Finite Group Databasebeta

← #11785176

Subgroups — #11785176

Order 1152.

837 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63898C211yesmaximal, characteristic
2#10592674C211yesmaximal, characteristic, complemented
3C2×C3×#809C211yesmaximal, characteristic
4C2×#63572C211yesmaximal, characteristic, complemented
5C2×#63563C211yesmaximal, characteristic
6C3×#4529C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#70153—31nomaximal
9#68892—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×D3×Dic3—21no—
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3750—21no—
15C2×#3750—21no—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×(C2×D3)⋊Dic3—21no—
21#63898—22no—
22#63898C414yescomplemented
23C3×#809—22no—
24#63572—22no—
25#63563—22no—
26C2×D4×Dic3—31no—
27C2×#893—31no—
28C2×C3×#102—31no—
29C2×#832—31no—
30C2×#821—31no—
31C2×Dic3⋊C8—31no—
32C2×Dic3⋊C8—31no—
33#4975—31no—
34#4975—31no—
35#4975—61no—
36C2×#809D311yescharacteristic
37C3×#340—31no—
38#4551—31no—
39#4529—31no—
40#4529D311yescharacteristic, complemented
41C23×C3×D3—21no—
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
45C22×C3⋊Dic3D411yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C22×C3×Dic3—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12C2×C412yes—
52C2×C3×D12D412yes—
53C2×C3×D12Q812yes—
54C2×D3×Dic3—24no—
55C2×D3×Dic3—42no—
56C2×D3×Dic3—42no—
57C32×C4⋊C4—21no—
58C32×C4⋊C4—21no—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)—21no—
61#3750—42no—
62#3750—42no—
63C4×C3⋊Dic3C2×C412yes—
64C4×C3⋊Dic3D412yes—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3C2×C412yes—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73(C2×D3)⋊Dic3—24no—
74#1802—91noSylow
75C22×C3×D4—31no—
76C23×Dic3—61no—
77C22×D12C2×D311yescharacteristic
78C22×C4×D3—61no—
79C22×C3×C8—31no—
80C22×C3×C8—31no—
81C2×C3×C4⋊C4—21no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4C2×D311yescharacteristic
84C2×C3×C4⋊C4C2×D311yescharacteristic
85C2×#217—61no—
86D4×Dic3—34no—
87D4×Dic3—62no—
88C2×(C2×D3)⋊C4—61no—
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—61no—
92C2×C4⋊Dic3C2×D311yescharacteristic
93C2×Dic3⋊C4—61no—
94C2×Dic3⋊C4—61no—
95C2×Dic3⋊C4—61no—
96C2×Dic3⋊C4—61no—
97C2×Dic3⋊C4—62no—
98C2×Dic3⋊C4—62no—
99C2×C4×Dic3—31no—
100C2×C4×Dic3—31no—
101C2×C4×Dic3—61no—
102C22×C3⋊C8C2×D311yescharacteristic
103C22×C3⋊C8C2×D311yescharacteristic
104#893—34no—
105#893—62no—
106C3×#102—62no—
107#832—62no—
108#821—62no—
109Dic3⋊C8—62no—
110Dic3⋊C8—62no—
111#809—22no—
112C23×C32C2×D411yescharacteristic
113C22×C3×D3—22no—
114C22×C3×D3—22no—
115C22×C3×D3—22no—
116C22×C3×D3—41no—
117C22×C3×D3—41no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×Q811yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3—41no—
134C2×C3⋊Dic3C22⋊C412yes—
135C2×C3⋊Dic3C22⋊C412yes—
136C2×C3⋊Dic3D812yes—
137C2×C3⋊Dic3SD1612yes—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C3×D12—22no—
142C3×D12—22no—
143C3×D12—22no—
144C3×D12C4⋊C414yescomplemented
145D3×Dic3—48no—
146C3×C3⋊C8—41no—
147C3×C3⋊C8—41no—
148C2×C4×D4—91no—
149C2×C4⋊C8—91no—
150C2×#102—31no—
151C2×#102—91no—
152#384—91no—
153#340—31no—
154#340—91no—
155C24×C3—61no—
156C23×D3—21no—
157C2×C3×D4—32no—
158C2×C3×D4—32no—
159C2×C3×D4—32no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C22×C3×C4—22no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—61no—
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C22×Dic3—21no—
171C22×Dic3—31no—
172C22×Dic3—31no—
173C22×Dic3—31no—
174C22×Dic3—31no—
175C22×Dic3—61no—
176C22×Dic3—61no—
177C22×Dic3—64no—
178C22×Dic3—62no—
179C22×Dic3—61no—
180C22×Dic3—61no—
181C22×Dic3—122no—
182C22×Dic3—122no—
183C2×D12—21no—
184C2×D12—21no—
185C2×D12—21no—
186C2×D12Dic612yes—
187C2×D12C4×D312yes—
188C2×D12#6712yes—
189C2×C4×D3—64no—
190C2×C4×D3—122no—
191C2×C4×D3—122no—
192C2×C3×C8—61no—
193C2×C3×C8—61no—
194C2×C3×C8—61no—
195C2×C3×C8—61no—
196C2×C3×C8—61no—
197C2×C3×C8—61no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—32no—
203C3×C4⋊C4—41no—
204C3×C4⋊C4—41no—
205C3×C4⋊C4—61no—
206#217—64no—
207(C2×D3)⋊C4—64no—
208C4⋊Dic3—21no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3—61no—
213C4⋊Dic3—121no—
214C4⋊Dic3—121no—
215C4⋊Dic3C4×D312yes—
216Dic3⋊C4—122no—
217Dic3⋊C4—122no—
218Dic3⋊C4—124no—
219Dic3⋊C4—124no—
220Dic3⋊C4—122no—
221Dic3⋊C4—122no—
222C4×Dic3—32no—
223C4×Dic3—32no—
224C4×Dic3—32no—
225C4×Dic3—32no—
226C4×Dic3—62no—
227C4×Dic3—62no—
228C2×C3⋊C8—21no—
229C2×C3⋊C8—21no—
230C2×C3⋊C8—21no—
231C2×C3⋊C8—21no—
232C2×C3⋊C8—21no—
233C2×C3⋊C8—21no—
234C22×C32C2×C22⋊C411yescharacteristic
235C22×C32#12111yescharacteristic
236C22×C32C22⋊Q811yescharacteristic
237C22×C32C2×D811yescharacteristic
238C22×C32C2×SD1611yescharacteristic
239C22×C32AGL(1,ℤ/8)11yescharacteristic
240C22×C32#13711yescharacteristic
241C2×C3×D3—24no—
242C2×C3×D3—42no—
243C2×C3×D3—42no—
244C2×C3×D3—42no—
245C2×C3×D3—42no—
246C2×C3×D3—42no—
247C2×C3×D3—42no—
248C32×C4—81no—
249C32×C4C2×C4⋊C411yescharacteristic
250C32×C4#11711yescharacteristic
251C32×C4#12111yescharacteristic
252C32×C4C22⋊Q811yescharacteristic
253C3⋊Dic3—22no—
254C3⋊Dic3—81no—
255C3⋊Dic3#10214yescomplemented
256C3×Dic3—42no—
257C22×D4—31no—
258C23×C4—181no—
259C22×C8—31no—
260C22×C8—31no—
261C4×D4—94no—
262C4×D4—182no—
263C2×C4⋊C4—31no—
264C2×C4⋊C4—91no—
265C2×C4⋊C4—181no—
266C2×C4⋊C4—181no—
267C2×C4⋊C4D3211yescharacteristic
268C2×C22⋊C4—181no—
269C2×C42—91no—
270C4⋊C8—182no—
271#102—62no—
272#102—182no—
273C23×C3—21no—
274C23×C3—62no—
275C23×C3—62no—
276C23×C3—62no—
277C23×C3—121no—
278C23×C3—121no—
279C23×C3—121no—
280C23×C3—121no—
281C23×C3D3×D411yescharacteristic
282C23×C3D3×D411yescharacteristic
283C22×D3—22no—
284C22×D3—22no—
285C22×D3—22no—
286C22×D3—41no—
287C22×D3—41no—
288C22×D3—41no—
289C22×D3—41no—
290C3×D4—34no—
291C3×D4—62no—
292C3×D4—62no—
293C3×D4—62no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—42no—
301C2×C3×C4—42no—
302C2×C3×C4—42no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—62no—
310C2×C3×C4—121no—
311C2×C3×C4—121no—
312C2×C3×C4C2×Dic611yescharacteristic
313C2×C3×C4C2×C4×D311yescharacteristic
314C2×C3×C4C2×C4×D311yescharacteristic
315C2×C3×C4#23511yescharacteristic
316C2×C3×C4#23511yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4#23711yescharacteristic
321C2×C3×C4#23711yescharacteristic
322C2×C3×C4D3×Q811yescharacteristic
323C2×C3×C4C2×#6711yescharacteristic
324C2×Dic3—22no—
325C2×Dic3—32no—
326C2×Dic3—32no—
327C2×Dic3—32no—
328C2×Dic3—32no—
329C2×Dic3—32no—
330C2×Dic3—32no—
331C2×Dic3—32no—
332C2×Dic3—32no—
333C2×Dic3—41no—
334C2×Dic3—41no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339C2×Dic3—62no—
340C2×Dic3—62no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×Dic3—128no—
346C2×Dic3—122no—
347C2×Dic3—122no—
348C2×Dic3—122no—
349C2×Dic3—121no—
350C2×Dic3—121no—
351C2×Dic3—121no—
352C2×Dic3—121no—
353C2×Dic3—121no—
354C2×Dic3—121no—
355D12—22no—
356D12—22no—
357D12—22no—
358D12Dic3⋊C414yescomplemented
359C4×D3—128no—
360C3×C8—121no—
361C3×C8—121no—
362C3⋊C8—41no—
363C3⋊C8—41no—
364C2×C32#38011yescharacteristic
365C2×C32C2×#10211yescharacteristic
366C2×C32#41711yescharacteristic
367C2×C32#45911yescharacteristic
368C2×C32#46111yescharacteristic
369C2×C32#47411yescharacteristic
370C2×C32#47611yescharacteristic
371C3×D3—44no—
372C24—61no—
373C2×D4—32no—
374C2×D4—32no—
375C2×D4—32no—
376C2×D4—61no—
377C2×D4—61no—
378C2×D4—61no—
379C22×C4—21no—
380C22×C4—61no—
381C22×C4—91no—
382C22×C4—91no—
383C22×C4—184no—
384C22×C4—181no—
385C22×C4—362no—
386C22×C4—362no—
387C22×C4C2×D3211yescharacteristic
388C2×C8—61no—
389C2×C8—61no—
390C2×C8—61no—
391C2×C8—61no—
392C2×C8—61no—
393C2×C8—61no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—32no—
397C4⋊C4—61no—
398C4⋊C4—181no—
399C4⋊C4—181no—
400C4⋊C4—362no—
401C4⋊C4—362no—
402C22⋊C4—184no—
403C42—92no—
404C42—92no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—64no—
413C22×C3—122no—
414C22×C3—122no—
415C22×C3—122no—
416C22×C3—122no—
417C22×C3—122no—
418C22×C3—122no—
419C22×C3#87811yescharacteristic
420C22×C3D3×C22⋊C411yescharacteristic
421C22×C3D3×C22⋊C411yescharacteristic
422C22×C3#88411yescharacteristic
423C22×C3#89611yescharacteristic
424C22×C3D3×D811yescharacteristic
425C22×C3D3×D811yescharacteristic
426C22×C3#91111yescharacteristic
427C22×C3D3×SD1611yescharacteristic
428C22×C3D3×SD1611yescharacteristic
429C22×C3#91411yescharacteristic
430C22×C3#91511yescharacteristic
431C22×C3#91811yescharacteristic
432C22×C3#93911yescharacteristic
433C2×D3—24no—
434C2×D3—42no—
435C2×D3—42no—
436C2×D3—42no—
437C2×D3—42no—
438C2×D3—42no—
439C2×D3—42no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—82no—
445C3×C4—81no—
446C3×C4—81no—
447C3×C4—122no—
448C3×C4#87211yescharacteristic
449C3×C4#87711yescharacteristic
450C3×C4#87811yescharacteristic
451C3×C4#88411yescharacteristic
452C3×C4D3×C4⋊C411yescharacteristic
453C3×C4#89611yescharacteristic
454C3×C4C2×Dic3⋊C411yescharacteristic
455C3×C4#93911yescharacteristic
456Dic3—34no—
457Dic3—34no—
458Dic3—42no—
459Dic3—64no—
460Dic3—64no—
461Dic3—62no—
462Dic3—62no—
463Dic3—242no—
464Dic3—241no—
465Dic3—241no—
466C32#180211yescharacteristic, complemented, Sylow
467C23—62no—
468C23—62no—
469C23—62no—
470C23—121no—
471C23—121no—
472C23—121no—
473C23—121no—
474C23#381111yescharacteristic
475D4—34no—
476D4—62no—
477D4—62no—
478D4—62no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—62no—
483C2×C4—92no—
484C2×C4—92no—
485C2×C4—92no—
486C2×C4—92no—
487C2×C4—121no—
488C2×C4—121no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4—368no—
492C2×C4—361no—
493C2×C4—361no—
494C2×C4—361no—
495C2×C4D3×Dic611yescharacteristic
496C2×C4#379511yescharacteristic
497C2×C4C4×D3211yescharacteristic
498C2×C4#380211yescharacteristic
499C2×C4#380411yescharacteristic
500C2×C4D3×#6711yescharacteristic
501C8—121no—
502C8—121no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—124no—
511C2×C3#466711yescharacteristic
512C2×C3#475911yescharacteristic
513C2×C3#476111yescharacteristic
514C2×C3D3×#10211yescharacteristic
515C2×C3D3×#10211yescharacteristic
516C2×C3#477111yescharacteristic
517C2×C3#478611yescharacteristic
518C2×C3#480311yescharacteristic
519C2×C3#481811yescharacteristic
520C2×C3#487011yescharacteristic
521C2×C3#489011yescharacteristic
522C2×C3#494211yescharacteristic
523C2×C3#515011yescharacteristic
524C2×C3#516211yescharacteristic
525D3—44no—
526C22—64no—
527C22—122no—
528C22—122no—
529C22—122no—
530C22—122no—
531C22—122no—
532C22—122no—
533C22#6389611yescharacteristic
534C22#6392111yescharacteristic
535C22#6392611yescharacteristic
536C22#6393711yescharacteristic
537C22#6394011yescharacteristic
538C22#6395111yescharacteristic
539C22#6397111yescharacteristic
540C4—81no—
541C4—94no—
542C4—122no—
543C4—182no—
544C4—721no—
545C4D3×Dic3⋊C411yescharacteristic
546C4#6387711yescharacteristic
547C4#6388511yescharacteristic
548C4#6389911yescharacteristic
549C3—21no—
550C3#6889211yescharacteristic, complemented
551C3#7015311yescharacteristic, complemented
552C2—124no—
553C2#1059047111yescharacteristic
554C2#1059047211yescharacteristic
555C2#1059059311yescharacteristic
556C2#1059061211yescharacteristic
557C2#1059136911yescharacteristic
558C2#1059143311yescharacteristic
559C2#1059156911yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1802
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592674C2semidirect
4. C2×#63572C2semidirect
6. C3×#4529C2semidirect
7. #10589164C2semidirect
22. #63898C4semidirect
40. #4529D3semidirect
144. C3×D12C4⋊C4semidirect
255. C3⋊Dic3#102semidirect
358. D12Dic3⋊C4semidirect
466. C32#1802semidirect
550. C3#68892semidirect
551. C3#70153semidirect

Maximal subgroups

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

subgroupindex
C2×#638982
#105926742
C2×C3×#8092
C2×#635722
C2×#635632
C3×#45292
#105891642
#701533
#688923