Finite Group Databasebeta

← #11878708

Subgroups — #11878708

Order 1152.

915 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593909C211yesmaximal, characteristic, complemented
2#10593907C211yesmaximal, characteristic
3#10592384C211yesmaximal, characteristic, complemented
4C3×#4693C211yesmaximal, characteristic, complemented
5C3×#4681C211yesmaximal, characteristic, complemented
6#10590824C214yesmaximal, complemented
7#10590748C214yesmaximal, complemented
8#10590375C211yesmaximal, characteristic, complemented
9#10590290C211yesmaximal, characteristic, complemented
10#81764—31nomaximal
11#81602—31nomaximal
12C2×#3797C2212yes—
13C2×#3796—21no—
14C42×C3⋊D3C2211yescharacteristic
15C2×C3×#204C2214yes—
16C3×#874C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×#869C2211yescharacteristic
20#63919—21no—
21#63919—21no—
22#63916—21no—
23#63916C2212yes—
24#63900—21no—
25#63900—21no—
26#63898—21no—
27#63898C2212yes—
28#63873C2212yes—
29#63863—21no—
30C2×#3715C2214yes—
31C32×C4×C8C2211yescharacteristic
32#63647C2212yes—
33#63641C2212yes—
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#816C2214yes—
36#63565C2214yes—
37#5725—31no—
38D3×C4⋊Q8—31no—
39D3×C4⋊Q8—31no—
40#5716—31no—
41C3×#492—31no—
42C3×#487—31no—
43#5170—34no—
44#5162—34no—
45#5093—31no—
46#5085—31no—
47#5079—31no—
48#5076—31no—
49#4818—34no—
50#4806—34no—
51#4693D311yescharacteristic, complemented
52#4685—31no—
53#4685—31no—
54#4685—61no—
55#4681D311yescharacteristic, complemented
56C2×C4×C3⋊D3D411yescharacteristic
57C2×C4×C3⋊D3D411yescharacteristic
58C2×C4×C3⋊D3C2311yescharacteristic
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12C2312yes—
62C2×C3×Dic6—21no—
63C2×C3×Dic6C2312yes—
64C2×C3×Dic6C2312yes—
65C2×#627—22no—
66C2×#626—22no—
67C2×#624—22no—
68C2×D3×Dic3—22no—
69#3797—44no—
70#3796—44no—
71C2×C32×C8C2312yes—
72C32×C42C2311yescharacteristic
73C4×C3⋊Dic3D411yescharacteristic
74C4×C3⋊Dic3D411yescharacteristic
75C4×C3⋊Dic3C2311yescharacteristic
76C2×C3⋊(C3⋊C8)C2312yes—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3—21no—
79C3×C4⋊Dic3—21no—
80C3×C4⋊Dic3—21no—
81C3×C4⋊Dic3—21no—
82C3×C4⋊Dic3C2312yes—
83C3×#204—44no—
84#3724—22no—
85#3724—22no—
86(C2×D3)⋊Dic3—22no—
87(C2×D3)⋊Dic3—22no—
88#3715—44no—
89#3206—91noSylow
90C2×#239—61no—
91C2×D3×Q8—32no—
92C2×D3×Q8—32no—
93C2×#237—61no—
94C2×C3×SD16—34no—
95C3×C4⋊Q8—31no—
96C3×C4⋊Q8—31no—
97C3×C4⋊Q8—31no—
98C3×#127—31no—
99#947—61no—
100#944—32no—
101#944—32no—
102C2×#215—34no—
103#938—32no—
104#938—61no—
105#936—61no—
106D4×Dic3—32no—
107D4×Dic3—61no—
108C2×#214—34no—
109C2×#204C2×D314yes—
110#895—32no—
111#895—61no—
112#893—32no—
113#893—61no—
114D3×C4⋊C4—61no—
115D3×C4⋊C4—61no—
116D3×C4⋊C4—61no—
117D3×C4⋊C4—61no—
118#888—61no—
119#888—61no—
120#888—61no—
121#888—61no—
122#874C2×D311yescharacteristic
123C42×D3—31no—
124C42×D3—31no—
125C42×D3—61no—
126#869C2×D311yescharacteristic
127#869C2×D311yescharacteristic
128#869C2×D311yescharacteristic
129C3×#103—34no—
130C3×C4×C8—21no—
131C3×C4×C8C2×D311yescharacteristic
132C3×C4×C8C2×D311yescharacteristic
133#835—34no—
134(C2×D3)⋊C8—32no—
135(C2×D3)⋊C8—32no—
136(C2×D3)⋊C8—62no—
137#816C2×D314yes—
138Dic3⋊C8—32no—
139Dic3⋊C8—32no—
140Dic3⋊C8—62no—
141#810—34no—
142C4×C3⋊C8—31no—
143C4×C3⋊C8—31no—
144C4×C3⋊C8—61no—
145C22×C3⋊D3C2×D411yescharacteristic
146C22×C3×D3—22no—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2411yescharacteristic
150C2×C3⋊Dic3C2×D411yescharacteristic
151C2×C3⋊Dic3C2×D411yescharacteristic
152C2×C3⋊Dic3C2×D411yescharacteristic
153C4×C3⋊D3—22no—
154C4×C3⋊D3—22no—
155C4×C3⋊D3SD1614yescomplemented
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C3×D12—24no—
160C3×D12—42no—
161C3×D12—42no—
162C3×Dic6—24no—
163C3×Dic6—24no—
164C3×Dic6—42no—
165#627—44no—
166#626—44no—
167#624—44no—
168D3×Dic3—44no—
169C32×C8—22no—
170C3⋊(C3⋊C8)—22no—
171#532—91no—
172C2×C4⋊Q8—91no—
173#492—31no—
174#492—91no—
175#487—31no—
176#487—91no—
177#461—94no—
178#448—94no—
179#431—91no—
180C2×C3×Q8—32no—
181C2×C3×Q8—32no—
182C2×C3×Q8—61no—
183C2×C3×D4—32no—
184C2×C3×D4—61no—
185C2×C3×D4—61no—
186C2×#67—62no—
187C22×Dic3—62no—
188#239—124no—
189D3×Q8—124no—
190D3×Q8—124no—
191#237—124no—
192C2×D12—21no—
193C2×D12—21no—
194C2×D12—62no—
195C2×D12C22×D312yes—
196C2×C4×D3—31no—
197C2×C4×D3—31no—
198C2×C4×D3—31no—
199C2×C4×D3—31no—
200C2×C4×D3—31no—
201C2×C4×D3—31no—
202C2×C4×D3—61no—
203C2×C4×D3—61no—
204C2×C4×D3—61no—
205C2×C4×D3—62no—
206C2×C4×D3—62no—
207C2×C4×D3—62no—
208C2×Dic6—21no—
209C2×Dic6—62no—
210C2×Dic6—62no—
211C2×Dic6C22×D312yes—
212C2×Dic6C22×D312yes—
213C3×SD16—124no—
214C2×C3×C8—22no—
215C2×C3×C8C22×D312yes—
216C2×C3×C8C22×D312yes—
217C3×C4⋊C4—32no—
218C3×C4⋊C4—61no—
219C3×C4⋊C4—61no—
220C3×C4⋊C4—61no—
221C3×C4⋊C4—61no—
222C3×C4⋊C4—61no—
223C3×C42—21no—
224C3×C42C22×D311yescharacteristic
225C3×C42C22×D311yescharacteristic
226#217—62no—
227#217—62no—
228#215—124no—
229#214—124no—
230(C2×D3)⋊C4—62no—
231(C2×D3)⋊C4—62no—
232C4⋊Dic3—21no—
233C4⋊Dic3—21no—
234C4⋊Dic3—21no—
235C4⋊Dic3—21no—
236C4⋊Dic3—21no—
237C4⋊Dic3C22×D312yes—
238Dic3⋊C4—62no—
239Dic3⋊C4—62no—
240Dic3⋊C4—62no—
241Dic3⋊C4—62no—
242C4×Dic3—31no—
243C4×Dic3—31no—
244C4×Dic3—31no—
245C4×Dic3—31no—
246C4×Dic3—31no—
247C4×Dic3—31no—
248C4×Dic3—61no—
249C4×Dic3—61no—
250C4×Dic3—61no—
251C2×C3⋊C8—32no—
252C2×C3⋊C8—32no—
253C2×C3⋊C8—62no—
254#204—44no—
255C22×C32C22×D411yescharacteristic
256C2×C3⋊D3—21no—
257C2×C3⋊D3—21no—
258C2×C3⋊D3C2×SD1612yes—
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—42no—
262C32×C4C2×SD1612yes—
263C32×C4#13712yes—
264C32×C4H(5,𝔽2)12yes—
265C3⋊Dic3—21no—
266C3⋊Dic3—21no—
267C3⋊Dic3C2×SD1612yes—
268C3×Dic3—42no—
269C3×Dic3—42no—
270C3×Dic3—42no—
271C2×#41—181no—
272C22×Q8—92no—
273C2×SD16—34no—
274C2×SD16—94no—
275C4⋊Q8—31no—
276C4⋊Q8—31no—
277C4⋊Q8—31no—
278C4⋊Q8—92no—
279C4⋊Q8—181no—
280C4⋊Q8—181no—
281#127—31no—
282#124—181no—
283#121—92no—
284#121—181no—
285C4×D4—92no—
286C4×D4—181no—
287C2×C4⋊C4—181no—
288C2×C4⋊C4—181no—
289C2×C42—91no—
290C4⋊C8—92no—
291#103—34no—
292#103—94no—
293C22⋊C8—92no—
294C4×C8—91no—
295C4×C8D3211yescharacteristic
296C23×C3—62no—
297C22×D3—22no—
298C22×D3—31no—
299C22×D3—31no—
300C22×D3—61no—
301C3×Q8—64no—
302C3×Q8—64no—
303C3×Q8—122no—
304C3×D4—64no—
305C3×D4—122no—
306C3×D4—122no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—62no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4D3×D411yescharacteristic
317C2×C3×C4C23×D311yescharacteristic
318C2×C3×C4C23×D311yescharacteristic
319#67—124no—
320C2×Dic3—22no—
321C2×Dic3—22no—
322C2×Dic3—22no—
323C2×Dic3—31no—
324C2×Dic3—31no—
325C2×Dic3—31no—
326C2×Dic3—31no—
327C2×Dic3—31no—
328C2×Dic3—31no—
329C2×Dic3—61no—
330C2×Dic3—61no—
331C2×Dic3—61no—
332C2×Dic3—124no—
333D12—24no—
334D12—42no—
335D12—42no—
336D12—124no—
337C4×D3—34no—
338C4×D3—34no—
339C4×D3—64no—
340C4×D3—62no—
341C4×D3—62no—
342C4×D3—62no—
343C4×D3—62no—
344C4×D3—122no—
345C4×D3—122no—
346C4×D3—124no—
347C4×D3—124no—
348C4×D3—124no—
349Dic6—24no—
350Dic6—24no—
351Dic6—42no—
352Dic6—124no—
353Dic6—124no—
354C3×C8—22no—
355C3×C8—22no—
356C3×C8—42no—
357C3⋊C8—62no—
358C3⋊C8—62no—
359C3⋊C8—122no—
360C2×C32#53511yescharacteristic
361C2×C32C22×SD1611yescharacteristic
362C2×C32C2×#13711yescharacteristic
363C3⋊D3—22no—
364C3×D3—82no—
365#41—364no—
366C2×Q8—32no—
367C2×Q8—32no—
368C2×Q8—61no—
369C2×Q8—182no—
370C2×Q8—364no—
371C2×D4—32no—
372C2×D4—61no—
373C2×D4—61no—
374C2×D4—182no—
375C22×C4—91no—
376C22×C4—91no—
377C22×C4—91no—
378C22×C4—182no—
379C22×C4—182no—
380SD16—124no—
381SD16—364no—
382C2×C8—92no—
383C2×C8C2×D3212yes—
384C4⋊C4—32no—
385C4⋊C4—61no—
386C4⋊C4—61no—
387C4⋊C4—61no—
388C4⋊C4—61no—
389C4⋊C4—61no—
390C4⋊C4—182no—
391C4⋊C4—182no—
392C22⋊C4—182no—
393C22⋊C4—182no—
394C42—91no—
395C42—91no—
396C42—91no—
397C42C2×D3211yescharacteristic
398C22×C3—21no—
399C22×C3—122no—
400C22×C3—122no—
401C22×C3—122no—
402C22×C3C2×D3×D411yescharacteristic
403C22×C3C2×D3×D411yescharacteristic
404C2×D3—32no—
405C2×D3—32no—
406C2×D3—42no—
407C2×D3—42no—
408C2×D3—42no—
409C2×D3—62no—
410C2×D3—61no—
411C2×D3—61no—
412C2×D3—61no—
413C2×D3—61no—
414C2×D3—121no—
415C2×D3—121no—
416C3×C4—22no—
417C3×C4—22no—
418C3×C4—22no—
419C3×C4—122no—
420C3×C4—122no—
421C3×C4—122no—
422C3×C4D3×SD1612yes—
423C3×C4D3×SD1612yes—
424C3×C4#91512yes—
425C3×C4#91812yes—
426C3×C4#100412yes—
427C3×C4#100912yes—
428Dic3—32no—
429Dic3—32no—
430Dic3—42no—
431Dic3—42no—
432Dic3—42no—
433Dic3—62no—
434Dic3—61no—
435Dic3—61no—
436Dic3—61no—
437Dic3—61no—
438Dic3—121no—
439Dic3—121no—
440C32#320611yescharacteristic, complemented, Sylow
441C23—62no—
442C23—91no—
443Q8—64no—
444Q8—64no—
445Q8—122no—
446Q8—364no—
447D4—64no—
448D4—122no—
449D4—122no—
450D4—364no—
451C2×C4—62no—
452C2×C4—62no—
453C2×C4—62no—
454C2×C4—91no—
455C2×C4—94no—
456C2×C4—91no—
457C2×C4—91no—
458C2×C4—182no—
459C2×C4—182no—
460C2×C4—364no—
461C2×C4—364no—
462C2×C4#380211yescharacteristic
463C2×C4#380211yescharacteristic
464C2×C4C22×D3211yescharacteristic
465C8—22no—
466C8—182no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—242no—
471C2×C3#567411yescharacteristic
472C2×C3#571511yescharacteristic
473C2×C3C2×D3×SD1611yescharacteristic
474C2×C3C2×D3×SD1611yescharacteristic
475C2×C3C2×#91511yescharacteristic
476C2×C3C2×#91811yescharacteristic
477D3—62no—
478D3—62no—
479D3—82no—
480D3—122no—
481C22—92no—
482C22—122no—
483C22—122no—
484C22—122no—
485C22—181no—
486C22—181no—
487C22C2×#380211yescharacteristic
488C4—92no—
489C4—122no—
490C4—122no—
491C4—122no—
492C4—181no—
493C4—181no—
494C4#6379612yes—
495C4#6381112yes—
496C4#6430712yes—
497C3—21no—
498C3#8160211yescharacteristic, complemented
499C3#8176411yescharacteristic, complemented
500C2—182no—
501C2—242no—
502C2#1059401011yescharacteristic
503C2C2×#6379611yescharacteristic
504C2C2×#6381111yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10593907C2
hypercenterC4×C8D32
hypocenterC32#3206
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. #10593909C2semidirect
3. #10592384C2semidirect
4. C3×#4693C2semidirect
5. C3×#4681C2semidirect
6. #10590824C2semidirect
7. #10590748C2semidirect
8. #10590375C2semidirect
9. #10590290C2semidirect
51. #4693D3semidirect
55. #4681D3semidirect
155. C4×C3⋊D3SD16semidirect
440. C32#3206semidirect
498. C3#81602semidirect
499. C3#81764semidirect

Maximal subgroups

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

subgroupindex
#105939092
#105939072
#105923842
C3×#46932
C3×#46812
#105908242
#105907482
#105903752
#105902902
#817643
#816023