Finite Group Databasebeta

← #11791038

Subgroups — #11791038

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3714C211yesmaximal, characteristic
2C2×#63648C211yesmaximal, characteristic, complemented
3C2×C3×#821C211yesmaximal, characteristic, complemented
4C2×C3×C8×Dic3C211yesmaximal, characteristic, complemented
5#10591320C211yesmaximal, characteristic, complemented
6#10591318C211yesmaximal, characteristic, complemented
7C2×#63575C211yesmaximal, characteristic, complemented
8#70190—31nomaximal
9#69776—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3722—22no—
18C2×(C2×D3)⋊Dic3—22no—
19C2×#3714—22no—
20C2×#3714—22no—
21C2×#3714C414yescomplemented
22#63648—22no—
23C3×#821—22no—
24C3×C8×Dic3—22no—
25#63575—22no—
26C22×#213—31no—
27C22×D24—31no—
28C2×C3×#102—31no—
29C2×C3×C4×C8—31no—
30#5221—31no—
31C2×#821—31no—
32C2×#821—31no—
33C2×#821—61no—
34C2×#821D311yescharacteristic, complemented
35C2×#818—31no—
36C2×C8×Dic3D311yescharacteristic, complemented
37#4988—31no—
38C2×#807—31no—
39#4939—31no—
40#4939—31no—
41C23×C3⋊D3—21no—
42C23×C3×D3—21no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
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×C32×C8—21no—
60C2×C32×C8—21no—
61C2×C32×C8D412yes—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4×Dic3—21no—
67C3×C4×Dic3—21no—
68C2×C3×C3⋊C8C2×C412yes—
69C2×C3×C3⋊C8D412yes—
70C2×C3×C3⋊C8D412yes—
71#3722—44no—
72(C2×D3)⋊Dic3—44no—
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—21no—
81C22×C3×C8—31no—
82C22×C3×C8C2×D311yescharacteristic
83C22×C3×C8C2×D311yescharacteristic
84C2×C3×C4⋊C4—31no—
85C2×C3×C42—31no—
86C2×#217—62no—
87C2×#213—34no—
88C2×#213—62no—
89C2×#213—62no—
90C2×(C2×D3)⋊C4—62no—
91C2×(C2×D3)⋊C4—62no—
92C2×(C2×D3)⋊C4—62no—
93C2×C4⋊Dic3—31no—
94C2×C4⋊Dic3—31no—
95C2×C4⋊Dic3—61no—
96C2×C4⋊Dic3C2×D311yescharacteristic
97C2×C4×Dic3C2×D311yescharacteristic
98C22×C3⋊C8C2×D311yescharacteristic
99C2×D24—34no—
100C2×D24—62no—
101C2×D24—62no—
102C3×#102—62no—
103C3×C4×C8—62no—
104#821—22no—
105#821—64no—
106#821—62no—
107#821—62no—
108#818—62no—
109C8×Dic3—22no—
110#807—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×C4C22×C411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—42no—
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×Dic3D814yescomplemented
139C3×D12—22no—
140C3×D12—22no—
141C3×D12—41no—
142C3×D12—41no—
143C32×C8—22no—
144C3×C3⋊C8C22⋊C414yescomplemented
145C22×D8—91no—
146C2×#107—91no—
147C2×#102—31no—
148C2×#102—91no—
149C2×C4×C8—31no—
150#390—91no—
151#390—91no—
152C24×C3—61no—
153C23×D3—21no—
154C23×D3—61no—
155C23×D3—61no—
156C23×D3—121no—
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—21no—
164C22×C3×C4—32no—
165C22×C3×C4—61no—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C22×Dic3—21no—
169C22×Dic3—61no—
170C22×Dic3—61no—
171C22×Dic3—121no—
172C22×Dic3D1212yes—
173C2×D12—21no—
174C2×D12—21no—
175C2×D12—21no—
176C2×D12—21no—
177C2×D12—21no—
178C2×D12—32no—
179C2×D12—32no—
180C2×D12—62no—
181C2×D12—62no—
182C2×D12—62no—
183C2×D12—61no—
184C2×D12—61no—
185C2×D12—61no—
186C2×D12—61no—
187C2×D12—61no—
188C2×D12—61no—
189C2×D12—61no—
190C2×D12—61no—
191C2×D12—61no—
192C2×D12—61no—
193C2×D12—121no—
194C2×D12—121no—
195C2×D12—121no—
196C2×D12C4×D312yes—
197C2×C3×C8—21no—
198C2×C3×C8—21no—
199C2×C3×C8—21no—
200C2×C3×C8—21no—
201C2×C3×C8—22no—
202C2×C3×C8—32no—
203C2×C3×C8—32no—
204C2×C3×C8—32no—
205C2×C3×C8—41no—
206C2×C3×C8—41no—
207C2×C3×C8D1212yes—
208C2×C3×C8#6712yes—
209C3×C4⋊C4—61no—
210C3×C4⋊C4—61no—
211C3×C42—61no—
212C3×C42—61no—
213#217—124no—
214#213—68no—
215(C2×D3)⋊C4—124no—
216(C2×D3)⋊C4—124no—
217(C2×D3)⋊C4—124no—
218C4⋊Dic3—21no—
219C4⋊Dic3—21no—
220C4⋊Dic3—62no—
221C4⋊Dic3—61no—
222C4⋊Dic3—61no—
223C4⋊Dic3—61no—
224C4⋊Dic3—61no—
225C4⋊Dic3—121no—
226C4×Dic3—21no—
227C4×Dic3—21no—
228C2×C3⋊C8C4×D312yes—
229C2×C3⋊C8D1212yes—
230C2×C3⋊C8#6712yes—
231D24—68no—
232C22×C32C4×D411yescharacteristic
233C22×C32#12111yescharacteristic
234C22×C32#12711yescharacteristic
235C22×C32C2×D812yes—
236C22×C32#13512yes—
237C2×C3⋊D3—42no—
238C2×C3⋊D3—44no—
239C2×C3⋊D3—82no—
240C2×C3⋊D3—81no—
241C2×C3⋊D3—81no—
242C2×C3×D3—42no—
243C2×C3×D3—44no—
244C2×C3×D3—82no—
245C2×C3×D3—81no—
246C2×C3×D3—81no—
247C32×C4C2×C22⋊C411yescharacteristic
248C32×C4C4×D411yescharacteristic
249C32×C4#12111yescharacteristic
250C32×C4#12411yescharacteristic
251C3⋊Dic3—81no—
252C3×Dic3—24no—
253C3×Dic3—81no—
254C22×D4—31no—
255C22×D4—91no—
256C2×D8—94no—
257C2×D8—182no—
258C2×D8—182no—
259C22×C8—31no—
260C22×C8D3211yescharacteristic
261C2×C4⋊C4—31no—
262C2×C4⋊C4—91no—
263C2×C22⋊C4—182no—
264C2×C22⋊C4—182no—
265C2×C42—31no—
266#107—182no—
267#102—62no—
268#102—182no—
269C4×C8—62no—
270C23×C3—21no—
271C23×C3—62no—
272C23×C3—121no—
273C23×C3—122no—
274C23×C3—122no—
275C23×C3—121no—
276C23×C3C2×D1211yescharacteristic
277C23×C3D3×D411yescharacteristic
278C22×D3—22no—
279C22×D3—41no—
280C22×D3—42no—
281C22×D3—42no—
282C22×D3—41no—
283C22×D3—62no—
284C22×D3—62no—
285C22×D3—122no—
286C22×D3—122no—
287C22×D3—122no—
288C22×D3—121no—
289C22×D3—121no—
290C22×D3—122no—
291C22×D3—122no—
292C22×D3—122no—
293C22×D3—122no—
294C22×D3—121no—
295C22×D3—121no—
296C22×D3—242no—
297C22×D3—242no—
298C3×D4—62no—
299C3×D4—62no—
300C3×D4—121no—
301C3×D4—121no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—34no—
309C2×C3×C4—62no—
310C2×C3×C4—62no—
311C2×C3×C4—121no—
312C2×C3×C4—122no—
313C2×C3×C4C2×C4×D311yescharacteristic
314C2×C3×C4C2×C4×D311yescharacteristic
315C2×C3×C4C2×D1211yescharacteristic
316C2×C3×C4C2×D1211yescharacteristic
317C2×C3×C4#23511yescharacteristic
318C2×C3×C4#23511yescharacteristic
319C2×C3×C4#23511yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4#23711yescharacteristic
323C2×C3×C4C2×#6711yescharacteristic
324C2×C3×C4C2×#6711yescharacteristic
325C2×Dic3—22no—
326C2×Dic3—22no—
327C2×Dic3—42no—
328C2×Dic3—41no—
329C2×Dic3—122no—
330C2×Dic3—121no—
331C2×Dic3—122no—
332C2×Dic3—122no—
333C2×Dic3—121no—
334C2×Dic3—242no—
335C2×Dic3D2414yescomplemented
336D12—22no—
337D12—22no—
338D12—41no—
339D12—41no—
340D12—64no—
341D12—62no—
342D12—62no—
343D12—62no—
344D12—62no—
345D12—122no—
346D12—122no—
347D12—122no—
348D12—121no—
349D12—121no—
350D12—121no—
351D12—121no—
352C3×C8—22no—
353C3×C8—22no—
354C3×C8—34no—
355C3×C8—42no—
356C3⋊C8(C2×D3)⋊C414yescomplemented
357C2×C32#39011yescharacteristic
358C2×C32C4×D812yes—
359C2×C32#46612yes—
360C2×C32#49311yescharacteristic
361C2×C32#49511yescharacteristic
362C3⋊D3—82no—
363C3×D3—82no—
364C24—61no—
365C24—181no—
366C2×D4—32no—
367C2×D4—61no—
368C2×D4—61no—
369C2×D4—61no—
370C2×D4—61no—
371C2×D4—61no—
372C2×D4—92no—
373C2×D4—181no—
374C2×D4—181no—
375C2×D4—181no—
376C2×D4—181no—
377C2×D4—181no—
378C22×C4—32no—
379C22×C4—61no—
380C22×C4—181no—
381C22×C4C2×D3211yescharacteristic
382D8—188no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—32no—
386C2×C8—32no—
387C2×C8—32no—
388C2×C8#62612yes—
389C4⋊C4—61no—
390C4⋊C4—61no—
391C4⋊C4—181no—
392C4⋊C4—181no—
393C22⋊C4—364no—
394C22⋊C4—364no—
395C42—61no—
396C42—61no—
397C22×C3—22no—
398C22×C3—22no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—122no—
403C22×C3—124no—
404C22×C3—241no—
405C22×C3—241no—
406C22×C3—242no—
407C22×C3C4×D1211yescharacteristic
408C22×C3#87411yescharacteristic
409C22×C3#67⋊C411yescharacteristic
410C22×C3#88411yescharacteristic
411C22×C3C2×D2412yes—
412C22×C3#90412yes—
413C22×C3D3×D812yes—
414C22×C3#91612yes—
415C22×C3#93011yescharacteristic
416C22×C3#94011yescharacteristic
417C2×D3—42no—
418C2×D3—44no—
419C2×D3—81no—
420C2×D3—81no—
421C2×D3—82no—
422C2×D3—124no—
423C2×D3—122no—
424C2×D3—124no—
425C2×D3—122no—
426C2×D3—124no—
427C2×D3—244no—
428C2×D3—244no—
429C2×D3—242no—
430C2×D3—242no—
431C2×D3—241no—
432C2×D3—241no—
433C2×D3—241no—
434C2×D3—241no—
435C2×D3—242no—
436C2×D3—242no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—64no—
442C3×C4—241no—
443C3×C4C4×D1211yescharacteristic
444C3×C4#87511yescharacteristic
445C3×C4D3×C22⋊C411yescharacteristic
446C3×C4#88511yescharacteristic
447C3×C4C2×(C2×D3)⋊C411yescharacteristic
448C3×C4C4×#6711yescharacteristic
449C3×C4#93011yescharacteristic
450C3×C4#93911yescharacteristic
451Dic3—24no—
452Dic3—81no—
453Dic3—242no—
454Dic3—241no—
455Dic3—241no—
456C32#197011yescharacteristic, complemented, Sylow
457C23—62no—
458C23—122no—
459C23—122no—
460C23—121no—
461C23—121no—
462C23—182no—
463C23—362no—
464C23—362no—
465C23—361no—
466C23—361no—
467C23D3×D1211yescharacteristic
468D4—62no—
469D4—62no—
470D4—121no—
471D4—121no—
472D4—182no—
473D4—182no—
474D4—361no—
475D4—361no—
476C2×C4—34no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—122no—
480C2×C4—121no—
481C2×C4—362no—
482C2×C4—361no—
483C2×C4#379811yescharacteristic
484C2×C4C4×D3211yescharacteristic
485C2×C4D3×D1211yescharacteristic
486C2×C4#380411yescharacteristic
487C2×C4C2×#62611yescharacteristic
488C2×C4D3×#6711yescharacteristic
489C8—22no—
490C8—34no—
491C2×C3—22no—
492C2×C3—22no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—242no—
497C2×C3C4×D2412yes—
498C2×C3#469511yescharacteristic
499C2×C3#469611yescharacteristic
500C2×C3#475612yes—
501C2×C3#477512yes—
502C2×C3#493911yescharacteristic
503C2×C3#495711yescharacteristic
504C2×C3#511512yes—
505C2×C3#515111yescharacteristic
506C2×C3#516811yescharacteristic
507D3—82no—
508D3—244no—
509D3—242no—
510D3—242no—
511C22—124no—
512C22—122no—
513C22—242no—
514C22—241no—
515C22—241no—
516C22—364no—
517C22—362no—
518C22—722no—
519C22—721no—
520C22—721no—
521C22D3×D2412yes—
522C22#6380612yes—
523C22#6388011yescharacteristic
524C22#6390611yescharacteristic
525C22#6391111yescharacteristic
526C4—64no—
527C4—241no—
528C4—721no—
529C4#6385211yescharacteristic
530C4C4×#62611yescharacteristic
531C4D3×(C2×D3)⋊C411yescharacteristic
532C4#6397811yescharacteristic
533C3—21no—
534C3#6977611yescharacteristic, complemented
535C3#7019011yescharacteristic, complemented
536C2—242no—
537C2—722no—
538C2#1059074512yes—
539C2#1059082612yes—
540C2#1059086211yescharacteristic
541C2#1059088011yescharacteristic
542C2#1059138311yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×#3714C2
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1970
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63648C2semidirect
3. C2×C3×#821C2semidirect
4. C2×C3×C8×Dic3C2semidirect
5. #10591320C2semidirect
6. #10591318C2semidirect
7. C2×#63575C2semidirect
21. C2×#3714C4semidirect
34. C2×#821D3semidirect
36. C2×C8×Dic3D3semidirect
138. C2×C3×Dic3D8semidirect
144. C3×C3⋊C8C22⋊C4semidirect
335. C2×Dic3D24semidirect
356. C3⋊C8(C2×D3)⋊C4semidirect
456. C32#1970semidirect
534. C3#69776semidirect
535. C3#70190semidirect

Maximal subgroups

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

subgroupindex
C22×#37142
C2×#636482
C2×C3×#8212
C2×C3×C8×Dic32
#105913202
#105913182
C2×#635752
#701903
#697763