Finite Group Databasebeta

← #11824525

Subgroups — #11824525

Order 1152.

2172 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×#64148C212yesmaximal, complemented
3C2×#64139C211yesmaximal, characteristic, complemented
4#10592912C212yesmaximal, complemented
5C2×#63658C211yesmaximal, characteristic, complemented
6#10592690C211yesmaximal, characteristic, complemented
7#10592680C211yesmaximal, characteristic, complemented
8#10592659C211yesmaximal, characteristic, complemented
9#10592657C212yesmaximal, complemented
10#10592652C211yesmaximal, characteristic, complemented
11#10592639C212yesmaximal, complemented
12#82380—34nomaximal
13C22×C32×D4C2211yescharacteristic
14C23×C32×C4C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C22×#638C2212yes—
17C22×#638C2212yes—
18C23×C3⋊Dic3C2212yes—
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C32×C4×D4—24no—
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×C32×C42C2211yescharacteristic
25C2×#3757C2212yes—
26#64148—28no—
27#64139—24no—
28C2×#3752C2212yes—
29C2×#3752C2212yes—
30C2×#3752C2212yes—
31C2×#3752C2212yes—
32C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
33C2×#3750C2212yes—
34#63658C2212yes—
35#63658C2212yes—
36#63658C2211yescharacteristic
37#63658C2211yescharacteristic
38#63658C2212yes—
39C2×C3×C4×D4D314yescomplemented
40C2×#939—38no—
41C2×#930—34no—
42#5213—38no—
43C2×C3⋊#95—34no—
44#4991—34no—
45#4981—34no—
46#4960—34no—
47#4958—38no—
48#4953—34no—
49#4940—38no—
50C24×C32C2311yescharacteristic
51C24×C32C2311yescharacteristic
52C23×C3⋊D3C2312yes—
53C2×C32×D4—22no—
54C2×C32×D4—22no—
55C2×C32×D4D414yescomplemented
56C22×C32×C4—22no—
57C22×C32×C4—42no—
58C22×C32×C4—42no—
59C22×C32×C4D414yescomplemented
60C22×C32×C4C2311yescharacteristic
61C22×C32×C4C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C2×#638—24no—
66C2×#638—24no—
67C2×#638—24no—
68C2×#638—24no—
69C2×#638—24no—
70C2×#638—42no—
71C22×C3⋊Dic3—24no—
72C22×C3⋊Dic3—24no—
73C22×C3⋊Dic3—42no—
74C22×C3⋊Dic3C2312yes—
75C22×C3⋊Dic3C2312yes—
76C22×C3⋊Dic3C2312yes—
77C2×C4⋊(C3⋊D3)—22no—
78C2×C4⋊(C3⋊D3)—42no—
79C32×C4⋊C4—22no—
80C32×C22⋊C4—22no—
81C32×C22⋊C4—22no—
82C32×C42—22no—
83#3757—24no—
84#3752—24no—
85#3752—24no—
86#3752—24no—
87#3752—42no—
88C4⋊(C3⋊Dic3)—22no—
89#3750—24no—
90#2543—91noSylow
91C22×C3×D4C2×D314yes—
92C23×C3×C4C2×D314yes—
93C23×C3×C4C2×D314yes—
94C22×#67—38no—
95C22×#67—38no—
96C23×Dic3—38no—
97C22×D12—34no—
98C3×C4×D4—216no—
99C2×C3×C4⋊C4C2×D314yes—
100C2×C3×C22⋊C4C2×D314yes—
101C2×C3×C22⋊C4C2×D314yes—
102C2×C3×C42C2×D314yes—
103C2×#217—38no—
104#939—632no—
105#930—616no—
106C2×(C2×D3)⋊C4—38no—
107C2×(C2×D3)⋊C4—38no—
108C2×(C2×D3)⋊C4—38no—
109C2×(C2×D3)⋊C4—38no—
110C2×C4⋊Dic3—34no—
111C2×Dic3⋊C4—38no—
112C3⋊#95—38no—
113C3⋊#95—38no—
114C3⋊#95—34no—
115C3⋊#95—34no—
116C3⋊#95—38no—
117C23×C32—22no—
118C23×C32—22no—
119C23×C32—21no—
120C23×C32—22no—
121C23×C32—21no—
122C23×C32—22no—
123C23×C32C2×D412yes—
124C23×C32C2×D412yes—
125C23×C32C2×D412yes—
126C23×C32#4112yes—
127C23×C32C2411yescharacteristic
128C22×C3⋊D3—22no—
129C22×C3⋊D3—22no—
130C22×C3⋊D3—22no—
131C22×C3⋊D3—22no—
132C22×C3⋊D3—22no—
133C22×C3⋊D3—22no—
134C22×C3⋊D3—22no—
135C32×D4—28no—
136C2×C32×C4—21no—
137C2×C32×C4—21no—
138C2×C32×C4—22no—
139C2×C32×C4—22no—
140C2×C32×C4—21no—
141C2×C32×C4—21no—
142C2×C32×C4—22no—
143C2×C32×C4—22no—
144C2×C32×C4—44no—
145C2×C32×C4—44no—
146C2×C32×C4C2×D412yes—
147C2×C32×C4C2×D412yes—
148C2×C32×C4C2×D412yes—
149#638—48no—
150#638—48no—
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—48no—
160C2×C3⋊Dic3#4114yes—
161C4⋊(C3⋊D3)—44no—
162C2×#121—92no—
163C2×#121—91no—
164C2×C4×D4C3⋊D311yescharacteristic, complemented
165#398—91no—
166#397—91no—
167#394—91no—
168#392—91no—
169#388—92no—
170#386—92no—
171#386—92no—
172C2×#95—91no—
173C24×C3C22×D314yes—
174C24×C3C22×D314yes—
175C23×D3—38no—
176C2×C3×D4—28no—
177C2×C3×D4—28no—
178C2×C3×D4D12116yescomplemented
179C22×C3×C4—28no—
180C22×C3×C4—48no—
181C22×C3×C4—48no—
182C22×C3×C4#67116yescomplemented
183C22×C3×C4C22×D314yes—
184C22×C3×C4C22×D314yes—
185C22×C3×C4C22×D314yes—
186C22×C3×C4C22×D314yes—
187C22×C3×C4C22×D314yes—
188C2×#67—616no—
189C2×#67—616no—
190C2×#67—616no—
191C2×#67—616no—
192C2×#67—616no—
193C2×#67—128no—
194C22×Dic3—38no—
195C22×Dic3—38no—
196C22×Dic3—38no—
197C22×Dic3—616no—
198C22×Dic3—616no—
199C22×Dic3—128no—
200C2×D12—68no—
201C2×D12—128no—
202C3×C4⋊C4—28no—
203C3×C22⋊C4—28no—
204C3×C22⋊C4—28no—
205C3×C42—28no—
206#217—616no—
207(C2×D3)⋊C4—616no—
208(C2×D3)⋊C4—616no—
209(C2×D3)⋊C4—616no—
210(C2×D3)⋊C4—128no—
211C4⋊Dic3—68no—
212Dic3⋊C4—616no—
213C22×C32—22no—
214C22×C32—22no—
215C22×C32—24no—
216C22×C32—24no—
217C22×C32—22no—
218C22×C32—24no—
219C22×C32—41no—
220C22×C32—41no—
221C22×C32—42no—
222C22×C32#12114yes—
223C22×C32C22×D411yescharacteristic
224C22×C32C22×D411yescharacteristic
225C22×C32C2×#4111yescharacteristic
226C22×C32C2×#4112yes—
227C22×C32H(5,𝔽2)12yes—
228C2×C3⋊D3—42no—
229C2×C3⋊D3—42no—
230C2×C3⋊D3—42no—
231C2×C3⋊D3—42no—
232C2×C3⋊D3—42no—
233C2×C3⋊D3—42no—
234C2×C3⋊D3—42no—
235C32×C4—22no—
236C32×C4—22no—
237C32×C4—22no—
238C32×C4—41no—
239C32×C4—41no—
240C3⋊Dic3—24no—
241C3⋊Dic3—42no—
242C3⋊Dic3—42no—
243C22×D4—92no—
244C22×D4—92no—
245C22×D4—91no—
246C22×D4C2×C3⋊D311yescharacteristic
247C23×C4—92no—
248C23×C4C2×C3⋊D311yescharacteristic
249C23×C4C2×C3⋊D311yescharacteristic
250#121—188no—
251#121—184no—
252C4×D4—24no—
253C2×C4⋊C4—92no—
254C2×C4⋊C4—91no—
255C2×C4⋊C4C2×C3⋊D311yescharacteristic
256C2×C22⋊C4—92no—
257C2×C22⋊C4—92no—
258C2×C22⋊C4—92no—
259C2×C22⋊C4—92no—
260C2×C22⋊C4—92no—
261C2×C22⋊C4C2×C3⋊D311yescharacteristic
262C2×C22⋊C4C2×C3⋊D311yescharacteristic
263C2×C42C2×C3⋊D311yescharacteristic
264#95—92no—
265#95—91no—
266#95—91no—
267#95—92no—
268#95—92no—
269C23×C3—28no—
270C23×C3—28no—
271C23×C3—24no—
272C23×C3—28no—
273C23×C3—28no—
274C23×C3—24no—
275C23×C3C2×D1218yes—
276C23×C3C2×D1218yes—
277C23×C3#23518yes—
278C23×C3C2×#6718yes—
279C23×C3C23×D314yes—
280C22×D3—68no—
281C22×D3—68no—
282C22×D3—68no—
283C22×D3—68no—
284C22×D3—68no—
285C22×D3—68no—
286C22×D3—68no—
287C3×D4—232no—
288C2×C3×C4—24no—
289C2×C3×C4—28no—
290C2×C3×C4—28no—
291C2×C3×C4—24no—
292C2×C3×C4—28no—
293C2×C3×C4—28no—
294C2×C3×C4—24no—
295C2×C3×C4—24no—
296C2×C3×C4—416no—
297C2×C3×C4—416no—
298C2×C3×C4C2×D1218yes—
299C2×C3×C4C2×#6718yes—
300C2×C3×C4C2×#6718yes—
301#67—1232no—
302#67—1232no—
303C2×Dic3—316no—
304C2×Dic3—68no—
305C2×Dic3—68no—
306C2×Dic3—68no—
307C2×Dic3—68no—
308C2×Dic3—68no—
309C2×Dic3—68no—
310C2×Dic3—68no—
311C2×Dic3—68no—
312C2×Dic3—1232no—
313D12—1216no—
314C2×C32—24no—
315C2×C32—42no—
316C2×C32C2×#12111yescharacteristic
317C2×C32#53211yescharacteristic
318C2×C32#53411yescharacteristic
319C2×C32#54612yes—
320C2×C32#55312yes—
321C3⋊D3—82no—
322C24—92no—
323C24C22×C3⋊D311yescharacteristic
324C24C22×C3⋊D311yescharacteristic
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—184no—
328C2×D4—184no—
329C2×D4—184no—
330C2×D4—184no—
331C2×D4—184no—
332C2×D4—182no—
333C2×D4—362no—
334C2×D4—362no—
335C2×D4C4⋊(C3⋊D3)14yescomplemented
336C22×C4—22no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—92no—
340C22×C4—92no—
341C22×C4—92no—
342C22×C4—184no—
343C22×C4—184no—
344C22×C4—362no—
345C22×C4#63814yescomplemented
346C22×C4C22×C3⋊D311yescharacteristic
347C22×C4C22×C3⋊D311yescharacteristic
348C22×C4C22×C3⋊D311yescharacteristic
349C22×C4C22×C3⋊D311yescharacteristic
350C22×C4C22×C3⋊D311yescharacteristic
351C4⋊C4—22no—
352C4⋊C4—184no—
353C4⋊C4—182no—
354C22⋊C4—22no—
355C22⋊C4—22no—
356C22⋊C4—184no—
357C22⋊C4—184no—
358C22⋊C4—184no—
359C22⋊C4—184no—
360C22⋊C4—362no—
361C42—22no—
362C22×C3—216no—
363C22×C3—28no—
364C22×C3—216no—
365C22×C3—28no—
366C22×C3—28no—
367C22×C3—216no—
368C22×C3—48no—
369C22×C3—44no—
370C22×C3—44no—
371C22×C3#930116yes—
372C22×C3C22×D1214yes—
373C22×C3C2×#23514yes—
374C22×C3#100418yes—
375C22×C3D3×#4118yes—
376C22×C3C22×#6714yes—
377C2×D3—128no—
378C2×D3—128no—
379C2×D3—128no—
380C2×D3—128no—
381C2×D3—128no—
382C2×D3—128no—
383C2×D3—128no—
384C3×C4—28no—
385C3×C4—28no—
386C3×C4—28no—
387C3×C4—44no—
388C3×C4—44no—
389Dic3—616no—
390Dic3—128no—
391Dic3—128no—
392C32#254311yescharacteristic, complemented, Sylow
393C23—22no—
394C23—22no—
395C23—21no—
396C23—22no—
397C23—22no—
398C23—21no—
399C23—182no—
400C23—182no—
401C23—182no—
402C23—182no—
403C23—182no—
404C23—182no—
405C23—182no—
406C23C2×C4⋊(C3⋊D3)12yes—
407C23C2×C4⋊(C3⋊D3)12yes—
408C23#382812yes—
409C23C2×#63812yes—
410C23C23×C3⋊D311yescharacteristic
411D4—28no—
412D4—364no—
413D4—368no—
414D4—368no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—21no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4—94no—
426C2×C4—182no—
427C2×C4—182no—
428C2×C4—182no—
429C2×C4—182no—
430C2×C4—182no—
431C2×C4—182no—
432C2×C4—182no—
433C2×C4—182no—
434C2×C4—368no—
435C2×C4C2×C4⋊(C3⋊D3)12yes—
436C2×C4C2×#63812yes—
437C2×C4C2×#63812yes—
438C2×C3—216no—
439C2×C3—48no—
440C2×C3#554018yes—
441C2×C3#555418yes—
442C2×C3C2×#93014yes—
443C2×C3#580414yes—
444C2×C3#583214yes—
445D3—248no—
446C22—24no—
447C22—22no—
448C22—24no—
449C22—22no—
450C22—22no—
451C22—24no—
452C22—42no—
453C22—41no—
454C22—41no—
455C22—362no—
456C22—362no—
457C22—362no—
458C22—362no—
459C22—362no—
460C22—362no—
461C22—362no—
462C22#6413914yes—
463C22C22×C4⋊(C3⋊D3)11yescharacteristic
464C22C2×#382811yescharacteristic
465C22#6436112yes—
466C22#41×C3⋊D312yes—
467C22C22×#63811yescharacteristic
468C4—22no—
469C4—22no—
470C4—22no—
471C4—41no—
472C4—41no—
473C4—184no—
474C4—362no—
475C4—362no—
476C3#8238014yescomplemented
477C2—24no—
478C2—42no—
479C2—722no—
480C2#1059601112yes—
481C2#1059602512yes—
482C2C2×#6413911yescharacteristic
483C2#1059627511yescharacteristic
484C2#1059630311yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4×D4C2
hypercenterC2×C4×D4C3⋊D3
hypocenterC32#2543
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
2. C2×#64148C2semidirect
3. C2×#64139C2semidirect
4. #10592912C2semidirect
5. C2×#63658C2semidirect
6. #10592690C2semidirect
7. #10592680C2semidirect
8. #10592659C2semidirect
9. #10592657C2semidirect
10. #10592652C2semidirect
11. #10592639C2semidirect
39. C2×C3×C4×D4D3semidirect
55. C2×C32×D4D4semidirect
59. C22×C32×C4D4semidirect
164. C2×C4×D4C3⋊D3semidirect
178. C2×C3×D4D12semidirect
182. C22×C3×C4#67semidirect
335. C2×D4C4⋊(C3⋊D3)semidirect
345. C22×C4#638semidirect
392. C32#2543semidirect
476. C3#82380semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×#641482
C2×#641392
#105929122
C2×#636582
#105926902
#105926802
#105926592
#105926572
#105926522
#105926392
#823803