Finite Group Databasebeta

← #11824504

Subgroups — #11824504

Order 1152.

1565 conjugacy classes of subgroups.

The subgroup lattice has 499 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic
2C2×C3×#924C212yesmaximal, complemented
3C2×#63873C211yesmaximal, characteristic, complemented
4C2×#63871C212yesmaximal, complemented
5#10591715C212yesmaximal, complemented
6#10591704C212yesmaximal
7#10591274C211yesmaximal, characteristic, complemented
8#10591244C212yesmaximal, complemented
9#10591203C212yesmaximal, complemented
10#82780—32nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×#638C2211yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C3×Dic6C2212yes—
15C2×#3757C2211yescharacteristic
16C4×#638—24no—
17C2×#3752C2211yescharacteristic
18C2×#3750C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×#217C2214yes—
21C2×C3×C4⋊Dic3C2212yes—
22C3×#924—28no—
23C2×C3×Dic3⋊C4C2214yes—
24C2×#3724C2212yes—
25C2×#3724C2212yes—
26C2×Dic3⋊Dic3C2214yes—
27C2×#3722C2214yes—
28C2×Dic32C2212yes—
29#63873—24no—
30#63871—28no—
31#63579C2212yes—
32C2×C3×C22⋊Q8—32no—
33C2×#946—32no—
34C2×#944—32no—
35C2×C4×#67—32no—
36C2×C4×#67—61no—
37C2×#924D312yescomplemented
38C2×#897—32no—
39#4993—34no—
40#4975—34no—
41Dic3×C4⋊C4—32no—
42#4957—34no—
43#4949—34no—
44C24×C32C2311yescharacteristic
45C23×C3⋊D3C2311yescharacteristic
46C22×C32×C4—22no—
47C22×C32×C4—24no—
48C22×C32×C4C2311yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C2×#638—22no—
51C2×#638—22no—
52C2×#638Q814yescomplemented
53C22×C3⋊Dic3C2311yescharacteristic
54C22×C3⋊Dic3C2311yescharacteristic
55C22×C3⋊Dic3C2311yescharacteristic
56C2×C4×C3⋊D3—22no—
57C2×C4×C3⋊D3—24no—
58C22×C3×Dic3C2314yes—
59C22×C3×Dic3C2314yes—
60C2×C3×Dic6—24no—
61C2×C3×Dic6—24no—
62C2×C3×Dic6—24no—
63#3757—22no—
64#3752—22no—
65#3750—22no—
66C4×C3⋊Dic3D414yes—
67C3×#217—28no—
68C3×C4⋊Dic3D418yescomplemented
69C3×Dic3⋊C4—28no—
70#3724—24no—
71#3724—24no—
72Dic3⋊Dic3—28no—
73#3722—28no—
74Dic32—24no—
75#2542—91noSylow
76C22×C3×Q8—32no—
77C23×C3×C4—21no—
78C23×C3×C4C2×D312yes—
79C22×#67—32no—
80C22×#67—61no—
81C22×C4×D3—32no—
82C22×C4×D3—61no—
83C22×Dic6C2×D312yes—
84C3×C22⋊Q8—68no—
85C2×C3×C4⋊C4—32no—
86C2×C3×C4⋊C4—34no—
87C2×C3×C22⋊C4—34no—
88C2×#217—32no—
89C2×#217—61no—
90C2×#217C2×D314yes—
91#946—68no—
92#944—68no—
93C4×#67—68no—
94C4×#67—68no—
95C2×(C2×D3)⋊C4—32no—
96C2×(C2×D3)⋊C4—34no—
97C2×(C2×D3)⋊C4—34no—
98C2×(C2×D3)⋊C4—61no—
99C2×C4⋊Dic3—34no—
100C2×C4⋊Dic3C2×D312yes—
101#924—28no—
102C2×Dic3⋊C4—32no—
103C2×Dic3⋊C4—34no—
104C2×Dic3⋊C4—34no—
105C2×Dic3⋊C4—34no—
106C2×Dic3⋊C4—61no—
107C2×Dic3⋊C4C2×D314yes—
108C2×C4×Dic3—32no—
109C2×C4×Dic3—34no—
110C2×C4×Dic3—61no—
111#897—68no—
112C3⋊#95—34no—
113C23×C32—21no—
114C23×C32—21no—
115C23×C32—22no—
116C23×C32—22no—
117C23×C32C2×Q812yes—
118C23×C32C2411yescharacteristic
119C22×C3⋊D3—21no—
120C22×C3⋊D3—21no—
121C22×C3⋊D3—22no—
122C22×C3⋊D3—22no—
123C22×C3⋊D3C2×Q812yes—
124C2×C32×C4—21no—
125C2×C32×C4—22no—
126C2×C32×C4—44no—
127C2×C32×C4C2×D412yes—
128C2×C32×C4C2×D414yes—
129#638—28no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3C2×D412yes—
134C2×C3⋊Dic3C2×D412yes—
135C2×C3⋊Dic3C2×Q812yes—
136C2×C3⋊Dic3#4112yes—
137C4×C3⋊D3—44no—
138C2×C3×Dic3—24no—
139C2×C3×Dic3—24no—
140C2×C3×Dic3—24no—
141C2×C3×Dic3—24no—
142C2×C3×Dic3—24no—
143C2×C3×Dic3C2×D418yes—
144C3×Dic6—48no—
145C2×C4⋊Q8—91no—
146C2×C22⋊Q8—32no—
147C2×C22⋊Q8—92no—
148C2×C4×D4—91no—
149#399—92no—
150#399—92no—
151#390—92no—
152#384—92no—
153C4×C4⋊C4—91no—
154C24×C3—21no—
155C24×C3C22×D312yes—
156C23×D3—32no—
157C23×D3—61no—
158C2×C3×Q8—64no—
159C2×C3×Q8—64no—
160C2×C3×Q8—64no—
161C22×C3×C4—24no—
162C22×C3×C4—24no—
163C22×C3×C4—24no—
164C22×C3×C4—24no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—34no—
168C22×C3×C4—34no—
169C22×C3×C4—44no—
170C22×C3×C4C22×D312yes—
171C22×C3×C4C22×D312yes—
172C2×#67—38no—
173C2×#67—64no—
174C2×#67—64no—
175C2×#67—64no—
176C2×#67—64no—
177C2×#67—64no—
178C22×Dic3—32no—
179C22×Dic3—32no—
180C22×Dic3—32no—
181C22×Dic3—61no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C22×Dic3C22×D314yes—
185C22×Dic3C22×D314yes—
186C2×C4×D3—64no—
187C2×C4×D3—64no—
188C2×C4×D3—64no—
189C2×C4×D3—64no—
190C2×C4×D3—124no—
191C2×Dic6—24no—
192C2×Dic6—24no—
193C2×Dic6—24no—
194C3×C4⋊C4—38no—
195C3×C4⋊C4—68no—
196C3×C22⋊C4—68no—
197#217—28no—
198#217—64no—
199#217—64no—
200(C2×D3)⋊C4—68no—
201(C2×D3)⋊C4—64no—
202(C2×D3)⋊C4—64no—
203(C2×D3)⋊C4—68no—
204C4⋊Dic3—68no—
205C4⋊Dic3#6718yescomplemented
206Dic3⋊C4—28no—
207Dic3⋊C4—68no—
208Dic3⋊C4—68no—
209Dic3⋊C4—64no—
210Dic3⋊C4—64no—
211Dic3⋊C4—68no—
212C4×Dic3—38no—
213C4×Dic3—64no—
214C4×Dic3—68no—
215C22×C32—22no—
216C22×C32—24no—
217C22×C32—41no—
218C22×C32—41no—
219C22×C32—42no—
220C22×C32C22×D411yescharacteristic
221C22×C32C22×D412yes—
222C22×C32C22×Q811yescharacteristic
223C22×C32C2×#4111yescharacteristic
224C22×C322−1+412yes—
225C2×C3⋊D3—22no—
226C2×C3⋊D3—24no—
227C2×C3⋊D3—41no—
228C2×C3⋊D3—41no—
229C2×C3⋊D3—42no—
230C32×C4—41no—
231C32×C4#12714yes—
232C3⋊Dic3—22no—
233C3⋊Dic3—41no—
234C3⋊Dic3C22⋊Q814yescomplemented
235C3×Dic3—28no—
236C3×Dic3—44no—
237C22×Q8—32no—
238C22×D4—91no—
239C23×C4—91no—
240C23×C4D3211yescharacteristic
241C4⋊Q8—184no—
242C22⋊Q8—68no—
243C22⋊Q8—188no—
244C4×D4—184no—
245C2×C4⋊C4—32no—
246C2×C4⋊C4—34no—
247C2×C4⋊C4—94no—
248C2×C4⋊C4—92no—
249C2×C4⋊C4—92no—
250C2×C4⋊C4—91no—
251C2×C22⋊C4—34no—
252C2×C22⋊C4—94no—
253C2×C22⋊C4—91no—
254C2×C22⋊C4—91no—
255C2×C42—91no—
256C2×C42—92no—
257#95—92no—
258C23×C3—22no—
259C23×C3—22no—
260C23×C3—22no—
261C23×C3—22no—
262C23×C3—22no—
263C23×C3—22no—
264C23×C3—22no—
265C23×C3—22no—
266C23×C3—21no—
267C23×C3—22no—
268C23×C3—42no—
269C23×C3—42no—
270C23×C3D3×Q814yes—
271C23×C3C23×D312yes—
272C22×D3—34no—
273C22×D3—62no—
274C22×D3—62no—
275C22×D3—62no—
276C22×D3—62no—
277C22×D3—62no—
278C22×D3—62no—
279C22×D3—62no—
280C22×D3—62no—
281C22×D3—62no—
282C22×D3—122no—
283C22×D3—122no—
284C3×Q8—128no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—24no—
290C2×C3×C4—22no—
291C2×C3×C4—38no—
292C2×C3×C4—42no—
293C2×C3×C4—48no—
294C2×C3×C4—48no—
295C2×C3×C4—64no—
296C2×C3×C4—64no—
297C2×C3×C4—64no—
298C2×C3×C4—64no—
299C2×C3×C4—64no—
300C2×C3×C4D3×D414yes—
301C2×C3×C4D3×D414yes—
302C2×C3×C4C2×#6714yes—
303#67—616no—
304#67—616no—
305C2×Dic3—24no—
306C2×Dic3—24no—
307C2×Dic3—24no—
308C2×Dic3—24no—
309C2×Dic3—24no—
310C2×Dic3—34no—
311C2×Dic3—34no—
312C2×Dic3—34no—
313C2×Dic3—34no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—62no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—122no—
325C2×Dic3—122no—
326C2×Dic3C2×#6718yes—
327C4×D3—128no—
328C4×D3—128no—
329Dic6—48no—
330C2×C32—42no—
331C2×C32C2×C22⋊Q811yescharacteristic
332C2×C32C2×#12711yescharacteristic
333C2×C32#53611yescharacteristic
334C2×C32#54712yes—
335C2×C32D4×Q812yes—
336C3⋊D3—42no—
337C24—91no—
338C24C2×D3211yescharacteristic
339C2×Q8—64no—
340C2×Q8—64no—
341C2×Q8—64no—
342C2×D4—94no—
343C2×D4—182no—
344C2×D4—182no—
345C22×C4—24no—
346C22×C4—22no—
347C22×C4—34no—
348C22×C4—34no—
349C22×C4—91no—
350C22×C4—91no—
351C22×C4—91no—
352C22×C4—184no—
353C22×C4—182no—
354C22×C4C2×D3211yescharacteristic
355C22×C4C2×D3211yescharacteristic
356C4⋊C4—38no—
357C4⋊C4—68no—
358C4⋊C4—182no—
359C4⋊C4—188no—
360C4⋊C4—184no—
361C4⋊C4—184no—
362C22⋊C4—68no—
363C22⋊C4—182no—
364C22⋊C4—188no—
365C22⋊C4—182no—
366C42—94no—
367C42—184no—
368C22×C3—24no—
369C22×C3—24no—
370C22×C3—24no—
371C22×C3—24no—
372C22×C3—22no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—22no—
376C22×C3—21no—
377C22×C3—44no—
378C22×C3—42no—
379C22×C3—44no—
380C22×C3—42no—
381C22×C3—42no—
382C22×C3—42no—
383C22×C3—42no—
384C22×C3—42no—
385C22×C3C2×D3×D412yes—
386C22×C3C2×D3×D412yes—
387C22×C3C2×D3×Q812yes—
388C22×C3#100712yes—
389C22×C3D3×#4112yes—
390C22×C3#101012yes—
391C22×C3C22×#6712yes—
392C2×D3—64no—
393C2×D3—64no—
394C2×D3—64no—
395C2×D3—64no—
396C2×D3—124no—
397C2×D3—122no—
398C2×D3—124no—
399C2×D3—122no—
400C2×D3—122no—
401C2×D3—122no—
402C2×D3—122no—
403C2×D3—122no—
404C3×C4—24no—
405C3×C4—42no—
406C3×C4—42no—
407C3×C4—68no—
408C3×C4—124no—
409C3×C4#94018yes—
410Dic3—28no—
411Dic3—38no—
412Dic3—44no—
413Dic3—64no—
414Dic3—64no—
415Dic3—122no—
416Dic3—122no—
417Dic3—122no—
418C32#254211yescharacteristic, complemented, Sylow
419C23—22no—
420C23—21no—
421C23—22no—
422C23—21no—
423C23—92no—
424C23—182no—
425C23—181no—
426C23—182no—
427C23—181no—
428C23#379712yes—
429C23C22×D3211yescharacteristic
430Q8—128no—
431D4—188no—
432C2×C4—22no—
433C2×C4—21no—
434C2×C4—38no—
435C2×C4—44no—
436C2×C4—64no—
437C2×C4—64no—
438C2×C4—64no—
439C2×C4—64no—
440C2×C4—64no—
441C2×C4—92no—
442C2×C4—92no—
443C2×C4—92no—
444C2×C4—92no—
445C2×C4—182no—
446C2×C4—182no—
447C2×C4—181no—
448C2×C4—364no—
449C2×C4D3×#6714yes—
450C2×C4#381112yes—
451C2×C3—22no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—22no—
455C2×C3—21no—
456C2×C3—44no—
457C2×C3—44no—
458C2×C3D3×C22⋊Q812yes—
459C2×C3#562812yes—
460C2×C3#563112yes—
461C2×C3#563212yes—
462C2×C3C2×#94012yes—
463C2×C3Q8×#6712yes—
464C2×C3#582412yes—
465D3—124no—
466D3—124no—
467C22—22no—
468C22—24no—
469C22—42no—
470C22—41no—
471C22—41no—
472C22—182no—
473C22—184no—
474C22—362no—
475C22—361no—
476C22—361no—
477C22#6429712yes—
478C22C2×#379711yescharacteristic
479C22#6430611yescharacteristic
480C22C2×D3×#6712yes—
481C22C2×#381111yescharacteristic
482C4—41no—
483C4—68no—
484C4—94no—
485C4—124no—
486C4—182no—
487C4—361no—
488C4#6397914yes—
489C3—21no—
490C3#8278012yescomplemented
491C2—42no—
492C2—362no—
493C2#1059480312yes—
494C2#1059480511yescharacteristic
495C2#1059489012yes—
496C2#1059492511yescharacteristic
497C2C2×#6397911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC23×C32×C4C22
prime radicalC22×#638C22
hypercenterC23×C4D32
hypocenterC32#2542
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#924C2semidirect
3. C2×#63873C2semidirect
4. C2×#63871C2semidirect
5. #10591715C2semidirect
7. #10591274C2semidirect
8. #10591244C2semidirect
9. #10591203C2semidirect
37. C2×#924D3semidirect
52. C2×#638Q8semidirect
68. C3×C4⋊Dic3D4semidirect
205. C4⋊Dic3#67semidirect
234. C3⋊Dic3C22⋊Q8semidirect
418. C32#2542semidirect
490. C3#82780semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C2×C3×#9242
C2×#638732
C2×#638712
#105917152
#105917042
#105912742
#105912442
#105912032
#827803