Finite Group Databasebeta

← #11793867

Subgroups — #11793867

Order 1152.

575 conjugacy classes of subgroups.

The subgroup lattice has 529 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594786C211yesmaximal, characteristic
2C2×C3×#825C211yesmaximal, characteristic, complemented
3C3×#5132C211yesmaximal, characteristic, complemented
4#10591115C211yesmaximal, characteristic, complemented
5C2×#63569C211yesmaximal, characteristic, complemented
6#10591076C211yesmaximal, characteristic, complemented
7#10589426C211yesmaximal, characteristic, complemented
8#70379—31nomaximal
9#70144—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63827—21no—
18#63827—21no—
19#63823—21no—
20#63823—21no—
21#63822—22no—
22C3×#825—21no—
23C3×#825—21no—
24C3×#824—21no—
25C3×#823—21no—
26Dic3⋊(C3⋊C8)—22no—
27#63569—21no—
28#63569—21no—
29#63560—21no—
30#63558—21no—
31#5822—31no—
32#5822—31no—
33C2×C3×#104—31no—
34C3×#413—31no—
35#5237—31no—
36C2×#837—31no—
37C2×#825D311yescharacteristic, complemented
38#5132—31no—
39#5132D311yescharacteristic, complemented
40#5118—31no—
41C2×#805—31no—
42#4924—31no—
43C3⋊#338—31no—
44C3⋊#338—31no—
45C3⋊#338—61no—
46C22×C32×C4C2311yescharacteristic
47C2×C3×#67—21no—
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C3×#235—21no—
51C3×#235—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C3×#235—21no—
56C3×#235—21no—
57C3×#235—21no—
58C2×C3×D12D411yescharacteristic
59C2×C3×D12D411yescharacteristic
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3—21no—
62C2×C3×Dic6D411yescharacteristic
63C2×C3×Dic6D411yescharacteristic
64C32×M16—21no—
65C32×M16—21no—
66C2×C32×C8—21no—
67#3748—21no—
68#3748—21no—
69#3748—21no—
70#3748—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C2×C3⋊(C3⋊C8)D412yes—
73C3×C4×Dic3—21no—
74C3×C4×Dic3D411yescharacteristic
75C3×C4×Dic3D411yescharacteristic
76C3×#208—21no—
77C3×#208—21no—
78C2×C3×C3⋊C8—21no—
79#3718—22no—
80#3715—22no—
81#3715—22no—
82#3713—22no—
83#2050—91noSylow
84C2×C3×#41—31no—
85C2×C3×#41—31no—
86C2×#235C2×D311yescharacteristic
87C2×#235C2×D311yescharacteristic
88C2×C3×M16—21no—
89C2×C3×M16—31no—
90C2×C3×M16C2×D311yescharacteristic
91C2×C3×M16C2×D311yescharacteristic
92C2×C3×C42—31no—
93#951—61no—
94#951—61no—
95#950—62no—
96#950—62no—
97#949—61no—
98#949—61no—
99#942—61no—
100#942—61no—
101#932—61no—
102#932—61no—
103C2×C4×Dic3C2×D311yescharacteristic
104C2×#208—31no—
105C2×#208—31no—
106C2×#208—31no—
107C2×#208—31no—
108C2×#208—61no—
109C2×#208—61no—
110C2×#208C2×D311yescharacteristic
111C3×#104—61no—
112C3×#104—61no—
113C3×#101—61no—
114C3×#100—61no—
115#837—61no—
116#837—61no—
117#836—61no—
118#833—61no—
119#825—21no—
120#825—21no—
121#824—21no—
122#824—61no—
123#823—21no—
124#823—61no—
125Dic3⋊C8—62no—
126#805—61no—
127#805—61no—
128C4⋊(C3⋊C8)—62no—
129C23×C32#4111yescharacteristic
130C22×C3×D3—21no—
131C22×C3×D3—21no—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C3×#67—41no—
139C3×#67—41no—
140C3×#67—41no—
141C3×#67—41no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—42no—
147C3×D12—21no—
148C3×D12—21no—
149C3×D12—21no—
150C3×D12—21no—
151C3×C4×D3—41no—
152C3×C4×D3—41no—
153C3×C4×D3—41no—
154C3×C4×D3—41no—
155C3×Dic6—21no—
156C3×Dic6—21no—
157C3×Dic6—21no—
158C3×Dic6—21no—
159C32×C8—41no—
160C3⋊(C3⋊C8)—22no—
161C3⋊(C3⋊C8)—41no—
162C3×C3⋊C8—41no—
163#575—91no—
164#423—91no—
165C2×#104—31no—
166C2×#104—91no—
167#413—31no—
168#413—91no—
169#338—91no—
170C3×#41—61no—
171C3×#41—61no—
172C3×#41—61no—
173C3×#41—61no—
174C3×#41—61no—
175C3×#41—61no—
176C3×#41—61no—
177C3×#41—61no—
178C2×C3×Q8—31no—
179C2×C3×Q8—31no—
180C2×C3×D4—31no—
181C2×C3×D4—31no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C22×C3×C4—21no—
185C22×C3×C4—61no—
186C22×C3×C4—61no—
187C22×C3×C4—61no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C2×#67—21no—
191C2×#67—21no—
192C22×Dic3—21no—
193#235—21no—
194#235—21no—
195#235—21no—
196#235—21no—
197#235—21no—
198#235—21no—
199#235—21no—
200#235—21no—
201C2×D12D1211yescharacteristic
202C2×D12#6711yescharacteristic
203C2×C4×D3—21no—
204C2×C4×D3—21no—
205C2×Dic6D1211yescharacteristic
206C2×Dic6#6711yescharacteristic
207C3×M16—21no—
208C3×M16—21no—
209C3×M16—21no—
210C3×M16—21no—
211C3×M16—41no—
212C3×M16—41no—
213C3×M16—61no—
214C3×M16—61no—
215C2×C3×C8—22no—
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C2×C3×C8—61no—
219C3×C42—31no—
220C3×C42—31no—
221C3×C42—61no—
222#216—62no—
223#216—62no—
224#215—62no—
225#215—62no—
226#214—62no—
227#214—62no—
228#213—62no—
229#213—62no—
230C4×Dic3—21no—
231C4×Dic3#6711yescharacteristic
232C4×Dic3#6711yescharacteristic
233#208—21no—
234#208—21no—
235#208—61no—
236#208—61no—
237#208—61no—
238#208—61no—
239#208—61no—
240#208—61no—
241#208—61no—
242#208—61no—
243#208—121no—
244#208—121no—
245#208—121no—
246#208—121no—
247C2×C3⋊C8—21no—
248C2×C3⋊C8—32no—
249C2×C3⋊C8—32no—
250C2×C3⋊C8—62no—
251C2×C3⋊C8—62no—
252C2×C3⋊C8—61no—
253C2×C3⋊C8—61no—
254C22×C32—41no—
255C22×C32#12111yescharacteristic
256C22×C32#12311yescharacteristic
257C22×C32#12311yescharacteristic
258C2×C3×D3—41no—
259C2×C3×D3—41no—
260C2×C3×D3—81no—
261C2×C3×D3—81no—
262C32×C4#12011yescharacteristic
263C32×C4#12111yescharacteristic
264C32×C4#12111yescharacteristic
265C32×C4#12411yescharacteristic
266C3×Dic3—22no—
267C3×Dic3—41no—
268C3×Dic3—41no—
269C3×Dic3—41no—
270C2×#41—31no—
271C2×#41—31no—
272#137—181no—
273#137—181no—
274AGL(1,ℤ/8)—181no—
275AGL(1,ℤ/8)—181no—
276#135—182no—
277C2×M16—31no—
278C2×M16—91no—
279C2×M16—91no—
280C2×M16D3211yescharacteristic
281C2×C42—31no—
282C4⋊C8—182no—
283#104—61no—
284#104—61no—
285#104—181no—
286#104—181no—
287#101—61no—
288#101—181no—
289#100—61no—
290#100—181no—
291C23×C3—21no—
292C23×C3—61no—
293C23×C3—61no—
294C23×C3#23511yescharacteristic
295C23×C3#23711yescharacteristic
296C22×D3—21no—
297C22×D3—21no—
298C3×Q8—61no—
299C3×Q8—61no—
300C3×Q8—61no—
301C3×Q8—61no—
302C3×D4—61no—
303C3×D4—61no—
304C3×D4—61no—
305C3×D4—61no—
306C3×D4—121no—
307C3×D4—121no—
308C3×D4—121no—
309C3×D4—121no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—61no—
317C2×C3×C4—61no—
318C2×C3×C4—61no—
319C2×C3×C4—61no—
320C2×C3×C4—122no—
321C2×C3×C4—121no—
322C2×C3×C4—121no—
323C2×C3×C4—121no—
324C2×C3×C4—121no—
325C2×C3×C4C2×D1211yescharacteristic
326C2×C3×C4#23511yescharacteristic
327C2×C3×C4#23511yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4#23711yescharacteristic
334C2×C3×C4#23711yescharacteristic
335C2×C3×C4C2×#6711yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337#67—41no—
338#67—41no—
339#67—41no—
340#67—41no—
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—21no—
344C2×Dic3—21no—
345C2×Dic3—42no—
346D12—21no—
347D12—21no—
348D12—21no—
349D12—21no—
350C4×D3—41no—
351C4×D3—41no—
352C4×D3—41no—
353C4×D3—41no—
354Dic6—21no—
355Dic6—21no—
356Dic6—21no—
357Dic6—21no—
358C3×C8—42no—
359C3×C8—41no—
360C3×C8—41no—
361C3×C8—121no—
362C3⋊C8—41no—
363C3⋊C8—62no—
364C3⋊C8—62no—
365C3⋊C8—122no—
366C3⋊C8—122no—
367C3⋊C8—121no—
368C3⋊C8—121no—
369C2×C32—21no—
370C2×C32—21no—
371C2×C32—21no—
372C2×C32#39411yescharacteristic
373C3×D3—81no—
374C3×D3—81no—
375#41—61no—
376#41—61no—
377#41—61no—
378#41—61no—
379#41—61no—
380#41—61no—
381#41—61no—
382#41—61no—
383C2×Q8—31no—
384C2×Q8—31no—
385C2×D4—31no—
386C2×D4—31no—
387C2×D4—61no—
388C2×D4—61no—
389C22×C4—61no—
390C22×C4—61no—
391C22×C4—61no—
392C22×C4C2×D3211yescharacteristic
393Q16—182no—
394SD16—182no—
395SD16—182no—
396D8—182no—
397M16—21no—
398M16—21no—
399M16—61no—
400M16—61no—
401M16—181no—
402M16—181no—
403M16—181no—
404M16—181no—
405C2×C8—21no—
406C2×C8—61no—
407C2×C8—92no—
408C2×C8—181no—
409C42—31no—
410C42—31no—
411C42—61no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—81no—
418C22×C3—121no—
419C22×C3—121no—
420C22×C3—241no—
421C22×C3—241no—
422C22×C3#88311yescharacteristic
423C22×C3#88311yescharacteristic
424C22×C3#88411yescharacteristic
425C22×C3#88611yescharacteristic
426C22×C3#92911yescharacteristic
427C22×C3#93911yescharacteristic
428C2×D3—41no—
429C2×D3—41no—
430C2×D3—81no—
431C2×D3—81no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—62no—
437C3×C4—121no—
438C3×C4—121no—
439C3×C4—121no—
440C3×C4#88211yescharacteristic
441C3×C4#88411yescharacteristic
442C3×C4#88511yescharacteristic
443C3×C4#88511yescharacteristic
444C3×C4#93011yescharacteristic
445C3×C4#93711yescharacteristic
446C3×C4#93811yescharacteristic
447C3×C4#93911yescharacteristic
448Dic3—22no—
449Dic3—41no—
450Dic3—41no—
451Dic3—41no—
452C32#205011yescharacteristic, complemented, Sylow
453C23—61no—
454C23—61no—
455C23#379511yescharacteristic
456Q8—61no—
457Q8—61no—
458Q8—61no—
459Q8—61no—
460D4—61no—
461D4—61no—
462D4—61no—
463D4—61no—
464D4—121no—
465D4—121no—
466D4—121no—
467D4—121no—
468C2×C4—61no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—61no—
472C2×C4—122no—
473C2×C4—121no—
474C2×C4—121no—
475C2×C4—121no—
476C2×C4—121no—
477C2×C4#379811yescharacteristic
478C2×C4D3×D1211yescharacteristic
479C2×C4#380211yescharacteristic
480C2×C4#380511yescharacteristic
481C2×C4D3×#6711yescharacteristic
482C2×C4D3×#6711yescharacteristic
483C8—41no—
484C8—121no—
485C8—182no—
486C8—361no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—41no—
495C2×C3—41no—
496C2×C3—41no—
497C2×C3—241no—
498C2×C3—241no—
499C2×C3#495911yescharacteristic
500C2×C3#496111yescharacteristic
501D3—81no—
502D3—81no—
503C22—41no—
504C22—121no—
505C22—121no—
506C22—241no—
507C22—241no—
508C22#6388511yescharacteristic
509C22#6389111yescharacteristic
510C22#6390511yescharacteristic
511C4—62no—
512C4—121no—
513C4—121no—
514C4—121no—
515C4#6390611yescharacteristic
516C4#6391511yescharacteristic
517C4#6392211yescharacteristic
518C4#6397011yescharacteristic
519C3—21no—
520C3#7014411yescharacteristic, complemented
521C3#7037911yescharacteristic, complemented
522C2—21no—
523C2—21no—
524C2—21no—
525C2—241no—
526C2—241no—
527C2#1059139011yescharacteristic
subgroupG/H
centerC4#63915
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#394
prime radical#10594786C2
hypercenterC2×M16D32
hypocenterC32#2050
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×C3×#825C2semidirect
3. C3×#5132C2semidirect
4. #10591115C2semidirect
5. C2×#63569C2semidirect
6. #10591076C2semidirect
7. #10589426C2semidirect
37. C2×#825D3semidirect
39. #5132D3semidirect
452. C32#2050semidirect
520. C3#70144semidirect
521. C3#70379semidirect

Maximal subgroups

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

subgroupindex
#105947862
C2×C3×#8252
C3×#51322
#105911152
C2×#635692
#105910762
#105894262
#703793
#701443