Finite Group Databasebeta

← #11866286

Subgroups — #11866286

Order 1152.

1137 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3744C211yesmaximal, characteristic, complemented
2#10594996C211yesmaximal, characteristic, complemented
3#10594856C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic
5C3×#5113C211yesmaximal, characteristic, complemented
6C3×#5102C211yesmaximal, characteristic, complemented
7#10591107C211yesmaximal, characteristic, complemented
8#10590860C214yesmaximal, complemented
9#10590760C214yesmaximal, complemented
10#79087—31nomaximal
11#78863—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×#634C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C2×#3744—24no—
17C2×#3744C2214yes—
18C3×#926C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21#63974—22no—
22#63962—22no—
23#63894—22no—
24#63894C2214yes—
25#63866C2212yescomplemented
26#63860C2212yescomplemented
27#63857—22no—
28C2×#3717C2212yes—
29#63825—24no—
30C2×#3714C2212yes—
31C3×#821C2212yescomplemented
32C3×#816C2212yescomplemented
33C3×Dic3⋊C8C2214yescomplemented
34#63567C2214yescomplemented
35#5825—31no—
36C2×#949—31no—
37C2×#908—31no—
38C22×#204—31no—
39C22×#204—31no—
40C22×#204—61no—
41#5526—31no—
42#5521—31no—
43#5521—31no—
44C3×#424—31no—
45C3×#416—31no—
46#5120—31no—
47#5113D311yescharacteristic, complemented
48#5102D311yescharacteristic, complemented
49#5004—31no—
50#4844—34no—
51#4841—34no—
52#4818—34no—
53#4787—34no—
54C23×C3⋊D3—21no—
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3—21no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)D414yes—
60C2×C4⋊(C3⋊D3)C2312yes—
61C2×#634—22no—
62C2×#634—22no—
63C2×#634—21no—
64C2×#634C2312yes—
65C2×C3×#67—21no—
66C3×#235—22no—
67C3×#235—22no—
68C2×C3×D12C2311yescharacteristic
69C2×C3×C4×D3—21no—
70C2×C3×Dic6C2311yescharacteristic
71C2×#624—24no—
72C2×C32×C8—22no—
73C2×C32×C8C2312yes—
74#3744—28no—
75C3×#217—21no—
76C3×#217D412yes—
77C3×C4⋊Dic3D412yes—
78C3×C4⋊Dic3C2312yes—
79C3×C4×Dic3—21no—
80C3×C4×Dic3C2312yes—
81C3×#208—22no—
82C2×C3×C3⋊C8C2312yes—
83Dic3⋊Dic3—24no—
84#3722—24no—
85(C2×D3)⋊Dic3—24no—
86#3717—24no—
87#3714—24no—
88#3042—91noSylow
89C2×C3×#41—31no—
90C2×#235C2×D311yescharacteristic
91C22×D12—31no—
92C22×D12—31no—
93C22×D12—61no—
94C22×Dic6—31no—
95C22×Dic6—31no—
96C22×Dic6—61no—
97C2×C3×M16—31no—
98C22×C3×C8—21no—
99C22×C3×C8C2×D311yescharacteristic
100C22×C3×C8C2×D311yescharacteristic
101C3×#117—31no—
102C3×#117—31no—
103#949—64no—
104#944—32no—
105C2×#215—32no—
106#936—32no—
107#935—62no—
108C2×#213—32no—
109#926C2×D311yescharacteristic
110#926C2×D311yescharacteristic
111#924—62no—
112C2×#208C2×D311yescharacteristic
113#908—64no—
114C2×D24—32no—
115C2×#204—32no—
116C2×#204—34no—
117C2×#204—34no—
118C2×#204—64no—
119C2×#204—64no—
120C2×#204—64no—
121C2×#204—68no—
122#897—62no—
123#893—34no—
124#893—62no—
125#886—62no—
126D3×C22⋊C4—62no—
127D3×C22⋊C4—62no—
128#875—32no—
129C4×D12—34no—
130C4×D12—62no—
131#869—32no—
132C3×C4⋊C8—34no—
133C3×#103—32no—
134C3×#102—32no—
135#821C2×D312yescomplemented
136#816—34no—
137#816C2×D312yescomplemented
138Dic3⋊C8C2×D314yescomplemented
139#810—34no—
140C23×C32C2×D411yescharacteristic
141C22×C3⋊D3—22no—
142C22×C3⋊D3—24no—
143C22×C3⋊D3—82no—
144C22×C3×D3—21no—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D412yes—
147C2×C32×C4#4112yes—
148C2×C32×C4C2411yescharacteristic
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—42no—
151C4⋊(C3⋊D3)—24no—
152C4⋊(C3⋊D3)—22no—
153C4⋊(C3⋊D3)C2×D414yes—
154#634—22no—
155#634—22no—
156#634—42no—
157C3×#67—42no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—21no—
160C2×C3×Dic3C2×D414yes—
161C3×D12—21no—
162C3×D12—21no—
163C3×C4×D3—42no—
164C3×Dic6—21no—
165C3×Dic6—21no—
166#624—84no—
167C32×C8—22no—
168C3×C3⋊C8—22no—
169C2×AGL(1,ℤ/8)—91no—
170C22×SD16—91no—
171#536—91no—
172#518—91no—
173#463—94no—
174#461—94no—
175#424—31no—
176#419—91no—
177#416—31no—
178C23×D3—61no—
179C23×D3—61no—
180C23×D3—121no—
181C3×#41—62no—
182C3×#41—62no—
183C2×C3×Q8—31no—
184C2×C3×D4—31no—
185C2×C3×D4—61no—
186C22×C3×C4—21no—
187C22×C3×C4—61no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C2×#67—21no—
191C22×Dic3—61no—
192C22×Dic3—61no—
193C22×Dic3—121no—
194#235—22no—
195#235—22no—
196C2×D12—34no—
197C2×D12—34no—
198C2×D12—32no—
199C2×D12—32no—
200C2×D12—64no—
201C2×D12—62no—
202C2×D12—61no—
203C2×D12—62no—
204C2×D12—61no—
205C2×D12—62no—
206C2×D12—122no—
207C2×D12—121no—
208C2×D12C22×D311yescharacteristic
209C2×C4×D3—21no—
210C2×C4×D3—64no—
211C2×C4×D3—64no—
212C2×Dic6—32no—
213C2×Dic6—32no—
214C2×Dic6—62no—
215C2×Dic6—64no—
216C2×Dic6—62no—
217C2×Dic6—62no—
218C2×Dic6—62no—
219C2×Dic6—62no—
220C2×Dic6—61no—
221C2×Dic6—61no—
222C2×Dic6—121no—
223C2×Dic6—122no—
224C2×Dic6C22×D311yescharacteristic
225C3×M16—62no—
226C2×C3×C8—24no—
227C2×C3×C8—22no—
228C2×C3×C8—22no—
229C2×C3×C8—22no—
230C2×C3×C8—32no—
231C2×C3×C8C22×D312yes—
232C2×C3×C8C22×D312yes—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—32no—
235C3×C22⋊C4—32no—
236C3×C22⋊C4—61no—
237C3×C42—32no—
238C3×C42—61no—
239#217—21no—
240#217—64no—
241#217D1212yes—
242#215—64no—
243#213—64no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—64no—
247C4⋊Dic3—64no—
248C4⋊Dic3D1212yes—
249C4⋊Dic3C22×D312yes—
250Dic3⋊C4—64no—
251C4×Dic3—21no—
252C4×Dic3C22×D312yes—
253#208—22no—
254C2×C3⋊C8C22×D312yes—
255D24—64no—
256#204—68no—
257#204—68no—
258#204—616no—
259#204—64no—
260C22×C32—22no—
261C22×C32#12112yes—
262C22×C32C22×D411yescharacteristic
263C2×C3⋊D3—24no—
264C2×C3⋊D3—44no—
265C2×C3⋊D3—84no—
266C2×C3×D3—41no—
267C2×C3×D3—42no—
268C32×C4#12112yes—
269C32×C4C22×D411yescharacteristic
270C32×C4C2×#4111yescharacteristic
271C3⋊Dic3—42no—
272C3×Dic3—24no—
273C3×Dic3—41no—
274C3×Dic3—42no—
275C2×#41—31no—
276C22×Q8—91no—
277C22×D4—91no—
278AGL(1,ℤ/8)—184no—
279C2×SD16—92no—
280C2×SD16—94no—
281C2×SD16—184no—
282C2×D8—92no—
283C2×M16—31no—
284C22×C8D3211yescharacteristic
285C4⋊Q8—92no—
286#124—92no—
287#123—182no—
288C22⋊Q8—182no—
289C4×D4—94no—
290C4×D4—182no—
291#117—31no—
292#117—31no—
293C2×C22⋊C4—182no—
294C4⋊C8—34no—
295#103—32no—
296#103—94no—
297#102—32no—
298C23×C3—21no—
299C23×C3—61no—
300C23×C3C2×D1211yescharacteristic
301C23×C3D3×D411yescharacteristic
302C22×D3—21no—
303C22×D3—62no—
304C22×D3—62no—
305C22×D3—64no—
306C22×D3—64no—
307C22×D3—122no—
308C22×D3—124no—
309C22×D3—242no—
310C22×D3—242no—
311C22×D3—244no—
312C3×Q8—61no—
313C3×Q8—61no—
314C3×D4—61no—
315C3×D4—61no—
316C3×D4—122no—
317C2×C3×C4—21no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—22no—
321C2×C3×C4—34no—
322C2×C3×C4—61no—
323C2×C3×C4—62no—
324C2×C3×C4—122no—
325C2×C3×C4C2×D1211yescharacteristic
326C2×C3×C4#23512yes—
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4D3×D412yes—
329C2×C3×C4D3×D412yes—
330C2×C3×C4#23912yes—
331C2×C3×C4C23×D311yescharacteristic
332C2×C3×C4C23×D311yescharacteristic
333#67—42no—
334C2×Dic3—22no—
335C2×Dic3—21no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—122no—
339C2×Dic3—124no—
340C2×Dic3—122no—
341C2×Dic3—122no—
342C2×Dic3C2×D1214yes—
343D12—21no—
344D12—21no—
345D12—34no—
346D12—34no—
347D12—64no—
348D12—64no—
349D12—64no—
350D12—62no—
351D12—62no—
352D12—122no—
353D12—124no—
354C4×D3—42no—
355C4×D3—244no—
356C4×D3—244no—
357Dic6—21no—
358Dic6—21no—
359Dic6—64no—
360Dic6—62no—
361Dic6—62no—
362Dic6—62no—
363Dic6—62no—
364Dic6—122no—
365Dic6—124no—
366Dic6—122no—
367Dic6—122no—
368C3×C8—24no—
369C3×C8—22no—
370C3×C8—22no—
371C3×C8—62no—
372C3⋊C8—22no—
373C2×C32—22no—
374C2×C32C2×#12111yescharacteristic
375C2×C32#57712yes—
376C3⋊D3—44no—
377C3×D3—81no—
378C24—181no—
379#41—62no—
380#41—62no—
381C2×Q8—31no—
382C2×Q8—92no—
383C2×Q8—181no—
384C2×Q8—182no—
385C2×Q8—182no—
386C2×D4—31no—
387C2×D4—61no—
388C2×D4—92no—
389C2×D4—94no—
390C2×D4—182no—
391C2×D4—181no—
392C22×C4—61no—
393C22×C4—184no—
394C22×C4—181no—
395C22×C4C2×D3211yescharacteristic
396SD16—188no—
397SD16—184no—
398D8—184no—
399M16—62no—
400C2×C8—22no—
401C2×C8—32no—
402C2×C8C2×D3212yes—
403C4⋊C4—32no—
404C4⋊C4—32no—
405C4⋊C4—184no—
406C22⋊C4—32no—
407C22⋊C4—61no—
408C22⋊C4—184no—
409C22⋊C4—184no—
410C42—32no—
411C42—61no—
412C22×C3—24no—
413C22×C3—22no—
414C22×C3—22no—
415C22×C3—21no—
416C22×C3—22no—
417C22×C3—122no—
418C22×C3—121no—
419C22×C3#88412yes—
420C22×C3#89512yes—
421C22×C3C22×D1211yescharacteristic
422C22×C3C2×D3×D411yescharacteristic
423C2×D3—41no—
424C2×D3—42no—
425C2×D3—64no—
426C2×D3—64no—
427C2×D3—124no—
428C2×D3—124no—
429C2×D3—124no—
430C2×D3—244no—
431C2×D3—244no—
432C2×D3—244no—
433C2×D3—248no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—22no—
437C3×C4—64no—
438C3×C4—122no—
439C3×C4—121no—
440C3×C4#88412yes—
441C3×C4#89512yes—
442C3×C4C2×#23511yescharacteristic
443C3×C4C2×D3×D411yescharacteristic
444C3×C4C2×D3×D411yescharacteristic
445C3×C4C2×#23911yescharacteristic
446Dic3—24no—
447Dic3—41no—
448Dic3—42no—
449Dic3—124no—
450Dic3—122no—
451Dic3—122no—
452C32#304211yescharacteristic, complemented, Sylow
453C23—61no—
454C23—182no—
455C23—184no—
456C23—722no—
457C23D3×D1211yescharacteristic
458Q8—61no—
459Q8—61no—
460Q8—182no—
461Q8—182no—
462Q8—362no—
463D4—61no—
464D4—61no—
465D4—94no—
466D4—122no—
467D4—182no—
468D4—184no—
469C2×C4—34no—
470C2×C4—62no—
471C2×C4—61no—
472C2×C4—122no—
473C2×C4—182no—
474C2×C4—362no—
475C2×C4—724no—
476C2×C4#379912yes—
477C2×C4D3×D1211yescharacteristic
478C2×C4#381112yes—
479C2×C4C22×D3211yescharacteristic
480C8—22no—
481C8—62no—
482C2×C3—24no—
483C2×C3—22no—
484C2×C3—22no—
485C2×C3—22no—
486C2×C3—21no—
487C2×C3—241no—
488C2×C3C2×#88411yescharacteristic
489C2×C3C2×#89511yescharacteristic
490C2×C3#575112yes—
491C2×C3#577012yes—
492D3—81no—
493D3—124no—
494D3—124no—
495D3—244no—
496C22—22no—
497C22—122no—
498C22—121no—
499C22—184no—
500C22—364no—
501C22—724no—
502C22#6391012yes—
503C22C2×D3×D1211yescharacteristic
504C4—64no—
505C4—122no—
506C4—121no—
507C4—362no—
508C4#6391012yes—
509C4C2×#379911yescharacteristic
510C4C2×#381111yescharacteristic
511C3—21no—
512C3#7886311yescharacteristic, complemented
513C3#7908711yescharacteristic, complemented
514C2—22no—
515C2—241no—
516C2—364no—
517C2#1059467912yes—
518C2C2×#6391011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalC2×#63825C2
hypercenterC22×C8D32
hypocenterC32#3042
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×#3744C2semidirect
2. #10594996C2semidirect
3. #10594856C2semidirect
5. C3×#5113C2semidirect
6. C3×#5102C2semidirect
7. #10591107C2semidirect
8. #10590860C2semidirect
9. #10590760C2semidirect
25. #63866C22semidirect
26. #63860C22semidirect
31. C3×#821C22semidirect
32. C3×#816C22semidirect
33. C3×Dic3⋊C8C22semidirect
34. #63567C22semidirect
47. #5113D3semidirect
48. #5102D3semidirect
135. #821C2×D3semidirect
137. #816C2×D3semidirect
138. Dic3⋊C8C2×D3semidirect
452. C32#3042semidirect
512. C3#78863semidirect
513. C3#79087semidirect

Maximal subgroups

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

subgroupindex
C22×#37442
#105949962
#105948562
C2×#638252
C3×#51132
C3×#51022
#105911072
#105908602
#105907602
#790873
#788633