Finite Group Databasebeta

← #11803878

Subgroups — #11803878

Order 1152.

1609 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63911C211yesmaximal, characteristic
2C2×#63894C211yesmaximal, characteristic, complemented
3C2×Dic3×D12C211yesmaximal, characteristic, complemented
4#10592638C211yesmaximal, characteristic, complemented
5C3×#4939C211yesmaximal, characteristic, complemented
6C3×#4932C211yesmaximal, characteristic, complemented
7#10591364C214yesmaximal, complemented
8#10591275C214yesmaximal, complemented
9#10591224C211yesmaximal, characteristic, complemented
10#76298—31nomaximal
11#73389—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×#626C2214yes—
15C22×#624C2212yes—
16C22×D3×Dic3C2212yes—
17C2×C32×C42C2211yescharacteristic
18C2×#3752C2214yes—
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C3×(C2×D3)⋊C4C2214yes—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×#3722C2212yes—
25C2×(C2×D3)⋊Dic3C2212yes—
26#63911C418yescomplemented
27#63894—24no—
28Dic3×D12—24no—
29C3×C3⋊#95C2212yes—
30C3×C3⋊#95C2212yes—
31#63579C2214yes—
32C2×#940—31no—
33C2×D4×Dic3—31no—
34C2×#893—31no—
35C2×#874—31no—
36C2×C4×D12—31no—
37C2×C4×D12—31no—
38C3×#390—31no—
39C3×#376—31no—
40#4977—31no—
41#4958—34no—
42#4956—34no—
43#4939—31no—
44#4939—31no—
45#4939—61no—
46#4939D311yescharacteristic, complemented
47#4936—31no—
48#4932D311yescharacteristic, complemented
49#4665—34no—
50#4665—34no—
51C23×C3⋊D3C2312yes—
52C23×C3×D3C2312yes—
53C22×C32×C4C2312yes—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3C2312yes—
56C2×C4⋊(C3⋊D3)—22no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)C2×C414yescomplemented
59C22×C3×Dic3C2312yes—
60C22×C3×Dic3C2312yes—
61C22×C3×Dic3C2311yescharacteristic
62C22×C3×Dic3C2311yescharacteristic
63C2×C3×D12—22no—
64C2×C3×D12—22no—
65C2×C3×D12C2×C414yescomplemented
66C2×#626—44no—
67C2×#626—44no—
68C2×#626C2×C4116yescomplemented
69C2×#624—24no—
70C2×#624—44no—
71C2×D3×Dic3—24no—
72C2×D3×Dic3—44no—
73C32×C42—22no—
74#3752—44no—
75C4⋊(C3⋊Dic3)—22no—
76C3×(C2×D3)⋊C4—44no—
77C3×C4⋊Dic3—22no—
78C3×C4×Dic3C2×C414yescomplemented
79C3×C4×Dic3D414yescomplemented
80#3722—24no—
81(C2×D3)⋊Dic3—24no—
82#2328—91noSylow
83C22×C3×D4—31no—
84C22×#67—34no—
85C23×Dic3—32no—
86C22×D12—31no—
87C22×D12—31no—
88C22×D12—34no—
89C22×D12—61no—
90C22×D12C2×D311yescharacteristic
91C22×C4×D3—32no—
92C22×C4×D3—32no—
93C22×C4×D3—32no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C22⋊C4—34no—
96C2×C3×C42—21no—
97C2×C3×C42—31no—
98C2×C3×C42—31no—
99C2×C3×C42C2×D311yescharacteristic
100C2×C3×C42C2×D311yescharacteristic
101C2×#217—32no—
102#940—38no—
103D4×Dic3—64no—
104C2×(C2×D3)⋊C4—32no—
105C2×(C2×D3)⋊C4—32no—
106C2×(C2×D3)⋊C4—32no—
107C2×(C2×D3)⋊C4—34no—
108C2×(C2×D3)⋊C4—34no—
109C2×(C2×D3)⋊C4—64no—
110C2×(C2×D3)⋊C4C2×D314yes—
111C2×C4⋊Dic3—31no—
112C2×C4⋊Dic3—31no—
113C2×C4⋊Dic3—61no—
114C2×C4⋊Dic3C2×D311yescharacteristic
115C2×C4×Dic3C2×D311yescharacteristic
116C2×C4×Dic3C2×D311yescharacteristic
117#893—64no—
118#874—38no—
119C4×D12—64no—
120C4×D12—64no—
121C3×#95—32no—
122C3×#95—32no—
123C3⋊#95—34no—
124C3⋊#95—34no—
125C3⋊#95C2×D312yes—
126C3⋊#95C2×D312yes—
127C23×C32C2411yescharacteristic
128C22×C3⋊D3—22no—
129C22×C3⋊D3—22no—
130C22×C3⋊D3—24no—
131C22×C3⋊D3—24no—
132C22×C3⋊D3C22×C414yes—
133C22×C3×D3—22no—
134C22×C3×D3—22no—
135C22×C3×D3—24no—
136C22×C3×D3—24no—
137C22×C3×D3C22×C414yes—
138C2×C32×C4—22no—
139C2×C32×C4—22no—
140C2×C32×C4—22no—
141C2×C32×C4C22×C412yes—
142C2×C32×C4C2×D412yes—
143C2×C32×C4#4112yes—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—24no—
146C4⋊(C3⋊D3)—28no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—24no—
153C2×C3×Dic3C22×C414yes—
154C2×C3×Dic3C2×D412yes—
155C2×C3×Dic3C2×D412yes—
156C3×D12—28no—
157#626—416no—
158#624—48no—
159D3×Dic3—48no—
160C2×#127—91no—
161C2×C4×D4—91no—
162C2×C4×D4—91no—
163#390—31no—
164#390—91no—
165#386—94no—
166#386—94no—
167#382—91no—
168#376—31no—
169C24×C3—32no—
170C23×D3—32no—
171C23×D3—32no—
172C23×D3—62no—
173C23×D3C22×D312yes—
174C2×C3×D4—34no—
175C2×C3×D4—62no—
176C2×C3×D4—62no—
177C22×C3×C4—21no—
178C22×C3×C4—22no—
179C22×C3×C4—32no—
180C22×C3×C4—31no—
181C22×C3×C4—31no—
182C22×C3×C4—32no—
183C22×C3×C4C22×D312yes—
184C22×C3×C4C22×D312yes—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C2×#67—316no—
188C2×#67—124no—
189C2×#67—124no—
190C22×Dic3—32no—
191C22×Dic3—32no—
192C22×Dic3—62no—
193C22×Dic3—64no—
194C22×Dic3—124no—
195C22×Dic3C22×D312yes—
196C22×Dic3C22×D312yes—
197C22×Dic3C22×D311yescharacteristic
198C22×Dic3C22×D311yescharacteristic
199C2×D12—22no—
200C2×D12—22no—
201C2×D12—34no—
202C2×D12—34no—
203C2×D12—316no—
204C2×D12—64no—
205C2×D12—62no—
206C2×D12—62no—
207C2×D12—62no—
208C2×D12—62no—
209C2×D12—122no—
210C2×D12—122no—
211C2×D12—124no—
212C2×D12—124no—
213C2×D12C4×D314yescomplemented
214C2×C4×D3—64no—
215C2×C4×D3—64no—
216C2×C4×D3—64no—
217C2×C4×D3—124no—
218C2×C4×D3—124no—
219C2×C4×D3—124no—
220C3×C4⋊C4—62no—
221C3×C22⋊C4—124no—
222C3×C42—22no—
223C3×C42—22no—
224C3×C42—34no—
225C3×C42—34no—
226C3×C42—42no—
227#217—64no—
228(C2×D3)⋊C4—44no—
229(C2×D3)⋊C4—64no—
230(C2×D3)⋊C4—64no—
231(C2×D3)⋊C4—64no—
232(C2×D3)⋊C4—124no—
233(C2×D3)⋊C4—124no—
234(C2×D3)⋊C4—128no—
235C4⋊Dic3—22no—
236C4⋊Dic3—62no—
237C4⋊Dic3—62no—
238C4⋊Dic3—122no—
239C4×Dic3C4×D314yescomplemented
240C4×Dic3D1214yescomplemented
241C22×C32C23×C411yescharacteristic
242C22×C32C22×D411yescharacteristic
243C22×C32C2×#4111yescharacteristic
244C22×C32H(5,𝔽2)12yes—
245C22×C32H(5,𝔽2)12yes—
246C2×C3⋊D3—24no—
247C2×C3⋊D3—28no—
248C2×C3⋊D3—42no—
249C2×C3⋊D3—42no—
250C2×C3⋊D3—44no—
251C2×C3×D3—24no—
252C2×C3×D3—28no—
253C2×C3×D3—42no—
254C2×C3×D3—42no—
255C2×C3×D3—44no—
256C32×C4—42no—
257C32×C4C4×D414yes—
258C3⋊Dic3—42no—
259C3×Dic3—24no—
260C3×Dic3—22no—
261C3×Dic3—22no—
262C3×Dic3—42no—
263C22×D4—31no—
264C22×D4—94no—
265C22×D4—91no—
266C23×C4—92no—
267C23×C4—92no—
268#127—98no—
269C4×D4—184no—
270C4×D4—184no—
271C2×C4⋊C4—31no—
272C2×C4⋊C4—91no—
273C2×C22⋊C4—34no—
274C2×C22⋊C4—92no—
275C2×C22⋊C4—92no—
276C2×C22⋊C4—94no—
277C2×C42—31no—
278C2×C42—31no—
279C2×C42D3211yescharacteristic
280#95—32no—
281#95—32no—
282#95—94no—
283C23×C3—21no—
284C23×C3—34no—
285C23×C3—62no—
286C23×C3—62no—
287C23×C3—64no—
288C23×C3—64no—
289C23×C3C23×D311yescharacteristic
290C23×C3C23×D311yescharacteristic
291C22×D3—22no—
292C22×D3—22no—
293C22×D3—24no—
294C22×D3—24no—
295C22×D3—34no—
296C22×D3—34no—
297C22×D3—64no—
298C22×D3—62no—
299C22×D3—62no—
300C22×D3—62no—
301C22×D3—62no—
302C22×D3—64no—
303C22×D3—64no—
304C22×D3—64no—
305C22×D3—64no—
306C22×D3—124no—
307C22×D3—122no—
308C22×D3—122no—
309C22×D3—124no—
310C22×D3C2×C4×D314yes—
311C3×D4—68no—
312C2×C3×C4—24no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—34no—
323C2×C3×C4—32no—
324C2×C3×C4—32no—
325C2×C3×C4—42no—
326C2×C3×C4—42no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—64no—
333C2×C3×C4C2×C4×D312yes—
334C2×C3×C4C2×C4×D312yes—
335C2×C3×C4C2×D1212yes—
336C2×C3×C4#23512yes—
337C2×C3×C4D3×D412yes—
338C2×C3×C4#23712yes—
339#67—1216no—
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—24no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—64no—
349C2×Dic3—64no—
350C2×Dic3—122no—
351C2×Dic3—124no—
352C2×Dic3—128no—
353C2×Dic3C2×C4×D314yes—
354C2×Dic3C2×D1212yes—
355C2×Dic3C2×D1212yes—
356D12—28no—
357D12—68no—
358D12—68no—
359D12—128no—
360D12—1216no—
361C4×D3—128no—
362C4×D3—128no—
363C4×D3—128no—
364C2×C32C2×C4×D411yescharacteristic
365C2×C32#51812yes—
366C2×C32#53511yescharacteristic
367C2×C32#53511yescharacteristic
368C2×C32#54012yes—
369C3⋊D3—44no—
370C3×D3—44no—
371C24—32no—
372C24—92no—
373C2×D4—34no—
374C2×D4—62no—
375C2×D4—62no—
376C2×D4—916no—
377C2×D4—94no—
378C2×D4—182no—
379C2×D4—182no—
380C2×D4—364no—
381C2×D4—364no—
382C22×C4—32no—
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—32no—
386C22×C4—92no—
387C22×C4—184no—
388C22×C4—184no—
389C22×C4—364no—
390C22×C4—364no—
391C22×C4C2×D3212yes—
392C22×C4C2×D3211yescharacteristic
393C4⋊C4—62no—
394C4⋊C4—182no—
395C22⋊C4—124no—
396C22⋊C4—184no—
397C22⋊C4—184no—
398C22⋊C4—364no—
399C42—22no—
400C42—34no—
401C42—34no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—22no—
405C22×C3—22no—
406C22×C3—21no—
407C22×C3—64no—
408C22×C3—68no—
409C22×C3—122no—
410C22×C3—122no—
411C22×C3—124no—
412C22×C3C22×C4×D311yescharacteristic
413C22×C3C22×C4×D311yescharacteristic
414C22×C3C22×D1211yescharacteristic
415C22×C3C2×#23511yescharacteristic
416C22×C3C2×D3×D411yescharacteristic
417C22×C3C2×#23711yescharacteristic
418C22×C3#100412yes—
419C22×C3#100912yes—
420C22×C3#100912yes—
421C22×C3#100912yes—
422C2×D3—24no—
423C2×D3—28no—
424C2×D3—42no—
425C2×D3—42no—
426C2×D3—44no—
427C2×D3—64no—
428C2×D3—64no—
429C2×D3—68no—
430C2×D3—68no—
431C2×D3—124no—
432C2×D3—128no—
433C2×D3—122no—
434C2×D3—122no—
435C2×D3—122no—
436C2×D3—122no—
437C2×D3—124no—
438C2×D3—124no—
439C2×D3—244no—
440C2×D3—242no—
441C2×D3—242no—
442C3×C4—24no—
443C3×C4—44no—
444C3×C4—42no—
445C3×C4—42no—
446C3×C4—62no—
447C3×C4—62no—
448C3×C4—64no—
449C3×C4—122no—
450C3×C4C4×D1214yes—
451C3×C4#67⋊C414yes—
452Dic3—24no—
453Dic3—22no—
454Dic3—22no—
455Dic3—42no—
456Dic3—122no—
457Dic3—122no—
458Dic3—242no—
459C32#232811yescharacteristic, complemented, Sylow
460C23—34no—
461C23—62no—
462C23—64no—
463C23—64no—
464C23—62no—
465C23—94no—
466C23—182no—
467C23—184no—
468C23—184no—
469C23—182no—
470C23C22×D3211yescharacteristic
471D4—68no—
472D4—188no—
473D4—3616no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—34no—
478C2×C4—32no—
479C2×C4—32no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—64no—
486C2×C4—182no—
487C2×C4—184no—
488C2×C4—368no—
489C2×C4—368no—
490C2×C4C4×D3212yes—
491C2×C4D3×D1212yes—
492C2×C4#380412yes—
493C2×C3—21no—
494C2×C3—22no—
495C2×C3—22no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—124no—
499C2×C3C2×C4×D1211yescharacteristic
500C2×C3C2×#67⋊C411yescharacteristic
501C2×C3#552112yes—
502C2×C3#552511yescharacteristic
503C2×C3#552511yescharacteristic
504C2×C3#553512yes—
505C2×C3#554512yes—
506C2×C3#561912yes—
507C2×C3#567411yescharacteristic
508C2×C3#571511yescharacteristic
509D3—44no—
510D3—124no—
511D3—124no—
512D3—244no—
513C22—64no—
514C22—68no—
515C22—124no—
516C22—122no—
517C22—122no—
518C22—184no—
519C22—188no—
520C22—364no—
521C22—362no—
522C22—362no—
523C22C2×C4×D3211yescharacteristic
524C22C2×D3×D1211yescharacteristic
525C22#6430712yes—
526C22#6430812yes—
527C22C2×#380411yescharacteristic
528C4—42no—
529C4—64no—
530C4—62no—
531C4—62no—
532C4—122no—
533C4—362no—
534C4#6388014yes—
535C3—21no—
536C3#7338911yescharacteristic, complemented
537C3#7629811yescharacteristic, complemented
538C2—124no—
539C2—364no—
540C2#1059399412yes—
541C2#1059400011yescharacteristic
542C2#1059400111yescharacteristic
543C2C2×#6388011yescharacteristic
544C2#1059498512yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC2×#63911C2
hypercenterC2×C42D32
hypocenterC32#2328
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×#63894C2semidirect
3. C2×Dic3×D12C2semidirect
4. #10592638C2semidirect
5. C3×#4939C2semidirect
6. C3×#4932C2semidirect
7. #10591364C2semidirect
8. #10591275C2semidirect
9. #10591224C2semidirect
26. #63911C4semidirect
46. #4939D3semidirect
48. #4932D3semidirect
58. C2×C4⋊(C3⋊D3)C2×C4semidirect
65. C2×C3×D12C2×C4semidirect
68. C2×#626C2×C4semidirect
78. C3×C4×Dic3C2×C4semidirect
79. C3×C4×Dic3D4semidirect
213. C2×D12C4×D3semidirect
239. C4×Dic3C4×D3semidirect
240. C4×Dic3D12semidirect
459. C32#2328semidirect
536. C3#73389semidirect
537. C3#76298semidirect

Maximal subgroups

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

subgroupindex
C2×#639112
C2×#638942
C2×Dic3×D122
#105926382
C3×#49392
C3×#49322
#105913642
#105912752
#105912242
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