Finite Group Databasebeta

← #11790792

Subgroups — #11790792

Order 1152.

805 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5832C211yesmaximal, characteristic
2C2×#63664C211yesmaximal, characteristic, complemented
3C2×C3×#837C211yesmaximal, characteristic, complemented
4C4×Dic32C211yesmaximal, characteristic, complemented
5#10591115C211yesmaximal, characteristic, complemented
6C2×#63569C211yesmaximal, characteristic, complemented
7C2×#63568C211yesmaximal, characteristic, complemented
8#71815—31nomaximal
9#70356—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#947C411yescharacteristic, complemented
15C3×#944C411yescharacteristic, complemented
16C3×#940C411yescharacteristic, complemented
17C3×#939—22no—
18C3×#936C411yescharacteristic, complemented
19C3×C4×#67—22no—
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C2×Dic32—22no—
24#63664—22no—
25C3×#837—22no—
26Dic3⋊(C3⋊C8)—22no—
27#63569—22no—
28#63568—22no—
29C3×#532—31no—
30#5832D311yescharacteristic
31C2×C3×#104—31no—
32C2×#837—31no—
33C2×#837—31no—
34C2×#837—31no—
35C2×#837—31no—
36C2×#837—61no—
37C2×#837D311yescharacteristic, complemented
38C2×#825—31no—
39#5118—31no—
40C42×Dic3—31no—
41C42×Dic3—31no—
42C2×#805—31no—
43#4924—31no—
44C32×#41—21no—
45C32×#41—21no—
46C32×#41—21no—
47C32×#41—21no—
48C2×C32×Q8C2×C411yescharacteristic
49C2×C32×D4—21no—
50C2×C32×D4C2×C411yescharacteristic
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3—21no—
54C2×C3×#67—21no—
55C2×C3×#67—22no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3D412yes—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C3×#235—21no—
62C2×C3×D12C2×C411yescharacteristic
63C2×C3×C4×D3—21no—
64C2×C3×Dic6C2×C411yescharacteristic
65C4×C3⋊Dic3—21no—
66C4×C3⋊Dic3D412yescomplemented
67#3748—21no—
68#3748—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C3×#217—22no—
71C3×(C2×D3)⋊C4—22no—
72C3×Dic3⋊C4—22no—
73C3×C4×Dic3—21no—
74C3×C4×Dic3C2×C411yescharacteristic
75C3×C4×Dic3C2×C411yescharacteristic
76C3×C4×Dic3D412yes—
77C3×C4×Dic3D412yescomplemented
78C3×#208—21no—
79C3×#208—21no—
80C2×C3×C3⋊C8—21no—
81Dic32—28no—
82#1962—91noSylow
83C2×C3×#41—21no—
84C2×C3×#41—31no—
85C2×C3×#41C2×D311yescharacteristic
86C2×C3×#41C2×D311yescharacteristic
87C2×#235C2×D311yescharacteristic
88C2×C3×M16—31no—
89C3×C4⋊Q8—31no—
90C3×#127—31no—
91C3×#124—31no—
92C3×#124—31no—
93C3×#121—62no—
94C3×C4×D4—62no—
95C2×C3×C42—31no—
96C2×C3×C42—31no—
97#947Dic311yescharacteristic, complemented
98#944Dic311yescharacteristic, complemented
99#940Dic311yescharacteristic, complemented
100#939—22no—
101#936Dic311yescharacteristic, complemented
102C4×#67—22no—
103C2×C4×Dic3—31no—
104C2×C4×Dic3—31no—
105C2×C4×Dic3—61no—
106C2×C4×Dic3—62no—
107C2×C4×Dic3—62no—
108C2×C4×Dic3C2×D311yescharacteristic
109C2×C4×Dic3C2×D311yescharacteristic
110C2×#208—31no—
111C2×#208—31no—
112C2×#208—61no—
113C2×#208C2×D311yescharacteristic
114C3×#104—62no—
115#837—22no—
116#837—62no—
117#837—62no—
118#837—62no—
119#837—64no—
120#837—62no—
121#825—62no—
122Dic3⋊C8—62no—
123#805—62no—
124C4⋊(C3⋊C8)—62no—
125C23×C32—21no—
126C23×C32C2×D411yescharacteristic
127C22×C3×D3—21no—
128C32×Q8—21no—
129C32×Q8—21no—
130C32×D4—21no—
131C32×D4—21no—
132C32×D4—41no—
133C32×D4—41no—
134C2×C32×C4—21no—
135C2×C32×C4—41no—
136C2×C32×C4—41no—
137C2×C32×C4C22×C411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C3⋊Dic3—24no—
144C2×C3⋊Dic3—22no—
145C3×#67—41no—
146C3×#67—41no—
147C3×#67—44no—
148C2×C3×Dic3—24no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—24no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3C22⋊C412yes—
153C2×C3×Dic3C22⋊C412yes—
154C3×D12—21no—
155C3×D12—21no—
156C3×C4×D3—41no—
157C3×C4×D3—41no—
158C3×Dic6—21no—
159C3×Dic6—21no—
160C3⋊(C3⋊C8)—41no—
161C3×C3⋊C8—41no—
162#532—31no—
163#423—91no—
164C2×#104—31no—
165C2×#104—91no—
166C2×#104—91no—
167C2×#104—91no—
168C43—91no—
169C3×#41—22no—
170C3×#41—22no—
171C3×#41—21no—
172C3×#41—21no—
173C3×#41—21no—
174C3×#41—21no—
175C3×#41—21no—
176C3×#41—21no—
177C3×#41—21no—
178C3×#41—21no—
179C3×#41—41no—
180C3×#41—41no—
181C3×#41—61no—
182C3×#41—61no—
183C3×#41—61no—
184C3×#41—61no—
185C2×C3×Q8—21no—
186C2×C3×Q8—31no—
187C2×C3×Q8C4×D311yescharacteristic
188C2×C3×Q8C2×Dic311yescharacteristic
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—31no—
193C2×C3×D4—41no—
194C2×C3×D4—62no—
195C2×C3×D4—61no—
196C2×C3×D4C4×D311yescharacteristic
197C2×C3×D4C2×Dic311yescharacteristic
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—32no—
202C22×C3×C4—41no—
203C22×C3×C4—61no—
204C22×C3×C4—61no—
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C2×#67—21no—
208C2×#67—22no—
209C22×Dic3—21no—
210C22×Dic3—61no—
211C22×Dic3—61no—
212C22×Dic3—121no—
213C22×Dic3#6712yes—
214#235—21no—
215#235—21no—
216#235—21no—
217#235—21no—
218C2×D12C2×Dic311yescharacteristic
219C2×C4×D3—21no—
220C2×Dic6C2×Dic311yescharacteristic
221C3×M16—61no—
222C3×M16—61no—
223C2×C3×C8—61no—
224C3×C4⋊C4—62no—
225C3×C22⋊C4—62no—
226C3×C22⋊C4—62no—
227C3×C42—31no—
228C3×C42—31no—
229C3×C42—32no—
230C3×C42—32no—
231C3×C42—61no—
232#217—22no—
233(C2×D3)⋊C4—22no—
234Dic3⋊C4—22no—
235C4×Dic3—21no—
236C4×Dic3—32no—
237C4×Dic3—32no—
238C4×Dic3—62no—
239C4×Dic3—68no—
240C4×Dic3—68no—
241C4×Dic3—61no—
242C4×Dic3—61no—
243C4×Dic3—121no—
244C4×Dic3C2×Dic311yescharacteristic
245C4×Dic3C2×Dic311yescharacteristic
246C4×Dic3#6712yes—
247C4×Dic3#6712yescomplemented
248#208—21no—
249#208—21no—
250#208—62no—
251#208—61no—
252#208—61no—
253#208—61no—
254#208—61no—
255#208—121no—
256C2×C3⋊C8—21no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C2×C3⋊C8—121no—
260C22×C32—22no—
261C22×C32—41no—
262C22×C32—42no—
263C22×C32C2×C22⋊C411yescharacteristic
264C22×C32#12111yescharacteristic
265C22×C32#12111yescharacteristic
266C2×C3×D3—41no—
267C2×C3×D3—42no—
268C32×C4—41no—
269C32×C4C4×D411yescharacteristic
270C32×C4C4×D411yescharacteristic
271C32×C4#12411yescharacteristic
272C32×C4#12711yescharacteristic
273C3⋊Dic3—24no—
274C3×Dic3—24no—
275C3×Dic3—22no—
276C3×Dic3—41no—
277C3×Dic3#10414yescomplemented
278C2×#41—31no—
279C2×#41D3211yescharacteristic
280C2×M16—31no—
281C2×M16—91no—
282C4⋊Q8—31no—
283#127—31no—
284#124—31no—
285#124—31no—
286#121—62no—
287C4×D4—62no—
288C2×C42—31no—
289C2×C42—31no—
290C2×C42—91no—
291C2×C42—182no—
292C4⋊C8—182no—
293#104—62no—
294#104—182no—
295#104—182no—
296#104—182no—
297C23×C3—21no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—41no—
301C23×C3—61no—
302C23×C3D3×D411yescharacteristic
303C23×C3C2×#6711yescharacteristic
304C22×D3—21no—
305C3×Q8—22no—
306C3×Q8—21no—
307C3×Q8—21no—
308C3×Q8—21no—
309C3×Q8—21no—
310C3×Q8—41no—
311C3×Q8—61no—
312C3×Q8—61no—
313C3×D4—22no—
314C3×D4—21no—
315C3×D4—21no—
316C3×D4—21no—
317C3×D4—21no—
318C3×D4—41no—
319C3×D4—42no—
320C3×D4—42no—
321C3×D4—41no—
322C3×D4—41no—
323C3×D4—41no—
324C3×D4—41no—
325C3×D4—61no—
326C3×D4—61no—
327C3×D4—124no—
328C3×D4—121no—
329C3×D4—121no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—32no—
339C2×C3×C4—32no—
340C2×C3×C4—41no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—64no—
348C2×C3×C4—64no—
349C2×C3×C4—62no—
350C2×C3×C4—61no—
351C2×C3×C4—121no—
352C2×C3×C4—121no—
353C2×C3×C4C2×C4×D311yescharacteristic
354C2×C3×C4#23511yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4#23711yescharacteristic
360C2×C3×C4#23711yescharacteristic
361C2×C3×C4#23711yescharacteristic
362C2×C3×C4C22×Dic311yescharacteristic
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365#67—41no—
366#67—41no—
367#67—44no—
368C2×Dic3—24no—
369C2×Dic3—22no—
370C2×Dic3—24no—
371C2×Dic3—21no—
372C2×Dic3—64no—
373C2×Dic3—64no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—122no—
377C2×Dic3—124no—
378C2×Dic3#21712yes—
379C2×Dic3#21712yes—
380D12—21no—
381D12—21no—
382C4×D3—41no—
383C4×D3—41no—
384Dic6—21no—
385Dic6—21no—
386C3×C8—121no—
387C3⋊C8—41no—
388C3⋊C8—122no—
389C3⋊C8—121no—
390C3⋊C8—121no—
391C2×C32—21no—
392C2×C32—21no—
393C2×C32—81no—
394C2×C32#39011yescharacteristic
395C2×C32C2×#10412yes—
396C3×D3—81no—
397#41—21no—
398#41—21no—
399#41—21no—
400#41—21no—
401#41—61no—
402#41—61no—
403#41—61no—
404#41—61no—
405C2×Q8—31no—
406C2×Q8D3×Dic311yescharacteristic
407C2×D4—21no—
408C2×D4—31no—
409C2×D4—62no—
410C2×D4—61no—
411C2×D4D3×Dic311yescharacteristic
412C22×C4—21no—
413C22×C4—32no—
414C22×C4—61no—
415C22×C4—61no—
416C22×C4—181no—
417C22×C4C2×D3211yescharacteristic
418M16—61no—
419M16—61no—
420M16—181no—
421M16—181no—
422C2×C8—61no—
423C2×C8—181no—
424C4⋊C4—62no—
425C22⋊C4—62no—
426C22⋊C4—62no—
427C42—31no—
428C42—31no—
429C42—32no—
430C42—32no—
431C42—61no—
432C42—92no—
433C42—188no—
434C42—181no—
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—42no—
445C22×C3—42no—
446C22×C3—82no—
447C22×C3—121no—
448C22×C3—122no—
449C22×C3D3×C22⋊C411yescharacteristic
450C22×C3#88411yescharacteristic
451C22×C3#93811yescharacteristic
452C22×C3#93811yescharacteristic
453C22×C3#93911yescharacteristic
454C22×C3C2×#21711yescharacteristic
455C2×D3—41no—
456C2×D3—42no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—34no—
462C3×C4—42no—
463C3×C4—41no—
464C3×C4—41no—
465C3×C4—64no—
466C3×C4—62no—
467C3×C4—121no—
468C3×C4#67⋊C411yescharacteristic
469C3×C4#88511yescharacteristic
470C3×C4C4×#6711yescharacteristic
471C3×C4D4×Dic311yescharacteristic
472C3×C4D4×Dic311yescharacteristic
473C3×C4#93611yescharacteristic
474C3×C4#94011yescharacteristic
475C3×C4#94011yescharacteristic
476Dic3—24no—
477Dic3—22no—
478Dic3—41no—
479Dic3—64no—
480Dic3—64no—
481Dic3—124no—
482Dic3#83714yescomplemented
483C32#196211yescharacteristic, complemented, Sylow
484C23—21no—
485C23—61no—
486C23D3×#6711yescharacteristic
487Q8—21no—
488Q8—21no—
489Q8—61no—
490Q8—61no—
491D4—21no—
492D4—21no—
493D4—41no—
494D4—41no—
495D4—61no—
496D4—61no—
497D4—124no—
498D4—121no—
499D4—121no—
500C2×C4—21no—
501C2×C4—32no—
502C2×C4—32no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—64no—
506C2×C4—64no—
507C2×C4—62no—
508C2×C4—61no—
509C2×C4—121no—
510C2×C4—121no—
511C2×C4—184no—
512C2×C4—182no—
513C2×C4C2×D3×Dic311yescharacteristic
514C2×C4#380411yescharacteristic
515C2×C4#380511yescharacteristic
516C2×C4D3×#6711yescharacteristic
517C2×C4D3×#6711yescharacteristic
518C2×C4#381111yescharacteristic
519C8—121no—
520C8—361no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—22no—
526C2×C3—21no—
527C2×C3—41no—
528C2×C3—41no—
529C2×C3—82no—
530C2×C3—81no—
531C2×C3—81no—
532C2×C3—241no—
533C2×C3D3×#10412yes—
534C2×C3#495711yescharacteristic
535C2×C3#522111yescharacteristic
536C2×C3C2×#83712yes—
537D3—81no—
538C22—22no—
539C22—42no—
540C22—41no—
541C22—122no—
542C22—121no—
543C22#6395811yescharacteristic
544C22D3×#21711yescharacteristic
545C22#6397011yescharacteristic
546C4—34no—
547C4—41no—
548C4—64no—
549C4—62no—
550C4—121no—
551C4—184no—
552C4#6395911yescharacteristic
553C4Dic3×#6711yescharacteristic
554C4#67⋊Dic311yescharacteristic
555C4#6397911yescharacteristic
556C3—21no—
557C3#7035611yescharacteristic, complemented
558C3#7181511yescharacteristic, complemented
559C2—21no—
560C2—21no—
561C2—81no—
562C2—241no—
563C2D3×#83712yes—
564C2#1059170711yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#5832C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1962
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#63664C2semidirect
3. C2×C3×#837C2semidirect
4. C4×Dic32C2semidirect
5. #10591115C2semidirect
6. C2×#63569C2semidirect
7. C2×#63568C2semidirect
14. C3×#947C4semidirect
15. C3×#944C4semidirect
16. C3×#940C4semidirect
18. C3×#936C4semidirect
37. C2×#837D3semidirect
66. C4×C3⋊Dic3D4semidirect
77. C3×C4×Dic3D4semidirect
97. #947Dic3semidirect
98. #944Dic3semidirect
99. #940Dic3semidirect
101. #936Dic3semidirect
247. C4×Dic3#67semidirect
277. C3×Dic3#104semidirect
482. Dic3#837semidirect
483. C32#1962semidirect
557. C3#70356semidirect
558. C3#71815semidirect

Maximal subgroups

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

subgroupindex
C3×#58322
C2×#636642
C2×C3×#8372
C4×Dic322
#105911152
C2×#635692
C2×#635682
#718153
#703563