Finite Group Databasebeta

← #11785323

Subgroups — #11785323

Order 1152.

709 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Dic3×#41C211yesmaximal, characteristic
2C2×#63664C211yesmaximal, characteristic
3C2×C3×#837C211yesmaximal, characteristic
4C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
5#10591115C211yesmaximal, characteristic, complemented
6#10589161C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#71646—31nomaximal
9#70355—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×Q8×Dic3C411yescharacteristic, complemented
14C3×Q8×Dic3C411yescharacteristic, complemented
15C3×D4×Dic3—21no—
16C3×D4×Dic3—21no—
17C3×D4×Dic3C411yescharacteristic, complemented
18C3×D4×Dic3C411yescharacteristic, complemented
19C3×#926—21no—
20C3×#926C2211yescharacteristic
21C2×C3×C4×Dic3—21no—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C2×Dic3⋊Dic3—21no—
26#63664—22no—
27C3×#837—22no—
28#63579—21no—
29Dic3⋊(C3⋊C8)—21no—
30Dic3⋊(C3⋊C8)—21no—
31C3×C4×#41—31no—
32Dic3×#41D311yescharacteristic
33C2×C3×#104—31no—
34C2×#837—31no—
35C2×#837—31no—
36C2×#837—61no—
37C2×#837D311yescharacteristic
38#5118—31no—
39C4×C4⋊Dic3—31no—
40C4×Dic3⋊C4—31no—
41#4924—31no—
42#4555—31no—
43#4532—31no—
44#4532—31no—
45#4523—31no—
46C32×#41—21no—
47C32×#41—21no—
48C32×#41D412yes—
49C32×#41Q812yes—
50C2×C32×Q8C2×C411yescharacteristic
51C2×C32×D4—21no—
52C2×C32×D4C2×C411yescharacteristic
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3D411yescharacteristic
60C22×C3×Dic3D411yescharacteristic
61C4×C3⋊Dic3—21no—
62C4×C3⋊Dic3—21no—
63#3748—21no—
64#3748—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C3×#217—21no—
67C3×#217—21no—
68C3×#217—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3C2×C411yescharacteristic
72C3×C4⋊Dic3C2×C411yescharacteristic
73C3×C4×Dic3—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—21no—
88C2×C3×#41C2×D311yescharacteristic
89C2×C3×#41C2×D311yescharacteristic
90C2×C3×M16—31no—
91C3×C4×Q8—31no—
92C3×C4×Q8—31no—
93C3×C4×D4—31no—
94C3×C4×D4—31no—
95C3×C4×D4—61no—
96C3×C4×D4—61no—
97C3×#117—31no—
98C3×#117—61no—
99C2×C3×C42—31no—
100C2×C3×C42—31no—
101C2×C3×C42—61no—
102Q8×Dic3Dic311yescharacteristic, complemented
103Q8×Dic3Dic311yescharacteristic, complemented
104D4×Dic3—21no—
105D4×Dic3—21no—
106D4×Dic3Dic311yescharacteristic, complemented
107D4×Dic3Dic311yescharacteristic, complemented
108#926—21no—
109#926C2×D311yescharacteristic
110C2×C4⋊Dic3—61no—
111C2×Dic3⋊C4—61no—
112C2×C4×Dic3—21no—
113C2×C4×Dic3—31no—
114C2×C4×Dic3—31no—
115C2×C4×Dic3—61no—
116C2×C4×Dic3C2×D311yescharacteristic
117C2×C4×Dic3C2×D311yescharacteristic
118C2×#208—31no—
119C2×#208—31no—
120C2×#208—61no—
121C2×#208C2×D311yescharacteristic
122C3×#104—62no—
123#837—22no—
124#837—64no—
125#837—62no—
126#837—62no—
127C3⋊#95—61no—
128C3⋊#95—61no—
129Dic3⋊C8—61no—
130Dic3⋊C8—61no—
131C4⋊(C3⋊C8)—61no—
132C4⋊(C3⋊C8)—61no—
133C23×C32—21no—
134C23×C32C2×D411yescharacteristic
135C32×Q8—21no—
136C32×Q8C4⋊C412yescomplemented
137C32×D4—22no—
138C32×D4—22no—
139C32×D4—21no—
140C32×D4C4⋊C412yescomplemented
141C2×C32×C4—21no—
142C2×C32×C4—22no—
143C2×C32×C4—22no—
144C2×C32×C4C22×C411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×Q811yescharacteristic
148C2×C32×C4#4111yescharacteristic
149C2×C32×C4#4111yescharacteristic
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—41no—
152C2×C3⋊Dic3—41no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—21no—
156C2×C3×Dic3—21no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3—42no—
159C2×C3×Dic3—41no—
160C2×C3×Dic3—41no—
161C2×C3×Dic3—42no—
162C2×C3×Dic3C22⋊C411yescharacteristic
163C2×C3×Dic3C22⋊C411yescharacteristic
164C2×C3×Dic3C22⋊C411yescharacteristic
165C2×C3×Dic3C22⋊C411yescharacteristic
166C3⋊(C3⋊C8)—41no—
167C3×C3⋊C8—41no—
168C4×#41—31no—
169#423—91no—
170C2×#104—31no—
171C2×#104—91no—
172C4×C4⋊C4—91no—
173#339—91no—
174#339—91no—
175C3×#41—21no—
176C3×#41—21no—
177C3×#41—21no—
178C3×#41—21no—
179C3×#41—22no—
180C3×#41—22no—
181C3×#41—41no—
182C3×#41—41no—
183C3×#41Dic612yes—
184C3×#41Dic612yes—
185C3×#41D1212yes—
186C3×#41#6712yes—
187C2×C3×Q8—21no—
188C2×C3×Q8C4×D311yescharacteristic
189C2×C3×Q8C2×Dic311yescharacteristic
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4—41no—
194C2×C3×D4C4×D311yescharacteristic
195C2×C3×D4C2×Dic311yescharacteristic
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—31no—
200C22×C3×C4—31no—
201C22×C3×C4—41no—
202C22×C3×C4—61no—
203C22×C3×C4—61no—
204C22×C3×C4—61no—
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C22×Dic3—21no—
208C22×Dic3—21no—
209C22×Dic3—21no—
210C22×Dic3—61no—
211C22×Dic3—61no—
212C22×Dic3—121no—
213C22×Dic3#6711yescharacteristic
214C22×Dic3#6711yescharacteristic
215C3×M16—61no—
216C3×M16—61no—
217C2×C3×C8—61no—
218C3×C4⋊C4—31no—
219C3×C4⋊C4—31no—
220C3×C4⋊C4—61no—
221C3×C4⋊C4—61no—
222C3×C22⋊C4—61no—
223C3×C22⋊C4—61no—
224C3×C22⋊C4—61no—
225C3×C42—31no—
226C3×C42—31no—
227C3×C42—31no—
228C3×C42—31no—
229C3×C42—61no—
230C3×C42—61no—
231C3×C42—61no—
232C3×C42—61no—
233C3×C42—61no—
234#217—21no—
235#217—21no—
236#217—21no—
237C4⋊Dic3—21no—
238C4⋊Dic3—21no—
239C4⋊Dic3—64no—
240C4⋊Dic3C2×Dic311yescharacteristic
241C4⋊Dic3C2×Dic311yescharacteristic
242Dic3⋊C4—64no—
243C4×Dic3—21no—
244C4×Dic3—21no—
245C4×Dic3—21no—
246C4×Dic3—21no—
247C4×Dic3—21no—
248C4×Dic3—62no—
249C4×Dic3—61no—
250C4×Dic3—61no—
251C4×Dic3—61no—
252C4×Dic3—61no—
253C4×Dic3—121no—
254C4×Dic3C2×Dic311yescharacteristic
255C4×Dic3C2×Dic311yescharacteristic
256C4×Dic3#6711yescharacteristic
257C4×Dic3#6711yescharacteristic
258#208—21no—
259#208—21no—
260#208—62no—
261#208—61no—
262#208—61no—
263#208—61no—
264#208—61no—
265#208—121no—
266C2×C3⋊C8—21no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8—61no—
269C2×C3⋊C8—121no—
270C22×C32—21no—
271C22×C32—21no—
272C22×C32—22no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32C2×C22⋊C411yescharacteristic
276C22×C32#12111yescharacteristic
277C22×C32C22⋊Q811yescharacteristic
278C32×C4—22no—
279C32×C4C2×C4⋊C411yescharacteristic
280C32×C4#11711yescharacteristic
281C32×C4#12111yescharacteristic
282C32×C4C22⋊Q811yescharacteristic
283C3⋊Dic3—42no—
284C3×Dic3—21no—
285C3×Dic3—21no—
286C3×Dic3—21no—
287C3×Dic3—42no—
288C3×Dic3—41no—
289C3×Dic3—41no—
290C3×Dic3#10412yescomplemented
291C2×#41D3211yescharacteristic
292C2×M16—31no—
293C2×M16—91no—
294C4×Q8—31no—
295C4×Q8—31no—
296C4×D4—31no—
297C4×D4—31no—
298C4×D4—61no—
299C4×D4—61no—
300#117—31no—
301#117—61no—
302C2×C4⋊C4—181no—
303C2×C42—31no—
304C2×C42—31no—
305C2×C42—61no—
306C2×C42—91no—
307C4⋊C8—181no—
308C4⋊C8—181no—
309#104—62no—
310#104—182no—
311#95—181no—
312C23×C3—21no—
313C23×C3—21no—
314C23×C3—21no—
315C23×C3—41no—
316C23×C3D3×D411yescharacteristic
317C23×C3C2×#6711yescharacteristic
318C3×Q8—21no—
319C3×Q8—21no—
320C3×Q8—22no—
321C3×Q8—41no—
322C3×Q8Dic3⋊C412yescomplemented
323C3×Q8C4⋊Dic312yescomplemented
324C3×D4—22no—
325C3×D4—22no—
326C3×D4—22no—
327C3×D4—22no—
328C3×D4—21no—
329C3×D4—21no—
330C3×D4—22no—
331C3×D4—41no—
332C3×D4—42no—
333C3×D4—42no—
334C3×D4Dic3⋊C412yescomplemented
335C3×D4C4⋊Dic312yescomplemented
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—31no—
349C2×C3×C4—31no—
350C2×C3×C4—31no—
351C2×C3×C4—31no—
352C2×C3×C4—42no—
353C2×C3×C4—42no—
354C2×C3×C4—41no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—61no—
358C2×C3×C4—61no—
359C2×C3×C4—122no—
360C2×C3×C4—121no—
361C2×C3×C4—122no—
362C2×C3×C4—121no—
363C2×C3×C4—121no—
364C2×C3×C4C2×Dic611yescharacteristic
365C2×C3×C4C2×Dic611yescharacteristic
366C2×C3×C4C2×C4×D311yescharacteristic
367C2×C3×C4C2×D1211yescharacteristic
368C2×C3×C4#23511yescharacteristic
369C2×C3×C4#23511yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4#23711yescharacteristic
372C2×C3×C4#23711yescharacteristic
373C2×C3×C4C22×Dic311yescharacteristic
374C2×C3×C4C2×#6711yescharacteristic
375C2×C3×C4C2×#6711yescharacteristic
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—21no—
379C2×Dic3—21no—
380C2×Dic3—41no—
381C2×Dic3—42no—
382C2×Dic3—41no—
383C2×Dic3—41no—
384C2×Dic3—42no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—122no—
388C2×Dic3—122no—
389C2×Dic3—121no—
390C2×Dic3—121no—
391C2×Dic3—122no—
392C2×Dic3—121no—
393C2×Dic3—121no—
394C2×Dic3#21711yescharacteristic
395C2×Dic3#21711yescharacteristic
396C2×Dic3#21711yescharacteristic
397C2×Dic3#21711yescharacteristic
398C3×C8—121no—
399C3⋊C8—41no—
400C3⋊C8—122no—
401C3⋊C8—121no—
402C3⋊C8—121no—
403C2×C32—21no—
404C2×C32—21no—
405C2×C32—42no—
406C2×C32#38011yescharacteristic
407C2×C32C2×#10411yescharacteristic
408C2×C32#42111yescharacteristic
409#41—21no—
410#41—21no—
411#41#62612yes—
412#41#62712yes—
413C2×Q8D3×Dic311yescharacteristic
414C2×D4—21no—
415C2×D4D3×Dic311yescharacteristic
416C22×C4—21no—
417C22×C4—31no—
418C22×C4—31no—
419C22×C4—61no—
420C22×C4—61no—
421C22×C4—61no—
422C22×C4—181no—
423C22×C4C2×D3211yescharacteristic
424M16—61no—
425M16—61no—
426M16—181no—
427M16—181no—
428C2×C8—61no—
429C2×C8—181no—
430C4⋊C4—31no—
431C4⋊C4—31no—
432C4⋊C4—61no—
433C4⋊C4—61no—
434C4⋊C4—184no—
435C22⋊C4—61no—
436C22⋊C4—61no—
437C22⋊C4—61no—
438C42—31no—
439C42—31no—
440C42—31no—
441C42—31no—
442C42—61no—
443C42—61no—
444C42—61no—
445C42—61no—
446C42—61no—
447C42—181no—
448C42—181no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—22no—
454C22×C3—22no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—41no—
459C22×C3—41no—
460C22×C3—42no—
461C22×C3—41no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3—41no—
465C22×C3—81no—
466C22×C3—81no—
467C22×C3#87811yescharacteristic
468C22×C3D3×C22⋊C411yescharacteristic
469C22×C3#92411yescharacteristic
470C22×C3#93011yescharacteristic
471C22×C3#93911yescharacteristic
472C22×C3C2×#21711yescharacteristic
473C3×C4—22no—
474C3×C4—22no—
475C3×C4—21no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—21no—
479C3×C4—32no—
480C3×C4—42no—
481C3×C4—61no—
482C3×C4—61no—
483C3×C4—61no—
484C3×C4—122no—
485C3×C4—121no—
486C3×C4—121no—
487C3×C4#87711yescharacteristic
488C3×C4#87811yescharacteristic
489C3×C4C2×Dic3⋊C411yescharacteristic
490C3×C4#92411yescharacteristic
491C3×C4C2×C4⋊Dic311yescharacteristic
492C3×C4#92611yescharacteristic
493C3×C4#93011yescharacteristic
494C3×C4#93911yescharacteristic
495Dic3—21no—
496Dic3—21no—
497Dic3—21no—
498Dic3—42no—
499Dic3—41no—
500Dic3—41no—
501Dic3—122no—
502Dic3—122no—
503Dic3—124no—
504Dic3#83712yescomplemented
505C32#180611yescharacteristic, complemented, Sylow
506C23—21no—
507C23D3×#6711yescharacteristic
508Q8—21no—
509Q8Dic3⋊Dic312yescomplemented
510D4—22no—
511D4—22no—
512D4—21no—
513D4Dic3⋊Dic312yescomplemented
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—31no—
518C2×C4—31no—
519C2×C4—31no—
520C2×C4—31no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—61no—
524C2×C4—61no—
525C2×C4—122no—
526C2×C4—121no—
527C2×C4—122no—
528C2×C4—121no—
529C2×C4—121no—
530C2×C4—182no—
531C2×C4—361no—
532C2×C4—361no—
533C2×C4C2×D3×Dic311yescharacteristic
534C2×C4#380411yescharacteristic
535C2×C4#380411yescharacteristic
536C2×C4C2×#62611yescharacteristic
537C2×C4C2×#62711yescharacteristic
538C2×C4D3×#6711yescharacteristic
539C8—121no—
540C8—361no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—41no—
549C2×C3—41no—
550C2×C3—42no—
551C2×C3—42no—
552C2×C3—82no—
553C2×C3D3×#10411yescharacteristic
554C2×C3#482111yescharacteristic
555C2×C3#494211yescharacteristic
556C2×C3#521211yescharacteristic
557C2×C3C2×#83711yescharacteristic
558C2×C3#523611yescharacteristic
559C22—21no—
560C22—21no—
561C22—22no—
562C22—41no—
563C22—41no—
564C22#6396411yescharacteristic
565C22D3×#21711yescharacteristic
566C22#6397811yescharacteristic
567C4—22no—
568C4—32no—
569C4—61no—
570C4—61no—
571C4—61no—
572C4—122no—
573C4—121no—
574C4—121no—
575C4—362no—
576C4#6395511yescharacteristic
577C4#6396411yescharacteristic
578C4C2×Dic3⋊Dic311yescharacteristic
579C4#6397811yescharacteristic
580C3—21no—
581C3#7035511yescharacteristic, complemented
582C3#7164611yescharacteristic, complemented
583C2—21no—
584C2—21no—
585C2—42no—
586C2D3×#83711yescharacteristic
587C2#1059167011yescharacteristic
588C2#1059171611yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32C2×C22⋊C4
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1806
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
4. C4×Dic3⋊Dic3C2semidirect
5. #10591115C2semidirect
6. #10589161C2semidirect
7. #10589160C2semidirect
13. C3×Q8×Dic3C4semidirect
14. C3×Q8×Dic3C4semidirect
17. C3×D4×Dic3C4semidirect
18. C3×D4×Dic3C4semidirect
102. Q8×Dic3Dic3semidirect
103. Q8×Dic3Dic3semidirect
106. D4×Dic3Dic3semidirect
107. D4×Dic3Dic3semidirect
136. C32×Q8C4⋊C4semidirect
140. C32×D4C4⋊C4semidirect
290. C3×Dic3#104semidirect
322. C3×Q8Dic3⋊C4semidirect
323. C3×Q8C4⋊Dic3semidirect
334. C3×D4Dic3⋊C4semidirect
335. C3×D4C4⋊Dic3semidirect
504. Dic3#837semidirect
505. C32#1806semidirect
509. Q8Dic3⋊Dic3semidirect
513. D4Dic3⋊Dic3semidirect
581. C3#70355semidirect
582. C3#71646semidirect

Maximal subgroups

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

subgroupindex
C3×Dic3×#412
C2×#636642
C2×C3×#8372
C4×Dic3⋊Dic32
#105911152
#105891612
#105891602
#716463
#703553