Finite Group Databasebeta

← #11866292

Subgroups — #11866292

Order 1152.

1137 conjugacy classes of subgroups.

The subgroup lattice has 529 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64117C211yesmaximal, characteristic
2#10594996C211yesmaximal, characteristic, complemented
3#10594866C211yesmaximal, characteristic, complemented
4C22×#3717C211yesmaximal, characteristic, complemented
5C3×#5120C211yesmaximal, characteristic, complemented
6C3×#5119C211yesmaximal, characteristic, complemented
7#10591105C211yesmaximal, characteristic, complemented
8#10590770C214yesmaximal, complemented
9#10590760C214yesmaximal, complemented
10#79087—31nomaximal
11#78976—31nomaximal
12C2×#3828C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16#64117—24no—
17C2×#3745C2212yes—
18C2×#3744C2212yes—
19C3×#926C2211yescharacteristic
20C3×#926C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22#63974—22no—
23#63966—22no—
24#63894—22no—
25#63894C2214yes—
26#63871—22no—
27#63866C2212yescomplemented
28#63864C2212yescomplemented
29C2×#3717—24no—
30C2×#3717C2214yes—
31C3×#816C2214yescomplemented
32C3×Dic3⋊C8C2214yescomplemented
33#63567C2212yescomplemented
34#63564C2212yescomplemented
35#5816—31no—
36C22×#215—31no—
37C2×#908—31no—
38C2×#908—31no—
39C2×#908—61no—
40C22×#204—31no—
41#5526—31no—
42#5521—31no—
43#5521—31no—
44C3×#424—31no—
45C3×#419—31no—
46#5120D311yescharacteristic, complemented
47#5119D311yescharacteristic, complemented
48#5113—31no—
49#5002—31no—
50#4844—34no—
51#4841—34no—
52#4819—34no—
53#4818—34no—
54C23×C3⋊D3—21no—
55C22×C32×C4C2311yescharacteristic
56C2×#638—21no—
57#3828—22no—
58#3828—22no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)—22no—
61C2×C4⋊(C3⋊D3)D414yes—
62C2×C4⋊(C3⋊D3)C2311yescharacteristic
63C2×C4⋊(C3⋊D3)C2312yes—
64C2×C4×C3⋊D3—21no—
65C2×#634C2311yescharacteristic
66C22×C3×Dic3—21no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71C2×#624—24no—
72C32×M16—22no—
73C2×C32×C8C2312yes—
74#3745—24no—
75#3744—24no—
76C3×#217—21no—
77C3×#217D412yes—
78C3×C4⋊Dic3D412yes—
79C3×C4⋊Dic3C2312yes—
80C3×C4×Dic3—21no—
81C3×C4×Dic3C2312yes—
82C2×C3×C3⋊C8—22no—
83C2×C3×C3⋊C8C2312yes—
84Dic3⋊Dic3—24no—
85#3722—24no—
86#3722—24no—
87#3717—28no—
88#3042—91noSylow
89C22×C3×Q8—31no—
90C2×#235—31no—
91C2×#235—31no—
92C2×#235—61no—
93C22×D12—31no—
94C22×D12—31no—
95C22×D12—61no—
96C22×Dic6C2×D311yescharacteristic
97C2×C3×M16—21no—
98C2×C3×M16C2×D311yescharacteristic
99C2×C3×M16C2×D311yescharacteristic
100C22×C3×C8—31no—
101C3×#117—31no—
102C3×#117—31no—
103#947—32no—
104#946—62no—
105#944—32no—
106C2×#215—34no—
107C2×#215—64no—
108#929—62no—
109#926C2×D311yescharacteristic
110#926C2×D311yescharacteristic
111C22×C3⋊C8C2×D311yescharacteristic
112#908—64no—
113#908—64no—
114#908—68no—
115C2×D24—32no—
116C2×D24—32no—
117C2×D24—62no—
118C2×#204—34no—
119C2×#204—32no—
120C2×#204—32no—
121C2×#204—62no—
122C2×#204—64no—
123#897—62no—
124#893—34no—
125#893—62no—
126#886—62no—
127D3×C22⋊C4—62no—
128D3×C22⋊C4—62no—
129#875—32no—
130C4×D12—34no—
131C4×D12—62no—
132#869—32no—
133C3×C4⋊C8—34no—
134C3×#103—34no—
135#821—32no—
136#816—32no—
137#816C2×D314yescomplemented
138Dic3⋊C8C2×D314yescomplemented
139#810—32no—
140#809—32no—
141C23×C32C2×D411yescharacteristic
142C22×C3⋊D3—22no—
143C22×C3⋊D3—24no—
144C22×C3⋊D3—21no—
145C22×C3⋊D3—82no—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D412yes—
148C2×C32×C4#4112yes—
149C2×C32×C4C2411yescharacteristic
150#638—42no—
151C2×C3⋊Dic3—21no—
152C4⋊(C3⋊D3)—21no—
153C4⋊(C3⋊D3)—24no—
154C4⋊(C3⋊D3)—22no—
155C4⋊(C3⋊D3)—21no—
156C4⋊(C3⋊D3)C2×D414yes—
157C4×C3⋊D3—42no—
158#634—21no—
159#634—21no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—42no—
163C2×C3×Dic3C2×D414yes—
164C3×Dic6—22no—
165C3×Dic6—22no—
166C3×Dic6—42no—
167#624—84no—
168C32×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—31no—
177#419—31no—
178#416—91no—
179C23×D3—61no—
180C23×D3—61no—
181C23×D3—121no—
182C2×C3×Q8—32no—
183C2×C3×Q8—61no—
184C2×C3×Q8—62no—
185C2×C3×Q8—62no—
186C22×C3×C4—21no—
187C22×C3×C4—61no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C2×#67—61no—
191C2×#67—61no—
192C2×#67—121no—
193C22×Dic3—21no—
194#235—64no—
195#235—62no—
196#235—62no—
197#235—62no—
198#235—62no—
199#235—122no—
200C2×D12—34no—
201C2×D12—34no—
202C2×D12—32no—
203C2×D12—32no—
204C2×D12—31no—
205C2×D12—31no—
206C2×D12—62no—
207C2×D12—61no—
208C2×D12—64no—
209C2×D12—61no—
210C2×D12—62no—
211C2×D12—61no—
212C2×D12—62no—
213C2×D12—122no—
214C2×D12—121no—
215C2×C4×D3—61no—
216C2×C4×D3—61no—
217C2×C4×D3—64no—
218C2×C4×D3—64no—
219C2×C4×D3—121no—
220C2×Dic6—22no—
221C2×Dic6—22no—
222C2×Dic6—21no—
223C2×Dic6—31no—
224C2×Dic6—31no—
225C2×Dic6—61no—
226C2×Dic6C22×D312yes—
227C3×M16—24no—
228C3×M16—22no—
229C3×M16—22no—
230C2×C3×C8—22no—
231C2×C3×C8—32no—
232C2×C3×C8—62no—
233C2×C3×C8C22×D312yes—
234C2×C3×C8C22×D312yes—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—32no—
237C3×C22⋊C4—32no—
238C3×C22⋊C4—61no—
239C3×C42—32no—
240C3×C42—61no—
241#217—21no—
242#217D1212yes—
243#215—68no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—64no—
247(C2×D3)⋊C4—64no—
248C4⋊Dic3—64no—
249C4⋊Dic3D1212yes—
250C4⋊Dic3C22×D312yes—
251Dic3⋊C4—64no—
252C4×Dic3—21no—
253C4×Dic3C22×D312yes—
254C2×C3⋊C8—22no—
255C2×C3⋊C8C22×D312yes—
256D24—64no—
257D24—64no—
258D24—68no—
259#204—64no—
260#204—64no—
261#204—68no—
262#204—68no—
263C22×C32—22no—
264C22×C32#12112yes—
265C22×C32C22×D411yescharacteristic
266C2×C3⋊D3—24no—
267C2×C3⋊D3—41no—
268C2×C3⋊D3—44no—
269C2×C3⋊D3—42no—
270C2×C3⋊D3—84no—
271C32×C4#12112yes—
272C32×C4C22×D411yescharacteristic
273C32×C4C2×#4111yescharacteristic
274C3⋊Dic3—41no—
275C3×Dic3—24no—
276C3×Dic3—42no—
277C3×Dic3—42no—
278C2×#41—91no—
279C22×Q8—31no—
280C22×D4—91no—
281AGL(1,ℤ/8)—184no—
282C2×SD16—94no—
283C2×SD16—92no—
284C2×SD16—184no—
285C2×D8—92no—
286C2×M16D3211yescharacteristic
287C22×C8—31no—
288C4⋊Q8—92no—
289#124—92no—
290#123—182no—
291C22⋊Q8—182no—
292C4×D4—94no—
293C4×D4—182no—
294#117—31no—
295#117—31no—
296C2×C22⋊C4—182no—
297C4⋊C8—34no—
298#103—34no—
299#103—92no—
300#102—92no—
301C23×C3—21no—
302C23×C3C2×D1211yescharacteristic
303C23×C3D3×D411yescharacteristic
304C22×D3—62no—
305C22×D3—62no—
306C22×D3—64no—
307C22×D3—64no—
308C22×D3—61no—
309C22×D3—61no—
310C22×D3—121no—
311C22×D3—122no—
312C22×D3—124no—
313C22×D3—242no—
314C22×D3—242no—
315C22×D3—244no—
316C3×Q8—62no—
317C3×Q8—62no—
318C3×Q8—122no—
319C2×C3×C4—21no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—22no—
323C2×C3×C4—34no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—122no—
327C2×C3×C4C2×D1211yescharacteristic
328C2×C3×C4#23512yes—
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D412yes—
331C2×C3×C4D3×D412yes—
332C2×C3×C4#23912yes—
333C2×C3×C4C23×D311yescharacteristic
334C2×C3×C4C23×D311yescharacteristic
335#67—124no—
336#67—122no—
337#67—122no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—42no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—121no—
344C2×Dic3C2×D1214yes—
345D12—34no—
346D12—34no—
347D12—64no—
348D12—62no—
349D12—64no—
350D12—64no—
351D12—62no—
352D12—61no—
353D12—61no—
354D12—61no—
355D12—62no—
356D12—61no—
357D12—122no—
358D12—124no—
359D12—121no—
360C4×D3—124no—
361C4×D3—122no—
362C4×D3—122no—
363C4×D3—244no—
364C4×D3—244no—
365Dic6—22no—
366Dic6—22no—
367Dic6—42no—
368Dic6—62no—
369Dic6—61no—
370Dic6—61no—
371Dic6—61no—
372Dic6—61no—
373Dic6—121no—
374C3×C8—24no—
375C3×C8—22no—
376C3×C8—22no—
377C3×C8—62no—
378C3⋊C8—22no—
379C2×C32—22no—
380C2×C32C2×#12111yescharacteristic
381C2×C32#57712yes—
382C3⋊D3—44no—
383C3⋊D3—81no—
384C24—181no—
385#41—182no—
386#41—182no—
387C2×Q8—32no—
388C2×Q8—61no—
389C2×Q8—62no—
390C2×Q8—62no—
391C2×Q8—91no—
392C2×D4—92no—
393C2×D4—91no—
394C2×D4—94no—
395C2×D4—181no—
396C2×D4—182no—
397C2×D4—181no—
398C22×C4—61no—
399C22×C4—184no—
400C22×C4—181no—
401C22×C4C2×D3211yescharacteristic
402SD16—184no—
403SD16—188no—
404D8—184no—
405M16—22no—
406C2×C8—32no—
407C2×C8—62no—
408C2×C8C2×D3212yes—
409C4⋊C4—32no—
410C4⋊C4—32no—
411C4⋊C4—184no—
412C22⋊C4—32no—
413C22⋊C4—61no—
414C22⋊C4—184no—
415C22⋊C4—184no—
416C42—32no—
417C42—61no—
418C22×C3—22no—
419C22×C3—22no—
420C22×C3—21no—
421C22×C3—22no—
422C22×C3—42no—
423C22×C3#88412yes—
424C22×C3#89512yes—
425C22×C3C22×D1211yescharacteristic
426C22×C3C2×D3×D411yescharacteristic
427C2×D3—64no—
428C2×D3—64no—
429C2×D3—124no—
430C2×D3—124no—
431C2×D3—124no—
432C2×D3—122no—
433C2×D3—121no—
434C2×D3—122no—
435C2×D3—121no—
436C2×D3—122no—
437C2×D3—244no—
438C2×D3—242no—
439C2×D3—244no—
440C2×D3—244no—
441C2×D3—248no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—22no—
445C3×C4—64no—
446C3×C4—122no—
447C3×C4—122no—
448C3×C4#88412yes—
449C3×C4#89512yes—
450C3×C4C2×#23511yescharacteristic
451C3×C4C2×D3×D411yescharacteristic
452C3×C4C2×D3×D411yescharacteristic
453C3×C4C2×#23911yescharacteristic
454Dic3—24no—
455Dic3—42no—
456Dic3—42no—
457Dic3—122no—
458Dic3—121no—
459Dic3—121no—
460C32#304211yescharacteristic, complemented, Sylow
461C23—182no—
462C23—184no—
463C23—181no—
464C23—722no—
465C23D3×D1211yescharacteristic
466Q8—62no—
467Q8—62no—
468Q8—122no—
469Q8—181no—
470Q8—181no—
471D4—94no—
472D4—182no—
473D4—181no—
474D4—181no—
475D4—184no—
476D4—362no—
477C2×C4—34no—
478C2×C4—62no—
479C2×C4—62no—
480C2×C4—122no—
481C2×C4—181no—
482C2×C4—362no—
483C2×C4—724no—
484C2×C4#379912yes—
485C2×C4D3×D1211yescharacteristic
486C2×C4#381112yes—
487C2×C4C22×D3211yescharacteristic
488C8—22no—
489C8—62no—
490C2×C3—22no—
491C2×C3—22no—
492C2×C3—22no—
493C2×C3—21no—
494C2×C3—42no—
495C2×C3C2×#88411yescharacteristic
496C2×C3C2×#89511yescharacteristic
497C2×C3#575112yes—
498C2×C3#577812yes—
499D3—124no—
500D3—124no—
501D3—244no—
502D3—242no—
503D3—241no—
504D3—241no—
505C22—22no—
506C22—184no—
507C22—364no—
508C22—362no—
509C22—361no—
510C22—724no—
511C22#6391012yes—
512C22C2×D3×D1211yescharacteristic
513C4—64no—
514C4—122no—
515C4—122no—
516C4—361no—
517C4#6391012yes—
518C4C2×#379911yescharacteristic
519C4C2×#381111yescharacteristic
520C3—21no—
521C3#7897611yescharacteristic, complemented
522C3#7908711yescharacteristic, complemented
523C2—22no—
524C2—364no—
525C2—721no—
526C2#1059471512yes—
527C2C2×#6391011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC2×#64117C2
hypercenterC2×M16D32
hypocenterC32#3042
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10594996C2semidirect
3. #10594866C2semidirect
4. C22×#3717C2semidirect
5. C3×#5120C2semidirect
6. C3×#5119C2semidirect
7. #10591105C2semidirect
8. #10590770C2semidirect
9. #10590760C2semidirect
27. #63866C22semidirect
28. #63864C22semidirect
31. C3×#816C22semidirect
32. C3×Dic3⋊C8C22semidirect
33. #63567C22semidirect
34. #63564C22semidirect
46. #5120D3semidirect
47. #5119D3semidirect
137. #816C2×D3semidirect
138. Dic3⋊C8C2×D3semidirect
460. C32#3042semidirect
521. C3#78976semidirect
522. C3#79087semidirect

Maximal subgroups

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

subgroupindex
C2×#641172
#105949962
#105948662
C22×#37172
C3×#51202
C3×#51192
#105911052
#105907702
#105907602
#790873
#789763