Finite Group Databasebeta

← #11787079

Subgroups — #11787079

Order 1152.

853 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5798C211yesmaximal, characteristic
2C2×#63661C211yesmaximal, characteristic
3C3×#5220C211yesmaximal, characteristic
4#10591693C212yesmaximal, complemented
5#10589186C212yesmaximal, complemented
6#71657—31nomaximal
7#69597—31nomaximal
8C22×C32×D4C2211yescharacteristic
9C23×C3×Dic3C2211yescharacteristic
10C2×#3757C2212yes—
11C2×C3×#217—21no—
12C2×C3×#217—21no—
13C2×C3×#217C2211yescharacteristic
14C2×C3×#217C2212yes—
15C3×D4×Dic3—22no—
16C3×D4×Dic3—22no—
17C3×#926—21no—
18C2×#3724—22no—
19#63661C414yescomplemented
20C3×C3⋊#95—21no—
21#63579—22no—
22C3×#518—31no—
23#5798D311yescharacteristic
24C3×#386—31no—
25#5220D311yescharacteristic
26C2×#834—31no—
27C2×#834—31no—
28C2×#834—61no—
29#5210—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—22no—
41C22×C3×Dic3—21no—
42C22×C3×Dic3—22no—
43C22×C3×Dic3—21no—
44C22×C3×Dic3—21no—
45C22×C3×Dic3—21no—
46C22×C3×Dic3—42no—
47C22×C3×Dic3D412yes—
48C22×C3×Dic3D412yes—
49#3757—22no—
50#3757C2×C414yescomplemented
51C3×#217—22no—
52C3×#217—22no—
53C3×#217—22no—
54C3×#217—22no—
55C3×#217—42no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4×Dic3—22no—
59#3724—44no—
60#1867—91noSylow
61C22×C3×D4—21no—
62C22×C3×D4C2×D311yescharacteristic
63C22×C3×D4C2×D311yescharacteristic
64C23×C3×C4—31no—
65C23×Dic3C2×D311yescharacteristic
66C3×C4×D4—62no—
67C3×C4×D4—62no—
68C3×#117—61no—
69C2×C3×C22⋊C4—32no—
70C2×C3×C22⋊C4—31no—
71C2×C3×C22⋊C4—61no—
72C2×C3×C22⋊C4—61no—
73C2×#217—21no—
74C2×#217—21no—
75C2×#217—32no—
76C2×#217—32no—
77C2×#217—62no—
78C2×#217C2×D311yescharacteristic
79C2×#217C2×D312yes—
80D4×Dic3—22no—
81D4×Dic3—22no—
82#926—21no—
83C2×Dic3⋊C4—62no—
84C2×Dic3⋊C4—62no—
85C3×#95—61no—
86#834—34no—
87#834—34no—
88#834—64no—
89C3⋊#95—21no—
90C3⋊#95—62no—
91C3⋊#95—62no—
92C23×C32—21no—
93C23×C32—21no—
94C23×C32—41no—
95C23×C32—41no—
96C23×C32—41no—
97C23×C32—41no—
98C23×C32C4⋊C412yescomplemented
99C23×C32C22×C411yescharacteristic
100C23×C32C2×D412yes—
101C23×C32C2×D411yescharacteristic
102C23×C32C2×Q811yescharacteristic
103C23×C32#4112yes—
104C32×D4—24no—
105C32×D4—24no—
106C2×C32×C4—21no—
107C2×C32×C4—21no—
108C2×C32×C4C4⋊C412yescomplemented
109C2×C3⋊Dic3—24no—
110C2×C3⋊Dic3—42no—
111C2×C3⋊Dic3—42no—
112C2×C3×Dic3—24no—
113C2×C3×Dic3—22no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—42no—
117C2×C3×Dic3—41no—
118C2×C3×Dic3—41no—
119C2×C3×Dic3—42no—
120C2×C3×Dic3—42no—
121C2×C3×Dic3—41no—
122C2×C3×Dic3—41no—
123C2×C3×Dic3—41no—
124C2×C3×Dic3—81no—
125C2×C3×Dic3—81no—
126#518—31no—
127C2×#99—91no—
128#386—31no—
129#385—92no—
130#342—92no—
131C24×C3—21no—
132C24×C3—21no—
133C24×C3#6711yescharacteristic
134C24×C3#6711yescharacteristic
135C24×C3C22×D311yescharacteristic
136C24×C3C22×D311yescharacteristic
137C2×C3×D4—22no—
138C2×C3×D4—22no—
139C2×C3×D4—22no—
140C2×C3×D4—22no—
141C2×C3×D4—22no—
142C2×C3×D4—22no—
143C2×C3×D4—42no—
144C2×C3×D4—42no—
145C2×C3×D4Dic612yes—
146C2×C3×D4Dic612yes—
147C2×C3×D4C4×D312yes—
148C2×C3×D4C4×D312yes—
149C22×C3×C4—21no—
150C22×C3×C4—32no—
151C22×C3×C4—32no—
152C22×C3×C4—62no—
153C22×C3×C4—61no—
154C22×C3×C4—61no—
155C22×C3×C4—61no—
156C22×C3×C4—61no—
157C22×C3×C4—122no—
158C22×C3×C4#6711yescharacteristic
159C22×C3×C4#6711yescharacteristic
160C22×Dic3—22no—
161C22×Dic3—21no—
162C22×Dic3—21no—
163C22×Dic3—21no—
164C22×Dic3—21no—
165C22×Dic3—42no—
166C22×Dic3—62no—
167C22×Dic3—62no—
168C22×Dic3—122no—
169C22×Dic3#6712yes—
170C22×Dic3#6712yes—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C22⋊C4—62no—
174C3×C22⋊C4—62no—
175C3×C22⋊C4—62no—
176C3×C22⋊C4—62no—
177C3×C22⋊C4—122no—
178C3×C42—62no—
179#217—22no—
180#217—22no—
181#217—22no—
182#217—22no—
183#217—34no—
184#217—34no—
185#217—42no—
186#217—64no—
187#217—62no—
188#217—62no—
189#217—122no—
190C4⋊Dic3—21no—
191C4⋊Dic3—21no—
192Dic3⋊C4—124no—
193Dic3⋊C4—124no—
194C4×Dic3—22no—
195C22×C32—22no—
196C22×C32—21no—
197C22×C32—22no—
198C22×C32—21no—
199C22×C32—22no—
200C22×C32—41no—
201C22×C32—41no—
202C22×C32—42no—
203C22×C32—42no—
204C22×C32—41no—
205C22×C32—41no—
206C22×C32—81no—
207C22×C32C2×C4⋊C411yescharacteristic
208C22×C32C4×D412yes—
209C22×C32#12011yescharacteristic
210C22×C32C22⋊Q812yes—
211C22×C32#12311yescharacteristic
212C32×C4—22no—
213C3⋊Dic3—44no—
214C3×Dic3—42no—
215C3×Dic3—42no—
216C3×Dic3—42no—
217C3×Dic3—81no—
218C22×D4D3211yescharacteristic
219C23×C4—31no—
220C4×D4—62no—
221C4×D4—62no—
222#117—61no—
223C2×C4⋊C4—182no—
224C2×C22⋊C4—32no—
225C2×C22⋊C4—31no—
226C2×C22⋊C4—61no—
227C2×C22⋊C4—61no—
228C2×C22⋊C4—92no—
229#99—94no—
230#95—61no—
231#95—182no—
232C23×C3—21no—
233C23×C3—21no—
234C23×C3—21no—
235C23×C3—21no—
236C23×C3—22no—
237C23×C3—22no—
238C23×C3—21no—
239C23×C3—21no—
240C23×C3—21no—
241C23×C3—22no—
242C23×C3—41no—
243C23×C3—41no—
244C23×C3—41no—
245C23×C3—41no—
246C23×C3—41no—
247C23×C3—41no—
248C23×C3—41no—
249C23×C3—41no—
250C23×C3—41no—
251C23×C3—41no—
252C23×C3—81no—
253C23×C3—81no—
254C23×C3—81no—
255C23×C3—81no—
256C23×C3Dic3⋊C412yescomplemented
257C23×C3Dic3⋊C412yescomplemented
258C23×C3C2×Dic611yescharacteristic
259C23×C3C2×Dic611yescharacteristic
260C23×C3C2×C4×D311yescharacteristic
261C23×C3C2×C4×D311yescharacteristic
262C23×C3#23512yes—
263C23×C3D3×D412yes—
264C23×C3#23712yes—
265C23×C3C2×#6711yescharacteristic
266C23×C3C2×#6711yescharacteristic
267C23×C3C2×#6712yes—
268C3×D4—24no—
269C3×D4—24no—
270C3×D4—24no—
271C3×D4—24no—
272C3×D4—44no—
273C3×D4—44no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—22no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—64no—
282C2×C3×C4—62no—
283C2×C3×C4—62no—
284C2×C3×C4—62no—
285C2×C3×C4—122no—
286C2×C3×C4—121no—
287C2×C3×C4—121no—
288C2×C3×C4—122no—
289C2×C3×C4—122no—
290C2×C3×C4—121no—
291C2×C3×C4—121no—
292C2×C3×C4—121no—
293C2×C3×C4—241no—
294C2×C3×C4—241no—
295C2×C3×C4Dic3⋊C412yescomplemented
296C2×C3×C4Dic3⋊C412yescomplemented
297C2×Dic3—24no—
298C2×Dic3—22no—
299C2×Dic3—22no—
300C2×Dic3—22no—
301C2×Dic3—41no—
302C2×Dic3—42no—
303C2×Dic3—41no—
304C2×Dic3—42no—
305C2×Dic3—42no—
306C2×Dic3—41no—
307C2×Dic3—41no—
308C2×Dic3—41no—
309C2×Dic3—64no—
310C2×Dic3—64no—
311C2×Dic3—81no—
312C2×Dic3—81no—
313C2×Dic3—124no—
314C2×Dic3—122no—
315C2×Dic3—122no—
316C2×Dic3—122no—
317C2×Dic3—122no—
318C2×Dic3—242no—
319C2×Dic3—242no—
320C2×C32—21no—
321C2×C32—22no—
322C2×C32—21no—
323C2×C32—22no—
324C2×C32—42no—
325C2×C32#38511yescharacteristic
326C2×C32B(4,𝔽2)11yescharacteristic
327C2×C32#45811yescharacteristic
328C24#62511yescharacteristic
329C24C2×D3211yescharacteristic
330C2×D4—22no—
331C2×D4—22no—
332C2×D4#62412yes—
333C2×D4#62712yes—
334C22×C4—32no—
335C22×C4—32no—
336C22×C4—61no—
337C22×C4—62no—
338C22×C4—61no—
339C22×C4—61no—
340C22×C4—61no—
341C22×C4—122no—
342C22×C4—182no—
343C22×C4#62511yescharacteristic
344C4⋊C4—61no—
345C4⋊C4—61no—
346C4⋊C4—364no—
347C22⋊C4—62no—
348C22⋊C4—62no—
349C22⋊C4—62no—
350C22⋊C4—62no—
351C22⋊C4—94no—
352C22⋊C4—122no—
353C22⋊C4—182no—
354C42—62no—
355C22×C3—22no—
356C22×C3—21no—
357C22×C3—22no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—22no—
361C22×C3—21no—
362C22×C3—22no—
363C22×C3—22no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—21no—
367C22×C3—22no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—42no—
371C22×C3—42no—
372C22×C3—41no—
373C22×C3—41no—
374C22×C3—42no—
375C22×C3—41no—
376C22×C3—41no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—42no—
380C22×C3—42no—
381C22×C3—42no—
382C22×C3—42no—
383C22×C3—41no—
384C22×C3—41no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3—81no—
388C22×C3—81no—
389C22×C3—82no—
390C22×C3—81no—
391C22×C3—81no—
392C22×C3—82no—
393C22×C3—81no—
394C22×C3—81no—
395C22×C3—82no—
396C22×C3#87812yes—
397C22×C3#67⋊C412yes—
398C22×C3C2×Dic3⋊C411yescharacteristic
399C22×C3C2×Dic3⋊C411yescharacteristic
400C22×C3#92412yes—
401C22×C3C4×#6712yes—
402C22×C3#92911yescharacteristic
403C22×C3#93511yescharacteristic
404C22×C3#93711yescharacteristic
405C22×C3#95311yescharacteristic
406C3×C4—22no—
407C3×C4—22no—
408C3×C4—42no—
409C3×C4—122no—
410C3×C4—122no—
411C3×C4—122no—
412C3×C4—241no—
413Dic3—42no—
414Dic3—42no—
415Dic3—42no—
416Dic3—81no—
417Dic3—124no—
418Dic3—124no—
419Dic3—244no—
420C32#186711yescharacteristic, complemented, Sylow
421C23—21no—
422C23—21no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23#372412yescomplemented
428C23#380412yes—
429C23C2×#62411yescharacteristic
430C23C2×#62511yescharacteristic
431C23C2×#62711yescharacteristic
432C23D3×#6712yes—
433D4—24no—
434D4—24no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—62no—
438C2×C4—64no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—122no—
442C2×C4—121no—
443C2×C4—121no—
444C2×C4—122no—
445C2×C4—122no—
446C2×C4—121no—
447C2×C4—121no—
448C2×C4—121no—
449C2×C4—184no—
450C2×C4—241no—
451C2×C4—241no—
452C2×C4—362no—
453C2×C4—362no—
454C2×C4#372412yescomplemented
455C2×C3—21no—
456C2×C3—22no—
457C2×C3—21no—
458C2×C3—22no—
459C2×C3—22no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—22no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—42no—
467C2×C3—41no—
468C2×C3—41no—
469C2×C3—42no—
470C2×C3—42no—
471C2×C3—42no—
472C2×C3—82no—
473C2×C3#494611yescharacteristic
474C2×C3#503211yescharacteristic
475C2×C3#505311yescharacteristic
476C2×C3#521011yescharacteristic
477C2×C3#524311yescharacteristic
478C2×C3#524411yescharacteristic
479C22—22no—
480C22—21no—
481C22—22no—
482C22—21no—
483C22—22no—
484C22—42no—
485C22—41no—
486C22—41no—
487C22—42no—
488C22—41no—
489C22—41no—
490C22—81no—
491C22#6395212yes—
492C22#6396111yescharacteristic
493C22#6396412yes—
494C22C2×#372411yescharacteristic
495C22#6397611yescharacteristic
496C4—22no—
497C4—122no—
498C4—122no—
499C4—122no—
500C4—241no—
501C4—364no—
502C3—21no—
503C3#6959711yescharacteristic, complemented
504C3#7165711yescharacteristic, complemented
505C2—21no—
506C2—22no—
507C2—21no—
508C2—22no—
509C2—42no—
510C2#1059153011yescharacteristic
511C2#1059153311yescharacteristic
512C2#1059169311yescharacteristic
subgroupG/H
centerC22#63976
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. #10591693C2semidirect
5. #10589186C2semidirect
19. #63661C4semidirect
50. #3757C2×C4semidirect
98. C23×C32C4⋊C4semidirect
108. C2×C32×C4C4⋊C4semidirect
256. C23×C3Dic3⋊C4semidirect
257. C23×C3Dic3⋊C4semidirect
295. C2×C3×C4Dic3⋊C4semidirect
296. C2×C3×C4Dic3⋊C4semidirect
420. C32#1867semidirect
427. C23#3724semidirect
454. C2×C4#3724semidirect
503. C3#69597semidirect
504. C3#71657semidirect

Maximal subgroups

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

subgroupindex
C3×#57982
C2×#636612
C3×#52202
#105916932
#105891862
#716573
#695973