Finite Group Databasebeta

← #11824496

Subgroups — #11824496

Order 1152.

1481 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic
2C2×#63964C214yesmaximal, complemented
3C2×#63918C211yesmaximal, characteristic, complemented
4#10592920C211yesmaximal, characteristic
5C3×#5221C211yesmaximal, characteristic
6#10591715C214yesmaximal, complemented
7#10591359C211yesmaximal, characteristic, complemented
8#10591349C211yesmaximal, characteristic, complemented
9C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
10#82379—31nomaximal
11#76349—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C23×C3×Dic3C2212yes—
14C22×#627C2212yes—
15C2×#3757C2214yes—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C3×#217C2212yes—
19C2×C3×#217C2214yes—
20C3×D4×Dic3—24no—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×#3724C2214yes—
26C2×Dic3⋊Dic3C2214yes—
27C2×Dic3⋊Dic3C2212yes—
28C2×Dic3⋊Dic3C2212yes—
29#63964—216no—
30#63918—24no—
31#63579C2212yes—
32C2×C3×C4×D4—31no—
33C2×D4×Dic3D311yescharacteristic
34C2×#924—34no—
35C2×#888—31no—
36C2×#878—34no—
37C2×#869—31no—
38C3×#390—31no—
39#5221—31no—
40#5221—31no—
41#5221—61no—
42#5221D311yescharacteristic
43#4975—31no—
44#4975—31no—
45#4975—31no—
46#4949—34no—
47#4949—34no—
48#4935—31no—
49C4×C4⋊Dic3—31no—
50C4×Dic3⋊C4—31no—
51C24×C32C2312yes—
52C2×C32×D4—22no—
53C2×C32×D4—22no—
54C2×C32×D4Q814yescomplemented
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3C2312yes—
57C22×C3⋊Dic3C2312yes—
58C22×C3×Dic3—24no—
59C22×C3×Dic3—28no—
60C22×C3×Dic3C2312yes—
61C22×C3×Dic3C2312yes—
62C22×C3×Dic3C2311yescharacteristic
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2311yescharacteristic
65C2×#627—24no—
66C2×#627—28no—
67#3757—28no—
68C4⋊(C3⋊Dic3)—22no—
69C4×C3⋊Dic3—22no—
70C3×#217—24no—
71C3×#217—28no—
72C3×C4⋊Dic3—22no—
73C3×C4⋊Dic3—22no—
74C3×C4×Dic3—22no—
75C3×C4×Dic3D414yes—
76#3724—28no—
77Dic3⋊Dic3—24no—
78Dic3⋊Dic3—28no—
79Dic3⋊Dic3D418yescomplemented
80#2542—91noSylow
81C22×C3×D4—21no—
82C22×C3×D4C2×D311yescharacteristic
83C22×C3×D4C2×D311yescharacteristic
84C23×C3×C4—32no—
85C23×Dic3C2×D312yes—
86C22×Dic6—32no—
87C22×Dic6—32no—
88C3×C4×D4—64no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C22⋊C4—32no—
92C2×C3×C22⋊C4—34no—
93C2×C3×C42—31no—
94C2×C3×C42—31no—
95C2×#217—34no—
96C2×#217—34no—
97C2×#217—64no—
98C2×#217C2×D312yes—
99C2×#217C2×D314yes—
100D4×Dic3—24no—
101C2×C4⋊Dic3—32no—
102C2×C4⋊Dic3—31no—
103C2×C4⋊Dic3—31no—
104C2×C4⋊Dic3—34no—
105C2×C4⋊Dic3—32no—
106C2×C4⋊Dic3—61no—
107C2×C4⋊Dic3C2×D311yescharacteristic
108C2×C4⋊Dic3C2×D311yescharacteristic
109#924—616no—
110C2×Dic3⋊C4—32no—
111C2×Dic3⋊C4—32no—
112C2×Dic3⋊C4—34no—
113C2×Dic3⋊C4—34no—
114C2×Dic3⋊C4—34no—
115C2×C4×Dic3—31no—
116C2×C4×Dic3—31no—
117C2×C4×Dic3—61no—
118C2×C4×Dic3C2×D311yescharacteristic
119C2×C4×Dic3C2×D311yescharacteristic
120#888—64no—
121#878—616no—
122#869—64no—
123C3⋊#95—32no—
124C3⋊#95—32no—
125C23×C32—24no—
126C23×C32—22no—
127C23×C32—22no—
128C23×C32—24no—
129C23×C32C2×Q814yes—
130C23×C32C2411yescharacteristic
131C32×D4—28no—
132C2×C32×C4C2×D412yes—
133C2×C32×C4C2×Q812yes—
134C2×C32×C4#4112yes—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—24no—
139C2×C3⋊Dic3C2×D414yes—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—24no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—24no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—48no—
148C2×C3×Dic3C2×D414yes—
149C2×C3×Dic3C2×D414yes—
150C2×C3×Dic3C2×D412yes—
151C2×C3×Dic3C2×D412yes—
152#627—48no—
153C2×C4⋊Q8—91no—
154C2×C22⋊Q8—94no—
155C2×C4×D4—31no—
156#399—94no—
157#390—31no—
158#390—91no—
159#384—91no—
160#384—91no—
161C4×C4⋊C4—91no—
162C24×C3—22no—
163C24×C3C22×D312yes—
164C24×C3C22×D312yes—
165C2×C3×D4—22no—
166C2×C3×D4—22no—
167C2×C3×D4—22no—
168C2×C3×D4—22no—
169C2×C3×D4—24no—
170C2×C3×D4—42no—
171C2×C3×D4—42no—
172C2×C3×D4Dic614yescomplemented
173C2×C3×D4Dic614yescomplemented
174C22×C3×C4—21no—
175C22×C3×C4—31no—
176C22×C3×C4—31no—
177C22×C3×C4—32no—
178C22×C3×C4—32no—
179C22×C3×C4—32no—
180C22×C3×C4—68no—
181C22×C3×C4—64no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C22×Dic3—28no—
185C22×Dic3—24no—
186C22×Dic3—32no—
187C22×Dic3—32no—
188C22×Dic3—32no—
189C22×Dic3—32no—
190C22×Dic3—62no—
191C22×Dic3—62no—
192C22×Dic3C22×D312yes—
193C22×Dic3C22×D312yes—
194C22×Dic3C22×D312yes—
195C22×Dic3C22×D311yescharacteristic
196C22×Dic3C22×D311yescharacteristic
197C2×Dic6—64no—
198C2×Dic6—68no—
199C2×Dic6—68no—
200C2×Dic6—64no—
201C3×C4⋊C4—62no—
202C3×C4⋊C4—62no—
203C3×C22⋊C4—68no—
204C3×C22⋊C4—64no—
205C3×C42—34no—
206C3×C42—62no—
207#217—28no—
208#217—24no—
209#217—68no—
210#217—68no—
211#217—128no—
212C4⋊Dic3—22no—
213C4⋊Dic3—22no—
214C4⋊Dic3—38no—
215C4⋊Dic3—64no—
216C4⋊Dic3—68no—
217C4⋊Dic3—62no—
218C4⋊Dic3—62no—
219C4⋊Dic3—122no—
220Dic3⋊C4—38no—
221Dic3⋊C4—68no—
222Dic3⋊C4—68no—
223Dic3⋊C4—68no—
224Dic3⋊C4—64no—
225C4×Dic3—22no—
226C4×Dic3—62no—
227C4×Dic3—62no—
228C4×Dic3—122no—
229C4×Dic3#6714yes—
230C22×C32—24no—
231C22×C32—28no—
232C22×C32—42no—
233C22×C32—42no—
234C22×C32—44no—
235C22×C32C22×D412yes—
236C22×C32C22×D411yescharacteristic
237C22×C32C22×Q811yescharacteristic
238C22×C32C2×#4111yescharacteristic
239C22×C322−1+412yes—
240C32×C4C22⋊Q814yescomplemented
241C3⋊Dic3—24no—
242C3⋊Dic3—42no—
243C3×Dic3—22no—
244C3×Dic3—24no—
245C3×Dic3—42no—
246C3×Dic3—42no—
247C3×Dic3#12714yes—
248C22×Q8—92no—
249C22×D4D3211yescharacteristic
250C23×C4—32no—
251C4⋊Q8—184no—
252C22⋊Q8—1816no—
253C4×D4—64no—
254C2×C4⋊C4—31no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—92no—
257C2×C4⋊C4—94no—
258C2×C4⋊C4—94no—
259C2×C4⋊C4—92no—
260C2×C4⋊C4—91no—
261C2×C22⋊C4—32no—
262C2×C22⋊C4—34no—
263C2×C22⋊C4—94no—
264C2×C42—31no—
265C2×C42—31no—
266C2×C42—91no—
267#95—92no—
268C23×C3—22no—
269C23×C3—24no—
270C23×C3—24no—
271C23×C3—22no—
272C23×C3—22no—
273C23×C3—24no—
274C23×C3—24no—
275C23×C3—22no—
276C23×C3—21no—
277C23×C3—24no—
278C23×C3—44no—
279C23×C3—42no—
280C23×C3—42no—
281C23×C3—44no—
282C23×C3C2×Dic614yes—
283C23×C3C2×Dic614yes—
284C23×C3C23×D311yescharacteristic
285C23×C3C23×D311yescharacteristic
286C3×D4—28no—
287C3×D4—28no—
288C3×D4—48no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—34no—
293C2×C3×C4—32no—
294C2×C3×C4—34no—
295C2×C3×C4—32no—
296C2×C3×C4—62no—
297C2×C3×C4—62no—
298C2×C3×C4—62no—
299C2×C3×C4—64no—
300C2×C3×C4—64no—
301C2×C3×C4—62no—
302C2×C3×C4—62no—
303C2×C3×C4—128no—
304C2×C3×C4C2×Dic612yes—
305C2×C3×C4C2×Dic612yes—
306C2×C3×C4#23512yes—
307C2×C3×C4D3×D412yes—
308C2×C3×C4#23712yes—
309C2×C3×C4C2×#6712yes—
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3—22no—
313C2×Dic3—24no—
314C2×Dic3—24no—
315C2×Dic3—22no—
316C2×Dic3—22no—
317C2×Dic3—34no—
318C2×Dic3—34no—
319C2×Dic3—48no—
320C2×Dic3—64no—
321C2×Dic3—62no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—64no—
326C2×Dic3—62no—
327C2×Dic3—64no—
328C2×Dic3—62no—
329C2×Dic3—122no—
330C2×Dic3—122no—
331C2×Dic3—122no—
332C2×Dic3—124no—
333C2×Dic3D3×D414yes—
334C2×Dic3D3×D414yes—
335C2×Dic3C2×#6712yes—
336C2×Dic3C2×#6712yes—
337Dic6—128no—
338Dic6—128no—
339C2×C32—44no—
340C2×C32C2×C22⋊Q811yescharacteristic
341C2×C32C2×#12711yescharacteristic
342C2×C32#53611yescharacteristic
343C2×C32#54712yes—
344C2×C32D4×Q812yes—
345C24C2×D3212yes—
346C2×Q8—188no—
347C2×Q8—184no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4#62714yescomplemented
351C22×C4—31no—
352C22×C4—31no—
353C22×C4—32no—
354C22×C4—32no—
355C22×C4—32no—
356C22×C4—64no—
357C22×C4—68no—
358C22×C4—92no—
359C22×C4—92no—
360C22×C4C2×D3211yescharacteristic
361C4⋊C4—62no—
362C4⋊C4—62no—
363C4⋊C4—98no—
364C4⋊C4—188no—
365C4⋊C4—184no—
366C4⋊C4—188no—
367C4⋊C4—182no—
368C22⋊C4—64no—
369C22⋊C4—68no—
370C22⋊C4—188no—
371C42—34no—
372C42—62no—
373C42—182no—
374C22×C3—24no—
375C22×C3—24no—
376C22×C3—28no—
377C22×C3—28no—
378C22×C3—22no—
379C22×C3—22no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—44no—
384C22×C3—48no—
385C22×C3—42no—
386C22×C3—42no—
387C22×C3—42no—
388C22×C3—44no—
389C22×C3—42no—
390C22×C3—44no—
391C22×C3—84no—
392C22×C3—82no—
393C22×C3—82no—
394C22×C3C22×Dic611yescharacteristic
395C22×C3C22×Dic611yescharacteristic
396C22×C3C2×#23511yescharacteristic
397C22×C3C2×D3×D412yes—
398C22×C3C2×D3×D412yes—
399C22×C3C2×D3×D411yescharacteristic
400C22×C3C2×#23711yescharacteristic
401C22×C3#101012yes—
402C22×C3#101012yes—
403C22×C3C22×#6711yescharacteristic
404C3×C4—24no—
405C3×C4—34no—
406C3×C4—62no—
407C3×C4—64no—
408C3×C4—122no—
409C3×C4—122no—
410C3×C4#87814yescomplemented
411C3×C4#92414yescomplemented
412Dic3—22no—
413Dic3—24no—
414Dic3—42no—
415Dic3—42no—
416Dic3—64no—
417Dic3—64no—
418Dic3—124no—
419Dic3—122no—
420Dic3—122no—
421Dic3—242no—
422Dic3#94014yes—
423C32#254211yescharacteristic, complemented, Sylow
424C23—24no—
425C23—24no—
426C23—22no—
427C23—22no—
428C23C2×#62714yes—
429C23C22×D3211yescharacteristic
430Q8—368no—
431D4—28no—
432C2×C4—34no—
433C2×C4—32no—
434C2×C4—34no—
435C2×C4—32no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—64no—
440C2×C4—64no—
441C2×C4—62no—
442C2×C4—62no—
443C2×C4—94no—
444C2×C4—128no—
445C2×C4—182no—
446C2×C4—182no—
447C2×C4—184no—
448C2×C4—182no—
449C2×C4#380412yes—
450C2×C4C2×#62712yes—
451C2×C4D3×#6712yes—
452C2×C3—22no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—22no—
456C2×C3—21no—
457C2×C3—44no—
458C2×C3—44no—
459C2×C3—84no—
460C2×C3C2×#87811yescharacteristic
461C2×C3D4×Dic612yes—
462C2×C3D4×Dic612yes—
463C2×C3#555112yes—
464C2×C3#561112yes—
465C2×C3#567511yescharacteristic
466C2×C3D3×#12711yescharacteristic
467C2×C3C2×#92411yescharacteristic
468C2×C3C2×#94011yescharacteristic
469C2×C3#582511yescharacteristic
470C22—24no—
471C22—28no—
472C22—44no—
473C22—42no—
474C22—42no—
475C22#6430912yes—
476C22D32×D412yes—
477C22C2×#380411yescharacteristic
478C22C22×#62711yescharacteristic
479C22C2×D3×#6711yescharacteristic
480C4—34no—
481C4—64no—
482C4—62no—
483C4—122no—
484C4—122no—
485C4—184no—
486C4—362no—
487C4#6396414yescomplemented
488C3—21no—
489C3#7634911yescharacteristic, complemented
490C3#8237911yescharacteristic, complemented
491C2—44no—
492C2#1059513612yes—
493C2#1059514711yescharacteristic
494C2D4×#62712yes—
495C2D3×#94011yescharacteristic
496C2C2×#6396411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
Fitting, prime radicalC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#2542
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63964C2semidirect
3. C2×#63918C2semidirect
6. #10591715C2semidirect
7. #10591359C2semidirect
8. #10591349C2semidirect
9. C4×Dic3⋊Dic3C2semidirect
54. C2×C32×D4Q8semidirect
79. Dic3⋊Dic3D4semidirect
172. C2×C3×D4Dic6semidirect
173. C2×C3×D4Dic6semidirect
240. C32×C4C22⋊Q8semidirect
350. C2×D4#627semidirect
410. C3×C4#878semidirect
411. C3×C4#924semidirect
423. C32#2542semidirect
487. C4#63964semidirect
489. C3#76349semidirect
490. C3#82379semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
C2×#639642
C2×#639182
#105929202
C3×#52212
#105917152
#105913592
#105913492
C4×Dic3⋊Dic32
#823793
#763493