C3—22no—
330C23×C3—21no—
331C23×C3—21no—
332C23×C3—61no—
333C22×D3—21no—
334C3×Q8—241no—
335C3×D4—22no—
336C3×D4—21no—
337C3×D4—21no—
338C3×D4—22no—
339C3×D4—32no—
340C3×D4—61no—
341C3×D4C2×Dic612yes—
342C3×D4D3×Q812yes—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—44no—
350C2×C3×C4—42no—
351C2×C3×C4—42no—
352C2×C3×C4—61no—
353C2×C3×C4—62no—
354C2×C3×C4—122no—
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361C2×Dic3—21no—
362C2×Dic3—22no—
363C2×Dic3—32no—
364C2×Dic3—32no—
365C2×Dic3—32no—
366C2×Dic3—32no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—64no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—128no—
373C2×Dic3—124no—
374C2×Dic3—124no—
375C2×Dic3—242no—
376D12—21no—
377D12C2×Dic612yescomplemented
378C4×D3—42no—
379C4×D3—242no—
380Dic6—64no—
381Dic6—62no—
382Dic6—62no—
383Dic6—81no—
384Dic6—128no—
385Dic6—124no—
386Dic6—124no—
387Dic6—124no—
388Dic6—122no—
389Dic6—122no—
390C3×C8—32no—
391C3×C8—61no—
392C3×C8—62no—
393C3⋊C8—22no—
394C3⋊C8—21no—
395C3⋊C8C2×Dic612yescomplemented
396C2×C32—42no—
397C2×C32D4×Q811yescharacteristic
398C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
399C2×C32#57711yescharacteristic
400C3×D3—42no—
401C2×Q8—61no—
402C2×Q8—91no—
403C2×Q8—182no—
404C2×Q8—181no—
405C2×Q8—364no—
406C2×D4—31no—
407C2×D4C2×D3211yescharacteristic
408C22×C4—21no—
409C22×C4—61no—
410C22×C4—182no—
411C22×C4—182no—
412D8—34no—
413C2×C8—31no—
414C2×C8—31no—
415C2×C8—32no—
416C4⋊C4—32no—
417C4⋊C4—31no—
418C4⋊C4—61no—
419C4⋊C4—91no—
420C4⋊C4—92no—
421C4⋊C4—92no—
422C4⋊C4—182no—
423C4⋊C4—182no—
424C4⋊C4—182no—
425C4⋊C4—181no—
426C4⋊C4C2×D3211yescharacteristic
427C22⋊C4—21no—
428C22⋊C4—61no—
429C22⋊C4—182no—
430C22⋊C4—182no—
431C42—92no—
432C42C2×D3211yescharacteristic
433C22×C3—24no—
434C22×C3—22no—
435C22×C3—22no—
436C22×C3—21no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—62no—
444C22×C3—121no—
445C22×C3—121no—
446C22×C3C2×D3×D411yescharacteristic
447C22×C3C2×D3×D411yescharacteristic
448C2×D3—22no—
449C2×D3—41no—
450C2×D3—41no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—22no—
456C3×C4—41no—
457C3×C4—42no—
458C3×C4—41no—
459C3×C4—41no—
460C3×C4—121no—
461C3×C4—122no—
462C3×C4#91112yes—
463C3×C4#91412yes—
464C3×C4C22×Dic611yescharacteristic
465C3×C4C2×D3×Q811yescharacteristic
466C3×C4#101011yescharacteristic
467C3×C4#101011yescharacteristic
468Dic3—41no—
469Dic3—42no—
470Dic3—64no—
471Dic3—62no—
472Dic3—62no—
473Dic3—62no—
474Dic3—62no—
475Dic3—122no—
476Dic3—124no—
477Dic3—122no—
478Dic3—122no—
479C32#338411yescharacteristic, complemented, Sylow
480C23—21no—
481C23—61no—
482Q8—182no—
483Q8—241no—
484Q8—364no—
485Q8—362no—
486D4—21no—
487D4—32no—
488D4—61no—
489D4D3×Dic612yes—
490C2×C4—21no—
491C2×C4—42no—
492C2×C4—61no—
493C2×C4—62no—
494C2×C4—92no—
495C2×C4—92no—
496C2×C4—122no—
497C2×C4—182no—
498C2×C4—364no—
499C2×C4—722no—
500C2×C4#381111yescharacteristic
501C2×C4#381111yescharacteristic
502C2×C4C22×D3211yescharacteristic
503C8—32no—
504C8—61no—
505C8—62no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—44no—
510C2×C3—42no—
511C2×C3—42no—
512C2×C3—122no—
513C2×C3D4×Dic611yescharacteristic
514C2×C3#563211yescharacteristic
515C2×C3C2×#91111yescharacteristic
516C2×C3C2×#91411yescharacteristic
517C2×C3#577011yescharacteristic
518C2×C3#577511yescharacteristic
519D3—42no—
520C22—22no—
521C22—41no—
522C22—41no—
523C22—62no—
524C22—121no—
525C22—121no—
526C22C2×#381111yescharacteristic
527C4—21no—
528C4—41no—
529C4—121no—
530C4—122no—
531C4—182no—
532C4—182no—
533C4—362no—
534C4#6393712yes—
535C4C2×D3×Dic611yescharacteristic
536C4#6429811yescharacteristic
537C3—21no—
538C3#7957611yescharacteristic, complemented
539C3#8108911yescharacteristic, complemented
540C2—42no—
541C2—122no—
542C2#1059491511yescharacteristic
543C2C2×#6393711yescharacteristic
544C2#1059546211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenterC4×D4D32
hypocenterC32#3384
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. D4×#634C2semidirect
2. #10593956C2semidirect
4. C3×#5008C2semidirect
5. #10591479C2semidirect
7. #10590546C2semidirect
8. #10590472C2semidirect
9. #10590303C2semidirect
10. #10590296C2semidirect
11. #10590272C2semidirect
53. #5008D3semidirect
87. C3×#213Q8semidirect
184. C3×D12C2×Q8semidirect
190. C3×C3⋊C8C2×Q8semidirect
252. #213Dic6semidirect
377. D12C2×Dic6semidirect
395. C3⋊C8C2×Dic6semidirect
479. C32#3384semidirect
538. C3#79576semidirect
539. C3#81089semidirect

Maximal subgroups

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

subgroupindex
D4×#6342
#105939562
C3×C4×#2132
C3×#50082
#105914792
#105914362
#105905462
#105904722
#105903032
#105902962
#105902722
#810893
#795763