Finite Group Databasebeta

← #11793896

Subgroups — #11793896

Order 1152.

713 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64158C211yesmaximal, characteristic
2C3×#5234C211yesmaximal, characteristic, complemented
3C3×#5232C211yesmaximal, characteristic, complemented
4C2×#63577C211yesmaximal, characteristic, complemented
5C2×#63564C211yesmaximal, characteristic, complemented
6C2×#63559C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#70307—31nomaximal
9#70003—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12#64158—22no—
13#64158—22no—
14C2×#3755—21no—
15C2×#3753—21no—
16C2×#3748C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#835—21no—
22C3×#832—21no—
23C3×#830—22no—
24#63577—22no—
25#63564—22no—
26#63559—22no—
27C2×#949—31no—
28C2×#949—31no—
29C2×#949—61no—
30C3×#417—31no—
31C3×#408—31no—
32#5234D311yescharacteristic, complemented
33#5232D311yescharacteristic, complemented
34C2×#823—31no—
35C2×#823—31no—
36C2×#822—31no—
37C2×#821—31no—
38C2×#819—31no—
39C2×#809—31no—
40#4554—31no—
41#4530—31no—
42C23×C3⋊D3—21no—
43C32×#41—21no—
44C32×#41—21no—
45C32×#41—21no—
46C32×#41—21no—
47C2×C32×Q8D411yescharacteristic
48C2×C32×D4—21no—
49C2×C32×D4D411yescharacteristic
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)D412yes—
58C22×C3×Dic3—21no—
59#3755—24no—
60#3753—24no—
61#3748—21no—
62#3748D412yes—
63C2×C3⋊(C3⋊C8)—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×#208—21no—
67C3×#208—21no—
68C3×#208—21no—
69C3×#208—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8D412yes—
75#2051—91noSylow
76C2×C3×#41—21no—
77C2×C3×#41C2×D311yescharacteristic
78C2×C3×#41C2×D311yescharacteristic
79C22×D12—31no—
80C22×D12—31no—
81C22×D12—61no—
82C2×C3×M16—31no—
83C2×C3×M16—31no—
84C22×C3×C8—31no—
85C2×C3×C4⋊C4—31no—
86#949—62no—
87#949—62no—
88#949—62no—
89#949—62no—
90#949—64no—
91#949—64no—
92C2×#215—62no—
93C2×#215—61no—
94C2×#215—61no—
95C2×#213—62no—
96C2×#213—61no—
97C2×#213—61no—
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×#208—31no—
100C2×#208—31no—
101C2×#208—61no—
102C2×#208C2×D311yescharacteristic
103C2×#208C2×D311yescharacteristic
104C22×C3⋊C8C2×D311yescharacteristic
105C3×#103—61no—
106C3×#102—61no—
107C3×C22⋊C8—62no—
108#835—21no—
109#832—21no—
110#830—22no—
111#823—62no—
112#823—62no—
113#822—62no—
114#821—62no—
115#819—62no—
116#809—62no—
117C23×C32—21no—
118C23×C32#4111yescharacteristic
119C22×C3⋊D3—22no—
120C22×C3⋊D3—41no—
121C22×C3⋊D3—41no—
122C22×C3⋊D3—81no—
123C22×C3⋊D3—81no—
124C32×Q8—21no—
125C32×Q8—21no—
126C32×D4—21no—
127C32×D4—21no—
128C32×D4—41no—
129C32×D4—41no—
130C2×C32×C4—21no—
131C2×C32×C4—41no—
132C2×C32×C4—41no—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C32×C4#4111yescharacteristic
139C4⋊(C3⋊D3)—22no—
140C4⋊(C3⋊D3)—22no—
141C4⋊(C3⋊D3)—41no—
142C4⋊(C3⋊D3)—41no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—81no—
145C3⋊(C3⋊C8)—22no—
146C3×C3⋊C8—22no—
147C3×C3⋊C8—41no—
148C3×C3⋊C8—41no—
149C2×AGL(1,ℤ/8)—91no—
150C2×#108—91no—
151#417—31no—
152C2×#102—91no—
153C2×#100—91no—
154#408—31no—
155#343—91no—
156C23×D3—61no—
157C23×D3—61no—
158C23×D3—121no—
159C3×#41—22no—
160C3×#41—22no—
161C3×#41—21no—
162C3×#41—21no—
163C3×#41—21no—
164C3×#41—21no—
165C3×#41—21no—
166C3×#41—21no—
167C3×#41—21no—
168C3×#41—21no—
169C3×#41—41no—
170C3×#41—41no—
171C2×C3×Q8—21no—
172C2×C3×Q8D1211yescharacteristic
173C2×C3×Q8#6711yescharacteristic
174C2×C3×D4—21no—
175C2×C3×D4—21no—
176C2×C3×D4—21no—
177C2×C3×D4—41no—
178C2×C3×D4D1211yescharacteristic
179C2×C3×D4#6711yescharacteristic
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—41no—
184C22×C3×C4—61no—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C22×Dic3—21no—
188C2×D12—32no—
189C2×D12—32no—
190C2×D12—62no—
191C2×D12—62no—
192C2×D12—62no—
193C2×D12—61no—
194C2×D12—61no—
195C2×D12—61no—
196C2×D12—61no—
197C2×D12—61no—
198C2×D12—61no—
199C2×D12—61no—
200C2×D12—61no—
201C2×D12—61no—
202C2×D12—61no—
203C2×D12—121no—
204C2×D12—121no—
205C2×D12—121no—
206C3×M16—61no—
207C3×M16—61no—
208C3×M16—61no—
209C3×M16—61no—
210C2×C3×C8—32no—
211C2×C3×C8—61no—
212C2×C3×C8—61no—
213C2×C3×C8—61no—
214C2×C3×C8—61no—
215C3×C4⋊C4—61no—
216C3×C4⋊C4—61no—
217#215—68no—
218#215—64no—
219#215—64no—
220#213—68no—
221#213—64no—
222#213—64no—
223C4⋊Dic3—21no—
224C4⋊Dic3—21no—
225#208—21no—
226#208—21no—
227#208—21no—
228#208—21no—
229#208—32no—
230#208—32no—
231#208—62no—
232#208—62no—
233#208—61no—
234#208—61no—
235C2×C3⋊C8—21no—
236C2×C3⋊C8—21no—
237C2×C3⋊C8—21no—
238C2×C3⋊C8—21no—
239C2×C3⋊C8—62no—
240C2×C3⋊C8—61no—
241C2×C3⋊C8—61no—
242C2×C3⋊C8#6712yes—
243C22×C32—21no—
244C22×C32—21no—
245C22×C32—41no—
246C22×C32—41no—
247C22×C32—41no—
248C22×C32#12111yescharacteristic
249C22×C32#12311yescharacteristic
250C22×C32#12411yescharacteristic
251C2×C3⋊D3—42no—
252C2×C3⋊D3—82no—
253C2×C3⋊D3—81no—
254C2×C3⋊D3—81no—
255C2×C3⋊D3—82no—
256C32×C4—41no—
257C32×C4#12011yescharacteristic
258C32×C4#12111yescharacteristic
259C32×C4#12111yescharacteristic
260C32×C4#12311yescharacteristic
261C3×Dic3—81no—
262C2×#41D3211yescharacteristic
263C22×D4—91no—
264AGL(1,ℤ/8)—182no—
265AGL(1,ℤ/8)—182no—
266C2×SD16—181no—
267C2×D8—181no—
268C2×M16—31no—
269C2×M16—31no—
270C2×M16—91no—
271C22×C8—31no—
272C2×C4⋊C4—31no—
273#108—182no—
274#103—61no—
275#102—61no—
276#102—182no—
277#100—182no—
278C22⋊C8—62no—
279C23×C3—21no—
280C23×C3—21no—
281C23×C3—21no—
282C23×C3—41no—
283C23×C3#23511yescharacteristic
284C23×C3#23711yescharacteristic
285C22×D3—62no—
286C22×D3—62no—
287C22×D3—122no—
288C22×D3—122no—
289C22×D3—122no—
290C22×D3—121no—
291C22×D3—121no—
292C22×D3—121no—
293C22×D3—121no—
294C22×D3—242no—
295C22×D3—242no—
296C22×D3—241no—
297C22×D3—241no—
298C22×D3—241no—
299C22×D3—241no—
300C3×Q8—22no—
301C3×Q8—21no—
302C3×Q8—21no—
303C3×Q8—21no—
304C3×Q8—21no—
305C3×Q8—41no—
306C3×D4—22no—
307C3×D4—21no—
308C3×D4—21no—
309C3×D4—21no—
310C3×D4—21no—
311C3×D4—41no—
312C3×D4—42no—
313C3×D4—42no—
314C3×D4—41no—
315C3×D4—41no—
316C3×D4—41no—
317C3×D4—41no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—41no—
327C2×C3×C4—42no—
328C2×C3×C4—42no—
329C2×C3×C4—41no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—121no—
334C2×C3×C4—241no—
335C2×C3×C4C2×D1211yescharacteristic
336C2×C3×C4#23511yescharacteristic
337C2×C3×C4#23511yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4#23711yescharacteristic
344C2×C3×C4#23711yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×Dic3—41no—
348C2×Dic3—81no—
349D12—64no—
350D12—62no—
351D12—62no—
352D12—62no—
353D12—62no—
354D12—122no—
355D12—122no—
356D12—122no—
357D12—121no—
358D12—121no—
359D12—121no—
360D12—121no—
361C3×C8—62no—
362C3×C8—121no—
363C3×C8—121no—
364C3⋊C8—22no—
365C3⋊C8—41no—
366C3⋊C8—41no—
367C3⋊C8—64no—
368C3⋊C8—62no—
369C3⋊C8—62no—
370C2×C32—21no—
371C2×C32—21no—
372C2×C32—81no—
373C2×C32#39411yescharacteristic
374C2×C32#47111yescharacteristic
375C2×C32#47211yescharacteristic
376C3⋊D3—82no—
377C24—181no—
378#41—21no—
379#41—21no—
380#41—21no—
381#41—21no—
382C2×Q8#62611yescharacteristic
383C2×D4—21no—
384C2×D4—92no—
385C2×D4—181no—
386C2×D4—181no—
387C2×D4—181no—
388C2×D4—181no—
389C2×D4—181no—
390C2×D4#62611yescharacteristic
391C22×C4—21no—
392C22×C4—61no—
393C22×C4C2×D3211yescharacteristic
394SD16—184no—
395D8—184no—
396M16—61no—
397M16—61no—
398M16—61no—
399M16—61no—
400M16—92no—
401M16—181no—
402C2×C8—32no—
403C2×C8—61no—
404C2×C8—61no—
405C2×C8—61no—
406C2×C8—61no—
407C2×C8—181no—
408C4⋊C4—61no—
409C4⋊C4—61no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3—42no—
420C22×C3—41no—
421C22×C3—41no—
422C22×C3—41no—
423C22×C3—41no—
424C22×C3—41no—
425C22×C3—41no—
426C22×C3—81no—
427C22×C3—81no—
428C22×C3#88311yescharacteristic
429C22×C3#88311yescharacteristic
430C22×C3#88511yescharacteristic
431C22×C3#88511yescharacteristic
432C22×C3#93011yescharacteristic
433C22×C3#93911yescharacteristic
434C2×D3—124no—
435C2×D3—122no—
436C2×D3—122no—
437C2×D3—242no—
438C2×D3—242no—
439C2×D3—242no—
440C2×D3—242no—
441C2×D3—244no—
442C2×D3—244no—
443C2×D3—241no—
444C2×D3—241no—
445C2×D3—241no—
446C2×D3—241no—
447C2×D3—242no—
448C2×D3—242no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—42no—
454C3×C4—41no—
455C3×C4—41no—
456C3×C4—241no—
457C3×C4#88211yescharacteristic
458C3×C4#88411yescharacteristic
459C3×C4#88411yescharacteristic
460C3×C4#88611yescharacteristic
461C3×C4#92911yescharacteristic
462C3×C4#93711yescharacteristic
463C3×C4#93811yescharacteristic
464C3×C4#93911yescharacteristic
465Dic3—81no—
466C32#205111yescharacteristic, complemented, Sylow
467C23—21no—
468C23—182no—
469C23—361no—
470C23—361no—
471C23—721no—
472C23—721no—
473C23#380411yescharacteristic
474Q8—21no—
475Q8—21no—
476D4—21no—
477D4—21no—
478D4—41no—
479D4—41no—
480D4—182no—
481D4—182no—
482D4—361no—
483D4—361no—
484C2×C4—21no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—121no—
488C2×C4—241no—
489C2×C4#380411yescharacteristic
490C2×C4#380411yescharacteristic
491C2×C4C2×#62611yescharacteristic
492C2×C4D3×#6711yescharacteristic
493C2×C4#381111yescharacteristic
494C2×C4#381111yescharacteristic
495C8—62no—
496C8—121no—
497C8—121no—
498C8—182no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—41no—
507C2×C3—41no—
508C2×C3—82no—
509C2×C3—81no—
510C2×C3—81no—
511C2×C3#495911yescharacteristic
512C2×C3#496111yescharacteristic
513C2×C3#514111yescharacteristic
514C2×C3#514211yescharacteristic
515C2×C3#519911yescharacteristic
516C2×C3#520311yescharacteristic
517D3—244no—
518D3—242no—
519D3—242no—
520C22—21no—
521C22—21no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22—362no—
526C22—722no—
527C22—722no—
528C22—721no—
529C22—721no—
530C22#6395311yescharacteristic
531C22#6397511yescharacteristic
532C22#6397811yescharacteristic
533C4—41no—
534C4—241no—
535C4#6395811yescharacteristic
536C4#6396611yescharacteristic
537C4#6397111yescharacteristic
538C4#6398111yescharacteristic
539C3—21no—
540C3#7000311yescharacteristic, complemented
541C3#7030711yescharacteristic, complemented
542C2—21no—
543C2—21no—
544C2—81no—
545C2—722no—
546C2#1059167711yescharacteristic
547C2#1059168011yescharacteristic
548C2#1059171211yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC22×C32#121
prime radicalC2×#64158C2
hypercenterC2×#41D32
hypocenterC32#2051
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#5234C2semidirect
3. C3×#5232C2semidirect
4. C2×#63577C2semidirect
5. C2×#63564C2semidirect
6. C2×#63559C2semidirect
7. #10589167C2semidirect
32. #5234D3semidirect
33. #5232D3semidirect
466. C32#2051semidirect
540. C3#70003semidirect
541. C3#70307semidirect

Maximal subgroups

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

subgroupindex
C2×#641582
C3×#52342
C3×#52322
C2×#635772
C2×#635642
C2×#635592
#105891672
#703073
#700033