Finite Group Databasebeta

← #11866289

Subgroups — #11866289

Order 1152.

1157 conjugacy classes of subgroups.

The subgroup lattice has 519 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595992C211yesmaximal, characteristic, complemented
2#10594855C211yesmaximal, characteristic, complemented
3C22×#3717C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic
5C3×#5004C211yesmaximal, characteristic, complemented
6C3×#5002C211yesmaximal, characteristic, complemented
7#10591119C211yesmaximal, characteristic, complemented
8#10590565C214yesmaximal, complemented
9#10590540C214yesmaximal, complemented
10#78976—31nomaximal
11#78863—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C32×#117C2211yescharacteristic
16#64135C2211yescharacteristic
17#64102C2214yes—
18C22⋊C4×C3⋊D3—22no—
19C4×C4⋊(C3⋊D3)—22no—
20C2×C3×#208C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22#63961—22no—
23#63873C2212yescomplemented
24#63863C2212yescomplemented
25#63856—22no—
26C2×#3717—24no—
27C2×#3717C2214yes—
28C2×#3717C2212yes—
29#63825—24no—
30C2×#3714C2212yes—
31C3×#810C2214yescomplemented
32C3×#810C2212yescomplemented
33C3×#809C2212yescomplemented
34#63572C2214yescomplemented
35#5825—31no—
36C2×#949—31no—
37#5816—31no—
38C22×#215—31no—
39C2×#908—31no—
40C22×#204—31no—
41#5521—31no—
42#5521—31no—
43#5521—61no—
44C3×#419—31no—
45C3×#416—31no—
46#5119—31no—
47#5102—31no—
48#5004D311yescharacteristic, complemented
49#5002D311yescharacteristic, complemented
50#4819—34no—
51#4818—34no—
52#4818—34no—
53#4787—34no—
54C23×C3⋊D3—21no—
55C22×C32×C4C2311yescharacteristic
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)D414yes—
59C2×C4⋊(C3⋊D3)C2312yes—
60C2×C4×C3⋊D3—24no—
61C2×C3×#67—21no—
62C22×C3×Dic3—21no—
63C3×#235—22no—
64C3×#235—22no—
65C2×C3×D12C2311yescharacteristic
66C2×C3×C4×D3—21no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71C2×C3×Dic6C2311yescharacteristic
72C32×C4⋊C4C2312yes—
73C32×C22⋊C4—21no—
74C32×C42—21no—
75#3757D412yes—
76#3752—24no—
77C4⋊(C3⋊Dic3)D412yes—
78C4×C3⋊Dic3C2312yes—
79C3×#208—22no—
80C2×C3×C3⋊C8—22no—
81C2×C3×C3⋊C8C2312yes—
82C2×C3×C3⋊C8C2312yes—
83#3724—24no—
84(C2×D3)⋊Dic3—24no—
85#3717—24no—
86#3717—28no—
87#3714—24no—
88#3042—91noSylow
89C2×C3×#41—31no—
90C22×C3×Q8—31no—
91C2×#235C2×D311yescharacteristic
92C22×D12—31no—
93C22×D12—31no—
94C22×D12—61no—
95C22×Dic6C2×D311yescharacteristic
96C2×C3×M16—31no—
97C22×C3×C8—31no—
98C3×#117—21no—
99C3×#117C2×D311yescharacteristic
100C3×#117C2×D311yescharacteristic
101#949—64no—
102#947—32no—
103#946—62no—
104#944—32no—
105#944—32no—
106C2×#215—34no—
107C2×#215—32no—
108C2×#215—64no—
109#936—32no—
110#935—62no—
111C2×#213—32no—
112#929—62no—
113#926—31no—
114#926—31no—
115#926—61no—
116#924—62no—
117C2×#208C2×D311yescharacteristic
118C22×C3⋊C8C2×D311yescharacteristic
119#908—64no—
120C2×D24—32no—
121C2×#204—34no—
122C2×#204—32no—
123C2×#204—64no—
124#893—34no—
125#893—34no—
126#893—64no—
127D3×C22⋊C4—62no—
128D3×C22⋊C4—62no—
129D3×C22⋊C4—64no—
130C4×D12—62no—
131C4×D12—62no—
132C4×D12—64no—
133C3×#103—32no—
134C3×#103—34no—
135C3×#102—32no—
136Dic3⋊C8—34no—
137Dic3⋊C8—34no—
138#810C2×D312yescomplemented
139#810C2×D314yescomplemented
140#809C2×D312yescomplemented
141C23×C32C2×D411yescharacteristic
142C22×C3⋊D3—22no—
143C22×C3⋊D3—24no—
144C22×C3⋊D3—82no—
145C22×C3×D3—21no—
146C2×C32×C4—22no—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D412yes—
149C2×C32×C4#4112yes—
150C2×C32×C4C2411yescharacteristic
151C2×C3⋊Dic3C2×D414yes—
152C4⋊(C3⋊D3)—24no—
153C4⋊(C3⋊D3)—22no—
154C4⋊(C3⋊D3)C2×D414yes—
155C4×C3⋊D3—84no—
156C3×#67—42no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—21no—
159C2×C3×Dic3—42no—
160C3×D12—21no—
161C3×D12—21no—
162C3×C4×D3—42no—
163C3×Dic6—22no—
164C3×Dic6—21no—
165C3×Dic6—22no—
166C3×Dic6—21no—
167C3×Dic6—42no—
168C3×C3⋊C8—22no—
169C3×C3⋊C8—22no—
170C2×AGL(1,ℤ/8)—91no—
171C22×SD16—91no—
172#536—91no—
173#518—91no—
174#463—94no—
175#461—94no—
176#424—91no—
177#419—31no—
178#416—31no—
179C23×D3—62no—
180C23×D3—61no—
181C23×D3—61no—
182C3×#41—62no—
183C3×#41—62no—
184C2×C3×Q8—31no—
185C2×C3×Q8—32no—
186C2×C3×Q8—61no—
187C2×C3×Q8—62no—
188C2×C3×Q8—62no—
189C2×C3×D4—31no—
190C2×C3×D4—61no—
191C22×C3×C4—21no—
192C22×C3×C4—61no—
193C22×C3×C4—61no—
194C22×C3×C4C22×D311yescharacteristic
195C22×C3×C4C22×D311yescharacteristic
196C2×#67—21no—
197C22×Dic3—21no—
198#235—22no—
199#235—22no—
200C2×D12—34no—
201C2×D12—34no—
202C2×D12—32no—
203C2×D12—32no—
204C2×D12—62no—
205C2×D12—64no—
206C2×D12—62no—
207C2×D12—64no—
208C2×D12—62no—
209C2×D12—62no—
210C2×D12—61no—
211C2×D12—61no—
212C2×D12C22×D311yescharacteristic
213C2×C4×D3—21no—
214C2×C4×D3—64no—
215C2×C4×D3—64no—
216C2×C4×D3—68no—
217C2×Dic6—22no—
218C2×Dic6—22no—
219C2×Dic6—21no—
220C2×Dic6C22×D312yes—
221C2×Dic6C22×D311yescharacteristic
222C3×M16—62no—
223C2×C3×C8—32no—
224C2×C3×C8—32no—
225C2×C3×C8—62no—
226C3×C4⋊C4—22no—
227C3×C4⋊C4C22×D312yes—
228C3×C4⋊C4C22×D312yes—
229C3×C22⋊C4—22no—
230C3×C22⋊C4—21no—
231C3×C22⋊C4—21no—
232C3×C42—22no—
233C3×C42—21no—
234C3×C42—21no—
235#217—32no—
236#217—32no—
237#217—62no—
238#217—64no—
239#215—68no—
240#215—64no—
241#213—64no—
242(C2×D3)⋊C4—64no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—68no—
246C4⋊Dic3—32no—
247C4⋊Dic3—32no—
248C4⋊Dic3—62no—
249Dic3⋊C4—64no—
250Dic3⋊C4—64no—
251C4×Dic3—32no—
252C4×Dic3—32no—
253C4×Dic3—62no—
254#208—22no—
255C2×C3⋊C8—22no—
256C2×C3⋊C8C22×D312yes—
257C2×C3⋊C8C22×D312yes—
258D24—64no—
259#204—68no—
260#204—64no—
261C22×C32—22no—
262C22×C32#12112yes—
263C22×C32C22×D411yescharacteristic
264C2×C3⋊D3—24no—
265C2×C3⋊D3—44no—
266C2×C3⋊D3—84no—
267C2×C3×D3—41no—
268C2×C3×D3—42no—
269C32×C4—42no—
270C32×C4#12112yes—
271C32×C4C22×D411yescharacteristic
272C32×C4C2×#4111yescharacteristic
273C3⋊Dic3—24no—
274C3×Dic3—42no—
275C3×Dic3—41no—
276C2×#41—31no—
277C22×Q8—31no—
278C22×D4—91no—
279AGL(1,ℤ/8)—184no—
280C2×SD16—94no—
281C2×SD16—92no—
282C2×SD16—184no—
283C2×D8—92no—
284C2×M16—31no—
285C22×C8—31no—
286C4⋊Q8—92no—
287#124—92no—
288#123—182no—
289C22⋊Q8—182no—
290C4×D4—94no—
291C4×D4—182no—
292#117—91no—
293#117D3211yescharacteristic
294C2×C22⋊C4—182no—
295C4⋊C8—94no—
296#103—32no—
297#103—34no—
298#102—32no—
299C23×C3—21no—
300C23×C3—61no—
301C23×C3D3×D411yescharacteristic
302C23×C3D3×D411yescharacteristic
303C22×D3—21no—
304C22×D3—64no—
305C22×D3—62no—
306C22×D3—62no—
307C22×D3—68no—
308C22×D3—64no—
309C22×D3—64no—
310C22×D3—242no—
311C22×D3—242no—
312C22×D3—244no—
313C3×Q8—62no—
314C3×Q8—61no—
315C3×Q8—62no—
316C3×Q8—61no—
317C3×Q8—122no—
318C3×D4—61no—
319C3×D4—61no—
320C3×D4—122no—
321C2×C3×C4—24no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—21no—
328C2×C3×C4—61no—
329C2×C3×C4—62no—
330C2×C3×C4—122no—
331C2×C3×C4—122no—
332C2×C3×C4#23512yes—
333C2×C3×C4#23512yes—
334C2×C3×C4D3×D412yes—
335C2×C3×C4D3×D412yes—
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4C23×D311yescharacteristic
339C2×C3×C4C23×D311yescharacteristic
340#67—42no—
341C2×Dic3—21no—
342C2×Dic3—22no—
343C2×Dic3—34no—
344C2×Dic3—34no—
345C2×Dic3—42no—
346C2×Dic3—64no—
347D12—21no—
348D12—21no—
349D12—34no—
350D12—34no—
351D12—64no—
352D12—64no—
353D12—68no—
354D12—64no—
355D12—64no—
356D12—62no—
357D12—62no—
358C4×D3—42no—
359C4×D3—244no—
360C4×D3—244no—
361C4×D3—248no—
362Dic6—22no—
363Dic6—21no—
364Dic6—22no—
365Dic6—21no—
366Dic6—42no—
367C3×C8—62no—
368C3×C8—62no—
369C3⋊C8—22no—
370C3⋊C8—22no—
371C2×C32—22no—
372C2×C32C2×#12111yescharacteristic
373C2×C32#57712yes—
374C3⋊D3—44no—
375C3×D3—81no—
376C24—181no—
377#41—62no—
378#41—62no—
379C2×Q8—32no—
380C2×Q8—31no—
381C2×Q8—61no—
382C2×Q8—62no—
383C2×Q8—62no—
384C2×D4—31no—
385C2×D4—61no—
386C2×D4—92no—
387C2×D4—94no—
388C2×D4—182no—
389C2×D4—181no—
390C22×C4—61no—
391C22×C4—61no—
392C22×C4—184no—
393C22×C4C2×D3211yescharacteristic
394SD16—188no—
395SD16—184no—
396D8—184no—
397M16—62no—
398C2×C8—32no—
399C2×C8—32no—
400C2×C8—62no—
401C4⋊C4—92no—
402C4⋊C4—184no—
403C4⋊C4C2×D3212yes—
404C22⋊C4—21no—
405C22⋊C4—92no—
406C22⋊C4—184no—
407C22⋊C4—184no—
408C42—21no—
409C42—92no—
410C22×C3—22no—
411C22×C3—22no—
412C22×C3—21no—
413C22×C3—22no—
414C22×C3—42no—
415C22×C3—121no—
416C22×C3—122no—
417C22×C3#88412yes—
418C22×C3#88412yes—
419C22×C3C2×D3×D411yescharacteristic
420C22×C3C2×D3×D411yescharacteristic
421C2×D3—41no—
422C2×D3—42no—
423C2×D3—68no—
424C2×D3—64no—
425C2×D3—64no—
426C2×D3—128no—
427C2×D3—124no—
428C2×D3—124no—
429C2×D3—244no—
430C2×D3—244no—
431C2×D3—248no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—22no—
435C3×C4—44no—
436C3×C4—42no—
437C3×C4—42no—
438C3×C4—121no—
439C3×C4—122no—
440C3×C4#88412yes—
441C3×C4#88412yes—
442C3×C4C2×#23511yescharacteristic
443C3×C4C2×#23511yescharacteristic
444C3×C4C2×D3×D411yescharacteristic
445C3×C4C2×D3×D411yescharacteristic
446Dic3—42no—
447Dic3—41no—
448Dic3—64no—
449Dic3—64no—
450Dic3—124no—
451C32#304211yescharacteristic, complemented, Sylow
452C23—61no—
453C23—182no—
454C23—184no—
455C23—722no—
456C23#381111yescharacteristic
457Q8—62no—
458Q8—61no—
459Q8—62no—
460Q8—61no—
461Q8—122no—
462D4—61no—
463D4—61no—
464D4—94no—
465D4—122no—
466D4—182no—
467D4—184no—
468C2×C4—22no—
469C2×C4—62no—
470C2×C4—61no—
471C2×C4—94no—
472C2×C4—122no—
473C2×C4—122no—
474C2×C4—724no—
475C2×C4#379812yes—
476C2×C4#380212yes—
477C2×C4#381111yescharacteristic
478C2×C4C22×D3211yescharacteristic
479C8—62no—
480C8—62no—
481C2×C3—22no—
482C2×C3—22no—
483C2×C3—22no—
484C2×C3—21no—
485C2×C3—42no—
486C2×C3—241no—
487C2×C3C2×#88411yescharacteristic
488C2×C3C2×#88411yescharacteristic
489C2×C3#577012yes—
490C2×C3#577812yes—
491D3—81no—
492D3—128no—
493D3—124no—
494D3—124no—
495C22—22no—
496C22—122no—
497C22—121no—
498C22—184no—
499C22—364no—
500C22—724no—
501C22#6391212yes—
502C22C2×#381111yescharacteristic
503C4—42no—
504C4—121no—
505C4—122no—
506C4—184no—
507C4#6391212yes—
508C4C2×#379811yescharacteristic
509C4C2×#380211yescharacteristic
510C3—21no—
511C3#7886311yescharacteristic, complemented
512C3#7897611yescharacteristic, complemented
513C2—22no—
514C2—241no—
515C2—364no—
516C2C2×#6391211yescharacteristic
517C2#1059547312yes—
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC2×#63825C2
hypercenter#117D32
hypocenterC32#3042
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595992C2semidirect
2. #10594855C2semidirect
3. C22×#3717C2semidirect
5. C3×#5004C2semidirect
6. C3×#5002C2semidirect
7. #10591119C2semidirect
8. #10590565C2semidirect
9. #10590540C2semidirect
23. #63873C22semidirect
24. #63863C22semidirect
31. C3×#810C22semidirect
32. C3×#810C22semidirect
33. C3×#809C22semidirect
34. #63572C22semidirect
48. #5004D3semidirect
49. #5002D3semidirect
138. #810C2×D3semidirect
139. #810C2×D3semidirect
140. #809C2×D3semidirect
451. C32#3042semidirect
511. C3#78863semidirect
512. C3#78976semidirect

Maximal subgroups

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

subgroupindex
#105959922
#105948552
C22×#37172
C2×#638252
C3×#50042
C3×#50022
#105911192
#105905652
#105905402
#789763
#788633