Finite Group Databasebeta

← #11792605

Subgroups — #11792605

Order 1152.

861 conjugacy classes of subgroups.

The subgroup lattice has 557 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic
2C2×#63860C211yesmaximal, characteristic
3C22×#3719C211yesmaximal, characteristic, complemented
4C2×#63643C211yesmaximal, characteristic, complemented
5#10591220C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic
7C3×#4550C211yesmaximal, characteristic, complemented
8#72058—31nomaximal
9#68677—31nomaximal
10C22×#634C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×C3×#204—22no—
18C2×C3×#204—22no—
19C2×C3×#204—22no—
20C2×(C2×D3)⋊Dic3—22no—
21#63860—22no—
22#63860—22no—
23C2×#3719—22no—
24C2×#3719—22no—
25C2×#3719—22no—
26#63643—22no—
27#63579—22no—
28#63563—22no—
29C22×C3×SD16—31no—
30C22×#216—31no—
31C2×#936—31no—
32C22×Dic12—31no—
33C22×#204D311yescharacteristic
34C2×#875—31no—
35#5229—31no—
36C2×#832—31no—
37C2×#821—31no—
38C2×#816—31no—
39C2×#816—31no—
40C2×#816—61no—
41#4929—31no—
42C3×#336—31no—
43#4550D311yescharacteristic, complemented
44C23×C3×D3—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3⋊Dic3—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634D412yes—
54C22×C3×Dic3—21no—
55C22×C3×Dic3D412yes—
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—
68C2×C32×C8—21no—
69C2×C32×C8—21no—
70C2×C32×C8D412yes—
71C4⋊(C3⋊Dic3)—21no—
72C4⋊(C3⋊Dic3)—21no—
73C3×C4×Dic3—21no—
74C3×C4×Dic3—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8D412yes—
78C3×#204—28no—
79(C2×D3)⋊Dic3—28no—
80#3719—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
89C2×C3×SD16—62no—
90C2×C3×SD16—62no—
91C2×C3×SD16—62no—
92C22×C3×C8—21no—
93C22×C3×C8—31no—
94C22×C3×C8C2×D311yescharacteristic
95C22×C3×C8C2×D311yescharacteristic
96C2×C3×C42—31no—
97C2×#217—62no—
98C2×#216—62no—
99C2×#216—62no—
100C2×#216—62no—
101#936—62no—
102#936—62no—
103C2×(C2×D3)⋊C4—62no—
104C2×C4⋊Dic3—31no—
105C2×C4⋊Dic3—31no—
106C2×C4⋊Dic3—61no—
107C2×C4×Dic3C2×D311yescharacteristic
108C22×C3⋊C8C2×D311yescharacteristic
109C2×Dic12—62no—
110C2×Dic12—62no—
111C2×Dic12—62no—
112C2×#204—22no—
113C2×#204—22no—
114C2×#204—22no—
115#875—62no—
116#875—62no—
117#832—62no—
118C3⋊#95—62no—
119C3⋊#95—62no—
120#821—62no—
121#816—64no—
122#816—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×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—41no—
138C2×C3⋊Dic3—41no—
139C2×C3⋊Dic3—41no—
140C2×C3⋊Dic3—42no—
141#634—22no—
142#634—22no—
143#634—41no—
144#634—41no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
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—
159C32×C8—22no—
160C3×C3⋊C8—22no—
161C22×Q16—91no—
162C22×SD16—31no—
163C2×#124—91no—
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—21no—
183C22×C3×C4—32no—
184C22×C3×C4—61no—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C22×Dic3—21no—
188C22×Dic3—61no—
189C22×Dic3—61no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C22×Dic3—121no—
193C22×Dic3—121no—
194C22×Dic3D1212yes—
195C2×D12—21no—
196C2×D12—21no—
197C2×D12—21no—
198C2×D12—21no—
199C2×D12—21no—
200C2×D12#6712yes—
201C2×Dic6—21no—
202C2×Dic6—21no—
203C2×Dic6—21no—
204C2×Dic6—21no—
205C2×Dic6—21no—
206C2×Dic6—32no—
207C2×Dic6—32no—
208C2×Dic6—62no—
209C2×Dic6—62no—
210C2×Dic6—62no—
211C2×Dic6—61no—
212C2×Dic6—61no—
213C2×Dic6—61no—
214C2×Dic6—61no—
215C2×Dic6—61no—
216C2×Dic6—61no—
217C2×Dic6—61no—
218C2×Dic6—61no—
219C2×Dic6—61no—
220C2×Dic6—61no—
221C2×Dic6—121no—
222C2×Dic6—121no—
223C2×Dic6—121no—
224C2×Dic6#6712yes—
225C3×SD16—68no—
226C2×C3×C8—21no—
227C2×C3×C8—21no—
228C2×C3×C8—21no—
229C2×C3×C8—21no—
230C2×C3×C8—22no—
231C2×C3×C8—32no—
232C2×C3×C8—41no—
233C2×C3×C8—41no—
234C2×C3×C8—61no—
235C2×C3×C8—61no—
236C2×C3×C8D1212yes—
237C2×C3×C8#6712yes—
238C3×C42—61no—
239C3×C42—61no—
240#217—68no—
241#216—68no—
242(C2×D3)⋊C4—68no—
243C4⋊Dic3—62no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246C4⋊Dic3—61no—
247C4⋊Dic3—61no—
248C4⋊Dic3—121no—
249C4×Dic3—21no—
250C4×Dic3—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8D1212yes—
254Dic12—68no—
255#204—28no—
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#12011yescharacteristic
267C32×C4#12011yescharacteristic
268C32×C4#12111yescharacteristic
269C32×C4#12111yescharacteristic
270C3⋊Dic3—42no—
271C3⋊Dic3—81no—
272C3×Dic3—42no—
273C3×Dic3—42no—
274C22×Q8—31no—
275C22×Q8—91no—
276C22×D4—31no—
277C2×Q16—182no—
278C2×Q16—182no—
279C2×Q16—182no—
280C2×SD16—62no—
281C2×SD16—62no—
282C2×SD16—62no—
283C22×C8—31no—
284C22×C8D3211yescharacteristic
285#124—182no—
286#124—182no—
287C2×C4⋊C4—91no—
288C2×C22⋊C4—182no—
289C2×C42—31no—
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×C3D3×D411yescharacteristic
301C22×D3—22no—
302C22×D3—42no—
303C22×D3—42no—
304C22×D3—41no—
305C22×D3—41no—
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—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—62no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—121no—
325C2×C3×C4—121no—
326C2×C3×C4C2×D1211yescharacteristic
327C2×C3×C4C2×D1211yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4#23711yescharacteristic
334C2×C3×C4#23911yescharacteristic
335C2×C3×C4C2×#6711yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337C2×C3×C4C2×#6711yescharacteristic
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—41no—
343C2×Dic3—41no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—122no—
347C2×Dic3—122no—
348C2×Dic3—122no—
349C2×Dic3—121no—
350C2×Dic3—121no—
351C2×Dic3—121no—
352C2×Dic3—121no—
353C2×Dic3—122no—
354C2×Dic3—121no—
355C2×Dic3—122no—
356C2×Dic3—122no—
357C2×Dic3—121no—
358C2×Dic3—242no—
359D12—22no—
360D12—22no—
361D12—41no—
362D12—41no—
363Dic6—22no—
364Dic6—22no—
365Dic6—41no—
366Dic6—41no—
367Dic6—64no—
368Dic6—62no—
369Dic6—62no—
370Dic6—62no—
371Dic6—62no—
372Dic6—122no—
373Dic6—122no—
374Dic6—122no—
375Dic6—121no—
376Dic6—121no—
377Dic6—121no—
378Dic6—121no—
379C3×C8—22no—
380C3×C8—22no—
381C3×C8—42no—
382C3×C8—62no—
383C3⋊C8—22no—
384C2×C32#39211yescharacteristic
385C2×C32#45212yes—
386C2×C32#46412yes—
387C2×C32#49511yescharacteristic
388C2×C32#49711yescharacteristic
389C3×D3—82no—
390C24—61no—
391C2×Q8—32no—
392C2×Q8—61no—
393C2×Q8—61no—
394C2×Q8—61no—
395C2×Q8—61no—
396C2×Q8—61no—
397C2×Q8—92no—
398C2×Q8—181no—
399C2×Q8—181no—
400C2×Q8—181no—
401C2×Q8—181no—
402C2×Q8—181no—
403C2×D4—32no—
404C2×D4—61no—
405C2×D4—61no—
406C2×D4—61no—
407C2×D4—61no—
408C2×D4—61no—
409C22×C4—32no—
410C22×C4—61no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4C2×D3211yescharacteristic
414Q16—188no—
415SD16—68no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—32no—
419C2×C8—61no—
420C2×C8—61no—
421C2×C8#62612yes—
422C4⋊C4—181no—
423C4⋊C4—181no—
424C22⋊C4—188no—
425C42—61no—
426C42—61no—
427C22×C3—22no—
428C22×C3—22no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—122no—
433C22×C3—124no—
434C22×C3—241no—
435C22×C3—241no—
436C22×C3—242no—
437C22×C3#87411yescharacteristic
438C22×C3#88211yescharacteristic
439C22×C3#89511yescharacteristic
440C22×C3#90412yes—
441C22×C3#90912yes—
442C22×C3#91512yes—
443C22×C3#91612yes—
444C22×C3#93711yescharacteristic
445C22×C3#93911yescharacteristic
446C22×C3#94011yescharacteristic
447C2×D3—44no—
448C2×D3—42no—
449C2×D3—82no—
450C2×D3—81no—
451C2×D3—81no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—122no—
457C3×C4—122no—
458C3×C4#88211yescharacteristic
459C3×C4#88211yescharacteristic
460C3×C4#89511yescharacteristic
461C3×C4#89511yescharacteristic
462C3×C4#93711yescharacteristic
463C3×C4#93811yescharacteristic
464C3×C4#93911yescharacteristic
465C3×C4#95311yescharacteristic
466Dic3—42no—
467Dic3—42no—
468Dic3—124no—
469Dic3—122no—
470Dic3—122no—
471Dic3—242no—
472Dic3—241no—
473Dic3—241no—
474C32#201511yescharacteristic, complemented, Sylow
475C23—62no—
476C23—122no—
477C23—122no—
478C23—121no—
479C23—121no—
480C23D3×D1211yescharacteristic
481Q8—62no—
482Q8—62no—
483Q8—121no—
484Q8—121no—
485Q8—182no—
486Q8—182no—
487Q8—361no—
488Q8—361no—
489D4—62no—
490D4—62no—
491D4—121no—
492D4—121no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—121no—
498C2×C4—121no—
499C2×C4—182no—
500C2×C4—361no—
501C2×C4—361no—
502C2×C4—362no—
503C2×C4—361no—
504C2×C4#379611yescharacteristic
505C2×C4D3×D1211yescharacteristic
506C2×C4#380211yescharacteristic
507C2×C4C2×#62611yescharacteristic
508C2×C4D3×#6711yescharacteristic
509C2×C4D3×#6711yescharacteristic
510C8—22no—
511C8—62no—
512C2×C3—22no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—22no—
517C2×C3—242no—
518C2×C3#467111yescharacteristic
519C2×C3#469611yescharacteristic
520C2×C3#471511yescharacteristic
521C2×C3#473312yes—
522C2×C3#484512yes—
523C2×C3#516612yes—
524C2×C3#516711yescharacteristic
525C2×C3#516811yescharacteristic
526C2×C3#517312yes—
527C2×C3#522311yescharacteristic
528D3—82no—
529C22—122no—
530C22—124no—
531C22—242no—
532C22—241no—
533C22—241no—
534C22#6380012yes—
535C22#6380612yes—
536C22#6388611yescharacteristic
537C22#6391111yescharacteristic
538C22#6392211yescharacteristic
539C4—122no—
540C4—122no—
541C4—362no—
542C4—721no—
543C4#6388611yescharacteristic
544C4#6391611yescharacteristic
545C4#6392211yescharacteristic
546C4#6397711yescharacteristic
547C3—21no—
548C3#6867711yescharacteristic, complemented
549C3#7205811yescharacteristic, complemented
550C2—242no—
551C2#1059085912yes—
552C2#1059086211yescharacteristic
553C2#1059089711yescharacteristic
554C2#1059096012yes—
555C2#1059139111yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×C8D32
hypocenterC32#2015
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C22×#3719C2semidirect
4. C2×#63643C2semidirect
5. #10591220C2semidirect
7. C3×#4550C2semidirect
43. #4550D3semidirect
474. C32#2015semidirect
548. C3#68677semidirect
549. C3#72058semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2042
C2×#638602
C22×#37192
C2×#636432
#105912202
C2×#635632
C3×#45502
#720583
#686773