Finite Group Databasebeta

← #11857551

Subgroups — #11857551

Order 1152.

1769 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64330C211yesmaximal, characteristic
2#10595957C211yesmaximal, characteristic, complemented
3#10595510C211yesmaximal, characteristic, complemented
4C2×C3×#806C212yesmaximal, complemented
5C2×#63580C212yesmaximal, complemented
6#10590406C214yesmaximal, complemented
7#10590404C214yesmaximal, complemented
8#78688—32nomaximal
9C22×#638C2211yescharacteristic
10C22×C3×#67C2212yes—
11#64330—22no—
12#64330—22no—
13#64330—24no—
14C2×#3811C2212yes—
15C2×D3×#67C414yescomplemented
16C2×#3805C2212yes—
17C2×#3804C414yescomplemented
18C2×C32×C22⋊C4C2211yescharacteristic, complemented
19C2×#3757C2211yescharacteristic, complemented
20C4×#638—22no—
21#64090—22no—
22C22⋊C4×C3⋊D3C2212yescomplemented
23#64086C2212yescomplemented
24C2×C3×#217C2212yescomplemented
25#63974C2212yescomplemented
26#63957C2212yescomplemented
27#63952—24no—
28C3×#806C2218yescomplemented
29#63580C2218yescomplemented
30C2×#1004—32no—
31#5486—32no—
32#5486—32no—
33#5486—61no—
34C2×C3×#99—32no—
35C2×#834—32no—
36C2×#806—32no—
37C2×#806D312yescomplemented
38D3×#99—38no—
39#4740—38no—
40C24×C32C2311yescharacteristic
41C23×C3⋊D3C2311yescharacteristic
42C23×C3×D3C2×C412yescomplemented
43C22×D32C2×C412yescomplemented
44C22×C32×C4—21no—
45C2×#638C2×C414yes—
46C2×#638D412yes—
47C2×#638D412yes—
48C2×#638D414yes—
49C22×C3⋊Dic3—21no—
50C22×C3⋊Dic3C2311yescharacteristic
51C2×C4×C3⋊D3—22no—
52C2×C3×#67—22no—
53C2×C3×#67—22no—
54C2×C3×#67—22no—
55C2×C3×#67—22no—
56C2×C3×#67C2×C414yescomplemented
57C2×C3×#67C2314yes—
58C22×C3×Dic3—22no—
59C22×C3×Dic3C2×C412yescomplemented
60#3811—24no—
61#3811—24no—
62D3×#67—28no—
63D3×#67—28no—
64C2×#627C2×C412yescomplemented
65C2×#626C2×C414yescomplemented
66C2×#625C2×C412yescomplemented
67C2×#624—22no—
68C2×#624C2×C412yescomplemented
69#3805—24no—
70#3805—24no—
71#3804—28no—
72#3804—28no—
73C2×D3×Dic3C2×C414yescomplemented
74C32×C22⋊C4—21no—
75C32×C22⋊C4C2312yes—
76#3757—21no—
77#3757C2312yes—
78#3752—22no—
79#3750—22no—
80C4×C3⋊Dic3—22no—
81C3×#217—22no—
82C3×#217C2314yes—
83#3724—22no—
84#3722—22no—
85Dic32—22no—
86#2883—91noSylow
87C22×C3×D4—32no—
88C22×#67—32no—
89C22×#67—34no—
90C22×#67—61no—
91C22×#67C2×D312yes—
92#1004—64no—
93#1004—64no—
94#1004—64no—
95#1004—64no—
96C2×#237—34no—
97C2×#237—34no—
98C2×D3×D4—34no—
99C2×D3×D4—34no—
100C2×#235—34no—
101C2×C3×C22⋊C4—21no—
102C2×C3×C22⋊C4—32no—
103C2×C3×C22⋊C4C2×D312yescomplemented
104C2×#217—32no—
105C2×#217—61no—
106C2×#217C2×D312yescomplemented
107C4×#67—64no—
108C4×#67—64no—
109C4×#67—64no—
110#67⋊C4—64no—
111#67⋊C4—64no—
112#67⋊C4—64no—
113D3×C22⋊C4—34no—
114D3×C22⋊C4—34no—
115D3×C22⋊C4—62no—
116#877—34no—
117#877—34no—
118#877—62no—
119C3×#99—38no—
120#834—38no—
121#806—38no—
122#806C2×D318yescomplemented
123C23×C32—81no—
124C23×C32C22×C412yes—
125C23×C32C2×D412yes—
126C23×C32C2×D411yescharacteristic
127C23×C32C2×D411yescharacteristic
128C23×C32C2411yescharacteristic
129C22×C3⋊D3—81no—
130C22×C3⋊D3C22×C412yes—
131C22×C3⋊D3C2×D412yes—
132C22×C3⋊D3C2×D412yes—
133C22×C3×D3—22no—
134C22×C3×D3—22no—
135C22×C3×D3—82no—
136C22×C3×D3C22×C414yes—
137C2×D32—24no—
138C2×D32—82no—
139C2×C32×C4—22no—
140C2×C32×C4—81no—
141#638C22⋊C418yes—
142#638C22⋊C418yes—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—81no—
145C2×C3⋊Dic3C22×C412yes—
146C2×C3⋊Dic3C2×D412yes—
147C2×C3⋊Dic3C2×D412yes—
148C4×C3⋊D3—82no—
149C3×#67—24no—
150C3×#67—24no—
151C3×#67—24no—
152C3×#67—24no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—24no—
156C2×C3×Dic3—82no—
157C2×C3×Dic3C22×C414yes—
158#627—24no—
159#626—28no—
160#625—24no—
161#624—24no—
162#624—82no—
163D3×Dic3—28no—
164C2×H(5,𝔽2)—91no—
165#518—91no—
166#518—91no—
167#410—94no—
168C2×#99—32no—
169C2×#99—94no—
170C2×#99—92no—
171C24×C3—21no—
172C24×C3—32no—
173C24×C3C22×D312yes—
174C23×D3—32no—
175C23×D3—34no—
176C23×D3—61no—
177C23×D3C4×D312yescomplemented
178C2×C3×D4—34no—
179C2×C3×D4—34no—
180C2×C3×D4—62no—
181C2×C3×D4—62no—
182C2×C3×D4—62no—
183C2×C3×D4—62no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—32no—
187C22×C3×C4—62no—
188C2×#67—22no—
189C2×#67—22no—
190C2×#67—22no—
191C2×#67—22no—
192C2×#67—34no—
193C2×#67—34no—
194C2×#67—34no—
195C2×#67—34no—
196C2×#67—34no—
197C2×#67—34no—
198C2×#67—34no—
199C2×#67—34no—
200C2×#67—62no—
201C2×#67—62no—
202C2×#67—64no—
203C2×#67—64no—
204C2×#67—68no—
205C2×#67—68no—
206C2×#67C4×D314yescomplemented
207C2×#67C22×D314yes—
208C22×Dic3—22no—
209C22×Dic3—32no—
210C22×Dic3—34no—
211C22×Dic3—61no—
212C22×Dic3—62no—
213C22×Dic3—62no—
214C22×Dic3C4×D312yescomplemented
215#237—68no—
216#237—68no—
217#237—68no—
218#237—68no—
219D3×D4—68no—
220D3×D4—68no—
221D3×D4—68no—
222D3×D4—68no—
223#235—68no—
224#235—68no—
225C2×D12—34no—
226C2×C4×D3—34no—
227C2×C4×D3—34no—
228C2×C4×D3—64no—
229C2×C4×D3—64no—
230C2×C4×D3—64no—
231C2×Dic6—34no—
232C3×C22⋊C4—22no—
233C3×C22⋊C4—22no—
234C3×C22⋊C4—22no—
235C3×C22⋊C4—34no—
236C3×C22⋊C4—62no—
237C3×C22⋊C4C22×D314yes—
238#217—22no—
239#217—34no—
240#217—62no—
241#217—62no—
242#217—62no—
243#217C22×D314yes—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—64no—
247Dic3⋊C4—64no—
248Dic3⋊C4—64no—
249Dic3⋊C4—64no—
250C4×Dic3—64no—
251C4×Dic3—64no—
252C4×Dic3—64no—
253C22×C32—41no—
254C22×C32—41no—
255C22×C32—41no—
256C22×C32—42no—
257C22×C32—42no—
258C22×C32C2×C22⋊C412yes—
259C22×C32C2×C22⋊C412yes—
260C22×C32C23×C411yescharacteristic
261C22×C32C22×D411yescharacteristic
262C22×C32C22×D411yescharacteristic
263C2×C3⋊D3—42no—
264C2×C3⋊D3—42no—
265C2×C3⋊D3—42no—
266C2×C3⋊D3C2×C22⋊C414yes—
267C2×C3×D3—24no—
268C2×C3×D3—44no—
269C2×C3×D3—82no—
270C2×C3×D3—82no—
271D32—84no—
272C32×C4—42no—
273C3⋊Dic3—42no—
274C3⋊Dic3C2×C22⋊C414yes—
275C3×Dic3—24no—
276C3×Dic3—44no—
277H(5,𝔽2)—184no—
278H(5,𝔽2)—182no—
279H(5,𝔽2)—182no—
280C2×#41—94no—
281C2×#41—92no—
282C22×D4—32no—
283C22×D4—92no—
284C22×D4—94no—
285C22×D4—91no—
286C4×D4—182no—
287C4×D4—184no—
288C4×D4—182no—
289#117—92no—
290#117—92no—
291C2×C22⋊C4—32no—
292C2×C22⋊C4—92no—
293C2×C22⋊C4—91no—
294C2×C22⋊C4—92no—
295C2×C22⋊C4D3211yescharacteristic, complemented
296#99—38no—
297#99—98no—
298C23×C3—21no—
299C23×C3—22no—
300C23×C3—22no—
301C23×C3—21no—
302C23×C3—21no—
303C23×C3—34no—
304C23×C3—62no—
305C23×C3—62no—
306C23×C3—82no—
307C23×C3—82no—
308C23×C3—242no—
309C23×C3C2×C4×D312yes—
310C23×C3C2×C4×D312yes—
311C23×C3D3×D412yes—
312C23×C3D3×D412yes—
313C23×C3D3×D412yes—
314C23×C3D3×D412yes—
315C23×C3C23×D312yes—
316C22×D3—22no—
317C22×D3—22no—
318C22×D3—34no—
319C22×D3—34no—
320C22×D3—34no—
321C22×D3—62no—
322C22×D3—62no—
323C22×D3—62no—
324C22×D3—68no—
325C22×D3—82no—
326C22×D3—244no—
327C22×D3—242no—
328C22×D3—242no—
329C22×D3C2×C4×D314yes—
330C3×D4—64no—
331C3×D4—64no—
332C3×D4—64no—
333C3×D4—64no—
334C2×C3×C4—24no—
335C2×C3×C4—24no—
336C2×C3×C4—34no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—64no—
340C2×C3×C4—82no—
341C2×C3×C4—82no—
342C2×C3×C4—242no—
343#67—24no—
344#67—24no—
345#67—24no—
346#67—24no—
347#67—38no—
348#67—38no—
349#67—38no—
350#67—38no—
351#67—68no—
352#67—68no—
353#67—68no—
354#67—68no—
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—24no—
358C2×Dic3—34no—
359C2×Dic3—34no—
360C2×Dic3—34no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—68no—
365C2×Dic3—64no—
366C2×Dic3—64no—
367C2×Dic3—82no—
368C2×Dic3—242no—
369C2×Dic3—242no—
370C2×Dic3C2×C4×D314yes—
371D12—68no—
372C4×D3—68no—
373C4×D3—68no—
374C4×D3—244no—
375C4×D3—244no—
376C4×D3—244no—
377Dic6—68no—
378C2×C32—21no—
379C2×C32—21no—
380C2×C32—21no—
381C2×C32—22no—
382C2×C32—22no—
383C2×C32C22×C22⋊C411yescharacteristic
384C3⋊D3—24no—
385C3×D3—44no—
386C24—32no—
387C24—92no—
388C24—91no—
389C24C2×D3211yescharacteristic
390#41—188no—
391#41—188no—
392#41—184no—
393#41—184no—
394C2×Q8—92no—
395C2×D4—34no—
396C2×D4—34no—
397C2×D4—62no—
398C2×D4—62no—
399C2×D4—62no—
400C2×D4—62no—
401C2×D4—94no—
402C2×D4—94no—
403C2×D4—94no—
404C2×D4—92no—
405C2×D4—92no—
406C2×D4—92no—
407C2×D4—184no—
408C2×D4—184no—
409C2×D4—188no—
410C2×D4—188no—
411C22×C4—21no—
412C22×C4—32no—
413C22×C4—62no—
414C22×C4—92no—
415C22×C4—94no—
416C22×C4—91no—
417C22×C4—182no—
418C22×C4—182no—
419C22×C4—181no—
420C4⋊C4—182no—
421C4⋊C4—182no—
422C22⋊C4—21no—
423C22⋊C4—34no—
424C22⋊C4—62no—
425C22⋊C4—92no—
426C22⋊C4—182no—
427C22⋊C4—182no—
428C22⋊C4—181no—
429C22⋊C4C2×D3212yes—
430C42—182no—
431C42—182no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3—42no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—42no—
444C22×C3—42no—
445C22×C3—42no—
446C22×C3—42no—
447C22×C3—64no—
448C22×C3—82no—
449C22×C3—82no—
450C22×C3—124no—
451C22×C3—242no—
452C22×C3—242no—
453C22×C3D3×C22⋊C412yes—
454C22×C3D3×C22⋊C412yes—
455C22×C3D3×C22⋊C412yes—
456C22×C3D3×C22⋊C412yes—
457C22×C3C22×C4×D312yes—
458C22×C3C2×D3×D412yes—
459C22×C3C2×D3×D412yes—
460C2×D3—24no—
461C2×D3—38no—
462C2×D3—44no—
463C2×D3—64no—
464C2×D3—82no—
465C2×D3—82no—
466C2×D3—124no—
467C2×D3—124no—
468C2×D3—124no—
469C2×D3—124no—
470C2×D3—242no—
471C2×D3—242no—
472C2×D3—248no—
473C3×C4—44no—
474C3×C4—44no—
475C3×C4—64no—
476C3×C4—124no—
477Dic3—24no—
478Dic3—38no—
479Dic3—44no—
480Dic3—64no—
481Dic3—124no—
482Dic3—124no—
483C32#288311yescharacteristic, complemented, Sylow
484C23—34no—
485C23—62no—
486C23—62no—
487C23—81no—
488C23—92no—
489C23—92no—
490C23—92no—
491C23—184no—
492C23—242no—
493C23—721no—
494C23—722no—
495C23C4×D3212yes—
496C23#380212yes—
497C23#381111yescharacteristic
498C23#381111yescharacteristic
499C23C22×D3211yescharacteristic
500Q8—184no—
501D4—64no—
502D4—64no—
503D4—64no—
504D4—64no—
505D4—98no—
506D4—98no—
507D4—188no—
508D4—184no—
509C2×C4—22no—
510C2×C4—34no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—64no—
514C2×C4—81no—
515C2×C4—92no—
516C2×C4—92no—
517C2×C4—92no—
518C2×C4—184no—
519C2×C4—188no—
520C2×C4—182no—
521C2×C4—242no—
522C2×C4—722no—
523C2×C4—722no—
524C2×C4—721no—
525C2×C3—22no—
526C2×C3—22no—
527C2×C3—22no—
528C2×C3—22no—
529C2×C3—22no—
530C2×C3—22no—
531C2×C3—22no—
532C2×C3—22no—
533C2×C3—21no—
534C2×C3—41no—
535C2×C3—41no—
536C2×C3—42no—
537C2×C3—42no—
538C2×C3—124no—
539C2×C3C2×D3×C22⋊C412yes—
540D3—44no—
541D3—68no—
542D3—124no—
543C22—41no—
544C22—42no—
545C22—41no—
546C22—42no—
547C22—41no—
548C22—64no—
549C22—94no—
550C22—124no—
551C22—242no—
552C22—242no—
553C22—362no—
554C22—362no—
555C22—362no—
556C22—724no—
557C22#6392112yes—
558C22#6392112yes—
559C22C2×C4×D3211yescharacteristic
560C22C2×#380211yescharacteristic
561C22C2×#381111yescharacteristic
562C4—42no—
563C4—64no—
564C4—94no—
565C4—124no—
566C4—362no—
567C3—21no—
568C3#7868812yescomplemented
569C2—21no—
570C2—21no—
571C2—21no—
572C2—22no—
573C2—22no—
574C2—124no—
575C2—184no—
576C2C2×#6392111yescharacteristic
subgroupG/H
centerC2C2×#63921
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C22⋊C4C22
socleC2×C32C22×C22⋊C4
prime radicalC2×#64330C2
cosocleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32#2883
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10595957C2semidirect
3. #10595510C2semidirect
4. C2×C3×#806C2semidirect
5. C2×#63580C2semidirect
6. #10590406C2semidirect
7. #10590404C2semidirect
15. C2×D3×#67C4semidirect
17. C2×#3804C4semidirect
18. C2×C32×C22⋊C4C22semidirect
19. C2×#3757C22semidirect
22. C22⋊C4×C3⋊D3C22semidirect
23. #64086C22semidirect
24. C2×C3×#217C22semidirect
25. #63974C22semidirect
26. #63957C22semidirect
28. C3×#806C22semidirect
29. #63580C22semidirect
37. C2×#806D3semidirect
42. C23×C3×D3C2×C4semidirect
43. C22×D32C2×C4semidirect
56. C2×C3×#67C2×C4semidirect
59. C22×C3×Dic3C2×C4semidirect
64. C2×#627C2×C4semidirect
65. C2×#626C2×C4semidirect
66. C2×#625C2×C4semidirect
68. C2×#624C2×C4semidirect
73. C2×D3×Dic3C2×C4semidirect
103. C2×C3×C22⋊C4C2×D3semidirect
106. C2×#217C2×D3semidirect
122. #806C2×D3semidirect
177. C23×D3C4×D3semidirect
206. C2×#67C4×D3semidirect
214. C22×Dic3C4×D3semidirect
295. C2×C22⋊C4D32semidirect
483. C32#2883semidirect
568. C3#78688semidirect

Maximal subgroups

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

subgroupindex
C2×#643302
#105959572
#105955102
C2×C3×#8062
C2×#635802
#105904062
#105904042
#786883