Finite Group Databasebeta

← #11789680

Subgroups — #11789680

Order 1152.

523 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592694C211yesmaximal, characteristic, complemented
2C3×#5001C211yesmaximal, characteristic
3C3×#4997C211yesmaximal, characteristic, complemented
4C2×#63563C211yesmaximal, characteristic
5C2×#63558C211yesmaximal, characteristic
6#10589168C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#70318—31nomaximal
9#69892—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63635—21no—
18#63634—21no—
19C3×#809—21no—
20C3×#809—21no—
21C3×#803—21no—
22C3×C4×C3⋊C8—21no—
23#63563—21no—
24#63563—21no—
25#63558C414yescomplemented
26C3×#418—31no—
27C3×#405—31no—
28C2×#833—31no—
29C2×#832—31no—
30C2×#823—31no—
31C2×#821—31no—
32#5001D311yescharacteristic
33#4997D311yescharacteristic, complemented
34#4995—31no—
35#4995—31no—
36#4995—61no—
37#4558—31no—
38#4554—31no—
39#4554—31no—
40#4552—31no—
41C23×C3×D3—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12C2×C412yes—
50C32×C4⋊C4D411yescharacteristic
51C32×C4⋊C4D411yescharacteristic
52C32×C22⋊C4—21no—
53C32×C42—21no—
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56#3748—21no—
57#3748C2×C412yes—
58C2×C3⋊(C3⋊C8)—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C3×#208C2×C412yes—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8D411yescharacteristic
68C2×C3×C3⋊C8D411yescharacteristic
69#1931—91noSylow
70C22×C3×D4—31no—
71C22×D12C2×D311yescharacteristic
72C2×C3×M16—31no—
73C2×C3×M16—31no—
74C22×C3×C8—31no—
75C3×#117—21no—
76C3×#117C2×D311yescharacteristic
77C3×#117C2×D311yescharacteristic
78C2×C4⋊Dic3—31no—
79C2×C4⋊Dic3—31no—
80C2×C4⋊Dic3—61no—
81C2×#208—31no—
82C2×#208—31no—
83C2×#208—61no—
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86C22×C3⋊C8C2×D311yescharacteristic
87C3×#102—61no—
88C3×#102—61no—
89C3×#97—61no—
90C3×C4×C8—61no—
91#833—34no—
92#832—61no—
93#832—61no—
94#823—34no—
95#821—61no—
96#821—61no—
97#809—21no—
98#809—21no—
99#808—62no—
100#808—61no—
101#808—61no—
102#807—62no—
103#807—61no—
104#807—61no—
105#803—21no—
106C4×C3⋊C8—21no—
107C23×C32#4111yescharacteristic
108C22×C3×D3—22no—
109C22×C3×D3—41no—
110C22×C3×D3—41no—
111C22×C3×D3—81no—
112C22×C3×D3—81no—
113C2×C32×C4—21no—
114C2×C32×C4—21no—
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C3⋊Dic3—41no—
122C2×C3⋊Dic3—81no—
123C3×D12—22no—
124C3×D12—22no—
125C3×D12—41no—
126C3×D12—41no—
127C3⋊(C3⋊C8)—22no—
128C3×C3⋊C8—22no—
129C3×C3⋊C8—21no—
130C3×C3⋊C8—21no—
131C3×C3⋊C8—41no—
132#428—91no—
133#418—31no—
134C2×#102—91no—
135C2×#100—91no—
136#405—31no—
137#343—91no—
138#341—91no—
139C24×C3—61no—
140C23×D3—21no—
141C2×C3×D4—32no—
142C2×C3×D4—61no—
143C2×C3×D4—61no—
144C2×C3×D4—61no—
145C2×C3×D4—61no—
146C2×C3×D4—61no—
147C22×C3×C4—21no—
148C22×C3×C4C22×D311yescharacteristic
149C22×C3×C4C22×D311yescharacteristic
150C22×Dic3—61no—
151C22×Dic3—61no—
152C22×Dic3—121no—
153C2×D12—21no—
154C2×D12—21no—
155C2×D12—21no—
156C2×D12—21no—
157C2×D12—21no—
158C2×D12C4×D312yes—
159C3×M16—32no—
160C3×M16—61no—
161C3×M16—61no—
162C3×M16—61no—
163C2×C3×C8—31no—
164C2×C3×C8—31no—
165C2×C3×C8—61no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C2×C3×C8—61no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4D1211yescharacteristic
172C3×C4⋊C4D1211yescharacteristic
173C3×C4⋊C4#6711yescharacteristic
174C3×C4⋊C4#6711yescharacteristic
175C3×C22⋊C4—21no—
176C3×C22⋊C4—21no—
177C3×C22⋊C4—41no—
178C3×C42—21no—
179C3×C42—21no—
180C3×C42—41no—
181C4⋊Dic3—62no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4⋊Dic3—61no—
185C4⋊Dic3—61no—
186C4⋊Dic3—121no—
187#208—21no—
188#208—21no—
189#208—21no—
190#208—32no—
191#208—32no—
192#208—62no—
193#208—62no—
194#208—61no—
195#208—61no—
196#208C4×D312yes—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—62no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8#6711yescharacteristic
205C2×C3⋊C8#6711yescharacteristic
206C22×C32—21no—
207C22×C32—21no—
208C22×C32#11711yescharacteristic
209C22×C32#12111yescharacteristic
210C22×C32#12611yescharacteristic
211C2×C3×D3—42no—
212C2×C3×D3—82no—
213C2×C3×D3—81no—
214C2×C3×D3—81no—
215C2×C3×D3—82no—
216C32×C4—41no—
217C32×C4—41no—
218C32×C4C4×D411yescharacteristic
219C32×C4C4×D411yescharacteristic
220C32×C4#12311yescharacteristic
221C32×C4#12411yescharacteristic
222C3⋊Dic3—81no—
223C22×D4—31no—
224C2×M16—31no—
225C2×M16—31no—
226C2×M16—91no—
227C22×C8—31no—
228#117D3211yescharacteristic
229C2×C4⋊C4—91no—
230#107—181no—
231#106—181no—
232#102—61no—
233#102—61no—
234#102—181no—
235#102—181no—
236#100—94no—
237#97—61no—
238C4×C8—61no—
239C23×C3—21no—
240C23×C3—62no—
241C23×C3—121no—
242C23×C3—121no—
243C23×C3—241no—
244C23×C3—241no—
245C23×C3#23511yescharacteristic
246C23×C3#23711yescharacteristic
247C22×D3—22no—
248C22×D3—41no—
249C22×D3—41no—
250C22×D3—81no—
251C22×D3—81no—
252C3×D4—62no—
253C3×D4—62no—
254C3×D4—121no—
255C3×D4—121no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4C2×C4×D311yescharacteristic
269C2×C3×C4C2×C4×D311yescharacteristic
270C2×C3×C4C2×D1211yescharacteristic
271C2×C3×C4#23511yescharacteristic
272C2×C3×C4#23511yescharacteristic
273C2×C3×C4#23511yescharacteristic
274C2×C3×C4#23511yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4#23711yescharacteristic
277C2×C3×C4#23711yescharacteristic
278C2×C3×C4C2×#6711yescharacteristic
279C2×C3×C4C2×#6711yescharacteristic
280C2×Dic3—122no—
281C2×Dic3—121no—
282C2×Dic3—121no—
283C2×Dic3—242no—
284C2×Dic3—241no—
285C2×Dic3—241no—
286D12—22no—
287D12—22no—
288D12—41no—
289D12—41no—
290C3×C8—62no—
291C3×C8—61no—
292C3×C8—61no—
293C3×C8—121no—
294C3⋊C8—22no—
295C3⋊C8—21no—
296C3⋊C8—21no—
297C3⋊C8—41no—
298C3⋊C8—64no—
299C3⋊C8—62no—
300C3⋊C8—62no—
301C2×C32—21no—
302C2×C32—21no—
303C2×C32#38811yescharacteristic
304C2×C32#47111yescharacteristic
305C2×C32#47211yescharacteristic
306C3×D3—82no—
307C24—61no—
308C2×D4—32no—
309C2×D4—61no—
310C2×D4—61no—
311C2×D4—61no—
312C2×D4—61no—
313C2×D4—61no—
314C22×C4—181no—
315C22×C4C2×D3211yescharacteristic
316M16—32no—
317M16—61no—
318M16—61no—
319M16—61no—
320M16—92no—
321M16—181no—
322C2×C8—31no—
323C2×C8—31no—
324C2×C8—61no—
325C2×C8—61no—
326C2×C8—61no—
327C2×C8—61no—
328C2×C8—181no—
329C4⋊C4—181no—
330C4⋊C4—181no—
331C4⋊C4#62611yescharacteristic
332C4⋊C4#62611yescharacteristic
333C22⋊C4—21no—
334C42—21no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—41no—
343C22×C3—41no—
344C22×C3—122no—
345C22×C3—242no—
346C22×C3—242no—
347C22×C3—241no—
348C22×C3—241no—
349C22×C3#87211yescharacteristic
350C22×C3#87611yescharacteristic
351C22×C3#87711yescharacteristic
352C22×C3#87911yescharacteristic
353C22×C3#93011yescharacteristic
354C22×C3#93911yescharacteristic
355C2×D3—42no—
356C2×D3—82no—
357C2×D3—81no—
358C2×D3—81no—
359C2×D3—82no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—41no—
365C3×C4—41no—
366C3×C4—41no—
367C3×C4—41no—
368C3×C4—81no—
369C3×C4—81no—
370C3×C4C4×D1211yescharacteristic
371C3×C4#87511yescharacteristic
372C3×C4#67⋊C411yescharacteristic
373C3×C4#88311yescharacteristic
374C3×C4C4×#6711yescharacteristic
375C3×C4C4×#6711yescharacteristic
376C3×C4#92911yescharacteristic
377C3×C4#93611yescharacteristic
378Dic3—242no—
379Dic3—241no—
380Dic3—241no—
381C32#193111yescharacteristic, complemented, Sylow
382C23—62no—
383C23—121no—
384C23—121no—
385C23—241no—
386C23—241no—
387C23#380411yescharacteristic
388D4—62no—
389D4—62no—
390D4—121no—
391D4—121no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—361no—
395C2×C4—721no—
396C2×C4#379511yescharacteristic
397C2×C4#379511yescharacteristic
398C2×C4#379811yescharacteristic
399C2×C4C4×D3211yescharacteristic
400C2×C4C2×#62611yescharacteristic
401C2×C4D3×#6711yescharacteristic
402C8—62no—
403C8—61no—
404C8—61no—
405C8—121no—
406C8—182no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—41no—
415C2×C3—41no—
416C2×C3—242no—
417C2×C3#494011yescharacteristic
418C2×C3#494511yescharacteristic
419C2×C3#514111yescharacteristic
420C2×C3#514211yescharacteristic
421C2×C3#519911yescharacteristic
422C2×C3#520011yescharacteristic
423D3—82no—
424C22—21no—
425C22—21no—
426C22—122no—
427C22—242no—
428C22—242no—
429C22—241no—
430C22—241no—
431C22#6385911yescharacteristic
432C22#6387711yescharacteristic
433C22#6397811yescharacteristic
434C4—41no—
435C4—41no—
436C4—721no—
437C4#6386011yescharacteristic
438C4#6387911yescharacteristic
439C4C4×#62611yescharacteristic
440C4#6390511yescharacteristic
441C3—21no—
442C3#6989211yescharacteristic, complemented
443C3#7031811yescharacteristic, complemented
444C2—21no—
445C2—21no—
446C2—242no—
447C2#1059128011yescharacteristic
448C2#1059167711yescharacteristic
449C2#1059167911yescharacteristic
subgroupG/H
centerC22#63978
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32#121
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1931
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. #10592694C2semidirect
3. C3×#4997C2semidirect
6. #10589168C2semidirect
7. #10589166C2semidirect
25. #63558C4semidirect
33. #4997D3semidirect
381. C32#1931semidirect
442. C3#69892semidirect
443. C3#70318semidirect

Maximal subgroups

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

subgroupindex
#105926942
C3×#50012
C3×#49972
C2×#635632
C2×#635582
#105891682
#105891662
#703183
#698923