Finite Group Databasebeta

← #11790758

Subgroups — #11790758

Order 1152.

925 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63911C211yesmaximal, characteristic
2C2×#63636C211yesmaximal, characteristic, complemented
3C3×#4977C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5C2×#63564C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic, complemented
7C2×#63554C211yesmaximal, characteristic, complemented
8#70160—31nomaximal
9#69553—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×#626—22no—
13C2×C32×C4⋊C4C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18#63911—22no—
19#63911C414yescomplemented
20#63636—22no—
21C3×C3⋊#95—22no—
22C3×#809—22no—
23#63564—22no—
24#63562—22no—
25#63554—22no—
26C2×#940—31no—
27C2×#874—31no—
28C2×C3×#102—31no—
29C3×#382—31no—
30C2×#832—31no—
31C2×#821—31no—
32C2×#815—31no—
33#4977D311yescharacteristic, complemented
34C2×#809—31no—
35C2×#809—31no—
36C2×#809—31no—
37C2×#809—31no—
38C2×#809—61no—
39C2×#809D311yescharacteristic, complemented
40C2×#803—31no—
41C23×C3⋊D3—21no—
42C23×C3×D3—21no—
43C22×C32×C4—21no—
44C22×C32×C4C2311yescharacteristic
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)C2×C412yes—
51C22×C3×Dic3—21no—
52C22×C3×Dic3D412yes—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12C2×C412yes—
59C2×#626—28no—
60C2×#626—44no—
61C2×#626—44no—
62C32×C4⋊C4—21no—
63C32×C4⋊C4—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)D412yescomplemented
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4×Dic3C2×C412yes—
70C3×C4×Dic3D412yes—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8D412yescomplemented
74#1961—91noSylow
75C22×C3×D4—31no—
76C22×#67—62no—
77C22×D12—31no—
78C22×D12—31no—
79C22×D12—61no—
80C22×D12—62no—
81C22×D12C2×D311yescharacteristic
82C22×C3×C8—31no—
83C2×C3×C4⋊C4—21no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4C2×D311yescharacteristic
86C2×C3×C4⋊C4C2×D311yescharacteristic
87C2×C3×C42—31no—
88#940—34no—
89#940—62no—
90C2×C4⋊Dic3C2×D311yescharacteristic
91C2×C4×Dic3C2×D311yescharacteristic
92C22×C3⋊C8—31no—
93C22×C3⋊C8—31no—
94C22×C3⋊C8—61no—
95C22×C3⋊C8C2×D311yescharacteristic
96#874—34no—
97#874—62no—
98C3×#102—62no—
99C3×#95—62no—
100#832—62no—
101C3⋊#95—22no—
102#821—62no—
103#815—62no—
104#809—22no—
105#809—62no—
106#809—62no—
107#809—62no—
108#809—64no—
109#809—62no—
110#803—62no—
111C23×C32C2×D411yescharacteristic
112C22×C3⋊D3—22no—
113C22×C3⋊D3—41no—
114C22×C3⋊D3—41no—
115C22×C3⋊D3—42no—
116C22×C3⋊D3—42no—
117C22×C3×D3—22no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
120C22×C3×D3—42no—
121C22×C3×D3—42no—
122C2×C32×C4—41no—
123C2×C32×C4—42no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C4⋊(C3⋊D3)—22no—
131C4⋊(C3⋊D3)—22no—
132C4⋊(C3⋊D3)—41no—
133C4⋊(C3⋊D3)—41no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—42no—
138C2×C3×Dic3C22⋊C414yes—
139C3×D12—22no—
140C3×D12—22no—
141C3×D12—41no—
142C3×D12—41no—
143#626—416no—
144C3⋊(C3⋊C8)—22no—
145C3×C3⋊C8—22no—
146C2×#127—91no—
147C2×#102—31no—
148C2×#102—91no—
149C2×#102—91no—
150C2×#102—91no—
151C2×#97—91no—
152#382—31no—
153C24×C3—61no—
154C23×D3—21no—
155C23×D3—61no—
156C23×D3—61no—
157C23×D3—121no—
158C2×C3×D4—32no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C2×C3×D4—61no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—32no—
168C22×C3×C4—41no—
169C22×C3×C4—61no—
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C22×D311yescharacteristic
172C2×#67—68no—
173C2×#67—124no—
174C2×#67—124no—
175C22×Dic3—21no—
176C22×Dic3#6712yes—
177C2×D12—21no—
178C2×D12—21no—
179C2×D12—21no—
180C2×D12—21no—
181C2×D12—21no—
182C2×D12—32no—
183C2×D12—32no—
184C2×D12—62no—
185C2×D12—62no—
186C2×D12—62no—
187C2×D12—61no—
188C2×D12—61no—
189C2×D12—61no—
190C2×D12—61no—
191C2×D12—61no—
192C2×D12—61no—
193C2×D12—61no—
194C2×D12—61no—
195C2×D12—68no—
196C2×D12—61no—
197C2×D12—61no—
198C2×D12—121no—
199C2×D12—121no—
200C2×D12—121no—
201C2×D12—124no—
202C2×D12—124no—
203C2×D12C4×D312yes—
204C2×C3×C8—32no—
205C2×C3×C8—61no—
206C2×C3×C8—61no—
207C3×C4⋊C4—22no—
208C3×C4⋊C4—21no—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—41no—
213C3×C4⋊C4—61no—
214C3×C4⋊C4—61no—
215C3×C42—32no—
216C3×C42—32no—
217C4⋊Dic3—21no—
218C4⋊Dic3—21no—
219C4×Dic3C4×D312yes—
220C4×Dic3D1212yes—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—32no—
224C2×C3⋊C8—32no—
225C2×C3⋊C8—62no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—61no—
230C2×C3⋊C8—121no—
231C2×C3⋊C8—121no—
232C2×C3⋊C8#6712yescomplemented
233C22×C32C2×C22⋊C411yescharacteristic
234C22×C32#12411yescharacteristic
235C22×C32#12711yescharacteristic
236C22×C32AGL(1,ℤ/8)12yes—
237C22×C32AGL(1,ℤ/8)12yes—
238C2×C3⋊D3—42no—
239C2×C3⋊D3—44no—
240C2×C3⋊D3—82no—
241C2×C3⋊D3—81no—
242C2×C3⋊D3—81no—
243C2×C3×D3—42no—
244C2×C3×D3—44no—
245C2×C3×D3—82no—
246C2×C3×D3—81no—
247C2×C3×D3—81no—
248C32×C4—81no—
249C32×C4C4×D411yescharacteristic
250C32×C4C4×D411yescharacteristic
251C32×C4#12111yescharacteristic
252C32×C4#12111yescharacteristic
253C3×Dic3—24no—
254C3×Dic3—81no—
255C22×D4—31no—
256C22×D4—91no—
257C22×D4—182no—
258C22×C8—31no—
259C22×C8—91no—
260#127—94no—
261#127—182no—
262C2×C4⋊C4—31no—
263C2×C4⋊C4D3211yescharacteristic
264C2×C42—31no—
265#102—62no—
266#102—182no—
267#102—182no—
268#102—182no—
269#97—182no—
270#95—62no—
271C23×C3—21no—
272C23×C3—62no—
273C23×C3—121no—
274C23×C3—121no—
275C23×C3—122no—
276C23×C3—122no—
277C23×C3D3×D411yescharacteristic
278C23×C3C2×#6711yescharacteristic
279C22×D3—22no—
280C22×D3—41no—
281C22×D3—42no—
282C22×D3—42no—
283C22×D3—41no—
284C22×D3—62no—
285C22×D3—62no—
286C22×D3—122no—
287C22×D3—122no—
288C22×D3—122no—
289C22×D3—121no—
290C22×D3—122no—
291C22×D3—122no—
292C22×D3—121no—
293C22×D3—121no—
294C22×D3—121no—
295C22×D3—122no—
296C22×D3—122no—
297C22×D3—242no—
298C22×D3—242no—
299C3×D4—62no—
300C3×D4—62no—
301C3×D4—121no—
302C3×D4—121no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—34no—
310C2×C3×C4—42no—
311C2×C3×C4—42no—
312C2×C3×C4—41no—
313C2×C3×C4—41no—
314C2×C3×C4—42no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—82no—
318C2×C3×C4—122no—
319C2×C3×C4—121no—
320C2×C3×C4C2×C4×D311yescharacteristic
321C2×C3×C4C2×C4×D311yescharacteristic
322C2×C3×C4C2×D1211yescharacteristic
323C2×C3×C4#23511yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4#23711yescharacteristic
329C2×C3×C4#23911yescharacteristic
330C2×C3×C4#23911yescharacteristic
331C2×C3×C4C2×#6711yescharacteristic
332#67—1216no—
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3—41no—
336C2×Dic3—42no—
337C2×Dic3(C2×D3)⋊C414yes—
338D12—22no—
339D12—22no—
340D12—41no—
341D12—41no—
342D12—64no—
343D12—62no—
344D12—62no—
345D12—62no—
346D12—62no—
347D12—122no—
348D12—122no—
349D12—122no—
350D12—1216no—
351D12—121no—
352D12—121no—
353D12—121no—
354D12—121no—
355C3×C8—62no—
356C3⋊C8—22no—
357C3⋊C8—62no—
358C3⋊C8—62no—
359C3⋊C8—122no—
360C2×C32#39011yescharacteristic
361C2×C32#41812yes—
362C2×C32#49012yes—
363C2×C32#49611yescharacteristic
364C2×C32#49611yescharacteristic
365C3⋊D3—82no—
366C3×D3—82no—
367C24—61no—
368C24—181no—
369C2×D4—32no—
370C2×D4—61no—
371C2×D4—61no—
372C2×D4—61no—
373C2×D4—61no—
374C2×D4—61no—
375C2×D4—92no—
376C2×D4—188no—
377C2×D4—181no—
378C2×D4—181no—
379C2×D4—181no—
380C2×D4—181no—
381C2×D4—181no—
382C2×D4—364no—
383C2×D4—364no—
384C22×C4—21no—
385C22×C4—32no—
386C22×C4—61no—
387C22×C4C2×D3211yescharacteristic
388C2×C8—32no—
389C2×C8—61no—
390C2×C8—61no—
391C2×C8—92no—
392C2×C8—181no—
393C2×C8—181no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—61no—
397C4⋊C4—61no—
398C42—32no—
399C42—32no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—22no—
403C22×C3—22no—
404C22×C3—21no—
405C22×C3—122no—
406C22×C3—124no—
407C22×C3—241no—
408C22×C3—241no—
409C22×C3—242no—
410C22×C3D3×C22⋊C411yescharacteristic
411C22×C3#88511yescharacteristic
412C22×C3#91112yes—
413C22×C3#91412yes—
414C22×C3C2×(C2×D3)⋊C411yescharacteristic
415C22×C3#94011yescharacteristic
416C22×C3#94011yescharacteristic
417C22×C3#94711yescharacteristic
418C22×C3#94912yes—
419C22×C3#94912yes—
420C2×D3—42no—
421C2×D3—44no—
422C2×D3—81no—
423C2×D3—81no—
424C2×D3—82no—
425C2×D3—124no—
426C2×D3—122no—
427C2×D3—122no—
428C2×D3—124no—
429C2×D3—124no—
430C2×D3—244no—
431C2×D3—244no—
432C2×D3—242no—
433C2×D3—242no—
434C2×D3—241no—
435C2×D3—241no—
436C2×D3—242no—
437C2×D3—241no—
438C2×D3—241no—
439C2×D3—242no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—64no—
445C3×C4—82no—
446C3×C4—81no—
447C3×C4—81no—
448C3×C4—241no—
449C3×C4#67⋊C411yescharacteristic
450C3×C4#88411yescharacteristic
451C3×C4#89311yescharacteristic
452C3×C4#89311yescharacteristic
453C3×C4#89511yescharacteristic
454C3×C4#89511yescharacteristic
455C3×C4C4×#6711yescharacteristic
456C3×C4#93911yescharacteristic
457Dic3—24no—
458Dic3—81no—
459C32#196111yescharacteristic, complemented, Sylow
460C23—62no—
461C23—121no—
462C23—122no—
463C23—122no—
464C23—121no—
465C23—182no—
466C23—361no—
467C23—362no—
468C23—362no—
469C23—361no—
470C23D3×#6711yescharacteristic
471D4—62no—
472D4—62no—
473D4—121no—
474D4—121no—
475D4—182no—
476D4—182no—
477D4—3616no—
478D4—361no—
479D4—361no—
480C2×C4—34no—
481C2×C4—42no—
482C2×C4—41no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—122no—
486C2×C4—121no—
487C2×C4#379611yescharacteristic
488C2×C4#379911yescharacteristic
489C2×C4C4×D3211yescharacteristic
490C2×C4D3×D1211yescharacteristic
491C2×C4D3×#6711yescharacteristic
492C2×C4#381111yescharacteristic
493C8—62no—
494C8—182no—
495C2×C3—22no—
496C2×C3—22no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—242no—
501C2×C3#476412yes—
502C2×C3#477012yes—
503C2×C3#495711yescharacteristic
504C2×C3#498811yescharacteristic
505C2×C3#500112yes—
506C2×C3#505811yescharacteristic
507C2×C3#505811yescharacteristic
508C2×C3#506712yes—
509C2×C3#515411yescharacteristic
510C2×C3#517611yescharacteristic
511D3—82no—
512D3—244no—
513D3—242no—
514D3—242no—
515C22—124no—
516C22—122no—
517C22—242no—
518C22—241no—
519C22—241no—
520C22—364no—
521C22—362no—
522C22—722no—
523C22—721no—
524C22—721no—
525C22#6390711yescharacteristic
526C22D3×(C2×D3)⋊C411yescharacteristic
527C22#6392512yes—
528C22#6393912yes—
529C22#6397911yescharacteristic
530C4—64no—
531C4—81no—
532C4—241no—
533C4#6388111yescharacteristic
534C4#6388611yescharacteristic
535C4#6390411yescharacteristic
536C4#6391011yescharacteristic
537C3—21no—
538C3#6955311yescharacteristic, complemented
539C3#7016011yescharacteristic, complemented
540C2—242no—
541C2—722no—
542C2#1059055012yes—
543C2#1059059212yes—
544C2#1059138411yescharacteristic
545C2#1059148311yescharacteristic
546C2#1059161911yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×#63911C2
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1961
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. C2×#63636C2semidirect
3. C3×#4977C2semidirect
4. C2×C3×#809C2semidirect
5. C2×#63564C2semidirect
6. C2×#63562C2semidirect
7. C2×#63554C2semidirect
19. #63911C4semidirect
33. #4977D3semidirect
39. C2×#809D3semidirect
66. C2×C3⋊(C3⋊C8)D4semidirect
73. C2×C3×C3⋊C8D4semidirect
232. C2×C3⋊C8#67semidirect
459. C32#1961semidirect
538. C3#69553semidirect
539. C3#70160semidirect

Maximal subgroups

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

subgroupindex
C2×#639112
C2×#636362
C3×#49772
C2×C3×#8092
C2×#635642
C2×#635622
C2×#635542
#701603
#695533