Finite Group Databasebeta

← #11787077

Subgroups — #11787077

Order 1152.

891 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5798C211yesmaximal, characteristic
2#10592919C211yesmaximal, characteristic
3C2×C3×#834C211yesmaximal, characteristic
4#10591719C212yesmaximal, complemented
5#10589186C212yesmaximal, complemented
6#71657—31nomaximal
7#70021—31nomaximal
8C22×C32×D4C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C2×#3757—21no—
11C2×#3757C2211yescharacteristic
12C2×C3×#217—21no—
13C2×C3×#217C2212yes—
14C2×C3×#217C2212yes—
15C3×D4×Dic3—22no—
16C3×D4×Dic3—22no—
17C3×#926—21no—
18C2×Dic3⋊Dic3—22no—
19#63658—21no—
20C3×#834C414yescomplemented
21#63579—22no—
22C3×#518—31no—
23#5798D311yescharacteristic
24C2×C3×#99—31no—
25#5220—31no—
26#5220—31no—
27#5220—61no—
28C2×#834D311yescharacteristic
29#4950—32no—
30#4946—32no—
31#4527—32no—
32#4526—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—22no—
42C22×C3⋊Dic3—21no—
43C22×C3⋊Dic3—42no—
44C22×C3×Dic3—22no—
45C22×C3×Dic3—21no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3D412yes—
48C22×C3×Dic3D412yes—
49#3757—22no—
50#3757—42no—
51C3×#217—22no—
52C3×#217—22no—
53C3×#217—22no—
54C3×#217—22no—
55C3×#217C2×C414yescomplemented
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4×Dic3—22no—
59Dic3⋊Dic3—44no—
60#1867—91noSylow
61C22×C3×D4—21no—
62C22×C3×D4C2×D311yescharacteristic
63C22×C3×D4C2×D311yescharacteristic
64C23×Dic3—31no—
65C23×Dic3—31no—
66C23×Dic3—61no—
67C3×C4×D4—62no—
68C3×C4×D4—62no—
69C3×#117—61no—
70C2×C3×C22⋊C4—32no—
71C2×C3×C22⋊C4—32no—
72C2×C3×C22⋊C4—61no—
73C2×#217—21no—
74C2×#217—31no—
75C2×#217—31no—
76C2×#217—61no—
77C2×#217—62no—
78C2×#217—61no—
79C2×#217—61no—
80C2×#217C2×D312yes—
81C2×#217C2×D312yes—
82D4×Dic3—22no—
83D4×Dic3—22no—
84#926—21no—
85C2×C4⋊Dic3—62no—
86C2×Dic3⋊C4—62no—
87C3×#99—34no—
88#834Dic314yescomplemented
89C3⋊#95—62no—
90C3⋊#95—62no—
91C3⋊#95—61no—
92C3⋊#95—61no—
93C3⋊#95—62no—
94C23×C32—21no—
95C23×C32—21no—
96C23×C32—41no—
97C23×C32—41no—
98C23×C32—41no—
99C23×C32—41no—
100C23×C32C4⋊C412yescomplemented
101C23×C32C22×C411yescharacteristic
102C23×C32C2×D411yescharacteristic
103C23×C32C2×D412yes—
104C23×C32C2×Q811yescharacteristic
105C23×C32#4112yes—
106C32×D4—24no—
107C32×D4—24no—
108C2×C32×C4—21no—
109C2×C32×C4—21no—
110C2×C32×C4C4⋊C412yescomplemented
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—24no—
113C2×C3⋊Dic3—41no—
114C2×C3⋊Dic3—42no—
115C2×C3⋊Dic3—41no—
116C2×C3⋊Dic3—41no—
117C2×C3⋊Dic3—41no—
118C2×C3⋊Dic3—41no—
119C2×C3×Dic3—24no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—42no—
123C2×C3×Dic3—42no—
124C2×C3×Dic3—42no—
125C2×C3×Dic3—42no—
126C2×C3×Dic3—81no—
127C2×C3×Dic3—81no—
128#518—31no—
129C2×#99—31no—
130#386—91no—
131#385—92no—
132#342—92no—
133C24×C3—21no—
134C24×C3—21no—
135C24×C3D1211yescharacteristic
136C24×C3#6711yescharacteristic
137C24×C3C22×D311yescharacteristic
138C24×C3C22×D311yescharacteristic
139C2×C3×D4—22no—
140C2×C3×D4—22no—
141C2×C3×D4—22no—
142C2×C3×D4—22no—
143C2×C3×D4—22no—
144C2×C3×D4—22no—
145C2×C3×D4—42no—
146C2×C3×D4—42no—
147C2×C3×D4Dic612yes—
148C2×C3×D4Dic612yes—
149C2×C3×D4C4×D312yes—
150C2×C3×D4C2×Dic312yes—
151C22×C3×C4—21no—
152C22×C3×C4—32no—
153C22×C3×C4—32no—
154C22×C3×C4—62no—
155C22×C3×C4—61no—
156C22×C3×C4—61no—
157C22×C3×C4D1211yescharacteristic
158C22×C3×C4#6711yescharacteristic
159C22×Dic3—22no—
160C22×Dic3—21no—
161C22×Dic3—21no—
162C22×Dic3—62no—
163C22×Dic3—61no—
164C22×Dic3—62no—
165C22×Dic3—62no—
166C22×Dic3—61no—
167C22×Dic3—62no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170C22×Dic3—122no—
171C22×Dic3—122no—
172C22×Dic3—122no—
173C22×Dic3—124no—
174C22×Dic3#6712yes—
175C22×Dic3#6712yes—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C22⋊C4—34no—
179C3×C22⋊C4—62no—
180C3×C22⋊C4—62no—
181C3×C22⋊C4—62no—
182C3×C22⋊C4—62no—
183C3×C42—62no—
184#217—22no—
185#217—22no—
186#217—22no—
187#217—22no—
188#217—62no—
189#217—62no—
190#217—122no—
191#217—122no—
192#217—122no—
193#217—124no—
194#217C2×Dic314yescomplemented
195C4⋊Dic3—21no—
196C4⋊Dic3—21no—
197C4⋊Dic3—124no—
198Dic3⋊C4—124no—
199C4×Dic3—22no—
200C22×C32—21no—
201C22×C32—21no—
202C22×C32—22no—
203C22×C32—22no—
204C22×C32—22no—
205C22×C32—41no—
206C22×C32—41no—
207C22×C32—42no—
208C22×C32—42no—
209C22×C32—41no—
210C22×C32—41no—
211C22×C32—81no—
212C22×C32C2×C4⋊C411yescharacteristic
213C22×C32C4×D412yes—
214C22×C32#12011yescharacteristic
215C22×C32C22⋊Q812yes—
216C22×C32#12311yescharacteristic
217C32×C4—22no—
218C3⋊Dic3—42no—
219C3⋊Dic3—81no—
220C3×Dic3—44no—
221C3×Dic3—42no—
222C3×Dic3—42no—
223C22×D4D3211yescharacteristic
224C23×C4—91no—
225C4×D4—62no—
226C4×D4—62no—
227#117—61no—
228C2×C4⋊C4—182no—
229C2×C22⋊C4—32no—
230C2×C22⋊C4—32no—
231C2×C22⋊C4—61no—
232C2×C22⋊C4—91no—
233C2×C22⋊C4—181no—
234#99—34no—
235#95—182no—
236#95—181no—
237C23×C3—21no—
238C23×C3—21no—
239C23×C3—21no—
240C23×C3—21no—
241C23×C3—22no—
242C23×C3—21no—
243C23×C3—22no—
244C23×C3—21no—
245C23×C3—21no—
246C23×C3—22no—
247C23×C3—41no—
248C23×C3—41no—
249C23×C3—41no—
250C23×C3—41no—
251C23×C3—41no—
252C23×C3—41no—
253C23×C3—42no—
254C23×C3—42no—
255C23×C3—41no—
256C23×C3—41no—
257C23×C3—41no—
258C23×C3—41no—
259C23×C3—42no—
260C23×C3—42no—
261C23×C3Dic3⋊C412yescomplemented
262C23×C3C4⋊Dic312yescomplemented
263C23×C3C2×Dic611yescharacteristic
264C23×C3C2×Dic611yescharacteristic
265C23×C3C2×C4×D311yescharacteristic
266C23×C3C2×D1211yescharacteristic
267C23×C3#23512yes—
268C23×C3D3×D412yes—
269C23×C3#23712yes—
270C23×C3C22×Dic311yescharacteristic
271C23×C3C2×#6711yescharacteristic
272C23×C3C2×#6712yes—
273C3×D4—24no—
274C3×D4—24no—
275C3×D4—24no—
276C3×D4—24no—
277C3×D4—44no—
278C3×D4—44no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—22no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4—64no—
289C2×C3×C4—122no—
290C2×C3×C4—122no—
291C2×C3×C4—122no—
292C2×C3×C4—122no—
293C2×C3×C4—241no—
294C2×C3×C4—241no—
295C2×C3×C4Dic3⋊C412yescomplemented
296C2×C3×C4C4⋊Dic312yescomplemented
297C2×Dic3—24no—
298C2×Dic3—22no—
299C2×Dic3—22no—
300C2×Dic3—42no—
301C2×Dic3—42no—
302C2×Dic3—42no—
303C2×Dic3—42no—
304C2×Dic3—64no—
305C2×Dic3—64no—
306C2×Dic3—64no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—81no—
310C2×Dic3—81no—
311C2×Dic3—124no—
312C2×Dic3—122no—
313C2×Dic3—122no—
314C2×Dic3—121no—
315C2×Dic3—122no—
316C2×Dic3—121no—
317C2×Dic3—122no—
318C2×Dic3—124no—
319C2×Dic3—121no—
320C2×Dic3—121no—
321C2×Dic3—122no—
322C2×Dic3—121no—
323C2×Dic3—121no—
324C2×Dic3—122no—
325C2×Dic3—122no—
326C2×Dic3—121no—
327C2×Dic3—121no—
328C2×Dic3—121no—
329C2×Dic3—121no—
330C2×C32—21no—
331C2×C32—21no—
332C2×C32—22no—
333C2×C32—22no—
334C2×C32—42no—
335C2×C32#38511yescharacteristic
336C2×C32B(4,𝔽2)11yescharacteristic
337C2×C32#45811yescharacteristic
338C24#62611yescharacteristic
339C24C2×D3211yescharacteristic
340C2×D4—22no—
341C2×D4—22no—
342C2×D4D3×Dic312yes—
343C2×D4#62712yes—
344C22×C4—32no—
345C22×C4—32no—
346C22×C4—62no—
347C22×C4—61no—
348C22×C4—61no—
349C22×C4—181no—
350C22×C4—182no—
351C22×C4—181no—
352C22×C4—362no—
353C22×C4#62611yescharacteristic
354C4⋊C4—61no—
355C4⋊C4—61no—
356C4⋊C4—364no—
357C22⋊C4—34no—
358C22⋊C4—62no—
359C22⋊C4—62no—
360C22⋊C4—62no—
361C22⋊C4—62no—
362C22⋊C4—182no—
363C22⋊C4—362no—
364C42—62no—
365C22×C3—22no—
366C22×C3—22no—
367C22×C3—22no—
368C22×C3—21no—
369C22×C3—22no—
370C22×C3—21no—
371C22×C3—22no—
372C22×C3—21no—
373C22×C3—22no—
374C22×C3—21no—
375C22×C3—22no—
376C22×C3—22no—
377C22×C3—22no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—22no—
381C22×C3—21no—
382C22×C3—42no—
383C22×C3—42no—
384C22×C3—42no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3—42no—
389C22×C3—42no—
390C22×C3—41no—
391C22×C3—42no—
392C22×C3—42no—
393C22×C3—42no—
394C22×C3—44no—
395C22×C3—42no—
396C22×C3—44no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—81no—
402C22×C3—81no—
403C22×C3—81no—
404C22×C3—81no—
405C22×C3—82no—
406C22×C3#87812yes—
407C22×C3#88211yescharacteristic
408C22×C3#88611yescharacteristic
409C22×C3C2×Dic3⋊C411yescharacteristic
410C22×C3#92412yes—
411C22×C3C2×C4⋊Dic311yescharacteristic
412C22×C3C4×#6712yes—
413C22×C3#92911yescharacteristic
414C22×C3D4×Dic312yes—
415C22×C3#95311yescharacteristic
416C3×C4—22no—
417C3×C4—22no—
418C3×C4—42no—
419C3×C4—124no—
420C3×C4—122no—
421C3×C4—122no—
422Dic3—44no—
423Dic3—42no—
424Dic3—42no—
425Dic3—124no—
426Dic3—122no—
427Dic3—122no—
428Dic3—242no—
429Dic3—241no—
430Dic3—241no—
431C32#186711yescharacteristic, complemented, Sylow
432C23—21no—
433C23—21no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23Dic3⋊Dic312yescomplemented
439C23C2×D3×Dic311yescharacteristic
440C23#380412yes—
441C23C2×#62611yescharacteristic
442C23C2×#62711yescharacteristic
443C23D3×#6712yes—
444D4—24no—
445D4—24no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—64no—
449C2×C4—62no—
450C2×C4—62no—
451C2×C4—122no—
452C2×C4—122no—
453C2×C4—122no—
454C2×C4—122no—
455C2×C4—182no—
456C2×C4—184no—
457C2×C4—241no—
458C2×C4—241no—
459C2×C4—362no—
460C2×C4—361no—
461C2×C4—361no—
462C2×C4—361no—
463C2×C4—361no—
464C2×C4—361no—
465C2×C4Dic3⋊Dic312yescomplemented
466C2×C3—22no—
467C2×C3—22no—
468C2×C3—22no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—22no—
472C2×C3—21no—
473C2×C3—22no—
474C2×C3—21no—
475C2×C3—22no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—42no—
480C2×C3—42no—
481C2×C3—42no—
482C2×C3—42no—
483C2×C3—82no—
484C2×C3#474111yescharacteristic
485C2×C3#474211yescharacteristic
486C2×C3#495011yescharacteristic
487C2×C3#521011yescharacteristic
488C2×C3#524311yescharacteristic
489C2×C3#524411yescharacteristic
490C22—22no—
491C22—21no—
492C22—22no—
493C22—21no—
494C22—22no—
495C22—41no—
496C22—42no—
497C22—41no—
498C22—42no—
499C22—41no—
500C22—41no—
501C22—81no—
502C22#6396412yes—
503C22C2×Dic3⋊Dic311yescharacteristic
504C22#6396611yescharacteristic
505C22Dic3×#6712yes—
506C22#6397711yescharacteristic
507C4—22no—
508C4—124no—
509C4—122no—
510C4—122no—
511C4—362no—
512C4—721no—
513C3—21no—
514C3#7002111yescharacteristic, complemented
515C3#7165711yescharacteristic, complemented
516C2—22no—
517C2—21no—
518C2—21no—
519C2—22no—
520C2—42no—
521C2#1059153111yescharacteristic
522C2#1059153411yescharacteristic
523C2#1059171811yescharacteristic
subgroupG/H
centerC22#63977
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. #10591719C2semidirect
5. #10589186C2semidirect
20. C3×#834C4semidirect
55. C3×#217C2×C4semidirect
88. #834Dic3semidirect
100. C23×C32C4⋊C4semidirect
110. C2×C32×C4C4⋊C4semidirect
194. #217C2×Dic3semidirect
261. C23×C3Dic3⋊C4semidirect
262. C23×C3C4⋊Dic3semidirect
295. C2×C3×C4Dic3⋊C4semidirect
296. C2×C3×C4C4⋊Dic3semidirect
431. C32#1867semidirect
438. C23Dic3⋊Dic3semidirect
465. C2×C4Dic3⋊Dic3semidirect
514. C3#70021semidirect
515. C3#71657semidirect

Maximal subgroups

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

subgroupindex
C3×#57982
#105929192
C2×C3×#8342
#105917192
#105891862
#716573
#700213