Finite Group Databasebeta

← #11793996

Subgroups — #11793996

Order 1152.

575 conjugacy classes of subgroups.

The subgroup lattice has 515 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594786C211yesmaximal, characteristic
2C3×#5006C211yesmaximal, characteristic, complemented
3C3×#5002C211yesmaximal, characteristic, complemented
4#10591231C211yesmaximal, characteristic, complemented
5#10591116C211yesmaximal, characteristic, complemented
6#10591084C211yesmaximal, characteristic, complemented
7#10589397C211yesmaximal, characteristic, complemented
8#70296—31nomaximal
9#70043—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C32×#117C2211yescharacteristic
13#64135C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63827—21no—
18#63827—21no—
19#63823—21no—
20#63823—21no—
21#63822—22no—
22C3×#810—21no—
23C3×#809—21no—
24C3×#806—22no—
25#63580—22no—
26Dic3⋊(C3⋊C8)—22no—
27#63566—21no—
28#63563—21no—
29#5822—31no—
30#5822—31no—
31C3×#416—31no—
32C3×#410—31no—
33#5240—31no—
34#5233—31no—
35#5113—31no—
36#5102—31no—
37#5006—31no—
38#5006D311yescharacteristic, complemented
39#5002D311yescharacteristic, complemented
40#4999—31no—
41#4531—31no—
42#4531—31no—
43#4531—61no—
44C22×C32×C4C2311yescharacteristic
45C2×C3×#67—21no—
46C2×C3×#67—21no—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235—21no—
50C3×#235—21no—
51C3×#235—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C2×C3×D12D411yescharacteristic
56C2×C3×D12D411yescharacteristic
57C2×C3×C4×D3—21no—
58C2×C3×C4×D3—21no—
59C2×C3×Dic6D411yescharacteristic
60C2×C3×Dic6D411yescharacteristic
61C32×C4⋊C4—21no—
62C32×C22⋊C4—21no—
63C32×C42—21no—
64#3757—21no—
65C4⋊(C3⋊Dic3)—21no—
66C4×C3⋊Dic3—21no—
67#3748—21no—
68#3748—21no—
69C2×C3⋊(C3⋊C8)D412yes—
70C3×#217D412yes—
71C3×C4⋊Dic3—21no—
72C3×C4×Dic3—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76#3718—22no—
77#3715—22no—
78#3715—22no—
79#3713—22no—
80#2053—91noSylow
81C2×C3×#41—31no—
82C2×C3×#41—31no—
83C2×#235C2×D311yescharacteristic
84C2×#235C2×D311yescharacteristic
85C22×C3×C8—31no—
86C3×#117—21no—
87C3×#117—31no—
88C3×#117C2×D311yescharacteristic
89C3×#117C2×D311yescharacteristic
90#951—61no—
91#951—61no—
92#950—62no—
93#950—62no—
94#949—61no—
95#949—61no—
96#942—61no—
97#942—61no—
98#932—61no—
99#932—61no—
100#926—31no—
101#926—31no—
102#926—61no—
103#926C2×D311yescharacteristic
104C2×#208—31no—
105C2×#208—31no—
106C2×#208—61no—
107C22×C3⋊C8C2×D311yescharacteristic
108C3×#103—61no—
109C3×#102—61no—
110C3×#99—62no—
111#835—61no—
112#834—62no—
113#832—61no—
114#821—61no—
115#816—61no—
116Dic3⋊C8—62no—
117#810—21no—
118#809—21no—
119#806—22no—
120#806—62no—
121C4⋊(C3⋊C8)—62no—
122C23×C32C2×D411yescharacteristic
123C22×C3×D3—21no—
124C22×C3×D3—21no—
125C2×C32×C4—41no—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C3⋊Dic3—41no—
133C3×#67—41no—
134C3×#67—41no—
135C3×#67—41no—
136C3×#67—41no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C3×D12—21no—
141C3×D12—21no—
142C3×D12—21no—
143C3×D12—21no—
144C3×C4×D3—41no—
145C3×C4×D3—41no—
146C3×C4×D3—41no—
147C3×C4×D3—41no—
148C3×Dic6—21no—
149C3×Dic6—21no—
150C3×Dic6—21no—
151C3×Dic6—21no—
152C3⋊(C3⋊C8)—22no—
153C3×C3⋊C8—41no—
154#575—91no—
155#424—91no—
156#416—31no—
157#416—91no—
158#410—31no—
159#410—91no—
160H(3,ℤ/4)—91no—
161C3×#41—61no—
162C3×#41—61no—
163C3×#41—61no—
164C3×#41—61no—
165C3×#41—61no—
166C3×#41—61no—
167C3×#41—61no—
168C3×#41—61no—
169C2×C3×Q8—31no—
170C2×C3×Q8—31no—
171C2×C3×D4—31no—
172C2×C3×D4—31no—
173C2×C3×D4—61no—
174C2×C3×D4—61no—
175C22×C3×C4—21no—
176C22×C3×C4—61no—
177C22×C3×C4—61no—
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C2×#67—21no—
181C2×#67—21no—
182#235—21no—
183#235—21no—
184#235—21no—
185#235—21no—
186#235—21no—
187#235—21no—
188#235—21no—
189#235—21no—
190C2×D12D1211yescharacteristic
191C2×D12#6711yescharacteristic
192C2×C4×D3—21no—
193C2×C4×D3—21no—
194C2×Dic6D1211yescharacteristic
195C2×Dic6#6711yescharacteristic
196C2×C3×C8—61no—
197C2×C3×C8—61no—
198C2×C3×C8—61no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—41no—
202C3×C4⋊C4—61no—
203C3×C22⋊C4—21no—
204C3×C22⋊C4—21no—
205C3×C22⋊C4—32no—
206C3×C22⋊C4—41no—
207C3×C42—22no—
208C3×C42—21no—
209C3×C42—21no—
210C3×C42—61no—
211#217—61no—
212#217—61no—
213#217—121no—
214#217#6712yes—
215#216—62no—
216#216—62no—
217#215—62no—
218#215—62no—
219#214—62no—
220#214—62no—
221#213—62no—
222#213—62no—
223C4⋊Dic3—21no—
224C4⋊Dic3—61no—
225C4⋊Dic3—61no—
226C4⋊Dic3—121no—
227C4×Dic3—21no—
228C4×Dic3—62no—
229C4×Dic3—61no—
230C4×Dic3—61no—
231#208—61no—
232#208—61no—
233#208—61no—
234#208—61no—
235#208—121no—
236#208—121no—
237C2×C3⋊C8—21no—
238C2×C3⋊C8—21no—
239C2×C3⋊C8—21no—
240C2×C3⋊C8—32no—
241C2×C3⋊C8—32no—
242C2×C3⋊C8—62no—
243C22×C32—41no—
244C22×C32#12111yescharacteristic
245C22×C32#12111yescharacteristic
246C22×C32#12111yescharacteristic
247C2×C3×D3—41no—
248C2×C3×D3—41no—
249C2×C3×D3—81no—
250C2×C3×D3—81no—
251C32×C4—81no—
252C32×C4#12011yescharacteristic
253C32×C4#12311yescharacteristic
254C32×C4#12311yescharacteristic
255C32×C4#12411yescharacteristic
256C3⋊Dic3—81no—
257C3×Dic3—42no—
258C3×Dic3—41no—
259C3×Dic3—41no—
260C2×#41—31no—
261C2×#41—31no—
262#137—181no—
263#137—181no—
264AGL(1,ℤ/8)—181no—
265AGL(1,ℤ/8)—181no—
266#135—182no—
267C2×M16—91no—
268C22×C8—31no—
269#117—31no—
270#117—91no—
271#117D3211yescharacteristic
272C4⋊C8—182no—
273#103—61no—
274#103—181no—
275#102—61no—
276#102—181no—
277#99—62no—
278#99—182no—
279C23×C3—21no—
280C23×C3—61no—
281C23×C3—61no—
282C23×C3D3×D411yescharacteristic
283C23×C3C2×#6711yescharacteristic
284C22×D3—21no—
285C22×D3—21no—
286C3×Q8—61no—
287C3×Q8—61no—
288C3×Q8—61no—
289C3×Q8—61no—
290C3×D4—61no—
291C3×D4—61no—
292C3×D4—61no—
293C3×D4—61no—
294C3×D4—121no—
295C3×D4—121no—
296C3×D4—121no—
297C3×D4—121no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—42no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—62no—
308C2×C3×C4—61no—
309C2×C3×C4—61no—
310C2×C3×C4—121no—
311C2×C3×C4—121no—
312C2×C3×C4—121no—
313C2×C3×C4—121no—
314C2×C3×C4C2×D1211yescharacteristic
315C2×C3×C4#23511yescharacteristic
316C2×C3×C4#23511yescharacteristic
317C2×C3×C4#23511yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4#23711yescharacteristic
323C2×C3×C4#23711yescharacteristic
324C2×C3×C4#23711yescharacteristic
325C2×C3×C4C2×#6711yescharacteristic
326#67—41no—
327#67—41no—
328#67—41no—
329#67—41no—
330C2×Dic3—21no—
331C2×Dic3—22no—
332C2×Dic3—21no—
333C2×Dic3—122no—
334C2×Dic3—121no—
335C2×Dic3—121no—
336D12—21no—
337D12—21no—
338D12—21no—
339D12—21no—
340C4×D3—41no—
341C4×D3—41no—
342C4×D3—41no—
343C4×D3—41no—
344Dic6—21no—
345Dic6—21no—
346Dic6—21no—
347Dic6—21no—
348C3×C8—121no—
349C3⋊C8—41no—
350C3⋊C8—62no—
351C3⋊C8—62no—
352C3⋊C8—122no—
353C2×C32—21no—
354C2×C32—21no—
355C2×C32—21no—
356C2×C32#39411yescharacteristic
357C3×D3—81no—
358C3×D3—81no—
359#41—61no—
360#41—61no—
361#41—61no—
362#41—61no—
363#41—61no—
364#41—61no—
365#41—61no—
366#41—61no—
367C2×Q8—31no—
368C2×Q8—31no—
369C2×D4—31no—
370C2×D4—31no—
371C2×D4—61no—
372C2×D4—61no—
373C22×C4—61no—
374C22×C4—61no—
375C22×C4C2×D3211yescharacteristic
376Q16—182no—
377SD16—182no—
378SD16—182no—
379D8—182no—
380M16—181no—
381M16—181no—
382C2×C8—61no—
383C2×C8—61no—
384C2×C8—61no—
385C2×C8—92no—
386C4⋊C4—21no—
387C4⋊C4—61no—
388C4⋊C4—181no—
389C22⋊C4—21no—
390C22⋊C4—32no—
391C22⋊C4—181no—
392C42—21no—
393C42—61no—
394C42—181no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—81no—
401C22×C3—121no—
402C22×C3—121no—
403C22×C3—241no—
404C22×C3—241no—
405C22×C3#88411yescharacteristic
406C22×C3#88411yescharacteristic
407C22×C3#93011yescharacteristic
408C22×C3#93811yescharacteristic
409C22×C3#93911yescharacteristic
410C22×C3#93911yescharacteristic
411C2×D3—41no—
412C2×D3—41no—
413C2×D3—81no—
414C2×D3—81no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—81no—
420C3×C4—81no—
421C3×C4—82no—
422C3×C4—122no—
423C3×C4—121no—
424C3×C4—121no—
425C3×C4#88211yescharacteristic
426C3×C4#88311yescharacteristic
427C3×C4#88311yescharacteristic
428C3×C4#88511yescharacteristic
429C3×C4#88511yescharacteristic
430C3×C4#88611yescharacteristic
431C3×C4#92911yescharacteristic
432C3×C4#93711yescharacteristic
433Dic3—42no—
434Dic3—41no—
435Dic3—41no—
436Dic3—241no—
437Dic3—241no—
438Dic3—242no—
439C32#205311yescharacteristic, complemented, Sylow
440C23—61no—
441C23—61no—
442C23D3×#6711yescharacteristic
443Q8—61no—
444Q8—61no—
445Q8—61no—
446Q8—61no—
447D4—61no—
448D4—61no—
449D4—61no—
450D4—61no—
451D4—121no—
452D4—121no—
453D4—121no—
454D4—121no—
455C2×C4—41no—
456C2×C4—62no—
457C2×C4—61no—
458C2×C4—61no—
459C2×C4—121no—
460C2×C4—121no—
461C2×C4—121no—
462C2×C4—121no—
463C2×C4—361no—
464C2×C4#379511yescharacteristic
465C2×C4#379811yescharacteristic
466C2×C4D3×D1211yescharacteristic
467C2×C4#380211yescharacteristic
468C2×C4#380511yescharacteristic
469C2×C4D3×#6711yescharacteristic
470C8—121no—
471C8—182no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—41no—
480C2×C3—41no—
481C2×C3—41no—
482C2×C3—241no—
483C2×C3—241no—
484C2×C3#495911yescharacteristic
485C2×C3#496111yescharacteristic
486D3—81no—
487D3—81no—
488C22—41no—
489C22—121no—
490C22—121no—
491C22—241no—
492C22—241no—
493C22#6388511yescharacteristic
494C22#6390611yescharacteristic
495C22#6397011yescharacteristic
496C4—81no—
497C4—122no—
498C4—121no—
499C4—121no—
500C4—721no—
501C4#6389111yescharacteristic
502C4#6390511yescharacteristic
503C4#6391511yescharacteristic
504C4#6392211yescharacteristic
505C3—21no—
506C3#7004311yescharacteristic, complemented
507C3#7029611yescharacteristic, complemented
508C2—21no—
509C2—21no—
510C2—21no—
511C2—241no—
512C2—241no—
513C2#1059139011yescharacteristic
subgroupG/H
centerC4#63915
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#394
prime radical#10594786C2
hypercenter#117D32
hypocenterC32#2053
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#5006C2semidirect
3. C3×#5002C2semidirect
4. #10591231C2semidirect
5. #10591116C2semidirect
6. #10591084C2semidirect
7. #10589397C2semidirect
38. #5006D3semidirect
39. #5002D3semidirect
439. C32#2053semidirect
506. C3#70043semidirect
507. C3#70296semidirect

Maximal subgroups

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

subgroupindex
#105947862
C3×#50062
C3×#50022
#105912312
#105911162
#105910842
#105893972
#702963
#700433