Finite Group Databasebeta

← #11794075

Subgroups — #11794075

Order 1152.

717 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3715C211yesmaximal, characteristic
2C2×C4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
3C3×#4939C211yesmaximal, characteristic
4C3×#4929C211yesmaximal, characteristic, complemented
5C2×#63565C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic
7#10589163C211yesmaximal, characteristic, complemented
8#69680—31nomaximal
9#69651—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×#3715—22no—
20C2×#3715—22no—
21C2×#3715—22no—
22C4⋊(C3⋊(C3⋊C8))—22no—
23C3×C3⋊#95—21no—
24C3×C3⋊#95—21no—
25#63565—22no—
26#63562—22no—
27C22×#215—31no—
28C22×#214—31no—
29C3×#391—31no—
30C3×#390—31no—
31C2×#835—31no—
32C2×#832—31no—
33C2×#810—31no—
34C2×#809—31no—
35#4939D311yescharacteristic
36#4929D311yescharacteristic, complemented
37C2×C4⋊(C3⋊C8)—31no—
38C2×C4⋊(C3⋊C8)—31no—
39C2×C4⋊(C3⋊C8)—61no—
40#4529—31no—
41#4529—31no—
42C23×C3×D3—21no—
43C22×C32×C4D411yescharacteristic
44C22×C32×C4D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3×Dic3—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12D412yes—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6D412yes—
61C32×C42—21no—
62C32×C42—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)D412yes—
69C3×(C2×D3)⋊C4—42no—
70C3×(C2×D3)⋊C4—42no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75#3715—28no—
76#2055—91noSylow
77C22×C3×Q8—31no—
78C22×C3×D4—31no—
79C22×D12C2×D311yescharacteristic
80C22×Dic6C2×D311yescharacteristic
81C2×C3×C4⋊C4—31no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C22⋊C4—61no—
84C2×C3×C22⋊C4—61no—
85C2×C3×C42—21no—
86C2×C3×C42C2×D311yescharacteristic
87C2×C3×C42C2×D311yescharacteristic
88C2×#215—62no—
89C2×#215—62no—
90C2×#215—62no—
91C2×#214—62no—
92C2×#214—62no—
93C2×#214—62no—
94C2×(C2×D3)⋊C4—21no—
95C2×(C2×D3)⋊C4—21no—
96C2×C4⋊Dic3C2×D311yescharacteristic
97C2×C4⋊Dic3C2×D311yescharacteristic
98C22×C3⋊C8—31no—
99C22×C3⋊C8—31no—
100C22×C3⋊C8—31no—
101C22×C3⋊C8—31no—
102C22×C3⋊C8—61no—
103C22×C3⋊C8—61no—
104C3×#95—61no—
105C3×#95—61no—
106#835—62no—
107#832—62no—
108C3⋊#95—21no—
109C3⋊#95—21no—
110#810—62no—
111#809—62no—
112C4⋊(C3⋊C8)—62no—
113C4⋊(C3⋊C8)—62no—
114C4⋊(C3⋊C8)—64no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—22no—
117C22×C3×D3—41no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
120C22×C3×D3—41no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C2×C32×C4—21no—
124C2×C32×C4—21no—
125C2×C32×C4—21no—
126C2×C32×C4—21no—
127C2×C32×C4—21no—
128C2×C32×C4SD1612yescomplemented
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C2×C3×Dic3—22no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C3×D12—22no—
145C3×D12—22no—
146C3×D12—41no—
147C3×D12—41no—
148C3×Dic6—22no—
149C3×Dic6—22no—
150C3×Dic6—41no—
151C3×Dic6—41no—
152C3⋊(C3⋊C8)—22no—
153C3⋊(C3⋊C8)—41no—
154C22×SD16—91no—
155C2×C4⋊C8—91no—
156C2×#103—91no—
157C2×#102—91no—
158#391—31no—
159#390—31no—
160#340—91no—
161C24×C3—61no—
162C23×D3—21no—
163C2×C3×Q8—32no—
164C2×C3×Q8—61no—
165C2×C3×Q8—61no—
166C2×C3×Q8—61no—
167C2×C3×Q8—61no—
168C2×C3×Q8—61no—
169C2×C3×D4—32no—
170C2×C3×D4—61no—
171C2×C3×D4—61no—
172C2×C3×D4—61no—
173C2×C3×D4—61no—
174C2×C3×D4—61no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—61no—
179C22×C3×C4—61no—
180C22×C3×C4—61no—
181C22×C3×C4#6711yescharacteristic
182C22×C3×C4#6711yescharacteristic
183C22×C3×C4#6711yescharacteristic
184C22×C3×C4#6711yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C22×Dic3—21no—
188C22×Dic3—21no—
189C22×Dic3—21no—
190C2×D12—21no—
191C2×D12—21no—
192C2×D12—21no—
193C2×D12—21no—
194C2×D12—21no—
195C2×D12D1212yes—
196C2×Dic6—21no—
197C2×Dic6—21no—
198C2×Dic6—21no—
199C2×Dic6—21no—
200C2×Dic6—21no—
201C2×Dic6D1212yes—
202C3×C4⋊C4—61no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4—61no—
205C3×C4⋊C4—61no—
206C3×C22⋊C4—122no—
207C3×C22⋊C4—122no—
208C3×C42—22no—
209C3×C42—22no—
210C3×C42—21no—
211C3×C42—21no—
212C3×C42—21no—
213C3×C42—21no—
214#215—68no—
215#214—68no—
216(C2×D3)⋊C4—42no—
217(C2×D3)⋊C4—42no—
218C4⋊Dic3—21no—
219C4⋊Dic3—21no—
220C4⋊Dic3—21no—
221C4⋊Dic3—21no—
222C2×C3⋊C8—32no—
223C2×C3⋊C8—32no—
224C2×C3⋊C8—62no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—62no—
230C2×C3⋊C8—61no—
231C2×C3⋊C8—61no—
232C2×C3⋊C8—61no—
233C2×C3⋊C8—61no—
234C2×C3⋊C8—61no—
235C2×C3⋊C8—61no—
236C2×C3⋊C8—121no—
237C2×C3⋊C8—121no—
238C2×C3⋊C8—121no—
239C2×C3⋊C8—121no—
240C22×C32#12111yescharacteristic
241C22×C32#12111yescharacteristic
242C22×C32#12111yescharacteristic
243C22×C32C2×SD1611yescharacteristic
244C22×C32#13511yescharacteristic
245C22×C32AGL(1,ℤ/8)11yescharacteristic
246C22×C32#13711yescharacteristic
247C2×C3×D3—42no—
248C2×C3×D3—42no—
249C2×C3×D3—42no—
250C2×C3×D3—81no—
251C2×C3×D3—81no—
252C2×C3×D3—81no—
253C2×C3×D3—81no—
254C32×C4—22no—
255C32×C4—41no—
256C32×C4#12011yescharacteristic
257C32×C4#12311yescharacteristic
258C32×C4#12311yescharacteristic
259C32×C4#12411yescharacteristic
260C3×Dic3—42no—
261C3×Dic3—81no—
262C3×Dic3—81no—
263C22×Q8—31no—
264C22×D4—31no—
265C2×SD16—182no—
266C2×SD16—182no—
267C2×SD16—182no—
268C22×C8—91no—
269C22×C8—91no—
270C2×C4⋊C4—31no—
271C2×C4⋊C4—31no—
272C2×C22⋊C4—61no—
273C2×C22⋊C4—61no—
274C2×C42D3211yescharacteristic
275C4⋊C8—182no—
276#103—182no—
277#102—182no—
278#95—61no—
279#95—61no—
280C23×C3—21no—
281C23×C3—62no—
282C23×C3—121no—
283C23×C3—121no—
284C23×C3—121no—
285C23×C3—121no—
286C23×C3—121no—
287C23×C3—121no—
288C23×C3C2×#6711yescharacteristic
289C23×C3C2×#6711yescharacteristic
290C22×D3—22no—
291C22×D3—41no—
292C22×D3—41no—
293C22×D3—41no—
294C22×D3—41no—
295C22×D3—41no—
296C22×D3—41no—
297C3×Q8—62no—
298C3×Q8—62no—
299C3×Q8—121no—
300C3×Q8—121no—
301C3×D4—62no—
302C3×D4—62no—
303C3×D4—121no—
304C3×D4—121no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—62no—
328C2×C3×C4—121no—
329C2×C3×C4—121no—
330C2×C3×C4—121no—
331C2×C3×C4—121no—
332C2×C3×C4—121no—
333C2×C3×C4—121no—
334C2×C3×C4—121no—
335C2×C3×C4—121no—
336C2×C3×C4#21412yescomplemented
337C2×C3×C4#21512yescomplemented
338C2×C3×C4C2×D1211yescharacteristic
339C2×C3×C4C2×D1211yescharacteristic
340C2×C3×C4#23511yescharacteristic
341C2×C3×C4#23511yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4#23711yescharacteristic
347C2×C3×C4#23711yescharacteristic
348C2×C3×C4#23711yescharacteristic
349C2×C3×C4#23711yescharacteristic
350C2×Dic3—22no—
351C2×Dic3—41no—
352C2×Dic3—41no—
353C2×Dic3—41no—
354C2×Dic3—41no—
355C2×Dic3—41no—
356C2×Dic3—41no—
357C2×Dic3—41no—
358C2×Dic3—41no—
359D12—22no—
360D12—22no—
361D12—41no—
362D12—41no—
363Dic6—22no—
364Dic6—22no—
365Dic6—41no—
366Dic6—41no—
367C3⋊C8—62no—
368C3⋊C8—62no—
369C3⋊C8—122no—
370C3⋊C8—122no—
371C3⋊C8—121no—
372C3⋊C8—121no—
373C2×C32#39411yescharacteristic
374C2×C32#46011yescharacteristic
375C2×C32#46111yescharacteristic
376C2×C32#46311yescharacteristic
377C2×C32#46411yescharacteristic
378C2×C32#46511yescharacteristic
379C2×C32#46811yescharacteristic
380C3×D3—82no—
381C24—61no—
382C2×Q8—32no—
383C2×Q8—61no—
384C2×Q8—61no—
385C2×Q8—61no—
386C2×Q8—61no—
387C2×Q8—61no—
388C2×D4—32no—
389C2×D4—61no—
390C2×D4—61no—
391C2×D4—61no—
392C2×D4—61no—
393C2×D4—61no—
394C22×C4—61no—
395C22×C4—61no—
396C22×C4—61no—
397C22×C4#62511yescharacteristic
398C22×C4#62511yescharacteristic
399C22×C4C2×D3211yescharacteristic
400SD16—188no—
401C2×C8—92no—
402C2×C8—181no—
403C2×C8—181no—
404C2×C8—181no—
405C2×C8—181no—
406C2×C8—181no—
407C4⋊C4—61no—
408C4⋊C4—61no—
409C4⋊C4—61no—
410C4⋊C4—61no—
411C22⋊C4—122no—
412C22⋊C4—122no—
413C42—21no—
414C42—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—122no—
423C22×C3—122no—
424C22×C3—122no—
425C22×C3—241no—
426C22×C3—241no—
427C22×C3—241no—
428C22×C3—241no—
429C22×C3#93011yescharacteristic
430C22×C3#93011yescharacteristic
431C22×C3#93211yescharacteristic
432C22×C3C2×#21411yescharacteristic
433C22×C3#93811yescharacteristic
434C22×C3#93811yescharacteristic
435C22×C3#93911yescharacteristic
436C22×C3#93911yescharacteristic
437C22×C3C2×#21511yescharacteristic
438C22×C3#94211yescharacteristic
439C22×C3#94911yescharacteristic
440C22×C3#95011yescharacteristic
441C22×C3#95011yescharacteristic
442C22×C3#95111yescharacteristic
443C2×D3—42no—
444C2×D3—42no—
445C2×D3—42no—
446C2×D3—81no—
447C2×D3—81no—
448C2×D3—81no—
449C2×D3—81no—
450C3×C4—24no—
451C3×C4—22no—
452C3×C4—22no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—42no—
458C3×C4—41no—
459C3×C4—41no—
460C3×C4—122no—
461C3×C4—241no—
462C3×C4—241no—
463C3×C4#88211yescharacteristic
464C3×C4#88211yescharacteristic
465C3×C4#88311yescharacteristic
466C3×C4#88311yescharacteristic
467C3×C4#88511yescharacteristic
468C3×C4#88511yescharacteristic
469C3×C4#88611yescharacteristic
470C3×C4#88611yescharacteristic
471Dic3—42no—
472Dic3—81no—
473Dic3—81no—
474C32#205511yescharacteristic, complemented, Sylow
475C23—62no—
476C23—121no—
477C23—121no—
478C23—121no—
479C23—121no—
480C23—121no—
481C23—121no—
482C23C2×#62511yescharacteristic
483Q8—62no—
484Q8—62no—
485Q8—121no—
486Q8—121no—
487D4—62no—
488D4—62no—
489D4—121no—
490D4—121no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—62no—
497C2×C4—121no—
498C2×C4—121no—
499C2×C4—121no—
500C2×C4—121no—
501C2×C4—121no—
502C2×C4—121no—
503C2×C4—121no—
504C2×C4—121no—
505C2×C4#371512yescomplemented
506C2×C4#379511yescharacteristic
507C2×C4#379511yescharacteristic
508C2×C4D3×D1211yescharacteristic
509C2×C4D3×D1211yescharacteristic
510C2×C4#380511yescharacteristic
511C2×C4#381111yescharacteristic
512C8—182no—
513C8—361no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—242no—
522C2×C3#496111yescharacteristic
523C2×C3#496111yescharacteristic
524C2×C3#501611yescharacteristic
525C2×C3#501911yescharacteristic
526C2×C3#502711yescharacteristic
527C2×C3#502811yescharacteristic
528C2×C3#504111yescharacteristic
529C2×C3#504211yescharacteristic
530C2×C3#504811yescharacteristic
531C2×C3#504911yescharacteristic
532C2×C3#505411yescharacteristic
533C2×C3#505711yescharacteristic
534C2×C3#507511yescharacteristic
535C2×C3#508311yescharacteristic
536D3—82no—
537C22—122no—
538C22—122no—
539C22—122no—
540C22—241no—
541C22—241no—
542C22—241no—
543C22—241no—
544C22#6382211yescharacteristic
545C22#6382311yescharacteristic
546C22C2×#371511yescharacteristic
547C22#6382711yescharacteristic
548C22#6390811yescharacteristic
549C22#6390811yescharacteristic
550C22#6398011yescharacteristic
551C4—22no—
552C4—41no—
553C4—122no—
554C4—241no—
555C4—241no—
556C4#6389111yescharacteristic
557C4#6389111yescharacteristic
558C4#6391311yescharacteristic
559C4#6392311yescharacteristic
560C3—21no—
561C3#6965111yescharacteristic, complemented
562C3#6968011yescharacteristic, complemented
563C2—242no—
564C2#1059026711yescharacteristic
565C2#1059034811yescharacteristic
566C2#1059036311yescharacteristic
567C2#1059036411yescharacteristic
568C2#1059117911yescharacteristic
569C2#1059118011yescharacteristic
570C2#1059139411yescharacteristic
subgroupG/H
centerC23C2×#625
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32#2055
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. C2×C4⋊(C3⋊(C3⋊C8))C2semidirect
4. C3×#4929C2semidirect
5. C2×#63565C2semidirect
7. #10589163C2semidirect
36. #4929D3semidirect
128. C2×C32×C4SD16semidirect
336. C2×C3×C4#214semidirect
337. C2×C3×C4#215semidirect
474. C32#2055semidirect
505. C2×C4#3715semidirect
561. C3#69651semidirect
562. C3#69680semidirect

Maximal subgroups

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

subgroupindex
C22×#37152
C2×C4⋊(C3⋊(C3⋊C8))2
C3×#49392
C3×#49292
C2×#635652
C2×#635622
#105891632
#696803
#696513