Finite Group Databasebeta

← #11898373

Subgroups — #11898373

Order 1152.

775 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594335C212yesmaximal, complemented
2#10592572C211yesmaximal, characteristic, complemented
3C3×#4873C211yesmaximal, characteristic, complemented
4C3×#4872C211yesmaximal, characteristic
5#10590896C211yesmaximal, characteristic, complemented
6#10590869C211yesmaximal, characteristic
7#10590864C211yesmaximal, characteristic
8C8×#627C211yesmaximal, characteristic, complemented
9#10590559C212yesmaximal, complemented
10#10590538C212yesmaximal, complemented
11#10590532C212yesmaximal, complemented
12#79710—31nomaximal
13#79579—31nomaximal
14C2×#3746C2211yescharacteristic
15#64096C2212yes—
16C2×C3×Dic12C2211yescharacteristic
17C2×C3×D24C2211yescharacteristic
18C3×#893C2212yes—
19C3×#887C2212yes—
20C4×#627C2211yescharacteristic
21#63866C2212yes—
22#63863C2212yes—
23#63862—22no—
24#63860C2212yes—
25#63859—22no—
26#63855—22no—
27#63851—22no—
28C2×#3719C2212yes—
29C2×#3716C2212yes—
30C2×#3715C2212yes—
31C32×#107C2211yescharacteristic
32C8×C3⋊Dic3C2211yescharacteristic
33#63637C2212yes—
34C3×C8×Dic3C2211yescharacteristic
35C3×C8×Dic3C2211yescharacteristic
36C3×#810C2212yes—
37C3×#809C2212yes—
38#63572C2211yescharacteristic
39Dic3⋊(C3⋊C8)C2211yescharacteristic
40Dic3⋊(C3⋊C8)C2211yescharacteristic
41#5568—32no—
42#5542—32no—
43C3×C4×Q16—31no—
44C3×C4×D8—31no—
45#5191—31no—
46#5183—31no—
47#5155—31no—
48#5155—31no—
49#5028—32no—
50#5019—32no—
51#4873—31no—
52#4873—31no—
53#4873—61no—
54#4873D311yescharacteristic, complemented
55#4872D311yescharacteristic
56#4818—32no—
57#4798—32no—
58#4767—32no—
59#4767—32no—
60#4699—31no—
61#4696—31no—
62C8×Dic6—31no—
63C8×Dic6—31no—
64C2×#634C2312yes—
65C2×C3×D12C2312yes—
66C2×C3×C4×D3—22no—
67C2×C3×Dic6C2312yes—
68C2×#627D411yescharacteristic
69C2×C32×C8C2311yescharacteristic
70C32×C4⋊C4C2312yes—
71#3750—22no—
72C4×C3⋊Dic3—22no—
73C4×C3⋊Dic3C2311yescharacteristic
74C2×C3⋊(C3⋊C8)C2311yescharacteristic
75#3746—22no—
76C3×(C2×D3)⋊C4—22no—
77C3×Dic3⋊C4—22no—
78C3×C4×Dic3—22no—
79C3×C4×Dic3C2311yescharacteristic
80C3×C4×Dic3C2311yescharacteristic
81C2×C3×C3⋊C8C2311yescharacteristic
82C2×C3×C3⋊C8C2311yescharacteristic
83C3×Dic12—22no—
84C3×D24—22no—
85#3724D411yescharacteristic
86Dic3⋊Dic3—22no—
87Dic3⋊Dic3—22no—
88Dic3⋊Dic3D411yescharacteristic
89Dic3⋊Dic3D411yescharacteristic
90(C2×D3)⋊Dic3—22no—
91(C2×D3)⋊Dic3—22no—
92(C2×D3)⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94#3719—42no—
95#3716—42no—
96#3715—42no—
97#3393—91noSylow
98C2×C3×Q16—31no—
99C2×C3×D8—31no—
100C3×C4×Q8—32no—
101C3×C4×D4—32no—
102#947—32no—
103#944—32no—
104C2×#216—32no—
105C2×#215—32no—
106#936—32no—
107#936—32no—
108C2×#214—32no—
109C2×#214—32no—
110#926—62no—
111#924—62no—
112C2×Dic12—31no—
113C2×Dic12—31no—
114C2×Dic12—32no—
115C2×Dic12—61no—
116C2×Dic12C2×D311yescharacteristic
117C2×D24C2×D311yescharacteristic
118C2×#204—32no—
119#898—62no—
120#896—62no—
121#893C2×D312yes—
122#887—32no—
123#887—32no—
124#887—62no—
125#887C2×D312yes—
126#879—62no—
127#879—62no—
128#876—62no—
129#875—32no—
130#872—62no—
131#869—32no—
132C4×Dic6—31no—
133C4×Dic6—31no—
134C3×#107—21no—
135C3×#107C2×D311yescharacteristic
136C3×#107C2×D311yescharacteristic
137C3×#103—32no—
138C3×#102—32no—
139C3×C4×C8—31no—
140C3×C4×C8—31no—
141Dic3⋊C8—31no—
142Dic3⋊C8—31no—
143Dic3⋊C8—31no—
144Dic3⋊C8—31no—
145C8×Dic3—31no—
146C8×Dic3—31no—
147C8×Dic3—61no—
148C8×Dic3C2×D311yescharacteristic
149C8×Dic3C2×D311yescharacteristic
150#810—32no—
151#810—32no—
152#810—62no—
153#810C2×D312yes—
154#809C2×D312yes—
155C4⋊(C3⋊C8)—31no—
156C4⋊(C3⋊C8)—31no—
157C22×C3×D3—22no—
158C2×C32×C4—22no—
159C2×C32×C4C2411yescharacteristic
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3C2×D411yescharacteristic
162C2×C3⋊Dic3C2×D411yescharacteristic
163#634—22no—
164#634—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3C2×D411yescharacteristic
167C2×C3×Dic3C2×D411yescharacteristic
168C2×C3×Dic3C2×D411yescharacteristic
169C2×C3×Dic3C2×D411yescharacteristic
170C3×D12—22no—
171C3×D12—22no—
172C3×C4×D3—44no—
173C3×Dic6—22no—
174C3×Dic6—22no—
175#627—22no—
176C32×C8#4112yes—
177C3⋊(C3⋊C8)—21no—
178C3×C3⋊C8—21no—
179C3×C3⋊C8—21no—
180#556—92no—
181#495—91no—
182#495—91no—
183#494—91no—
184#464—92no—
185#464—92no—
186#461—92no—
187C8×Q8—91no—
188C4×Q16—31no—
189C4×Q16—91no—
190C4×D8—31no—
191C2×C3×Q8—32no—
192C2×C3×D4—32no—
193C22×C3×C4—62no—
194C2×D12C22×D312yes—
195C2×C4×D3—22no—
196C2×Dic6—31no—
197C2×Dic6—31no—
198C2×Dic6—32no—
199C2×Dic6—32no—
200C2×Dic6—62no—
201C2×Dic6C22×D312yes—
202C3×Q16—62no—
203C3×D8—62no—
204C2×C3×C8—21no—
205C2×C3×C8—31no—
206C2×C3×C8—31no—
207C2×C3×C8C22×D311yescharacteristic
208C2×C3×C8C22×D311yescharacteristic
209C3×C4⋊C4—22no—
210C3×C4⋊C4—62no—
211C3×C4⋊C4C22×D312yes—
212C3×C4⋊C4C22×D312yes—
213C3×C22⋊C4—62no—
214C3×C42—31no—
215C3×C42—31no—
216C3×C42—62no—
217#217—62no—
218#217—62no—
219#217—62no—
220#217—62no—
221#216—122no—
222#215—122no—
223#214—122no—
224#214—122no—
225(C2×D3)⋊C4—22no—
226(C2×D3)⋊C4—62no—
227(C2×D3)⋊C4—62no—
228(C2×D3)⋊C4—62no—
229(C2×D3)⋊C4—62no—
230C4⋊Dic3—31no—
231C4⋊Dic3—31no—
232C4⋊Dic3—62no—
233C4⋊Dic3—62no—
234Dic3⋊C4—22no—
235Dic3⋊C4—31no—
236Dic3⋊C4—31no—
237Dic3⋊C4—31no—
238Dic3⋊C4—31no—
239Dic3⋊C4—62no—
240Dic3⋊C4—62no—
241Dic3⋊C4—62no—
242Dic3⋊C4—62no—
243Dic3⋊C4—122no—
244C4×Dic3—22no—
245C4×Dic3—31no—
246C4×Dic3—31no—
247C4×Dic3—61no—
248C4×Dic3—62no—
249C4×Dic3—62no—
250C4×Dic3—122no—
251C4×Dic3C22×D311yescharacteristic
252C4×Dic3C22×D311yescharacteristic
253C2×C3⋊C8—31no—
254C2×C3⋊C8—31no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8C22×D311yescharacteristic
257C2×C3⋊C8C22×D311yescharacteristic
258Dic12—22no—
259Dic12—64no—
260Dic12—62no—
261Dic12—62no—
262Dic12—122no—
263D24—22no—
264#204—122no—
265C22×C32C22×D411yescharacteristic
266C2×C3×D3—42no—
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C32×C4—42no—
270C32×C4C2×#4111yescharacteristic
271C32×C4H(5,𝔽2)11yescharacteristic
272C3⋊Dic3—21no—
273C3⋊Dic3—21no—
274C3⋊Dic3—42no—
275C3×Dic3—21no—
276C3×Dic3—21no—
277C3×Dic3—21no—
278C3×Dic3—42no—
279C3×Dic3#13512yes—
280C2×Q16—31no—
281C2×Q16—92no—
282C2×Q16—91no—
283C2×SD16—92no—
284C2×SD16—92no—
285C2×D8—31no—
286C4⋊Q8—92no—
287#126—182no—
288#126—182no—
289#124—92no—
290#124—92no—
291C22⋊Q8—182no—
292C4×Q8—32no—
293C4×Q8—91no—
294C4×Q8—92no—
295C4×D4—32no—
296#117—182no—
297#107D3211yescharacteristic
298C4⋊C8—91no—
299C4⋊C8—91no—
300C4⋊C8—91no—
301#103—32no—
302#103—92no—
303#102—32no—
304C4×C8—31no—
305C4×C8—31no—
306C4×C8—91no—
307C23×C3—62no—
308C22×D3—22no—
309C3×Q8—62no—
310C3×Q8—62no—
311C3×D4—62no—
312C3×D4—62no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—21no—
316C2×C3×C4—31no—
317C2×C3×C4—31no—
318C2×C3×C4—31no—
319C2×C3×C4—31no—
320C2×C3×C4—42no—
321C2×C3×C4—62no—
322C2×C3×C4—124no—
323C2×C3×C4C23×D311yescharacteristic
324C2×C3×C4C23×D311yescharacteristic
325C2×Dic3—22no—
326C2×Dic3—31no—
327C2×Dic3—31no—
328C2×Dic3—31no—
329C2×Dic3—31no—
330C2×Dic3—61no—
331C2×Dic3—61no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—122no—
335C2×Dic3D3×D411yescharacteristic
336C2×Dic3D3×D411yescharacteristic
337C2×Dic3D3×D411yescharacteristic
338C2×Dic3D3×D411yescharacteristic
339D12—22no—
340D12—22no—
341C4×D3—44no—
342Dic6—22no—
343Dic6—22no—
344Dic6—62no—
345Dic6—62no—
346Dic6—64no—
347Dic6—62no—
348Dic6—62no—
349Dic6—62no—
350Dic6—62no—
351Dic6—122no—
352C3×C8—22no—
353C3×C8—61no—
354C3×C8—61no—
355C3×C8#23512yes—
356C3×C8#23512yes—
357C3⋊C8—21no—
358C3⋊C8—21no—
359C3⋊C8—61no—
360C3⋊C8—61no—
361C3⋊C8—121no—
362C2×C32#55011yescharacteristic
363C2×C32C2×#13511yescharacteristic
364C2×C32#57811yescharacteristic
365C3×D3—82no—
366C2×Q8—32no—
367C2×Q8—91no—
368C2×Q8—92no—
369C2×D4—32no—
370C22×C4—62no—
371Q16—62no—
372Q16—182no—
373Q16—362no—
374SD16—362no—
375SD16—362no—
376D8—62no—
377C2×C8—31no—
378C2×C8—31no—
379C2×C8—91no—
380C2×C8C2×D3211yescharacteristic
381C4⋊C4—62no—
382C4⋊C4—91no—
383C4⋊C4—91no—
384C4⋊C4—91no—
385C4⋊C4—182no—
386C4⋊C4—182no—
387C4⋊C4—182no—
388C4⋊C4C2×D3212yes—
389C22⋊C4—62no—
390C22⋊C4—182no—
391C22⋊C4—182no—
392C22⋊C4—182no—
393C22⋊C4—182no—
394C42—31no—
395C42—31no—
396C42—62no—
397C42—91no—
398C42—182no—
399C22×C3—21no—
400C22×C3—122no—
401C22×C3—122no—
402C22×C3—122no—
403C22×C3C2×D3×D411yescharacteristic
404C22×C3C2×D3×D411yescharacteristic
405C2×D3—42no—
406C2×D3—42no—
407C2×D3—42no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—32no—
411C3×C4—42no—
412C3×C4—42no—
413C3×C4—61no—
414C3×C4—61no—
415C3×C4—61no—
416C3×C4—82no—
417C3×C4—122no—
418C3×C4C2×#23511yescharacteristic
419C3×C4C2×#23511yescharacteristic
420C3×C4#100911yescharacteristic
421C3×C4#100911yescharacteristic
422Dic3—21no—
423Dic3—21no—
424Dic3—21no—
425Dic3—42no—
426Dic3—62no—
427Dic3—61no—
428Dic3—61no—
429Dic3—61no—
430Dic3—61no—
431Dic3—121no—
432Dic3—124no—
433Dic3—122no—
434Dic3—122no—
435Dic3#91212yes—
436C32#339311yescharacteristic, complemented, Sylow
437C23—62no—
438Q8—62no—
439Q8—62no—
440Q8—182no—
441Q8—182no—
442Q8—182no—
443D4—62no—
444D4—62no—
445C2×C4—22no—
446C2×C4—31no—
447C2×C4—31no—
448C2×C4—31no—
449C2×C4—31no—
450C2×C4—62no—
451C2×C4—91no—
452C2×C4—91no—
453C2×C4—124no—
454C2×C4—182no—
455C2×C4C22×D3211yescharacteristic
456C8—61no—
457C8—61no—
458C8—181no—
459C8#379812yes—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—242no—
464C2×C3#555311yescharacteristic
465C2×C3#555311yescharacteristic
466C2×C3C2×#91211yescharacteristic
467C2×C3#576611yescharacteristic
468C2×C3D3×#13511yescharacteristic
469C2×C3#577111yescharacteristic
470D3—82no—
471C22—122no—
472C22—122no—
473C22—122no—
474C22D32×D411yescharacteristic
475C4—32no—
476C4—42no—
477C4—61no—
478C4—61no—
479C4—61no—
480C4—122no—
481C4—181no—
482C4—181no—
483C4—362no—
484C4C2×#379811yescharacteristic
485C4#6432011yescharacteristic
486C3—21no—
487C3#7957911yescharacteristic, complemented
488C3#7971011yescharacteristic, complemented
489C2—242no—
490C2#1059452011yescharacteristic
491C2D3×#91211yescharacteristic
492C2#1059476811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC2×C3×D24C22
hypercenter#107D32
hypocenterC32#3393
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. #10594335C2semidirect
2. #10592572C2semidirect
3. C3×#4873C2semidirect
5. #10590896C2semidirect
8. C8×#627C2semidirect
9. #10590559C2semidirect
10. #10590538C2semidirect
11. #10590532C2semidirect
54. #4873D3semidirect
436. C32#3393semidirect
487. C3#79579semidirect
488. C3#79710semidirect

Maximal subgroups

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

subgroupindex
#105943352
#105925722
C3×#48732
C3×#48722
#105908962
#105908692
#105908642
C8×#6272
#105905592
#105905382
#105905322
#797103
#795793