Finite Group Databasebeta

← #11792608

Subgroups — #11792608

Order 1152.

873 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#875C211yesmaximal, characteristic
2C22×#3719C211yesmaximal, characteristic, complemented
3C22×#3716C211yesmaximal, characteristic
4#10592628C211yesmaximal, characteristic, complemented
5C2×#63566C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic
7C3×#4524C211yesmaximal, characteristic, complemented
8#71729—31nomaximal
9#68677—31nomaximal
10C22×#634C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—22no—
16C22×C3×C3⋊C8C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C3×#875—22no—
19C3×#875—22no—
20C2×#3719—22no—
21C2×#3719—22no—
22C2×#3719—22no—
23C2×#3716—22no—
24C2×#3716—22no—
25C2×#3716—22no—
26#63658—22no—
27#63566—22no—
28#63563—22no—
29C2×C3×#124—31no—
30C22×#216—31no—
31C22×#214—31no—
32C22×Dic12—31no—
33C22×#204—31no—
34C2×#875D311yescharacteristic
35C2×#835—31no—
36C2×#832—31no—
37C2×#821—31no—
38C2×#816—31no—
39#4929—31no—
40#4929—31no—
41#4929—61no—
42C3×#336—31no—
43#4524D311yescharacteristic, complemented
44C23×C3×D3—21no—
45C22×C32×C4D412yes—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634—21no—
54C2×#634D412yes—
55C22×C3×Dic3—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12D412yes—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6D412yes—
68C32×C42—21no—
69C32×C42—21no—
70C4⋊(C3⋊Dic3)—21no—
71C4⋊(C3⋊Dic3)—21no—
72C3×(C2×D3)⋊C4—28no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8D412yes—
78C2×C3×C3⋊C8D412yes—
79#3719—28no—
80#3716—28no—
81#2015—91noSylow
82C22×C3×Q8—31no—
83C22×C3×D4—31no—
84C22×D12C2×D311yescharacteristic
85C22×Dic6—31no—
86C22×Dic6—31no—
87C22×Dic6—61no—
88C22×Dic6C2×D311yescharacteristic
89C22×C3×C8—31no—
90C22×C3×C8—31no—
91C3×#124—62no—
92C3×#124—62no—
93C2×C3×C22⋊C4—62no—
94C2×C3×C42—21no—
95C2×C3×C42C2×D311yescharacteristic
96C2×C3×C42C2×D311yescharacteristic
97C2×#216—62no—
98C2×#216—62no—
99C2×#216—62no—
100C2×#214—62no—
101C2×#214—62no—
102C2×#214—62no—
103C2×(C2×D3)⋊C4—22no—
104C2×C4⋊Dic3—31no—
105C2×C4⋊Dic3—31no—
106C2×C4⋊Dic3—61no—
107C22×C3⋊C8C2×D311yescharacteristic
108C22×C3⋊C8C2×D311yescharacteristic
109C2×Dic12—62no—
110C2×Dic12—62no—
111C2×Dic12—62no—
112C2×#204—62no—
113C2×#204—62no—
114C2×#204—62no—
115#875—22no—
116#875—22no—
117#835—62no—
118#832—62no—
119C3⋊#95—64no—
120C3⋊#95—62no—
121C3⋊#95—62no—
122#821—62no—
123#816—62no—
124C23×C32C2×D411yescharacteristic
125C22×C3×D3—22no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—42no—
129C22×C3×D3—42no—
130C2×C32×C4—22no—
131C2×C32×C4—22no—
132C2×C32×C4—22no—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4#4111yescharacteristic
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—41no—
141C2×C3⋊Dic3—41no—
142C2×C3⋊Dic3—41no—
143C2×C3⋊Dic3—42no—
144#634—22no—
145#634—22no—
146#634—41no—
147#634—41no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C3×D12—22no—
152C3×D12—22no—
153C3×D12—41no—
154C3×D12—41no—
155C3×Dic6—22no—
156C3×Dic6—22no—
157C3×Dic6—41no—
158C3×Dic6—41no—
159C3×C3⋊C8—22no—
160C3×C3⋊C8—22no—
161C22×Q16—91no—
162C22×SD16—91no—
163C2×#124—31no—
164C2×#103—91no—
165C2×#102—91no—
166#391—91no—
167#336—31no—
168C24×C3—61no—
169C23×D3—21no—
170C2×C3×Q8—32no—
171C2×C3×Q8—61no—
172C2×C3×Q8—61no—
173C2×C3×Q8—61no—
174C2×C3×Q8—61no—
175C2×C3×Q8—61no—
176C2×C3×D4—32no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C2×C3×D4—61no—
181C2×C3×D4—61no—
182C22×C3×C4—22no—
183C22×C3×C4—21no—
184C22×C3×C4—61no—
185C22×C3×C4D1212yes—
186C22×C3×C4#6712yes—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C22×Dic3—21no—
190C22×Dic3—62no—
191C22×Dic3—61no—
192C22×Dic3—61no—
193C22×Dic3—62no—
194C22×Dic3—61no—
195C22×Dic3—61no—
196C2×D12—21no—
197C2×D12—21no—
198C2×D12—21no—
199C2×D12—21no—
200C2×D12—21no—
201C2×D12#6712yes—
202C2×Dic6—21no—
203C2×Dic6—21no—
204C2×Dic6—21no—
205C2×Dic6—21no—
206C2×Dic6—21no—
207C2×Dic6—32no—
208C2×Dic6—32no—
209C2×Dic6—62no—
210C2×Dic6—61no—
211C2×Dic6—61no—
212C2×Dic6—61no—
213C2×Dic6—61no—
214C2×Dic6—61no—
215C2×Dic6—61no—
216C2×Dic6—61no—
217C2×Dic6—61no—
218C2×Dic6—62no—
219C2×Dic6—61no—
220C2×Dic6—61no—
221C2×Dic6—121no—
222C2×Dic6—121no—
223C2×Dic6—121no—
224C2×Dic6—121no—
225C2×Dic6#6712yes—
226C2×C3×C8—32no—
227C2×C3×C8—32no—
228C2×C3×C8—61no—
229C2×C3×C8—61no—
230C2×C3×C8—61no—
231C2×C3×C8—61no—
232C3×C22⋊C4—68no—
233C3×C42—21no—
234C3×C42—21no—
235C3×C42—21no—
236C3×C42—21no—
237C3×C42—41no—
238C3×C42—41no—
239#216—68no—
240#214—68no—
241(C2×D3)⋊C4—28no—
242C4⋊Dic3—61no—
243C4⋊Dic3—61no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246C4⋊Dic3—121no—
247C4⋊Dic3—121no—
248C2×C3⋊C8—21no—
249C2×C3⋊C8—21no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8D1212yes—
253C2×C3⋊C8D1212yes—
254Dic12—68no—
255#204—68no—
256C22×C32#12011yescharacteristic
257C22×C32#12111yescharacteristic
258C22×C32#12711yescharacteristic
259C22×C32#13512yes—
260C22×C32#13712yes—
261C2×C3×D3—42no—
262C2×C3×D3—44no—
263C2×C3×D3—82no—
264C2×C3×D3—81no—
265C2×C3×D3—81no—
266C32×C4—42no—
267C32×C4#12011yescharacteristic
268C32×C4#12011yescharacteristic
269C32×C4#12111yescharacteristic
270C32×C4#12111yescharacteristic
271C3⋊Dic3—42no—
272C3⋊Dic3—81no—
273C3×Dic3—42no—
274C22×Q8—31no—
275C22×Q8—91no—
276C22×D4—31no—
277C2×Q16—182no—
278C2×Q16—182no—
279C2×Q16—182no—
280C2×SD16—182no—
281C2×SD16—182no—
282C2×SD16—182no—
283C22×C8—31no—
284C22×C8—31no—
285#124—62no—
286#124—62no—
287C2×C4⋊C4—91no—
288C2×C22⋊C4—62no—
289C2×C42D3211yescharacteristic
290#103—182no—
291#102—182no—
292#95—182no—
293C23×C3—21no—
294C23×C3—62no—
295C23×C3—121no—
296C23×C3—121no—
297C23×C3—122no—
298C23×C3—122no—
299C23×C3C2×D1211yescharacteristic
300C23×C3C2×#6711yescharacteristic
301C22×D3—22no—
302C22×D3—41no—
303C22×D3—41no—
304C22×D3—42no—
305C22×D3—42no—
306C3×Q8—62no—
307C3×Q8—62no—
308C3×Q8—121no—
309C3×Q8—121no—
310C3×D4—62no—
311C3×D4—62no—
312C3×D4—121no—
313C3×D4—121no—
314C2×C3×C4—24no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
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—42no—
328C2×C3×C4—42no—
329C2×C3×C4—62no—
330C2×C3×C4—121no—
331C2×C3×C4—121no—
332C2×C3×C4C2×D1211yescharacteristic
333C2×C3×C4C2×D1211yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4#23711yescharacteristic
341C2×C3×C4#23911yescharacteristic
342C2×C3×C4C2×#6711yescharacteristic
343C2×C3×C4C2×#6711yescharacteristic
344C2×Dic3—22no—
345C2×Dic3—41no—
346C2×Dic3—41no—
347C2×Dic3—64no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—122no—
351C2×Dic3—122no—
352C2×Dic3—121no—
353C2×Dic3—121no—
354C2×Dic3—121no—
355C2×Dic3—121no—
356C2×Dic3—122no—
357C2×Dic3—124no—
358C2×Dic3—121no—
359C2×Dic3—122no—
360C2×Dic3—121no—
361C2×Dic3—122no—
362D12—22no—
363D12—22no—
364D12—41no—
365D12—41no—
366Dic6—22no—
367Dic6—22no—
368Dic6—41no—
369Dic6—41no—
370Dic6—62no—
371Dic6—62no—
372Dic6—62no—
373Dic6—62no—
374Dic6—122no—
375Dic6—122no—
376Dic6—122no—
377Dic6—122no—
378Dic6—121no—
379Dic6—121no—
380Dic6—121no—
381Dic6—121no—
382C3×C8—62no—
383C3×C8—62no—
384C3⋊C8—22no—
385C3⋊C8—22no—
386C2×C32#39211yescharacteristic
387C2×C32#45212yes—
388C2×C32#46412yes—
389C2×C32#49511yescharacteristic
390C2×C32#49711yescharacteristic
391C3×D3—82no—
392C24—61no—
393C2×Q8—32no—
394C2×Q8—61no—
395C2×Q8—61no—
396C2×Q8—61no—
397C2×Q8—61no—
398C2×Q8—61no—
399C2×Q8—92no—
400C2×Q8—181no—
401C2×Q8—181no—
402C2×Q8—181no—
403C2×Q8—181no—
404C2×Q8—181no—
405C2×D4—32no—
406C2×D4—61no—
407C2×D4—61no—
408C2×D4—61no—
409C2×D4—61no—
410C2×D4—61no—
411C22×C4—61no—
412C22×C4—181no—
413C22×C4—181no—
414C22×C4#62612yes—
415C22×C4C2×D3211yescharacteristic
416Q16—188no—
417SD16—188no—
418C2×C8—32no—
419C2×C8—32no—
420C2×C8—61no—
421C2×C8—61no—
422C2×C8—61no—
423C2×C8—61no—
424C4⋊C4—181no—
425C4⋊C4—181no—
426C22⋊C4—68no—
427C42—21no—
428C42—21no—
429C22×C3—22no—
430C22×C3—22no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—122no—
435C22×C3—124no—
436C22×C3—241no—
437C22×C3—241no—
438C22×C3—242no—
439C22×C3#87411yescharacteristic
440C22×C3#88211yescharacteristic
441C22×C3#89511yescharacteristic
442C22×C3#90412yes—
443C22×C3#90912yes—
444C22×C3#93811yescharacteristic
445C22×C3#94011yescharacteristic
446C22×C3#95012yes—
447C22×C3#95112yes—
448C22×C3#95311yescharacteristic
449C2×D3—42no—
450C2×D3—44no—
451C2×D3—82no—
452C2×D3—81no—
453C2×D3—81no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—44no—
459C3×C4—42no—
460C3×C4—42no—
461C3×C4—122no—
462C3×C4#88211yescharacteristic
463C3×C4#88211yescharacteristic
464C3×C4#89511yescharacteristic
465C3×C4#89511yescharacteristic
466C3×C4#93711yescharacteristic
467C3×C4#93711yescharacteristic
468C3×C4#93911yescharacteristic
469C3×C4#93911yescharacteristic
470Dic3—42no—
471Dic3—124no—
472Dic3—122no—
473Dic3—122no—
474Dic3—242no—
475Dic3—241no—
476Dic3—241no—
477C32#201511yescharacteristic, complemented, Sylow
478C23—62no—
479C23—122no—
480C23—122no—
481C23—121no—
482C23—121no—
483C23C2×#62611yescharacteristic
484Q8—62no—
485Q8—62no—
486Q8—121no—
487Q8—121no—
488Q8—182no—
489Q8—182no—
490Q8—361no—
491Q8—361no—
492D4—62no—
493D4—62no—
494D4—121no—
495D4—121no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—62no—
500C2×C4—121no—
501C2×C4—121no—
502C2×C4—182no—
503C2×C4—361no—
504C2×C4—361no—
505C2×C4—362no—
506C2×C4—361no—
507C2×C4#379611yescharacteristic
508C2×C4D3×D1211yescharacteristic
509C2×C4D3×D1211yescharacteristic
510C2×C4#380211yescharacteristic
511C2×C4D3×#6711yescharacteristic
512C2×C4D3×#6711yescharacteristic
513C8—62no—
514C8—62no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—22no—
519C2×C3—22no—
520C2×C3—242no—
521C2×C3#467111yescharacteristic
522C2×C3#469611yescharacteristic
523C2×C3#471511yescharacteristic
524C2×C3#473312yes—
525C2×C3#484512yes—
526C2×C3#505412yes—
527C2×C3#505911yescharacteristic
528C2×C3#506011yescharacteristic
529C2×C3#522311yescharacteristic
530C2×C3#523912yes—
531D3—82no—
532C22—122no—
533C22—124no—
534C22—241no—
535C22—241no—
536C22—242no—
537C22#6382912yes—
538C22#6383112yes—
539C22#6391111yescharacteristic
540C22#6391611yescharacteristic
541C22#6397711yescharacteristic
542C4—42no—
543C4—122no—
544C4—362no—
545C4—721no—
546C4#6388611yescharacteristic
547C4#6388611yescharacteristic
548C4#6392211yescharacteristic
549C4#6392211yescharacteristic
550C3—21no—
551C3#6867711yescharacteristic, complemented
552C3#7172911yescharacteristic, complemented
553C2—242no—
554C2#1059037011yescharacteristic
555C2#1059037211yescharacteristic
556C2#1059037812yes—
557C2#1059117312yes—
558C2#1059139111yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32#2015
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C22×#3719C2semidirect
4. #10592628C2semidirect
5. C2×#63566C2semidirect
7. C3×#4524C2semidirect
43. #4524D3semidirect
477. C32#2015semidirect
551. C3#68677semidirect
552. C3#71729semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8752
C22×#37192
C22×#37162
#105926282
C2×#635662
C2×#635632
C3×#45242
#717293
#686773