Finite Group Databasebeta

← #11895174

Subgroups — #11895174

Order 1152.

880 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#634C211yesmaximal, characteristic
2#10593864C211yesmaximal, characteristic, complemented
3C3×#5019C211yesmaximal, characteristic
4C3×C4×#214C211yesmaximal, characteristic
5#10591497C212yesmaximal
6#10591445C212yesmaximal
7#10590567C212yesmaximal, complemented
8#10590497C212yesmaximal, complemented
9#10590301C211yesmaximal, characteristic, complemented
10#10590287C211yesmaximal, characteristic, complemented
11#10590254C211yesmaximal, characteristic, complemented
12#80414—31nomaximal
13#79619—31nomaximal
14C22×#634—21no—
15C32×C4×D4C2211yescharacteristic
16D4×C3⋊Dic3C2212yes—
17#64133—21no—
18#64097C2212yes—
19#64087—22no—
20#64078C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C2×C3×#214C2211yescharacteristic
23C2×C3×#214C2212yes—
24C3×#869C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63873C2212yes—
27#63869—21no—
28#63847—22no—
29#63844—21no—
30#63843C2212yes—
31C3×#832C2211yescharacteristic
32C3×#810C2212yes—
33C3×#810C2211yescharacteristic
34C3×#808C2211yescharacteristic
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63573C2212yes—
38#63572C2212yes—
39#63566C2212yes—
40#63566C2212yes—
41#63566C2212yes—
42#63553C2212yes—
43#5721—31no—
44#5567—31no—
45D4×Dic6—31no—
46D4×Dic6—31no—
47D4×Dic6—61no—
48C3×#461—31no—
49C3×C4×SD16—31no—
50#5162—32no—
51#5162—32no—
52Dic3×SD16—32no—
53#5079—31no—
54#5020—31no—
55#5019D311yescharacteristic
56C4×#214D311yescharacteristic
57#4854—32no—
58#4851—31no—
59#4830—31no—
60#4792—32no—
61#4792—32no—
62#4791—32no—
63#4758—32no—
64#4681—31no—
65C8×Dic6—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×Dic6C2312yes—
74C2×C3×Dic6C2311yescharacteristic
75C32×C4⋊C4C2311yescharacteristic
76C32×C22⋊C4—21no—
77C32×C42C2311yescharacteristic
78#3757—22no—
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)D411yescharacteristic
81C4⋊(C3⋊Dic3)C2312yes—
82#3750—22no—
83#3750D412yes—
84C4×C3⋊Dic3C2312yes—
85C3×#214—22no—
86C3×#214—24no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—21no—
91C3×C4×Dic3—21no—
92C2×C3×C3⋊C8C2312yes—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95#3724—22no—
96#3724—22no—
97Dic3⋊Dic3—22no—
98Dic32—22no—
99#3359—91noSylow
100C22×Dic6—61no—
101C22×Dic6—61no—
102C22×Dic6—62no—
103C2×C3×SD16—32no—
104C2×C3×SD16—31no—
105C3×C4⋊Q8—31no—
106C3×C4×Q8—31no—
107C3×C4×D4—21no—
108C3×C4×D4C2×D311yescharacteristic
109C3×C4×D4C2×D311yescharacteristic
110Q8×Dic3—32no—
111#944—32no—
112#944—32no—
113D4×Dic3—32no—
114D4×Dic3—32no—
115D4×Dic3—62no—
116C2×#214C2×D311yescharacteristic
117C2×#214C2×D312yes—
118#924—61no—
119#924—61no—
120#924—62no—
121#890—61no—
122#889—62no—
123#889—62no—
124#888—32no—
125#888—32no—
126#888—62no—
127#887—32no—
128#887—61no—
129#878—62no—
130#878—62no—
131#878—64no—
132#870—61no—
133#869—31no—
134#869—31no—
135#869—61no—
136#869C2×D311yescharacteristic
137C4×Dic6—31no—
138C4×Dic6—31no—
139C4×Dic6—61no—
140C4×Dic6—61no—
141C4×Dic6C2×D311yescharacteristic
142C3×#106—31no—
143C3×C4⋊C8—31no—
144C3×#103—32no—
145C3×#103—31no—
146C3×#102—31no—
147C3×C4×C8—31no—
148#835—32no—
149#835—32no—
150#835—32no—
151#832C2×D311yescharacteristic
152#817—32no—
153#816—32no—
154#816—32no—
155#816—32no—
156Dic3⋊C8—32no—
157Dic3⋊C8—32no—
158C8×Dic3—32no—
159C8×Dic3—32no—
160#810C2×D311yescharacteristic
161#810C2×D312yes—
162#808—32no—
163#808C2×D311yescharacteristic
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C4×C3⋊C8C2×D311yescharacteristic
166C23×C32—21no—
167C32×D4—21no—
168C32×D4#4112yes—
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—42no—
179#634—44no—
180#634SD1614yescomplemented
181C2×C3×Dic3—21no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—21no—
184C3×Dic6—21no—
185C3×Dic6—22no—
186C3×Dic6—22no—
187C3×Dic6—21no—
188C3×C3⋊C8—21no—
189C3×C3⋊C8—22no—
190C3×C3⋊C8—21no—
191#557—91no—
192D4×Q8—91no—
193#487—91no—
194#487—92no—
195#475—92no—
196#475—91no—
197#461—31no—
198#461—92no—
199C8×Q8—91no—
200C4×SD16—31no—
201C4×SD16—92no—
202C2×C3×Q8—31no—
203C2×C3×Q8—32no—
204C2×C3×D4—21no—
205C2×C3×D4C22×D311yescharacteristic
206C2×C3×D4C22×D311yescharacteristic
207C22×C3×C4—22no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×Dic3—62no—
211C22×Dic3—62no—
212C22×Dic3—64no—
213C2×Dic6—31no—
214C2×Dic6—31no—
215C2×Dic6—61no—
216C2×Dic6—62no—
217C2×Dic6—62no—
218C2×Dic6—62no—
219C2×Dic6—64no—
220C2×Dic6—61no—
221C2×Dic6—61no—
222C2×Dic6—124no—
223C2×Dic6—124no—
224C2×Dic6—128no—
225C2×Dic6C22×D311yescharacteristic
226C2×Dic6C22×D312yes—
227C3×SD16—64no—
228C3×SD16—62no—
229C2×C3×C8—31no—
230C2×C3×C8—32no—
231C2×C3×C8—31no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—31no—
234C3×C4⋊C4—61no—
235C3×C4⋊C4—61no—
236C3×C4⋊C4—61no—
237C3×C4⋊C4C22×D311yescharacteristic
238C3×C4⋊C4C22×D311yescharacteristic
239C3×C22⋊C4—22no—
240C3×C22⋊C4—21no—
241C3×C22⋊C4—21no—
242C3×C42—21no—
243C3×C42—61no—
244C3×C42C22×D311yescharacteristic
245C3×C42C22×D311yescharacteristic
246#217—62no—
247#217—62no—
248#217—64no—
249#214—22no—
250#214—24no—
251C4⋊Dic3—21no—
252C4⋊Dic3—21no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255C4⋊Dic3—32no—
256C4⋊Dic3—32no—
257C4⋊Dic3—61no—
258C4⋊Dic3—62no—
259C4⋊Dic3—62no—
260C4⋊Dic3—62no—
261C4⋊Dic3—61no—
262C4⋊Dic3—61no—
263C4⋊Dic3C22×D311yescharacteristic
264Dic3⋊C4—21no—
265Dic3⋊C4—32no—
266Dic3⋊C4—32no—
267Dic3⋊C4—62no—
268Dic3⋊C4—62no—
269Dic3⋊C4—62no—
270Dic3⋊C4—62no—
271Dic3⋊C4—62no—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274Dic3⋊C4—62no—
275Dic3⋊C4—64no—
276C4×Dic3—21no—
277C4×Dic3—32no—
278C4×Dic3—32no—
279C4×Dic3—62no—
280C4×Dic3—62no—
281C4×Dic3—62no—
282C2×C3⋊C8C22×D311yescharacteristic
283C2×C3⋊C8C22×D311yescharacteristic
284C2×C3⋊C8C22×D312yes—
285C22×C32—22no—
286C22×C32—41no—
287C22×C32—41no—
288C22×C32C22×D411yescharacteristic
289C32×C4—21no—
290C32×C4—41no—
291C32×C4C2×SD1612yes—
292C32×C4C2×#4111yescharacteristic
293C32×C42−1+411yescharacteristic
294C3⋊Dic3—22no—
295C3⋊Dic3—42no—
296C3⋊Dic3C2×SD1614yes—
297C3×Dic3—41no—
298C3×Dic3—42no—
299C3×Dic3—41no—
300C22×Q8—181no—
301C2×SD16—31no—
302C2×SD16—32no—
303C4⋊Q8—31no—
304C4⋊Q8—92no—
305C4⋊Q8—92no—
306C4⋊Q8—91no—
307#125—181no—
308#125—182no—
309C22⋊Q8—182no—
310C22⋊Q8—181no—
311C4×Q8—31no—
312C4×Q8—91no—
313C4×Q8—92no—
314C4×Q8—181no—
315C4×D4—92no—
316C4×D4D3211yescharacteristic
317#106—31no—
318#106—92no—
319C4⋊C8—31no—
320C4⋊C8—92no—
321#103—31no—
322#103—32no—
323#103—92no—
324#103—92no—
325#103—92no—
326#102—31no—
327C4×C8—31no—
328C4×C8—92no—
329C23×C3—22no—
330C23×C3—21no—
331C23×C3—21no—
332C3×Q8—62no—
333C3×Q8—61no—
334C3×Q8—62no—
335C3×Q8—61no—
336C3×D4—22no—
337C3×D4—21no—
338C3×D4—21no—
339C3×D4—22no—
340C3×D4#23512yes—
341C3×D4#23712yes—
342C2×C3×C4—22no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—44no—
349C2×C3×C4—42no—
350C2×C3×C4—42no—
351C2×C3×C4—61no—
352C2×C3×C4—62no—
353C2×C3×C4—61no—
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×Dic3—21no—
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—124no—
373C2×Dic3—124no—
374C2×Dic3—128no—
375Dic6—21no—
376Dic6—22no—
377Dic6—21no—
378Dic6—22no—
379Dic6—34no—
380Dic6—34no—
381Dic6—64no—
382Dic6—124no—
383Dic6—124no—
384Dic6—128no—
385Dic6—124no—
386Dic6—122no—
387Dic6—122no—
388C3×C8—62no—
389C3×C8—61no—
390C3×C8—61no—
391C3⋊C8—21no—
392C3⋊C8—22no—
393C3⋊C8—21no—
394C2×C32—42no—
395C2×C32#54811yescharacteristic
396C2×C32C22×SD1611yescharacteristic
397C2×C32#57811yescharacteristic
398C2×Q8—31no—
399C2×Q8—32no—
400C2×Q8—91no—
401C2×Q8—182no—
402C2×Q8—181no—
403C2×Q8—364no—
404C2×D4C2×D3211yescharacteristic
405C22×C4—21no—
406C22×C4—182no—
407SD16—62no—
408SD16—64no—
409C2×C8—31no—
410C2×C8—31no—
411C2×C8—32no—
412C4⋊C4—31no—
413C4⋊C4—61no—
414C4⋊C4—61no—
415C4⋊C4—61no—
416C4⋊C4—92no—
417C4⋊C4—91no—
418C4⋊C4—92no—
419C4⋊C4—182no—
420C4⋊C4—182no—
421C4⋊C4—182no—
422C4⋊C4—182no—
423C4⋊C4—181no—
424C4⋊C4C2×D3211yescharacteristic
425C22⋊C4—21no—
426C22⋊C4—182no—
427C42—61no—
428C42—92no—
429C42—182no—
430C42C2×D3211yescharacteristic
431C22×C3—24no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—21no—
435C22×C3—42no—
436C22×C3—42no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3C2×D3×D411yescharacteristic
442C22×C3C2×D3×D411yescharacteristic
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—22no—
448C3×C4—41no—
449C3×C4—42no—
450C3×C4—41no—
451C3×C4—41no—
452C3×C4—121no—
453C3×C4—122no—
454C3×C4—121no—
455C3×C4D3×SD1612yes—
456C3×C4D3×SD1612yes—
457C3×C4C2×#23511yescharacteristic
458C3×C4C2×#23711yescharacteristic
459C3×C4#101011yescharacteristic
460C3×C4#101011yescharacteristic
461Dic3—34no—
462Dic3—34no—
463Dic3—41no—
464Dic3—41no—
465Dic3—42no—
466Dic3—64no—
467Dic3—62no—
468Dic3—62no—
469Dic3—122no—
470Dic3—124no—
471Dic3—122no—
472Dic3—122no—
473C32#335911yescharacteristic, complemented, Sylow
474C23—21no—
475Q8—61no—
476Q8—62no—
477Q8—61no—
478Q8—62no—
479Q8—94no—
480Q8—364no—
481Q8—362no—
482D4—21no—
483D4#379512yes—
484C2×C4—21no—
485C2×C4—42no—
486C2×C4—61no—
487C2×C4—61no—
488C2×C4—62no—
489C2×C4—92no—
490C2×C4—92no—
491C2×C4—182no—
492C2×C4—364no—
493C2×C4#381111yescharacteristic
494C2×C4#381111yescharacteristic
495C2×C4C22×D3211yescharacteristic
496C8—61no—
497C8—62no—
498C8—61no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—44no—
503C2×C3—42no—
504C2×C3—42no—
505C2×C3#555211yescharacteristic
506C2×C3#559811yescharacteristic
507C2×C3C2×D3×SD1611yescharacteristic
508C2×C3C2×D3×SD1611yescharacteristic
509C2×C3#577111yescharacteristic
510C2×C3#577911yescharacteristic
511C22—22no—
512C22—41no—
513C22—41no—
514C22C2×#381111yescharacteristic
515C4—21no—
516C4—41no—
517C4—94no—
518C4—121no—
519C4—122no—
520C4—121no—
521C4—182no—
522C4—362no—
523C4#6393012yes—
524C4C2×#379511yescharacteristic
525C4#6429811yescharacteristic
526C3—21no—
527C3#7961911yescharacteristic, complemented
528C3#8041411yescharacteristic, complemented
529C2—42no—
530C2#1059491811yescharacteristic
531C2C2×#6393011yescharacteristic
532C2#1059547211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenterC4×D4D32
hypocenterC32#3359
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
2. #10593864C2semidirect
7. #10590567C2semidirect
8. #10590497C2semidirect
9. #10590301C2semidirect
10. #10590287C2semidirect
11. #10590254C2semidirect
180. #634SD16semidirect
473. C32#3359semidirect
527. C3#79619semidirect
528. C3#80414semidirect

Maximal subgroups

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

subgroupindex
D4×#6342
#105938642
C3×#50192
C3×C4×#2142
#105914972
#105914452
#105905672
#105904972
#105903012
#105902872
#105902542
#804143
#796193