Finite Group Databasebeta

← #11898310

Subgroups — #11898310

Order 1152.

879 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593902C211yesmaximal, characteristic
2#10593860C211yesmaximal, characteristic, complemented
3#10592392C211yesmaximal, characteristic, complemented
4C3×C4×#204C211yesmaximal, characteristic, complemented
5C3×C8×Dic6C211yesmaximal, characteristic, complemented
6#10590879C212yesmaximal, complemented
7#10590877C212yesmaximal, complemented
8#10590760C212yesmaximal, complemented
9#10590758C212yesmaximal, complemented
10#10590367C211yesmaximal, characteristic, complemented
11#10590365C211yesmaximal, characteristic, complemented
12#79911—31nomaximal
13#79637—31nomaximal
14C2×#3799—21no—
15C2×#3744C2212yes—
16C2×#3744C2212yes—
17#64083C2211yescharacteristic
18#64078C2211yescharacteristic
19C2×C3×#204C2211yescharacteristic
20C3×C4×D12C2211yescharacteristic
21C3×C4×Dic6C2211yescharacteristic
22C3×C4×Dic6C2211yescharacteristic
23#63911C2212yes—
24#63910—22no—
25#63909—21no—
26#63894C2212yes—
27#63869—21no—
28#63866C2212yes—
29#63845—22no—
30#63844C2212yes—
31Dic3×Dic6—21no—
32C2×#3717C2212yes—
33C2×#3716C2212yes—
34C32×C4×C8C2211yescharacteristic
35C3×#821C2211yescharacteristic
36C3×#817C2211yescharacteristic
37C3×#816C2211yescharacteristic
38C3×Dic3⋊C8C2212yes—
39C3×C8×Dic3C2212yes—
40C3×C4⋊(C3⋊C8)C2211yescharacteristic
41#63567C2212yes—
42#63564C2212yes—
43#5577—31no—
44#5570—31no—
45#5567—31no—
46#5553—31no—
47C3×C8×Q8—31no—
48C3×C4×SD16—31no—
49#5175—32no—
50#5027—31no—
51#5019—31no—
52#4852—32no—
53#4848—31no—
54#4848—32no—
55#4841—31no—
56#4841—32no—
57#4818—32no—
58#4762—32no—
59#4693—32no—
60#4693—31no—
61#4693—31no—
62#4693—61no—
63C4×#204—32no—
64C4×#204D311yescharacteristic, complemented
65C8×Dic6D311yescharacteristic, complemented
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)C2312yes—
69C2×#634C2312yes—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6C2311yescharacteristic
74C2×#626—22no—
75C2×#626—22no—
76C2×#624—22no—
77#3799—44no—
78C2×C32×C8C2311yescharacteristic
79C2×C32×C8C2311yescharacteristic
80C32×C42C2311yescharacteristic
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)—21no—
83#3744—24no—
84#3744—42no—
85C3×(C2×D3)⋊C4—21no—
86C3×C4⋊Dic3D411yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×C4⋊Dic3C2311yescharacteristic
89C3×Dic3⋊C4—21no—
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3—21no—
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8C2312yes—
94C3×#204—22no—
95#3724—22no—
96Dic3⋊Dic3—22no—
97Dic3⋊Dic3—22no—
98#3722—22no—
99Dic32—22no—
100#3717—42no—
101#3716—42no—
102#3392—91noSylow
103C2×#239—61no—
104C2×#235—61no—
105C2×C3×SD16—31no—
106C3×C4×Q8—31no—
107C3×C4×Q8—31no—
108C3×C4×D4—31no—
109Q8×Dic3—61no—
110#944—32no—
111C2×#215—32no—
112#940—32no—
113C2×#214—32no—
114#930—61no—
115C2×#204—32no—
116C2×#204—32no—
117C2×#204—32no—
118C2×#204—32no—
119C2×#204—32no—
120C2×#204—32no—
121C2×#204—62no—
122C2×#204—62no—
123C2×#204C2×D311yescharacteristic
124#895—62no—
125#895—61no—
126#893—32no—
127#890—61no—
128#890—62no—
129#889—62no—
130#887—32no—
131#884—62no—
132#874—32no—
133#874—31no—
134#874—31no—
135#874—61no—
136C4×D12—32no—
137C4×D12C2×D311yescharacteristic
138#870—61no—
139#869—32no—
140#869—31no—
141#869—31no—
142#869—61no—
143C4×Dic6—32no—
144C4×Dic6—61no—
145C4×Dic6C2×D311yescharacteristic
146C4×Dic6C2×D311yescharacteristic
147C3×#106—31no—
148C3×C4⋊C8—32no—
149C3×C4⋊C8—31no—
150C3×#103—31no—
151C3×#102—31no—
152C3×C4×C8—21no—
153C3×C4×C8—32no—
154C3×C4×C8C2×D311yescharacteristic
155C3×C4×C8C2×D311yescharacteristic
156#821—32no—
157#821C2×D311yescharacteristic
158#817C2×D311yescharacteristic
159#816—32no—
160#816C2×D311yescharacteristic
161Dic3⋊C8C2×D312yes—
162C8×Dic3C2×D312yes—
163#810—32no—
164#809—32no—
165C4⋊(C3⋊C8)C2×D311yescharacteristic
166C22×C3⋊D3—22no—
167C22×C3×D3—21no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3—22no—
172C4⋊(C3⋊D3)—22no—
173C4⋊(C3⋊D3)—22no—
174C4⋊(C3⋊D3)—42no—
175C4⋊(C3⋊D3)—81no—
176#634—22no—
177#634—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3C2×D412yes—
182C2×C3×Dic3C2×D412yes—
183C3×D12—21no—
184C3×D12—21no—
185C3×C4×D3—42no—
186C3×Dic6—21no—
187C3×Dic6—21no—
188C3×Dic6SD1614yescomplemented
189#626—44no—
190#626—82no—
191#624—44no—
192C32×C8—21no—
193C32×C8#4112yescomplemented
194C3×C3⋊C8—22no—
195#557—91no—
196#550—91no—
197#492—92no—
198#492—91no—
199#461—92no—
200#461—91no—
201#460—92no—
202#460—91no—
203C8×Q8—31no—
204C4×SD16—31no—
205C4×SD16—92no—
206C2×C3×Q8—31no—
207C2×C3×Q8—31no—
208C2×C3×D4—31no—
209C22×C3×C4—61no—
210C2×#67—62no—
211C2×#67—62no—
212#239—124no—
213#235—124no—
214C2×D12—32no—
215C2×D12—32no—
216C2×D12—62no—
217C2×D12—62no—
218C2×D12—61no—
219C2×D12—61no—
220C2×D12—62no—
221C2×D12—61no—
222C2×D12—61no—
223C2×D12—121no—
224C2×D12—121no—
225C2×D12C22×D311yescharacteristic
226C2×C4×D3—21no—
227C2×C4×D3—62no—
228C2×C4×D3—62no—
229C2×Dic6—32no—
230C2×Dic6—32no—
231C2×Dic6—62no—
232C2×Dic6D1211yescharacteristic
233C2×Dic6C22×D311yescharacteristic
234C3×SD16—62no—
235C2×C3×C8—21no—
236C2×C3×C8—21no—
237C2×C3×C8—32no—
238C2×C3×C8C22×D311yescharacteristic
239C2×C3×C8C22×D311yescharacteristic
240C2×C3×C8C22×D311yescharacteristic
241C2×C3×C8C22×D311yescharacteristic
242C3×C4⋊C4—32no—
243C3×C4⋊C4—31no—
244C3×C4⋊C4—31no—
245C3×C4⋊C4—31no—
246C3×C4⋊C4—61no—
247C3×C22⋊C4—61no—
248C3×C42—21no—
249C3×C42—32no—
250C3×C42—61no—
251C3×C42C22×D311yescharacteristic
252C3×C42C22×D311yescharacteristic
253#215—122no—
254#214—122no—
255(C2×D3)⋊C4—21no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—62no—
258C4⋊Dic3—62no—
259C4⋊Dic3—62no—
260C4⋊Dic3—61no—
261C4⋊Dic3—61no—
262C4⋊Dic3—61no—
263C4⋊Dic3—61no—
264C4⋊Dic3—121no—
265C4⋊Dic3—121no—
266C4⋊Dic3D1211yescharacteristic
267C4⋊Dic3C22×D311yescharacteristic
268C4⋊Dic3C22×D311yescharacteristic
269Dic3⋊C4—21no—
270Dic3⋊C4—62no—
271Dic3⋊C4—62no—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274Dic3⋊C4D1212yes—
275C4×Dic3—21no—
276C4×Dic3—62no—
277C4×Dic3—62no—
278C4×Dic3C22×D312yes—
279C2×C3⋊C8C22×D312yes—
280#204—22no—
281#204—64no—
282#204—64no—
283#204—124no—
284#204—122no—
285#204—122no—
286#204—124no—
287#204—122no—
288#204—122no—
289C22×C32C22×D411yescharacteristic
290C2×C3⋊D3—42no—
291C2×C3⋊D3—42no—
292C2×C3⋊D3—42no—
293C2×C3×D3—41no—
294C2×C3×D3—41no—
295C2×C3×D3—41no—
296C32×C4—21no—
297C32×C4C2×SD1612yes—
298C32×C4C2×#4111yescharacteristic
299C32×C4H(5,𝔽2)11yescharacteristic
300C3⋊Dic3—42no—
301C3×Dic3—22no—
302C3×Dic3—41no—
303C3×Dic3—41no—
304C3×Dic3—41no—
305C3×Dic3C2×SD1614yes—
306C2×#41—181no—
307C2×SD16—31no—
308C2×SD16—92no—
309C2×SD16—92no—
310C2×SD16—92no—
311C2×SD16—92no—
312C4⋊Q8—92no—
313C4⋊Q8—91no—
314#127—92no—
315#127—91no—
316#125—181no—
317#125—182no—
318#121—182no—
319#121—181no—
320C4×Q8—31no—
321C4×Q8—31no—
322C4×Q8—92no—
323C4×Q8—181no—
324C4×D4—31no—
325C4×D4—92no—
326#106—31no—
327C4⋊C8—32no—
328C4⋊C8—31no—
329#103—31no—
330#103—92no—
331#102—31no—
332#102—92no—
333C4×C8—32no—
334C4×C8D3211yescharacteristic
335C23×C3—61no—
336C22×D3—21no—
337C22×D3—62no—
338C22×D3—62no—
339C22×D3—122no—
340C3×Q8—34no—
341C3×Q8—61no—
342C3×Q8—61no—
343C3×D4—61no—
344C3×D4—61no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—61no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—122no—
354C2×C3×C4C2×D1211yescharacteristic
355C2×C3×C4C2×D1211yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360#67—124no—
361#67—242no—
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—122no—
368C2×Dic3C2×D1212yes—
369C2×Dic3C2×D1212yes—
370D12—21no—
371D12—21no—
372D12—62no—
373D12—62no—
374D12—62no—
375D12—62no—
376D12—122no—
377D12—122no—
378D12—124no—
379D12—122no—
380D12—122no—
381D12—242no—
382D12—241no—
383D12—241no—
384D12—242no—
385D12—242no—
386C4×D3—42no—
387C4×D3—124no—
388C4×D3—124no—
389Dic6—21no—
390Dic6—21no—
391Dic6—62no—
392Dic6—62no—
393Dic6—62no—
394Dic6—62no—
395Dic6—122no—
396Dic6—122no—
397Dic6#20414yescomplemented
398C3×C8—22no—
399C3×C8—21no—
400C3×C8—21no—
401C3×C8—22no—
402C3×C8—62no—
403C3×C8#23512yescomplemented
404C3×C8#23912yescomplemented
405C3⋊C8—22no—
406C2×C32#55011yescharacteristic
407C2×C32C22×SD1611yescharacteristic
408C2×C32#57711yescharacteristic
409C3⋊D3—82no—
410C3×D3—81no—
411#41—364no—
412C2×Q8—31no—
413C2×Q8—31no—
414C2×Q8—92no—
415C2×D4—31no—
416C2×D4—92no—
417C2×D4—182no—
418C2×D4—182no—
419C2×D4—181no—
420C2×D4—181no—
421C22×C4—61no—
422C22×C4—182no—
423SD16—62no—
424SD16—184no—
425SD16—362no—
426SD16—362no—
427SD16—362no—
428C2×C8—32no—
429C2×C8C2×D3211yescharacteristic
430C2×C8C2×D3211yescharacteristic
431C4⋊C4—32no—
432C4⋊C4—31no—
433C4⋊C4—31no—
434C4⋊C4—31no—
435C4⋊C4—61no—
436C4⋊C4—182no—
437C4⋊C4—182no—
438C4⋊C4—182no—
439C4⋊C4—181no—
440C4⋊C4—181no—
441C22⋊C4—61no—
442C22⋊C4—182no—
443C42—32no—
444C42—61no—
445C42—182no—
446C42C2×D3211yescharacteristic
447C22×C3—21no—
448C22×C3—121no—
449C22×C3—121no—
450C22×C3—121no—
451C22×C3C22×D1211yescharacteristic
452C22×C3C2×D3×D411yescharacteristic
453C2×D3—41no—
454C2×D3—41no—
455C2×D3—41no—
456C2×D3—122no—
457C2×D3—122no—
458C2×D3—122no—
459C2×D3—122no—
460C2×D3—122no—
461C2×D3—122no—
462C2×D3—242no—
463C2×D3—242no—
464C2×D3—242no—
465C3×C4—22no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—22no—
470C3×C4—21no—
471C3×C4—34no—
472C3×C4—62no—
473C3×C4—121no—
474C3×C4—121no—
475C3×C4—121no—
476C3×C4C2×#20412yes—
477C3×C4D3×SD1612yes—
478C3×C4C2×#23511yescharacteristic
479C3×C4C2×#23911yescharacteristic
480C3×C4#100911yescharacteristic
481C3×C4#100911yescharacteristic
482Dic3—22no—
483Dic3—41no—
484Dic3—41no—
485Dic3—41no—
486Dic3—122no—
487Dic3—122no—
488Dic3—242no—
489Dic3C2×#20414yes—
490C32#339211yescharacteristic, complemented, Sylow
491C23—61no—
492C23—182no—
493Q8—34no—
494Q8—61no—
495Q8—61no—
496Q8—182no—
497Q8—182no—
498D4—61no—
499D4—61no—
500D4—182no—
501D4—182no—
502D4—364no—
503D4—362no—
504D4—721no—
505D4—722no—
506C2×C4—32no—
507C2×C4—32no—
508C2×C4—61no—
509C2×C4—61no—
510C2×C4—61no—
511C2×C4—122no—
512C2×C4—182no—
513C2×C4—364no—
514C2×C4D3×D1211yescharacteristic
515C2×C4D3×D1211yescharacteristic
516C2×C4C22×D3211yescharacteristic
517C8—21no—
518C8—62no—
519C8#379912yescomplemented
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—241no—
524C2×C3#555311yescharacteristic
525C2×C3#557711yescharacteristic
526C2×C3C22×#20411yescharacteristic
527C2×C3#575111yescharacteristic
528C2×C3C2×D3×SD1611yescharacteristic
529C2×C3#577011yescharacteristic
530D3—81no—
531D3—242no—
532D3—242no—
533D3—482no—
534C22—121no—
535C22—121no—
536C22—121no—
537C22—362no—
538C22—362no—
539C22—362no—
540C22C2×D3×D1211yescharacteristic
541C4—21no—
542C4—34no—
543C4—62no—
544C4—121no—
545C4—121no—
546C4—121no—
547C4—362no—
548C4D3×#20412yes—
549C4C2×#379911yescharacteristic
550C4#6430811yescharacteristic
551C3—21no—
552C3#7963711yescharacteristic, complemented
553C3#7991111yescharacteristic, complemented
554C2—241no—
555C2—722no—
556C2#1059390211yescharacteristic
557C2C2×D3×#20411yescharacteristic
558C2#1059467911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10593902C2
hypercenterC4×C8D32
hypocenterC32#3392
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10593860C2semidirect
3. #10592392C2semidirect
4. C3×C4×#204C2semidirect
5. C3×C8×Dic6C2semidirect
6. #10590879C2semidirect
7. #10590877C2semidirect
8. #10590760C2semidirect
9. #10590758C2semidirect
10. #10590367C2semidirect
11. #10590365C2semidirect
64. C4×#204D3semidirect
65. C8×Dic6D3semidirect
188. C3×Dic6SD16semidirect
193. C32×C8#41semidirect
397. Dic6#204semidirect
403. C3×C8#235semidirect
404. C3×C8#239semidirect
490. C32#3392semidirect
519. C8#3799semidirect
552. C3#79637semidirect
553. C3#79911semidirect

Maximal subgroups

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

subgroupindex
#105939022
#105938602
#105923922
C3×C4×#2042
C3×C8×Dic62
#105908792
#105908772
#105907602
#105907582
#105903672
#105903652
#799113
#796373