Finite Group Databasebeta

← #11791046

Subgroups — #11791046

Order 1152.

897 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
1C22×#3714C211yesmaximal, characteristic
2#10592638C211yesmaximal, characteristic, complemented
3C3×#4939C211yesmaximal, characteristic, complemented
4C2×C3×C4×C3⋊C8C211yesmaximal, characteristic, complemented
5C2×#63575C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic, complemented
8#69776—31nomaximal
9#69647—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×#3752—22no—
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—22no—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×#3714—22no—
20C2×#3714—22no—
21C2×#3714C414yescomplemented
22C3×C4×C3⋊C8—22no—
23#63575—22no—
24#63564—22no—
25#63563—22no—
26C22×#213—31no—
27C22×D24—31no—
28C2×C3×C4×C8—31no—
29C3×#390—31no—
30C2×#832—31no—
31C2×#821—31no—
32C2×#821—31no—
33C2×#818—31no—
34C2×#809—31no—
35C2×#807—31no—
36#4939—31no—
37#4939—31no—
38#4939—61no—
39#4939D311yescharacteristic, complemented
40C2×C4×C3⋊C8D311yescharacteristic, complemented
41C23×C3⋊D3—21no—
42C23×C3×D3—21no—
43C22×C32×C4D412yes—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—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)—21no—
51C2×C4⋊(C3⋊D3)C2×C412yes—
52C22×C3×Dic3—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12C2×C412yes—
59C32×C42—21no—
60C32×C42—21no—
61#3752—44no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—21no—
64C3×(C2×D3)⋊C4—44no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8C2×C412yes—
70C2×C3×C3⋊C8D412yes—
71C2×C3×C3⋊C8D412yes—
72C2×C3×C3⋊C8D412yes—
73#3714—28no—
74#1970—91noSylow
75C22×C3×D4—31no—
76C22×D12—31no—
77C22×D12—31no—
78C22×D12—61no—
79C22×D12C2×D311yescharacteristic
80C22×C3×C8—31no—
81C22×C3×C8—31no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C22⋊C4—62no—
84C2×C3×C42—21no—
85C2×C3×C42C2×D311yescharacteristic
86C2×C3×C42C2×D311yescharacteristic
87C2×#213—34no—
88C2×#213—62no—
89C2×#213—62no—
90C2×(C2×D3)⋊C4—22no—
91C2×(C2×D3)⋊C4—64no—
92C2×(C2×D3)⋊C4—62no—
93C2×(C2×D3)⋊C4—62no—
94C2×C4⋊Dic3—31no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—61no—
97C2×C4⋊Dic3C2×D311yescharacteristic
98C22×C3⋊C8C2×D311yescharacteristic
99C22×C3⋊C8C2×D311yescharacteristic
100C2×D24—34no—
101C2×D24—62no—
102C2×D24—62no—
103C3×C4×C8—62no—
104#832—62no—
105#821—62no—
106#821—62no—
107#818—62no—
108#809—62no—
109#807—62no—
110C4×C3⋊C8—22no—
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—22no—
123C2×C32×C4—22no—
124C2×C32×C4D814yescomplemented
125C2×C32×C4C22×C411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3—42no—
133C4⋊(C3⋊D3)—22no—
134C4⋊(C3⋊D3)—22no—
135C4⋊(C3⋊D3)—41no—
136C4⋊(C3⋊D3)—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—42no—
139C3×D12—22no—
140C3×D12—22no—
141C3×D12—41no—
142C3×D12—41no—
143C3×C3⋊C8—22no—
144C3×C3⋊C8C22⋊C414yescomplemented
145C22×D8—91no—
146C2×#107—91no—
147C2×#102—91no—
148C2×#102—91no—
149C2×C4×C8—31no—
150#390—31no—
151#390—91no—
152C24×C3—61no—
153C23×D3—21no—
154C23×D3—62no—
155C23×D3—61no—
156C23×D3—61no—
157C2×C3×D4—32no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C22×C3×C4—22no—
164C22×C3×C4—21no—
165C22×C3×C4—61no—
166C22×C3×C4D1212yes—
167C22×C3×C4#6712yes—
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C22×Dic3—21no—
171C22×Dic3—62no—
172C22×Dic3—61no—
173C22×Dic3—61no—
174C2×D12—21no—
175C2×D12—21no—
176C2×D12—21no—
177C2×D12—21no—
178C2×D12—21no—
179C2×D12—32no—
180C2×D12—32no—
181C2×D12—62no—
182C2×D12—61no—
183C2×D12—61no—
184C2×D12—61no—
185C2×D12—61no—
186C2×D12—61no—
187C2×D12—61no—
188C2×D12—61no—
189C2×D12—61no—
190C2×D12—62no—
191C2×D12—61no—
192C2×D12—61no—
193C2×D12—121no—
194C2×D12—121no—
195C2×D12—121no—
196C2×D12—121no—
197C2×D12C4×D312yes—
198C2×C3×C8—32no—
199C2×C3×C8—32no—
200C2×C3×C8—32no—
201C2×C3×C8—32no—
202C2×C3×C8—61no—
203C2×C3×C8—61no—
204C3×C4⋊C4—61no—
205C3×C4⋊C4—61no—
206C3×C22⋊C4—124no—
207C3×C42—21no—
208C3×C42—21no—
209C3×C42—21no—
210C3×C42—21no—
211C3×C42—41no—
212C3×C42—41no—
213#213—68no—
214(C2×D3)⋊C4—44no—
215(C2×D3)⋊C4—128no—
216(C2×D3)⋊C4—124no—
217(C2×D3)⋊C4—124no—
218C4⋊Dic3—21no—
219C4⋊Dic3—21no—
220C4⋊Dic3—61no—
221C4⋊Dic3—61no—
222C4⋊Dic3—61no—
223C4⋊Dic3—61no—
224C4⋊Dic3—121no—
225C4⋊Dic3—121no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—21no—
228C2×C3⋊C8C4×D312yes—
229C2×C3⋊C8D1212yes—
230C2×C3⋊C8D1212yes—
231C2×C3⋊C8#6712yes—
232D24—68no—
233C22×C32C4×D411yescharacteristic
234C22×C32#12111yescharacteristic
235C22×C32#12711yescharacteristic
236C22×C32C2×D812yes—
237C22×C32#13512yes—
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—24no—
249C32×C4C2×C22⋊C411yescharacteristic
250C32×C4C4×D411yescharacteristic
251C32×C4#12111yescharacteristic
252C32×C4#12411yescharacteristic
253C3⋊Dic3—81no—
254C3×Dic3—81no—
255C22×D4—31no—
256C22×D4—91no—
257C2×D8—94no—
258C2×D8—182no—
259C2×D8—182no—
260C22×C8—31no—
261C22×C8—31no—
262C2×C4⋊C4—31no—
263C2×C4⋊C4—91no—
264C2×C22⋊C4—62no—
265C2×C22⋊C4—182no—
266C2×C42D3211yescharacteristic
267#107—182no—
268#102—182no—
269#102—182no—
270C4×C8—62no—
271C23×C3—21no—
272C23×C3—62no—
273C23×C3—121no—
274C23×C3—122no—
275C23×C3—122no—
276C23×C3—121no—
277C23×C3C2×D1211yescharacteristic
278C23×C3C2×#6711yescharacteristic
279C22×D3—22no—
280C22×D3—42no—
281C22×D3—41no—
282C22×D3—41no—
283C22×D3—42no—
284C22×D3—64no—
285C22×D3—62no—
286C22×D3—62no—
287C22×D3—124no—
288C22×D3—122no—
289C22×D3—122no—
290C22×D3—124no—
291C22×D3—121no—
292C22×D3—122no—
293C22×D3—122no—
294C22×D3—121no—
295C22×D3—122no—
296C22×D3—121no—
297C22×D3—121no—
298C22×D3—122no—
299C3×D4—62no—
300C3×D4—62no—
301C3×D4—121no—
302C3×D4—121no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—24no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—42no—
315C2×C3×C4—42no—
316C2×C3×C4—121no—
317C2×C3×C4—122no—
318C2×C3×C4D2414yescomplemented
319C2×C3×C4#21314yescomplemented
320C2×C3×C4C2×C4×D311yescharacteristic
321C2×C3×C4C2×C4×D311yescharacteristic
322C2×C3×C4C2×D1211yescharacteristic
323C2×C3×C4C2×D1211yescharacteristic
324C2×C3×C4#23511yescharacteristic
325C2×C3×C4#23511yescharacteristic
326C2×C3×C4#23511yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4#23711yescharacteristic
331C2×C3×C4C2×#6711yescharacteristic
332C2×Dic3—42no—
333C2×Dic3—41no—
334C2×Dic3—122no—
335C2×Dic3—124no—
336C2×Dic3—121no—
337C2×Dic3—122no—
338C2×Dic3—122no—
339C2×Dic3—121no—
340D12—22no—
341D12—22no—
342D12—41no—
343D12—41no—
344D12—62no—
345D12—62no—
346D12—62no—
347D12—62no—
348D12—122no—
349D12—122no—
350D12—122no—
351D12—122no—
352D12—121no—
353D12—121no—
354D12—121no—
355D12—121no—
356C3×C8—34no—
357C3×C8—62no—
358C3⋊C8—22no—
359C3⋊C8(C2×D3)⋊C414yescomplemented
360C2×C32#39011yescharacteristic
361C2×C32C4×D812yes—
362C2×C32#46612yes—
363C2×C32#49311yescharacteristic
364C2×C32#49511yescharacteristic
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—181no—
377C2×D4—181no—
378C2×D4—181no—
379C2×D4—181no—
380C2×D4—181no—
381C22×C4—61no—
382C22×C4—181no—
383C22×C4#62612yes—
384C22×C4C2×D3211yescharacteristic
385D8—188no—
386C2×C8—32no—
387C2×C8—32no—
388C2×C8—32no—
389C2×C8—32no—
390C2×C8—61no—
391C2×C8—61no—
392C4⋊C4—61no—
393C4⋊C4—61no—
394C4⋊C4—181no—
395C4⋊C4—181no—
396C22⋊C4—124no—
397C22⋊C4—364no—
398C42—21no—
399C42—21no—
400C22×C3—22no—
401C22×C3—22no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—122no—
406C22×C3—124no—
407C22×C3—241no—
408C22×C3—241no—
409C22×C3—242no—
410C22×C3C4×D1211yescharacteristic
411C22×C3#87411yescharacteristic
412C22×C3C2×D2412yes—
413C22×C3#90412yes—
414C22×C3C4×#6711yescharacteristic
415C22×C3#93011yescharacteristic
416C22×C3C2×#21312yes—
417C22×C3#93911yescharacteristic
418C22×C3#94011yescharacteristic
419C22×C3#95012yes—
420C2×D3—42no—
421C2×D3—44no—
422C2×D3—82no—
423C2×D3—81no—
424C2×D3—81no—
425C2×D3—124no—
426C2×D3—128no—
427C2×D3—122no—
428C2×D3—124no—
429C2×D3—122no—
430C2×D3—124no—
431C2×D3—242no—
432C2×D3—242no—
433C2×D3—244no—
434C2×D3—241no—
435C2×D3—241no—
436C2×D3—242no—
437C2×D3—241no—
438C2×D3—241no—
439C2×D3—242no—
440C3×C4—24no—
441C3×C4—24no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—44no—
447C3×C4—241no—
448C3×C4C4×D1211yescharacteristic
449C3×C4#87511yescharacteristic
450C3×C4D3×C22⋊C411yescharacteristic
451C3×C4#67⋊C411yescharacteristic
452C3×C4#88411yescharacteristic
453C3×C4#88511yescharacteristic
454C3×C4C2×(C2×D3)⋊C411yescharacteristic
455C3×C4#93011yescharacteristic
456Dic3—81no—
457Dic3—242no—
458Dic3—241no—
459Dic3—241no—
460C32#197011yescharacteristic, complemented, Sylow
461C23—62no—
462C23—122no—
463C23—122no—
464C23—121no—
465C23—121no—
466C23—182no—
467C23—362no—
468C23—362no—
469C23—361no—
470C23—361no—
471C23C2×#62611yescharacteristic
472D4—62no—
473D4—62no—
474D4—121no—
475D4—121no—
476D4—182no—
477D4—182no—
478D4—361no—
479D4—361no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—122no—
483C2×C4—121no—
484C2×C4—362no—
485C2×C4—361no—
486C2×C4#371414yescomplemented
487C2×C4#379811yescharacteristic
488C2×C4C4×D3211yescharacteristic
489C2×C4D3×D1211yescharacteristic
490C2×C4D3×D1211yescharacteristic
491C2×C4#380411yescharacteristic
492C2×C4D3×#6711yescharacteristic
493C8—34no—
494C8—62no—
495C2×C3—22no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—22no—
500C2×C3—242no—
501C2×C3C4×D2412yes—
502C2×C3#469511yescharacteristic
503C2×C3#469611yescharacteristic
504C2×C3#493911yescharacteristic
505C2×C3#495711yescharacteristic
506C2×C3C4×#21312yes—
507C2×C3#503812yes—
508C2×C3#505911yescharacteristic
509C2×C3#507311yescharacteristic
510C2×C3#511512yes—
511D3—82no—
512D3—244no—
513D3—242no—
514D3—242no—
515C22—124no—
516C22—122no—
517C22—241no—
518C22—241no—
519C22—242no—
520C22—364no—
521C22—362no—
522C22—721no—
523C22—721no—
524C22—722no—
525C22C2×#371412yes—
526C22#6382912yes—
527C22C4×#62611yescharacteristic
528C22#6391111yescharacteristic
529C22#6397811yescharacteristic
530C4—24no—
531C4—241no—
532C4—721no—
533C4#6385211yescharacteristic
534C4#6388011yescharacteristic
535C4#6390611yescharacteristic
536C4D3×(C2×D3)⋊C411yescharacteristic
537C3—21no—
538C3#6964711yescharacteristic, complemented
539C3#6977611yescharacteristic, complemented
540C2—242no—
541C2—722no—
542C2C4×#371412yes—
543C2#1059035011yescharacteristic
544C2#1059037011yescharacteristic
545C2#1059116412yes—
546C2#1059138311yescharacteristic
subgroupG/H
centerC23C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×#3714C2
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1970
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10592638C2semidirect
3. C3×#4939C2semidirect
4. C2×C3×C4×C3⋊C8C2semidirect
5. C2×#63575C2semidirect
6. C2×#63564C2semidirect
7. C2×#63563C2semidirect
21. C2×#3714C4semidirect
39. #4939D3semidirect
40. C2×C4×C3⋊C8D3semidirect
124. C2×C32×C4D8semidirect
144. C3×C3⋊C8C22⋊C4semidirect
318. C2×C3×C4D24semidirect
319. C2×C3×C4#213semidirect
359. C3⋊C8(C2×D3)⋊C4semidirect
460. C32#1970semidirect
486. C2×C4#3714semidirect
538. C3#69647semidirect
539. C3#69776semidirect

Maximal subgroups

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

subgroupindex
C22×#37142
#105926382
C3×#49392
C2×C3×C4×C3⋊C82
C2×#635752
C2×#635642
C2×#635632
#697763
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