Finite Group Databasebeta

← #11795409

Subgroups — #11795409

Order 1152.

607 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#4939C211yesmaximal, characteristic
2C3×#4936C211yesmaximal, characteristic, complemented
3C2×#63576C211yesmaximal, characteristic, complemented
4C2×#63574C211yesmaximal, characteristic, complemented
5C2×#63562C211yesmaximal, characteristic
6C2×#63562C211yesmaximal, characteristic
7#10589390C211yesmaximal, characteristic, complemented
8#69654—31nomaximal
9#69558—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—22no—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C3×C3⋊#95—22no—
19#63576—22no—
20#63574—22no—
21#63562—22no—
22#63562—22no—
23C3×#390—31no—
24C3×#382—31no—
25C2×#832—31no—
26C2×#832—31no—
27C2×#809—31no—
28C2×#809—31no—
29C2×#808—31no—
30C2×#808—31no—
31C2×#807—31no—
32C2×#807—31no—
33#4939D311yescharacteristic
34#4936D311yescharacteristic, complemented
35#4524—31no—
36#4524—31no—
37#4524—61no—
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—
52C2×C3⋊(C3⋊C8)—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)D412yes—
57C2×C3⋊(C3⋊C8)D412yes—
58C3×(C2×D3)⋊C4—44no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65#2092—91noSylow
66C22×C3×D4—31no—
67C22×D12C2×D311yescharacteristic
68C2×C3×C4⋊C4—31no—
69C2×C3×C4⋊C4—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⋊Dic3C2×D311yescharacteristic
77C2×C4⋊Dic3C2×D311yescharacteristic
78C2×C4⋊Dic3C2×D311yescharacteristic
79C22×C3⋊C8—31no—
80C22×C3⋊C8—31no—
81C22×C3⋊C8—31no—
82C22×C3⋊C8—31no—
83C22×C3⋊C8—61no—
84C22×C3⋊C8—61no—
85C3×#95—62no—
86#832—62no—
87#832—62no—
88C3⋊#95—22no—
89#809—62no—
90#809—62no—
91#808—62no—
92#808—62no—
93#807—62no—
94#807—62no—
95C23×C32C2×D411yescharacteristic
96C22×C3×D3—22no—
97C22×C3×D3—41no—
98C22×C3×D3—41no—
99C22×C3×D3—42no—
100C22×C3×D3—42no—
101C2×C32×C4—22no—
102C2×C32×C4—22no—
103C2×C32×C4—22no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×Q811yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C3×Dic3—41no—
111C2×C3×Dic3—41no—
112C2×C3×Dic3—41no—
113C2×C3×Dic3—42no—
114C2×C3×Dic3—42no—
115C2×C3×Dic3—42no—
116C3×D12—22no—
117C3×D12—22no—
118C3×D12—41no—
119C3×D12—41no—
120C3⋊(C3⋊C8)—22no—
121C3⋊(C3⋊C8)—22no—
122C2×#107—91no—
123C2×#106—91no—
124C2×#102—91no—
125C2×#102—91no—
126#390—31no—
127#382—31no—
128#336—91no—
129C24×C3—61no—
130C23×D3—21no—
131C2×C3×D4—32no—
132C2×C3×D4—61no—
133C2×C3×D4—61no—
134C2×C3×D4—61no—
135C2×C3×D4—61no—
136C2×C3×D4—61no—
137C22×C3×C4—22no—
138C22×C3×C4—21no—
139C22×C3×C4—61no—
140C22×C3×C4—61no—
141C22×C3×C4—61no—
142C22×C3×C4#6712yes—
143C22×C3×C4#6712yes—
144C22×C3×C4C22×D311yescharacteristic
145C22×C3×C4C22×D311yescharacteristic
146C22×Dic3—21no—
147C22×Dic3—21no—
148C22×Dic3—21no—
149C2×D12—21no—
150C2×D12—21no—
151C2×D12—21no—
152C2×D12—21no—
153C2×D12—21no—
154C2×D12Dic612yes—
155C3×C4⋊C4—61no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4—61no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4—61no—
161C3×C22⋊C4—124no—
162C3×C42—21no—
163C3×C42—21no—
164C3×C42—21no—
165C3×C42—21no—
166C3×C42—41no—
167C3×C42—41no—
168(C2×D3)⋊C4—44no—
169C4⋊Dic3—21no—
170C4⋊Dic3—21no—
171C4⋊Dic3—21no—
172C4⋊Dic3—21no—
173C4⋊Dic3—21no—
174C4⋊Dic3—21no—
175C2×C3⋊C8—32no—
176C2×C3⋊C8—32no—
177C2×C3⋊C8—32no—
178C2×C3⋊C8—32no—
179C2×C3⋊C8—62no—
180C2×C3⋊C8—62no—
181C2×C3⋊C8—61no—
182C2×C3⋊C8—61no—
183C2×C3⋊C8—61no—
184C2×C3⋊C8—61no—
185C2×C3⋊C8—61no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—61no—
189C2×C3⋊C8—121no—
190C2×C3⋊C8—121no—
191C2×C3⋊C8—121no—
192C2×C3⋊C8—121no—
193C22×C32C22⋊Q811yescharacteristic
194C22×C32#12311yescharacteristic
195C22×C32#12711yescharacteristic
196C22×C32#13512yes—
197C22×C32AGL(1,ℤ/8)12yes—
198C2×C3×D3—42no—
199C2×C3×D3—44no—
200C2×C3×D3—82no—
201C2×C3×D3—81no—
202C2×C3×D3—81no—
203C32×C4—42no—
204C32×C4C22⋊Q811yescharacteristic
205C32×C4C22⋊Q811yescharacteristic
206C32×C4#12311yescharacteristic
207C32×C4#12311yescharacteristic
208C3×Dic3—81no—
209C3×Dic3—81no—
210C3×Dic3—81no—
211C22×D4—31no—
212C22×C8—91no—
213C22×C8—91no—
214C2×C4⋊C4—31no—
215C2×C4⋊C4—31no—
216C2×C4⋊C4—31no—
217C2×C22⋊C4—62no—
218C2×C42D3211yescharacteristic
219#107—182no—
220#106—182no—
221#102—182no—
222#102—182no—
223#95—62no—
224C23×C3—21no—
225C23×C3—62no—
226C23×C3—121no—
227C23×C3—121no—
228C23×C3—122no—
229C23×C3—122no—
230C23×C3C2×#6711yescharacteristic
231C23×C3C2×#6711yescharacteristic
232C22×D3—22no—
233C22×D3—42no—
234C22×D3—41no—
235C22×D3—41no—
236C22×D3—42no—
237C3×D4—62no—
238C3×D4—62no—
239C3×D4—121no—
240C3×D4—121no—
241C2×C3×C4—24no—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—42no—
255C2×C3×C4—42no—
256C2×C3×C4—122no—
257C2×C3×C4—121no—
258C2×C3×C4—121no—
259C2×C3×C4—121no—
260C2×C3×C4—122no—
261C2×C3×C4—122no—
262C2×C3×C4C2×Dic611yescharacteristic
263C2×C3×C4#23511yescharacteristic
264C2×C3×C4#23511yescharacteristic
265C2×C3×C4#23511yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4#23711yescharacteristic
271C2×C3×C4#23711yescharacteristic
272C2×C3×C4D3×Q811yescharacteristic
273C2×C3×C4#23911yescharacteristic
274C2×Dic3—42no—
275C2×Dic3—41no—
276C2×Dic3—41no—
277C2×Dic3—41no—
278C2×Dic3—42no—
279C2×Dic3—42no—
280D12—22no—
281D12—22no—
282D12—41no—
283D12—41no—
284C3⋊C8—62no—
285C3⋊C8—62no—
286C3⋊C8—62no—
287C3⋊C8—62no—
288C3⋊C8—122no—
289C3⋊C8—122no—
290C2×C32#39911yescharacteristic
291C2×C32#47812yes—
292C2×C32#48212yes—
293C2×C32#49511yescharacteristic
294C2×C32#49611yescharacteristic
295C3×D3—82no—
296C24—61no—
297C2×D4—32no—
298C2×D4—61no—
299C2×D4—61no—
300C2×D4—61no—
301C2×D4—61no—
302C2×D4—61no—
303C22×C4—61no—
304C22×C4—61no—
305C22×C4—61no—
306C22×C4#62512yes—
307C22×C4C2×D3211yescharacteristic
308C2×C8—92no—
309C2×C8—92no—
310C2×C8—181no—
311C2×C8—181no—
312C2×C8—181no—
313C2×C8—181no—
314C4⋊C4—61no—
315C4⋊C4—61no—
316C4⋊C4—61no—
317C4⋊C4—61no—
318C4⋊C4—61no—
319C4⋊C4—61no—
320C22⋊C4—124no—
321C42—21no—
322C42—21no—
323C22×C3—22no—
324C22×C3—22no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—122no—
329C22×C3—124no—
330C22×C3—242no—
331C22×C3—241no—
332C22×C3—241no—
333C22×C3#92411yescharacteristic
334C22×C3#92911yescharacteristic
335C22×C3#93212yes—
336C22×C3#93511yescharacteristic
337C22×C3#94011yescharacteristic
338C22×C3#94011yescharacteristic
339C22×C3#94611yescharacteristic
340C22×C3#94912yes—
341C22×C3#95012yes—
342C22×C3#95012yes—
343C2×D3—42no—
344C2×D3—44no—
345C2×D3—82no—
346C2×D3—81no—
347C2×D3—81no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—44no—
353C3×C4—42no—
354C3×C4—42no—
355C3×C4—241no—
356C3×C4—241no—
357C3×C4—241no—
358C3×C4#87811yescharacteristic
359C3×C4#87811yescharacteristic
360C3×C4#88311yescharacteristic
361C3×C4#88311yescharacteristic
362C3×C4#89411yescharacteristic
363C3×C4#89411yescharacteristic
364C3×C4#89611yescharacteristic
365C3×C4#89611yescharacteristic
366Dic3—81no—
367Dic3—81no—
368Dic3—81no—
369C32#209211yescharacteristic, complemented, Sylow
370C23—62no—
371C23—122no—
372C23—122no—
373C23—121no—
374C23—121no—
375C23C2×#62511yescharacteristic
376D4—62no—
377D4—62no—
378D4—121no—
379D4—121no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—122no—
384C2×C4—122no—
385C2×C4—122no—
386C2×C4—121no—
387C2×C4—121no—
388C2×C4—121no—
389C2×C4D3×Dic611yescharacteristic
390C2×C4#379911yescharacteristic
391C2×C4#380211yescharacteristic
392C2×C4#380211yescharacteristic
393C2×C4#380411yescharacteristic
394C2×C4#380411yescharacteristic
395C8—182no—
396C8—182no—
397C2×C3—22no—
398C2×C3—21no—
399C2×C3—22no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—242no—
403C2×C3#494911yescharacteristic
404C2×C3#499311yescharacteristic
405C2×C3#500312yes—
406C2×C3#500912yes—
407C2×C3#503512yes—
408C2×C3#505811yescharacteristic
409C2×C3#505911yescharacteristic
410C2×C3#505911yescharacteristic
411C2×C3#506612yes—
412C2×C3#507411yescharacteristic
413D3—82no—
414C22—124no—
415C22—122no—
416C22—242no—
417C22—241no—
418C22—241no—
419C22#6382212yes—
420C22#6382312yes—
421C22#6385611yescharacteristic
422C22#6391411yescharacteristic
423C22#6396111yescharacteristic
424C4—42no—
425C4—241no—
426C4—241no—
427C4—241no—
428C4#6385411yescharacteristic
429C4#6385411yescharacteristic
430C4#6389911yescharacteristic
431C4#6389911yescharacteristic
432C3—21no—
433C3#6955811yescharacteristic, complemented
434C3#6965411yescharacteristic, complemented
435C2—242no—
436C2#1059027012yes—
437C2#1059035311yescharacteristic
438C2#1059035411yescharacteristic
439C2#1059109012yes—
440C2#1059132411yescharacteristic
subgroupG/H
centerC23C2×#625
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
2. C3×#4936C2semidirect
3. C2×#63576C2semidirect
4. C2×#63574C2semidirect
7. #10589390C2semidirect
34. #4936D3semidirect
369. C32#2092semidirect
433. C3#69558semidirect
434. C3#69654semidirect

Maximal subgroups

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

subgroupindex
C3×#49392
C3×#49362
C2×#635762
C2×#635742
C2×#635622
#105893902
#696543
#695583