Finite Group Databasebeta

← #11897573

Subgroups — #11897573

Order 1152.

862 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596201C211yesmaximal, characteristic, complemented
2#10593904C211yesmaximal, characteristic, complemented
3C3×#5084C211yesmaximal, characteristic, complemented
4C3×#5080C211yesmaximal, characteristic, complemented
5#10590564C212yesmaximal, complemented
6#10590474C212yesmaximal, complemented
7#10590462C212yesmaximal
8#10590433C212yesmaximal, complemented
9C4×#3714C211yesmaximal, characteristic
10#10590313C211yesmaximal, characteristic, complemented
11#10590296C211yesmaximal, characteristic, complemented
12#81905—31nomaximal
13#81089—31nomaximal
14C2×D3×Dic6—21no—
15C32×C4⋊Q8C2211yescharacteristic
16#64155—22no—
17#64106—21no—
18#64102C2212yes—
19C4⋊C4×C3⋊D3—21no—
20#64099C2212yes—
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×#869C2211yescharacteristic
25#63919C2212yes—
26#63899—22no—
27#63898C2212yes—
28#63856—21no—
29C2×#3714C2211yescharacteristic
30C3×#809C2212yes—
31C3×#808C2212yes—
32C3×#808C2212yes—
33C3×#808C2212yes—
34C3×C4⋊(C3⋊C8)C2211yescharacteristic
35C3×C4×C3⋊C8C2211yescharacteristic
36#63575C2212yes—
37#63575C2211yescharacteristic
38#63572C2212yes—
39#63564C2212yes—
40#63564C2211yescharacteristic
41#63563C2211yescharacteristic
42#63555C2212yes—
43#5730—31no—
44#5730—31no—
45#5730—61no—
46#5727—31no—
47D4×Dic6—31no—
48C3×#498—31no—
49C3×#476—31no—
50#5087—31no—
51#5084D311yescharacteristic, complemented
52#5080D311yescharacteristic, complemented
53C4×#213—31no—
54#4871—32no—
55#4870—32no—
56#4870—32no—
57#4869—32no—
58#4856—32no—
59#4856—32no—
60#4846—31no—
61#4831—31no—
62#4785—32no—
63#4766—32no—
64C4×D24—31no—
65#4679—31no—
66C2×C32×Q8—21no—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C4×C3⋊D3—22no—
70C2×#634D411yescharacteristic
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×Dic6—21no—
74C2×#627—22no—
75C2×D3×Dic3—22no—
76D3×Dic6—44no—
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2312yes—
79C32×C42C2311yescharacteristic
80#3752—21no—
81#3752—22no—
82C4⋊(C3⋊Dic3)—22no—
83C4⋊(C3⋊Dic3)D411yescharacteristic
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85#3750—22no—
86#3750D412yes—
87C4×C3⋊Dic3C2312yes—
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
95#3724—22no—
96(C2×D3)⋊Dic3—22no—
97#3714Q814yescomplemented
98#3384—91noSylow
99C2×D3×Q8—61no—
100C22×Dic6—61no—
101C3×C4⋊Q8—21no—
102C3×C4⋊Q8—31no—
103C3×C4⋊Q8C2×D311yescharacteristic
104C3×C4⋊Q8C2×D311yescharacteristic
105C3×C4×D4—31no—
106#946—62no—
107#946—62no—
108#946—61no—
109#946—64no—
110D4×Dic3—32no—
111C2×#213—31no—
112#924—61no—
113C2×D24—31no—
114#897—61no—
115#897—61no—
116#897—62no—
117#896—62no—
118#893—32no—
119#893—32no—
120#893—32no—
121#893—62no—
122D3×C4⋊C4—61no—
123D3×C4⋊C4—61no—
124D3×C4⋊C4—62no—
125#890—32no—
126#890—32no—
127#890—62no—
128#888—32no—
129#888—32no—
130#878—62no—
131C4×D12—31no—
132C4×D12—31no—
133C4×D12—61no—
134C4×D12C2×D311yescharacteristic
135#869C2×D311yescharacteristic
136C4×Dic6—31no—
137C4×Dic6—31no—
138C4×Dic6—61no—
139C3×#106—32no—
140C3×#106—32no—
141C3×#106—32no—
142C3×C4⋊C8—31no—
143C3×#102—32no—
144C3×C4×C8—31no—
145#832—31no—
146#821—31no—
147#821—31no—
148#821—32no—
149#818—31no—
150#818—32no—
151#815—32no—
152#815—32no—
153Dic3⋊C8—32no—
154Dic3⋊C8—32no—
155#809—32no—
156#809—31no—
157#809C2×D312yes—
158#808C2×D312yes—
159#808C2×D312yes—
160#808C2×D312yes—
161#807—32no—
162#807—31no—
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C4×C3⋊C8C2×D311yescharacteristic
165C22×C3⋊D3—21no—
166C22×C3×D3—21no—
167C32×Q8—81no—
168C2×C32×C4—22no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3C2×D412yes—
174C2×C3⋊Dic3C2×D412yes—
175C4⋊(C3⋊D3)—21no—
176C4⋊(C3⋊D3)C2×Q812yescomplemented
177C4×C3⋊D3—42no—
178C4×C3⋊D3—82no—
179#634—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—21no—
182C3×D12—21no—
183C3×D12C2×Q812yes—
184C3×C4×D3—42no—
185C3×Dic6—42no—
186#627—44no—
187D3×Dic3—44no—
188C3×C3⋊C8—21no—
189C3×C3⋊C8—22no—
190C3×C3⋊C8C2×Q812yescomplemented
191#554—91no—
192D4×Q8—91no—
193#501—92no—
194#498—31no—
195#478—92no—
196#476—31no—
197#476—92no—
198#474—91no—
199#446—91no—
200#442—92no—
201C4×D8—91no—
202C2×C3×Q8—22no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—61no—
206C2×C3×D4—31no—
207C22×C3×C4—61no—
208C22×Dic3—62no—
209D3×Q8—124no—
210C2×D12—31no—
211C2×D12—31no—
212C2×D12—61no—
213C2×D12C22×D311yescharacteristic
214C2×C4×D3—21no—
215C2×C4×D3—62no—
216C2×C4×D3—62no—
217C2×C4×D3—61no—
218C2×C4×D3—61no—
219C2×C4×D3—62no—
220C2×C4×D3—62no—
221C2×C4×D3—64no—
222C2×Dic6—21no—
223C2×Dic6—31no—
224C2×Dic6—31no—
225C2×Dic6—61no—
226C2×Dic6—62no—
227C2×Dic6—62no—
228C2×Dic6—124no—
229C2×C3×C8—31no—
230C2×C3×C8—31no—
231C2×C3×C8—32no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—22no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—32no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4C22×D312yes—
240C3×C4⋊C4C22×D312yes—
241C3×C22⋊C4—61no—
242C3×C42—21no—
243C3×C42C22×D311yescharacteristic
244C3×C42C22×D311yescharacteristic
245#217—62no—
246#213—34no—
247(C2×D3)⋊C4—21no—
248(C2×D3)⋊C4—62no—
249(C2×D3)⋊C4—62no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—61no—
254(C2×D3)⋊C4—61no—
255C4⋊Dic3—21no—
256C4⋊Dic3—31no—
257C4⋊Dic3—31no—
258C4⋊Dic3—31no—
259C4⋊Dic3—31no—
260C4⋊Dic3—61no—
261C4⋊Dic3—61no—
262C4⋊Dic3—62no—
263C4⋊Dic3—62no—
264C4⋊Dic3—64no—
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—
278C2×C3⋊C8C22×D311yescharacteristic
279C2×C3⋊C8C22×D312yes—
280C2×C3⋊C8C22×D311yescharacteristic
281D24—34no—
282C22×C32C22×D411yescharacteristic
283C2×C3⋊D3—22no—
284C2×C3⋊D3—41no—
285C2×C3⋊D3—41no—
286C2×C3×D3—22no—
287C2×C3×D3—41no—
288C2×C3×D3—41no—
289C32×C4—21no—
290C32×C4—42no—
291C32×C4AGL(1,ℤ/8)12yes—
292C32×C4C22×Q811yescharacteristic
293C32×C42−1+411yescharacteristic
294C3⋊Dic3—22no—
295C3⋊Dic3—22no—
296C3⋊Dic3—41no—
297C3×Dic3—42no—
298C3×Dic3—41no—
299C22×Q8—181no—
300C2×D8—91no—
301C4⋊Q8—31no—
302C4⋊Q8—92no—
303C4⋊Q8D3211yescharacteristic
304#125—92no—
305C22⋊Q8—182no—
306C22⋊Q8—181no—
307C22⋊Q8—181no—
308C22⋊Q8—182no—
309C4×Q8—91no—
310C4×D4—31no—
311C4×D4—92no—
312C4×D4—92no—
313C4×D4—91no—
314C2×C4⋊C4—181no—
315#107—91no—
316#107—92no—
317#106—32no—
318#106—32no—
319#106—32no—
320C4⋊C8—31no—
321C4⋊C8—92no—
322#102—32no—
323#102—91no—
324#102—92no—
325#102—91no—
326#97—92no—
327C4×C8—31no—
328C23×C3—61no—
329C22×D3—21no—
330C22×D3—62no—
331C22×D3—61no—
332C22×D3—61no—
333C3×Q8—81no—
334C3×Q8—81no—
335C3×Q8—82no—
336C3×Q8—122no—
337C3×D4—32no—
338C3×D4—61no—
339C2×C3×C4—24no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—61no—
346C2×C3×C4—62no—
347C2×C3×C4—122no—
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×Dic3—21no—
355C2×Dic3—22no—
356C2×Dic3—32no—
357C2×Dic3—32no—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—124no—
366D12—21no—
367D12—32no—
368D12—32no—
369D12—62no—
370D12—62no—
371D12—61no—
372D12—61no—
373D12D3×Q812yes—
374C4×D3—42no—
375C4×D3—124no—
376C4×D3—124no—
377C4×D3—122no—
378C4×D3—122no—
379C4×D3—242no—
380C4×D3—242no—
381C4×D3—244no—
382Dic6—42no—
383Dic6—62no—
384Dic6—62no—
385Dic6—122no—
386Dic6—124no—
387Dic6—124no—
388C3×C8—32no—
389C3×C8—62no—
390C3×C8—61no—
391C3⋊C8—21no—
392C3⋊C8—22no—
393C3⋊C8D3×Q812yescomplemented
394C2×C32D4×Q811yescharacteristic
395C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
396C2×C32#57711yescharacteristic
397C3⋊D3—42no—
398C3×D3—42no—
399C2×Q8—21no—
400C2×Q8—61no—
401C2×Q8—91no—
402C2×Q8—182no—
403C2×Q8—364no—
404C2×D4—31no—
405C2×D4—91no—
406C22×C4—61no—
407C22×C4—182no—
408C22×C4—182no—
409C22×C4—181no—
410D8—94no—
411C2×C8—31no—
412C2×C8—31no—
413C2×C8—32no—
414C4⋊C4—21no—
415C4⋊C4—31no—
416C4⋊C4—32no—
417C4⋊C4—61no—
418C4⋊C4—91no—
419C4⋊C4—92no—
420C4⋊C4—91no—
421C4⋊C4—182no—
422C4⋊C4—182no—
423C4⋊C4—182no—
424C4⋊C4C2×D3212yes—
425C22⋊C4—61no—
426C22⋊C4—182no—
427C22⋊C4—182no—
428C22⋊C4—181no—
429C42—92no—
430C42C2×D3211yescharacteristic
431C22×C3—21no—
432C22×C3—62no—
433C22×C3—121no—
434C22×C3—121no—
435C22×C3C2×D3×D411yescharacteristic
436C22×C3C2×D3×D411yescharacteristic
437C2×D3—22no—
438C2×D3—41no—
439C2×D3—41no—
440C2×D3—64no—
441C2×D3—62no—
442C2×D3—62no—
443C2×D3—122no—
444C2×D3—122no—
445C2×D3—121no—
446C2×D3—121no—
447C2×D3—121no—
448C2×D3—121no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—22no—
454C3×C4—41no—
455C3×C4—44no—
456C3×C4—42no—
457C3×C4—42no—
458C3×C4—121no—
459C3×C4—122no—
460C3×C4#91412yes—
461C3×C4#91412yes—
462C3×C4C2×D3×Q811yescharacteristic
463C3×C4C2×D3×Q811yescharacteristic
464C3×C4#100711yescharacteristic
465C3×C4#101011yescharacteristic
466Dic3—42no—
467Dic3—41no—
468Dic3—62no—
469Dic3—62no—
470Dic3—62no—
471Dic3—62no—
472Dic3—122no—
473Dic3—122no—
474Dic3—122no—
475Dic3—121no—
476Dic3—121no—
477C32#338411yescharacteristic, complemented, Sylow
478C23—61no—
479C23—181no—
480Q8—81no—
481Q8—122no—
482Q8—182no—
483Q8—364no—
484D4—32no—
485D4—61no—
486D4—92no—
487D4—181no—
488C2×C4—22no—
489C2×C4—61no—
490C2×C4—62no—
491C2×C4—92no—
492C2×C4—92no—
493C2×C4—122no—
494C2×C4—181no—
495C2×C4—364no—
496C2×C4—362no—
497C2×C4—722no—
498C2×C4#381111yescharacteristic
499C2×C4#381111yescharacteristic
500C2×C4C22×D3211yescharacteristic
501C8—32no—
502C8—61no—
503C8—62no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—122no—
508C2×C3#563211yescharacteristic
509C2×C3#572711yescharacteristic
510C2×C3C2×#91411yescharacteristic
511C2×C3C2×#91411yescharacteristic
512C2×C3#576211yescharacteristic
513C2×C3#577511yescharacteristic
514D3—42no—
515D3—124no—
516D3—122no—
517D3—122no—
518C22—62no—
519C22—121no—
520C22—121no—
521C22—182no—
522C22—361no—
523C22—361no—
524C22C2×#381111yescharacteristic
525C4—21no—
526C4—42no—
527C4—121no—
528C4—122no—
529C4—182no—
530C4—182no—
531C4—361no—
532C4#6394112yes—
533C4#6431511yescharacteristic
534C4D32×Q811yescharacteristic
535C3—21no—
536C3#8108911yescharacteristic, complemented
537C3#8190511yescharacteristic, complemented
538C2—122no—
539C2—362no—
540C2#1059511511yescharacteristic
541C2C2×#6394111yescharacteristic
542C2#1059536111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
hypercenterC4⋊Q8D32
hypocenterC32#3384
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596201C2semidirect
2. #10593904C2semidirect
3. C3×#5084C2semidirect
4. C3×#5080C2semidirect
5. #10590564C2semidirect
6. #10590474C2semidirect
8. #10590433C2semidirect
10. #10590313C2semidirect
11. #10590296C2semidirect
51. #5084D3semidirect
52. #5080D3semidirect
97. #3714Q8semidirect
176. C4⋊(C3⋊D3)C2×Q8semidirect
190. C3×C3⋊C8C2×Q8semidirect
393. C3⋊C8D3×Q8semidirect
477. C32#3384semidirect
536. C3#81089semidirect
537. C3#81905semidirect

Maximal subgroups

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

subgroupindex
#105962012
#105939042
C3×#50842
C3×#50802
#105905642
#105904742
#105904622
#105904332
C4×#37142
#105903132
#105902962
#819053
#810893