Finite Group Databasebeta

← #11787876

Subgroups — #11787876

Order 1152.

1057 conjugacy classes of subgroups.

The subgroup lattice has 521 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595992C211yesmaximal, characteristic, complemented
2C2×#63911C211yesmaximal, characteristic
3C3×#5001C211yesmaximal, characteristic, complemented
4#10591086C211yesmaximal, characteristic, complemented
5C2×#63559C211yesmaximal, characteristic, complemented
6C3×#4532C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#70323—31nomaximal
9#68760—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×#626—22no—
13C32×#117C2211yescharacteristic
14#64135C2211yescharacteristic
15#64102—22no—
16C22⋊C4×C3⋊D3—22no—
17C4×C4⋊(C3⋊D3)—22no—
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21#63911—22no—
22#63911C414yescomplemented
23C3×#809—22no—
24#63563—22no—
25#63559—22no—
26C2×#940—31no—
27#5521—31no—
28#5521—31no—
29#5521—61no—
30C2×#874—31no—
31C3×#418—31no—
32#5215—31no—
33#5131—31no—
34C2×#823—31no—
35C2×#823—31no—
36#5001D311yescharacteristic, complemented
37C3×#339—31no—
38#4555—31no—
39#4532D311yescharacteristic, complemented
40#4523—31no—
41C23×C3⋊D3D412yes—
42C23×C3×D3—21no—
43C22×C32×C4C2311yescharacteristic
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)C2×C412yes—
49C2×C4⋊(C3⋊D3)D412yes—
50C2×C4×C3⋊D3—24no—
51C22×C3×Dic3—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12C2×C412yescomplemented
58C2×#626—28no—
59C2×#626—48no—
60C32×C4⋊C4D412yescomplemented
61C32×C22⋊C4—21no—
62C32×C42—21no—
63#3757—21no—
64#3752—24no—
65C4⋊(C3⋊Dic3)D412yescomplemented
66C4×C3⋊Dic3—21no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3C2×C412yescomplemented
69C3×#208—21no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75#1887—91noSylow
76C22×C3×D4—31no—
77C22×#67—62no—
78C22×D12—31no—
79C22×D12—31no—
80C22×D12—61no—
81C22×D12—62no—
82C22×D12C2×D311yescharacteristic
83C2×C3×M16—31no—
84C2×C3×M16—31no—
85C3×#117—21no—
86C3×#117C2×D311yescharacteristic
87C3×#117C2×D311yescharacteristic
88C2×C3×C42—31no—
89#940—34no—
90#940—62no—
91#926—31no—
92#926—31no—
93#926—61no—
94C2×C4×Dic3C2×D311yescharacteristic
95C2×#208C2×D311yescharacteristic
96C2×#208C2×D311yescharacteristic
97#893—64no—
98#893—62no—
99#893—62no—
100D3×C22⋊C4—62no—
101D3×C22⋊C4—62no—
102D3×C22⋊C4—64no—
103#874—34no—
104#874—62no—
105C4×D12—62no—
106C4×D12—62no—
107C4×D12—64no—
108C3×#102—62no—
109#832—62no—
110#823—62no—
111#823—62no—
112#821—62no—
113#809—22no—
114C23×C32C2×D411yescharacteristic
115C22×C3⋊D3—22no—
116C22×C3⋊D3—22no—
117C22×C3⋊D3—44no—
118C22×C3⋊D3C22⋊C414yes—
119C22×C3×D3—22no—
120C22×C3×D3—44no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C2×C32×C4—22no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C3⋊Dic3—22no—
131C4⋊(C3⋊D3)—22no—
132C4⋊(C3⋊D3)—22no—
133C4⋊(C3⋊D3)—22no—
134C4⋊(C3⋊D3)—22no—
135C4×C3⋊D3—84no—
136C2×C3×Dic3—24no—
137C2×C3×Dic3—22no—
138C3×D12—22no—
139C3×D12—22no—
140C3×D12—41no—
141C3×D12—41no—
142#626—416no—
143C3×C3⋊C8—41no—
144C3×C3⋊C8—41no—
145C2×#127—91no—
146#518—91no—
147#418—31no—
148#418—91no—
149C2×#100—91no—
150#339—31no—
151#339—91no—
152C24×C3—61no—
153C23×D3—21no—
154C23×D3—32no—
155C23×D3—32no—
156C23×D3—62no—
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—61no—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C2×#67—68no—
168C2×#67—128no—
169C22×Dic3—21no—
170C2×D12—21no—
171C2×D12—21no—
172C2×D12—21no—
173C2×D12—21no—
174C2×D12—21no—
175C2×D12—32no—
176C2×D12—32no—
177C2×D12—32no—
178C2×D12—32no—
179C2×D12—62no—
180C2×D12—62no—
181C2×D12—62no—
182C2×D12—62no—
183C2×D12—62no—
184C2×D12—62no—
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—68no—
194C2×D12—128no—
195C2×D12C4×D312yescomplemented
196C2×C4×D3—68no—
197C2×C4×D3—64no—
198C2×C4×D3—64no—
199C3×M16—61no—
200C3×M16—61no—
201C3×M16—61no—
202C3×M16—61no—
203C2×C3×C8—61no—
204C2×C3×C8—61no—
205C3×C4⋊C4—22no—
206C3×C4⋊C4D1212yescomplemented
207C3×C4⋊C4#6712yescomplemented
208C3×C22⋊C4—22no—
209C3×C22⋊C4—21no—
210C3×C22⋊C4—21no—
211C3×C42—22no—
212C3×C42—21no—
213C3×C42—21no—
214C3×C42—32no—
215C3×C42—61no—
216#217—62no—
217#217—61no—
218#217—61no—
219(C2×D3)⋊C4—68no—
220(C2×D3)⋊C4—64no—
221(C2×D3)⋊C4—64no—
222C4⋊Dic3—32no—
223C4⋊Dic3—32no—
224C4⋊Dic3—62no—
225C4×Dic3—21no—
226C4×Dic3—62no—
227C4×Dic3—61no—
228C4×Dic3—61no—
229C4×Dic3C4×D312yescomplemented
230#208—21no—
231#208—21no—
232#208—21no—
233#208—21no—
234C2×C3⋊C8—21no—
235C2×C3⋊C8—21no—
236C22×C32—22no—
237C22×C32C2×C22⋊C411yescharacteristic
238C22×C32#12011yescharacteristic
239C22×C32#12311yescharacteristic
240C2×C3⋊D3—24no—
241C2×C3⋊D3—44no—
242C2×C3⋊D3—44no—
243C2×C3⋊D3—82no—
244C2×C3×D3—44no—
245C2×C3×D3—42no—
246C2×C3×D3—82no—
247C2×C3×D3—82no—
248C32×C4—42no—
249C32×C4C4×D411yescharacteristic
250C32×C4C4×D411yescharacteristic
251C32×C4#12111yescharacteristic
252C32×C4#12111yescharacteristic
253C3⋊Dic3—42no—
254C3×Dic3—24no—
255C22×D4—31no—
256C22×D4—91no—
257C22×D4—182no—
258C2×M16—31no—
259C2×M16—31no—
260#127—94no—
261#127—182no—
262C4×D4—182no—
263C4×D4—182no—
264#117—91no—
265#117D3211yescharacteristic
266C2×C22⋊C4—182no—
267C2×C42—31no—
268#102—62no—
269#102—182no—
270#100—182no—
271C23×C3—21no—
272C23×C3—62no—
273C23×C3—124no—
274C23×C3—121no—
275C23×C3—121no—
276C23×C3D3×D411yescharacteristic
277C23×C3D3×D411yescharacteristic
278C22×D3—22no—
279C22×D3—34no—
280C22×D3—34no—
281C22×D3—44no—
282C22×D3—41no—
283C22×D3—41no—
284C22×D3—64no—
285C22×D3—64no—
286C22×D3—62no—
287C22×D3—62no—
288C22×D3—64no—
289C22×D3—62no—
290C22×D3—62no—
291C22×D3—124no—
292C22×D3—124no—
293C22×D3—244no—
294C3×D4—62no—
295C3×D4—62no—
296C3×D4—121no—
297C3×D4—121no—
298C2×C3×C4—24no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—64no—
308C2×C3×C4—62no—
309C2×C3×C4C2×C4×D311yescharacteristic
310C2×C3×C4C2×C4×D311yescharacteristic
311C2×C3×C4C2×D1211yescharacteristic
312C2×C3×C4#23511yescharacteristic
313C2×C3×C4#23511yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4D3×D411yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4#23711yescharacteristic
319C2×C3×C4#23911yescharacteristic
320C2×C3×C4C2×#6711yescharacteristic
321#67—1216no—
322C2×Dic3—24no—
323C2×Dic3—22no—
324C2×Dic3—64no—
325C2×Dic3—62no—
326C2×Dic3—62no—
327D12—22no—
328D12—22no—
329D12—41no—
330D12—41no—
331D12—64no—
332D12—64no—
333D12—64no—
334D12—64no—
335D12—62no—
336D12—62no—
337D12—62no—
338D12—62no—
339D12—62no—
340D12—62no—
341D12—62no—
342D12—62no—
343D12—1216no—
344C4×D3—248no—
345C4×D3—244no—
346C4×D3—244no—
347C3×C8—121no—
348C3×C8—121no—
349C3⋊C8—41no—
350C3⋊C8—41no—
351C2×C32—21no—
352C2×C32—21no—
353C2×C32#38611yescharacteristic
354C2×C32#45312yes—
355C3⋊D3—44no—
356C3×D3—82no—
357C24—61no—
358C24—92no—
359C2×D4—32no—
360C2×D4—61no—
361C2×D4—61no—
362C2×D4—61no—
363C2×D4—61no—
364C2×D4—61no—
365C2×D4—92no—
366C2×D4—92no—
367C2×D4—188no—
368C2×D4—181no—
369C2×D4—181no—
370C2×D4—181no—
371C2×D4—181no—
372C2×D4—368no—
373C22×C4—61no—
374C22×C4—184no—
375C22×C4C2×D3211yescharacteristic
376M16—61no—
377M16—61no—
378M16—61no—
379M16—61no—
380C2×C8—61no—
381C2×C8—61no—
382C4⋊C4—92no—
383C4⋊C4#62612yescomplemented
384C22⋊C4—21no—
385C22⋊C4—184no—
386C22⋊C4—181no—
387C42—21no—
388C42—32no—
389C42—61no—
390C42—181no—
391C22×C3—22no—
392C22×C3—22no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—42no—
397C22×C3—124no—
398C22×C3—122no—
399C22×C3—242no—
400C22×C3—242no—
401C22×C3D3×C22⋊C411yescharacteristic
402C22×C3D3×C22⋊C411yescharacteristic
403C22×C3#88211yescharacteristic
404C22×C3#88311yescharacteristic
405C22×C3#89411yescharacteristic
406C22×C3#93711yescharacteristic
407C2×D3—44no—
408C2×D3—42no—
409C2×D3—68no—
410C2×D3—64no—
411C2×D3—64no—
412C2×D3—82no—
413C2×D3—82no—
414C2×D3—128no—
415C2×D3—124no—
416C2×D3—124no—
417C2×D3—124no—
418C2×D3—124no—
419C2×D3—244no—
420C2×D3—242no—
421C2×D3—242no—
422C2×D3—244no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—44no—
428C3×C4—42no—
429C3×C4—42no—
430C3×C4—64no—
431C3×C4C4×D1211yescharacteristic
432C3×C4#67⋊C411yescharacteristic
433C3×C4#88411yescharacteristic
434C3×C4#88411yescharacteristic
435C3×C4#89311yescharacteristic
436C3×C4#89511yescharacteristic
437C3×C4C4×#6711yescharacteristic
438C3×C4#93811yescharacteristic
439Dic3—24no—
440Dic3—124no—
441Dic3—122no—
442Dic3—122no—
443C32#188711yescharacteristic, complemented, Sylow
444C23—62no—
445C23—94no—
446C23—124no—
447C23—121no—
448C23—121no—
449C23—182no—
450C23—182no—
451C23—364no—
452C23#381111yescharacteristic
453D4—62no—
454D4—62no—
455D4—121no—
456D4—121no—
457D4—182no—
458D4—182no—
459D4—182no—
460D4—182no—
461D4—3616no—
462C2×C4—22no—
463C2×C4—64no—
464C2×C4—62no—
465C2×C4—182no—
466C2×C4—724no—
467C2×C4#379611yescharacteristic
468C2×C4#379811yescharacteristic
469C2×C4C4×D3211yescharacteristic
470C2×C4#380211yescharacteristic
471C2×C4C2×#62611yescharacteristic
472C2×C4#381111yescharacteristic
473C8—121no—
474C8—121no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—22no—
481C2×C3—41no—
482C2×C3—41no—
483C2×C3—242no—
484C2×C3#466511yescharacteristic
485C2×C3#482212yes—
486C2×C3#495611yescharacteristic
487C2×C3#519812yes—
488D3—82no—
489D3—128no—
490D3—124no—
491D3—124no—
492C22—22no—
493C22—124no—
494C22—122no—
495C22—184no—
496C22—242no—
497C22—242no—
498C22—364no—
499C22—364no—
500C22—722no—
501C22#6385311yescharacteristic
502C22#6392111yescharacteristic
503C22#6398111yescharacteristic
504C4—42no—
505C4—64no—
506C4—362no—
507C4#6388111yescharacteristic
508C4C4×#62611yescharacteristic
509C4#6391211yescharacteristic
510C4#6391611yescharacteristic
511C3—21no—
512C3#6876011yescharacteristic, complemented
513C3#7032311yescharacteristic, complemented
514C2—21no—
515C2—21no—
516C2—242no—
517C2—364no—
518C2#1059138711yescharacteristic
519C2#1059166712yes—
subgroupG/H
centerC22#63981
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32#120
prime radicalC2×#63911C2
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1887
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595992C2semidirect
3. C3×#5001C2semidirect
4. #10591086C2semidirect
5. C2×#63559C2semidirect
6. C3×#4532C2semidirect
7. #10589162C2semidirect
22. #63911C4semidirect
36. #5001D3semidirect
39. #4532D3semidirect
57. C2×C3×D12C2×C4semidirect
60. C32×C4⋊C4D4semidirect
65. C4⋊(C3⋊Dic3)D4semidirect
68. C3×C4×Dic3C2×C4semidirect
195. C2×D12C4×D3semidirect
206. C3×C4⋊C4D12semidirect
207. C3×C4⋊C4#67semidirect
229. C4×Dic3C4×D3semidirect
383. C4⋊C4#626semidirect
443. C32#1887semidirect
512. C3#68760semidirect
513. C3#70323semidirect

Maximal subgroups

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

subgroupindex
#105959922
C2×#639112
C3×#50012
#105910862
C2×#635592
C3×#45322
#105891622
#703233
#687603