Finite Group Databasebeta

← #11774279

Subgroups — #11774279

Order 1152.

597 conjugacy classes of subgroups.

The subgroup lattice has 487 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3796C211yesmaximal, characteristic
2C3⋊D3×C4⋊C8C211yesmaximal, characteristic, complemented
3#10590297C211yesmaximal, characteristic, complemented
4C3×#4484C211yesmaximal, characteristic, complemented
5C3×#4483C211yesmaximal, characteristic, complemented
6#10589084C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#68230—31nomaximal
9#68166—31nomaximal
10C2×#3796C411yescharacteristic
11C2×C8×C3⋊D3—21no—
12C42×C3⋊D3C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15C4×#626—21no—
16#63898C411yescharacteristic
17#63881—21no—
18#63878—21no—
19C4×D3×Dic3—21no—
20#63849C411yescharacteristic
21#63843C411yescharacteristic
22C32×C4⋊C8C2211yescharacteristic
23#63641—21no—
24C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
25C3×C4×C3⋊C8C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27#63572—21no—
28#63557—21no—
29C4×#239—31no—
30C4×#237—31no—
31D3×C4⋊C8—31no—
32D3×C4⋊C8—31no—
33D3×C4⋊C8—61no—
34#4685—31no—
35#4685—31no—
36C3×Q8⋊C8—31no—
37C3×D4⋊C8—31no—
38#4535—31no—
39D4⋊(C3⋊C8)—31no—
40#4484D311yescharacteristic, complemented
41#4483D311yescharacteristic, complemented
42#4459—31no—
43#4456—31no—
44C2×C4×C3⋊D3C2×C411yescharacteristic
45C2×C4×C3⋊D3D411yescharacteristic
46C2×C4×C3⋊D3D411yescharacteristic
47C2×C3×D12C2×C411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×Dic6C2×C411yescharacteristic
50C2×#626—21no—
51C2×D3×Dic3—21no—
52C2×D3×Dic3—21no—
53#3796—22no—
54#3796C814yescomplemented
55C2×C32×C8—21no—
56C32×C42C2311yescharacteristic
57C4×C3⋊Dic3C2×C411yescharacteristic
58C4×C3⋊Dic3D411yescharacteristic
59C4×C3⋊Dic3D411yescharacteristic
60C2×C3⋊(C3⋊C8)—21no—
61C8×C3⋊D3—42no—
62C3×(C2×D3)⋊C4—21no—
63C3×C4⋊Dic3C2×C411yescharacteristic
64C3×C4⋊Dic3C2×C411yescharacteristic
65C3×Dic3⋊C4—21no—
66C3×C4×Dic3—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69Dic3⋊Dic3—21no—
70#3722—21no—
71(C2×D3)⋊Dic3—21no—
72Dic32—21no—
73Dic32—21no—
74#1477—91noSylow
75C2×#239—31no—
76C2×#237—31no—
77C3×C4×Q8—31no—
78C3×C4×D4—31no—
79Q8×Dic3—31no—
80D4×Dic3—31no—
81C4×#67—61no—
82C2×C4×Dic3—61no—
83C2×D3×C8—61no—
84C2×D3×C8—61no—
85C2×D3×C8—62no—
86#893—31no—
87#893—61no—
88#892—31no—
89#892—31no—
90#892—61no—
91#887—31no—
92#67⋊C4—61no—
93#877—61no—
94C4×D12—61no—
95C4×D12C2×D311yescharacteristic
96C42×D3—31no—
97C42×D3—31no—
98C42×D3—61no—
99C42×D3—61no—
100C4×Dic6C2×D311yescharacteristic
101C3×C4⋊C8—21no—
102C3×C4⋊C8C2×D311yescharacteristic
103C3×C4⋊C8C2×D311yescharacteristic
104C3×C4×C8—31no—
105C3×C4×C8—31no—
106(C2×D3)⋊C8—61no—
107(C2×D3)⋊C8—61no—
108Dic3⋊C8—61no—
109Dic3⋊C8—61no—
110Dic3⋊C8—61no—
111Dic3⋊C8—61no—
112Dic3⋊C8—62no—
113C4⋊(C3⋊C8)—31no—
114C4⋊(C3⋊C8)—31no—
115C4⋊(C3⋊C8)—61no—
116C4×C3⋊C8C2×D311yescharacteristic
117C4×C3⋊C8C2×D311yescharacteristic
118C22×C3⋊D3C22⋊C411yescharacteristic
119C22×C3×D3—21no—
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C3⋊Dic3C22⋊C411yescharacteristic
124C2×C3⋊Dic3C22⋊C411yescharacteristic
125C2×C3⋊Dic3C22⋊C411yescharacteristic
126C4×C3⋊D3—21no—
127C4×C3⋊D3—21no—
128C4×C3⋊D3—41no—
129C4×C3⋊D3C2×C812yes—
130C4×C3⋊D3M1612yes—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C3×D12—21no—
135C3×D12C2×C812yescomplemented
136C3×C4×D3—41no—
137C3×C4×D3—41no—
138C3×Dic6—21no—
139C3×Dic6C2×C812yescomplemented
140#626—24no—
141D3×Dic3—24no—
142D3×Dic3—42no—
143C32×C8—41no—
144C3⋊(C3⋊C8)—41no—
145C3×C3⋊C8—41no—
146C3×C3⋊C8—41no—
147C4×#41—91no—
148#431—91no—
149C2×C4⋊C8—91no—
150Q8⋊C8—31no—
151Q8⋊C8—91no—
152D4⋊C8—31no—
153D4⋊C8—91no—
154C2×C3×Q8—31no—
155C2×C3×D4—31no—
156C22×C3×C4—61no—
157C2×#67—61no—
158C22×Dic3—61no—
159C22×Dic3—61no—
160#239—34no—
161#239—62no—
162#237—34no—
163#237—62no—
164C2×D12—61no—
165C2×D12C4×D311yescharacteristic
166C2×C4×D3—21no—
167C2×C4×D3—31no—
168C2×C4×D3—31no—
169C2×C4×D3—31no—
170C2×C4×D3—31no—
171C2×C4×D3—31no—
172C2×C4×D3—31no—
173C2×C4×D3—61no—
174C2×C4×D3—61no—
175C2×C4×D3—61no—
176C2×C4×D3—61no—
177C2×C4×D3—61no—
178C2×Dic6C4×D311yescharacteristic
179C2×C3×C8—22no—
180C2×C3×C8—21no—
181C2×C3×C8—21no—
182C2×C3×C8—61no—
183C2×C3×C8—61no—
184C3×C4⋊C4—31no—
185C3×C4⋊C4—31no—
186C3×C4⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C42—21no—
189C3×C42—61no—
190C3×C42C22×D311yescharacteristic
191C3×C42C22×D311yescharacteristic
192#217—61no—
193(C2×D3)⋊C4—21no—
194(C2×D3)⋊C4—61no—
195(C2×D3)⋊C4—61no—
196(C2×D3)⋊C4—61no—
197C4⋊Dic3—61no—
198C4⋊Dic3C4×D311yescharacteristic
199C4⋊Dic3C4×D311yescharacteristic
200Dic3⋊C4—21no—
201Dic3⋊C4—61no—
202C4×Dic3—21no—
203C4×Dic3—31no—
204C4×Dic3—31no—
205C4×Dic3—31no—
206C4×Dic3—31no—
207C4×Dic3—31no—
208C4×Dic3—31no—
209C4×Dic3—61no—
210C4×Dic3—61no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213C4×Dic3—61no—
214C4×Dic3—61no—
215C4×Dic3—61no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—62no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—61no—
221D3×C8—124no—
222D3×C8—122no—
223D3×C8—122no—
224C22×C32C2×C22⋊C411yescharacteristic
225C2×C3⋊D3—21no—
226C2×C3⋊D3—21no—
227C2×C3⋊D3C22⋊C812yes—
228C2×C3×D3—22no—
229C2×C3×D3—41no—
230C2×C3×D3—41no—
231C32×C4—21no—
232C32×C4C22×C811yescharacteristic
233C32×C4C2×M1611yescharacteristic
234C32×C4AGL(1,ℤ/8)11yescharacteristic
235C32×C4#13711yescharacteristic
236C3⋊Dic3—21no—
237C3⋊Dic3—21no—
238C3⋊Dic3C22⋊C812yes—
239C3×Dic3—22no—
240C3×Dic3—41no—
241C3×Dic3—41no—
242C2×#41—91no—
243C22×C8—181no—
244C4×Q8—31no—
245C4×Q8—91no—
246C4×D4—31no—
247C4×D4—91no—
248C4×D4—181no—
249C4×D4—181no—
250#117—91no—
251#117—181no—
252C2×C42—91no—
253C2×C42—181no—
254C4⋊C8—91no—
255C4⋊C8—181no—
256C4⋊C8—181no—
257C4⋊C8D3211yescharacteristic
258C22⋊C8—181no—
259C4×C8—31no—
260C4×C8—31no—
261C23×C3—61no—
262C22×D3—21no—
263C22×D3—31no—
264C22×D3—31no—
265C22×D3—61no—
266C3×Q8—32no—
267C3×Q8—61no—
268C3×D4—32no—
269C3×D4—61no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—61no—
274C2×C3×C4—61no—
275C2×C3×C4—61no—
276C2×C3×C4—121no—
277C2×C3×C4—121no—
278C2×C3×C4C2×C4×D311yescharacteristic
279C2×C3×C4C2×C4×D311yescharacteristic
280C2×C3×C4D3×D411yescharacteristic
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284#67—64no—
285C2×Dic3—21no—
286C2×Dic3—21no—
287C2×Dic3—21no—
288C2×Dic3—31no—
289C2×Dic3—31no—
290C2×Dic3—31no—
291C2×Dic3—31no—
292C2×Dic3—31no—
293C2×Dic3—31no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—61no—
297C2×Dic3—64no—
298C2×Dic3—122no—
299D12—21no—
300D12—64no—
301D12D3×C812yescomplemented
302C4×D3—32no—
303C4×D3—32no—
304C4×D3—32no—
305C4×D3—32no—
306C4×D3—41no—
307C4×D3—41no—
308C4×D3—62no—
309C4×D3—62no—
310C4×D3—64no—
311C4×D3—62no—
312C4×D3—62no—
313C4×D3—61no—
314C4×D3—61no—
315C4×D3—61no—
316C4×D3—61no—
317C4×D3—121no—
318C4×D3—121no—
319C4×D3—122no—
320C4×D3—122no—
321Dic6—21no—
322Dic6D3×C812yescomplemented
323C3×C8—42no—
324C3×C8—41no—
325C3×C8—41no—
326C3×C8—121no—
327C3×C8—121no—
328C3⋊C8—41no—
329C3⋊C8—41no—
330C3⋊C8—122no—
331C3⋊C8—121no—
332C3⋊C8—121no—
333C2×C32C2×C22⋊C811yescharacteristic
334C2×C32#41711yescharacteristic
335C2×C32#42111yescharacteristic
336C3⋊D3—22no—
337C3×D3—42no—
338#41—94no—
339#41—182no—
340C2×Q8—31no—
341C2×D4—31no—
342C2×D4—181no—
343C22×C4—61no—
344C22×C4—91no—
345C22×C4—91no—
346C22×C4—91no—
347C22×C4—181no—
348C22×C4—181no—
349C2×C8—21no—
350C2×C8—61no—
351C2×C8—61no—
352C2×C8—181no—
353C2×C8—362no—
354C4⋊C4—31no—
355C4⋊C4—31no—
356C4⋊C4—61no—
357C4⋊C4—181no—
358C22⋊C4—61no—
359C22⋊C4—181no—
360C22⋊C4—181no—
361C42—61no—
362C42—91no—
363C42—91no—
364C42—91no—
365C42—181no—
366C42—181no—
367C42C2×D3211yescharacteristic
368C22×C3—21no—
369C22×C3—62no—
370C22×C3—121no—
371C22×C3—121no—
372C22×C3D3×C22⋊C411yescharacteristic
373C22×C3D3×C22⋊C411yescharacteristic
374C2×D3—22no—
375C2×D3—32no—
376C2×D3—32no—
377C2×D3—41no—
378C2×D3—41no—
379C2×D3—62no—
380C2×D3—62no—
381C2×D3—62no—
382C2×D3—61no—
383C2×D3—61no—
384C2×D3—61no—
385C2×D3—61no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—41no—
393C3×C4—62no—
394C3×C4—121no—
395C3×C4—121no—
396C3×C4C2×D3×C811yescharacteristic
397C3×C4C2×D3×C811yescharacteristic
398C3×C4D3×M1611yescharacteristic
399C3×C4D3×M1611yescharacteristic
400C3×C4#91111yescharacteristic
401C3×C4#91411yescharacteristic
402C3×C4#91511yescharacteristic
403C3×C4#91811yescharacteristic
404Dic3—22no—
405Dic3—32no—
406Dic3—32no—
407Dic3—41no—
408Dic3—41no—
409Dic3—62no—
410Dic3—62no—
411Dic3—61no—
412Dic3—61no—
413Dic3—61no—
414Dic3—61no—
415Dic3—121no—
416C32#147711yescharacteristic, complemented, Sylow
417C23—61no—
418C23—91no—
419Q8—32no—
420Q8—61no—
421D4—32no—
422D4—61no—
423D4—184no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—61no—
427C2×C4—91no—
428C2×C4—92no—
429C2×C4—92no—
430C2×C4—91no—
431C2×C4—91no—
432C2×C4—121no—
433C2×C4—121no—
434C2×C4—184no—
435C2×C4—181no—
436C2×C4—181no—
437C2×C4—361no—
438C2×C4—362no—
439C2×C4C4×D3211yescharacteristic
440C2×C4#380211yescharacteristic
441C2×C4#381111yescharacteristic
442C8—41no—
443C8—121no—
444C8—121no—
445C8—361no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—122no—
450C2×C3D3×C22⋊C811yescharacteristic
451C2×C3D3×C22⋊C811yescharacteristic
452C2×C3#477111yescharacteristic
453C2×C3#480311yescharacteristic
454C2×C3#482111yescharacteristic
455C2×C3#482111yescharacteristic
456D3—42no—
457D3—64no—
458D3—62no—
459D3—62no—
460C22—62no—
461C22—92no—
462C22—121no—
463C22—121no—
464C22—181no—
465C22—181no—
466C22#6392111yescharacteristic
467C4—21no—
468C4—62no—
469C4—92no—
470C4—121no—
471C4—121no—
472C4—181no—
473C4—181no—
474C4D32×C811yescharacteristic
475C4#6379111yescharacteristic
476C4#6393711yescharacteristic
477C4#6395111yescharacteristic
478C3—21no—
479C3#6816611yescharacteristic, complemented
480C3#6823011yescharacteristic, complemented
481C2—122no—
482C2—182no—
483C2#1059061211yescharacteristic
484C2#1059093511yescharacteristic
485C2#1059100911yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC32×C4C22×C8
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3796C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1477
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×C4⋊C8C2semidirect
3. #10590297C2semidirect
4. C3×#4484C2semidirect
5. C3×#4483C2semidirect
6. #10589084C2semidirect
7. #10589081C2semidirect
40. #4484D3semidirect
41. #4483D3semidirect
54. #3796C8semidirect
135. C3×D12C2×C8semidirect
139. C3×Dic6C2×C8semidirect
301. D12D3×C8semidirect
322. Dic6D3×C8semidirect
416. C32#1477semidirect
479. C3#68166semidirect
480. C3#68230semidirect

Maximal subgroups

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

subgroupindex
C4×#37962
C3⋊D3×C4⋊C82
#105902972
C3×#44842
C3×#44832
#105890842
#105890812
#682303
#681663