Finite Group Databasebeta

← #11898366

Subgroups — #11898366

Order 1152.

771 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593942C212yesmaximal, complemented
2C8×#634C211yesmaximal, characteristic, complemented
3C3×C4×Dic12C211yesmaximal, characteristic, complemented
4C3×#4696C211yesmaximal, characteristic
5#10590905C211yesmaximal, characteristic, complemented
6#10590869C211yesmaximal, characteristic
7#10590818C211yesmaximal, characteristic, complemented
8#10590796C212yesmaximal, complemented
9#10590777C211yesmaximal, characteristic
10#10590748C212yesmaximal, complemented
11#10590267C212yesmaximal, complemented
12#81813—31nomaximal
13#79710—31nomaximal
14C4×#634C2211yescharacteristic
15C2×C3×Dic12C2211yescharacteristic
16C2×C3×Dic12C2211yescharacteristic
17C2×C3×D24C2211yescharacteristic
18C2×C3×#204C2212yes—
19C3×#875C2212yes—
20C3×C4×Dic6C2212yes—
21#63898C2212yes—
22#63896—22no—
23#63877—22no—
24#63873C2212yes—
25#63863C2212yes—
26#63861—22no—
27#63859—22no—
28#63843C2212yes—
29C2×#3718C2212yes—
30C2×#3715C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63641C2211yescharacteristic
33#63641C2211yescharacteristic
34C8×C3⋊Dic3C2211yescharacteristic
35C8×C3⋊Dic3C2211yescharacteristic
36C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
37C3×#818C2211yescharacteristic
38C3×#816C2212yes—
39#63565C2212yes—
40#63562C2212yes—
41#5671—32no—
42#5568—32no—
43C3×#495—31no—
44C3×C4×Q16—31no—
45#5191—31no—
46#5183—31no—
47#5183—31no—
48Dic3×Q16—31no—
49#5166—32no—
50#5162—32no—
51#5155—31no—
52Dic3×D8—31no—
53#5054—32no—
54#5028—32no—
55#4873—31no—
56#4872—31no—
57#4818—32no—
58#4798—32no—
59C4×Dic12D311yescharacteristic, complemented
60#4696D311yescharacteristic
61C8×Dic6—31no—
62C8×Dic6—31no—
63C8×Dic6—61no—
64C2×#634D411yescharacteristic
65C2×C3×D12C2312yes—
66C2×C3×Dic6C2312yes—
67C2×C3×Dic6C2312yes—
68C2×D3×Dic3—22no—
69C2×C32×C8C2311yescharacteristic
70C2×C32×C8C2311yescharacteristic
71C32×C42C2311yescharacteristic
72C4⋊(C3⋊Dic3)D411yescharacteristic
73#3750D411yescharacteristic
74#3750D411yescharacteristic
75C4×C3⋊Dic3C2311yescharacteristic
76C4×C3⋊Dic3C2311yescharacteristic
77C2×C3⋊(C3⋊C8)C2311yescharacteristic
78C2×C3⋊(C3⋊C8)C2311yescharacteristic
79C3×(C2×D3)⋊C4—22no—
80C3×(C2×D3)⋊C4—22no—
81C3×C4⋊Dic3C2312yes—
82C3×Dic3⋊C4—22no—
83C3×C4×Dic3—22no—
84C3×Dic12—22no—
85C3×Dic12—22no—
86C3×D24—22no—
87C3×#204—42no—
88#3724—22no—
89#3724—22no—
90Dic3⋊Dic3—22no—
91(C2×D3)⋊Dic3—22no—
92(C2×D3)⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94Dic32—22no—
95#3718—42no—
96#3715—42no—
97#3393—91noSylow
98C2×C3×Q16—31no—
99C2×C3×Q16—31no—
100C2×C3×SD16—32no—
101C2×C3×D8—31no—
102C3×#124—32no—
103C3×C4×Q8—32no—
104#947—32no—
105Q8×Dic3—32no—
106#944—32no—
107#944—32no—
108C2×#216—32no—
109C2×#216—32no—
110C2×#215—32no—
111#936—32no—
112D4×Dic3—32no—
113C2×#214—32no—
114C2×Dic12C2×D311yescharacteristic
115C2×Dic12C2×D311yescharacteristic
116C2×D24C2×D311yescharacteristic
117C2×#204C2×D312yes—
118#898—62no—
119#896—62no—
120#893—32no—
121#887—32no—
122#879—62no—
123#879—62no—
124#878—62no—
125#877—62no—
126#876—62no—
127#875C2×D312yes—
128#872—62no—
129C4×Dic6—31no—
130C4×Dic6—31no—
131C4×Dic6—61no—
132C4×Dic6C2×D312yes—
133C3×#107—31no—
134C3×#103—32no—
135C3×C4×C8—21no—
136C3×C4×C8C2×D311yescharacteristic
137C3×C4×C8C2×D311yescharacteristic
138#835—32no—
139#832—32no—
140#818C2×D311yescharacteristic
141#816C2×D312yes—
142Dic3⋊C8—31no—
143Dic3⋊C8—31no—
144Dic3⋊C8—31no—
145Dic3⋊C8—31no—
146Dic3⋊C8—61no—
147Dic3⋊C8—61no—
148C8×Dic3—31no—
149C8×Dic3—31no—
150C8×Dic3—31no—
151C8×Dic3—31no—
152C8×Dic3—61no—
153C8×Dic3—61no—
154#810—32no—
155#809—32no—
156C4⋊(C3⋊C8)—31no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—61no—
159C22×C3×D3—22no—
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2411yescharacteristic
163C2×C3⋊Dic3C2×D411yescharacteristic
164C2×C3⋊Dic3C2×D411yescharacteristic
165C2×C3⋊Dic3C2×D411yescharacteristic
166C2×C3⋊Dic3C2×D411yescharacteristic
167#634—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C3×D12—22no—
172C3×D12—22no—
173C3×Dic6—22no—
174C3×Dic6—22no—
175C3×Dic6—22no—
176C3×Dic6—22no—
177D3×Dic3—44no—
178C32×C8—21no—
179C32×C8#4112yes—
180C3⋊(C3⋊C8)—21no—
181C3⋊(C3⋊C8)—21no—
182#556—92no—
183#495—31no—
184#495—91no—
185#494—91no—
186#464—92no—
187#464—92no—
188#461—92no—
189C8×Q8—91no—
190C4×Q16—31no—
191C4×Q16—91no—
192C4×D8—91no—
193C2×C3×Q8—32no—
194C2×C3×Q8—32no—
195C2×C3×D4—32no—
196C22×Dic3—62no—
197C2×D12C22×D312yes—
198C2×C4×D3—62no—
199C2×Dic6—31no—
200C2×Dic6—31no—
201C2×Dic6—61no—
202C2×Dic6C22×D312yes—
203C2×Dic6C22×D312yes—
204C3×Q16—62no—
205C3×Q16—62no—
206C3×SD16—122no—
207C3×D8—62no—
208C2×C3×C8—21no—
209C2×C3×C8—21no—
210C2×C3×C8C22×D311yescharacteristic
211C2×C3×C8C22×D311yescharacteristic
212C2×C3×C8C22×D311yescharacteristic
213C2×C3×C8C22×D311yescharacteristic
214C3×C4⋊C4—32no—
215C3×C4⋊C4—62no—
216C3×C22⋊C4—62no—
217C3×C22⋊C4—62no—
218C3×C42—21no—
219C3×C42—62no—
220C3×C42C22×D311yescharacteristic
221C3×C42C22×D311yescharacteristic
222#217—62no—
223#217—62no—
224#217—62no—
225#216—122no—
226#216—122no—
227#215—122no—
228#214—122no—
229(C2×D3)⋊C4—22no—
230(C2×D3)⋊C4—22no—
231(C2×D3)⋊C4—62no—
232(C2×D3)⋊C4—62no—
233(C2×D3)⋊C4—62no—
234C4⋊Dic3—31no—
235C4⋊Dic3—31no—
236C4⋊Dic3—61no—
237C4⋊Dic3—62no—
238C4⋊Dic3C22×D312yes—
239Dic3⋊C4—22no—
240Dic3⋊C4—31no—
241Dic3⋊C4—31no—
242Dic3⋊C4—31no—
243Dic3⋊C4—31no—
244Dic3⋊C4—61no—
245Dic3⋊C4—61no—
246Dic3⋊C4—62no—
247Dic3⋊C4—62no—
248Dic3⋊C4—62no—
249Dic3⋊C4—62no—
250Dic3⋊C4—62no—
251C4×Dic3—22no—
252C4×Dic3—31no—
253C4×Dic3—31no—
254C4×Dic3—31no—
255C4×Dic3—31no—
256C4×Dic3—61no—
257C4×Dic3—61no—
258C4×Dic3—62no—
259C4×Dic3—62no—
260C2×C3⋊C8—31no—
261C2×C3⋊C8—31no—
262C2×C3⋊C8—31no—
263C2×C3⋊C8—31no—
264C2×C3⋊C8—61no—
265C2×C3⋊C8—61no—
266Dic12—22no—
267Dic12—22no—
268D24—22no—
269#204—42no—
270C22×C32C22×D411yescharacteristic
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C2×C3×D3—42no—
274C32×C4—21no—
275C32×C4—21no—
276C32×C4C2×#4111yescharacteristic
277C32×C4H(5,𝔽2)11yescharacteristic
278C3⋊Dic3—21no—
279C3⋊Dic3—21no—
280C3⋊Dic3—21no—
281C3⋊Dic3#13512yes—
282C3×Dic3—42no—
283C3×Dic3—42no—
284C3×Dic3—42no—
285C2×Q16—31no—
286C2×Q16—31no—
287C2×Q16—92no—
288C2×SD16—32no—
289C2×SD16—92no—
290C2×D8—31no—
291C4⋊Q8—92no—
292#126—182no—
293#126—182no—
294#124—32no—
295#124—92no—
296C22⋊Q8—182no—
297C4×Q8—32no—
298C4×Q8—91no—
299C4×Q8—92no—
300C4×D4—92no—
301#117—182no—
302#107—31no—
303C4⋊C8—91no—
304C4⋊C8—91no—
305C4⋊C8—91no—
306#103—32no—
307#103—92no—
308#102—92no—
309C4×C8—91no—
310C4×C8—91no—
311C4×C8D3211yescharacteristic
312C23×C3—62no—
313C22×D3—22no—
314C3×Q8—62no—
315C3×Q8—62no—
316C3×Q8—62no—
317C3×Q8—62no—
318C3×D4—62no—
319C3×D4—62no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4C23×D311yescharacteristic
331C2×C3×C4C23×D311yescharacteristic
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3—31no—
336C2×Dic3—31no—
337C2×Dic3—31no—
338C2×Dic3—31no—
339C2×Dic3—31no—
340C2×Dic3—31no—
341C2×Dic3—31no—
342C2×Dic3—31no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—124no—
348D12—22no—
349D12—22no—
350C4×D3—124no—
351Dic6—22no—
352Dic6—22no—
353Dic6—22no—
354Dic6—22no—
355Dic6—62no—
356Dic6—62no—
357Dic6—64no—
358C3×C8—21no—
359C3×C8—21no—
360C3×C8—22no—
361C3×C8—41no—
362C3×C8#23512yes—
363C3×C8#23712yes—
364C3⋊C8—61no—
365C3⋊C8—61no—
366C3⋊C8—61no—
367C3⋊C8—61no—
368C3⋊C8—121no—
369C3⋊C8—121no—
370C2×C32#55011yescharacteristic
371C2×C32C2×#13511yescharacteristic
372C2×C32#57811yescharacteristic
373C3×D3—82no—
374C2×Q8—32no—
375C2×Q8—32no—
376C2×Q8—91no—
377C2×D4—32no—
378C22×C4—182no—
379Q16—62no—
380Q16—62no—
381Q16—362no—
382SD16—122no—
383SD16—362no—
384D8—62no—
385C2×C8—91no—
386C2×C8—91no—
387C2×C8C2×D3211yescharacteristic
388C2×C8C2×D3211yescharacteristic
389C4⋊C4—32no—
390C4⋊C4—62no—
391C4⋊C4—91no—
392C4⋊C4—91no—
393C4⋊C4—91no—
394C4⋊C4—182no—
395C4⋊C4—182no—
396C4⋊C4—182no—
397C22⋊C4—62no—
398C22⋊C4—62no—
399C22⋊C4—182no—
400C22⋊C4—182no—
401C22⋊C4—182no—
402C42—62no—
403C42—91no—
404C42—91no—
405C42—182no—
406C42C2×D3211yescharacteristic
407C22×C3—21no—
408C22×C3—122no—
409C22×C3—122no—
410C22×C3—122no—
411C22×C3C2×D3×D411yescharacteristic
412C22×C3C2×D3×D411yescharacteristic
413C2×D3—42no—
414C2×D3—42no—
415C2×D3—42no—
416C3×C4—22no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—41no—
424C3×C4—122no—
425C3×C4—122no—
426C3×C4—122no—
427C3×C4C2×#23511yescharacteristic
428C3×C4C2×#23711yescharacteristic
429C3×C4#100411yescharacteristic
430C3×C4#100911yescharacteristic
431Dic3—32no—
432Dic3—32no—
433Dic3—42no—
434Dic3—42no—
435Dic3—42no—
436Dic3—62no—
437Dic3—62no—
438Dic3—61no—
439Dic3—61no—
440Dic3—61no—
441Dic3—61no—
442Dic3—61no—
443Dic3—61no—
444Dic3—121no—
445Dic3—121no—
446C32#339311yescharacteristic, complemented, Sylow
447C23—62no—
448Q8—62no—
449Q8—62no—
450Q8—62no—
451Q8—62no—
452Q8—182no—
453D4—62no—
454D4—62no—
455C2×C4—62no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—91no—
459C2×C4—91no—
460C2×C4—91no—
461C2×C4—91no—
462C2×C4—364no—
463C2×C4#380211yescharacteristic
464C2×C4#380211yescharacteristic
465C2×C4C22×D3211yescharacteristic
466C8—21no—
467C8—181no—
468C8—181no—
469C8#379512yes—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—242no—
474C2×C3#555311yescharacteristic
475C2×C3#571811yescharacteristic
476C2×C3#576611yescharacteristic
477C2×C3D3×#13511yescharacteristic
478C2×C3D3×#13511yescharacteristic
479C2×C3#577111yescharacteristic
480D3—82no—
481C22—122no—
482C22—122no—
483C22—122no—
484C22C2×#380211yescharacteristic
485C4—21no—
486C4—21no—
487C4—92no—
488C4—122no—
489C4—122no—
490C4—122no—
491C4—181no—
492C4—181no—
493C4—181no—
494C4C2×#379511yescharacteristic
495C4#6430711yescharacteristic
496C3—21no—
497C3#7971011yescharacteristic, complemented
498C3#8181311yescharacteristic, complemented
499C2—242no—
500C2#1059390611yescharacteristic
501C2#1059468411yescharacteristic
502C2#1059470311yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×C3×D24C22
hypercenterC4×C8D32
hypocenterC32#3393
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. #10593942C2semidirect
2. C8×#634C2semidirect
3. C3×C4×Dic12C2semidirect
5. #10590905C2semidirect
7. #10590818C2semidirect
8. #10590796C2semidirect
10. #10590748C2semidirect
11. #10590267C2semidirect
59. C4×Dic12D3semidirect
446. C32#3393semidirect
497. C3#79710semidirect
498. C3#81813semidirect

Maximal subgroups

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

subgroupindex
#105939422
C8×#6342
C3×C4×Dic122
C3×#46962
#105909052
#105908692
#105908182
#105907962
#105907772
#105907482
#105902672
#818133
#797103