Finite Group Databasebeta

← #11895417

Subgroups — #11895417

Order 1152.

940 conjugacy classes of subgroups.

The subgroup lattice has 569 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596189C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3C3×#5075C211yesmaximal, characteristic, complemented
4C3×#5070C211yesmaximal, characteristic, complemented
5#10591495C212yesmaximal, complemented
6#10591445C212yesmaximal, complemented
7#10591444C212yesmaximal, complemented
8#10591402C212yesmaximal, complemented
9C4×#3717C211yesmaximal, characteristic, complemented
10#10590300C211yesmaximal, characteristic, complemented
11#10590254C211yesmaximal, characteristic, complemented
12#81588—31nomaximal
13#80369—31nomaximal
14C2×#3830—21no—
15C32×#127C2211yescharacteristic
16#64149C2212yes—
17#64148—22no—
18#64147—21no—
19D4×C3⋊Dic3C2212yes—
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C2×C3×#214C2212yes—
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63919C2212yes—
26#63918—21no—
27#63844—21no—
28#63843C2212yes—
29#63839—22no—
30C2×#3717C2211yescharacteristic
31C3×#832C2212yes—
32C3×#832C2212yes—
33C3×#832C2212yes—
34C3×C4⋊(C3⋊C8)C2211yescharacteristic
35C3×C4×C3⋊C8C2211yescharacteristic
36#63573C2211yescharacteristic
37#63573C2212yes—
38#63572C2212yes—
39#63566C2211yescharacteristic
40#63564C2212yes—
41#63564C2211yescharacteristic
42#63553C2212yes—
43#5722—31no—
44#5718—31no—
45#5718—31no—
46#5718—61no—
47Q8×Dic6—31no—
48C3×#486—31no—
49C3×#460—31no—
50#5163—32no—
51Dic3×SD16—32no—
52#5084—31no—
53#5075D311yescharacteristic, complemented
54#5070D311yescharacteristic, complemented
55C4×#215—31no—
56#4842—31no—
57#4830—31no—
58#4762—32no—
59#4761—32no—
60#4761—32no—
61#4760—32no—
62#4760—32no—
63#4758—32no—
64C4×#204—31no—
65C8×Dic6—31no—
66C2×C32×D4—21no—
67C2×C32×D4—21no—
68C2×C32×D4C2312yes—
69C2×#638—22no—
70C2×#638—22no—
71C22×C3⋊Dic3—22no—
72#3830—44no—
73C2×C4⋊(C3⋊D3)C2311yescharacteristic
74C2×C4×C3⋊D3—21no—
75C2×#634D411yescharacteristic
76C2×C3×Dic6—21no—
77C2×C3×Dic6C2311yescharacteristic
78C2×#627—22no—
79C32×C42C2311yescharacteristic
80#3757—22no—
81#3752—21no—
82C4⋊(C3⋊Dic3)D411yescharacteristic
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84#3750D412yes—
85C4×C3⋊Dic3C2312yes—
86C3×#214—24no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2312yes—
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—
96Dic3⋊Dic3—22no—
97Dic32—22no—
98#3717—22no—
99#3362—91noSylow
100C2×#237—61no—
101C2×#237—61no—
102C2×#237—62no—
103C2×C3×SD16—32no—
104C3×C4⋊Q8—31no—
105C3×#127—21no—
106C3×#127C2×D311yescharacteristic
107C3×#127C2×D311yescharacteristic
108C3×C4×Q8—31no—
109Q8×Dic3—32no—
110#944—62no—
111C2×#215—31no—
112#940—32no—
113#940—32no—
114#940—62no—
115#939—62no—
116#939—62no—
117#939—64no—
118#938—61no—
119#938—61no—
120#938—62no—
121D4×Dic3—32no—
122D4×Dic3—32no—
123D4×Dic3—62no—
124C2×#214C2×D312yes—
125C2×#204—31no—
126#888—32no—
127#888—32no—
128#888—61no—
129#888—62no—
130#887—32no—
131#887—61no—
132C4×D12—31no—
133C4×D12—31no—
134C4×D12—61no—
135#869—61no—
136#869C2×D311yescharacteristic
137C4×Dic6—31no—
138C4×Dic6—31no—
139C4×Dic6—61no—
140C4×Dic6—61no—
141C4×Dic6C2×D311yescharacteristic
142C3×C4⋊C8—31no—
143C3×#102—32no—
144C3×#102—32no—
145C3×#102—32no—
146C3×C4×C8—31no—
147#835—31no—
148#832C2×D312yes—
149#832C2×D312yes—
150#832C2×D312yes—
151#821—32no—
152#821—31no—
153#817—32no—
154#817—31no—
155#816—31no—
156Dic3⋊C8—32no—
157Dic3⋊C8—32no—
158C8×Dic3—32no—
159C8×Dic3—32no—
160#809—31no—
161#809—32no—
162#808—32no—
163#808—31no—
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C4×C3⋊C8C2×D311yescharacteristic
166C23×C32—22no—
167C22×C3⋊D3—21no—
168C32×D4—22no—
169C32×D4—22no—
170C32×D4—42no—
171C32×D4—81no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175#638—44no—
176#638—82no—
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—44no—
179C2×C3⋊Dic3C2×D412yes—
180C2×C3⋊Dic3C2×D412yes—
181C4⋊(C3⋊D3)—21no—
182C4⋊(C3⋊D3)—21no—
183C4×C3⋊D3—42no—
184#634SD1614yescomplemented
185C2×C3×Dic3—21no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—21no—
188C3×Dic6—21no—
189C3×Dic6—81no—
190C3×Dic6#4112yescomplemented
191#627—82no—
192C3×C3⋊C8—21no—
193C3×C3⋊C8—22no—
194C3×C3⋊C8—21no—
195Q82—91no—
196#550—91no—
197#486—31no—
198#486—92no—
199#476—92no—
200#476—91no—
201#460—31no—
202#460—92no—
203C8×Q8—91no—
204C4×SD16—91no—
205C4×SD16—92no—
206C2×C3×Q8—31no—
207C2×C3×Q8—61no—
208C2×C3×D4—22no—
209C2×C3×D4—22no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—22no—
215C2×C3×D4C22×D312yes—
216C2×C3×D4C22×D312yes—
217C2×#67—62no—
218C2×#67—62no—
219C2×#67—62no—
220C2×#67—62no—
221C2×#67—64no—
222C2×#67—64no—
223C22×Dic3—62no—
224C22×Dic3—62no—
225C22×Dic3—64no—
226#237—124no—
227#237—124no—
228#237—128no—
229C2×D12—31no—
230C2×D12—31no—
231C2×D12—61no—
232C2×C4×D3—62no—
233C2×C4×D3—61no—
234C2×C4×D3—61no—
235C2×Dic6—21no—
236C2×Dic6—31no—
237C2×Dic6—31no—
238C2×Dic6—61no—
239C2×Dic6—62no—
240C2×Dic6—62no—
241C2×Dic6C22×D311yescharacteristic
242C3×SD16—64no—
243C2×C3×C8—31no—
244C2×C3×C8—32no—
245C2×C3×C8—31no—
246C3×C4⋊C4—32no—
247C3×C4⋊C4—31no—
248C3×C4⋊C4—61no—
249C3×C4⋊C4—61no—
250C3×C42—21no—
251C3×C42—61no—
252C3×C42C22×D311yescharacteristic
253C3×C42C22×D311yescharacteristic
254#217—62no—
255#217—62no—
256#217—64no—
257#215—62no—
258#214—24no—
259(C2×D3)⋊C4—62no—
260(C2×D3)⋊C4—61no—
261(C2×D3)⋊C4—61no—
262C4⋊Dic3—21no—
263C4⋊Dic3—31no—
264C4⋊Dic3—31no—
265C4⋊Dic3—31no—
266C4⋊Dic3—31no—
267C4⋊Dic3—61no—
268C4⋊Dic3—61no—
269C4⋊Dic3—62no—
270C4⋊Dic3C22×D311yescharacteristic
271C4⋊Dic3C22×D312yes—
272Dic3⋊C4—21no—
273Dic3⋊C4—32no—
274Dic3⋊C4—32no—
275Dic3⋊C4—62no—
276Dic3⋊C4—62no—
277Dic3⋊C4—62no—
278Dic3⋊C4—62no—
279C4×Dic3—21no—
280C4×Dic3—32no—
281C4×Dic3—32no—
282C4×Dic3—62no—
283C4×Dic3—62no—
284C4×Dic3—62no—
285C2×C3⋊C8C22×D311yescharacteristic
286C2×C3⋊C8C22×D311yescharacteristic
287C2×C3⋊C8C22×D312yes—
288#204—62no—
289C22×C32—42no—
290C22×C32—42no—
291C22×C32—42no—
292C22×C32C22×D411yescharacteristic
293C2×C3⋊D3—41no—
294C2×C3⋊D3—41no—
295C2×C3⋊D3—41no—
296C32×C4—21no—
297C32×C4C2×SD1612yes—
298C32×C4C2×#4111yescharacteristic
299C32×C42−1+411yescharacteristic
300C3⋊Dic3—22no—
301C3⋊Dic3—41no—
302C3⋊Dic3C2×SD1614yes—
303C3×Dic3—22no—
304C3×Dic3—41no—
305C3×Dic3—42no—
306C2×#41—181no—
307C2×SD16—32no—
308C2×SD16—91no—
309C4⋊Q8—31no—
310C4⋊Q8—92no—
311C4⋊Q8—181no—
312C4⋊Q8—182no—
313#127—92no—
314#127D3211yescharacteristic
315#121—181no—
316#121—182no—
317C4×Q8—31no—
318C4×Q8—91no—
319C4×Q8—92no—
320C4×Q8—181no—
321C4×D4—92no—
322C4×D4—91no—
323#106—91no—
324#106—92no—
325C4⋊C8—31no—
326C4⋊C8—92no—
327#103—91no—
328#102—32no—
329#102—32no—
330#102—32no—
331#102—91no—
332#102—92no—
333C4×C8—31no—
334C4×C8—92no—
335C23×C3—24no—
336C23×C3—22no—
337C23×C3—22no—
338C22×D3—62no—
339C22×D3—61no—
340C22×D3—61no—
341C3×Q8—32no—
342C3×Q8—61no—
343C3×Q8—241no—
344C3×D4—22no—
345C3×D4—22no—
346C3×D4—22no—
347C3×D4—22no—
348C3×D4—42no—
349C3×D4—42no—
350C3×D4—44no—
351C3×D4—42no—
352C3×D4—42no—
353C3×D4—81no—
354C3×D4—81no—
355C3×D4—82no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—61no—
360C2×C3×C4—62no—
361C2×C3×C4—61no—
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367C2×C3×C4C23×D311yescharacteristic
368#67—124no—
369#67—124no—
370#67—128no—
371#67—242no—
372#67—242no—
373#67—244no—
374C2×Dic3—21no—
375C2×Dic3—21no—
376C2×Dic3—22no—
377C2×Dic3—32no—
378C2×Dic3—32no—
379C2×Dic3—32no—
380C2×Dic3—32no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—61no—
385C2×Dic3—61no—
386C2×Dic3—124no—
387C2×Dic3—124no—
388C2×Dic3—128no—
389D12—61no—
390D12—61no—
391D12—61no—
392D12—61no—
393D12—121no—
394D12—121no—
395C4×D3—124no—
396C4×D3—122no—
397C4×D3—122no—
398Dic6—21no—
399Dic6—34no—
400Dic6—34no—
401Dic6—64no—
402Dic6—81no—
403Dic6—242no—
404Dic6—242no—
405Dic6#23712yescomplemented
406C3×C8—61no—
407C3×C8—62no—
408C3×C8—61no—
409C3⋊C8—22no—
410C3⋊C8—21no—
411C3⋊C8—21no—
412C2×C32—82no—
413C2×C32#54811yescharacteristic
414C2×C32C22×SD1611yescharacteristic
415C2×C32#57611yescharacteristic
416C3⋊D3—81no—
417#41—364no—
418C2×Q8—31no—
419C2×Q8—61no—
420C2×Q8—91no—
421C2×Q8—182no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—91no—
425C2×D4—182no—
426C2×D4—182no—
427C2×D4C2×D3212yes—
428C22×C4—182no—
429C22×C4—181no—
430SD16—64no—
431SD16—182no—
432C2×C8—31no—
433C2×C8—31no—
434C2×C8—32no—
435C4⋊C4—31no—
436C4⋊C4—32no—
437C4⋊C4—61no—
438C4⋊C4—61no—
439C4⋊C4—92no—
440C4⋊C4—91no—
441C4⋊C4—91no—
442C4⋊C4—182no—
443C4⋊C4—182no—
444C22⋊C4—182no—
445C22⋊C4—181no—
446C42—61no—
447C42—92no—
448C42—182no—
449C42C2×D3211yescharacteristic
450C22×C3—21no—
451C22×C3—44no—
452C22×C3—44no—
453C22×C3—44no—
454C22×C3—42no—
455C22×C3—42no—
456C22×C3—42no—
457C22×C3—42no—
458C22×C3—42no—
459C22×C3—42no—
460C22×C3C2×D3×D411yescharacteristic
461C22×C3C2×D3×D411yescharacteristic
462C2×D3—122no—
463C2×D3—122no—
464C2×D3—122no—
465C2×D3—121no—
466C2×D3—121no—
467C2×D3—121no—
468C2×D3—121no—
469C2×D3—121no—
470C2×D3—121no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—22no—
476C3×C4—41no—
477C3×C4—62no—
478C3×C4—121no—
479C3×C4—122no—
480C3×C4D3×SD1612yes—
481C3×C4D3×SD1612yes—
482C3×C4C2×#23711yescharacteristic
483C3×C4D3×#4111yescharacteristic
484C3×C4#101011yescharacteristic
485C3×C4#101011yescharacteristic
486Dic3—22no—
487Dic3—34no—
488Dic3—34no—
489Dic3—42no—
490Dic3—41no—
491Dic3—64no—
492Dic3—62no—
493Dic3—62no—
494Dic3—122no—
495Dic3—122no—
496Dic3—121no—
497Dic3—121no—
498C32#336211yescharacteristic, complemented, Sylow
499C23—22no—
500C23—181no—
501Q8—32no—
502Q8—61no—
503Q8—94no—
504Q8—241no—
505Q8—722no—
506D4—22no—
507D4—22no—
508D4—42no—
509D4—81no—
510D4—181no—
511D4—181no—
512D4—364no—
513D4—722no—
514C2×C4—61no—
515C2×C4—61no—
516C2×C4—62no—
517C2×C4—92no—
518C2×C4—92no—
519C2×C4—181no—
520C2×C4—364no—
521C2×C4—362no—
522C2×C4#381111yescharacteristic
523C2×C4#381111yescharacteristic
524C2×C4C22×D3211yescharacteristic
525C8—61no—
526C8—62no—
527C8—61no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—84no—
532C2×C3—82no—
533C2×C3—82no—
534C2×C3#559811yescharacteristic
535C2×C3#567711yescharacteristic
536C2×C3#575711yescharacteristic
537C2×C3C2×D3×SD1611yescharacteristic
538C2×C3C2×D3×SD1611yescharacteristic
539C2×C3#577411yescharacteristic
540D3—242no—
541D3—241no—
542D3—241no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—361no—
547C22—361no—
548C22—361no—
549C22C2×#381111yescharacteristic
550C4—21no—
551C4—62no—
552C4—94no—
553C4—122no—
554C4—121no—
555C4—182no—
556C4—361no—
557C4#6393012yes—
558C4#6430911yescharacteristic
559C4D3×#23711yescharacteristic
560C3—21no—
561C3#8036911yescharacteristic, complemented
562C3#8158811yescharacteristic, complemented
563C2—82no—
564C2—721no—
565C2#1059510211yescharacteristic
566C2C2×#6393011yescharacteristic
567C2#1059516111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
prime radical#10596189C2
hypercenter#127D32
hypocenterC32#3362
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #10593856C2semidirect
3. C3×#5075C2semidirect
4. C3×#5070C2semidirect
5. #10591495C2semidirect
6. #10591445C2semidirect
7. #10591444C2semidirect
8. #10591402C2semidirect
9. C4×#3717C2semidirect
10. #10590300C2semidirect
11. #10590254C2semidirect
53. #5075D3semidirect
54. #5070D3semidirect
184. #634SD16semidirect
190. C3×Dic6#41semidirect
405. Dic6#237semidirect
498. C32#3362semidirect
561. C3#80369semidirect
562. C3#81588semidirect

Maximal subgroups

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

subgroupindex
#105961892
#105938562
C3×#50752
C3×#50702
#105914952
#105914452
#105914442
#105914022
C4×#37172
#105903002
#105902542
#815883
#803693