Finite Group Databasebeta

← #11789681

Subgroups — #11789681

Order 1152.

529 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#10592696C211yesmaximal, characteristic, complemented
2C3×#5001C211yesmaximal, characteristic
3C3×#4995C211yesmaximal, characteristic, complemented
4C2×#63562C211yesmaximal, characteristic
5C2×#63558C211yesmaximal, characteristic
6#10589167C211yesmaximal, characteristic, complemented
7#10589165C211yesmaximal, characteristic, complemented
8#70673—31nomaximal
9#70318—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63630—21no—
18C4×C3⋊(C3⋊C8)—21no—
19C3×#809—21no—
20C3×#809—21no—
21C3×#808—21no—
22C3×#807—21no—
23#63562—21no—
24#63562—21no—
25#63558C414yescomplemented
26C3×#428—31no—
27C3×#418—31no—
28C2×#833—31no—
29C2×#832—31no—
30C2×#823—31no—
31#5001D311yescharacteristic
32#4997—31no—
33#4997—31no—
34#4997—61no—
35#4995D311yescharacteristic, complemented
36C2×#809—31no—
37#4558—31no—
38#4558—31no—
39#4554—31no—
40#4530—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—
54#3748—21no—
55#3748C2×C412yes—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)D411yescharacteristic
60C2×C3⋊(C3⋊C8)D411yescharacteristic
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×#208—21no—
64C3×#208—21no—
65C3×#208—21no—
66C3×#208C2×C412yes—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69#1931—91noSylow
70C22×C3×D4—31no—
71C22×D12C2×D311yescharacteristic
72C2×C3×M16—31no—
73C2×C3×M16—31no—
74C3×#117—21no—
75C3×#117C2×D311yescharacteristic
76C3×#117C2×D311yescharacteristic
77C2×C3×C4⋊C4—31no—
78C2×C4⋊Dic3C2×D311yescharacteristic
79C2×#208—31no—
80C2×#208—31no—
81C2×#208—61no—
82C2×#208C2×D311yescharacteristic
83C2×#208C2×D311yescharacteristic
84C22×C3⋊C8—31no—
85C22×C3⋊C8—31no—
86C22×C3⋊C8—61no—
87C3×#107—61no—
88C3×#106—61no—
89C3×#102—61no—
90C3×#102—61no—
91#833—34no—
92#832—61no—
93#832—61no—
94#823—34no—
95#809—21no—
96#809—21no—
97#809—61no—
98#809—61no—
99#808—21no—
100#807—21no—
101#803—61no—
102#803—61no—
103#803—62no—
104C4×C3⋊C8—61no—
105C4×C3⋊C8—61no—
106C4×C3⋊C8—62no—
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)—21no—
129C3⋊(C3⋊C8)—21no—
130C3×C3⋊C8—22no—
131C3×C3⋊C8—41no—
132#428—31no—
133#418—31no—
134C2×#102—91no—
135C2×#100—91no—
136#405—91no—
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×C4—61no—
149C22×C3×C4C22×D311yescharacteristic
150C22×C3×C4C22×D311yescharacteristic
151C22×Dic3—21no—
152C2×D12—21no—
153C2×D12—21no—
154C2×D12—21no—
155C2×D12—21no—
156C2×D12—21no—
157C2×D12C4×D312yes—
158C3×M16—32no—
159C3×M16—61no—
160C3×M16—61no—
161C3×M16—61no—
162C2×C3×C8—61no—
163C2×C3×C8—61no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—61no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4#6711yescharacteristic
169C3×C4⋊C4#6711yescharacteristic
170C3×C4⋊C4#6711yescharacteristic
171C3×C4⋊C4#6711yescharacteristic
172C3×C22⋊C4—22no—
173C3×C22⋊C4—21no—
174C3×C22⋊C4—21no—
175C3×C42—22no—
176C3×C42—21no—
177C3×C42—21no—
178C4⋊Dic3—21no—
179C4⋊Dic3—21no—
180#208—21no—
181#208—21no—
182#208—21no—
183#208—32no—
184#208—32no—
185#208—62no—
186#208—62no—
187#208—61no—
188#208—61no—
189#208C4×D312yes—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8—31no—
193C2×C3⋊C8—31no—
194C2×C3⋊C8—31no—
195C2×C3⋊C8—31no—
196C2×C3⋊C8—61no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—62no—
199C2×C3⋊C8—62no—
200C2×C3⋊C8—62no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—61no—
207C22×C32—21no—
208C22×C32—21no—
209C22×C32#11711yescharacteristic
210C22×C32#12111yescharacteristic
211C22×C32#12611yescharacteristic
212C2×C3×D3—42no—
213C2×C3×D3—82no—
214C2×C3×D3—81no—
215C2×C3×D3—81no—
216C2×C3×D3—82no—
217C32×C4—41no—
218C32×C4—41no—
219C32×C4C4×D411yescharacteristic
220C32×C4C4×D411yescharacteristic
221C32×C4#12311yescharacteristic
222C32×C4#12411yescharacteristic
223C3×Dic3—81no—
224C22×D4—31no—
225C2×M16—31no—
226C2×M16—31no—
227C2×M16—91no—
228C22×C8—91no—
229#117D3211yescharacteristic
230C2×C4⋊C4—31no—
231#107—61no—
232#106—61no—
233#102—61no—
234#102—61no—
235#102—181no—
236#102—181no—
237#100—94no—
238#97—181no—
239C4×C8—181no—
240C23×C3—21no—
241C23×C3—62no—
242C23×C3—121no—
243C23×C3—121no—
244C23×C3—241no—
245C23×C3—241no—
246C23×C3#23711yescharacteristic
247C23×C3#23711yescharacteristic
248C22×D3—22no—
249C22×D3—41no—
250C22×D3—41no—
251C22×D3—81no—
252C22×D3—81no—
253C3×D4—62no—
254C3×D4—62no—
255C3×D4—121no—
256C3×D4—121no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
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—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—121no—
270C2×C3×C4—241no—
271C2×C3×C4C2×C4×D311yescharacteristic
272C2×C3×C4C2×C4×D311yescharacteristic
273C2×C3×C4#23511yescharacteristic
274C2×C3×C4#23511yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4#23711yescharacteristic
278C2×C3×C4#23711yescharacteristic
279C2×C3×C4#23911yescharacteristic
280C2×C3×C4#23911yescharacteristic
281C2×C3×C4C2×#6711yescharacteristic
282C2×C3×C4C2×#6711yescharacteristic
283C2×Dic3—41no—
284C2×Dic3—81no—
285D12—22no—
286D12—22no—
287D12—41no—
288D12—41no—
289C3×C8—62no—
290C3×C8—121no—
291C3⋊C8—22no—
292C3⋊C8—41no—
293C3⋊C8—62no—
294C3⋊C8—62no—
295C3⋊C8—64no—
296C3⋊C8—62no—
297C3⋊C8—61no—
298C3⋊C8—61no—
299C3⋊C8—62no—
300C3⋊C8—61no—
301C3⋊C8—61no—
302C2×C32—21no—
303C2×C32—21no—
304C2×C32#38811yescharacteristic
305C2×C32#47111yescharacteristic
306C2×C32#47211yescharacteristic
307C3×D3—82no—
308C24—61no—
309C2×D4—32no—
310C2×D4—61no—
311C2×D4—61no—
312C2×D4—61no—
313C2×D4—61no—
314C2×D4—61no—
315C22×C4—61no—
316C22×C4C2×D3211yescharacteristic
317M16—32no—
318M16—61no—
319M16—61no—
320M16—61no—
321M16—92no—
322M16—181no—
323C2×C8—61no—
324C2×C8—61no—
325C2×C8—91no—
326C2×C8—91no—
327C2×C8—181no—
328C2×C8—181no—
329C2×C8—181no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C4⋊C4#62511yescharacteristic
333C4⋊C4#62511yescharacteristic
334C22⋊C4—21no—
335C42—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—122no—
346C22×C3—242no—
347C22×C3—242no—
348C22×C3—241no—
349C22×C3—241no—
350C22×C3#87711yescharacteristic
351C22×C3#87911yescharacteristic
352C22×C3#89211yescharacteristic
353C22×C3#89811yescharacteristic
354C22×C3#93911yescharacteristic
355C22×C3#93911yescharacteristic
356C2×D3—42no—
357C2×D3—82no—
358C2×D3—81no—
359C2×D3—81no—
360C2×D3—82no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—42no—
366C3×C4—42no—
367C3×C4—41no—
368C3×C4—41no—
369C3×C4—41no—
370C3×C4—41no—
371C3×C4—241no—
372C3×C4#67⋊C411yescharacteristic
373C3×C4#88311yescharacteristic
374C3×C4#89311yescharacteristic
375C3×C4#89411yescharacteristic
376C3×C4C4×#6711yescharacteristic
377C3×C4C4×#6711yescharacteristic
378C3×C4#93611yescharacteristic
379C3×C4#94711yescharacteristic
380Dic3—81no—
381C32#193111yescharacteristic, complemented, Sylow
382C23—62no—
383C23—121no—
384C23—121no—
385C23—241no—
386C23—241no—
387C23#380511yescharacteristic
388D4—62no—
389D4—62no—
390D4—121no—
391D4—121no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—121no—
395C2×C4—241no—
396C2×C4#379611yescharacteristic
397C2×C4#379611yescharacteristic
398C2×C4#379811yescharacteristic
399C2×C4C4×D3211yescharacteristic
400C2×C4C2×#62511yescharacteristic
401C2×C4#381111yescharacteristic
402C8—62no—
403C8—121no—
404C8—181no—
405C8—181no—
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#494511yescharacteristic
418C2×C3#499011yescharacteristic
419C2×C3#519911yescharacteristic
420C2×C3#519911yescharacteristic
421C2×C3#520011yescharacteristic
422C2×C3#520311yescharacteristic
423D3—82no—
424C22—21no—
425C22—21no—
426C22—122no—
427C22—242no—
428C22—242no—
429C22—241no—
430C22—241no—
431C22#6386211yescharacteristic
432C22#6387811yescharacteristic
433C22#6398011yescharacteristic
434C4—41no—
435C4—41no—
436C4—241no—
437C4#6385311yescharacteristic
438C4#6386311yescharacteristic
439C4#6388111yescharacteristic
440C4C4×#62511yescharacteristic
441C3—21no—
442C3#7031811yescharacteristic, complemented
443C3#7067311yescharacteristic, complemented
444C2—21no—
445C2—21no—
446C2—242no—
447C2#1059128311yescharacteristic
448C2#1059167811yescharacteristic
449C2#1059168111yescharacteristic
subgroupG/H
centerC22#63980
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. #10592696C2semidirect
3. C3×#4995C2semidirect
6. #10589167C2semidirect
7. #10589165C2semidirect
25. #63558C4semidirect
35. #4995D3semidirect
381. C32#1931semidirect
442. C3#70318semidirect
443. C3#70673semidirect

Maximal subgroups

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

subgroupindex
#105926962
C3×#50012
C3×#49952
C2×#635622
C2×#635582
#105891672
#105891652
#706733
#703183