Finite Group Databasebeta

← #11877007

Subgroups — #11877007

Order 1152.

951 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5725C211yesmaximal, characteristic, complemented
2#10593970C211yesmaximal, characteristic, complemented
3#10592787C211yesmaximal, characteristic, complemented
4C3×#5080C211yesmaximal, characteristic, complemented
5#10590589C214yesmaximal, complemented
6#10590586C214yesmaximal, complemented
7#10590350C211yesmaximal, characteristic, complemented
8C4×#3711C211yesmaximal, characteristic, complemented
9#10590277C211yesmaximal, characteristic, complemented
10#83295—31nomaximal
11#81888—31nomaximal
12C2×C3×#239—21no—
13C2×#3799—21no—
14C32×C4⋊Q8C2211yescharacteristic
15#64083C2211yescharacteristic
16C3×#947—21no—
17C3×#895—21no—
18C3×#895C2212yes—
19C3×#893—21no—
20C3×#893C2212yes—
21C3×#874C2211yescharacteristic
22C3×C42×D3C2211yescharacteristic
23C3×#869C2211yescharacteristic
24#63909—21no—
25#63909C2212yes—
26#63894—21no—
27#63894C2212yes—
28#63864—21no—
29C2×#3714C2214yes—
30C2×#3711C2212yes—
31#63636C2214yes—
32C4×C3⋊(C3⋊C8)C2211yescharacteristic
33C3×#808C2214yes—
34C3×C4×C3⋊C8C2211yescharacteristic
35#63562C2214yes—
36#63554C2212yes—
37C3×#532—31no—
38#5725—31no—
39#5725D311yescharacteristic, complemented
40#5477—31no—
41C3×#498—31no—
42#5088—31no—
43#5088—31no—
44#5088—31no—
45#5088—61no—
46#5080D311yescharacteristic, complemented
47#5073—31no—
48#5070—31no—
49#5039—34no—
50#5014—34no—
51C4×#208—31no—
52#4869—34no—
53#4865—34no—
54#4695—31no—
55C4×ΓL(1,𝔽25)—31no—
56C2×C32×Q8—21no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)C2312yes—
60C3×#239—44no—
61C2×C3×D12—22no—
62C2×C3×D12—21no—
63C2×C3×D12—21no—
64C2×C3×D12C2312yes—
65C2×C3×C4×D3—22no—
66C2×C3×C4×D3D411yescharacteristic
67C2×C3×C4×D3D411yescharacteristic
68C2×C3×C4×D3C2311yescharacteristic
69C2×C3×Dic6—21no—
70C2×#626—22no—
71C2×#624—22no—
72#3799—44no—
73C32×C4⋊C4—21no—
74C32×C4⋊C4C2312yes—
75C32×C42C2311yescharacteristic
76C2×C3⋊(C3⋊C8)C2312yes—
77C3×(C2×D3)⋊C4—22no—
78C3×(C2×D3)⋊C4—22no—
79C3×C4⋊Dic3—21no—
80C3×C4⋊Dic3C2312yes—
81C3×C4×Dic3D411yescharacteristic
82C3×C4×Dic3D411yescharacteristic
83C3×C4×Dic3C2311yescharacteristic
84C2×C3×C3⋊C8C2312yes—
85#3722—22no—
86#3722—22no—
87#3714—28no—
88#3711—24no—
89#3184—91noSylow
90C2×C3×#41—61no—
91C2×#239—21no—
92C2×#239—61no—
93C2×#235—61no—
94C3×C4⋊Q8—21no—
95C3×C4⋊Q8—31no—
96C3×C4⋊Q8C2×D311yescharacteristic
97C3×C4⋊Q8C2×D311yescharacteristic
98C3×#127—31no—
99C3×#124—61no—
100C3×#121—32no—
101C3×#121—61no—
102C3×C4×D4—32no—
103C3×C4×D4—61no—
104C2×C3×C42—31no—
105#947—21no—
106#947—61no—
107C2×#213—34no—
108#930—32no—
109#930—61no—
110C2×#208—32no—
111C2×D24—34no—
112C2×ΓL(1,𝔽25)—32no—
113#895—21no—
114#895—32no—
115#895—61no—
116#895C2×D312yes—
117#893—21no—
118#893—32no—
119#893—61no—
120#893C2×D312yes—
121#875—61no—
122#874—31no—
123#874—31no—
124#874—61no—
125#874C2×D311yescharacteristic
126C4×D12—32no—
127C4×D12—61no—
128C42×D3C2×D311yescharacteristic
129#869C2×D311yescharacteristic
130C3×#106—34no—
131C3×C4×C8—31no—
132#832—34no—
133#815—32no—
134#809—34no—
135#809—34no—
136#809—34no—
137#809—64no—
138#808C2×D314yes—
139#803—32no—
140C4×C3⋊C8—31no—
141C4×C3⋊C8—31no—
142C4×C3⋊C8—61no—
143C4×C3⋊C8C2×D311yescharacteristic
144C22×C3⋊D3—22no—
145C22×C3×D3—22no—
146C22×C3×D3C2×D411yescharacteristic
147C32×Q8—42no—
148C2×C32×C4—22no—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2411yescharacteristic
152C4⋊(C3⋊D3)—24no—
153C4⋊(C3⋊D3)—42no—
154C4⋊(C3⋊D3)—42no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3C2×D411yescharacteristic
157C2×C3×Dic3C2×D411yescharacteristic
158C2×C3×Dic3C2×D411yescharacteristic
159C3×D12—24no—
160C3×D12—44no—
161C3×D12—42no—
162C3×D12—42no—
163C3×C4×D3—22no—
164C3×C4×D3—22no—
165C3×C4×D3—22no—
166C3×C4×D3—44no—
167C3×Dic6—42no—
168#626—44no—
169#624—44no—
170C3⋊(C3⋊C8)—22no—
171C3×C3⋊C8#4114yescomplemented
172#532—31no—
173#532—91no—
174#498—31no—
175#493—91no—
176#486—91no—
177#486—91no—
178#469—94no—
179#442—94no—
180C4×M16—91no—
181C3×#41—124no—
182C2×C3×Q8—21no—
183C2×C3×Q8—21no—
184C2×C3×Q8—41no—
185C2×C3×Q8—61no—
186C2×C3×D4—32no—
187C2×C3×D4—62no—
188C2×C3×D4—61no—
189C2×C3×D4—61no—
190C22×C3×C4—31no—
191C22×C3×C4—31no—
192C22×C3×C4—31no—
193C22×C3×C4—62no—
194C2×#67—62no—
195#239—44no—
196#239—124no—
197#235—124no—
198C2×D12—22no—
199C2×D12—21no—
200C2×D12—21no—
201C2×D12—32no—
202C2×D12—32no—
203C2×D12—62no—
204C2×D12—62no—
205C2×D12—61no—
206C2×D12—61no—
207C2×D12—61no—
208C2×D12—61no—
209C2×D12—121no—
210C2×D12—121no—
211C2×D12C22×D312yes—
212C2×C4×D3—22no—
213C2×C4×D3—62no—
214C2×C4×D3—62no—
215C2×C4×D3#6711yescharacteristic
216C2×C4×D3#6711yescharacteristic
217C2×C4×D3C22×D311yescharacteristic
218C2×Dic6—21no—
219C2×C3×C8—32no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—41no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4C22×D312yes—
227C3×C4⋊C4C22×D312yes—
228C3×C22⋊C4—62no—
229C3×C22⋊C4—62no—
230C3×C42—21no—
231C3×C42—31no—
232C3×C42—31no—
233C3×C42—31no—
234C3×C42C22×D311yescharacteristic
235C3×C42C22×D311yescharacteristic
236#213—68no—
237(C2×D3)⋊C4—22no—
238(C2×D3)⋊C4—22no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—62no—
243C4⋊Dic3—21no—
244C4⋊Dic3C22×D312yes—
245C4×Dic3#6711yescharacteristic
246C4×Dic3#6711yescharacteristic
247C4×Dic3C22×D311yescharacteristic
248#208—64no—
249C2×C3⋊C8—32no—
250C2×C3⋊C8—32no—
251C2×C3⋊C8—62no—
252C2×C3⋊C8C22×D312yes—
253D24—68no—
254ΓL(1,𝔽25)—64no—
255C22×C32C22×D411yescharacteristic
256C2×C3⋊D3—42no—
257C2×C3⋊D3—42no—
258C2×C3⋊D3—42no—
259C2×C3×D3—21no—
260C2×C3×D3—21no—
261C2×C3×D3—21no—
262C2×C3×D3—42no—
263C2×C3×D3—42no—
264C2×C3×D3—42no—
265C32×C4—42no—
266C32×C4AGL(1,ℤ/8)12yes—
267C32×C4AGL(1,ℤ/8)12yes—
268C32×C4C2×#4112yes—
269C3×Dic3—21no—
270C3×Dic3—21no—
271C3×Dic3—21no—
272C3×Dic3—42no—
273C2×#41—61no—
274C2×#41—181no—
275C2×D8—94no—
276C2×M16—92no—
277C4⋊Q8—31no—
278C4⋊Q8D3211yescharacteristic
279#127—31no—
280#127—91no—
281#124—61no—
282#124—181no—
283#121—32no—
284#121—61no—
285#121—92no—
286#121—181no—
287C4×D4—32no—
288C4×D4—61no—
289C4×D4—92no—
290C4×D4—181no—
291C2×C42—31no—
292#106—34no—
293#102—94no—
294#102—94no—
295#97—92no—
296C4×C8—31no—
297C4×C8—91no—
298C23×C3—31no—
299C23×C3—62no—
300C22×D3—22no—
301C22×D3—62no—
302C22×D3—62no—
303C22×D3—122no—
304C22×D3C2×#6711yescharacteristic
305C3×Q8—42no—
306C3×Q8—42no—
307C3×Q8—82no—
308C3×Q8—122no—
309C3×D4—64no—
310C3×D4—124no—
311C3×D4—122no—
312C3×D4—122no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—31no—
319C2×C3×C4—31no—
320C2×C3×C4—31no—
321C2×C3×C4—42no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—124no—
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4C2×#6711yescharacteristic
330C2×C3×C4C2×#6711yescharacteristic
331C2×C3×C4C23×D311yescharacteristic
332C2×C3×C4C23×D311yescharacteristic
333#67—124no—
334C2×Dic3—22no—
335C2×Dic3C2×#6711yescharacteristic
336C2×Dic3C2×#6711yescharacteristic
337C2×Dic3C2×#6711yescharacteristic
338D12—24no—
339D12—44no—
340D12—42no—
341D12—42no—
342D12—64no—
343D12—64no—
344D12—124no—
345D12—124no—
346D12—122no—
347D12—122no—
348D12—122no—
349D12—122no—
350D12—242no—
351D12—242no—
352C4×D3—22no—
353C4×D3—22no—
354C4×D3—22no—
355C4×D3—44no—
356C4×D3—124no—
357C4×D3—124no—
358Dic6—42no—
359C3×C8—34no—
360C3⋊C8—62no—
361C3⋊C8—62no—
362C3⋊C8—122no—
363C3⋊C8#23914yescomplemented
364C2×C32#53211yescharacteristic
365C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
366C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
367C3⋊D3—82no—
368C3×D3—41no—
369C3×D3—82no—
370#41—124no—
371#41—364no—
372C2×Q8—21no—
373C2×Q8—61no—
374C2×D4—32no—
375C2×D4—62no—
376C2×D4—61no—
377C2×D4—61no—
378C2×D4—92no—
379C2×D4—182no—
380C2×D4—181no—
381C2×D4—181no—
382C22×C4—31no—
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—62no—
386C22×C4—182no—
387D8—188no—
388M16—184no—
389C2×C8—32no—
390C2×C8—92no—
391C4⋊C4—21no—
392C4⋊C4—32no—
393C4⋊C4—61no—
394C4⋊C4C2×D3212yes—
395C22⋊C4—62no—
396C22⋊C4—62no—
397C22⋊C4—182no—
398C22⋊C4—182no—
399C42—31no—
400C42—31no—
401C42—31no—
402C42C2×D3211yescharacteristic
403C22×C3—21no—
404C22×C3—61no—
405C22×C3—61no—
406C22×C3—61no—
407C22×C3—122no—
408C22×C3—122no—
409C22×C3—122no—
410C22×C3C2×D3×D411yescharacteristic
411C22×C3C22×#6711yescharacteristic
412C2×D3—21no—
413C2×D3—21no—
414C2×D3—21no—
415C2×D3—42no—
416C2×D3—42no—
417C2×D3—42no—
418C2×D3—122no—
419C2×D3—122no—
420C2×D3—122no—
421C2×D3—122no—
422C2×D3—122no—
423C2×D3—122no—
424C2×D3—242no—
425C2×D3—242no—
426C2×D3—242no—
427C3×C4—22no—
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—42no—
431C3×C4—42no—
432C3×C4—61no—
433C3×C4—61no—
434C3×C4—61no—
435C3×C4—82no—
436C3×C4—122no—
437C3×C4#91412yes—
438C3×C4#91412yes—
439C3×C4#93212yes—
440C3×C4#94912yes—
441C3×C4C2×#23912yes—
442C3×C4D3×#4112yes—
443Dic3—21no—
444Dic3—21no—
445Dic3—21no—
446Dic3—42no—
447C32#318411yescharacteristic, complemented, Sylow
448C23—31no—
449C23—62no—
450C23—182no—
451Q8—42no—
452Q8—122no—
453D4—64no—
454D4—124no—
455D4—122no—
456D4—122no—
457D4—184no—
458D4—364no—
459D4—362no—
460D4—362no—
461C2×C4—22no—
462C2×C4—31no—
463C2×C4—31no—
464C2×C4—31no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—124no—
470C2×C4—364no—
471C2×C4D3×#6711yescharacteristic
472C2×C4D3×#6711yescharacteristic
473C2×C4C22×D3211yescharacteristic
474C8—34no—
475C8—182no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—121no—
480C2×C3—242no—
481C2×C3#572511yescharacteristic
482C2×C3C2×#91411yescharacteristic
483C2×C3C2×#91411yescharacteristic
484C2×C3C2×#93211yescharacteristic
485C2×C3C2×#94911yescharacteristic
486C2×C3#583211yescharacteristic
487D3—41no—
488D3—82no—
489D3—242no—
490D3—242no—
491D3—482no—
492C22—61no—
493C22—61no—
494C22—61no—
495C22—122no—
496C22—122no—
497C22—122no—
498C22—362no—
499C22—362no—
500C22—362no—
501C22C2×D3×#6711yescharacteristic
502C4—42no—
503C4—61no—
504C4—61no—
505C4—61no—
506C4—122no—
507C4#6393412yes—
508C4#6393912yes—
509C4D3×#23912yes—
510C3—21no—
511C3#8188811yescharacteristic, complemented
512C3#8329511yescharacteristic, complemented
513C2—121no—
514C2—242no—
515C2—722no—
516C2C2×#6393411yescharacteristic
517C2C2×#6393911yescharacteristic
518C2#1059536011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
hypercenterC4⋊Q8D32
hypocenterC32#3184
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5725C2semidirect
2. #10593970C2semidirect
3. #10592787C2semidirect
4. C3×#5080C2semidirect
5. #10590589C2semidirect
6. #10590586C2semidirect
7. #10590350C2semidirect
8. C4×#3711C2semidirect
9. #10590277C2semidirect
39. #5725D3semidirect
46. #5080D3semidirect
171. C3×C3⋊C8#41semidirect
363. C3⋊C8#239semidirect
447. C32#3184semidirect
511. C3#81888semidirect
512. C3#83295semidirect

Maximal subgroups

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

subgroupindex
C3×#57252
#105939702
#105927872
C3×#50802
#105905892
#105905862
#105903502
C4×#37112
#105902772
#832953
#818883