Finite Group Databasebeta

← #11866279

Subgroups — #11866279

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×#3754C211yesmaximal, characteristic, complemented
2C3×#5798C211yesmaximal, characteristic, complemented
3C2×C3×#932C211yesmaximal, characteristic
4#10594856C211yesmaximal, characteristic, complemented
5#10591489C214yesmaximal, complemented
6#10591468C214yesmaximal, complemented
7#10591117C211yesmaximal, characteristic, complemented
8#10591107C211yesmaximal, characteristic, complemented
9#10591083C211yesmaximal, characteristic, complemented
10#83935—31nomaximal
11#82544—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C22×#634C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15C2×#3754—24no—
16C2×#3754C2214yes—
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×#217—22no—
19C3×D4×Dic3—22no—
20C3×D4×Dic3C2214yes—
21C2×C3×#214C2212yes—
22C3×#932—24no—
23C2×C3×#213C2212yes—
24C3×#926C2211yescharacteristic
25C3×#926C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27#63962—22no—
28#63866C2212yescomplemented
29#63860C2212yescomplemented
30#63857—22no—
31Dic3⋊(C3⋊C8)C2214yescomplemented
32#63567C2214yescomplemented
33#63565C2212yescomplemented
34#63562C2212yescomplemented
35C2×C3×AGL(1,ℤ/8)—31no—
36C3×#518—31no—
37#5825—31no—
38#5798D311yescharacteristic, complemented
39C22×#214—31no—
40C22×#214—31no—
41C22×#214—61no—
42C2×#932D311yescharacteristic
43#5526—31no—
44#5233—31no—
45#5162—34no—
46#5153—34no—
47#5120—31no—
48#5119—31no—
49#5019—34no—
50#5016—34no—
51#5004—31no—
52#5002—31no—
53#4999—31no—
54C24×C32—21no—
55C2×C32×D4—21no—
56C2×C32×D4—22no—
57C2×C32×D4D414yes—
58C2×C32×D4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3—21no—
61C2×#634—22no—
62C2×#634—22no—
63C2×#634—21no—
64C2×#634C2312yes—
65C2×C3×#67—21no—
66C22×C3×Dic3—24no—
67C3×#235—22no—
68C3×#235—22no—
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×Dic6C2311yescharacteristic
72#3754—28no—
73C2×C3⋊(C3⋊C8)—22no—
74C2×C3⋊(C3⋊C8)C2312yes—
75C3×#217—21no—
76C3×#217—24no—
77C3×#217D412yes—
78C3×#214—24no—
79C3×#213—24no—
80C3×C4⋊Dic3D412yes—
81C3×C4⋊Dic3C2312yes—
82C3×C4×Dic3—21no—
83C3×C4×Dic3C2312yes—
84C3×#208—22no—
85C2×C3×C3⋊C8C2312yes—
86Dic3⋊Dic3—24no—
87(C2×D3)⋊Dic3—24no—
88#3042—91noSylow
89C2×C3×#41—31no—
90C22×C3×D4—21no—
91C22×C3×D4C2×D311yescharacteristic
92C22×C3×D4C2×D311yescharacteristic
93C2×#235C2×D311yescharacteristic
94C22×Dic6—31no—
95C22×Dic6—31no—
96C22×Dic6—61no—
97C3×AGL(1,ℤ/8)—64no—
98C2×C3×SD16—32no—
99C2×C3×D8—32no—
100C2×C3×M16—31no—
101C3×C4×D4—34no—
102C3×C4×D4—62no—
103C3×#117—31no—
104C3×#117—31no—
105C2×C3×C22⋊C4—62no—
106C2×#217—22no—
107#944—32no—
108#936—32no—
109#935—62no—
110D4×Dic3—22no—
111D4×Dic3C2×D314yes—
112C2×#214—34no—
113C2×#214—34no—
114C2×#214—64no—
115C2×#214—68no—
116C2×#214—64no—
117C2×#214—64no—
118C2×#214C2×D312yes—
119#932—24no—
120C2×#213C2×D312yes—
121#926C2×D311yescharacteristic
122#926C2×D311yescharacteristic
123#924—62no—
124C2×#208C2×D311yescharacteristic
125C22×C3⋊C8—31no—
126C22×C3⋊C8—31no—
127C22×C3⋊C8—61no—
128#897—62no—
129#886—62no—
130#875—32no—
131#869—32no—
132#835—32no—
133#832—32no—
134#816—34no—
135Dic3⋊C8—34no—
136#810—32no—
137#810—34no—
138#809—32no—
139C4⋊(C3⋊C8)—34no—
140C23×C32—22no—
141C23×C32—24no—
142C23×C32—82no—
143C23×C32C2×D411yescharacteristic
144C22×C3×D3—21no—
145C32×D4—24no—
146C32×D4—22no—
147C32×D4C2×D414yes—
148C2×C32×C4C2×D412yes—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4#4112yes—
151C2×C32×C4C2411yescharacteristic
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—42no—
154#634—22no—
155#634—22no—
156#634—42no—
157C3×#67—42no—
158C2×C3×Dic3—21no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—84no—
161C2×C3×Dic3C2×D414yes—
162C3×D12—21no—
163C3×D12—21no—
164C3×C4×D3—42no—
165C3×Dic6—21no—
166C3×Dic6—21no—
167C3⋊(C3⋊C8)—22no—
168C3×C3⋊C8—22no—
169C2×AGL(1,ℤ/8)—31no—
170C22×SD16—91no—
171#536—91no—
172#518—31no—
173#463—94no—
174#461—94no—
175#424—91no—
176#419—91no—
177#416—91no—
178C24×C3—21no—
179C24×C3—21no—
180C24×C3—41no—
181C3×#41—62no—
182C3×#41—62no—
183C2×C3×Q8—31no—
184C2×C3×D4—22no—
185C2×C3×D4—21no—
186C2×C3×D4—22no—
187C2×C3×D4—21no—
188C2×C3×D4—24no—
189C2×C3×D4—22no—
190C2×C3×D4—31no—
191C2×C3×D4—42no—
192C2×C3×D4—41no—
193C2×C3×D4—61no—
194C2×C3×D4D1214yes—
195C2×C3×D4#6714yes—
196C2×C3×D4C22×D312yes—
197C2×C3×D4C22×D312yes—
198C22×C3×C4—21no—
199C22×C3×C4—64no—
200C22×C3×C4—61no—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C2×#67—21no—
204C22×Dic3—24no—
205C22×Dic3—61no—
206C22×Dic3—61no—
207C22×Dic3—121no—
208#235—22no—
209#235—22no—
210C2×D12C22×D311yescharacteristic
211C2×C4×D3—21no—
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×SD16—64no—
226C3×D8—64no—
227C3×M16—62no—
228C2×C3×C8—32no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—32no—
231C3×C22⋊C4—32no—
232C3×C22⋊C4—64no—
233C3×C22⋊C4—61no—
234C3×C42—32no—
235C3×C42—61no—
236#217—21no—
237#217—24no—
238#217—64no—
239#217#6712yes—
240#214—24no—
241#214—616no—
242#214—68no—
243#214—68no—
244#213—24no—
245(C2×D3)⋊C4—64no—
246C4⋊Dic3—64no—
247C4⋊Dic3#6712yes—
248C4⋊Dic3C22×D312yes—
249Dic3⋊C4—64no—
250C4×Dic3—21no—
251C4×Dic3C22×D312yes—
252#208—22no—
253C2×C3⋊C8—32no—
254C2×C3⋊C8—32no—
255C2×C3⋊C8—62no—
256C2×C3⋊C8—64no—
257C2×C3⋊C8—62no—
258C2×C3⋊C8—62no—
259C2×C3⋊C8C22×D312yes—
260C22×C32—22no—
261C22×C32—24no—
262C22×C32—44no—
263C22×C32—84no—
264C22×C32#12112yes—
265C22×C32C22×D411yescharacteristic
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×D4D3211yescharacteristic
278AGL(1,ℤ/8)—64no—
279C2×SD16—32no—
280C2×SD16—94no—
281C2×SD16—184no—
282C2×D8—32no—
283C2×M16—31no—
284C22×C8—91no—
285C4⋊Q8—92no—
286#124—92no—
287#123—182no—
288C22⋊Q8—182no—
289C4×D4—34no—
290C4×D4—62no—
291#117—31no—
292#117—31no—
293C2×C22⋊C4—62no—
294C4⋊C8—94no—
295#103—94no—
296#103—92no—
297#102—92no—
298C23×C3—22no—
299C23×C3—22no—
300C23×C3—24no—
301C23×C3—24no—
302C23×C3—21no—
303C23×C3—42no—
304C23×C3—44no—
305C23×C3—61no—
306C23×C3—82no—
307C23×C3—82no—
308C23×C3—84no—
309C23×C3D3×D411yescharacteristic
310C23×C3C2×#6711yescharacteristic
311C22×D3—21no—
312C3×Q8—61no—
313C3×Q8—61no—
314C3×D4—24no—
315C3×D4—24no—
316C3×D4—22no—
317C3×D4—22no—
318C3×D4—24no—
319C3×D4—42no—
320C3×D4—44no—
321C3×D4—61no—
322C3×D4—61no—
323C3×D4—122no—
324C3×D4C2×D1214yes—
325C3×D4C2×#6714yes—
326C2×C3×C4—21no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—34no—
331C2×C3×C4—62no—
332C2×C3×C4—61no—
333C2×C3×C4—122no—
334C2×C3×C4—244no—
335C2×C3×C4C2×D1212yes—
336C2×C3×C4#23512yes—
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4#23712yes—
339C2×C3×C4C2×#6712yes—
340C2×C3×C4C2×#6711yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343#67—42no—
344C2×Dic3—21no—
345C2×Dic3—22no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—84no—
349C2×Dic3—122no—
350C2×Dic3—124no—
351C2×Dic3—122no—
352C2×Dic3—122no—
353C2×Dic3C2×#6714yes—
354D12—21no—
355D12—21no—
356C4×D3—42no—
357Dic6—21no—
358Dic6—21no—
359Dic6—64no—
360Dic6—62no—
361Dic6—62no—
362Dic6—62no—
363Dic6—62no—
364Dic6—122no—
365Dic6—124no—
366Dic6—122no—
367Dic6—122no—
368C3×C8—62no—
369C3⋊C8—22no—
370C3⋊C8—64no—
371C3⋊C8—62no—
372C3⋊C8—62no—
373C2×C32—22no—
374C2×C32—44no—
375C2×C32C2×#12111yescharacteristic
376C2×C32#57712yes—
377C3×D3—81no—
378C24—21no—
379#41—62no—
380#41—62no—
381C2×Q8—31no—
382C2×Q8—92no—
383C2×Q8—181no—
384C2×Q8—182no—
385C2×Q8—182no—
386C2×D4—22no—
387C2×D4—21no—
388C2×D4—31no—
389C2×D4—61no—
390C2×D4#62614yes—
391C2×D4C2×D3212yes—
392C22×C4—64no—
393C22×C4—61no—
394C22×C4—181no—
395C22×C4C2×D3211yescharacteristic
396SD16—64no—
397SD16—188no—
398D8—64no—
399M16—62no—
400C2×C8—32no—
401C2×C8—92no—
402C2×C8—182no—
403C4⋊C4—32no—
404C4⋊C4—32no—
405C4⋊C4—184no—
406C22⋊C4—32no—
407C22⋊C4—64no—
408C22⋊C4—61no—
409C22⋊C4—184no—
410C42—32no—
411C42—61no—
412C22×C3—24no—
413C22×C3—22no—
414C22×C3—22no—
415C22×C3—24no—
416C22×C3—24no—
417C22×C3—21no—
418C22×C3—22no—
419C22×C3—44no—
420C22×C3—44no—
421C22×C3—44no—
422C22×C3—84no—
423C22×C3—84no—
424C22×C3—84no—
425C22×C3—88no—
426C22×C3—121no—
427C22×C3—122no—
428C22×C3#93012yes—
429C22×C3#93912yes—
430C22×C3C2×D3×D411yescharacteristic
431C22×C3C22×#6711yescharacteristic
432C2×D3—42no—
433C2×D3—41no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—22no—
437C3×C4—64no—
438C3×C4—122no—
439C3×C4—121no—
440C3×C4#93012yes—
441C3×C4#93912yes—
442C3×C4C22×D1211yescharacteristic
443C3×C4C2×#23511yescharacteristic
444C3×C4C2×#23711yescharacteristic
445C3×C4C22×#6711yescharacteristic
446Dic3—24no—
447Dic3—41no—
448Dic3—42no—
449Dic3—124no—
450Dic3—122no—
451Dic3—122no—
452C32#304211yescharacteristic, complemented, Sylow
453C23—22no—
454C23—24no—
455C23—61no—
456C23—82no—
457C23D3×#6711yescharacteristic
458Q8—61no—
459Q8—61no—
460Q8—182no—
461Q8—182no—
462Q8—362no—
463D4—22no—
464D4—24no—
465D4—61no—
466D4—61no—
467D4—122no—
468D4C2×#62614yes—
469C2×C4—34no—
470C2×C4—62no—
471C2×C4—61no—
472C2×C4—122no—
473C2×C4—182no—
474C2×C4—244no—
475C2×C4—362no—
476C2×C4#380412yes—
477C2×C4C2×#62612yes—
478C2×C4D3×#6711yescharacteristic
479C2×C4C22×D3211yescharacteristic
480C8—62no—
481C8—182no—
482C2×C3—24no—
483C2×C3—22no—
484C2×C3—22no—
485C2×C3—22no—
486C2×C3—21no—
487C2×C3—44no—
488C2×C3—44no—
489C2×C3—84no—
490C2×C3—241no—
491C2×C3#577512yes—
492C2×C3C2×#93011yescharacteristic
493C2×C3C2×#93911yescharacteristic
494C2×C3#583612yes—
495D3—81no—
496C22—22no—
497C22—24no—
498C22—44no—
499C22—84no—
500C22—122no—
501C22—121no—
502C22#6397812yes—
503C22C2×D3×#6711yescharacteristic
504C4—64no—
505C4—122no—
506C4—121no—
507C4—362no—
508C4#6397812yes—
509C4C2×#380411yescharacteristic
510C4C22×#62611yescharacteristic
511C3—21no—
512C3#8254411yescharacteristic, complemented
513C3#8393511yescharacteristic, complemented
514C2—22no—
515C2—44no—
516C2—241no—
517C2#1059510612yes—
518C2C2×#6397811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×#932C2
hypercenterC22×D4D32
hypocenterC32#3042
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3754C2semidirect
2. C3×#5798C2semidirect
4. #10594856C2semidirect
5. #10591489C2semidirect
6. #10591468C2semidirect
7. #10591117C2semidirect
8. #10591107C2semidirect
9. #10591083C2semidirect
28. #63866C22semidirect
29. #63860C22semidirect
31. Dic3⋊(C3⋊C8)C22semidirect
32. #63567C22semidirect
33. #63565C22semidirect
34. #63562C22semidirect
38. #5798D3semidirect
452. C32#3042semidirect
512. C3#82544semidirect
513. C3#83935semidirect

Maximal subgroups

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

subgroupindex
C22×#37542
C3×#57982
C2×C3×#9322
#105948562
#105914892
#105914682
#105911172
#105911072
#105910832
#839353
#825443