Finite Group Databasebeta

← #11787042

Subgroups — #11787042

Order 1152.

595 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63814C211yesmaximal, characteristic
2C2×C3×#805C211yesmaximal, characteristic
3C2×#63577C211yesmaximal, characteristic, complemented
4#10591119C211yesmaximal, characteristic, complemented
5#10591084C211yesmaximal, characteristic
6#10589389C211yesmaximal, characteristic, complemented
7C3×#4524C211yesmaximal, characteristic, complemented
8#70376—31nomaximal
9#68694—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C22×C3×C3⋊C8C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3711—21no—
18#63814—22no—
19#63814—22no—
20C2×D3×C3⋊C8—21no—
21C3×#805—22no—
22#63577—22no—
23#63572—21no—
24#63572—21no—
25#63566C411yescharacteristic, complemented
26#63566C411yescharacteristic, complemented
27#63563C411yescharacteristic, complemented
28#63563C411yescharacteristic, complemented
29C2×#948—31no—
30C2×#901—31no—
31C2×C3×#104—31no—
32#5233—31no—
33C2×#822—31no—
34#5119—31no—
35#5113—31no—
36C2×#819—31no—
37#5102—31no—
38C2×#805D311yescharacteristic
39C3×#336—31no—
40#4524D311yescharacteristic, complemented
41#4523—31no—
42#4523—31no—
43#4523—61no—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C2×C3×#67—21no—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235D412yes—
50C3×#235Q812yes—
51C2×C3×D12C2×C411yescharacteristic
52C2×C3×C4×D3—21no—
53C2×C3×Dic6C2×C411yescharacteristic
54C32×C42—21no—
55C32×C42—21no—
56#3757—21no—
57C4⋊(C3⋊Dic3)C2×C411yescharacteristic
58C4⋊(C3⋊Dic3)C2×C411yescharacteristic
59C4×C3⋊Dic3—21no—
60#3748—21no—
61#3748D412yes—
62C2×C3⋊(C3⋊C8)—21no—
63C3×#208—21no—
64C3×#208—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8C2×C411yescharacteristic
71C2×C3×C3⋊C8C2×C411yescharacteristic
72C2×C3×C3⋊C8D411yescharacteristic
73C2×C3×C3⋊C8D411yescharacteristic
74#3711—24no—
75D3×C3⋊C8—24no—
76#1866—91noSylow
77C2×C3×#41—31no—
78C2×#235C2×D311yescharacteristic
79C2×C3×M16—31no—
80C22×C3×C8—31no—
81C22×C3×C8—31no—
82C2×C3×C42—21no—
83C2×C3×C42C2×D311yescharacteristic
84C2×C3×C42C2×D311yescharacteristic
85#948—62no—
86#948—62no—
87#926—31no—
88#926—31no—
89#926—61no—
90C2×#208—31no—
91C2×#208—31no—
92C2×#208—61no—
93C2×#208—61no—
94C2×#208C2×D311yescharacteristic
95C22×C3⋊C8—61no—
96C22×C3⋊C8C2×D311yescharacteristic
97C22×C3⋊C8C2×D311yescharacteristic
98#901—62no—
99#901—62no—
100C2×ΓL(1,𝔽25)—61no—
101C2×D3×C8—61no—
102C3×#104—62no—
103#835—31no—
104#835—31no—
105#832—31no—
106#832—31no—
107#822—62no—
108#821—31no—
109#821—31no—
110#819—62no—
111#816—31no—
112#816—31no—
113Dic3⋊C8—61no—
114Dic3⋊C8—61no—
115Dic3⋊C8—61no—
116Dic3⋊C8—61no—
117#805—22no—
118C23×C32#4111yescharacteristic
119C22×C3×D3—21no—
120C2×C32×C4—22no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×Q811yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—21no—
131C3×#67—22no—
132C3×#67—22no—
133C2×C3×Dic3—21no—
134C3×D12—21no—
135C3×D12C4⋊C412yes—
136C3×C4×D3—22no—
137C3×C4×D3—22no—
138C3×Dic6—21no—
139C3×Dic6C4⋊C412yes—
140C3⋊(C3⋊C8)—22no—
141C3×C3⋊C8—21no—
142C3×C3⋊C8—21no—
143C3×C3⋊C8—21no—
144C3×C3⋊C8—21no—
145C3×C3⋊C8—41no—
146C2×#131—91no—
147C2×#108—91no—
148#424—91no—
149C2×#104—31no—
150#416—91no—
151#339—91no—
152#336—31no—
153C3×#41—32no—
154C3×#41—32no—
155C3×#41—61no—
156C3×#41—61no—
157C2×C3×Q8—31no—
158C2×C3×D4—31no—
159C2×C3×D4—61no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—41no—
164C22×C3×C4—61no—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C2×#67—21no—
168#235—21no—
169#235—21no—
170#235Dic612yes—
171#235#6712yes—
172C2×D12C4×D311yescharacteristic
173C2×C4×D3—21no—
174C2×Dic6C4×D311yescharacteristic
175C3×M16—61no—
176C3×M16—61no—
177C2×C3×C8—31no—
178C2×C3×C8—31no—
179C2×C3×C8—31no—
180C2×C3×C8—31no—
181C2×C3×C8—61no—
182C2×C3×C8—61no—
183C2×C3×C8—61no—
184C2×C3×C8—61no—
185C2×C3×C8—61no—
186C3×C42—22no—
187C3×C42—21no—
188C3×C42—21no—
189C3×C42—21no—
190C3×C42—21no—
191C3×C42—41no—
192#217—61no—
193#217—61no—
194#217—121no—
195C4⋊Dic3—31no—
196C4⋊Dic3—31no—
197C4⋊Dic3—31no—
198C4⋊Dic3—31no—
199C4⋊Dic3—61no—
200C4⋊Dic3—61no—
201C4×Dic3—61no—
202C4×Dic3—61no—
203C4×Dic3—121no—
204#208—21no—
205#208—21no—
206#208—32no—
207#208—32no—
208#208—62no—
209#208—64no—
210#208—61no—
211#208—61no—
212#208—121no—
213C2×C3⋊C8—21no—
214C2×C3⋊C8—21no—
215C2×C3⋊C8—21no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—64no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—61no—
221C2×C3⋊C8—121no—
222C2×C3⋊C8C4×D311yescharacteristic
223C2×C3⋊C8C4×D311yescharacteristic
224C2×C3⋊C8D1211yescharacteristic
225C2×C3⋊C8D1211yescharacteristic
226ΓL(1,𝔽25)—64no—
227D3×C8—64no—
228C22×C32—21no—
229C22×C32—21no—
230C22×C32C4×D411yescharacteristic
231C22×C32C22⋊Q811yescharacteristic
232C22×C32#12311yescharacteristic
233C2×C3×D3—22no—
234C2×C3×D3—41no—
235C2×C3×D3—41no—
236C32×C4—42no—
237C32×C4C2×C4⋊C411yescharacteristic
238C32×C4C4×D411yescharacteristic
239C32×C4#12011yescharacteristic
240C32×C4C22⋊Q811yescharacteristic
241C3⋊Dic3—41no—
242C3⋊Dic3—41no—
243C3×Dic3—22no—
244C2×#41—31no—
245#131—182no—
246#131—182no—
247C2×M16—31no—
248C2×M16—91no—
249C2×M16—181no—
250C22×C8—31no—
251C22×C8—31no—
252C22×C8—181no—
253#117—91no—
254C2×C42D3211yescharacteristic
255#108—182no—
256C4⋊C8—181no—
257C4⋊C8—181no—
258#104—62no—
259#103—91no—
260#103—91no—
261#102—91no—
262#102—91no—
263C23×C3—21no—
264C23×C3—61no—
265C23×C3#23511yescharacteristic
266C23×C3#23711yescharacteristic
267C22×D3—21no—
268C3×Q8—32no—
269C3×Q8—61no—
270C3×D4—32no—
271C3×D4—62no—
272C3×D4—62no—
273C3×D4—61no—
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—42no—
283C2×C3×C4—42no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—42no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—61no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4C2×Dic611yescharacteristic
293C2×C3×C4C2×C4×D311yescharacteristic
294C2×C3×C4C2×C4×D311yescharacteristic
295C2×C3×C4C2×D1211yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4#23711yescharacteristic
301C2×C3×C4#23711yescharacteristic
302C2×C3×C4D3×Q811yescharacteristic
303C2×C3×C4C2×#6711yescharacteristic
304#67—22no—
305#67—22no—
306C2×Dic3—21no—
307C2×Dic3—61no—
308C2×Dic3—61no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—121no—
312C2×Dic3—121no—
313D12—21no—
314D12Dic3⋊C412yes—
315C4×D3—22no—
316C4×D3—22no—
317Dic6—21no—
318Dic6Dic3⋊C412yes—
319C3×C8—61no—
320C3×C8—61no—
321C3×C8—61no—
322C3×C8—61no—
323C3×C8—121no—
324C3⋊C8—21no—
325C3⋊C8—21no—
326C3⋊C8—21no—
327C3⋊C8—21no—
328C3⋊C8—41no—
329C3⋊C8—62no—
330C3⋊C8—62no—
331C3⋊C8—122no—
332C2×C32—21no—
333C2×C32—21no—
334C2×C32#38511yescharacteristic
335C2×C32#44311yescharacteristic
336C2×C32#44411yescharacteristic
337C3×D3—42no—
338#41—32no—
339#41—32no—
340#41—61no—
341#41—61no—
342C2×Q8—31no—
343C2×D4—31no—
344C2×D4—61no—
345C22×C4—21no—
346C22×C4—61no—
347C22×C4C2×D3211yescharacteristic
348M16—61no—
349M16—61no—
350M16—92no—
351M16—184no—
352M16—181no—
353C2×C8—31no—
354C2×C8—31no—
355C2×C8—31no—
356C2×C8—31no—
357C2×C8—61no—
358C2×C8—61no—
359C2×C8—61no—
360C2×C8—61no—
361C2×C8—61no—
362C2×C8—184no—
363C2×C8—181no—
364C4⋊C4—91no—
365C4⋊C4—91no—
366C22⋊C4—181no—
367C42—21no—
368C42—21no—
369C42—181no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—62no—
380C22×C3—121no—
381C22×C3—121no—
382C22×C3C4×D1211yescharacteristic
383C22×C3#87811yescharacteristic
384C22×C3#67⋊C411yescharacteristic
385C22×C3#88311yescharacteristic
386C22×C3#89611yescharacteristic
387C22×C3#93511yescharacteristic
388C2×D3—22no—
389C2×D3—41no—
390C2×D3—41no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—42no—
396C3×C4—42no—
397C3×C4—44no—
398C3×C4—62no—
399C3×C4#87811yescharacteristic
400C3×C4#67⋊C411yescharacteristic
401C3×C4#67⋊C411yescharacteristic
402C3×C4#88211yescharacteristic
403C3×C4D3×C4⋊C411yescharacteristic
404C3×C4#89711yescharacteristic
405C3×C4C2×Dic3⋊C411yescharacteristic
406C3×C4#93711yescharacteristic
407Dic3—22no—
408Dic3—121no—
409Dic3—121no—
410Dic3—121no—
411Dic3—121no—
412Dic3—241no—
413Dic3—241no—
414C32#186611yescharacteristic, complemented, Sylow
415C23—61no—
416C23#380411yescharacteristic
417Q8—32no—
418Q8—61no—
419D4—32no—
420D4—62no—
421D4—62no—
422D4—61no—
423C2×C4—22no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—61no—
427C2×C4—62no—
428C2×C4—62no—
429C2×C4—181no—
430C2×C4—181no—
431C2×C4D3×Dic611yescharacteristic
432C2×C4C4×D3211yescharacteristic
433C2×C4D3×D1211yescharacteristic
434C2×C4#380211yescharacteristic
435C2×C4#380511yescharacteristic
436C2×C4D3×#6711yescharacteristic
437C8—61no—
438C8—61no—
439C8—61no—
440C8—61no—
441C8—121no—
442C8—182no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—41no—
451C2×C3—41no—
452C2×C3—122no—
453C2×C3#466811yescharacteristic
454C2×C3#470011yescharacteristic
455C2×C3#471711yescharacteristic
456C2×C3#482311yescharacteristic
457C2×C3#482411yescharacteristic
458C2×C3#494611yescharacteristic
459D3—42no—
460C22—21no—
461C22—21no—
462C22—62no—
463C22—121no—
464C22—121no—
465C22#6388011yescharacteristic
466C22#6389911yescharacteristic
467C22#6396911yescharacteristic
468C4—42no—
469C4—62no—
470C4—361no—
471C4—361no—
472C4D3×Dic3⋊C411yescharacteristic
473C4#6389311yescharacteristic
474C4#6390211yescharacteristic
475C4#6392211yescharacteristic
476C3—21no—
477C3#6869411yescharacteristic, complemented
478C3#7037611yescharacteristic, complemented
479C2—21no—
480C2—21no—
481C2—122no—
482C2#1059034111yescharacteristic
483C2#1059034211yescharacteristic
484C2#1059137311yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C4×D4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1866
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C2×#63577C2semidirect
4. #10591119C2semidirect
6. #10589389C2semidirect
7. C3×#4524C2semidirect
25. #63566C4semidirect
26. #63566C4semidirect
27. #63563C4semidirect
28. #63563C4semidirect
40. #4524D3semidirect
414. C32#1866semidirect
477. C3#68694semidirect
478. C3#70376semidirect

Maximal subgroups

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

subgroupindex
C2×#638142
C2×C3×#8052
C2×#635772
#105911192
#105910842
#105893892
C3×#45242
#703763
#686943