Finite Group Databasebeta

← #11785328

Subgroups — #11785328

Order 1152.

679 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5522C211yesmaximal, characteristic
2C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
3#10591115C211yesmaximal, characteristic, complemented
4C2×#63569C211yesmaximal, characteristic
5C2×#63568C211yesmaximal, characteristic
6#10589398C211yesmaximal, characteristic, complemented
7C3×#4532C211yesmaximal, characteristic, complemented
8#71646—31nomaximal
9#68770—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#893C411yescharacteristic, complemented
18C3×#893C411yescharacteristic, complemented
19C3×#887C411yescharacteristic, complemented
20C3×#887C411yescharacteristic, complemented
21C3×#67⋊C4—21no—
22C3×#67⋊C4—21no—
23C3×#872—21no—
24C3×C42×D3—21no—
25C2×Dic3⋊Dic3—21no—
26#63579—21no—
27Dic3⋊(C3⋊C8)—21no—
28Dic3⋊(C3⋊C8)—21no—
29#63569—22no—
30#63568—22no—
31C3×C4×#41—31no—
32#5522D311yescharacteristic
33C2×#837—31no—
34C2×#837—31no—
35C2×#825—31no—
36#5118—31no—
37C4×C4⋊Dic3—31no—
38C4×Dic3⋊C4—31no—
39C2×#805—31no—
40#4924—31no—
41C3×#339—31no—
42#4532—31no—
43#4532—31no—
44#4532—61no—
45#4532D311yescharacteristic, complemented
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C22×C3×Dic3D411yescharacteristic
52C3×#235—21no—
53C3×#235—21no—
54C3×#235D412yes—
55C3×#235Q812yes—
56C2×C3×D12C2×C411yescharacteristic
57C2×C3×C4×D3—21no—
58C2×C3×C4×D3—21no—
59C2×C3×C4×D3—21no—
60C2×C3×Dic6C2×C411yescharacteristic
61C32×C4⋊C4C2×C411yescharacteristic
62C32×C4⋊C4C2×C411yescharacteristic
63C32×C22⋊C4—21no—
64C32×C42—21no—
65C4×C3⋊Dic3—21no—
66C4×C3⋊Dic3—21no—
67#3748—21no—
68#3748—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C3×(C2×D3)⋊C4—21no—
71C3×(C2×D3)⋊C4—21no—
72C3×Dic3⋊C4—21no—
73C3×Dic3⋊C4—21no—
74C3×C4×Dic3—21no—
75C3×C4×Dic3—21no—
76C3×C4×Dic3—21no—
77C3×C4×Dic3—21no—
78C3×C4×Dic3C2×C411yescharacteristic
79C3×C4×Dic3C2×C411yescharacteristic
80C3×C4×Dic3D411yescharacteristic
81C3×C4×Dic3D411yescharacteristic
82C3×#208—21no—
83C3×#208—21no—
84C2×C3×C3⋊C8—21no—
85Dic3⋊Dic3—24no—
86#1806—91noSylow
87C2×C3×#41—31no—
88C2×#235C2×D311yescharacteristic
89C2×C3×M16—31no—
90C3×C4×Q8—31no—
91C3×C4×Q8—31no—
92C3×C4×D4—31no—
93C3×C4×D4—31no—
94C3×C4×D4—61no—
95C3×C4×D4—61no—
96C3×#117—21no—
97C3×#117—61no—
98C3×#117C2×D311yescharacteristic
99C3×#117C2×D311yescharacteristic
100C2×C3×C42—31no—
101C2×C3×C42—31no—
102C2×C3×C42—61no—
103C2×C4⋊Dic3—61no—
104C2×Dic3⋊C4—61no—
105C2×C4×Dic3—31no—
106C2×C4×Dic3—31no—
107C2×C4×Dic3—61no—
108C2×C4×Dic3C2×D311yescharacteristic
109C2×C4×Dic3C2×D311yescharacteristic
110C2×#208—31no—
111C2×#208—31no—
112C2×#208—61no—
113C2×#208C2×D311yescharacteristic
114#893Dic311yescharacteristic, complemented
115#893Dic311yescharacteristic, complemented
116#887Dic311yescharacteristic, complemented
117#887Dic311yescharacteristic, complemented
118#67⋊C4—21no—
119#67⋊C4—21no—
120#872—21no—
121C42×D3—21no—
122#837—62no—
123#837—62no—
124C3⋊#95—61no—
125C3⋊#95—61no—
126#825—62no—
127Dic3⋊C8—61no—
128Dic3⋊C8—61no—
129#805—62no—
130C4⋊(C3⋊C8)—61no—
131C4⋊(C3⋊C8)—61no—
132C23×C32C2×D411yescharacteristic
133C22×C3×D3—21no—
134C2×C32×C4—21no—
135C2×C32×C4—21no—
136C2×C32×C4C22×C411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×Q811yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—41no—
144C2×C3⋊Dic3—41no—
145C3×#67—22no—
146C3×#67—22no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3C22⋊C411yescharacteristic
154C2×C3×Dic3C22⋊C411yescharacteristic
155C2×C3×Dic3C22⋊C411yescharacteristic
156C2×C3×Dic3C22⋊C411yescharacteristic
157C3×D12—21no—
158C3×D12C4⋊C412yescomplemented
159C3×C4×D3—22no—
160C3×C4×D3—22no—
161C3×C4×D3—42no—
162C3×C4×D3—42no—
163C3×Dic6—21no—
164C3×Dic6C4⋊C412yescomplemented
165C3⋊(C3⋊C8)—41no—
166C3×C3⋊C8—41no—
167C4×#41—31no—
168#423—91no—
169C2×#104—91no—
170C2×#104—91no—
171C4×C4⋊C4—91no—
172#339—31no—
173#339—91no—
174C3×#41—32no—
175C3×#41—32no—
176C3×#41—61no—
177C3×#41—61no—
178C2×C3×Q8—31no—
179C2×C3×D4—31no—
180C2×C3×D4—61no—
181C22×C3×C4—21no—
182C22×C3×C4—31no—
183C22×C3×C4—31no—
184C22×C3×C4—61no—
185C22×C3×C4—61no—
186C22×C3×C4—61no—
187C22×C3×C4—61no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C2×#67—21no—
191C22×Dic3—21no—
192C22×Dic3—61no—
193C22×Dic3—61no—
194C22×Dic3—121no—
195C22×Dic3#6711yescharacteristic
196C22×Dic3#6711yescharacteristic
197#235—21no—
198#235—21no—
199#235Dic612yes—
200#235D1212yes—
201C2×D12C2×Dic311yescharacteristic
202C2×C4×D3—21no—
203C2×C4×D3—21no—
204C2×C4×D3—21no—
205C2×Dic6C2×Dic311yescharacteristic
206C3×M16—61no—
207C3×M16—61no—
208C2×C3×C8—61no—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—61no—
212C3×C4⋊C4—61no—
213C3×C4⋊C4C4×D311yescharacteristic
214C3×C4⋊C4C4×D311yescharacteristic
215C3×C4⋊C4C2×Dic311yescharacteristic
216C3×C4⋊C4C2×Dic311yescharacteristic
217C3×C22⋊C4—21no—
218C3×C22⋊C4—21no—
219C3×C22⋊C4—41no—
220C3×C22⋊C4—61no—
221C3×C22⋊C4—61no—
222C3×C42—21no—
223C3×C42—21no—
224C3×C42—31no—
225C3×C42—31no—
226C3×C42—31no—
227C3×C42—31no—
228C3×C42—41no—
229C3×C42—61no—
230C3×C42—61no—
231C3×C42—61no—
232C3×C42—61no—
233(C2×D3)⋊C4—21no—
234(C2×D3)⋊C4—21no—
235C4⋊Dic3—64no—
236Dic3⋊C4—21no—
237Dic3⋊C4—21no—
238Dic3⋊C4—64no—
239C4×Dic3—21no—
240C4×Dic3—21no—
241C4×Dic3—21no—
242C4×Dic3—21no—
243C4×Dic3—62no—
244C4×Dic3—61no—
245C4×Dic3—61no—
246C4×Dic3—61no—
247C4×Dic3—61no—
248C4×Dic3—121no—
249C4×Dic3C2×Dic311yescharacteristic
250C4×Dic3C2×Dic311yescharacteristic
251C4×Dic3#6711yescharacteristic
252C4×Dic3#6711yescharacteristic
253#208—21no—
254#208—21no—
255#208—62no—
256#208—61no—
257#208—61no—
258#208—61no—
259#208—61no—
260#208—121no—
261C2×C3⋊C8—21no—
262C2×C3⋊C8—61no—
263C2×C3⋊C8—61no—
264C2×C3⋊C8—121no—
265C22×C32—21no—
266C22×C32—21no—
267C22×C32C2×C22⋊C411yescharacteristic
268C22×C32#12111yescharacteristic
269C22×C32C22⋊Q811yescharacteristic
270C2×C3×D3—22no—
271C2×C3×D3—41no—
272C2×C3×D3—41no—
273C32×C4—41no—
274C32×C4—41no—
275C32×C4C2×C4⋊C411yescharacteristic
276C32×C4#11711yescharacteristic
277C32×C4#12111yescharacteristic
278C32×C4C22⋊Q811yescharacteristic
279C3⋊Dic3—42no—
280C3×Dic3—22no—
281C3×Dic3—21no—
282C3×Dic3—21no—
283C3×Dic3—21no—
284C3×Dic3—42no—
285C3×Dic3#10412yescomplemented
286C2×#41—31no—
287C2×M16—31no—
288C2×M16—91no—
289C4×Q8—31no—
290C4×Q8—31no—
291C4×D4—31no—
292C4×D4—31no—
293C4×D4—61no—
294C4×D4—61no—
295#117—61no—
296#117D3211yescharacteristic
297C2×C4⋊C4—181no—
298C2×C42—31no—
299C2×C42—31no—
300C2×C42—61no—
301C2×C42—91no—
302C4⋊C8—181no—
303C4⋊C8—181no—
304#104—182no—
305#104—182no—
306#95—181no—
307C23×C3—21no—
308C23×C3—61no—
309C23×C3D3×D411yescharacteristic
310C23×C3C2×#6711yescharacteristic
311C22×D3—21no—
312C3×Q8—32no—
313C3×Q8—61no—
314C3×D4—32no—
315C3×D4—62no—
316C3×D4—62no—
317C3×D4—61no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—31no—
329C2×C3×C4—31no—
330C2×C3×C4—31no—
331C2×C3×C4—31no—
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4—62no—
335C2×C3×C4—61no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—122no—
340C2×C3×C4—122no—
341C2×C3×C4—121no—
342C2×C3×C4—121no—
343C2×C3×C4—121no—
344C2×C3×C4C2×Dic611yescharacteristic
345C2×C3×C4C2×C4×D311yescharacteristic
346C2×C3×C4C2×D1211yescharacteristic
347C2×C3×C4#23511yescharacteristic
348C2×C3×C4#23511yescharacteristic
349C2×C3×C4#23511yescharacteristic
350C2×C3×C4#23511yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×Q811yescharacteristic
354C2×C3×C4C22×Dic311yescharacteristic
355C2×C3×C4C2×#6711yescharacteristic
356#67—22no—
357#67—22no—
358C2×Dic3—21no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—41no—
362C2×Dic3—41no—
363C2×Dic3—41no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—122no—
367C2×Dic3—122no—
368C2×Dic3—121no—
369C2×Dic3—121no—
370C2×Dic3—122no—
371C2×Dic3—121no—
372C2×Dic3—121no—
373C2×Dic3#21711yescharacteristic
374C2×Dic3#21711yescharacteristic
375C2×Dic3#21711yescharacteristic
376C2×Dic3#21711yescharacteristic
377D12—21no—
378D12C4⋊Dic312yescomplemented
379C4×D3—22no—
380C4×D3—22no—
381C4×D3—42no—
382C4×D3—42no—
383Dic6—21no—
384Dic6C4⋊Dic312yescomplemented
385C3×C8—121no—
386C3⋊C8—41no—
387C3⋊C8—122no—
388C3⋊C8—121no—
389C3⋊C8—121no—
390C2×C32—21no—
391C2×C32—21no—
392C2×C32#38011yescharacteristic
393C2×C32C2×#10411yescharacteristic
394C2×C32#42111yescharacteristic
395C3×D3—42no—
396#41—32no—
397#41—32no—
398#41—61no—
399#41—61no—
400C2×Q8—31no—
401C2×D4—31no—
402C2×D4—61no—
403C22×C4—31no—
404C22×C4—31no—
405C22×C4—61no—
406C22×C4—61no—
407C22×C4—61no—
408C22×C4—61no—
409C22×C4—181no—
410C22×C4C2×D3211yescharacteristic
411M16—61no—
412M16—61no—
413M16—181no—
414M16—181no—
415C2×C8—61no—
416C2×C8—181no—
417C4⋊C4—61no—
418C4⋊C4—61no—
419C4⋊C4—184no—
420C4⋊C4D3×Dic311yescharacteristic
421C4⋊C4D3×Dic311yescharacteristic
422C22⋊C4—21no—
423C22⋊C4—61no—
424C22⋊C4—61no—
425C42—21no—
426C42—31no—
427C42—31no—
428C42—31no—
429C42—31no—
430C42—61no—
431C42—61no—
432C42—61no—
433C42—61no—
434C42—181no—
435C42—181no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—62no—
446C22×C3—121no—
447C22×C3—121no—
448C22×C3D3×C22⋊C411yescharacteristic
449C22×C3#88411yescharacteristic
450C22×C3#89611yescharacteristic
451C22×C3#92411yescharacteristic
452C22×C3#93011yescharacteristic
453C22×C3C2×#21711yescharacteristic
454C2×D3—22no—
455C2×D3—41no—
456C2×D3—41no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—32no—
462C3×C4—41no—
463C3×C4—41no—
464C3×C4—41no—
465C3×C4—41no—
466C3×C4—62no—
467C3×C4—61no—
468C3×C4—61no—
469C3×C4—61no—
470C3×C4—81no—
471C3×C4—81no—
472C3×C4—122no—
473C3×C4#87211yescharacteristic
474C3×C4#88411yescharacteristic
475C3×C4D3×C4⋊C411yescharacteristic
476C3×C4#89611yescharacteristic
477C3×C4#92411yescharacteristic
478C3×C4C2×C4⋊Dic311yescharacteristic
479C3×C4#92611yescharacteristic
480C3×C4#93011yescharacteristic
481Dic3—22no—
482Dic3—21no—
483Dic3—21no—
484Dic3—21no—
485Dic3—42no—
486Dic3—122no—
487Dic3—122no—
488Dic3—124no—
489Dic3#83712yescomplemented
490C32#180611yescharacteristic, complemented, Sylow
491C23—61no—
492C23D3×#6711yescharacteristic
493Q8—32no—
494Q8—61no—
495D4—32no—
496D4—62no—
497D4—62no—
498D4—61no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—31no—
502C2×C4—31no—
503C2×C4—31no—
504C2×C4—31no—
505C2×C4—62no—
506C2×C4—61no—
507C2×C4—62no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—122no—
511C2×C4—122no—
512C2×C4—121no—
513C2×C4—121no—
514C2×C4—121no—
515C2×C4—182no—
516C2×C4—361no—
517C2×C4—361no—
518C2×C4D3×Dic611yescharacteristic
519C2×C4#379811yescharacteristic
520C2×C4#379811yescharacteristic
521C2×C4D3×D1211yescharacteristic
522C2×C4C2×D3×Dic311yescharacteristic
523C2×C4D3×#6711yescharacteristic
524C8—121no—
525C8—361no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—41no—
534C2×C3—41no—
535C2×C3—122no—
536C2×C3#466711yescharacteristic
537C2×C3D3×#10411yescharacteristic
538C2×C3#482111yescharacteristic
539C2×C3#521211yescharacteristic
540C2×C3C2×#83711yescharacteristic
541C2×C3#523611yescharacteristic
542D3—42no—
543C22—21no—
544C22—21no—
545C22—62no—
546C22—121no—
547C22—121no—
548C22#6385111yescharacteristic
549C22#6390611yescharacteristic
550C22D3×#21711yescharacteristic
551C4—32no—
552C4—41no—
553C4—41no—
554C4—62no—
555C4—61no—
556C4—61no—
557C4—61no—
558C4—122no—
559C4—362no—
560C4#6385111yescharacteristic
561C4#6385511yescharacteristic
562C4D3×C4⋊Dic311yescharacteristic
563C4#6390611yescharacteristic
564C3—21no—
565C3#6877011yescharacteristic, complemented
566C3#7164611yescharacteristic, complemented
567C2—21no—
568C2—21no—
569C2—122no—
570C2#1059129511yescharacteristic
571C2D3×#83711yescharacteristic
572C2#1059167011yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1806
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C4×Dic3⋊Dic3C2semidirect
3. #10591115C2semidirect
6. #10589398C2semidirect
7. C3×#4532C2semidirect
17. C3×#893C4semidirect
18. C3×#893C4semidirect
19. C3×#887C4semidirect
20. C3×#887C4semidirect
45. #4532D3semidirect
114. #893Dic3semidirect
115. #893Dic3semidirect
116. #887Dic3semidirect
117. #887Dic3semidirect
158. C3×D12C4⋊C4semidirect
164. C3×Dic6C4⋊C4semidirect
285. C3×Dic3#104semidirect
378. D12C4⋊Dic3semidirect
384. Dic6C4⋊Dic3semidirect
489. Dic3#837semidirect
490. C32#1806semidirect
565. C3#68770semidirect
566. C3#71646semidirect

Maximal subgroups

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

subgroupindex
C3×#55222
C4×Dic3⋊Dic32
#105911152
C2×#635692
C2×#635682
#105893982
C3×#45322
#716463
#687703