Finite Group Databasebeta

← #11787078

Subgroups — #11787078

Order 1152.

917 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596269C211yesmaximal, characteristic
2C3×#5220C211yesmaximal, characteristic
3C2×C3×#834C211yesmaximal, characteristic
4#10591718C212yesmaximal, complemented
5#10589187C212yesmaximal, complemented
6#70021—31nomaximal
7#69597—31nomaximal
8C22×C32×D4C2211yescharacteristic
9C23×C3×Dic3C2211yescharacteristic
10C2×#3757—21no—
11C2×#3757C2212yes—
12D4×C3⋊Dic3—22no—
13D4×C3⋊Dic3—22no—
14#64135—21no—
15C2×C3×#217—21no—
16C2×C3×#217C2211yescharacteristic
17C2×C3×#217C2212yes—
18C2×Dic3⋊Dic3—22no—
19C3×#834C414yescomplemented
20C3×C3⋊#95—21no—
21#63579—22no—
22#5798—31no—
23#5798—31no—
24#5798—61no—
25C2×C3×#99—31no—
26C3×#386—31no—
27#5220D311yescharacteristic
28C2×#834D311yescharacteristic
29#5210—32no—
30#4950—32no—
31#4527—32no—
32#4527—32no—
33C24×C32D411yescharacteristic
34C24×C32C2311yescharacteristic
35C2×C32×D4—22no—
36C2×C32×D4—22no—
37C2×C32×D4C2×C412yes—
38C2×C32×D4Q812yes—
39C22×C32×C4D411yescharacteristic
40C22×C3⋊Dic3—21no—
41C22×C3⋊Dic3—21no—
42C22×C3⋊Dic3D412yes—
43C22×C3⋊Dic3D412yes—
44C22×C3×Dic3—21no—
45C22×C3×Dic3—22no—
46C22×C3×Dic3—22no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3—42no—
49#3757—22no—
50#3757—22no—
51#3757—22no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)—21no—
54C4×C3⋊Dic3—22no—
55C3×#217—22no—
56C3×#217—22no—
57C3×#217—42no—
58C3×#217C2×C414yescomplemented
59Dic3⋊Dic3—44no—
60#1867—91noSylow
61C22×C3×D4—21no—
62C22×C3×D4C2×D311yescharacteristic
63C22×C3×D4C2×D311yescharacteristic
64C23×C3×C4—31no—
65C23×Dic3C2×D311yescharacteristic
66C2×C3×C22⋊C4—32no—
67C2×C3×C22⋊C4—31no—
68C2×C3×C22⋊C4—61no—
69C2×#217—21no—
70C2×#217—32no—
71C2×#217—32no—
72C2×#217—62no—
73C2×#217—62no—
74C2×#217—61no—
75C2×#217—61no—
76C2×#217C2×D311yescharacteristic
77C2×#217C2×D312yes—
78D4×Dic3—62no—
79D4×Dic3—62no—
80D4×Dic3—62no—
81D4×Dic3—62no—
82D4×Dic3—64no—
83D4×Dic3—64no—
84#926—62no—
85#926—61no—
86#926—61no—
87C2×C4⋊Dic3—62no—
88C2×Dic3⋊C4—62no—
89C3×#99—34no—
90C3×#95—61no—
91#834Dic314yescomplemented
92C3⋊#95—21no—
93C3⋊#95—62no—
94C3⋊#95—62no—
95C23×C32—21no—
96C23×C32—21no—
97C23×C32—41no—
98C23×C32—41no—
99C23×C32—41no—
100C23×C32—41no—
101C23×C32C4⋊C412yescomplemented
102C23×C32C22×C411yescharacteristic
103C23×C32C2×D411yescharacteristic
104C23×C32C2×D412yes—
105C23×C32C2×Q811yescharacteristic
106C23×C32#4112yes—
107C32×D4—24no—
108C32×D4—24no—
109C2×C32×C4—21no—
110C2×C32×C4—21no—
111C2×C32×C4C4⋊C412yescomplemented
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—42no—
115C2×C3⋊Dic3—42no—
116C2×C3⋊Dic3—81no—
117C2×C3⋊Dic3—81no—
118C2×C3×Dic3—24no—
119C2×C3×Dic3—22no—
120C2×C3×Dic3—24no—
121C2×C3×Dic3—42no—
122C2×C3×Dic3—42no—
123C2×C3×Dic3—42no—
124C2×C3×Dic3—41no—
125C2×C3×Dic3—41no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—41no—
128C2×C3×Dic3—41no—
129#518—91no—
130C2×#99—31no—
131#386—31no—
132#385—92no—
133#342—92no—
134C24×C3—21no—
135C24×C3—21no—
136C24×C3D1211yescharacteristic
137C24×C3#6711yescharacteristic
138C24×C3C22×D311yescharacteristic
139C24×C3C22×D311yescharacteristic
140C2×C3×D4—24no—
141C2×C3×D4—24no—
142C2×C3×D4—22no—
143C2×C3×D4—22no—
144C2×C3×D4—22no—
145C2×C3×D4—22no—
146C2×C3×D4—22no—
147C2×C3×D4—22no—
148C2×C3×D4Dic612yes—
149C2×C3×D4Dic612yes—
150C2×C3×D4C4×D312yes—
151C2×C3×D4C2×Dic312yes—
152C22×C3×C4—21no—
153C22×C3×C4—61no—
154C22×C3×C4—62no—
155C22×C3×C4—62no—
156C22×C3×C4—61no—
157C22×C3×C4—122no—
158C22×C3×C4D1211yescharacteristic
159C22×C3×C4#6711yescharacteristic
160C22×Dic3—22no—
161C22×Dic3—22no—
162C22×Dic3—21no—
163C22×Dic3—21no—
164C22×Dic3—32no—
165C22×Dic3—32no—
166C22×Dic3—32no—
167C22×Dic3—32no—
168C22×Dic3—42no—
169C22×Dic3—62no—
170C22×Dic3—62no—
171C22×Dic3—62no—
172C22×Dic3—62no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C22×Dic3—61no—
176C22×Dic3—61no—
177C3×C22⋊C4—34no—
178C3×C22⋊C4—62no—
179C3×C22⋊C4—62no—
180C3×C22⋊C4—122no—
181#217—22no—
182#217—22no—
183#217—42no—
184#217—64no—
185#217—64no—
186#217—62no—
187#217—62no—
188#217—64no—
189#217—62no—
190#217—62no—
191#217—62no—
192#217—62no—
193#217C2×Dic314yescomplemented
194C4⋊Dic3—62no—
195C4⋊Dic3—62no—
196C4⋊Dic3—61no—
197C4⋊Dic3—61no—
198C4⋊Dic3—61no—
199C4⋊Dic3—61no—
200C4⋊Dic3—124no—
201Dic3⋊C4—124no—
202C4×Dic3—64no—
203C4×Dic3—62no—
204C4×Dic3—62no—
205C22×C32—22no—
206C22×C32—22no—
207C22×C32—21no—
208C22×C32—22no—
209C22×C32—21no—
210C22×C32—41no—
211C22×C32—41no—
212C22×C32—41no—
213C22×C32—41no—
214C22×C32—42no—
215C22×C32—42no—
216C22×C32—81no—
217C22×C32C2×C4⋊C411yescharacteristic
218C22×C32C4×D412yes—
219C22×C32#12011yescharacteristic
220C22×C32C22⋊Q812yes—
221C22×C32#12311yescharacteristic
222C32×C4—22no—
223C3⋊Dic3—42no—
224C3⋊Dic3—42no—
225C3×Dic3—44no—
226C3×Dic3—42no—
227C3×Dic3—81no—
228C22×D4D3211yescharacteristic
229C23×C4—31no—
230C4×D4—182no—
231C4×D4—182no—
232#117—181no—
233C2×C4⋊C4—182no—
234C2×C22⋊C4—32no—
235C2×C22⋊C4—31no—
236C2×C22⋊C4—61no—
237C2×C22⋊C4—92no—
238C2×C22⋊C4—181no—
239#99—34no—
240#95—61no—
241#95—182no—
242C23×C3—22no—
243C23×C3—22no—
244C23×C3—21no—
245C23×C3—21no—
246C23×C3—21no—
247C23×C3—21no—
248C23×C3—22no—
249C23×C3—21no—
250C23×C3—22no—
251C23×C3—21no—
252C23×C3—21no—
253C23×C3—22no—
254C23×C3—41no—
255C23×C3—41no—
256C23×C3—41no—
257C23×C3—41no—
258C23×C3—41no—
259C23×C3—41no—
260C23×C3—41no—
261C23×C3—41no—
262C23×C3—81no—
263C23×C3—81no—
264C23×C3—81no—
265C23×C3—81no—
266C23×C3Dic3⋊C412yescomplemented
267C23×C3C4⋊Dic312yescomplemented
268C23×C3C2×Dic611yescharacteristic
269C23×C3C2×Dic611yescharacteristic
270C23×C3C2×C4×D311yescharacteristic
271C23×C3C2×D1211yescharacteristic
272C23×C3D3×D412yes—
273C23×C3D3×D412yes—
274C23×C3#23712yes—
275C23×C3#23712yes—
276C23×C3C22×Dic311yescharacteristic
277C23×C3C2×#6711yescharacteristic
278C3×D4—28no—
279C3×D4—28no—
280C3×D4—24no—
281C3×D4—24no—
282C3×D4—24no—
283C3×D4—24no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—22no—
291C2×C3×C4—64no—
292C2×C3×C4—62no—
293C2×C3×C4—64no—
294C2×C3×C4—122no—
295C2×C3×C4—122no—
296C2×C3×C4—122no—
297C2×C3×C4—121no—
298C2×C3×C4—121no—
299C2×C3×C4—121no—
300C2×C3×C4—121no—
301C2×C3×C4—121no—
302C2×C3×C4Dic3⋊C412yescomplemented
303C2×C3×C4C4⋊Dic312yescomplemented
304C2×Dic3—24no—
305C2×Dic3—22no—
306C2×Dic3—24no—
307C2×Dic3—42no—
308C2×Dic3—42no—
309C2×Dic3—41no—
310C2×Dic3—42no—
311C2×Dic3—41no—
312C2×Dic3—41no—
313C2×Dic3—41no—
314C2×Dic3—41no—
315C2×Dic3—64no—
316C2×Dic3—64no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—122no—
322C2×Dic3—122no—
323C2×Dic3—122no—
324C2×Dic3—122no—
325C2×Dic3—242no—
326C2×Dic3—242no—
327C2×Dic3—242no—
328C2×Dic3—242no—
329C2×Dic3—241no—
330C2×Dic3—241no—
331C2×Dic3—241no—
332C2×Dic3—241no—
333C2×C32—22no—
334C2×C32—21no—
335C2×C32—21no—
336C2×C32—22no—
337C2×C32—42no—
338C2×C32#38511yescharacteristic
339C2×C32B(4,𝔽2)11yescharacteristic
340C2×C32#45811yescharacteristic
341C24#62611yescharacteristic
342C24C2×D3211yescharacteristic
343C2×D4—22no—
344C2×D4—22no—
345C2×D4D3×Dic312yes—
346C2×D4#62712yes—
347C22×C4—61no—
348C22×C4—62no—
349C22×C4—62no—
350C22×C4—61no—
351C22×C4—92no—
352C22×C4—92no—
353C22×C4—122no—
354C22×C4—181no—
355C22×C4—181no—
356C22×C4#62611yescharacteristic
357C4⋊C4—181no—
358C4⋊C4—181no—
359C4⋊C4—364no—
360C22⋊C4—34no—
361C22⋊C4—62no—
362C22⋊C4—62no—
363C22⋊C4—122no—
364C22⋊C4—182no—
365C22⋊C4—182no—
366C22⋊C4—182no—
367C42—182no—
368C22×C3—22no—
369C22×C3—21no—
370C22×C3—22no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—22no—
374C22×C3—21no—
375C22×C3—22no—
376C22×C3—24no—
377C22×C3—22no—
378C22×C3—22no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—22no—
382C22×C3—21no—
383C22×C3—22no—
384C22×C3—42no—
385C22×C3—42no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—42no—
392C22×C3—42no—
393C22×C3—41no—
394C22×C3—42no—
395C22×C3—42no—
396C22×C3—42no—
397C22×C3—42no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—41no—
402C22×C3—81no—
403C22×C3—82no—
404C22×C3—81no—
405C22×C3—82no—
406C22×C3—81no—
407C22×C3—81no—
408C22×C3—82no—
409C22×C3#87812yes—
410C22×C3#87812yes—
411C22×C3#67⋊C412yes—
412C22×C3#88211yescharacteristic
413C22×C3#88611yescharacteristic
414C22×C3C2×Dic3⋊C411yescharacteristic
415C22×C3C2×C4⋊Dic311yescharacteristic
416C22×C3D4×Dic312yes—
417C22×C3#93511yescharacteristic
418C22×C3#93711yescharacteristic
419C3×C4—24no—
420C3×C4—22no—
421C3×C4—22no—
422C3×C4—124no—
423C3×C4—122no—
424C3×C4—241no—
425Dic3—44no—
426Dic3—42no—
427Dic3—81no—
428Dic3—124no—
429Dic3—124no—
430Dic3—122no—
431Dic3—122no—
432Dic3—122no—
433Dic3—122no—
434C32#186711yescharacteristic, complemented, Sylow
435C23—21no—
436C23—21no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23Dic3⋊Dic312yescomplemented
442C23C2×D3×Dic311yescharacteristic
443C23#380512yes—
444C23C2×#62611yescharacteristic
445C23C2×#62711yescharacteristic
446C23#381112yes—
447D4—24no—
448D4—24no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—62no—
452C2×C4—64no—
453C2×C4—64no—
454C2×C4—122no—
455C2×C4—122no—
456C2×C4—121no—
457C2×C4—122no—
458C2×C4—121no—
459C2×C4—121no—
460C2×C4—121no—
461C2×C4—121no—
462C2×C4—182no—
463C2×C4—182no—
464C2×C4—362no—
465C2×C4—362no—
466C2×C4—721no—
467C2×C4—721no—
468C2×C4Dic3⋊Dic312yescomplemented
469C2×C3—22no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—22no—
473C2×C3—21no—
474C2×C3—22no—
475C2×C3—21no—
476C2×C3—22no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—41no—
481C2×C3—41no—
482C2×C3—42no—
483C2×C3—42no—
484C2×C3—44no—
485C2×C3—42no—
486C2×C3—42no—
487C2×C3#474111yescharacteristic
488C2×C3#474211yescharacteristic
489C2×C3#494611yescharacteristic
490C2×C3#495011yescharacteristic
491C2×C3#503211yescharacteristic
492C2×C3#505311yescharacteristic
493C22—22no—
494C22—21no—
495C22—22no—
496C22—21no—
497C22—22no—
498C22—41no—
499C22—42no—
500C22—41no—
501C22—42no—
502C22—41no—
503C22—41no—
504C22—81no—
505C22#6396211yescharacteristic
506C22C2×Dic3⋊Dic311yescharacteristic
507C22#67⋊Dic312yes—
508C22#6398111yescharacteristic
509C22#6398212yes—
510C4—22no—
511C4—124no—
512C4—122no—
513C4—241no—
514C4—362no—
515C4—362no—
516C3—21no—
517C3#6959711yescharacteristic, complemented
518C3#7002111yescharacteristic, complemented
519C2—22no—
520C2—21no—
521C2—21no—
522C2—22no—
523C2—42no—
524C2#1059153211yescharacteristic
525C2#1059153511yescharacteristic
526C2#1059171911yescharacteristic
subgroupG/H
centerC22#63981
commutatorC23×C32C22×C4
FrattiniC24C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32#120
cosocleC24×C32C23
hypercenterC22×D4D32
hypocenterC32#1867
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #10591718C2semidirect
5. #10589187C2semidirect
19. C3×#834C4semidirect
58. C3×#217C2×C4semidirect
91. #834Dic3semidirect
101. C23×C32C4⋊C4semidirect
111. C2×C32×C4C4⋊C4semidirect
193. #217C2×Dic3semidirect
266. C23×C3Dic3⋊C4semidirect
267. C23×C3C4⋊Dic3semidirect
302. C2×C3×C4Dic3⋊C4semidirect
303. C2×C3×C4C4⋊Dic3semidirect
434. C32#1867semidirect
441. C23Dic3⋊Dic3semidirect
468. C2×C4Dic3⋊Dic3semidirect
517. C3#69597semidirect
518. C3#70021semidirect

Maximal subgroups

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

subgroupindex
#105962692
C3×#52202
C2×C3×#8342
#105917182
#105891872
#700213
#695973