Finite Group Databasebeta

← #11793857

Subgroups — #11793857

Order 1152.

663 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596293C211yesmaximal, characteristic
2C3×#5237C211yesmaximal, characteristic, complemented
3C2×C3×#837C211yesmaximal, characteristic, complemented
4#10591115C211yesmaximal, characteristic, complemented
5C2×#63570C211yesmaximal, characteristic, complemented
6#10591078C211yesmaximal, characteristic, complemented
7#10589159C211yesmaximal, characteristic, complemented
8#70379—31nomaximal
9#70144—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12#64160—21no—
13#64159—22no—
14#64158—21no—
15#64151—21no—
16#64141—21no—
17C2×#3748C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C3×#837—21no—
23C3×#837—21no—
24C3×#836—21no—
25C3×#833—21no—
26Dic3⋊(C3⋊C8)—22no—
27#63570—21no—
28#63570—21no—
29#63561—21no—
30#63559—21no—
31#5822—31no—
32#5822—31no—
33#5822—61no—
34C2×C3×#104—31no—
35C3×#413—31no—
36#5237D311yescharacteristic, complemented
37C2×#837D311yescharacteristic, complemented
38C2×#825—31no—
39#5132—31no—
40#5132—31no—
41#5118—31no—
42C2×#805—31no—
43#4924—31no—
44C3⋊#338—31no—
45C3⋊#338—31no—
46C32×#41—21no—
47C32×#41—21no—
48C32×#41—21no—
49C32×#41—21no—
50C2×C32×Q8D411yescharacteristic
51C2×C32×D4—21no—
52C2×C32×D4D411yescharacteristic
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C2×#638—21no—
56#3828—21no—
57#3828—21no—
58#3828—21no—
59#3828—21no—
60C2×C4⋊(C3⋊D3)D411yescharacteristic
61C2×C4×C3⋊D3—21no—
62C2×#634D411yescharacteristic
63C22×C3×Dic3—21no—
64#3756—22no—
65#3755—22no—
66#3754—22no—
67#3753—22no—
68#3748—21no—
69#3748—21no—
70C2×C3⋊(C3⋊C8)D412yes—
71C3×C4×Dic3—21no—
72C3×C4×Dic3D411yescharacteristic
73C3×C4×Dic3D411yescharacteristic
74C3×#208—21no—
75C3×#208—21no—
76C3×#208—21no—
77C3×#208—21no—
78C3×#208—21no—
79C3×#208—21no—
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8—21no—
83#2050—91noSylow
84C2×C3×#41—21no—
85C2×C3×#41C2×D311yescharacteristic
86C2×C3×#41C2×D311yescharacteristic
87C2×#235—31no—
88C2×#235—31no—
89C2×#235—61no—
90C2×C3×M16—31no—
91C2×C3×M16—31no—
92C2×C3×M16—31no—
93C2×C3×C42—31no—
94#951—61no—
95#951—61no—
96#951—62no—
97#950—62no—
98#950—62no—
99#950—64no—
100#949—61no—
101#949—61no—
102#949—62no—
103#942—62no—
104#942—61no—
105#942—61no—
106#932—62no—
107#932—61no—
108#932—61no—
109C2×C4×Dic3C2×D311yescharacteristic
110C2×#208—31no—
111C2×#208—31no—
112C2×#208—61no—
113C2×#208C2×D311yescharacteristic
114C2×#208C2×D311yescharacteristic
115C2×#208C2×D311yescharacteristic
116C3×#104—61no—
117C3×#104—61no—
118C3×#101—61no—
119C3×#100—61no—
120#837—21no—
121#837—21no—
122#836—21no—
123#833—21no—
124#825—61no—
125#825—61no—
126#824—61no—
127#824—61no—
128#823—61no—
129#823—61no—
130Dic3⋊C8—62no—
131#805—61no—
132#805—61no—
133C4⋊(C3⋊C8)—62no—
134C23×C32—21no—
135C23×C32#4111yescharacteristic
136C22×C3⋊D3—21no—
137C32×Q8—21no—
138C32×Q8—21no—
139C32×D4—21no—
140C32×D4—21no—
141C32×D4—41no—
142C32×D4—41no—
143C2×C32×C4—21no—
144C2×C32×C4—41no—
145C2×C32×C4—41no—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4#4111yescharacteristic
151C2×C32×C4#4111yescharacteristic
152#638—41no—
153#638—41no—
154C2×C3⋊Dic3—21no—
155C4⋊(C3⋊D3)—21no—
156C4⋊(C3⋊D3)—21no—
157C4×C3⋊D3—41no—
158C4×C3⋊D3—41no—
159#634—21no—
160#634—21no—
161C2×C3×Dic3—21no—
162C2×C3×Dic3—21no—
163C2×C3×Dic3—42no—
164C3⋊(C3⋊C8)—22no—
165C3×C3⋊C8—41no—
166C3×C3⋊C8—41no—
167C3×C3⋊C8—41no—
168#575—91no—
169#423—91no—
170C2×#104—31no—
171C2×#104—91no—
172#413—31no—
173#413—91no—
174#338—91no—
175C3×#41—22no—
176C3×#41—22no—
177C3×#41—21no—
178C3×#41—21no—
179C3×#41—21no—
180C3×#41—21no—
181C3×#41—21no—
182C3×#41—21no—
183C3×#41—21no—
184C3×#41—21no—
185C3×#41—41no—
186C3×#41—41no—
187C2×C3×Q8—21no—
188C2×C3×Q8D1211yescharacteristic
189C2×C3×Q8#6711yescharacteristic
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4—41no—
194C2×C3×D4D1211yescharacteristic
195C2×C3×D4#6711yescharacteristic
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—41no—
200C22×C3×C4—61no—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C2×#67—61no—
204C2×#67—61no—
205C2×#67—121no—
206C22×Dic3—21no—
207#235—62no—
208#235—62no—
209#235—61no—
210#235—61no—
211#235—61no—
212#235—61no—
213#235—61no—
214#235—61no—
215#235—61no—
216#235—61no—
217#235—121no—
218#235—121no—
219C2×D12—31no—
220C2×D12—31no—
221C2×D12—61no—
222C2×C4×D3—61no—
223C2×C4×D3—61no—
224C2×C4×D3—121no—
225C2×Dic6—31no—
226C2×Dic6—31no—
227C2×Dic6—61no—
228C3×M16—61no—
229C3×M16—61no—
230C3×M16—61no—
231C3×M16—61no—
232C3×M16—61no—
233C3×M16—61no—
234C2×C3×C8—61no—
235C2×C3×C8—61no—
236C2×C3×C8—61no—
237C3×C42—31no—
238C3×C42—31no—
239C3×C42—61no—
240#216—64no—
241#216—62no—
242#216—62no—
243#215—64no—
244#215—62no—
245#215—62no—
246#214—64no—
247#214—62no—
248#214—62no—
249#213—64no—
250#213—62no—
251#213—62no—
252C4×Dic3—21no—
253C4×Dic3#6711yescharacteristic
254C4×Dic3#6711yescharacteristic
255#208—21no—
256#208—21no—
257#208—21no—
258#208—21no—
259#208—21no—
260#208—21no—
261#208—62no—
262#208—62no—
263#208—61no—
264#208—61no—
265#208—61no—
266#208—61no—
267C2×C3⋊C8—21no—
268C2×C3⋊C8—21no—
269C2×C3⋊C8—21no—
270C2×C3⋊C8—32no—
271C2×C3⋊C8—32no—
272C2×C3⋊C8—62no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32—81no—
276C22×C32#12111yescharacteristic
277C22×C32#12311yescharacteristic
278C22×C32#12311yescharacteristic
279C2×C3⋊D3—41no—
280C2×C3⋊D3—81no—
281C32×C4—41no—
282C32×C4#12011yescharacteristic
283C32×C4#12111yescharacteristic
284C32×C4#12111yescharacteristic
285C32×C4#12411yescharacteristic
286C3⋊Dic3—41no—
287C3×Dic3—22no—
288C3×Dic3—41no—
289C2×#41—91no—
290C2×#41D3211yescharacteristic
291#137—181no—
292#137—181no—
293AGL(1,ℤ/8)—181no—
294AGL(1,ℤ/8)—181no—
295#135—182no—
296C2×M16—31no—
297C2×M16—31no—
298C2×M16—31no—
299C2×M16—91no—
300C2×C42—31no—
301C4⋊C8—182no—
302#104—61no—
303#104—61no—
304#104—181no—
305#104—181no—
306#101—61no—
307#101—181no—
308#100—61no—
309#100—181no—
310C23×C3—21no—
311C23×C3—21no—
312C23×C3—21no—
313C23×C3—41no—
314C23×C3#23511yescharacteristic
315C23×C3#23711yescharacteristic
316C22×D3—61no—
317C22×D3—61no—
318C22×D3—121no—
319C3×Q8—22no—
320C3×Q8—21no—
321C3×Q8—21no—
322C3×Q8—21no—
323C3×Q8—21no—
324C3×Q8—41no—
325C3×D4—22no—
326C3×D4—21no—
327C3×D4—21no—
328C3×D4—21no—
329C3×D4—21no—
330C3×D4—41no—
331C3×D4—42no—
332C3×D4—42no—
333C3×D4—41no—
334C3×D4—41no—
335C3×D4—41no—
336C3×D4—41no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—41no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—122no—
355C2×C3×C4C2×D1211yescharacteristic
356C2×C3×C4#23511yescharacteristic
357C2×C3×C4#23511yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4#23711yescharacteristic
364C2×C3×C4#23711yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C2×#6711yescharacteristic
367#67—122no—
368#67—122no—
369#67—121no—
370#67—121no—
371#67—121no—
372#67—121no—
373C2×Dic3—21no—
374C2×Dic3—21no—
375C2×Dic3—42no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378C2×Dic3—121no—
379D12—62no—
380D12—61no—
381D12—61no—
382D12—61no—
383D12—61no—
384D12—121no—
385C4×D3—122no—
386C4×D3—122no—
387C4×D3—121no—
388C4×D3—121no—
389C4×D3—121no—
390C4×D3—121no—
391Dic6—62no—
392Dic6—61no—
393Dic6—61no—
394Dic6—61no—
395Dic6—61no—
396Dic6—121no—
397C3×C8—121no—
398C3×C8—121no—
399C3×C8—121no—
400C3⋊C8—41no—
401C3⋊C8—41no—
402C3⋊C8—41no—
403C3⋊C8—64no—
404C3⋊C8—62no—
405C3⋊C8—62no—
406C2×C32—21no—
407C2×C32—21no—
408C2×C32—21no—
409C2×C32—81no—
410C2×C32#39411yescharacteristic
411C3⋊D3—81no—
412#41—21no—
413#41—21no—
414#41—21no—
415#41—21no—
416#41—181no—
417#41—181no—
418#41—181no—
419#41—181no—
420C2×Q8—91no—
421C2×Q8#62611yescharacteristic
422C2×D4—21no—
423C2×D4—91no—
424C2×D4—181no—
425C2×D4#62611yescharacteristic
426C22×C4—21no—
427C22×C4—61no—
428C22×C4—181no—
429C22×C4C2×D3211yescharacteristic
430Q16—182no—
431SD16—182no—
432SD16—182no—
433D8—182no—
434M16—61no—
435M16—61no—
436M16—61no—
437M16—61no—
438M16—61no—
439M16—61no—
440M16—181no—
441M16—181no—
442C2×C8—61no—
443C2×C8—61no—
444C2×C8—61no—
445C2×C8—92no—
446C42—31no—
447C42—31no—
448C42—61no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—41no—
453C22×C3—41no—
454C22×C3—42no—
455C22×C3—41no—
456C22×C3—41no—
457C22×C3—81no—
458C22×C3—81no—
459C22×C3—81no—
460C22×C3—82no—
461C22×C3#88311yescharacteristic
462C22×C3#88311yescharacteristic
463C22×C3#88411yescharacteristic
464C22×C3#88611yescharacteristic
465C22×C3#92911yescharacteristic
466C22×C3#93911yescharacteristic
467C2×D3—122no—
468C2×D3—121no—
469C2×D3—121no—
470C2×D3—242no—
471C2×D3—241no—
472C2×D3—241no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—21no—
477C3×C4—42no—
478C3×C4—41no—
479C3×C4—41no—
480C3×C4—62no—
481C3×C4—121no—
482C3×C4#88211yescharacteristic
483C3×C4#88411yescharacteristic
484C3×C4#88511yescharacteristic
485C3×C4#88511yescharacteristic
486C3×C4#93011yescharacteristic
487C3×C4#93711yescharacteristic
488C3×C4#93811yescharacteristic
489C3×C4#93911yescharacteristic
490Dic3—22no—
491Dic3—41no—
492Dic3—122no—
493Dic3—121no—
494Dic3—121no—
495C32#205011yescharacteristic, complemented, Sylow
496C23—21no—
497C23—181no—
498C23#380411yescharacteristic
499Q8—21no—
500Q8—21no—
501Q8—181no—
502Q8—181no—
503D4—21no—
504D4—21no—
505D4—41no—
506D4—41no—
507D4—181no—
508D4—181no—
509D4—361no—
510D4—361no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—61no—
515C2×C4—61no—
516C2×C4—122no—
517C2×C4—181no—
518C2×C4—361no—
519C2×C4—361no—
520C2×C4#380411yescharacteristic
521C2×C4#380411yescharacteristic
522C2×C4C2×#62611yescharacteristic
523C2×C4D3×#6711yescharacteristic
524C2×C4#381111yescharacteristic
525C2×C4#381111yescharacteristic
526C8—121no—
527C8—121no—
528C8—121no—
529C8—182no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—41no—
538C2×C3—41no—
539C2×C3—41no—
540C2×C3—82no—
541C2×C3—81no—
542C2×C3—81no—
543C2×C3#495911yescharacteristic
544C2×C3#496111yescharacteristic
545D3—242no—
546D3—241no—
547D3—241no—
548C22—41no—
549C22—41no—
550C22—81no—
551C22—361no—
552C22—721no—
553C22#6396611yescharacteristic
554C22#6397111yescharacteristic
555C22#6397511yescharacteristic
556C4—41no—
557C4—62no—
558C4—121no—
559C4—361no—
560C4#6395311yescharacteristic
561C4#6395811yescharacteristic
562C4#6397811yescharacteristic
563C4#6398111yescharacteristic
564C3—21no—
565C3#7014411yescharacteristic, complemented
566C3#7037911yescharacteristic, complemented
567C2—21no—
568C2—21no—
569C2—21no—
570C2—81no—
571C2—721no—
572C2#1059171211yescharacteristic
subgroupG/H
centerC4#63953
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#394
prime radical#10596293C2
hypercenterC2×#41D32
hypocenterC32#2050
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×#5237C2semidirect
3. C2×C3×#837C2semidirect
4. #10591115C2semidirect
5. C2×#63570C2semidirect
6. #10591078C2semidirect
7. #10589159C2semidirect
36. #5237D3semidirect
37. C2×#837D3semidirect
495. C32#2050semidirect
565. C3#70144semidirect
566. C3#70379semidirect

Maximal subgroups

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

subgroupindex
#105962932
C3×#52372
C2×C3×#8372
#105911152
C2×#635702
#105910782
#105891592
#703793
#701443