Finite Group Databasebeta

← #11788216

Subgroups — #11788216

Order 1152.

771 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5524C211yesmaximal, characteristic
2C2×#63855C211yesmaximal, characteristic, complemented
3C2×#63569C211yesmaximal, characteristic, complemented
4C2×#63568C211yesmaximal, characteristic, complemented
5#10591069C211yesmaximal, characteristic, complemented
6#10589398C211yesmaximal, characteristic, complemented
7C3×#4532C211yesmaximal, characteristic, complemented
8#71712—31nomaximal
9#68757—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×C4×D3C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#897C412yescomplemented
18C3×#895C412yescomplemented
19C3×#886—21no—
20C3×#882—21no—
21C3×C4×D12—22no—
22C2×Dic3⋊Dic3—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63855—22no—
25#63855—22no—
26#63569—22no—
27#63568—22no—
28(C2×D3)⋊(C3⋊C8)—22no—
29C3×#525—31no—
30C2×#926—31no—
31#5524D311yescharacteristic
32C2×#872—31no—
33C2×#837—31no—
34C2×#837—31no—
35#5207—31no—
36C2×#825—31no—
37#5126—31no—
38C2×#805—31no—
39C3×#339—31no—
40#4532—31no—
41#4532—31no—
42#4532—61no—
43#4532D311yescharacteristic, complemented
44C23×C3×D3D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C3×#235—21no—
51C3×#235—21no—
52C3×#235—21no—
53C3×#235—21no—
54C2×C3×D12—22no—
55C2×C3×D12C2×C411yescharacteristic
56C2×C3×C4×D3—21no—
57C2×C3×C4×D3—21no—
58C2×C3×C4×D3—21no—
59C2×C3×C4×D3—21no—
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3C2×C412yes—
62C2×C3×C4×D3D412yes—
63C2×C3×Dic6C2×C411yescharacteristic
64C32×C4⋊C4C2×C412yes—
65C32×C22⋊C4—21no—
66C32×C42—21no—
67C4×C3⋊Dic3—21no—
68C4×C3⋊Dic3D412yescomplemented
69#3748—21no—
70#3748—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C3×(C2×D3)⋊C4—22no—
73C3×(C2×D3)⋊C4—22no—
74C3×C4⋊Dic3—22no—
75C3×C4×Dic3—21no—
76C3×C4×Dic3D412yescomplemented
77C3×#208—21no—
78C3×#208—21no—
79C2×C3×C3⋊C8—21no—
80Dic3⋊Dic3—24no—
81(C2×D3)⋊Dic3—24no—
82#1897—91noSylow
83C2×C3×#41—31no—
84C23×C3×C4—31no—
85C2×#235C2×D311yescharacteristic
86C22×C4×D3C2×D311yescharacteristic
87C2×C3×M16—31no—
88C3×#123—61no—
89C3×C22⋊Q8—32no—
90C3×#121—32no—
91C3×#120—61no—
92C3×C4×D4—62no—
93C3×#117—21no—
94C3×#117C2×D311yescharacteristic
95C3×#117C2×D311yescharacteristic
96C2×C3×C42—31no—
97C2×#217—61no—
98C2×(C2×D3)⋊C4—61no—
99#926—62no—
100#926—62no—
101C2×C4⋊Dic3—61no—
102C2×Dic3⋊C4—61no—
103C2×C4×Dic3—31no—
104C2×C4×Dic3—31no—
105C2×C4×Dic3—61no—
106C2×C4×Dic3C2×D311yescharacteristic
107C2×#208—31no—
108C2×#208—31no—
109C2×#208—61no—
110C2×#208C2×D311yescharacteristic
111#897Dic312yescomplemented
112#895Dic312yescomplemented
113#886—21no—
114#882—21no—
115C4×D12—22no—
116#872—62no—
117#872—62no—
118#837—62no—
119#837—62no—
120#830—62no—
121#825—62no—
122(C2×D3)⋊C8—62no—
123#805—62no—
124C23×C32C2×D411yescharacteristic
125C22×C3×D3—21no—
126C22×C3×D3—21no—
127C22×C3×D3—21no—
128C22×C3×D3—42no—
129C22×C3×D3C22⋊C412yes—
130C2×C32×C4—22no—
131C2×C32×C4C22×C411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—42no—
139C3×#67—41no—
140C3×#67—41no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—42no—
146C2×C3×Dic3C22⋊C412yes—
147C3×D12—21no—
148C3×D12—21no—
149C3×D12—44no—
150C3×C4×D3—22no—
151C3×C4×D3—22no—
152C3×C4×D3—22no—
153C3×C4×D3—22no—
154C3×C4×D3—41no—
155C3×C4×D3—41no—
156C3×Dic6—21no—
157C3×Dic6—21no—
158C3⋊(C3⋊C8)—41no—
159C3×C3⋊C8—41no—
160#525—31no—
161C2×#117—91no—
162C2×#104—91no—
163C2×#104—91no—
164#407—91no—
165#339—31no—
166#339—91no—
167C24×C3—31no—
168C23×D3#6711yescharacteristic
169C3×#41—61no—
170C3×#41—61no—
171C3×#41—61no—
172C3×#41—61no—
173C2×C3×Q8—31no—
174C2×C3×D4—31no—
175C2×C3×D4—62no—
176C2×C3×D4—61no—
177C22×C3×C4—21no—
178C22×C3×C4—31no—
179C22×C3×C4—32no—
180C22×C3×C4—32no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4—61no—
184C22×C3×C4—61no—
185C22×C3×C4—61no—
186C22×C3×C4—61no—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C2×#67—21no—
190C22×Dic3—21no—
191C22×Dic3—61no—
192C22×Dic3—61no—
193C22×Dic3—121no—
194C22×Dic3#6711yescharacteristic
195#235—21no—
196#235—21no—
197#235—21no—
198#235—21no—
199C2×D12—22no—
200C2×D12C2×Dic311yescharacteristic
201C2×C4×D3—21no—
202C2×C4×D3—21no—
203C2×C4×D3—21no—
204C2×C4×D3—21no—
205C2×C4×D3—21no—
206C2×C4×D3C2×Dic312yes—
207C2×C4×D3#6712yes—
208C2×Dic6C2×Dic311yescharacteristic
209C3×M16—61no—
210C3×M16—61no—
211C2×C3×C8—61no—
212C3×C4⋊C4—22no—
213C3×C4⋊C4—62no—
214C3×C4⋊C4C4×D312yes—
215C3×C4⋊C4C2×Dic312yes—
216C3×C22⋊C4—21no—
217C3×C22⋊C4—21no—
218C3×C22⋊C4—41no—
219C3×C22⋊C4—62no—
220C3×C22⋊C4—62no—
221C3×C42—21no—
222C3×C42—21no—
223C3×C42—32no—
224C3×C42—41no—
225C3×C42—61no—
226#217—64no—
227(C2×D3)⋊C4—22no—
228(C2×D3)⋊C4—22no—
229(C2×D3)⋊C4—64no—
230C4⋊Dic3—22no—
231C4⋊Dic3—64no—
232Dic3⋊C4—64no—
233C4×Dic3—21no—
234C4×Dic3—32no—
235C4×Dic3—32no—
236C4×Dic3—62no—
237C4×Dic3—61no—
238C4×Dic3—61no—
239C4×Dic3—121no—
240C4×Dic3D1212yescomplemented
241#208—21no—
242#208—21no—
243#208—62no—
244#208—61no—
245#208—61no—
246#208—61no—
247#208—61no—
248#208—121no—
249C2×C3⋊C8—21no—
250C2×C3⋊C8—61no—
251C2×C3⋊C8—61no—
252C2×C3⋊C8—121no—
253C22×C32—22no—
254C22×C32C2×C22⋊C411yescharacteristic
255C22×C32#12011yescharacteristic
256C22×C32#12311yescharacteristic
257C2×C3×D3—22no—
258C2×C3×D3—22no—
259C2×C3×D3—22no—
260C2×C3×D3—42no—
261C2×C3×D3—42no—
262C2×C3×D3—41no—
263C2×C3×D3—42no—
264C32×C4—42no—
265C32×C4C4×D411yescharacteristic
266C32×C4C4×D411yescharacteristic
267C32×C4#12111yescharacteristic
268C32×C4#12111yescharacteristic
269C3⋊Dic3—42no—
270C3×Dic3—22no—
271C3×Dic3—42no—
272C3×Dic3—41no—
273C2×#41—31no—
274C23×C4—31no—
275C2×M16—31no—
276C2×M16—91no—
277#123—61no—
278C22⋊Q8—32no—
279#121—32no—
280#120—61no—
281C4×D4—62no—
282#117—182no—
283#117—182no—
284#117D3211yescharacteristic
285C2×C4⋊C4—181no—
286C2×C22⋊C4—181no—
287C2×C42—31no—
288C2×C42—91no—
289#104—182no—
290#104—182no—
291C22⋊C8—182no—
292C23×C3—21no—
293C23×C3—32no—
294C23×C3—61no—
295C23×C3—61no—
296C23×C3—61no—
297C23×C3—122no—
298C23×C3D3×D411yescharacteristic
299C23×C3C2×#6711yescharacteristic
300C22×D3—21no—
301C22×D3—21no—
302C22×D3—21no—
303C22×D3—42no—
304C22×D3#21712yes—
305C3×Q8—61no—
306C3×Q8—61no—
307C3×D4—61no—
308C3×D4—61no—
309C3×D4—124no—
310C3×D4—121no—
311C3×D4—121no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—32no—
321C2×C3×C4—42no—
322C2×C3×C4—61no—
323C2×C3×C4—61no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—61no—
329C2×C3×C4—62no—
330C2×C3×C4—122no—
331C2×C3×C4—121no—
332C2×C3×C4—121no—
333C2×C3×C4C2×C4×D311yescharacteristic
334C2×C3×C4C2×D1211yescharacteristic
335C2×C3×C4#23511yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4#23711yescharacteristic
341C2×C3×C4#23711yescharacteristic
342C2×C3×C4#23911yescharacteristic
343C2×C3×C4C22×Dic311yescharacteristic
344C2×C3×C4C2×#6711yescharacteristic
345#67—41no—
346#67—41no—
347C2×Dic3—21no—
348C2×Dic3—21no—
349C2×Dic3—22no—
350C2×Dic3—21no—
351C2×Dic3—42no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—122no—
355C2×Dic3—122no—
356C2×Dic3—122no—
357C2×Dic3—124no—
358C2×Dic3#21712yes—
359D12—21no—
360D12—21no—
361D12—44no—
362C4×D3—22no—
363C4×D3—22no—
364C4×D3—22no—
365C4×D3—22no—
366C4×D3—41no—
367C4×D3—41no—
368Dic6—21no—
369Dic6—21no—
370C3×C8—121no—
371C3⋊C8—41no—
372C3⋊C8—122no—
373C3⋊C8—121no—
374C3⋊C8—121no—
375C2×C32—21no—
376C2×C32—21no—
377C2×C32#38611yescharacteristic
378C2×C32#42112yes—
379C3×D3—42no—
380C3×D3—81no—
381C24—31no—
382#41—61no—
383#41—61no—
384#41—61no—
385#41—61no—
386C2×Q8—31no—
387C2×D4—31no—
388C2×D4—62no—
389C2×D4—61no—
390C22×C4—31no—
391C22×C4—32no—
392C22×C4—32no—
393C22×C4—61no—
394C22×C4—61no—
395C22×C4—61no—
396C22×C4—61no—
397C22×C4—61no—
398C22×C4—61no—
399C22×C4—181no—
400C22×C4C2×D3211yescharacteristic
401M16—61no—
402M16—61no—
403M16—181no—
404M16—181no—
405C2×C8—61no—
406C2×C8—181no—
407C4⋊C4—62no—
408C4⋊C4—184no—
409C4⋊C4D3×Dic312yes—
410C22⋊C4—21no—
411C22⋊C4—62no—
412C22⋊C4—62no—
413C22⋊C4—184no—
414C42—21no—
415C42—32no—
416C42—61no—
417C42—92no—
418C42—181no—
419C22×C3—22no—
420C22×C3—22no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—42no—
425C22×C3—62no—
426C22×C3—62no—
427C22×C3—62no—
428C22×C3—122no—
429C22×C3—122no—
430C22×C3—121no—
431C22×C3—122no—
432C22×C3D3×C22⋊C411yescharacteristic
433C22×C3#88211yescharacteristic
434C22×C3#89411yescharacteristic
435C22×C3#93511yescharacteristic
436C22×C3#93711yescharacteristic
437C22×C3C2×#21711yescharacteristic
438C2×D3—22no—
439C2×D3—22no—
440C2×D3—22no—
441C2×D3—42no—
442C2×D3—42no—
443C2×D3—41no—
444C2×D3—42no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—42no—
450C3×C4—42no—
451C3×C4—62no—
452C3×C4—82no—
453C3×C4—122no—
454C3×C4—121no—
455C3×C4C4×D1211yescharacteristic
456C3×C4#88411yescharacteristic
457C3×C4#89311yescharacteristic
458C3×C4#89511yescharacteristic
459C3×C4D4×Dic311yescharacteristic
460C3×C4D4×Dic311yescharacteristic
461C3×C4#93911yescharacteristic
462C3×C4#93911yescharacteristic
463Dic3—22no—
464Dic3—42no—
465Dic3—41no—
466Dic3—122no—
467Dic3—122no—
468Dic3—124no—
469C32#189711yescharacteristic, complemented, Sylow
470C23—32no—
471C23—61no—
472C23—61no—
473C23—61no—
474C23—122no—
475C23D3×#6711yescharacteristic
476Q8—61no—
477Q8—61no—
478D4—61no—
479D4—61no—
480D4—124no—
481D4—121no—
482D4—121no—
483C2×C4—22no—
484C2×C4—32no—
485C2×C4—61no—
486C2×C4—61no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—61no—
493C2×C4—122no—
494C2×C4—121no—
495C2×C4—121no—
496C2×C4—182no—
497C2×C4—362no—
498C2×C4#379511yescharacteristic
499C2×C4#379611yescharacteristic
500C2×C4D3×D1211yescharacteristic
501C2×C4#380211yescharacteristic
502C2×C4C2×D3×Dic311yescharacteristic
503C2×C4D3×#6711yescharacteristic
504C8—121no—
505C8—361no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—22no—
512C2×C3—41no—
513C2×C3—41no—
514C2×C3—122no—
515C2×C3—241no—
516C2×C3#466511yescharacteristic
517C2×C3#482112yes—
518C2×C3#522011yescharacteristic
519C2×C3#523612yes—
520D3—42no—
521D3—81no—
522C22—22no—
523C22—62no—
524C22—62no—
525C22—62no—
526C22—122no—
527C22—122no—
528C22—121no—
529C22—122no—
530C22#6388411yescharacteristic
531C22#6392211yescharacteristic
532C22D3×#21711yescharacteristic
533C4—42no—
534C4—62no—
535C4—122no—
536C4—121no—
537C4—362no—
538C4#6388511yescharacteristic
539C4#6388611yescharacteristic
540C4Dic3×D1211yescharacteristic
541C4#6389811yescharacteristic
542C3—21no—
543C3#6875711yescharacteristic, complemented
544C3#7171211yescharacteristic, complemented
545C2—21no—
546C2—21no—
547C2—122no—
548C2—241no—
549C2#1059137611yescharacteristic
550C2#1059167012yes—
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#5524C2
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1897
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. C2×#63855C2semidirect
3. C2×#63569C2semidirect
4. C2×#63568C2semidirect
5. #10591069C2semidirect
6. #10589398C2semidirect
7. C3×#4532C2semidirect
17. C3×#897C4semidirect
18. C3×#895C4semidirect
43. #4532D3semidirect
68. C4×C3⋊Dic3D4semidirect
76. C3×C4×Dic3D4semidirect
111. #897Dic3semidirect
112. #895Dic3semidirect
240. C4×Dic3D12semidirect
469. C32#1897semidirect
543. C3#68757semidirect
544. C3#71712semidirect

Maximal subgroups

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

subgroupindex
C3×#55242
C2×#638552
C2×#635692
C2×#635682
#105910692
#105893982
C3×#45322
#717123
#687573