Finite Group Databasebeta

← #11793899

Subgroups — #11793899

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×#64141C211yesmaximal, characteristic
2C2×C3×#833C211yesmaximal, characteristic, complemented
3C2×C3×#832C211yesmaximal, characteristic, complemented
4C2×#63577C211yesmaximal, characteristic, complemented
5#10591106C211yesmaximal, characteristic, complemented
6#10591073C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#70196—31nomaximal
9#70092—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12C2×#3754—21no—
13#64141—22no—
14#64141—22no—
15C2×#3753—21no—
16C2×#3748C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#833—22no—
22C3×#832—22no—
23#63577—22no—
24#63567—21no—
25#63564—21no—
26#63557—22no—
27C2×#932—31no—
28C2×#932—31no—
29C2×#932—61no—
30C2×C3×#102—31no—
31C2×C3×#100—31no—
32C2×#833D311yescharacteristic, complemented
33C2×#832D311yescharacteristic, complemented
34#5133—31no—
35#5129—31no—
36C2×#822—31no—
37#5110—31no—
38C2×#819—31no—
39#4966—31no—
40#4554—31no—
41#4530—31no—
42C24×C32—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4D412yes—
49C22×C32×C4C2311yescharacteristic
50C2×#638—21no—
51#3828—21no—
52#3828—21no—
53#3828—21no—
54#3828—21no—
55C2×C4⋊(C3⋊D3)D411yescharacteristic
56C2×C4×C3⋊D3—21no—
57C2×#634D411yescharacteristic
58C22×C3×Dic3—21no—
59#3754—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
76C22×C3×D4—21no—
77C22×C3×D4C2×D311yescharacteristic
78C22×C3×D4C2×D311yescharacteristic
79C2×#235—31no—
80C2×#235—31no—
81C2×#235—61no—
82C2×C3×M16—31no—
83C2×C3×M16—31no—
84C22×C3×C8—31no—
85C2×C3×C4⋊C4—31no—
86C2×#214—61no—
87C2×#214—61no—
88C2×#214—62no—
89#932—62no—
90#932—62no—
91#932—64no—
92#932—64no—
93#932—62no—
94#932—62no—
95C2×#213—61no—
96C2×#213—61no—
97C2×#213—62no—
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×#208—31no—
100C2×#208—31no—
101C2×#208—61no—
102C2×#208C2×D311yescharacteristic
103C2×#208C2×D311yescharacteristic
104C22×C3⋊C8C2×D311yescharacteristic
105C3×#102—62no—
106C3×#100—62no—
107#833—22no—
108#832—22no—
109#822—62no—
110#821—61no—
111(C2×D3)⋊C8—62no—
112(C2×D3)⋊C8—62no—
113#819—62no—
114#816—61no—
115#810—61no—
116#809—61no—
117C23×C32—22no—
118C23×C32—41no—
119C23×C32—41no—
120C23×C32—81no—
121C23×C32—81no—
122C23×C32#4111yescharacteristic
123C22×C3⋊D3—21no—
124C32×D4—22no—
125C32×D4—22no—
126C32×D4—41no—
127C32×D4—41no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C32×C4#4111yescharacteristic
134#638—41no—
135#638—41no—
136C2×C3⋊Dic3—21no—
137C4⋊(C3⋊D3)—21no—
138C4⋊(C3⋊D3)—21no—
139C4×C3⋊D3—41no—
140C4×C3⋊D3—41no—
141#634—21no—
142#634—21no—
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—91no—
152C2×#102—31no—
153C2×#100—31no—
154#408—91no—
155#343—91no—
156C24×C3—21no—
157C24×C3—21no—
158C24×C3—41no—
159C2×C3×D4—22no—
160C2×C3×D4—22no—
161C2×C3×D4—21no—
162C2×C3×D4—21no—
163C2×C3×D4—21no—
164C2×C3×D4—21no—
165C2×C3×D4—21no—
166C2×C3×D4—21no—
167C2×C3×D4—21no—
168C2×C3×D4—21no—
169C2×C3×D4—21no—
170C2×C3×D4—21no—
171C2×C3×D4—22no—
172C2×C3×D4—41no—
173C2×C3×D4—41no—
174C2×C3×D4—41no—
175C2×C3×D4D1212yes—
176C2×C3×D4#6712yes—
177C22×C3×C4—21no—
178C22×C3×C4—61no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C2×#67—61no—
182C2×#67—61no—
183C2×#67—121no—
184C22×Dic3—21no—
185#235—62no—
186#235—62no—
187#235—61no—
188#235—61no—
189#235—61no—
190#235—61no—
191#235—61no—
192#235—61no—
193#235—61no—
194#235—61no—
195#235—121no—
196#235—121no—
197C2×D12—31no—
198C2×D12—31no—
199C2×D12—61no—
200C2×C4×D3—61no—
201C2×C4×D3—61no—
202C2×C4×D3—121no—
203C2×Dic6—31no—
204C2×Dic6—31no—
205C2×Dic6—61no—
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#214—68no—
218#214—64no—
219#214—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—42no—
246C22×C32—82no—
247C22×C32—82no—
248C22×C32—81no—
249C22×C32—81no—
250C22×C32#12111yescharacteristic
251C22×C32#12311yescharacteristic
252C22×C32#12411yescharacteristic
253C2×C3⋊D3—41no—
254C2×C3⋊D3—41no—
255C2×C3⋊D3—41no—
256C32×C4#12011yescharacteristic
257C32×C4#12111yescharacteristic
258C32×C4#12111yescharacteristic
259C32×C4#12311yescharacteristic
260C3⋊Dic3—41no—
261C3×Dic3—81no—
262C2×#41—91no—
263C22×D4D3211yescharacteristic
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—181no—
275#102—62no—
276#102—181no—
277#100—62no—
278C22⋊C8—182no—
279C23×C3—22no—
280C23×C3—22no—
281C23×C3—21no—
282C23×C3—42no—
283C23×C3—42no—
284C23×C3—42no—
285C23×C3—41no—
286C23×C3—41no—
287C23×C3—41no—
288C23×C3—41no—
289C23×C3—81no—
290C23×C3—81no—
291C23×C3—81no—
292C23×C3—81no—
293C23×C3—82no—
294C23×C3—82no—
295C23×C3#23511yescharacteristic
296C23×C3#23711yescharacteristic
297C22×D3—61no—
298C22×D3—61no—
299C22×D3—121no—
300C3×D4—24no—
301C3×D4—22no—
302C3×D4—22no—
303C3×D4—22no—
304C3×D4—22no—
305C3×D4—42no—
306C3×D4—42no—
307C3×D4—42no—
308C3×D4—41no—
309C3×D4—41no—
310C3×D4—41no—
311C3×D4—41no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—121no—
319C2×C3×C4—241no—
320C2×C3×C4C2×D1211yescharacteristic
321C2×C3×C4#23511yescharacteristic
322C2×C3×C4#23511yescharacteristic
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4#23711yescharacteristic
329C2×C3×C4#23711yescharacteristic
330C2×C3×C4C2×#6711yescharacteristic
331C2×C3×C4C2×#6711yescharacteristic
332#67—122no—
333#67—122no—
334#67—121no—
335#67—121no—
336#67—121no—
337#67—121no—
338C2×Dic3—41no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—81no—
342C2×Dic3—121no—
343D12—62no—
344D12—61no—
345D12—61no—
346D12—61no—
347D12—61no—
348D12—121no—
349C4×D3—122no—
350C4×D3—122no—
351C4×D3—121no—
352C4×D3—121no—
353C4×D3—121no—
354C4×D3—121no—
355Dic6—62no—
356Dic6—61no—
357Dic6—61no—
358Dic6—61no—
359Dic6—61no—
360Dic6—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—82no—
373C2×C32#39411yescharacteristic
374C2×C32#47111yescharacteristic
375C2×C32#47211yescharacteristic
376C3⋊D3—81no—
377C24—21no—
378#41—181no—
379#41—181no—
380#41—181no—
381#41—181no—
382C2×Q8—91no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—91no—
389C2×D4—181no—
390C2×D4#62612yes—
391C22×C4—61no—
392C22×C4—181no—
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—44no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—82no—
423C22×C3—82no—
424C22×C3—82no—
425C22×C3—82no—
426C22×C3—82no—
427C22×C3—82no—
428C22×C3—84no—
429C22×C3—84no—
430C22×C3—81no—
431C22×C3—81no—
432C22×C3—81no—
433C22×C3—81no—
434C22×C3#88411yescharacteristic
435C22×C3#88511yescharacteristic
436C22×C3#88511yescharacteristic
437C22×C3#88611yescharacteristic
438C22×C3#92911yescharacteristic
439C22×C3#93811yescharacteristic
440C2×D3—122no—
441C2×D3—121no—
442C2×D3—121no—
443C2×D3—121no—
444C2×D3—121no—
445C2×D3—121no—
446C2×D3—121no—
447C2×D3—241no—
448C2×D3—241no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—241no—
454C3×C4#88211yescharacteristic
455C3×C4#88311yescharacteristic
456C3×C4#88311yescharacteristic
457C3×C4#88411yescharacteristic
458C3×C4#93011yescharacteristic
459C3×C4#93711yescharacteristic
460C3×C4#93911yescharacteristic
461C3×C4#93911yescharacteristic
462Dic3—81no—
463Dic3—122no—
464Dic3—121no—
465Dic3—121no—
466C32#205111yescharacteristic, complemented, Sylow
467C23—22no—
468C23—41no—
469C23—41no—
470C23—81no—
471C23—81no—
472C23—181no—
473C23#380411yescharacteristic
474Q8—181no—
475Q8—181no—
476D4—22no—
477D4—22no—
478D4—41no—
479D4—41no—
480D4—181no—
481D4—181no—
482D4—361no—
483D4—361no—
484C2×C4—121no—
485C2×C4—181no—
486C2×C4—241no—
487C2×C4—361no—
488C2×C4—361no—
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—84no—
509C2×C3—82no—
510C2×C3—82no—
511C2×C3#474811yescharacteristic
512C2×C3#474911yescharacteristic
513C2×C3#495911yescharacteristic
514C2×C3#496111yescharacteristic
515C2×C3#516011yescharacteristic
516C2×C3#517711yescharacteristic
517D3—242no—
518D3—241no—
519D3—241no—
520C22—21no—
521C22—21no—
522C22—42no—
523C22—82no—
524C22—82no—
525C22—81no—
526C22—81no—
527C22—361no—
528C22—361no—
529C22—361no—
530C22#6395311yescharacteristic
531C22#6395811yescharacteristic
532C22#6396611yescharacteristic
533C4—241no—
534C4—361no—
535C4#6397111yescharacteristic
536C4#6397511yescharacteristic
537C4#6397811yescharacteristic
538C4#6398111yescharacteristic
539C3—21no—
540C3#7009211yescharacteristic, complemented
541C3#7019611yescharacteristic, complemented
542C2—21no—
543C2—21no—
544C2—82no—
545C2—721no—
546C2#1059140611yescharacteristic
547C2#1059140711yescharacteristic
548C2#1059171211yescharacteristic
subgroupG/H
centerC22#63958
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC22×C32#121
prime radicalC2×#64141C2
hypercenterC22×D4D32
hypocenterC32#2051
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#833C2semidirect
3. C2×C3×#832C2semidirect
4. C2×#63577C2semidirect
5. #10591106C2semidirect
6. #10591073C2semidirect
7. #10589167C2semidirect
32. C2×#833D3semidirect
33. C2×#832D3semidirect
466. C32#2051semidirect
540. C3#70092semidirect
541. C3#70196semidirect

Maximal subgroups

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

subgroupindex
C2×#641412
C2×C3×#8332
C2×C3×#8322
C2×#635772
#105911062
#105910732
#105891672
#701963
#700923