Finite Group Databasebeta

← #11807141

Subgroups — #11807141

Order 1152.

1085 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#944C211yesmaximal, characteristic
2#10592928C211yesmaximal, characteristic
3C3×#5229C211yesmaximal, characteristic
4#10591268C212yesmaximal
5#10591265C212yesmaximal
6#10591261C212yesmaximal
7#10591242C212yesmaximal
8#10591241C212yesmaximal
9Dic3×Dic3⋊C4C212yesmaximal
10#83230—31nomaximal
11#76494—31nomaximal
12C22×C32×Q8C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C3×#944C418yescomplemented
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×Dic3⋊C4C2212yes—
19C2×C3×Dic3⋊C4C2212yes—
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×Dic3⋊Dic3C2212yes—
23C2×Dic3⋊Dic3C2212yes—
24C2×Dic3⋊Dic3C2212yes—
25C2×Dic32C2212yes—
26C2×Dic32C2212yes—
27C2×Dic32C2212yes—
28#63658C2212yes—
29#63658C2212yes—
30C3×C3⋊#95C2212yes—
31C3×C3⋊#95C2212yes—
32#63579C2212yes—
33#63579C2212yes—
34C2×C3×C4⋊Q8—31no—
35C2×#944D311yescharacteristic
36C3×#391—31no—
37#5229—31no—
38#5229—31no—
39#5229—32no—
40#5229—61no—
41#5229D311yescharacteristic
42#4984—32no—
43#4984—32no—
44#4976—32no—
45Dic3×C4⋊C4—32no—
46Dic3×C4⋊C4—32no—
47C4×C4⋊Dic3—32no—
48C4×Dic3⋊C4—32no—
49#4649—32no—
50#4649—32no—
51#4647—32no—
52#4646—32no—
53C2×C32×Q8—41no—
54C2×C32×Q8—41no—
55C2×C32×Q8C2×C414yes—
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3C2312yes—
60C22×C3⋊Dic3C2312yes—
61C22×C3×Dic3C2312yes—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2312yes—
65C2×C3×Dic6—41no—
66C2×C3×Dic6—41no—
67C2×C3×Dic6C2×C414yes—
68C4⋊(C3⋊Dic3)—41no—
69C4×C3⋊Dic3—41no—
70C3×C4⋊Dic3—41no—
71C3×Dic3⋊C4C2×C418yes—
72C3×Dic3⋊C4C2×C418yes—
73C3×C4×Dic3—41no—
74C3×C4×Dic3C2×C414yes—
75Dic3⋊Dic3—24no—
76Dic3⋊Dic3—42no—
77Dic3⋊Dic3Q818yescomplemented
78Dic32—24no—
79Dic32—24no—
80Dic32—42no—
81#2369—91noSylow
82C22×C3×Q8—21no—
83C22×C3×Q8—31no—
84C22×C3×Q8C2×D311yescharacteristic
85C22×C3×Q8C2×D311yescharacteristic
86C22×Dic6C2×D311yescharacteristic
87C3×C4⋊Q8—38no—
88C2×C3×C4⋊C4—32no—
89C2×C3×C4⋊C4—32no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C42—31no—
92C2×C3×C42—31no—
93#944Dic318yescomplemented
94C2×C4⋊Dic3—32no—
95C2×C4⋊Dic3—32no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—32no—
99C2×C4⋊Dic3—61no—
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×Dic3⋊C4—32no—
102C2×Dic3⋊C4—32no—
103C2×Dic3⋊C4—32no—
104C2×Dic3⋊C4C2×D312yes—
105C2×Dic3⋊C4C2×D312yes—
106C2×C4×Dic3—32no—
107C2×C4×Dic3—32no—
108C2×C4×Dic3—32no—
109C2×C4×Dic3—32no—
110C2×C4×Dic3—31no—
111C2×C4×Dic3—31no—
112C2×C4×Dic3—32no—
113C2×C4×Dic3—32no—
114C2×C4×Dic3—61no—
115C2×C4×Dic3C2×D311yescharacteristic
116C2×C4×Dic3C2×D311yescharacteristic
117C3×#95—32no—
118C3×#95—32no—
119C3⋊#95—32no—
120C3⋊#95—32no—
121C3⋊#95—32no—
122C3⋊#95—32no—
123C3⋊#95—32no—
124C3⋊#95—32no—
125C3⋊#95—32no—
126C3⋊#95—32no—
127C3⋊#95—62no—
128C3⋊#95—62no—
129C3⋊#95C2×D312yes—
130C3⋊#95C2×D312yes—
131C23×C32C2411yescharacteristic
132C32×Q8—44no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4—21no—
136C2×C32×C4—21no—
137C2×C32×C4—21no—
138C2×C32×C4—21no—
139C2×C32×C4C22×C412yes—
140C2×C32×C4C22×C412yes—
141C2×C32×C4C22×C412yes—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3C2×Q814yes—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3C22×C414yes—
156C2×C3×Dic3C22×C414yes—
157C2×C3×Dic3C2×Q814yes—
158C2×C3×Dic3C2×Q814yes—
159C2×C3×Dic3#4114yes—
160C3×Dic6—44no—
161C2×C4⋊Q8—31no—
162#391—31no—
163#391—92no—
164#391—91no—
165#389—92no—
166#389—92no—
167C4×C4⋊C4—92no—
168C4×C4⋊C4—92no—
169C4×C4⋊C4—92no—
170C2×C3×Q8—24no—
171C2×C3×Q8—34no—
172C2×C3×Q8—41no—
173C2×C3×Q8—41no—
174C2×C3×Q8—41no—
175C2×C3×Q8—41no—
176C2×C3×Q8—42no—
177C2×C3×Q8—42no—
178C2×C3×Q8—121no—
179C2×C3×Q8—121no—
180C2×C3×Q8C4×D314yes—
181C2×C3×Q8C2×Dic314yes—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—32no—
186C22×C3×C4—32no—
187C22×C3×C4—32no—
188C22×C3×C4—32no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C22×Dic3—32no—
196C22×Dic3—32no—
197C22×Dic3—32no—
198C22×Dic3—32no—
199C22×Dic3—62no—
200C22×Dic3—62no—
201C22×Dic3C22×D312yes—
202C22×Dic3C22×D312yes—
203C22×Dic3C22×D312yes—
204C22×Dic3C22×D312yes—
205C2×Dic6—41no—
206C2×Dic6—41no—
207C2×Dic6C2×Dic314yes—
208C3×C4⋊C4—38no—
209C3×C4⋊C4—38no—
210C3×C4⋊C4—121no—
211C3×C42—34no—
212C3×C42—121no—
213C4⋊Dic3—38no—
214C4⋊Dic3—41no—
215C4⋊Dic3—64no—
216C4⋊Dic3—122no—
217C4⋊Dic3—121no—
218C4⋊Dic3—121no—
219C4⋊Dic3—122no—
220Dic3⋊C4—38no—
221Dic3⋊C4—64no—
222Dic3⋊C4—122no—
223Dic3⋊C4C2×Dic318yes—
224Dic3⋊C4C2×Dic318yes—
225C4×Dic3—41no—
226C4×Dic3—64no—
227C4×Dic3—64no—
228C4×Dic3—64no—
229C4×Dic3—64no—
230C4×Dic3—122no—
231C4×Dic3—122no—
232C4×Dic3—121no—
233C4×Dic3—121no—
234C4×Dic3—122no—
235C4×Dic3C2×Dic314yes—
236C22×C32C23×C411yescharacteristic
237C22×C32C22×Q812yes—
238C22×C32C2×#4112yes—
239C22×C32H(5,𝔽2)11yescharacteristic
240C22×C32H(5,𝔽2)11yescharacteristic
241C32×C4—22no—
242C32×C4—22no—
243C32×C4—22no—
244C3⋊Dic3—24no—
245C3⋊Dic3—42no—
246C3×Dic3—24no—
247C3×Dic3—24no—
248C3×Dic3—42no—
249C3×Dic3C4×Q818yes—
250C22×Q8—31no—
251C22×Q8D3211yescharacteristic
252C4⋊Q8—38no—
253C2×C4⋊C4—32no—
254C2×C4⋊C4—32no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—92no—
257C2×C4⋊C4—92no—
258C2×C4⋊C4—92no—
259C2×C4⋊C4—91no—
260C2×C42—31no—
261C2×C42—31no—
262C2×C42—92no—
263C2×C42—92no—
264C2×C42—92no—
265C2×C42—91no—
266#95—32no—
267#95—32no—
268#95—92no—
269#95—92no—
270#95—92no—
271#95—92no—
272C23×C3—21no—
273C23×C3C23×D311yescharacteristic
274C23×C3C23×D311yescharacteristic
275C3×Q8—44no—
276C3×Q8—44no—
277C3×Q8—48no—
278C3×Q8—124no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—34no—
297C2×C3×C4—34no—
298C2×C3×C4—34no—
299C2×C3×C4—34no—
300C2×C3×C4—34no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—62no—
306C2×C3×C4—62no—
307C2×C3×C4—62no—
308C2×C3×C4—62no—
309C2×C3×C4—62no—
310C2×C3×C4—62no—
311C2×C3×C4—62no—
312C2×C3×C4C2×C4×D312yes—
313C2×C3×C4C2×C4×D312yes—
314C2×C3×C4C2×C4×D312yes—
315C2×C3×C4C22×Dic312yes—
316C2×C3×C4C22×Dic312yes—
317C2×C3×C4C22×Dic312yes—
318C2×Dic3—22no—
319C2×Dic3—22no—
320C2×Dic3—22no—
321C2×Dic3—22no—
322C2×Dic3—22no—
323C2×Dic3—22no—
324C2×Dic3—22no—
325C2×Dic3—34no—
326C2×Dic3—34no—
327C2×Dic3—64no—
328C2×Dic3—62no—
329C2×Dic3—62no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—122no—
339C2×Dic3—122no—
340C2×Dic3—122no—
341C2×Dic3—122no—
342C2×Dic3—122no—
343C2×Dic3D3×Q814yes—
344C2×Dic3D3×Q814yes—
345C2×Dic3#23914yes—
346C2×Dic3C22×Dic314yes—
347C2×Dic3C22×Dic314yes—
348Dic6—44no—
349C2×C32C2×C4×Q812yes—
350C2×C32#51811yescharacteristic
351C2×C32#55412yes—
352C2×C32#55511yescharacteristic
353C2×C32Q8211yescharacteristic
354C2×Q8—34no—
355C2×Q8—41no—
356C2×Q8—41no—
357C2×Q8—121no—
358C2×Q8—121no—
359C2×Q8D3×Dic314yes—
360C22×C4—32no—
361C22×C4—32no—
362C22×C4—32no—
363C22×C4—32no—
364C22×C4—92no—
365C22×C4—92no—
366C22×C4C2×D3211yescharacteristic
367C22×C4C2×D3211yescharacteristic
368C22×C4C2×D3211yescharacteristic
369C4⋊C4—38no—
370C4⋊C4—38no—
371C4⋊C4—98no—
372C4⋊C4—121no—
373C4⋊C4—184no—
374C4⋊C4—361no—
375C4⋊C4—362no—
376C42—34no—
377C42—121no—
378C42—184no—
379C42—184no—
380C42—361no—
381C42—362no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3C22×C4×D311yescharacteristic
388C22×C3#100411yescharacteristic
389C22×C3#100411yescharacteristic
390C22×C3#100411yescharacteristic
391C22×C3#100411yescharacteristic
392C22×C3C2×D3×Q812yes—
393C22×C3C2×D3×Q812yes—
394C22×C3C2×#23912yes—
395C22×C3D3×#4112yes—
396C22×C3C23×Dic311yescharacteristic
397C3×C4—24no—
398C3×C4—22no—
399C3×C4—22no—
400C3×C4—22no—
401C3×C4—22no—
402C3×C4—22no—
403C3×C4—22no—
404C3×C4—38no—
405C3×C4—42no—
406C3×C4—42no—
407C3×C4—64no—
408C3×C4—64no—
409C3×C4—122no—
410Dic3—24no—
411Dic3—24no—
412Dic3—42no—
413Dic3—64no—
414Dic3—64no—
415Dic3—124no—
416Dic3—122no—
417Dic3—122no—
418Dic3—242no—
419Dic3Q8×Dic318yes—
420C32#236911yescharacteristic, complemented, Sylow
421C23C22×D3211yescharacteristic
422Q8—44no—
423Q8—124no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—34no—
431C2×C4—34no—
432C2×C4—34no—
433C2×C4—34no—
434C2×C4—34no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—62no—
442C2×C4—94no—
443C2×C4—182no—
444C2×C4—182no—
445C2×C4—182no—
446C2×C4—182no—
447C2×C4—182no—
448C2×C4C2×D3×Dic312yes—
449C2×C4C2×D3×Dic312yes—
450C2×C4C2×D3×Dic312yes—
451C2×C3—22no—
452C2×C3—22no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3#548611yescharacteristic
457C2×C3C4×D3×Q812yes—
458C2×C3#563612yes—
459C2×C3#567011yescharacteristic
460C2×C3#572211yescharacteristic
461C2×C3#572211yescharacteristic
462C2×C3#573012yes—
463C2×C3#573411yescharacteristic
464C2×C3#579811yescharacteristic
465C2×C3C2×Q8×Dic312yes—
466C22D32×Q812yes—
467C22D3×#23912yes—
468C22C22×D3×Dic311yescharacteristic
469C22#6433011yescharacteristic
470C22#6433011yescharacteristic
471C4—22no—
472C4—22no—
473C4—22no—
474C4—38no—
475C4—64no—
476C4—64no—
477C4—122no—
478C4—184no—
479C4—362no—
480C3—21no—
481C3#7649411yescharacteristic, complemented
482C3#8323011yescharacteristic, complemented
483C2D3×Q8×Dic312yes—
484C2#1059537212yes—
485C2#1059538511yescharacteristic
486C2#1059542111yescharacteristic
487C2#1059550611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×Q8C22
socle, prime radical, cosocleC23×C32C24
hypercenterC22×Q8D32
hypocenterC32#2369
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
16. C3×#944C4semidirect
77. Dic3⋊Dic3Q8semidirect
93. #944Dic3semidirect
420. C32#2369semidirect
481. C3#76494semidirect
482. C3#83230semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9442
#105929282
C3×#52292
#105912682
#105912652
#105912612
#105912422
#105912412
Dic3×Dic3⋊C42
#832303
#764943