Finite Group Databasebeta

← #11859406

Subgroups — #11859406

Order 1152.

822 conjugacy classes of subgroups.

The subgroup lattice has 403 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64287C211yesmaximal, characteristic, complemented
2C2×#64283C211yesmaximal, characteristic, complemented
3#10596077C211yesmaximal, characteristic
4#10593823C211yesmaximal, characteristic, complemented
5#10593821C212yesmaximal, complemented
6#10593820C212yesmaximal, complemented
7#10593803C211yesmaximal, characteristic, complemented
8#10593755C211yesmaximal, characteristic, complemented
9#10593748C211yesmaximal, characteristic, complemented
10#10593742C212yesmaximal, complemented
11#10593740C212yesmaximal, complemented
12C2×#3830C2211yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14C2×#3792C2211yescharacteristic
15C2×#3792C2211yescharacteristic
16C2×#3792C2212yescomplemented
17C22×#622C2212yescomplemented
18#64287—24no—
19#64283—24no—
20C2×#3788C2211yescharacteristic
21C2×#3788C2211yescharacteristic
22C2×#3788C2211yescharacteristic
23C2×#3788C2211yescharacteristic
24C2×#3787C2211yescharacteristic
25C2×#3787C2211yescharacteristic
26C32×#121C411yescharacteristic
27#64147C411yescharacteristic
28#64146C412yes—
29D4×C3⋊Dic3C2212yes—
30#64133C411yescharacteristic
31#64106C411yescharacteristic
32#64101C2211yescharacteristic
33#64092C412yes—
34#64090C2212yes—
35C22⋊#622C2212yes—
36C22⋊#622C2212yescomplemented
37C22⋊#622C2212yescomplemented
38#63779C2212yescomplemented
39#63778C2212yes—
40#63777C2212yescomplemented
41C4⋊#622C2212yescomplemented
42C4×#622C2212yescomplemented
43#5606—62no—
44C23×C3⋊D3C2×C411yescharacteristic
45C2×C32×D4C2×C411yescharacteristic
46C2×C32×D4C2×C412yes—
47C22×C32×C4C2×C411yescharacteristic
48C2×#638C2×C412yes—
49C2×#638C2×C412yes—
50C22×C3⋊Dic3C2312yes—
51C22×C3⋊Dic3C2311yescharacteristic
52#3830—22no—
53#3830—22no—
54C2×C4×C3⋊D3—22no—
55C2×C4×C3⋊D3—22no—
56C2×C4×C3⋊D3C2×C411yescharacteristic
57C2×C4×C3⋊D3C2×C411yescharacteristic
58C2×C4×C3⋊D3C2311yescharacteristic
59C2×C4×C3⋊D3C2311yescharacteristic
60C2×#634C2×C411yescharacteristic
61#3792—22no—
62#3792—22no—
63#3792—24no—
64C2×#622—24no—
65C2×#622C2311yescharacteristic
66C2×#622C2311yescharacteristic
67C2×#622C2312yes—
68C2×#622C2312yes—
69C2×#622C2311yescharacteristic
70C2×#622C2311yescharacteristic
71#3788—22no—
72#3788—22no—
73#3788—22no—
74#3788—22no—
75#3787—22no—
76#3787D414yescomplemented
77C32×C4⋊C4C2×C411yescharacteristic
78C32×C22⋊C4C2×C412yes—
79#3757C2×C412yes—
80#3757C2×C412yes—
81#3752C2×C412yes—
82#3752C2×C412yes—
83C4⋊(C3⋊Dic3)C2×C412yes—
84C4⋊(C3⋊Dic3)C2×C411yescharacteristic
85#3750C2×C412yes—
86C4×C3⋊Dic3C2312yes—
87#2930—91nomaximal, Sylow
88C2×#237—62no—
89C22×C4×D3—62no—
90C3×#121—22no—
91#938—62no—
92#937—64no—
93D4×Dic3—64no—
94#924—62no—
95#897—62no—
96#892—62no—
97#883—64no—
98#67⋊C4—64no—
99C23×C32C22×C411yescharacteristic
100C23×C32C22×C412yes—
101C22×C3⋊D3—22no—
102C22×C3⋊D3—41no—
103C22×C3⋊D3—41no—
104C22×C3⋊D3C22×C411yescharacteristic
105C22×C3⋊D3C22×C411yescharacteristic
106C32×D4—22no—
107C32×D4—42no—
108C2×C32×C4—22no—
109C2×C32×C4C22×C412yes—
110C2×C32×C4C22×C411yescharacteristic
111C2×C32×C4C22×C411yescharacteristic
112#638—24no—
113#638—42no—
114C2×C3⋊Dic3—22no—
115C2×C3⋊Dic3—21no—
116C2×C3⋊Dic3—21no—
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3C22×C412yes—
119C2×C3⋊Dic3C22×C412yes—
120C2×C3⋊Dic3C22×C411yescharacteristic
121C2×C3⋊Dic3C2411yescharacteristic
122C4×C3⋊D3—22no—
123C4×C3⋊D3—22no—
124C4×C3⋊D3—21no—
125C4×C3⋊D3—21no—
126C4×C3⋊D3C2×D412yes—
127C4×C3⋊D3#4112yes—
128#634—22no—
129#622—21no—
130#622—21no—
131#622—22no—
132#622—22no—
133#622C2×D412yes—
134#622C2×D412yes—
135C2×#131—91no—
136C22×M16—91no—
137#525—91no—
138#436—92no—
139#436—92no—
140#435—92no—
141#435—92no—
142#424—91no—
143#408—91no—
144#407—91no—
145#405—91no—
146C23×D3—62no—
147C2×C3×D4—24no—
148C2×C3×D4—22no—
149C22×C3×C4—22no—
150C2×#67—64no—
151C2×#67—64no—
152C22×Dic3—64no—
153C22×Dic3—62no—
154#237—124no—
155#237—124no—
156C2×C4×D3—62no—
157C2×C4×D3—62no—
158C2×C4×D3—62no—
159C2×C4×D3—62no—
160C2×C4×D3—124no—
161C2×C4×D3—124no—
162C2×Dic6—62no—
163C3×C4⋊C4—22no—
164C3×C22⋊C4—24no—
165#217—64no—
166#217—64no—
167(C2×D3)⋊C4—64no—
168(C2×D3)⋊C4—64no—
169C4⋊Dic3—64no—
170C4⋊Dic3—62no—
171Dic3⋊C4—64no—
172C4×Dic3—64no—
173C22×C32—21no—
174C22×C32—22no—
175C22×C32—21no—
176C22×C32—22no—
177C22×C32—22no—
178C22×C32—21no—
179C22×C32C23×C411yescharacteristic
180C2×C3⋊D3—21no—
181C2×C3⋊D3—21no—
182C2×C3⋊D3—21no—
183C2×C3⋊D3—21no—
184C2×C3⋊D3—21no—
185C2×C3⋊D3—44no—
186C2×C3⋊D3C4×D412yes—
187C32×C4—21no—
188C32×C4—22no—
189C32×C4C4×D412yes—
190C3⋊Dic3—22no—
191C3⋊Dic3—21no—
192C3⋊Dic3—22no—
193C3⋊Dic3C22×D411yescharacteristic
194C3⋊Dic3C2×#4111yescharacteristic
195C2×#41—91no—
196C23×C4—91no—
197#131—184no—
198C2×M16—91no—
199C2×M16—91no—
200C2×M16—91no—
201C2×M16—91no—
202C2×M16—91no—
203C2×M16—91no—
204C2×M16—92no—
205C2×M16—184no—
206C22×C8—91no—
207C22×C8—91no—
208C22×C8—92no—
209#123—92no—
210C22⋊Q8—91no—
211C22⋊Q8—91no—
212#121—91no—
213#121#15711yescharacteristic
214#120—92no—
215C4×D4—92no—
216C4×D4—92no—
217#117—91no—
218C4⋊C8—92no—
219C4⋊C8—92no—
220C22⋊C8—92no—
221C22⋊C8—92no—
222C22⋊C8—92no—
223C22⋊C8—92no—
224#97—92no—
225C4×C8—92no—
226C23×C3—22no—
227C23×C3—24no—
228C22×D3—62no—
229C22×D3—62no—
230C22×D3—124no—
231C22×D3—124no—
232C22×D3—124no—
233C3×D4—44no—
234C3×D4—48no—
235C2×C3×C4—22no—
236C2×C3×C4—24no—
237C2×C3×C4—22no—
238C2×C3×C4—44no—
239#67—128no—
240#67—128no—
241C2×Dic3—62no—
242C2×Dic3—64no—
243C2×Dic3—64no—
244C2×Dic3—62no—
245C2×Dic3—122no—
246C2×Dic3—122no—
247C2×Dic3—124no—
248C2×Dic3—124no—
249C4×D3—64no—
250C4×D3—64no—
251C4×D3—122no—
252C4×D3—122no—
253C4×D3—124no—
254C4×D3—124no—
255Dic6—124no—
256C2×C32—41no—
257C2×C32—42no—
258C2×C32C2×C4×D411yescharacteristic
259C2×C32#56811yescharacteristic
260C2×C32#56811yescharacteristic
261C3⋊D3—22no—
262C3⋊D3—41no—
263C24—91no—
264#41—182no—
265#41—182no—
266C2×Q8—91no—
267C2×D4—92no—
268C2×D4—92no—
269C2×D4C2×#15711yescharacteristic
270C2×D4C2×#15712yes—
271C22×C4—91no—
272C22×C4—92no—
273C22×C4—91no—
274C22×C4—91no—
275C22×C4—91no—
276C22×C4—91no—
277C22×C4—182no—
278C22×C4—182no—
279C22×C4C2×#15711yescharacteristic
280M16—182no—
281M16—182no—
282M16—182no—
283M16—182no—
284M16—184no—
285M16—182no—
286M16—182no—
287C2×C8—91no—
288C2×C8—91no—
289C2×C8—94no—
290C2×C8—92no—
291C2×C8—92no—
292C2×C8—91no—
293C2×C8—91no—
294C2×C8—184no—
295C2×C8—182no—
296C4⋊C4—91no—
297C4⋊C4—92no—
298C4⋊C4—92no—
299C4⋊C4C2×#15711yescharacteristic
300C22⋊C4—92no—
301C22⋊C4—92no—
302C22⋊C4—92no—
303C22⋊C4—92no—
304C22⋊C4C2×#15712yes—
305C42—92no—
306C22×C3—24no—
307C22×C3—22no—
308C22×C3—42no—
309C22×C3—42no—
310C22×C3—44no—
311C22×C3—44no—
312C22×C3—44no—
313C2×D3—64no—
314C2×D3—64no—
315C2×D3—122no—
316C2×D3—122no—
317C2×D3—122no—
318C2×D3—122no—
319C2×D3—1216no—
320C3×C4—24no—
321C3×C4—42no—
322C3×C4—44no—
323Dic3—62no—
324Dic3—62no—
325Dic3—124no—
326Dic3—122no—
327Dic3—124no—
328C32#293011yescharacteristic, complemented, Sylow
329C23—91no—
330C23—91no—
331C23—182no—
332C23—361no—
333C23—361no—
334C23C22×#15711yescharacteristic
335C23C22×#15712yes—
336Q8—182no—
337D4—22no—
338D4—42no—
339D4—184no—
340D4—362no—
341C2×C4—22no—
342C2×C4—91no—
343C2×C4—92no—
344C2×C4—92no—
345C2×C4—92no—
346C2×C4—91no—
347C2×C4—92no—
348C2×C4—181no—
349C2×C4—181no—
350C2×C4—182no—
351C2×C4—182no—
352C2×C4—181no—
353C2×C4—181no—
354C2×C4—182no—
355C2×C4—182no—
356C2×C4C22×#15712yes—
357C2×C4C22×#15711yescharacteristic
358C2×C4C22×#15711yescharacteristic
359C8—92no—
360C8—92no—
361C8—182no—
362C8—181no—
363C8—181no—
364C8—182no—
365C2×C3—22no—
366C2×C3—22no—
367C2×C3—22no—
368C2×C3—44no—
369C2×C3—84no—
370D3—124no—
371D3—124no—
372C22—21no—
373C22—22no—
374C22—21no—
375C22—22no—
376C22—22no—
377C22—21no—
378C22—92no—
379C22—181no—
380C22—181no—
381C22—181no—
382C22—181no—
383C22—181no—
384C22—364no—
385C22C23×#15711yescharacteristic
386C4—22no—
387C4—21no—
388C4—91no—
389C4—91no—
390C4—181no—
391C4—182no—
392C4—182no—
393C4D4×#15712yes—
394C3—22no—
395C2—41no—
396C2—42no—
397C2—182no—
398C2—361no—
399C2#1059664011yescharacteristic
400C2C2×D4×#15711yescharacteristic
401C2#1059664811yescharacteristic
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×#121C4
prime radical#10596077C2
cosocleC2×C3⋊Dic3C24
hypercenter#121#157
hypocenterC32#2930
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#64287C2semidirect
2. C2×#64283C2semidirect
4. #10593823C2semidirect
5. #10593821C2semidirect
6. #10593820C2semidirect
7. #10593803C2semidirect
8. #10593755C2semidirect
9. #10593748C2semidirect
10. #10593742C2semidirect
11. #10593740C2semidirect
16. C2×#3792C22semidirect
17. C22×#622C22semidirect
36. C22⋊#622C22semidirect
37. C22⋊#622C22semidirect
38. #63779C22semidirect
40. #63777C22semidirect
41. C4⋊#622C22semidirect
42. C4×#622C22semidirect
76. #3787D4semidirect
328. C32#2930semidirect

Maximal subgroups

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

subgroupindex
C2×#642872
C2×#642832
#105960772
#105938232
#105938212
#105938202
#105938032
#105937552
#105937482
#105937422
#105937402
#29309