Finite Group Databasebeta

← #11877005

Subgroups — #11877005

Order 1152.

941 conjugacy classes of subgroups.

The subgroup lattice has 515 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5725C211yesmaximal, characteristic, complemented
2#10593897C211yesmaximal, characteristic, complemented
3#10592779C211yesmaximal, characteristic, complemented
4C3×#5088C211yesmaximal, characteristic, complemented
5#10590504C214yesmaximal, complemented
6#10590455C214yesmaximal, complemented
7#10590352C211yesmaximal, characteristic, complemented
8C4×#3711C211yesmaximal, characteristic, complemented
9#10590273C211yesmaximal, characteristic, complemented
10#83295—31nomaximal
11#81560—31nomaximal
12C2×C3×#239—21no—
13C2×#3795—21no—
14C32×C4⋊Q8C2211yescharacteristic
15#64078C2211yescharacteristic
16C3×#947—21no—
17C3×#895—21no—
18C3×#895C2212yes—
19C3×#893—21no—
20C3×#893C2212yes—
21C3×#874C2211yescharacteristic
22C3×#874C2211yescharacteristic
23C3×C42×D3C2211yescharacteristic
24#63908—21no—
25#63908C2212yes—
26Dic3×D12—21no—
27Dic3×D12C2212yes—
28#63860—21no—
29C2×#3713C2214yes—
30C2×#3711C2212yes—
31#63635C2214yes—
32C4×C3⋊(C3⋊C8)C2211yescharacteristic
33C3×#809C2214yes—
34C3×C4×C3⋊C8C2211yescharacteristic
35#63563C2214yes—
36#63554C2212yes—
37C3×#532—31no—
38#5725D311yescharacteristic, complemented
39#5716—31no—
40#5477—31no—
41C3×#486—31no—
42#5088D311yescharacteristic, complemented
43#5080—31no—
44#5080—31no—
45#5080—61no—
46#5073—31no—
47#5073—31no—
48#5070—31no—
49#5039—34no—
50#5014—34no—
51C4×#208—31no—
52#4785—34no—
53#4782—34no—
54#4694—31no—
55C4×ΓL(1,𝔽25)—31no—
56C2×C32×Q8—21no—
57C2×#634—21no—
58C3×#239—44no—
59C2×C3×D12—22no—
60C2×C3×D12—21no—
61C2×C3×D12—21no—
62C2×C3×D12—21no—
63C2×C3×D12—21no—
64C2×C3×D12C2312yes—
65C2×C3×D12C2312yes—
66C2×C3×C4×D3—22no—
67C2×C3×C4×D3D411yescharacteristic
68C2×C3×C4×D3D411yescharacteristic
69C2×C3×C4×D3C2311yescharacteristic
70C2×#625—22no—
71C2×D3×Dic3—22no—
72#3795—44no—
73C32×C4⋊C4—21no—
74C32×C4⋊C4C2312yes—
75C32×C42C2311yescharacteristic
76C4⋊(C3⋊Dic3)—21no—
77C4⋊(C3⋊Dic3)C2312yes—
78C2×C3⋊(C3⋊C8)C2312yes—
79C3×(C2×D3)⋊C4—22no—
80C3×(C2×D3)⋊C4—22no—
81C3×C4×Dic3D411yescharacteristic
82C3×C4×Dic3D411yescharacteristic
83C3×C4×Dic3C2311yescharacteristic
84C2×C3×C3⋊C8C2312yes—
85(C2×D3)⋊Dic3—22no—
86(C2×D3)⋊Dic3—22no—
87#3713—28no—
88#3711—24no—
89#3184—91noSylow
90C2×C3×#41—61no—
91C2×#239—21no—
92C2×#237—61no—
93C2×#235—61no—
94C3×C4⋊Q8—21no—
95C3×C4⋊Q8C2×D311yescharacteristic
96C3×C4⋊Q8C2×D311yescharacteristic
97C3×#127—31no—
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#938—32no—
107#938—61no—
108#936—61no—
109D4×Dic3—32no—
110D4×Dic3—61no—
111C2×#213—34no—
112C2×#213—34no—
113#930—32no—
114#930—61no—
115C2×#208—32no—
116C2×ΓL(1,𝔽25)—32no—
117#895—21no—
118#895C2×D312yes—
119#893—21no—
120#893C2×D312yes—
121#875—61no—
122#874C2×D311yescharacteristic
123#874C2×D311yescharacteristic
124C4×D12—32no—
125C4×D12—61no—
126C42×D3C2×D311yescharacteristic
127#869—31no—
128#869—31no—
129#869—61no—
130C3×#102—34no—
131C3×C4×C8—31no—
132#832—34no—
133#821—34no—
134#815—32no—
135#809C2×D314yes—
136#808—34no—
137#808—34no—
138#808—64no—
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
152C2×C3⋊Dic3—22no—
153#634—42no—
154C2×C3×Dic3C2×D411yescharacteristic
155C2×C3×Dic3C2×D411yescharacteristic
156C2×C3×Dic3C2×D411yescharacteristic
157C3×D12—24no—
158C3×D12—24no—
159C3×D12—44no—
160C3×D12—42no—
161C3×D12—42no—
162C3×D12—42no—
163C3×D12—42no—
164C3×C4×D3—22no—
165C3×C4×D3—22no—
166C3×C4×D3—22no—
167C3×C4×D3—44no—
168#625—44no—
169D3×Dic3—44no—
170C3⋊(C3⋊C8)#4114yescomplemented
171C3×C3⋊C8—22no—
172#532—31no—
173#532—91no—
174#498—91no—
175#493—91no—
176#486—31no—
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×D4—32no—
186C2×C3×D4—32no—
187C2×C3×D4—62no—
188C2×C3×D4—61no—
189C2×C3×D4—61no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C22×C3×C4—31no—
193C22×C3×C4—31no—
194C22×C3×C4—31no—
195C22×C3×C4—62no—
196C2×#67—62no—
197C2×#67—62no—
198C22×Dic3—62no—
199#239—44no—
200#237—124no—
201#235—124no—
202C2×D12—22no—
203C2×D12—21no—
204C2×D12—21no—
205C2×D12—21no—
206C2×D12—21no—
207C2×D12C22×D312yes—
208C2×D12C22×D312yes—
209C2×C4×D3—22no—
210C2×C4×D3—62no—
211C2×C4×D3#6711yescharacteristic
212C2×C4×D3#6711yescharacteristic
213C2×C4×D3C22×D311yescharacteristic
214C2×Dic6—61no—
215C2×Dic6—61no—
216C2×Dic6—121no—
217C2×C3×C8—32no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—22no—
221C3×C4⋊C4—41no—
222C3×C4⋊C4C22×D312yes—
223C3×C4⋊C4C22×D312yes—
224C3×C22⋊C4—62no—
225C3×C22⋊C4—62no—
226C3×C42—21no—
227C3×C42—31no—
228C3×C42—31no—
229C3×C42—31no—
230C3×C42C22×D311yescharacteristic
231C3×C42C22×D311yescharacteristic
232#217—62no—
233#217—62no—
234#213—68no—
235#213—68no—
236(C2×D3)⋊C4—22no—
237(C2×D3)⋊C4—22no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—62no—
240C4⋊Dic3—32no—
241C4⋊Dic3—32no—
242C4⋊Dic3—62no—
243C4⋊Dic3—61no—
244C4⋊Dic3—61no—
245C4⋊Dic3—121no—
246C4×Dic3#6711yescharacteristic
247C4×Dic3#6711yescharacteristic
248C4×Dic3C22×D311yescharacteristic
249#208—64no—
250C2×C3⋊C8—32no—
251C2×C3⋊C8—32no—
252C2×C3⋊C8—62no—
253C2×C3⋊C8C22×D312yes—
254ΓL(1,𝔽25)—64no—
255C22×C32C22×D411yescharacteristic
256C2×C3×D3—21no—
257C2×C3×D3—21no—
258C2×C3×D3—21no—
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—42no—
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—42no—
270C3×Dic3—21no—
271C3×Dic3—21no—
272C3×Dic3—21no—
273C2×#41—61no—
274C2×#41—181no—
275C2×D8—94no—
276C2×M16—92no—
277C4⋊Q8—91no—
278C4⋊Q8D3211yescharacteristic
279#127—31no—
280#127—31no—
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—94no—
293#102—34no—
294#102—94no—
295#97—92no—
296C4×C8—31no—
297C4×C8—91no—
298C23×C3—31no—
299C23×C3—62no—
300C23×C3—62no—
301C22×D3—22no—
302C22×D3—22no—
303C22×D3C2×#6711yescharacteristic
304C3×Q8—42no—
305C3×Q8—42no—
306C3×Q8—82no—
307C3×D4—64no—
308C3×D4—64no—
309C3×D4—124no—
310C3×D4—122no—
311C3×D4—122no—
312C3×D4—122no—
313C3×D4—122no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—31no—
320C2×C3×C4—31no—
321C2×C3×C4—31no—
322C2×C3×C4—42no—
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—
334#67—124no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—122no—
338C2×Dic3—124no—
339C2×Dic3C2×#6711yescharacteristic
340C2×Dic3C2×#6711yescharacteristic
341C2×Dic3C2×#6711yescharacteristic
342D12—24no—
343D12—24no—
344D12—44no—
345D12—42no—
346D12—42no—
347D12—42no—
348D12—42no—
349C4×D3—22no—
350C4×D3—22no—
351C4×D3—22no—
352C4×D3—44no—
353C4×D3—124no—
354Dic6—122no—
355Dic6—122no—
356Dic6—242no—
357C3×C8—62no—
358C3⋊C8—22no—
359C3⋊C8—34no—
360C3⋊C8—34no—
361C3⋊C8—64no—
362C2×C32#53211yescharacteristic
363C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
364C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
365C3×D3—41no—
366C3×D3—82no—
367C3×D3—82no—
368#41—124no—
369#41—364no—
370C2×Q8—21no—
371C2×Q8—181no—
372C2×D4—32no—
373C2×D4—32no—
374C2×D4—62no—
375C2×D4—61no—
376C2×D4—61no—
377C2×D4—61no—
378C2×D4—61no—
379C2×D4—182no—
380C22×C4—31no—
381C22×C4—31no—
382C22×C4—31no—
383C22×C4—62no—
384C22×C4—182no—
385D8—188no—
386M16—184no—
387C2×C8—32no—
388C2×C8—92no—
389C4⋊C4—21no—
390C4⋊C4—92no—
391C4⋊C4—181no—
392C4⋊C4C2×D3212yes—
393C22⋊C4—62no—
394C22⋊C4—62no—
395C22⋊C4—182no—
396C22⋊C4—182no—
397C42—31no—
398C42—31no—
399C42—31no—
400C42C2×D3211yescharacteristic
401C22×C3—21no—
402C22×C3—61no—
403C22×C3—61no—
404C22×C3—61no—
405C22×C3—122no—
406C22×C3—122no—
407C22×C3—122no—
408C22×C3—122no—
409C22×C3—122no—
410C22×C3—122no—
411C22×C3C2×D3×D411yescharacteristic
412C22×C3C22×#6711yescharacteristic
413C2×D3—21no—
414C2×D3—21no—
415C2×D3—21no—
416C2×D3—42no—
417C2×D3—42no—
418C2×D3—42no—
419C2×D3—42no—
420C2×D3—42no—
421C2×D3—42no—
422C3×C4—22no—
423C3×C4—22no—
424C3×C4—22no—
425C3×C4—42no—
426C3×C4—42no—
427C3×C4—61no—
428C3×C4—61no—
429C3×C4—61no—
430C3×C4—82no—
431C3×C4#91112yes—
432C3×C4#91412yes—
433C3×C4#93212yes—
434C3×C4#94912yes—
435C3×C4D3×#4112yes—
436C3×C4D3×#4112yes—
437Dic3—21no—
438Dic3—21no—
439Dic3—21no—
440Dic3—122no—
441Dic3—122no—
442Dic3—242no—
443C32#318411yescharacteristic, complemented, Sylow
444C23—31no—
445C23—62no—
446C23—62no—
447Q8—42no—
448Q8—362no—
449D4—64no—
450D4—64no—
451D4—124no—
452D4—122no—
453D4—122no—
454D4—122no—
455D4—122no—
456D4—364no—
457C2×C4—22no—
458C2×C4—31no—
459C2×C4—31no—
460C2×C4—31no—
461C2×C4—62no—
462C2×C4—62no—
463C2×C4—62no—
464C2×C4—124no—
465C2×C4—182no—
466C2×C4—364no—
467C2×C4D3×#6711yescharacteristic
468C2×C4D3×#6711yescharacteristic
469C2×C4C22×D3211yescharacteristic
470C8—62no—
471C8—94no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—121no—
476C2×C3—242no—
477C2×C3—242no—
478C2×C3#566811yescharacteristic
479C2×C3C2×#91111yescharacteristic
480C2×C3C2×#91411yescharacteristic
481C2×C3C2×#93211yescharacteristic
482C2×C3C2×#94911yescharacteristic
483C2×C3#583211yescharacteristic
484D3—41no—
485D3—82no—
486D3—82no—
487C22—61no—
488C22—61no—
489C22—61no—
490C22—122no—
491C22—122no—
492C22—122no—
493C22—122no—
494C22—122no—
495C22—122no—
496C22C2×D3×#6711yescharacteristic
497C4—42no—
498C4—61no—
499C4—61no—
500C4—61no—
501C4—362no—
502C4#6393212yes—
503C4#6393912yes—
504C4#6431912yes—
505C3—21no—
506C3#8156011yescharacteristic, complemented
507C3#8329511yescharacteristic, complemented
508C2—121no—
509C2—242no—
510C2—242no—
511C2C2×#6393211yescharacteristic
512C2C2×#6393911yescharacteristic
513C2#1059535911yescharacteristic
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. #10593897C2semidirect
3. #10592779C2semidirect
4. C3×#5088C2semidirect
5. #10590504C2semidirect
6. #10590455C2semidirect
7. #10590352C2semidirect
8. C4×#3711C2semidirect
9. #10590273C2semidirect
38. #5725D3semidirect
42. #5088D3semidirect
170. C3⋊(C3⋊C8)#41semidirect
443. C32#3184semidirect
506. C3#81560semidirect
507. C3#83295semidirect

Maximal subgroups

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

subgroupindex
C3×#57252
#105938972
#105927792
C3×#50882
#105905042
#105904552
#105903522
C4×#37112
#105902732
#832953
#815603