Finite Group Databasebeta

← #11793986

Subgroups — #11793986

Order 1152.

659 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596293C211yesmaximal, characteristic
2C3×#5240C211yesmaximal, characteristic, complemented
3C3×#5233C211yesmaximal, characteristic, complemented
4#10591232C211yesmaximal, characteristic, complemented
5#10591116C211yesmaximal, characteristic, complemented
6#10591105C211yesmaximal, characteristic, complemented
7#10589157C211yesmaximal, characteristic, complemented
8#70296—31nomaximal
9#70043—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12#64160—21no—
13#64159—22no—
14#64158—21no—
15#64151—21no—
16#64141—21no—
17C2×#3748C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C3×#926C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#835—21no—
23C3×#834—22no—
24C3×#832—21no—
25#63581—22no—
26Dic3⋊(C3⋊C8)—22no—
27#63567—21no—
28#63564—21no—
29#5822—31no—
30#5822—31no—
31#5822—61no—
32C3×#416—31no—
33C3×#410—31no—
34#5240D311yescharacteristic, complemented
35#5233D311yescharacteristic, complemented
36#5113—31no—
37#5102—31no—
38#5006—31no—
39#5006—31no—
40#5002—31no—
41#4999—31no—
42#4531—31no—
43#4531—31no—
44C32×#41—21no—
45C32×#41—21no—
46C32×#41—21no—
47C32×#41—21no—
48C2×C32×Q8D411yescharacteristic
49C2×C32×D4—21no—
50C2×C32×D4D411yescharacteristic
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C2×#638—21no—
54#3828—21no—
55#3828—21no—
56#3828—21no—
57#3828—21no—
58C2×C4⋊(C3⋊D3)D411yescharacteristic
59C2×C4×C3⋊D3—21no—
60C2×#634D411yescharacteristic
61#3756—22no—
62#3755—22no—
63#3754—22no—
64#3753—22no—
65#3748—21no—
66#3748—21no—
67C2×C3⋊(C3⋊C8)D412yes—
68C3×#217—21no—
69C3×#217—21no—
70C3×#217D412yes—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×C4×Dic3—21no—
75C3×C4×Dic3—21no—
76C3×C4×Dic3—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
80#2053—91noSylow
81C2×C3×#41—21no—
82C2×C3×#41C2×D311yescharacteristic
83C2×C3×#41C2×D311yescharacteristic
84C2×#235—31no—
85C2×#235—31no—
86C2×#235—61no—
87C22×C3×C8—31no—
88C3×#117—31no—
89C3×#117—31no—
90C3×#117—31no—
91#951—61no—
92#951—61no—
93#951—62no—
94#950—62no—
95#950—62no—
96#950—64no—
97#949—61no—
98#949—61no—
99#949—62no—
100#942—62no—
101#942—61no—
102#942—61no—
103#932—62no—
104#932—61no—
105#932—61no—
106#926C2×D311yescharacteristic
107#926C2×D311yescharacteristic
108#926C2×D311yescharacteristic
109C2×#208—31no—
110C2×#208—31no—
111C2×#208—61no—
112C22×C3⋊C8C2×D311yescharacteristic
113C3×#103—61no—
114C3×#102—61no—
115C3×#99—62no—
116#835—21no—
117#834—22no—
118#832—21no—
119#821—61no—
120#816—61no—
121Dic3⋊C8—62no—
122#810—61no—
123#809—61no—
124#806—62no—
125#806—62no—
126C4⋊(C3⋊C8)—62no—
127C23×C32—21no—
128C23×C32C2×D411yescharacteristic
129C22×C3⋊D3—21no—
130C32×Q8—21no—
131C32×Q8—21no—
132C32×D4—21no—
133C32×D4—21no—
134C32×D4—41no—
135C32×D4—41no—
136C2×C32×C4—21no—
137C2×C32×C4—41no—
138C2×C32×C4—41no—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C32×C4#4111yescharacteristic
145#638—41no—
146#638—41no—
147C2×C3⋊Dic3—21no—
148C4⋊(C3⋊D3)—21no—
149C4⋊(C3⋊D3)—21no—
150C4×C3⋊D3—41no—
151C4×C3⋊D3—41no—
152#634—21no—
153#634—21no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—41no—
157C3⋊(C3⋊C8)—22no—
158C3×C3⋊C8—41no—
159#575—91no—
160#424—91no—
161#416—31no—
162#416—91no—
163#410—31no—
164#410—91no—
165H(3,ℤ/4)—91no—
166C3×#41—22no—
167C3×#41—22no—
168C3×#41—21no—
169C3×#41—21no—
170C3×#41—21no—
171C3×#41—21no—
172C3×#41—21no—
173C3×#41—21no—
174C3×#41—21no—
175C3×#41—21no—
176C3×#41—41no—
177C3×#41—41no—
178C2×C3×Q8—21no—
179C2×C3×Q8D1211yescharacteristic
180C2×C3×Q8#6711yescharacteristic
181C2×C3×D4—21no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4—41no—
185C2×C3×D4D1211yescharacteristic
186C2×C3×D4#6711yescharacteristic
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—41no—
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C22×D311yescharacteristic
193C2×#67—61no—
194C2×#67—61no—
195C2×#67—121no—
196#235—62no—
197#235—62no—
198#235—61no—
199#235—61no—
200#235—61no—
201#235—61no—
202#235—61no—
203#235—61no—
204#235—61no—
205#235—61no—
206#235—121no—
207#235—121no—
208C2×D12—31no—
209C2×D12—31no—
210C2×D12—61no—
211C2×C4×D3—61no—
212C2×C4×D3—61no—
213C2×C4×D3—121no—
214C2×Dic6—31no—
215C2×Dic6—31no—
216C2×Dic6—61no—
217C2×C3×C8—61no—
218C2×C3×C8—61no—
219C2×C3×C8—61no—
220C3×C4⋊C4—61no—
221C3×C4⋊C4—61no—
222C3×C4⋊C4—61no—
223C3×C22⋊C4—32no—
224C3×C22⋊C4—61no—
225C3×C22⋊C4—61no—
226C3×C42—61no—
227C3×C42—61no—
228C3×C42—61no—
229#217—21no—
230#217—21no—
231#217#6712yes—
232#216—64no—
233#216—62no—
234#216—62no—
235#215—64no—
236#215—62no—
237#215—62no—
238#214—64no—
239#214—62no—
240#214—62no—
241#213—64no—
242#213—62no—
243#213—62no—
244C4⋊Dic3—21no—
245C4⋊Dic3—21no—
246C4⋊Dic3—21no—
247C4×Dic3—21no—
248C4×Dic3—21no—
249C4×Dic3—21no—
250#208—62no—
251#208—62no—
252#208—61no—
253#208—61no—
254#208—61no—
255#208—61no—
256C2×C3⋊C8—21no—
257C2×C3⋊C8—21no—
258C2×C3⋊C8—21no—
259C2×C3⋊C8—32no—
260C2×C3⋊C8—32no—
261C2×C3⋊C8—62no—
262C22×C32—41no—
263C22×C32—41no—
264C22×C32—81no—
265C22×C32#12111yescharacteristic
266C22×C32#12111yescharacteristic
267C22×C32#12111yescharacteristic
268C2×C3⋊D3—41no—
269C2×C3⋊D3—81no—
270C32×C4—41no—
271C32×C4#12011yescharacteristic
272C32×C4#12311yescharacteristic
273C32×C4#12311yescharacteristic
274C32×C4#12411yescharacteristic
275C3⋊Dic3—41no—
276C3×Dic3—42no—
277C3×Dic3—81no—
278C3×Dic3—81no—
279C2×#41—91no—
280C2×#41D3211yescharacteristic
281#137—181no—
282#137—181no—
283AGL(1,ℤ/8)—181no—
284AGL(1,ℤ/8)—181no—
285#135—182no—
286C2×M16—91no—
287C22×C8—31no—
288#117—31no—
289#117—31no—
290#117—31no—
291C4⋊C8—182no—
292#103—61no—
293#103—181no—
294#102—61no—
295#102—181no—
296#99—62no—
297#99—182no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—41no—
302C23×C3D3×D411yescharacteristic
303C23×C3C2×#6711yescharacteristic
304C22×D3—61no—
305C22×D3—61no—
306C22×D3—121no—
307C3×Q8—22no—
308C3×Q8—21no—
309C3×Q8—21no—
310C3×Q8—21no—
311C3×Q8—21no—
312C3×Q8—41no—
313C3×D4—22no—
314C3×D4—21no—
315C3×D4—21no—
316C3×D4—21no—
317C3×D4—21no—
318C3×D4—41no—
319C3×D4—42no—
320C3×D4—42no—
321C3×D4—41no—
322C3×D4—41no—
323C3×D4—41no—
324C3×D4—41no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—41no—
334C2×C3×C4—42no—
335C2×C3×C4—42no—
336C2×C3×C4—41no—
337C2×C3×C4—41no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—62no—
341C2×C3×C4—121no—
342C2×C3×C4—121no—
343C2×C3×C4C2×D1211yescharacteristic
344C2×C3×C4#23511yescharacteristic
345C2×C3×C4#23511yescharacteristic
346C2×C3×C4#23511yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4#23711yescharacteristic
352C2×C3×C4#23711yescharacteristic
353C2×C3×C4#23711yescharacteristic
354C2×C3×C4C2×#6711yescharacteristic
355#67—122no—
356#67—122no—
357#67—121no—
358#67—121no—
359#67—121no—
360#67—121no—
361C2×Dic3—22no—
362C2×Dic3—41no—
363C2×Dic3—41no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—121no—
367D12—62no—
368D12—61no—
369D12—61no—
370D12—61no—
371D12—61no—
372D12—121no—
373C4×D3—122no—
374C4×D3—122no—
375C4×D3—121no—
376C4×D3—121no—
377C4×D3—121no—
378C4×D3—121no—
379Dic6—62no—
380Dic6—61no—
381Dic6—61no—
382Dic6—61no—
383Dic6—61no—
384Dic6—121no—
385C3×C8—121no—
386C3⋊C8—41no—
387C3⋊C8—64no—
388C3⋊C8—62no—
389C3⋊C8—62no—
390C2×C32—21no—
391C2×C32—21no—
392C2×C32—21no—
393C2×C32—81no—
394C2×C32#39411yescharacteristic
395C3⋊D3—81no—
396#41—21no—
397#41—21no—
398#41—21no—
399#41—21no—
400#41—181no—
401#41—181no—
402#41—181no—
403#41—181no—
404C2×Q8—91no—
405C2×Q8#62611yescharacteristic
406C2×D4—21no—
407C2×D4—91no—
408C2×D4—181no—
409C2×D4#62611yescharacteristic
410C22×C4—21no—
411C22×C4—181no—
412C22×C4C2×D3211yescharacteristic
413Q16—182no—
414SD16—182no—
415SD16—182no—
416D8—182no—
417M16—181no—
418M16—181no—
419C2×C8—61no—
420C2×C8—61no—
421C2×C8—61no—
422C2×C8—92no—
423C4⋊C4—61no—
424C4⋊C4—61no—
425C4⋊C4—61no—
426C22⋊C4—32no—
427C22⋊C4—61no—
428C22⋊C4—61no—
429C42—61no—
430C42—61no—
431C42—61no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—42no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—81no—
441C22×C3—81no—
442C22×C3—81no—
443C22×C3—82no—
444C22×C3#88411yescharacteristic
445C22×C3#88411yescharacteristic
446C22×C3#93011yescharacteristic
447C22×C3#93811yescharacteristic
448C22×C3#93911yescharacteristic
449C22×C3#93911yescharacteristic
450C2×D3—122no—
451C2×D3—121no—
452C2×D3—121no—
453C2×D3—242no—
454C2×D3—241no—
455C2×D3—241no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—42no—
461C3×C4—41no—
462C3×C4—41no—
463C3×C4—122no—
464C3×C4—241no—
465C3×C4—241no—
466C3×C4#88211yescharacteristic
467C3×C4#88311yescharacteristic
468C3×C4#88311yescharacteristic
469C3×C4#88511yescharacteristic
470C3×C4#88511yescharacteristic
471C3×C4#88611yescharacteristic
472C3×C4#92911yescharacteristic
473C3×C4#93711yescharacteristic
474Dic3—42no—
475Dic3—81no—
476Dic3—81no—
477Dic3—122no—
478Dic3—121no—
479Dic3—121no—
480C32#205311yescharacteristic, complemented, Sylow
481C23—21no—
482C23—181no—
483C23D3×#6711yescharacteristic
484Q8—21no—
485Q8—21no—
486Q8—181no—
487Q8—181no—
488D4—21no—
489D4—21no—
490D4—41no—
491D4—41no—
492D4—181no—
493D4—181no—
494D4—361no—
495D4—361no—
496C2×C4—21no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—62no—
500C2×C4—121no—
501C2×C4—121no—
502C2×C4—181no—
503C2×C4—361no—
504C2×C4—361no—
505C2×C4#380411yescharacteristic
506C2×C4#380411yescharacteristic
507C2×C4#380411yescharacteristic
508C2×C4C2×#62611yescharacteristic
509C2×C4#381111yescharacteristic
510C2×C4#381111yescharacteristic
511C8—121no—
512C8—182no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—41no—
521C2×C3—41no—
522C2×C3—41no—
523C2×C3—82no—
524C2×C3—81no—
525C2×C3—81no—
526C2×C3#495911yescharacteristic
527C2×C3#496111yescharacteristic
528D3—242no—
529D3—241no—
530D3—241no—
531C22—41no—
532C22—41no—
533C22—81no—
534C22—361no—
535C22—721no—
536C22#6395811yescharacteristic
537C22#6397111yescharacteristic
538C22#6397811yescharacteristic
539C4—41no—
540C4—122no—
541C4—241no—
542C4—241no—
543C4—361no—
544C4#6395311yescharacteristic
545C4#6396611yescharacteristic
546C4#6397511yescharacteristic
547C4#6398111yescharacteristic
548C3—21no—
549C3#7004311yescharacteristic, complemented
550C3#7029611yescharacteristic, complemented
551C2—21no—
552C2—21no—
553C2—21no—
554C2—81no—
555C2—721no—
556C2#1059171211yescharacteristic
subgroupG/H
centerC4#63953
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#394
prime radical#10596293C2
hypercenterC2×#41D32
hypocenterC32#2053
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#5240C2semidirect
3. C3×#5233C2semidirect
4. #10591232C2semidirect
5. #10591116C2semidirect
6. #10591105C2semidirect
7. #10589157C2semidirect
34. #5240D3semidirect
35. #5233D3semidirect
480. C32#2053semidirect
549. C3#70043semidirect
550. C3#70296semidirect

Maximal subgroups

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

subgroupindex
#105962932
C3×#52402
C3×#52332
#105912322
#105911162
#105911052
#105891572
#702963
#700433