Finite Group Databasebeta

← #11895881

Subgroups — #11895881

Order 1152.

804 conjugacy classes of subgroups.

The subgroup lattice has 535 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593903C211yesmaximal, characteristic, complemented
2#10593879C211yesmaximal, characteristic, complemented
3#10592540C211yesmaximal, characteristic, complemented
4C3×#4846C211yesmaximal, characteristic, complemented
5C3×#4831C211yesmaximal, characteristic, complemented
6#10590895C212yesmaximal, complemented
7#10590860C212yesmaximal
8#10590805C212yesmaximal, complemented
9#10590773C212yesmaximal, complemented
10C4×#3714C211yesmaximal, characteristic
11#10590288C211yesmaximal, characteristic, complemented
12#80993—31nomaximal
13#79970—31nomaximal
14C2×#3797—21no—
15C2×#3744C2212yes—
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17#64078C2211yescharacteristic
18C3×C4×D12C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21#63918C2212yes—
22#63895—22no—
23#63894C2212yes—
24#63871—21no—
25#63861—22no—
26#63860C2212yes—
27#63856—21no—
28#63844C2212yes—
29#63841—21no—
30C2×#3714C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32#63643C2212yes—
33C3×#821C2212yes—
34C3×#818C2212yes—
35C3×#815C2212yes—
36C3×Dic3⋊C8C2212yes—
37C3×C4×C3⋊C8C2211yescharacteristic
38#63575C2211yescharacteristic
39#63567C2212yes—
40#63567C2212yes—
41#63564C2211yescharacteristic
42#63563C2211yescharacteristic
43#5727—31no—
44#5584—31no—
45Q8×D12—31no—
46#5542—31no—
47C3×#474—31no—
48C3×#446—31no—
49#5093—31no—
50C4×#213—31no—
51#4889—32no—
52#4875—32no—
53#4850—32no—
54#4846D311yescharacteristic, complemented
55#4844—32no—
56#4841—31no—
57#4841—31no—
58#4841—61no—
59#4831D311yescharacteristic, complemented
60#4787—32no—
61#4765—32no—
62#4714—32no—
63#4710—32no—
64C4×D24—31no—
65#4681—31no—
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×#634C2312yes—
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×#627—22no—
74C2×#624—22no—
75#3797—44no—
76C2×C32×C8C2312yes—
77C32×C42C2311yescharacteristic
78#3752—21no—
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82#3744—24no—
83C3×(C2×D3)⋊C4—21no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2311yescharacteristic
87C3×C4⋊Dic3C2312yes—
88C3×Dic3⋊C4D412yes—
89C3×C4×Dic3C2312yes—
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2311yescharacteristic
92#3724—22no—
93Dic3⋊Dic3—22no—
94#3722—22no—
95(C2×D3)⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97Dic32—22no—
98#3714—22no—
99#3367—91noSylow
100C2×D3×Q8—61no—
101C2×D3×Q8—61no—
102C3×C4⋊Q8—31no—
103C3×C4×Q8—31no—
104C3×C4×D4—31no—
105#946—61no—
106#946—61no—
107#936—32no—
108C2×#213—31no—
109#926—61no—
110#924—61no—
111C2×D24—31no—
112C2×#204—32no—
113C2×#204—32no—
114C2×#204—62no—
115#898—62no—
116#897—62no—
117#897—61no—
118#896—62no—
119#893—32no—
120#892—61no—
121#888—32no—
122#887—32no—
123#879—62no—
124#875—32no—
125C4×D12—31no—
126C4×D12—31no—
127C4×D12—32no—
128C4×D12—61no—
129C4×D12C2×D311yescharacteristic
130#869—32no—
131#869—31no—
132#869—31no—
133#869—61no—
134#869C2×D311yescharacteristic
135C4×Dic6—32no—
136C4×Dic6C2×D311yescharacteristic
137C3×#107—32no—
138C3×C4⋊C8—21no—
139C3×C4⋊C8—32no—
140C3×C4⋊C8C2×D311yescharacteristic
141C3×C4⋊C8C2×D311yescharacteristic
142C3×#102—32no—
143C3×#97—32no—
144C3×C4×C8—31no—
145#832—31no—
146#821—31no—
147#821—31no—
148#821C2×D312yes—
149#818—31no—
150#818C2×D312yes—
151#816—32no—
152#816—32no—
153#816—32no—
154#816—32no—
155#816—62no—
156#815C2×D312yes—
157Dic3⋊C8C2×D312yes—
158#810—32no—
159#810—32no—
160#809—31no—
161#807—31no—
162C4×C3⋊C8C2×D311yescharacteristic
163C22×C3⋊D3—21no—
164C22×C3×D3—21no—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—21no—
170C4⋊(C3⋊D3)—21no—
171C4⋊(C3⋊D3)#4112yes—
172C4×C3⋊D3—42no—
173#634—22no—
174#634—22no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×D412yes—
179C3×D12—21no—
180C3×D12—21no—
181C3×C4×D3—42no—
182C3×Dic6—22no—
183C3×Dic6—42no—
184#627—44no—
185#624—44no—
186C32×C8—22no—
187C3×C3⋊C8—21no—
188C3×C3⋊C8—21no—
189#556—91no—
190D4×Q8—91no—
191#489—92no—
192#487—91no—
193#477—92no—
194#474—31no—
195#463—92no—
196#461—91no—
197#446—31no—
198#440—92no—
199C4×D8—91no—
200C2×C3×Q8—31no—
201C2×C3×Q8—61no—
202C2×C3×D4—31no—
203C22×C3×C4—61no—
204D3×Q8—124no—
205D3×Q8—124no—
206C2×D12—31no—
207C2×D12—31no—
208C2×D12—61no—
209C2×D12C22×D311yescharacteristic
210C2×C4×D3—21no—
211C2×C4×D3—62no—
212C2×C4×D3—61no—
213C2×C4×D3—61no—
214C2×C4×D3—62no—
215C2×C4×D3—121no—
216C2×Dic6—21no—
217C2×Dic6—32no—
218C2×Dic6—32no—
219C2×Dic6—62no—
220C2×Dic6—62no—
221C2×Dic6—62no—
222C2×Dic6D1211yescharacteristic
223C2×C3×C8—22no—
224C2×C3×C8—31no—
225C2×C3×C8—31no—
226C2×C3×C8C22×D312yes—
227C2×C3×C8C22×D312yes—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—31no—
231C3×C4⋊C4—32no—
232C3×C4⋊C4—61no—
233C3×C22⋊C4—61no—
234C3×C42—21no—
235C3×C42—32no—
236C3×C42C22×D311yescharacteristic
237C3×C42C22×D311yescharacteristic
238#217—62no—
239#217—62no—
240#213—62no—
241(C2×D3)⋊C4—21no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—61no—
246(C2×D3)⋊C4—61no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—121no—
249C4⋊Dic3—21no—
250C4⋊Dic3—31no—
251C4⋊Dic3—31no—
252C4⋊Dic3—61no—
253C4⋊Dic3—62no—
254C4⋊Dic3—61no—
255C4⋊Dic3—61no—
256C4⋊Dic3—61no—
257C4⋊Dic3—61no—
258C4⋊Dic3—121no—
259C4⋊Dic3—121no—
260C4⋊Dic3D1211yescharacteristic
261C4⋊Dic3C22×D312yes—
262C4⋊Dic3C22×D311yescharacteristic
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4D1212yes—
267C4×Dic3—62no—
268C4×Dic3—62no—
269C4×Dic3C22×D312yes—
270C2×C3⋊C8C22×D311yescharacteristic
271C2×C3⋊C8C22×D311yescharacteristic
272D24—62no—
273#204—64no—
274#204—64no—
275#204—124no—
276C22×C32C22×D411yescharacteristic
277C2×C3⋊D3—22no—
278C2×C3⋊D3—41no—
279C2×C3⋊D3—41no—
280C2×C3×D3—41no—
281C2×C3×D3—41no—
282C2×C3×D3—41no—
283C32×C4—21no—
284C32×C4AGL(1,ℤ/8)12yes—
285C32×C4C2×#4111yescharacteristic
286C32×C42−1+411yescharacteristic
287C3⋊Dic3—42no—
288C3⋊Dic3—41no—
289C3×Dic3—22no—
290C3×Dic3—22no—
291C3×Dic3—42no—
292C3×Dic3—41no—
293C22×Q8—181no—
294C2×SD16—92no—
295C2×D8—91no—
296C4⋊Q8—31no—
297C4⋊Q8—92no—
298C4⋊Q8—91no—
299#126—182no—
300#124—92no—
301C22⋊Q8—182no—
302C22⋊Q8—181no—
303C22⋊Q8—181no—
304C4×Q8—31no—
305C4×Q8—92no—
306C4×D4—31no—
307C4×D4—92no—
308C4×D4—91no—
309#117—181no—
310#107—32no—
311#107—91no—
312C4⋊C8—32no—
313C4⋊C8D3211yescharacteristic
314#103—92no—
315#103—92no—
316#103—92no—
317#102—32no—
318#102—91no—
319#102—91no—
320#97—32no—
321C4×C8—31no—
322C23×C3—61no—
323C22×D3—21no—
324C22×D3—61no—
325C22×D3—61no—
326C22×D3—121no—
327C3×Q8—62no—
328C3×Q8—122no—
329C3×D4—61no—
330C3×D4—61no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—32no—
335C2×C3×C4—32no—
336C2×C3×C4—61no—
337C2×C3×C4—62no—
338C2×C3×C4—122no—
339C2×C3×C4C2×D1211yescharacteristic
340C2×C3×C4C2×D1211yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344C2×C3×C4C23×D311yescharacteristic
345C2×Dic3—21no—
346C2×Dic3—22no—
347C2×Dic3—62no—
348C2×Dic3—61no—
349C2×Dic3—62no—
350C2×Dic3—61no—
351C2×Dic3—121no—
352C2×Dic3—122no—
353C2×Dic3C2×D1212yes—
354C2×Dic3C2×D1212yes—
355D12—21no—
356D12—21no—
357D12—32no—
358D12—32no—
359D12—62no—
360D12—61no—
361D12—61no—
362D12—121no—
363C4×D3—42no—
364C4×D3—124no—
365C4×D3—124no—
366C4×D3—122no—
367C4×D3—122no—
368C4×D3—242no—
369Dic6—22no—
370Dic6—42no—
371Dic6—62no—
372Dic6—62no—
373Dic6—62no—
374Dic6—62no—
375Dic6—122no—
376Dic6—122no—
377Dic6—124no—
378Dic6—124no—
379C3×C8—22no—
380C3×C8—22no—
381C3×C8—42no—
382C3×C8—61no—
383C3×C8—61no—
384C3⋊C8—21no—
385C3⋊C8—21no—
386C2×C32#54811yescharacteristic
387C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
388C2×C32#57811yescharacteristic
389C3⋊D3—42no—
390C3×D3—81no—
391C2×Q8—31no—
392C2×Q8—61no—
393C2×Q8—92no—
394C2×Q8—182no—
395C2×Q8—364no—
396C2×D4—31no—
397C2×D4—91no—
398C22×C4—61no—
399C22×C4—182no—
400C22×C4—181no—
401SD16—184no—
402D8—182no—
403C2×C8—31no—
404C2×C8—31no—
405C2×C8C2×D3212yes—
406C4⋊C4—31no—
407C4⋊C4—32no—
408C4⋊C4—32no—
409C4⋊C4—31no—
410C4⋊C4—61no—
411C4⋊C4—91no—
412C4⋊C4—182no—
413C4⋊C4—182no—
414C4⋊C4—181no—
415C4⋊C4—181no—
416C22⋊C4—61no—
417C22⋊C4—182no—
418C22⋊C4—182no—
419C22⋊C4—182no—
420C22⋊C4—181no—
421C42—32no—
422C42—182no—
423C42C2×D3211yescharacteristic
424C22×C3—21no—
425C22×C3—121no—
426C22×C3—121no—
427C22×C3—121no—
428C22×C3C22×D1211yescharacteristic
429C22×C3C2×D3×D411yescharacteristic
430C2×D3—41no—
431C2×D3—41no—
432C2×D3—41no—
433C2×D3—62no—
434C2×D3—62no—
435C2×D3—122no—
436C2×D3—121no—
437C2×D3—121no—
438C2×D3—121no—
439C2×D3—121no—
440C2×D3—241no—
441C2×D3—241no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—22no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—41no—
448C3×C4—62no—
449C3×C4—62no—
450C3×C4—122no—
451C3×C4—121no—
452C3×C4#90812yes—
453C3×C4#91112yes—
454C3×C4#100711yescharacteristic
455C3×C4#100711yescharacteristic
456C3×C4D3×#4111yescharacteristic
457C3×C4D3×#4111yescharacteristic
458Dic3—22no—
459Dic3—22no—
460Dic3—42no—
461Dic3—41no—
462Dic3—122no—
463Dic3—121no—
464Dic3—121no—
465Dic3—122no—
466Dic3—242no—
467Dic3—241no—
468C32#336711yescharacteristic, complemented, Sylow
469C23—61no—
470C23—181no—
471Q8—62no—
472Q8—122no—
473Q8—182no—
474Q8—182no—
475Q8—364no—
476D4—61no—
477D4—61no—
478D4—92no—
479D4—181no—
480C2×C4—32no—
481C2×C4—32no—
482C2×C4—61no—
483C2×C4—62no—
484C2×C4—122no—
485C2×C4—182no—
486C2×C4—181no—
487C2×C4—364no—
488C2×C4—362no—
489C2×C4D3×D1211yescharacteristic
490C2×C4D3×D1211yescharacteristic
491C2×C4C22×D3211yescharacteristic
492C8—22no—
493C8—61no—
494C8—61no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—241no—
499C2×C3#557611yescharacteristic
500C2×C3#563311yescharacteristic
501C2×C3C2×#90811yescharacteristic
502C2×C3#575311yescharacteristic
503C2×C3C2×#91111yescharacteristic
504C2×C3#577911yescharacteristic
505D3—81no—
506D3—122no—
507D3—122no—
508D3—242no—
509C22—121no—
510C22—121no—
511C22—121no—
512C22—182no—
513C22—361no—
514C22—361no—
515C22C2×D3×D1211yescharacteristic
516C4—21no—
517C4—62no—
518C4—62no—
519C4—121no—
520C4—122no—
521C4—362no—
522C4—361no—
523C4#6379512yes—
524C4#6431211yescharacteristic
525C4#6431611yescharacteristic
526C3—21no—
527C3#7997011yescharacteristic, complemented
528C3#8099311yescharacteristic, complemented
529C2—241no—
530C2—362no—
531C2#1059432911yescharacteristic
532C2C2×#6379511yescharacteristic
533C2#1059472111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
hypercenterC4⋊C8D32
hypocenterC32#3367
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #10593903C2semidirect
2. #10593879C2semidirect
3. #10592540C2semidirect
4. C3×#4846C2semidirect
5. C3×#4831C2semidirect
6. #10590895C2semidirect
8. #10590805C2semidirect
9. #10590773C2semidirect
11. #10590288C2semidirect
54. #4846D3semidirect
59. #4831D3semidirect
468. C32#3367semidirect
527. C3#79970semidirect
528. C3#80993semidirect

Maximal subgroups

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

subgroupindex
#105939032
#105938792
#105925402
C3×#48462
C3×#48312
#105908952
#105908602
#105908052
#105907732
C4×#37142
#105902882
#809933
#799703