Finite Group Databasebeta

← #11805629

Subgroups — #11805629

Order 1152.

1980 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×C4×#638C211yesmaximal, characteristic
3C2×#64101C211yesmaximal, characteristic, complemented
4#10592912C212yesmaximal
5#10592911C211yesmaximal, characteristic, complemented
6C4×#3757C212yesmaximal, complemented
7#10592689C212yesmaximal, complemented
8#10592686C211yesmaximal, characteristic, complemented
9#10592677C212yesmaximal, complemented
10#10592676C211yesmaximal, characteristic, complemented
11C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
12#82161—34nomaximal
13C23×C32×C4C2212yes—
14C23×C32×C4C2211yescharacteristic
15C22×#638C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C2×C32×C4⋊C4—24no—
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C32×C4⋊C4C2212yes—
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×#3757C2212yes—
22C2×#3757C2211yescharacteristic
23C4×#638C418yescomplemented
24C2×#3752C2212yes—
25C2×#3752C2212yes—
26C2×#3752C2211yescharacteristic
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30C2×C4×C3⋊Dic3C2212yes—
31C2×C4×C3⋊Dic3C2212yes—
32C2×C4×C3⋊Dic3C2211yescharacteristic
33#64101—24no—
34#63658C2212yes—
35#63658C2212yes—
36#63658C2212yes—
37#63658C2212yes—
38#63658C2212yes—
39C22×C3×C4⋊C4D314yescomplemented
40C2×C4×#67—34no—
41C2×#892—34no—
42#5213—38no—
43#5212—34no—
44C4×#217—38no—
45#4990—38no—
46#4987—34no—
47#4978—38no—
48#4977—34no—
49Dic3×C4⋊C4—34no—
50C24×C32C2311yescharacteristic
51C23×C3⋊D3C2311yescharacteristic
52C22×C32×C4—22no—
53C22×C32×C4—22no—
54C22×C32×C4—24no—
55C22×C32×C4—24no—
56C22×C32×C4—42no—
57C22×C32×C4C2×C414yes—
58C22×C32×C4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C22×C32×C4C2312yes—
61C22×C32×C4C2311yescharacteristic
62C2×#638—22no—
63C2×#638—22no—
64C2×#638C2×C414yes—
65C22×C3⋊Dic3C2312yes—
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C2×C4×C3⋊D3—22no—
71C2×C4×C3⋊D3—22no—
72C2×C4×C3⋊D3C2×C414yescomplemented
73C32×C4⋊C4—24no—
74C32×C4⋊C4—22no—
75C32×C4⋊C4D414yescomplemented
76#3757—24no—
77#3757C2×C414yes—
78#3752—24no—
79#3752—42no—
80#3752C2×C414yescomplemented
81C4⋊(C3⋊Dic3)—22no—
82C4⋊(C3⋊Dic3)—22no—
83#3750C2×C414yescomplemented
84C4×C3⋊Dic3—24no—
85C4×C3⋊Dic3—42no—
86C4×C3⋊Dic3C2×C414yescomplemented
87#2352—91noSylow
88C23×C3×C4C2×D318yes—
89C23×C3×C4C2×D314yes—
90C22×#67—34no—
91C22×C4×D3—34no—
92C2×C3×C4⋊C4—216no—
93C2×C3×C4⋊C4C2×D314yes—
94C2×C3×C4⋊C4C2×D318yes—
95C2×C3×C4⋊C4C2×D314yes—
96C2×#217—34no—
97C2×#217—38no—
98C4×#67—332no—
99C2×(C2×D3)⋊C4—34no—
100C2×(C2×D3)⋊C4—38no—
101C2×(C2×D3)⋊C4—38no—
102C2×C4⋊Dic3—34no—
103C2×C4⋊Dic3—34no—
104C2×Dic3⋊C4—34no—
105C2×C4×Dic3—34no—
106C2×C4×Dic3—38no—
107C2×C4×Dic3—38no—
108#892—616no—
109C3⋊#95—38no—
110C3⋊#95—38no—
111C3⋊#95—38no—
112C3⋊#95—38no—
113C3⋊#95—38no—
114C23×C32—21no—
115C23×C32—21no—
116C23×C32—21no—
117C23×C32—21no—
118C23×C32C22×C412yes—
119C23×C32#4112yes—
120C23×C32#4112yes—
121C23×C32C2411yescharacteristic
122C22×C3⋊D3—21no—
123C22×C3⋊D3—21no—
124C22×C3⋊D3—21no—
125C22×C3⋊D3—21no—
126C22×C3⋊D3—21no—
127C22×C3⋊D3—21no—
128C22×C3⋊D3C22×C412yes—
129C2×C32×C4—21no—
130C2×C32×C4—21no—
131C2×C32×C4—22no—
132C2×C32×C4—22no—
133C2×C32×C4—28no—
134C2×C32×C4—22no—
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C32×C4—48no—
138C2×C32×C4C22×C412yes—
139C2×C32×C4C22×C412yes—
140C2×C32×C4C2×D414yes—
141C2×C32×C4C2×D412yes—
142C2×C32×C4#4112yes—
143#638—28no—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3—21no—
147C2×C3⋊Dic3—21no—
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3C22×C412yes—
157C2×C3⋊Dic3C22×C412yes—
158C2×C3⋊Dic3C22×C412yes—
159C4×C3⋊D3—28no—
160C2×C4×D4—91no—
161C2×#117—91no—
162C22×C4⋊C4C3⋊D311yescharacteristic, complemented
163#388—92no—
164#387—92no—
165#386—92no—
166#382—91no—
167#380—91no—
168#380—91no—
169C4×C4⋊C4—91no—
170C4×C22⋊C4—92no—
171C24×C3C22×D314yes—
172C23×D3—34no—
173C22×C3×C4—28no—
174C22×C3×C4—28no—
175C22×C3×C4—216no—
176C22×C3×C4—216no—
177C22×C3×C4—48no—
178C22×C3×C4C4×D3116yes—
179C22×C3×C4C22×D318yes—
180C22×C3×C4C22×D314yes—
181C22×C3×C4C22×D318yes—
182C22×C3×C4C22×D314yes—
183C2×#67—316no—
184C2×#67—68no—
185C2×#67—68no—
186C22×Dic3—34no—
187C22×Dic3—34no—
188C22×Dic3—34no—
189C22×Dic3—38no—
190C22×Dic3—38no—
191C2×C4×D3—316no—
192C2×C4×D3—68no—
193C2×C4×D3—68no—
194C3×C4⋊C4—216no—
195C3×C4⋊C4—28no—
196C3×C4⋊C4#67116yescomplemented
197#217—316no—
198#217—616no—
199(C2×D3)⋊C4—316no—
200(C2×D3)⋊C4—616no—
201(C2×D3)⋊C4—128no—
202C4⋊Dic3—68no—
203C4⋊Dic3—68no—
204Dic3⋊C4—316no—
205C4×Dic3—316no—
206C4×Dic3—616no—
207C4×Dic3—128no—
208C22×C32—22no—
209C22×C32—22no—
210C22×C32—22no—
211C22×C32—22no—
212C22×C32—22no—
213C22×C32—22no—
214C22×C32#11714yescomplemented
215C22×C32C23×C411yescharacteristic
216C22×C32C22×D411yescharacteristic
217C22×C32C2×#4111yescharacteristic
218C22×C32C2×#4111yescharacteristic
219C22×C32C2×#4111yescharacteristic
220C22×C32H(5,𝔽2)11yescharacteristic
221C22×C322−1+411yescharacteristic
222C2×C3⋊D3—22no—
223C2×C3⋊D3—22no—
224C2×C3⋊D3—22no—
225C2×C3⋊D3—41no—
226C2×C3⋊D3—41no—
227C2×C3⋊D3—41no—
228C2×C3⋊D3—41no—
229C32×C4—22no—
230C32×C4—24no—
231C32×C4—42no—
232C32×C4C4×D414yes—
233C3⋊Dic3—22no—
234C3⋊Dic3—22no—
235C3⋊Dic3—22no—
236C3⋊Dic3—42no—
237C3⋊Dic3—42no—
238C22×D4—91no—
239C23×C4—91no—
240C23×C4C2×C3⋊D312yes—
241C23×C4C2×C3⋊D311yescharacteristic
242C4×D4—98no—
243#117—184no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—91no—
246C2×C4⋊C4—91no—
247C2×C4⋊C4—91no—
248C2×C4⋊C4C2×C3⋊D311yescharacteristic
249C2×C4⋊C4C2×C3⋊D312yes—
250C2×C4⋊C4C2×C3⋊D311yescharacteristic
251C2×C22⋊C4—91no—
252C2×C22⋊C4—91no—
253C2×C22⋊C4—92no—
254C2×C22⋊C4—92no—
255C2×C22⋊C4—92no—
256C2×C42—91no—
257C2×C42—92no—
258C2×C42—92no—
259#95—92no—
260#95—92no—
261#95—92no—
262#95—92no—
263#95—92no—
264C23×C3—24no—
265C23×C3—24no—
266C23×C3—24no—
267C23×C3—24no—
268C23×C3C2×C4×D318yes—
269C23×C3#23718yes—
270C23×C3#23918yes—
271C23×C3C23×D314yes—
272C22×D3—38no—
273C22×D3—64no—
274C22×D3—64no—
275C22×D3—64no—
276C22×D3—64no—
277C22×D3—64no—
278C22×D3—64no—
279C2×C3×C4—24no—
280C2×C3×C4—28no—
281C2×C3×C4—28no—
282C2×C3×C4—24no—
283C2×C3×C4—232no—
284C2×C3×C4—28no—
285C2×C3×C4—28no—
286C2×C3×C4—28no—
287C2×C3×C4—432no—
288C2×C3×C4C2×C4×D318yes—
289C2×C3×C4C2×C4×D318yes—
290C2×C3×C4#23518yes—
291C2×C3×C4C2×#67116yes—
292C2×C3×C4C2×#6718yes—
293#67—632no—
294C2×Dic3—38no—
295C2×Dic3—38no—
296C2×Dic3—38no—
297C2×Dic3—64no—
298C2×Dic3—64no—
299C2×Dic3—64no—
300C2×Dic3—64no—
301C2×Dic3—64no—
302C2×Dic3—64no—
303C2×Dic3—68no—
304C2×Dic3—68no—
305C2×Dic3—68no—
306C2×Dic3—68no—
307C2×Dic3—68no—
308C2×Dic3—68no—
309C4×D3—632no—
310C2×C32—24no—
311C2×C32C2×#11711yescharacteristic
312C2×C32C2×C4×D411yescharacteristic
313C2×C32#52011yescharacteristic
314C2×C32#54611yescharacteristic
315C2×C32#54811yescharacteristic
316C2×C32#55211yescharacteristic
317C2×C32#55311yescharacteristic
318C3⋊D3—42no—
319C24—91no—
320C24C22×C3⋊D311yescharacteristic
321C2×D4—94no—
322C2×D4—182no—
323C2×D4—182no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—24no—
327C22×C4—24no—
328C22×C4—42no—
329C22×C4—91no—
330C22×C4—91no—
331C22×C4—91no—
332C22×C4—94no—
333C22×C4—92no—
334C22×C4—92no—
335C22×C4—182no—
336C22×C4—182no—
337C22×C4C4×C3⋊D314yes—
338C22×C4C22×C3⋊D312yes—
339C22×C4C22×C3⋊D311yescharacteristic
340C22×C4C22×C3⋊D312yes—
341C22×C4C22×C3⋊D311yescharacteristic
342C4⋊C4—24no—
343C4⋊C4—22no—
344C4⋊C4—94no—
345C4⋊C4—182no—
346C4⋊C4—182no—
347C4⋊C4#63814yescomplemented
348C22⋊C4—94no—
349C22⋊C4—94no—
350C22⋊C4—184no—
351C22⋊C4—184no—
352C22⋊C4—362no—
353C42—94no—
354C42—184no—
355C42—362no—
356C22×C3—28no—
357C22×C3—28no—
358C22×C3—28no—
359C22×C3—28no—
360C22×C3—28no—
361C22×C3—28no—
362C22×C3#892116yescomplemented
363C22×C3C22×C4×D314yes—
364C22×C3C2×#23514yes—
365C22×C3C2×#23714yes—
366C22×C3#100414yes—
367C22×C3C2×#23914yes—
368C22×C3#100714yes—
369C22×C3C22×#6714yes—
370C2×D3—68no—
371C2×D3—68no—
372C2×D3—68no—
373C2×D3—124no—
374C2×D3—124no—
375C2×D3—124no—
376C2×D3—124no—
377C3×C4—28no—
378C3×C4—216no—
379C3×C4—48no—
380C3×C4C4×#67116yes—
381Dic3—68no—
382Dic3—68no—
383Dic3—68no—
384Dic3—128no—
385Dic3—128no—
386C32#235211yescharacteristic, complemented, Sylow
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—92no—
392C23—181no—
393C23—181no—
394C23—181no—
395C23—181no—
396C23—181no—
397C23—181no—
398C23C2×C4×C3⋊D312yes—
399C23#383012yes—
400C23#383212yes—
401C23C23×C3⋊D311yescharacteristic
402D4—188no—
403C2×C4—21no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—21no—
407C2×C4—28no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—48no—
412C2×C4—92no—
413C2×C4—92no—
414C2×C4—92no—
415C2×C4—181no—
416C2×C4—181no—
417C2×C4—181no—
418C2×C4—181no—
419C2×C4—181no—
420C2×C4—181no—
421C2×C4—188no—
422C2×C4—182no—
423C2×C4—182no—
424C2×C4—182no—
425C2×C4—182no—
426C2×C4—182no—
427C2×C4—182no—
428C2×C4C2×C4×C3⋊D312yes—
429C2×C4C2×C4×C3⋊D312yes—
430C2×C4#382812yes—
431C2×C4C2×#63814yes—
432C2×C4C2×#63812yes—
433C2×C3—216no—
434C2×C3C2×#89214yes—
435C2×C3#550414yes—
436C2×C3#551314yes—
437C2×C3#551414yes—
438C2×C3C2×C4×#6714yes—
439C2×C3#580614yes—
440C2×C3#581714yes—
441D3—128no—
442C22—22no—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—182no—
449C22—182no—
450C22—182no—
451C22—361no—
452C22—361no—
453C22—361no—
454C22—361no—
455C22#6410114yescomplemented
456C22C22×C4×C3⋊D311yescharacteristic
457C22C2×#382811yescharacteristic
458C22C2×#383011yescharacteristic
459C22#6436111yescharacteristic
460C22C2×#383211yescharacteristic
461C22#6436411yescharacteristic
462C22C22×#63811yescharacteristic
463C4—22no—
464C4—24no—
465C4—42no—
466C4—182no—
467C4—182no—
468C4—182no—
469C4—362no—
470C4—362no—
471C4C4×#63814yes—
472C3#8216114yescomplemented
473C2—24no—
474C2—362no—
475C2C2×#6410111yescharacteristic
476C2#1059597511yescharacteristic
477C2#1059598411yescharacteristic
478C2#1059598511yescharacteristic
479C2C2×C4×#63811yescharacteristic
480C2#1059627711yescharacteristic
481C2#1059628811yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC22×C32×C4⋊C4C2
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC22×C4⋊C4C3⋊D3
hypocenterC32#2352
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C32×C4⋊C4C2semidirect
3. C2×#64101C2semidirect
5. #10592911C2semidirect
6. C4×#3757C2semidirect
7. #10592689C2semidirect
8. #10592686C2semidirect
9. #10592677C2semidirect
10. #10592676C2semidirect
11. C4⋊C4×C3⋊Dic3C2semidirect
23. C4×#638C4semidirect
39. C22×C3×C4⋊C4D3semidirect
72. C2×C4×C3⋊D3C2×C4semidirect
75. C32×C4⋊C4D4semidirect
80. #3752C2×C4semidirect
83. #3750C2×C4semidirect
86. C4×C3⋊Dic3C2×C4semidirect
162. C22×C4⋊C4C3⋊D3semidirect
196. C3×C4⋊C4#67semidirect
214. C22×C32#117semidirect
347. C4⋊C4#638semidirect
362. C22×C3#892semidirect
386. C32#2352semidirect
455. C22#64101semidirect
472. C3#82161semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C4⋊C42
C2×C4×#6382
C2×#641012
#105929122
#105929112
C4×#37572
#105926892
#105926862
#105926772
#105926762
C4⋊C4×C3⋊Dic32
#821613