Finite Group Databasebeta

← #11788681

Subgroups — #11788681

Order 1152.

753 conjugacy classes of subgroups.

The subgroup lattice has 543 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64160C211yesmaximal, characteristic
2C2×C3×#948C211yesmaximal, characteristic
3C3×#5232C211yesmaximal, characteristic
4C2×#63567C211yesmaximal, characteristic, complemented
5C2×#63561C211yesmaximal, characteristic, complemented
6#10589167C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#72019—31nomaximal
9#70304—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×#634C2211yescharacteristic
12#64160—22no—
13#64160C414yescomplemented
14C2×#3756—21no—
15C2×#3754—21no—
16C2×#3748C2211yescharacteristic
17C3×#948—22no—
18C3×#948—22no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×#208—21no—
21C2×C3×#208C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C22×C3×C3⋊C8—21no—
24C22×C3×C3⋊C8C2211yescharacteristic
25C3×#835—21no—
26C3×#832—21no—
27#63567—21no—
28#63567—21no—
29#63561—22no—
30C2×C3×#131—31no—
31C2×#951—31no—
32C2×#951—31no—
33C2×#951—61no—
34C2×#948D311yescharacteristic
35C3×#417—31no—
36#5232D311yescharacteristic
37C2×#824—31no—
38C2×#824—31no—
39C2×#816—31no—
40C2×#810—31no—
41#4558—31no—
42#4554—31no—
43#4552—31no—
44#4530—31no—
45C32×#41—21no—
46C32×#41—21no—
47C32×#41C2×C412yes—
48C32×#41D412yes—
49C2×C32×Q8D411yescharacteristic
50C2×C32×D4—21no—
51C2×C32×D4D411yescharacteristic
52C22×C32×C4—21no—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C2×#634—21no—
56C2×#634—21no—
57C2×#634—21no—
58C2×#634—21no—
59C2×#634—21no—
60C2×#634C2×C412yes—
61C22×C3×Dic3—21no—
62#3756—24no—
63#3754—24no—
64#3748—21no—
65#3748C2×C412yes—
66C2×C3⋊(C3⋊C8)—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×#208—24no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208—21no—
73C3×#208D412yes—
74C2×C3×C3⋊C8—24no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8D411yescharacteristic
80C2×C3×C3⋊C8D411yescharacteristic
81#1908—91noSylow
82C2×C3×#41—21no—
83C2×C3×#41C2×D311yescharacteristic
84C2×C3×#41C2×D311yescharacteristic
85C22×Dic6—31no—
86C22×Dic6—31no—
87C22×Dic6—61no—
88C3×#131—62no—
89C3×#131—62no—
90C2×C3×M16—31no—
91C2×C3×M16—31no—
92C2×C3×M16—61no—
93C22×C3×C8—31no—
94C22×C3×C8—61no—
95C2×C3×C4⋊C4—31no—
96#951—34no—
97#951—34no—
98#951—64no—
99#951—64no—
100#951—62no—
101#951—62no—
102#948—22no—
103#948—22no—
104C2×#216—62no—
105C2×#216—61no—
106C2×#216—61no—
107C2×#214—62no—
108C2×#214—61no—
109C2×#214—61no—
110C2×C4⋊Dic3C2×D311yescharacteristic
111C2×#208—21no—
112C2×#208—31no—
113C2×#208—31no—
114C2×#208—61no—
115C2×#208C2×D311yescharacteristic
116C2×#208C2×D311yescharacteristic
117C22×C3⋊C8—21no—
118C22×C3⋊C8C2×D311yescharacteristic
119C3×#103—61no—
120C3×#102—61no—
121#835—21no—
122#832—21no—
123#824—62no—
124#824—62no—
125#816—61no—
126#816—61no—
127#810—61no—
128#810—61no—
129C23×C32—21no—
130C23×C32#4111yescharacteristic
131C32×Q8—21no—
132C32×Q8C22⋊C412yes—
133C32×D4—22no—
134C32×D4—22no—
135C32×D4—21no—
136C32×D4C22⋊C412yes—
137C2×C32×C4—21no—
138C2×C32×C4—22no—
139C2×C32×C4—22no—
140C2×C32×C4C22×C411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4#4111yescharacteristic
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—41no—
148C2×C3⋊Dic3—41no—
149#634—22no—
150#634—22no—
151#634—41no—
152#634—41no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—81no—
155C3⋊(C3⋊C8)—22no—
156C3×C3⋊C8—21no—
157C3×C3⋊C8—22no—
158C3×C3⋊C8—21no—
159C3×C3⋊C8—41no—
160C2×#137—91no—
161C2×#131—31no—
162#417—31no—
163C2×#103—91no—
164C2×#101—91no—
165#343—91no—
166#341—91no—
167C3×#41—21no—
168C3×#41—21no—
169C3×#41—21no—
170C3×#41—21no—
171C3×#41—22no—
172C3×#41—22no—
173C3×#41—41no—
174C3×#41—41no—
175C3×#41C4×D312yes—
176C3×#41C4×D312yes—
177C3×#41D1212yes—
178C3×#41#6712yes—
179C2×C3×Q8—21no—
180C2×C3×Q8D1211yescharacteristic
181C2×C3×Q8#6711yescharacteristic
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4—41no—
186C2×C3×D4D1211yescharacteristic
187C2×C3×D4#6711yescharacteristic
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—41no—
192C22×C3×C4—61no—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C22×Dic3—21no—
196C22×Dic3—61no—
197C22×Dic3—61no—
198C22×Dic3—121no—
199C2×Dic6—32no—
200C2×Dic6—32no—
201C2×Dic6—62no—
202C2×Dic6—62no—
203C2×Dic6—62no—
204C2×Dic6—61no—
205C2×Dic6—61no—
206C2×Dic6—61no—
207C2×Dic6—61no—
208C2×Dic6—61no—
209C2×Dic6—61no—
210C2×Dic6—61no—
211C2×Dic6—61no—
212C2×Dic6—61no—
213C2×Dic6—61no—
214C2×Dic6—121no—
215C2×Dic6—121no—
216C2×Dic6—121no—
217C3×M16—32no—
218C3×M16—64no—
219C3×M16—61no—
220C3×M16—61no—
221C3×M16—61no—
222C2×C3×C8—31no—
223C2×C3×C8—31no—
224C2×C3×C8—64no—
225C2×C3×C8—61no—
226C2×C3×C8—61no—
227C2×C3×C8—61no—
228C2×C3×C8—61no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4—61no—
231#216—68no—
232#216—64no—
233#216—64no—
234#214—68no—
235#214—64no—
236#214—64no—
237C4⋊Dic3—21no—
238C4⋊Dic3—21no—
239#208—24no—
240#208—21no—
241#208—21no—
242#208—21no—
243#208—32no—
244#208—32no—
245#208—62no—
246#208—62no—
247#208—61no—
248#208—61no—
249#208#6712yes—
250C2×C3⋊C8—24no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—62no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8#6711yescharacteristic
259C2×C3⋊C8#6711yescharacteristic
260C22×C32—21no—
261C22×C32—21no—
262C22×C32—22no—
263C22×C32—41no—
264C22×C32—41no—
265C22×C32C4×D411yescharacteristic
266C22×C32#12111yescharacteristic
267C22×C32#12311yescharacteristic
268C32×C4—22no—
269C32×C4C2×C22⋊C411yescharacteristic
270C32×C4C4×D411yescharacteristic
271C32×C4#12011yescharacteristic
272C32×C4#12111yescharacteristic
273C3⋊Dic3—42no—
274C3×Dic3—81no—
275C2×#41D3211yescharacteristic
276C22×Q8—91no—
277#137—94no—
278#137—182no—
279C2×Q16—181no—
280C2×SD16—181no—
281#131—62no—
282#131—62no—
283C2×M16—31no—
284C2×M16—31no—
285C2×M16—61no—
286C2×M16—91no—
287C22×C8—31no—
288C22×C8—61no—
289C2×C4⋊C4—31no—
290#103—61no—
291#103—181no—
292#103—181no—
293#102—61no—
294#101—182no—
295C23×C3—21no—
296C23×C3—21no—
297C23×C3—21no—
298C23×C3—41no—
299C23×C3#23511yescharacteristic
300C23×C3#23711yescharacteristic
301C3×Q8—21no—
302C3×Q8—21no—
303C3×Q8—22no—
304C3×Q8—41no—
305C3×Q8(C2×D3)⋊C412yes—
306C3×Q8(C2×D3)⋊C412yes—
307C3×D4—22no—
308C3×D4—22no—
309C3×D4—22no—
310C3×D4—22no—
311C3×D4—21no—
312C3×D4—21no—
313C3×D4—22no—
314C3×D4—41no—
315C3×D4—42no—
316C3×D4—42no—
317C3×D4(C2×D3)⋊C412yes—
318C3×D4(C2×D3)⋊C412yes—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—42no—
332C2×C3×C4—42no—
333C2×C3×C4—41no—
334C2×C3×C4—121no—
335C2×C3×C4—241no—
336C2×C3×C4C2×C4×D311yescharacteristic
337C2×C3×C4C2×C4×D311yescharacteristic
338C2×C3×C4C2×D1211yescharacteristic
339C2×C3×C4C2×D1211yescharacteristic
340C2×C3×C4#23511yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4#23711yescharacteristic
344C2×C3×C4C2×#6711yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C2×#6711yescharacteristic
348C2×Dic3—41no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—81no—
352C2×Dic3—122no—
353C2×Dic3—122no—
354C2×Dic3—122no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357C2×Dic3—121no—
358C2×Dic3—121no—
359Dic6—64no—
360Dic6—62no—
361Dic6—62no—
362Dic6—62no—
363Dic6—62no—
364Dic6—122no—
365Dic6—122no—
366Dic6—122no—
367Dic6—121no—
368Dic6—121no—
369Dic6—121no—
370Dic6—121no—
371C3×C8—61no—
372C3×C8—61no—
373C3×C8—62no—
374C3×C8—121no—
375C3⋊C8—21no—
376C3⋊C8—22no—
377C3⋊C8—21no—
378C3⋊C8—41no—
379C3⋊C8—64no—
380C3⋊C8—62no—
381C3⋊C8—62no—
382C2×C32—21no—
383C2×C32—21no—
384C2×C32—42no—
385C2×C32#38611yescharacteristic
386C2×C32#47111yescharacteristic
387C2×C32#47311yescharacteristic
388#41—21no—
389#41—21no—
390#41#62412yes—
391#41#62612yes—
392C2×Q8—92no—
393C2×Q8—181no—
394C2×Q8—181no—
395C2×Q8—181no—
396C2×Q8—181no—
397C2×Q8—181no—
398C2×Q8#62611yescharacteristic
399C2×D4—21no—
400C2×D4#62611yescharacteristic
401C22×C4—21no—
402C22×C4—61no—
403C22×C4—181no—
404C22×C4C2×D3211yescharacteristic
405Q16—184no—
406SD16—184no—
407M16—32no—
408M16—64no—
409M16—61no—
410M16—61no—
411M16—61no—
412M16—92no—
413M16—181no—
414C2×C8—31no—
415C2×C8—31no—
416C2×C8—64no—
417C2×C8—61no—
418C2×C8—61no—
419C2×C8—61no—
420C2×C8—61no—
421C2×C8—181no—
422C4⋊C4—61no—
423C4⋊C4—61no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—22no—
429C22×C3—22no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—41no—
434C22×C3—41no—
435C22×C3—42no—
436C22×C3—41no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—81no—
441C22×C3—81no—
442C22×C3#67⋊C411yescharacteristic
443C22×C3#88611yescharacteristic
444C22×C3C4×#6711yescharacteristic
445C22×C3#92911yescharacteristic
446C22×C3#93011yescharacteristic
447C22×C3#93911yescharacteristic
448C3×C4—22no—
449C3×C4—22no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—42no—
455C3×C4—241no—
456C3×C4#67⋊C411yescharacteristic
457C3×C4#88211yescharacteristic
458C3×C4C2×(C2×D3)⋊C411yescharacteristic
459C3×C4C2×(C2×D3)⋊C411yescharacteristic
460C3×C4C4×#6711yescharacteristic
461C3×C4#93011yescharacteristic
462C3×C4#93911yescharacteristic
463C3×C4#95311yescharacteristic
464Dic3—81no—
465Dic3—124no—
466Dic3—122no—
467Dic3—122no—
468C32#190811yescharacteristic, complemented, Sylow
469C23—21no—
470C23#380411yescharacteristic
471Q8—21no—
472Q8—182no—
473Q8—182no—
474Q8—361no—
475Q8—361no—
476Q8#372212yes—
477D4—22no—
478D4—22no—
479D4—21no—
480D4#372212yes—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—121no—
485C2×C4—182no—
486C2×C4—241no—
487C2×C4—361no—
488C2×C4—361no—
489C2×C4#380411yescharacteristic
490C2×C4C2×#62411yescharacteristic
491C2×C4C2×#62611yescharacteristic
492C2×C4C2×#62611yescharacteristic
493C2×C4D3×#6711yescharacteristic
494C2×C4D3×#6711yescharacteristic
495C8—61no—
496C8—61no—
497C8—62no—
498C8—121no—
499C8—182no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—41no—
508C2×C3—41no—
509C2×C3—42no—
510C2×C3—42no—
511C2×C3—82no—
512C2×C3#495811yescharacteristic
513C2×C3#514111yescharacteristic
514C2×C3#514311yescharacteristic
515C2×C3#520011yescharacteristic
516C2×C3#520411yescharacteristic
517C2×C3#521311yescharacteristic
518C22—21no—
519C22—21no—
520C22—22no—
521C22—41no—
522C22—41no—
523C22#6395211yescharacteristic
524C22#6396611yescharacteristic
525C22#6397811yescharacteristic
526C4—22no—
527C4—241no—
528C4—362no—
529C4#6395211yescharacteristic
530C4C2×#372211yescharacteristic
531C4#6397711yescharacteristic
532C4#6397811yescharacteristic
533C3—21no—
534C3#7030411yescharacteristic, complemented
535C3#7201911yescharacteristic, complemented
536C2—21no—
537C2—21no—
538C2—42no—
539C2#1059167911yescharacteristic
540C2#1059168211yescharacteristic
541C2#1059171111yescharacteristic
subgroupG/H
centerC22#63978
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC22×C32#121
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1908
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. C2×#63567C2semidirect
5. C2×#63561C2semidirect
6. #10589167C2semidirect
7. #10589166C2semidirect
13. #64160C4semidirect
468. C32#1908semidirect
534. C3#70304semidirect
535. C3#72019semidirect

Maximal subgroups

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

subgroupindex
C2×#641602
C2×C3×#9482
C3×#52322
C2×#635672
C2×#635612
#105891672
#105891662
#720193
#703043