Finite Group Databasebeta

← #11795411

Subgroups — #11795411

Order 1152.

625 conjugacy classes of subgroups.

The subgroup lattice has 447 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592635C211yesmaximal, characteristic, complemented
2C3×#4939C211yesmaximal, characteristic
3C2×#63575C211yesmaximal, characteristic, complemented
4C2×#63573C211yesmaximal, characteristic, complemented
5C2×#63563C211yesmaximal, characteristic
6C2×#63563C211yesmaximal, characteristic
7C3×#4524C211yesmaximal, characteristic, complemented
8#69654—31nomaximal
9#68680—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—22no—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18#63658—22no—
19#63575—22no—
20#63573—22no—
21#63563—22no—
22#63563—22no—
23C3×#390—31no—
24C2×#832—31no—
25C2×#832—31no—
26C2×#821—31no—
27C2×#821—31no—
28C2×#818—31no—
29C2×#817—31no—
30C2×#808—31no—
31C2×#807—31no—
32#4939D311yescharacteristic
33#4936—31no—
34#4936—31no—
35#4936—61no—
36C3×#336—31no—
37#4524D311yescharacteristic, complemented
38C23×C3×D3—21no—
39C22×C32×C4D412yes—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3—21no—
42C22×C3⋊Dic3—21no—
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×D12Q812yes—
50C32×C42—21no—
51C32×C42—21no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56C3×(C2×D3)⋊C4—44no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C2×C3×C3⋊C8—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8D412yes—
64C2×C3×C3⋊C8D412yes—
65#2092—91noSylow
66C22×C3×D4—31no—
67C22×D12C2×D311yescharacteristic
68C22×C3×C8—31no—
69C22×C3×C8—31no—
70C2×C3×C4⋊C4—31no—
71C2×C3×C22⋊C4—62no—
72C2×C3×C42—21no—
73C2×C3×C42C2×D311yescharacteristic
74C2×C3×C42C2×D311yescharacteristic
75C2×(C2×D3)⋊C4—22no—
76C2×C4⋊Dic3—31no—
77C2×C4⋊Dic3—31no—
78C2×C4⋊Dic3—31no—
79C2×C4⋊Dic3—31no—
80C2×C4⋊Dic3—61no—
81C2×C4⋊Dic3—61no—
82C2×C4⋊Dic3C2×D311yescharacteristic
83C22×C3⋊C8C2×D311yescharacteristic
84C22×C3⋊C8C2×D311yescharacteristic
85#832—62no—
86#832—62no—
87C3⋊#95—64no—
88C3⋊#95—62no—
89C3⋊#95—62no—
90#821—62no—
91#821—62no—
92#818—62no—
93#817—62no—
94#808—62no—
95#807—62no—
96C23×C32C2×D411yescharacteristic
97C22×C3×D3—22no—
98C22×C3×D3—41no—
99C22×C3×D3—41no—
100C22×C3×D3—42no—
101C22×C3×D3—42no—
102C2×C32×C4—22no—
103C2×C32×C4—22no—
104C2×C32×C4—22no—
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×Q811yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C2×C3⋊Dic3—41no—
112C2×C3⋊Dic3—41no—
113C2×C3⋊Dic3—42no—
114C2×C3⋊Dic3—42no—
115C2×C3×Dic3—41no—
116C2×C3×Dic3—42no—
117C3×D12—22no—
118C3×D12—22no—
119C3×D12—41no—
120C3×D12—41no—
121C3×C3⋊C8—22no—
122C3×C3⋊C8—22no—
123C2×#107—91no—
124C2×#106—91no—
125C2×#102—91no—
126C2×#102—91no—
127#390—31no—
128#382—91no—
129#336—31no—
130C24×C3—61no—
131C23×D3—21no—
132C2×C3×D4—32no—
133C2×C3×D4—61no—
134C2×C3×D4—61no—
135C2×C3×D4—61no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C22×C3×C4—22no—
139C22×C3×C4—21no—
140C22×C3×C4—61no—
141C22×C3×C4D1212yes—
142C22×C3×C4#6712yes—
143C22×C3×C4C22×D311yescharacteristic
144C22×C3×C4C22×D311yescharacteristic
145C22×Dic3—21no—
146C22×Dic3—62no—
147C22×Dic3—62no—
148C22×Dic3—61no—
149C22×Dic3—61no—
150C22×Dic3—61no—
151C22×Dic3—61no—
152C2×D12—21no—
153C2×D12—21no—
154C2×D12—21no—
155C2×D12—21no—
156C2×D12—21no—
157C2×D12Dic612yes—
158C2×C3×C8—32no—
159C2×C3×C8—32no—
160C2×C3×C8—61no—
161C2×C3×C8—61no—
162C2×C3×C8—61no—
163C2×C3×C8—61no—
164C3×C4⋊C4—61no—
165C3×C4⋊C4—61no—
166C3×C22⋊C4—124no—
167C3×C42—22no—
168C3×C42—22no—
169C3×C42—21no—
170C3×C42—21no—
171C3×C42—21no—
172C3×C42—21no—
173(C2×D3)⋊C4—44no—
174C4⋊Dic3—21no—
175C4⋊Dic3—21no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178C4⋊Dic3—61no—
179C4⋊Dic3—61no—
180C4⋊Dic3—61no—
181C4⋊Dic3—61no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4⋊Dic3—121no—
185C4⋊Dic3—121no—
186C4⋊Dic3—121no—
187C4⋊Dic3—121no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—21no—
192C2×C3⋊C8D1212yes—
193C2×C3⋊C8D1212yes—
194C22×C32C22⋊Q811yescharacteristic
195C22×C32#12311yescharacteristic
196C22×C32#12711yescharacteristic
197C22×C32#13512yes—
198C22×C32AGL(1,ℤ/8)12yes—
199C2×C3×D3—42no—
200C2×C3×D3—44no—
201C2×C3×D3—82no—
202C2×C3×D3—81no—
203C2×C3×D3—81no—
204C32×C4—42no—
205C32×C4C22⋊Q811yescharacteristic
206C32×C4C22⋊Q811yescharacteristic
207C32×C4#12311yescharacteristic
208C32×C4#12311yescharacteristic
209C3⋊Dic3—81no—
210C3⋊Dic3—81no—
211C3×Dic3—81no—
212C22×D4—31no—
213C22×C8—31no—
214C22×C8—31no—
215C2×C4⋊C4—31no—
216C2×C4⋊C4—91no—
217C2×C4⋊C4—91no—
218C2×C22⋊C4—62no—
219C2×C42D3211yescharacteristic
220#107—182no—
221#106—182no—
222#102—182no—
223#102—182no—
224#95—182no—
225C23×C3—21no—
226C23×C3—62no—
227C23×C3—121no—
228C23×C3—121no—
229C23×C3—122no—
230C23×C3—122no—
231C23×C3C2×D1211yescharacteristic
232C23×C3C2×#6711yescharacteristic
233C22×D3—22no—
234C22×D3—42no—
235C22×D3—41no—
236C22×D3—41no—
237C22×D3—42no—
238C3×D4—62no—
239C3×D4—62no—
240C3×D4—121no—
241C3×D4—121no—
242C2×C3×C4—24no—
243C2×C3×C4—22no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—42no—
256C2×C3×C4—42no—
257C2×C3×C4—121no—
258C2×C3×C4—122no—
259C2×C3×C4C2×Dic611yescharacteristic
260C2×C3×C4C2×D1211yescharacteristic
261C2×C3×C4C2×D1211yescharacteristic
262C2×C3×C4#23511yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4#23711yescharacteristic
266C2×C3×C4#23711yescharacteristic
267C2×C3×C4#23711yescharacteristic
268C2×C3×C4#23711yescharacteristic
269C2×C3×C4#23711yescharacteristic
270C2×C3×C4D3×Q811yescharacteristic
271C2×Dic3—42no—
272C2×Dic3—41no—
273C2×Dic3—122no—
274C2×Dic3—122no—
275C2×Dic3—124no—
276C2×Dic3—124no—
277C2×Dic3—121no—
278C2×Dic3—121no—
279C2×Dic3—122no—
280C2×Dic3—122no—
281C2×Dic3—122no—
282C2×Dic3—121no—
283C2×Dic3—121no—
284C2×Dic3—122no—
285D12—22no—
286D12—22no—
287D12—41no—
288D12—41no—
289C3×C8—62no—
290C3×C8—62no—
291C3⋊C8—22no—
292C3⋊C8—22no—
293C2×C32#39911yescharacteristic
294C2×C32#47812yes—
295C2×C32#48212yes—
296C2×C32#49511yescharacteristic
297C2×C32#49611yescharacteristic
298C3×D3—82no—
299C24—61no—
300C2×D4—32no—
301C2×D4—61no—
302C2×D4—61no—
303C2×D4—61no—
304C2×D4—61no—
305C2×D4—61no—
306C22×C4—61no—
307C22×C4—181no—
308C22×C4—181no—
309C22×C4#62612yes—
310C22×C4C2×D3211yescharacteristic
311C2×C8—32no—
312C2×C8—32no—
313C2×C8—61no—
314C2×C8—61no—
315C2×C8—61no—
316C2×C8—61no—
317C4⋊C4—61no—
318C4⋊C4—61no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4—181no—
323C22⋊C4—124no—
324C42—21no—
325C42—21no—
326C22×C3—22no—
327C22×C3—22no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—122no—
332C22×C3—124no—
333C22×C3—241no—
334C22×C3—241no—
335C22×C3—242no—
336C22×C3#87411yescharacteristic
337C22×C3#88611yescharacteristic
338C22×C3#89711yescharacteristic
339C22×C3#90412yes—
340C22×C3#90812yes—
341C22×C3#92411yescharacteristic
342C22×C3#93212yes—
343C22×C3#93511yescharacteristic
344C22×C3#94011yescharacteristic
345C22×C3#95012yes—
346C2×D3—42no—
347C2×D3—44no—
348C2×D3—82no—
349C2×D3—81no—
350C2×D3—81no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—44no—
356C3×C4—42no—
357C3×C4—42no—
358C3×C4—241no—
359C3×C4#87811yescharacteristic
360C3×C4#87811yescharacteristic
361C3×C4#88311yescharacteristic
362C3×C4#88311yescharacteristic
363C3×C4#88611yescharacteristic
364C3×C4#88611yescharacteristic
365C3×C4#89711yescharacteristic
366C3×C4#89711yescharacteristic
367Dic3—81no—
368Dic3—242no—
369Dic3—242no—
370Dic3—241no—
371Dic3—241no—
372Dic3—241no—
373Dic3—241no—
374C32#209211yescharacteristic, complemented, Sylow
375C23—62no—
376C23—122no—
377C23—122no—
378C23—121no—
379C23—121no—
380C23C2×#62611yescharacteristic
381D4—62no—
382D4—62no—
383D4—121no—
384D4—121no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—122no—
389C2×C4—121no—
390C2×C4—362no—
391C2×C4—362no—
392C2×C4—361no—
393C2×C4—361no—
394C2×C4D3×Dic611yescharacteristic
395C2×C4#379511yescharacteristic
396C2×C4D3×D1211yescharacteristic
397C2×C4D3×D1211yescharacteristic
398C2×C4#380511yescharacteristic
399C2×C4#380511yescharacteristic
400C8—62no—
401C8—62no—
402C2×C3—22no—
403C2×C3—21no—
404C2×C3—22no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—242no—
408C2×C3#467711yescharacteristic
409C2×C3#469611yescharacteristic
410C2×C3#471211yescharacteristic
411C2×C3#473712yes—
412C2×C3#484712yes—
413C2×C3#494911yescharacteristic
414C2×C3#500912yes—
415C2×C3#503512yes—
416C2×C3#505911yescharacteristic
417C2×C3#507411yescharacteristic
418D3—82no—
419C22—124no—
420C22—122no—
421C22—242no—
422C22—241no—
423C22—241no—
424C22#6382912yes—
425C22#6383012yes—
426C22#6385711yescharacteristic
427C22#6391111yescharacteristic
428C22#6396211yescharacteristic
429C4—42no—
430C4—241no—
431C4—721no—
432C4—721no—
433C4#6389111yescharacteristic
434C4#6389111yescharacteristic
435C4#6389311yescharacteristic
436C4#6389311yescharacteristic
437C3—21no—
438C3#6868011yescharacteristic, complemented
439C3#6965411yescharacteristic, complemented
440C2—242no—
441C2#1059027112yes—
442C2#1059037011yescharacteristic
443C2#1059037111yescharacteristic
444C2#1059109312yes—
445C2#1059131711yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32#2092
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10592635C2semidirect
3. C2×#63575C2semidirect
4. C2×#63573C2semidirect
7. C3×#4524C2semidirect
37. #4524D3semidirect
374. C32#2092semidirect
438. C3#68680semidirect
439. C3#69654semidirect

Maximal subgroups

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

subgroupindex
#105926352
C3×#49392
C2×#635752
C2×#635732
C2×#635632
C3×#45242
#696543
#686803