Finite Group Databasebeta

← #11895965

Subgroups — #11895965

Order 1152.

818 conjugacy classes of subgroups.

The subgroup lattice has 541 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5553C211yesmaximal, characteristic
2#10593860C211yesmaximal, characteristic, complemented
3#10592706C211yesmaximal, characteristic, complemented
4C3×C4×#214C211yesmaximal, characteristic, complemented
5#10591477C212yesmaximal, complemented
6#10591438C212yesmaximal, complemented
7#10590545C212yesmaximal, complemented
8#10590478C212yesmaximal, complemented
9#10590364C211yesmaximal, characteristic, complemented
10#10590273C211yesmaximal, characteristic, complemented
11#10590258C211yesmaximal, characteristic, complemented
12#83587—31nomaximal
13#79625—31nomaximal
14C2×C3×#235—21no—
15C32×C4×D4C2211yescharacteristic
16#64078C2211yescharacteristic
17C3×#940C2212yes—
18C2×C3×#214C2211yescharacteristic
19C3×#930—21no—
20C3×#893C2212yes—
21C3×#884—22no—
22C3×#874C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63869C2212yes—
26#63866—21no—
27#63845—22no—
28#63844—21no—
29Dic3×Dic6C2212yes—
30C2×#3715C2212yes—
31#63659C2212yes—
32#63634C2212yes—
33C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
34C3×#832C2211yescharacteristic
35C3×#810C2211yescharacteristic
36C3×#808C2211yescharacteristic
37C3×C4×C3⋊C8C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63563C2212yes—
40#63563C2212yes—
41#63562C2212yes—
42#63554C2212yes—
43C3×#550—31no—
44#5570—31no—
45#5567—31no—
46#5553D311yescharacteristic
47C3×C4×SD16—31no—
48#5163—32no—
49#5075—32no—
50#5075—31no—
51#5071—32no—
52#5070—31no—
53#5027—31no—
54#5024—31no—
55#5018—32no—
56C4×#214D311yescharacteristic, complemented
57#5009—32no—
58#5007—31no—
59#5007—31no—
60#5007—61no—
61#4871—32no—
62#4817—32no—
63#4764—32no—
64#4694—31no—
65#4679—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#634—21no—
69C2×C3×#67—22no—
70C2×C3×#67—22no—
71C3×#235—44no—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12C2312yes—
75C2×C3×C4×D3—22no—
76C2×C3×Dic6D411yescharacteristic
77C2×C3×Dic6C2311yescharacteristic
78C32×C4⋊C4C2311yescharacteristic
79C32×C22⋊C4—21no—
80C32×C42C2311yescharacteristic
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)C2312yes—
83C2×C3⋊(C3⋊C8)C2312yes—
84C3×#214—22no—
85C3×(C2×D3)⋊C4—22no—
86C3×C4⋊Dic3D411yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—21no—
89C3×Dic3⋊C4D412yes—
90C3×C4×Dic3—21no—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94#3724—22no—
95Dic3⋊Dic3—22no—
96Dic3⋊Dic3—22no—
97Dic32—22no—
98#3715—24no—
99#3368—91noSylow
100C2×C3×#41—61no—
101C2×#235—21no—
102C2×C3×SD16—31no—
103C3×#127—32no—
104C3×#127—31no—
105C3×#121—62no—
106C3×#121—61no—
107C3×C4×Q8—31no—
108C3×C4×Q8—31no—
109C3×C4×D4—21no—
110C3×C4×D4—32no—
111C3×C4×D4C2×D311yescharacteristic
112C3×C4×D4C2×D311yescharacteristic
113Q8×Dic3—32no—
114#944—61no—
115C2×#215—32no—
116#940C2×D312yes—
117C2×#214—32no—
118C2×#214C2×D311yescharacteristic
119#930—21no—
120#893C2×D312yes—
121#890—32no—
122#890—62no—
123#889—62no—
124#887—61no—
125#884—22no—
126#874C2×D311yescharacteristic
127#870—32no—
128#869—31no—
129#869—31no—
130#869—61no—
131#869—61no—
132C4×Dic6—32no—
133C4×Dic6—61no—
134C4×Dic6C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C3×#106—31no—
137C3×#103—31no—
138C3×#102—31no—
139C3×C4×C8—31no—
140#832—32no—
141#832—32no—
142#832—32no—
143#832—32no—
144#832—32no—
145#832—62no—
146#832C2×D311yescharacteristic
147#821—32no—
148#821—32no—
149#815—32no—
150Dic3⋊C8—32no—
151#810C2×D311yescharacteristic
152#809—32no—
153#808C2×D311yescharacteristic
154#807—32no—
155#807—32no—
156#807—62no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—31no—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)—61no—
161#803—32no—
162C4×C3⋊C8C2×D311yescharacteristic
163C23×C32—21no—
164C22×C3×D3—22no—
165C32×D4—21no—
166C32×D4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—42no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—22no—
173#634—42no—
174C3×#67—44no—
175C3×#67—82no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C3×D12—22no—
181C3×D12—22no—
182C3×D12—42no—
183C3×D12—81no—
184C3×C4×D3—44no—
185C3×Dic6—22no—
186C3×Dic6—21no—
187C3×Dic6#4112yescomplemented
188C3⋊(C3⋊C8)—22no—
189C3×C3⋊C8—21no—
190C3×C3⋊C8—21no—
191#557—91no—
192#550—31no—
193#490—92no—
194#486—91no—
195#478—92no—
196#474—91no—
197#460—91no—
198#460—92no—
199#446—91no—
200#440—92no—
201C4×SD16—31no—
202C3×#41—124no—
203C2×C3×Q8—31no—
204C2×C3×Q8—31no—
205C2×C3×D4—21no—
206C2×C3×D4—32no—
207C2×C3×D4—62no—
208C2×C3×D4—62no—
209C2×C3×D4—61no—
210C2×C3×D4—61no—
211C2×C3×D4C22×D311yescharacteristic
212C2×C3×D4C22×D311yescharacteristic
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—41no—
216C22×C3×C4—62no—
217C2×#67—22no—
218C2×#67—22no—
219#235—44no—
220C2×D12—21no—
221C2×D12—21no—
222C2×D12C22×D312yes—
223C2×C4×D3—22no—
224C2×Dic6—61no—
225C2×Dic6—61no—
226C2×Dic6—121no—
227C2×Dic6#6711yescharacteristic
228C2×Dic6C22×D311yescharacteristic
229C3×SD16—62no—
230C2×C3×C8—31no—
231C2×C3×C8—31no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—31no—
234C3×C4⋊C4—32no—
235C3×C4⋊C4—31no—
236C3×C4⋊C4—61no—
237C3×C4⋊C4C22×D311yescharacteristic
238C3×C4⋊C4C22×D311yescharacteristic
239C3×C22⋊C4—21no—
240C3×C22⋊C4—21no—
241C3×C22⋊C4—41no—
242C3×C22⋊C4—62no—
243C3×C42—21no—
244C3×C42—32no—
245C3×C42—61no—
246C3×C42C22×D311yescharacteristic
247C3×C42C22×D311yescharacteristic
248#215—64no—
249#214—22no—
250#214—64no—
251(C2×D3)⋊C4—22no—
252C4⋊Dic3—32no—
253C4⋊Dic3—32no—
254C4⋊Dic3—62no—
255C4⋊Dic3—61no—
256C4⋊Dic3—61no—
257C4⋊Dic3—62no—
258C4⋊Dic3—62no—
259C4⋊Dic3—121no—
260C4⋊Dic3#6711yescharacteristic
261C4⋊Dic3C22×D311yescharacteristic
262Dic3⋊C4—21no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4#6712yes—
268C4×Dic3—21no—
269C4×Dic3—62no—
270C4×Dic3—62no—
271C4×Dic3C22×D312yes—
272C2×C3⋊C8—32no—
273C2×C3⋊C8—32no—
274C2×C3⋊C8—62no—
275C2×C3⋊C8C22×D311yescharacteristic
276C2×C3⋊C8C22×D311yescharacteristic
277C22×C32—41no—
278C22×C32—41no—
279C22×C32—41no—
280C22×C32C22×D411yescharacteristic
281C2×C3×D3—42no—
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C32×C4—21no—
285C32×C4—41no—
286C32×C4AGL(1,ℤ/8)12yes—
287C32×C4C2×#4111yescharacteristic
288C32×C42−1+411yescharacteristic
289C3⋊Dic3—42no—
290C3×Dic3—22no—
291C3×Dic3—22no—
292C3×Dic3—22no—
293C3×Dic3—41no—
294C2×#41—61no—
295C2×SD16—31no—
296C2×SD16—92no—
297C4⋊Q8—91no—
298C4⋊Q8—181no—
299#127—32no—
300#127—31no—
301#125—92no—
302#125—182no—
303#121—62no—
304#121—61no—
305C4×Q8—31no—
306C4×Q8—31no—
307C4×Q8—92no—
308C4×Q8—181no—
309C4×D4—32no—
310C4×D4D3211yescharacteristic
311#107—92no—
312#106—31no—
313C4⋊C8—92no—
314C4⋊C8—91no—
315#103—31no—
316#102—31no—
317#102—92no—
318#102—92no—
319#102—92no—
320#102—92no—
321#97—92no—
322C4×C8—31no—
323C23×C3—21no—
324C23×C3—21no—
325C23×C3—41no—
326C23×C3—62no—
327C22×D3—22no—
328C3×Q8—32no—
329C3×Q8—62no—
330C3×Q8—61no—
331C3×D4—22no—
332C3×D4—21no—
333C3×D4—21no—
334C3×D4—21no—
335C3×D4—21no—
336C3×D4—41no—
337C3×D4—62no—
338C3×D4—62no—
339C3×D4—124no—
340C3×D4—122no—
341C3×D4—241no—
342C3×D4—242no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—41no—
351C2×C3×C4—42no—
352C2×C3×C4—42no—
353C2×C3×C4—61no—
354C2×C3×C4—61no—
355C2×C3×C4—82no—
356C2×C3×C4—124no—
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C23×D311yescharacteristic
362C2×C3×C4C23×D311yescharacteristic
363#67—44no—
364#67—82no—
365C2×Dic3—21no—
366C2×Dic3—21no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—122no—
370C2×Dic3C2×#6712yes—
371C2×Dic3C2×#6712yes—
372D12—22no—
373D12—22no—
374D12—42no—
375D12—81no—
376C4×D3—44no—
377Dic6—22no—
378Dic6—21no—
379Dic6—122no—
380Dic6—122no—
381Dic6—242no—
382Dic6#23512yescomplemented
383C3×C8—61no—
384C3×C8—61no—
385C3⋊C8—21no—
386C3⋊C8—21no—
387C3⋊C8—62no—
388C3⋊C8—62no—
389C3⋊C8—122no—
390C2×C32—81no—
391C2×C32#54811yescharacteristic
392C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
393C2×C32#57711yescharacteristic
394C3×D3—82no—
395#41—124no—
396C2×Q8—31no—
397C2×Q8—31no—
398C2×Q8—181no—
399C2×D4—32no—
400C2×D4—62no—
401C2×D4—62no—
402C2×D4—61no—
403C2×D4—61no—
404C2×D4C2×D3211yescharacteristic
405C22×C4—21no—
406C22×C4—62no—
407SD16—62no—
408SD16—184no—
409C2×C8—31no—
410C2×C8—31no—
411C2×C8—92no—
412C4⋊C4—31no—
413C4⋊C4—32no—
414C4⋊C4—31no—
415C4⋊C4—61no—
416C4⋊C4—92no—
417C4⋊C4—182no—
418C4⋊C4—182no—
419C4⋊C4—182no—
420C4⋊C4—181no—
421C4⋊C4C2×D3211yescharacteristic
422C22⋊C4—21no—
423C22⋊C4—62no—
424C42—32no—
425C42—61no—
426C42—182no—
427C42C2×D3211yescharacteristic
428C22×C3—21no—
429C22×C3—42no—
430C22×C3—41no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3—41no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—81no—
437C22×C3—81no—
438C22×C3—122no—
439C22×C3—122no—
440C22×C3—122no—
441C22×C3C2×D3×D411yescharacteristic
442C22×C3C22×#6711yescharacteristic
443C2×D3—42no—
444C2×D3—42no—
445C2×D3—42no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—22no—
451C3×C4—41no—
452C3×C4—41no—
453C3×C4—41no—
454C3×C4—62no—
455C3×C4—62no—
456C3×C4—62no—
457C3×C4—81no—
458C3×C4—121no—
459C3×C4#91412yes—
460C3×C4#93212yes—
461C3×C4C2×#23511yescharacteristic
462C3×C4D3×#4111yescharacteristic
463C3×C4#101011yescharacteristic
464C3×C4#101011yescharacteristic
465Dic3—22no—
466Dic3—22no—
467Dic3—22no—
468Dic3—41no—
469Dic3—122no—
470Dic3—122no—
471Dic3—242no—
472C32#336811yescharacteristic, complemented, Sylow
473C23—21no—
474C23—62no—
475Q8—32no—
476Q8—61no—
477Q8—62no—
478Q8—362no—
479D4—21no—
480D4—21no—
481D4—62no—
482D4—62no—
483D4—124no—
484D4—122no—
485D4—241no—
486D4—242no—
487C2×C4—21no—
488C2×C4—32no—
489C2×C4—32no—
490C2×C4—42no—
491C2×C4—61no—
492C2×C4—61no—
493C2×C4—124no—
494C2×C4—182no—
495C2×C4D3×#6711yescharacteristic
496C2×C4D3×#6711yescharacteristic
497C2×C4C22×D3211yescharacteristic
498C8—61no—
499C8—61no—
500C8—182no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—82no—
505C2×C3—81no—
506C2×C3—81no—
507C2×C3—242no—
508C2×C3#555211yescharacteristic
509C2×C3C2×#91411yescharacteristic
510C2×C3#577011yescharacteristic
511C2×C3C2×#93211yescharacteristic
512C2×C3#583111yescharacteristic
513C2×C3#583611yescharacteristic
514D3—82no—
515C22—41no—
516C22—41no—
517C22—41no—
518C22—122no—
519C22—122no—
520C22—122no—
521C22C2×D3×#6711yescharacteristic
522C4—21no—
523C4—41no—
524C4—62no—
525C4—62no—
526C4—62no—
527C4—121no—
528C4—362no—
529C4#6393412yes—
530C4#6429811yescharacteristic
531C4D3×#23511yescharacteristic
532C3—21no—
533C3#7962511yescharacteristic, complemented
534C3#8358711yescharacteristic, complemented
535C2—81no—
536C2—242no—
537C2#1059489911yescharacteristic
538C2C2×#6393411yescharacteristic
539C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#5553C2
hypercenterC4×D4D32
hypocenterC32#3368
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. #10593860C2semidirect
3. #10592706C2semidirect
4. C3×C4×#214C2semidirect
5. #10591477C2semidirect
6. #10591438C2semidirect
7. #10590545C2semidirect
8. #10590478C2semidirect
9. #10590364C2semidirect
10. #10590273C2semidirect
11. #10590258C2semidirect
56. C4×#214D3semidirect
187. C3×Dic6#41semidirect
382. Dic6#235semidirect
472. C32#3368semidirect
533. C3#79625semidirect
534. C3#83587semidirect

Maximal subgroups

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

subgroupindex
C3×#55532
#105938602
#105927062
C3×C4×#2142
#105914772
#105914382
#105905452
#105904782
#105903642
#105902732
#105902582
#835873
#796253