Finite Group Databasebeta

← #11794547

Subgroups — #11794547

Order 1152.

637 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
2C3×#4939C211yesmaximal, characteristic
3C3×#4928C211yesmaximal, characteristic, complemented
4C2×#63576C211yesmaximal, characteristic, complemented
5C2×#63562C211yesmaximal, characteristic
6C2×#63562C211yesmaximal, characteristic
7#10589163C211yesmaximal, characteristic, complemented
8#69653—31nomaximal
9#69630—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—21no—
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×Dic3⋊C4—21no—
20C4⋊(C3⋊(C3⋊C8))—22no—
21C3×C3⋊#95—21no—
22#63576—22no—
23#63562—22no—
24#63562—22no—
25C3×#390—31no—
26C3×#389—31no—
27C2×#832—31no—
28C2×#832—31no—
29C2×#809—31no—
30C2×#809—31no—
31C2×#807—31no—
32C2×#807—31no—
33#4939D311yescharacteristic
34#4928D311yescharacteristic, complemented
35C2×C4⋊(C3⋊C8)—31no—
36C2×C4⋊(C3⋊C8)—31no—
37C2×C4⋊(C3⋊C8)—61no—
38#4529—31no—
39#4529—31no—
40C23×C3×D3—21no—
41C22×C32×C4D411yescharacteristic
42C22×C32×C4D411yescharacteristic
43C22×C32×C4C2311yescharacteristic
44C22×C3×Dic3—21no—
45C22×C3×Dic3—21no—
46C22×C3×Dic3—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12Q812yes—
53C32×C42—21no—
54C32×C42—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)D412yes—
61C3×(C2×D3)⋊C4—42no—
62C3×(C2×D3)⋊C4—42no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3D412yes—
69C3×Dic3⋊C4—42no—
70#2067—91noSylow
71C22×C3×D4—31no—
72C22×D12C2×D311yescharacteristic
73C2×C3×C4⋊C4—31no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C4⋊C4—61no—
77C2×C3×C22⋊C4—61no—
78C2×C3×C22⋊C4—61no—
79C2×C3×C42—21no—
80C2×C3×C42C2×D311yescharacteristic
81C2×C3×C42C2×D311yescharacteristic
82C2×(C2×D3)⋊C4—21no—
83C2×(C2×D3)⋊C4—21no—
84C2×C4⋊Dic3C2×D311yescharacteristic
85C2×C4⋊Dic3C2×D311yescharacteristic
86C2×C4⋊Dic3C2×D311yescharacteristic
87C2×Dic3⋊C4—21no—
88C22×C3⋊C8—31no—
89C22×C3⋊C8—31no—
90C22×C3⋊C8—31no—
91C22×C3⋊C8—31no—
92C22×C3⋊C8—61no—
93C22×C3⋊C8—61no—
94C3×#95—61no—
95#832—62no—
96#832—62no—
97C3⋊#95—21no—
98#809—62no—
99#809—62no—
100#807—62no—
101#807—62no—
102C4⋊(C3⋊C8)—62no—
103C4⋊(C3⋊C8)—62no—
104C4⋊(C3⋊C8)—64no—
105C23×C32C2×D411yescharacteristic
106C22×C3×D3—22no—
107C22×C3×D3—41no—
108C22×C3×D3—41no—
109C22×C3×D3—41no—
110C22×C3×D3—41no—
111C22×C3×D3—41no—
112C22×C3×D3—41no—
113C2×C32×C4—21no—
114C2×C32×C4—21no—
115C2×C32×C4—21no—
116C2×C32×C4—21no—
117C2×C32×C4—21no—
118C2×C32×C4D812yes—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×Q811yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C2×C3×Dic3—22no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—41no—
128C2×C3×Dic3—41no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C3×D12—22no—
135C3×D12—22no—
136C3×D12—41no—
137C3×D12—41no—
138C3⋊(C3⋊C8)—22no—
139C3⋊(C3⋊C8)—41no—
140C2×#107—91no—
141C2×C4⋊C8—91no—
142C2×#102—91no—
143C2×#102—91no—
144#390—31no—
145#389—31no—
146#340—91no—
147C24×C3—61no—
148C23×D3—21no—
149C2×C3×D4—32no—
150C2×C3×D4—61no—
151C2×C3×D4—61no—
152C2×C3×D4—61no—
153C2×C3×D4—61no—
154C2×C3×D4—61no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—61no—
159C22×C3×C4—61no—
160C22×C3×C4—61no—
161C22×C3×C4#6711yescharacteristic
162C22×C3×C4#6711yescharacteristic
163C22×C3×C4#6711yescharacteristic
164C22×C3×C4#6711yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C22×Dic3—21no—
168C22×Dic3—21no—
169C22×Dic3—21no—
170C2×D12—21no—
171C2×D12—21no—
172C2×D12—21no—
173C2×D12—21no—
174C2×D12—21no—
175C2×D12Dic612yes—
176C3×C4⋊C4—32no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—122no—
183C3×C22⋊C4—122no—
184C3×C22⋊C4—122no—
185C3×C42—22no—
186C3×C42—22no—
187C3×C42—21no—
188C3×C42—21no—
189C3×C42—21no—
190C3×C42—21no—
191(C2×D3)⋊C4—42no—
192(C2×D3)⋊C4—42no—
193C4⋊Dic3—21no—
194C4⋊Dic3—21no—
195C4⋊Dic3—21no—
196C4⋊Dic3—21no—
197C4⋊Dic3—21no—
198C4⋊Dic3D1212yes—
199Dic3⋊C4—42no—
200C2×C3⋊C8—32no—
201C2×C3⋊C8—32no—
202C2×C3⋊C8—62no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—62no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—61no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—121no—
215C2×C3⋊C8—121no—
216C2×C3⋊C8—121no—
217C2×C3⋊C8—121no—
218C22×C32#12111yescharacteristic
219C22×C32#12111yescharacteristic
220C22×C32C22⋊Q811yescharacteristic
221C22×C32C2×D811yescharacteristic
222C22×C32#13511yescharacteristic
223C22×C32AGL(1,ℤ/8)11yescharacteristic
224C22×C32#13711yescharacteristic
225C2×C3×D3—42no—
226C2×C3×D3—42no—
227C2×C3×D3—42no—
228C2×C3×D3—81no—
229C2×C3×D3—81no—
230C2×C3×D3—81no—
231C2×C3×D3—81no—
232C32×C4—22no—
233C32×C4—41no—
234C32×C4#12111yescharacteristic
235C32×C4C22⋊Q811yescharacteristic
236C32×C4C22⋊Q811yescharacteristic
237C32×C4#12611yescharacteristic
238C3×Dic3—42no—
239C3×Dic3—81no—
240C3×Dic3—81no—
241C22×D4—31no—
242C22×C8—91no—
243C22×C8—91no—
244C2×C4⋊C4—31no—
245C2×C4⋊C4—31no—
246C2×C4⋊C4—31no—
247C2×C4⋊C4—61no—
248C2×C22⋊C4—61no—
249C2×C22⋊C4—61no—
250C2×C42D3211yescharacteristic
251#107—182no—
252C4⋊C8—182no—
253#102—182no—
254#102—182no—
255#95—61no—
256C23×C3—21no—
257C23×C3—62no—
258C23×C3—121no—
259C23×C3—121no—
260C23×C3—121no—
261C23×C3—121no—
262C23×C3—121no—
263C23×C3—121no—
264C23×C3C2×#6711yescharacteristic
265C23×C3C2×#6711yescharacteristic
266C22×D3—22no—
267C22×D3—41no—
268C22×D3—41no—
269C22×D3—41no—
270C22×D3—41no—
271C22×D3—41no—
272C22×D3—41no—
273C3×D4—62no—
274C3×D4—62no—
275C3×D4—121no—
276C3×D4—121no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—22no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—22no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—62no—
300C2×C3×C4—121no—
301C2×C3×C4—121no—
302C2×C3×C4—121no—
303C2×C3×C4—121no—
304C2×C3×C4—121no—
305C2×C3×C4—121no—
306C2×C3×C4—121no—
307C2×C3×C4—121no—
308C2×C3×C4#21312yes—
309C2×C3×C4#21312yes—
310C2×C3×C4C2×Dic611yescharacteristic
311C2×C3×C4C2×D1211yescharacteristic
312C2×C3×C4#23511yescharacteristic
313C2×C3×C4#23511yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4D3×D411yescharacteristic
317C2×C3×C4#23711yescharacteristic
318C2×C3×C4#23711yescharacteristic
319C2×C3×C4#23711yescharacteristic
320C2×C3×C4D3×Q811yescharacteristic
321C2×C3×C4#23911yescharacteristic
322C2×Dic3—22no—
323C2×Dic3—41no—
324C2×Dic3—41no—
325C2×Dic3—41no—
326C2×Dic3—41no—
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331D12—22no—
332D12—22no—
333D12—41no—
334D12—41no—
335C3⋊C8—62no—
336C3⋊C8—62no—
337C3⋊C8—122no—
338C3⋊C8—122no—
339C3⋊C8—121no—
340C3⋊C8—121no—
341C2×C32#39611yescharacteristic
342C2×C32#45911yescharacteristic
343C2×C32#46411yescharacteristic
344C2×C32#46611yescharacteristic
345C2×C32#46811yescharacteristic
346C2×C32#47411yescharacteristic
347C2×C32#47811yescharacteristic
348C3×D3—82no—
349C24—61no—
350C2×D4—32no—
351C2×D4—61no—
352C2×D4—61no—
353C2×D4—61no—
354C2×D4—61no—
355C2×D4—61no—
356C22×C4—61no—
357C22×C4—61no—
358C22×C4—61no—
359C22×C4#62511yescharacteristic
360C22×C4#62511yescharacteristic
361C22×C4C2×D3211yescharacteristic
362C2×C8—92no—
363C2×C8—181no—
364C2×C8—181no—
365C2×C8—181no—
366C2×C8—181no—
367C2×C8—181no—
368C4⋊C4—32no—
369C4⋊C4—61no—
370C4⋊C4—61no—
371C4⋊C4—61no—
372C4⋊C4—61no—
373C4⋊C4—61no—
374C4⋊C4—122no—
375C22⋊C4—122no—
376C22⋊C4—122no—
377C42—21no—
378C42—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—122no—
387C22×C3—122no—
388C22×C3—122no—
389C22×C3—241no—
390C22×C3—241no—
391C22×C3—241no—
392C22×C3—241no—
393C22×C3#92411yescharacteristic
394C22×C3#93011yescharacteristic
395C22×C3C2×#21311yescharacteristic
396C22×C3C2×#21311yescharacteristic
397C22×C3#93211yescharacteristic
398C22×C3#93811yescharacteristic
399C22×C3#93911yescharacteristic
400C22×C3#93911yescharacteristic
401C22×C3#94211yescharacteristic
402C22×C3#94611yescharacteristic
403C22×C3#94911yescharacteristic
404C22×C3#95011yescharacteristic
405C22×C3#95011yescharacteristic
406C22×C3#95111yescharacteristic
407C2×D3—42no—
408C2×D3—42no—
409C2×D3—42no—
410C2×D3—81no—
411C2×D3—81no—
412C2×D3—81no—
413C2×D3—81no—
414C3×C4—24no—
415C3×C4—22no—
416C3×C4—22no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—42no—
422C3×C4—41no—
423C3×C4—41no—
424C3×C4—122no—
425C3×C4—241no—
426C3×C4—241no—
427C3×C4#87811yescharacteristic
428C3×C4#87811yescharacteristic
429C3×C4#87911yescharacteristic
430C3×C4#88411yescharacteristic
431C3×C4#89511yescharacteristic
432C3×C4#89611yescharacteristic
433C3×C4#89711yescharacteristic
434C3×C4#89811yescharacteristic
435Dic3—42no—
436Dic3—81no—
437Dic3—81no—
438C32#206711yescharacteristic, complemented, Sylow
439C23—62no—
440C23—121no—
441C23—121no—
442C23—121no—
443C23—121no—
444C23—121no—
445C23—121no—
446C23C2×#62511yescharacteristic
447D4—62no—
448D4—62no—
449D4—121no—
450D4—121no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—62no—
457C2×C4—121no—
458C2×C4—121no—
459C2×C4—121no—
460C2×C4—121no—
461C2×C4—121no—
462C2×C4—121no—
463C2×C4—121no—
464C2×C4—121no—
465C2×C4#371312yes—
466C2×C4D3×Dic611yescharacteristic
467C2×C4#379511yescharacteristic
468C2×C4#379911yescharacteristic
469C2×C4D3×D1211yescharacteristic
470C2×C4#380511yescharacteristic
471C2×C4#381111yescharacteristic
472C8—182no—
473C8—361no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—242no—
482C2×C3#494811yescharacteristic
483C2×C3#499411yescharacteristic
484C2×C3#500711yescharacteristic
485C2×C3#500911yescharacteristic
486C2×C3#501511yescharacteristic
487C2×C3#502811yescharacteristic
488C2×C3#503811yescharacteristic
489C2×C3#503811yescharacteristic
490C2×C3#504211yescharacteristic
491C2×C3#504911yescharacteristic
492C2×C3#505411yescharacteristic
493C2×C3#506611yescharacteristic
494C2×C3#507211yescharacteristic
495C2×C3#508711yescharacteristic
496D3—82no—
497C22—122no—
498C22—122no—
499C22—122no—
500C22—241no—
501C22—241no—
502C22—241no—
503C22—241no—
504C22C2×#371311yescharacteristic
505C22#6382211yescharacteristic
506C22#6382311yescharacteristic
507C22#6382711yescharacteristic
508C22#6385611yescharacteristic
509C22#6390811yescharacteristic
510C22#6398011yescharacteristic
511C4—22no—
512C4—41no—
513C4—122no—
514C4—241no—
515C4—241no—
516C4#6386111yescharacteristic
517C4#6389311yescharacteristic
518C4#6389611yescharacteristic
519C4#6391011yescharacteristic
520C3—21no—
521C3#6963011yescharacteristic, complemented
522C3#6965311yescharacteristic, complemented
523C2—242no—
524C2#1059026711yescharacteristic
525C2#1059026911yescharacteristic
526C2#1059027011yescharacteristic
527C2#1059034711yescharacteristic
528C2#1059116611yescharacteristic
529C2#1059118011yescharacteristic
530C2#1059131911yescharacteristic
subgroupG/H
centerC23C2×#625
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32#2067
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
1. C2×C4⋊(C3⋊(C3⋊C8))C2semidirect
3. C3×#4928C2semidirect
4. C2×#63576C2semidirect
7. #10589163C2semidirect
34. #4928D3semidirect
438. C32#2067semidirect
521. C3#69630semidirect
522. C3#69653semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊(C3⋊(C3⋊C8))2
C3×#49392
C3×#49282
C2×#635762
C2×#635622
#105891632
#696533
#696303