Finite Group Databasebeta

← #11791044

Subgroups — #11791044

Order 1152.

937 conjugacy classes of subgroups.

The subgroup lattice has 563 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3753C211yesmaximal, characteristic
2C3×#5221C211yesmaximal, characteristic, complemented
3C2×C3×#832C211yesmaximal, characteristic, complemented
4#10591320C211yesmaximal, characteristic, complemented
5C2×#63576C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic, complemented
7C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
8#70190—31nomaximal
9#69647—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×#3753—22no—
13C2×#3753—22no—
14C2×#3753C414yescomplemented
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×#217—22no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×#3722—22no—
22C3×#832—22no—
23#63576—22no—
24#63564—22no—
25Dic3×C3⋊C8—22no—
26C22×#213—31no—
27C22×#213—31no—
28C22×#213—61no—
29C2×C3×#102—31no—
30C3×#390—31no—
31#5221D311yescharacteristic, complemented
32C2×#832D311yescharacteristic, complemented
33C2×#821—31no—
34C2×C8×Dic3—31no—
35#4988—31no—
36C2×#809—31no—
37C2×#807—31no—
38C2×#807—31no—
39#4939—31no—
40C2×C4×C3⋊C8—31no—
41C24×C32—21no—
42C23×C3⋊D3—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4C2×C412yes—
49C22×C32×C4C2311yescharacteristic
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)C2×C412yes—
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3D412yes—
59#3753—28no—
60C2×C3⋊(C3⋊C8)C2×C412yes—
61C2×C3⋊(C3⋊C8)D412yes—
62C2×C3⋊(C3⋊C8)D412yes—
63C3×#217—44no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4×Dic3—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8D412yes—
73#3722—44no—
74#1970—91noSylow
75C22×C3×D4—21no—
76C22×C3×D4C2×D311yescharacteristic
77C22×C3×D4C2×D311yescharacteristic
78C22×D12—31no—
79C22×D12—31no—
80C22×D12—61no—
81C22×C3×C8—31no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C22⋊C4—62no—
85C2×C3×C42—31no—
86C2×#217—22no—
87C2×#213—34no—
88C2×#213—34no—
89C2×#213—64no—
90C2×#213—62no—
91C2×#213—62no—
92C2×#213—62no—
93C2×#213—62no—
94C2×#213—64no—
95C2×#213—64no—
96C2×(C2×D3)⋊C4—62no—
97C2×(C2×D3)⋊C4—62no—
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×C4⋊Dic3C2×D311yescharacteristic
100C2×C4×Dic3C2×D311yescharacteristic
101C22×C3⋊C8—31no—
102C22×C3⋊C8—31no—
103C22×C3⋊C8—61no—
104C22×C3⋊C8C2×D311yescharacteristic
105C3×#102—62no—
106#832—22no—
107#821—62no—
108C8×Dic3—62no—
109#809—62no—
110#807—62no—
111#807—62no—
112C4×C3⋊C8—62no—
113C23×C32—22no—
114C23×C32—41no—
115C23×C32—41no—
116C23×C32—42no—
117C23×C32—42no—
118C23×C32C2×D411yescharacteristic
119C22×C3⋊D3—22no—
120C22×C3⋊D3—41no—
121C22×C3⋊D3—41no—
122C22×C3⋊D3—42no—
123C22×C3⋊D3—42no—
124C32×D4—22no—
125C32×D4—22no—
126C32×D4—41no—
127C32×D4—41no—
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C4⋊(C3⋊D3)—22no—
135C4⋊(C3⋊D3)—22no—
136C4⋊(C3⋊D3)—41no—
137C4⋊(C3⋊D3)—41no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—42no—
143C2×C3×Dic3—42no—
144C2×C3×Dic3D814yescomplemented
145C3⋊(C3⋊C8)C22⋊C414yescomplemented
146C3×C3⋊C8—22no—
147C22×D8—91no—
148C2×#107—91no—
149C2×#102—31no—
150C2×#102—91no—
151C2×C4×C8—91no—
152#390—31no—
153#390—91no—
154C24×C3—21no—
155C24×C3—21no—
156C24×C3—41no—
157C23×D3—61no—
158C23×D3—61no—
159C23×D3—121no—
160C2×C3×D4—22no—
161C2×C3×D4—22no—
162C2×C3×D4—21no—
163C2×C3×D4—21no—
164C2×C3×D4—21no—
165C2×C3×D4—21no—
166C2×C3×D4—21no—
167C2×C3×D4—21no—
168C2×C3×D4—21no—
169C2×C3×D4—21no—
170C2×C3×D4—21no—
171C2×C3×D4—21no—
172C2×C3×D4—22no—
173C2×C3×D4—41no—
174C2×C3×D4—41no—
175C2×C3×D4—41no—
176C2×C3×D4C4×D312yes—
177C2×C3×D4C4×D312yes—
178C22×C3×C4—21no—
179C22×C3×C4—32no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C22×Dic3—21no—
185C22×Dic3—21no—
186C22×Dic3#6712yes—
187C2×D12—32no—
188C2×D12—32no—
189C2×D12—62no—
190C2×D12—62no—
191C2×D12—62no—
192C2×D12—61no—
193C2×D12—61no—
194C2×D12—61no—
195C2×D12—61no—
196C2×D12—61no—
197C2×D12—61no—
198C2×D12—61no—
199C2×D12—61no—
200C2×D12—61no—
201C2×D12—61no—
202C2×D12—121no—
203C2×D12—121no—
204C2×D12—121no—
205C2×C3×C8—32no—
206C2×C3×C8—61no—
207C2×C3×C8—61no—
208C3×C4⋊C4—61no—
209C3×C4⋊C4—61no—
210C3×C4⋊C4—61no—
211C3×C4⋊C4—61no—
212C3×C22⋊C4—124no—
213C3×C42—61no—
214C3×C42—61no—
215#217—44no—
216#213—68no—
217#213—68no—
218#213—616no—
219(C2×D3)⋊C4—124no—
220(C2×D3)⋊C4—124no—
221C4⋊Dic3—21no—
222C4⋊Dic3—21no—
223C4⋊Dic3—21no—
224C4⋊Dic3—21no—
225C4×Dic3—21no—
226C4×Dic3—21no—
227C2×C3⋊C8—21no—
228C2×C3⋊C8—21no—
229C2×C3⋊C8—32no—
230C2×C3⋊C8—32no—
231C2×C3⋊C8—32no—
232C2×C3⋊C8—32no—
233C2×C3⋊C8—32no—
234C2×C3⋊C8—32no—
235C2×C3⋊C8—62no—
236C2×C3⋊C8—62no—
237C2×C3⋊C8—62no—
238C2×C3⋊C8#6712yes—
239C22×C32—42no—
240C22×C32—44no—
241C22×C32—82no—
242C22×C32—81no—
243C22×C32—81no—
244C22×C32C4×D411yescharacteristic
245C22×C32#12111yescharacteristic
246C22×C32#12711yescharacteristic
247C22×C32C2×D812yes—
248C22×C32#13512yes—
249C2×C3⋊D3—42no—
250C2×C3⋊D3—44no—
251C2×C3⋊D3—82no—
252C2×C3⋊D3—81no—
253C2×C3⋊D3—81no—
254C32×C4C2×C22⋊C411yescharacteristic
255C32×C4C4×D411yescharacteristic
256C32×C4#12111yescharacteristic
257C32×C4#12411yescharacteristic
258C3×Dic3—24no—
259C3×Dic3—81no—
260C3×Dic3—81no—
261C22×D4—91no—
262C22×D4D3211yescharacteristic
263C2×D8—94no—
264C2×D8—182no—
265C2×D8—182no—
266C22×C8—31no—
267C22×C8—91no—
268C2×C4⋊C4—31no—
269C2×C4⋊C4—31no—
270C2×C22⋊C4—62no—
271C2×C22⋊C4—182no—
272C2×C42—31no—
273#107—182no—
274#102—62no—
275#102—182no—
276C4×C8—182no—
277C23×C3—22no—
278C23×C3—22no—
279C23×C3—21no—
280C23×C3—42no—
281C23×C3—42no—
282C23×C3—42no—
283C23×C3—41no—
284C23×C3—42no—
285C23×C3—42no—
286C23×C3—42no—
287C23×C3—41no—
288C23×C3—41no—
289C23×C3—41no—
290C23×C3—42no—
291C23×C3—82no—
292C23×C3—82no—
293C23×C3D3×D411yescharacteristic
294C23×C3C2×#6711yescharacteristic
295C22×D3—62no—
296C22×D3—62no—
297C22×D3—122no—
298C22×D3—122no—
299C22×D3—122no—
300C22×D3—121no—
301C22×D3—122no—
302C22×D3—122no—
303C22×D3—122no—
304C22×D3—121no—
305C22×D3—121no—
306C22×D3—121no—
307C22×D3—122no—
308C22×D3—242no—
309C22×D3—242no—
310C3×D4—24no—
311C3×D4—22no—
312C3×D4—22no—
313C3×D4—22no—
314C3×D4—22no—
315C3×D4—42no—
316C3×D4—42no—
317C3×D4—42no—
318C3×D4—41no—
319C3×D4—41no—
320C3×D4—41no—
321C3×D4—41no—
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—34no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—122no—
332C2×C3×C4—122no—
333C2×C3×C4—121no—
334C2×C3×C4—121no—
335C2×C3×C4C2×C4×D311yescharacteristic
336C2×C3×C4C2×C4×D311yescharacteristic
337C2×C3×C4#23511yescharacteristic
338C2×C3×C4#23511yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4#23711yescharacteristic
345C2×C3×C4#23711yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×Dic3—22no—
348C2×Dic3—22no—
349C2×Dic3—42no—
350C2×Dic3—42no—
351C2×Dic3—41no—
352C2×Dic3—41no—
353C2×Dic3#21314yescomplemented
354D12—64no—
355D12—62no—
356D12—62no—
357D12—62no—
358D12—62no—
359D12—122no—
360D12—122no—
361D12—122no—
362D12—121no—
363D12—121no—
364D12—121no—
365D12—121no—
366C3×C8—62no—
367C3⋊C8—22no—
368C3⋊C8—34no—
369C3⋊C8—34no—
370C3⋊C8—64no—
371C2×C32—82no—
372C2×C32#39011yescharacteristic
373C2×C32C4×D812yes—
374C2×C32#46612yes—
375C2×C32#49311yescharacteristic
376C2×C32#49511yescharacteristic
377C3⋊D3—82no—
378C24—21no—
379C24—181no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—92no—
386C2×D4—181no—
387C2×D4—181no—
388C2×D4—181no—
389C2×D4—181no—
390C2×D4—181no—
391C2×D4#62412yes—
392C22×C4—32no—
393C22×C4—61no—
394C22×C4—61no—
395C22×C4C2×D3211yescharacteristic
396D8—188no—
397C2×C8—32no—
398C2×C8—61no—
399C2×C8—61no—
400C2×C8—92no—
401C2×C8—92no—
402C2×C8—92no—
403C4⋊C4—61no—
404C4⋊C4—61no—
405C4⋊C4—61no—
406C4⋊C4—61no—
407C22⋊C4—124no—
408C22⋊C4—364no—
409C42—61no—
410C42—61no—
411C22×C3—22no—
412C22×C3—22no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—44no—
417C22×C3—42no—
418C22×C3—42no—
419C22×C3—44no—
420C22×C3—44no—
421C22×C3—84no—
422C22×C3—84no—
423C22×C3—82no—
424C22×C3—82no—
425C22×C3—81no—
426C22×C3—81no—
427C22×C3—82no—
428C22×C3—82no—
429C22×C3—81no—
430C22×C3—81no—
431C22×C3#67⋊C411yescharacteristic
432C22×C3#88411yescharacteristic
433C22×C3D3×D812yes—
434C22×C3#91612yes—
435C22×C3C4×#6711yescharacteristic
436C22×C3C2×#21312yes—
437C22×C3#93911yescharacteristic
438C22×C3#94011yescharacteristic
439C22×C3#94011yescharacteristic
440C22×C3#95012yes—
441C2×D3—124no—
442C2×D3—122no—
443C2×D3—122no—
444C2×D3—124no—
445C2×D3—124no—
446C2×D3—244no—
447C2×D3—244no—
448C2×D3—242no—
449C2×D3—242no—
450C2×D3—241no—
451C2×D3—241no—
452C2×D3—242no—
453C2×D3—242no—
454C2×D3—241no—
455C2×D3—241no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—64no—
461C3×C4—241no—
462C3×C4—241no—
463C3×C4D3×C22⋊C411yescharacteristic
464C3×C4D3×C22⋊C411yescharacteristic
465C3×C4#67⋊C411yescharacteristic
466C3×C4#88411yescharacteristic
467C3×C4#88511yescharacteristic
468C3×C4#88511yescharacteristic
469C3×C4C4×#6711yescharacteristic
470C3×C4#93911yescharacteristic
471Dic3—24no—
472Dic3—81no—
473Dic3—81no—
474C32#197011yescharacteristic, complemented, Sylow
475C23—22no—
476C23—42no—
477C23—42no—
478C23—41no—
479C23—41no—
480C23—182no—
481C23—362no—
482C23—362no—
483C23—361no—
484C23—361no—
485C23D3×#6711yescharacteristic
486D4—22no—
487D4—22no—
488D4—41no—
489D4—41no—
490D4—182no—
491D4—182no—
492D4—361no—
493D4—361no—
494C2×C4—34no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—122no—
498C2×C4—122no—
499C2×C4—121no—
500C2×C4—121no—
501C2×C4#380411yescharacteristic
502C2×C4#380411yescharacteristic
503C2×C4C2×#62411yescharacteristic
504C2×C4D3×#6711yescharacteristic
505C2×C4#381111yescharacteristic
506C2×C4#381111yescharacteristic
507C8—62no—
508C8—94no—
509C2×C3—22no—
510C2×C3—21no—
511C2×C3—22no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—84no—
515C2×C3—82no—
516C2×C3—82no—
517C2×C3#475612yes—
518C2×C3#477512yes—
519C2×C3#495711yescharacteristic
520C2×C3#495711yescharacteristic
521C2×C3C4×#21312yes—
522C2×C3#503812yes—
523C2×C3#505911yescharacteristic
524C2×C3#507311yescharacteristic
525C2×C3#515111yescharacteristic
526C2×C3#516811yescharacteristic
527D3—244no—
528D3—242no—
529D3—242no—
530C22—44no—
531C22—42no—
532C22—82no—
533C22—81no—
534C22—81no—
535C22—364no—
536C22—362no—
537C22—722no—
538C22—721no—
539C22—721no—
540C22D3×#21312yes—
541C22#6393512yes—
542C22#6395211yescharacteristic
543C22#6397111yescharacteristic
544C22#6397911yescharacteristic
545C4—64no—
546C4—241no—
547C4—241no—
548C4#6395211yescharacteristic
549C4#6395311yescharacteristic
550C4#6397111yescharacteristic
551C4#6397411yescharacteristic
552C3—21no—
553C3#6964711yescharacteristic, complemented
554C3#7019011yescharacteristic, complemented
555C2—82no—
556C2—722no—
557C2#1059140012yes—
558C2#1059144912yes—
559C2#1059147311yescharacteristic
560C2#1059148211yescharacteristic
561C2#1059170411yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC22×#3753C2
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1970
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C3×#5221C2semidirect
3. C2×C3×#832C2semidirect
4. #10591320C2semidirect
5. C2×#63576C2semidirect
6. C2×#63564C2semidirect
7. C2×Dic3×C3⋊C8C2semidirect
14. C2×#3753C4semidirect
31. #5221D3semidirect
32. C2×#832D3semidirect
144. C2×C3×Dic3D8semidirect
145. C3⋊(C3⋊C8)C22⋊C4semidirect
353. C2×Dic3#213semidirect
474. C32#1970semidirect
553. C3#69647semidirect
554. C3#70190semidirect

Maximal subgroups

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

subgroupindex
C22×#37532
C3×#52212
C2×C3×#8322
#105913202
C2×#635762
C2×#635642
C2×Dic3×C3⋊C82
#701903
#696473