Finite Group Databasebeta

← #11864180

Subgroups — #11864180

Order 1152.

2262 conjugacy classes of subgroups.

The subgroup lattice has 441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic
2C2×C32×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×#64151C212yesmaximal, complemented
4#10592906C211yesmaximal, characteristic, complemented
5#10592749C212yesmaximal, complemented
6#10592746C214yesmaximal, complemented
7#10592745C212yesmaximal, complemented
8#10592665C212yesmaximal, complemented
9#82735—34nomaximal
10C22×C32×Q8C2211yescharacteristic, complemented
11C23×C32×C4C2211yescharacteristic
12C22×#638—21no—
13C2×#3828—21no—
14C2×#3828—21no—
15C2×#3828—28no—
16C2×#3828C2212yes—
17C2×#3828C2212yes—
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3—21no—
20C22×#634C2211yescharacteristic
21C32×C22⋊Q8—21no—
22C32×C22⋊Q8—21no—
23C32×C22⋊Q8C2212yes—
24C32×C22⋊Q8C2212yescomplemented
25C2×C32×C4⋊C4—21no—
26C2×C32×C4⋊C4C2211yescharacteristic, complemented
27C2×C32×C22⋊C4—21no—
28C2×#3756C2214yescomplemented
29#64151—28no—
30C2×#3755C2214yescomplemented
31C2×#3748C2212yescomplemented
32#63657C2212yes—
33#63657C2212yescomplemented
34#63637C2214yescomplemented
35#63636C2214yescomplemented
36C22×#235—34no—
37C2×C3×C22⋊Q8D314yescomplemented
38C2×#942—38no—
39#5207—34no—
40#5050—38no—
41#5047—316no—
42#5046—38no—
43#4966—38no—
44C24×C32D411yescharacteristic
45C23×C3⋊D3—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8—24no—
48C2×C32×Q8C2312yes—
49C22×C32×C4—24no—
50C22×C32×C4—21no—
51C22×C32×C4—21no—
52C22×C32×C4D411yescharacteristic
53C22×C32×C4D411yescharacteristic
54C22×C32×C4D411yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C2×#638—28no—
59C2×#638—22no—
60C2×#638—22no—
61C22×C3⋊Dic3—21no—
62#3828—28no—
63#3828—28no—
64#3828—24no—
65#3828—24no—
66#3828—24no—
67#3828D418yes—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)—24no—
70C2×C4⋊(C3⋊D3)C2312yes—
71C2×C4×C3⋊D3—28no—
72C2×C4×C3⋊D3—22no—
73C2×C4×C3⋊D3—22no—
74C2×#634—21no—
75C2×#634—24no—
76C2×#634C2312yes—
77C32×C4⋊C4—22no—
78C32×C4⋊C4—22no—
79C32×C4⋊C4—21no—
80C32×C4⋊C4C2312yes—
81C32×C22⋊C4—22no—
82C32×C22⋊C4—22no—
83#3756—28no—
84#3755—28no—
85#3748—24no—
86C2×C3⋊(C3⋊C8)C2314yes—
87#3007—91noSylow
88C22×C3×Q8C2×D314yescomplemented
89C23×C3×C4C2×D314yes—
90C22×#67—64no—
91C2×#235—38no—
92C2×#235—38no—
93C2×#235—632no—
94C2×#235—64no—
95C2×#235—64no—
96C22×D12—34no—
97C22×C4×D3—64no—
98C22×Dic6—34no—
99C3×C22⋊Q8—24no—
100C3×C22⋊Q8—24no—
101C3×C22⋊Q8C2×D318yes—
102C3×C22⋊Q8C2×D318yescomplemented
103C2×C3×C4⋊C4—24no—
104C2×C3×C4⋊C4C2×D314yescomplemented
105C2×C3×C22⋊C4—24no—
106C2×#216—316no—
107#942—632no—
108C2×#215—316no—
109C2×#208—38no—
110#830—38no—
111#830—38no—
112#810—316no—
113#809—316no—
114C23×C32—22no—
115C23×C32—22no—
116C23×C32—41no—
117C23×C32C2×D411yescharacteristic
118C23×C32C2×D411yescharacteristic
119C23×C32C2×D411yescharacteristic
120C22×C3⋊D3—24no—
121C22×C3⋊D3—22no—
122C22×C3⋊D3—42no—
123C22×C3⋊D3—42no—
124C32×Q8—24no—
125C32×Q8—42no—
126C2×C32×C4—22no—
127C2×C32×C4—22no—
128C2×C32×C4—22no—
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4—22no—
132C2×C32×C4—22no—
133C2×C32×C4—42no—
134C2×C32×C4—42no—
135C2×C32×C4C2×D414yes—
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2411yescharacteristic
140#638—28no—
141#638—28no—
142C2×C3⋊Dic3—24no—
143C2×C3⋊Dic3—22no—
144C4⋊(C3⋊D3)—24no—
145C4⋊(C3⋊D3)—22no—
146C4⋊(C3⋊D3)C2×D414yes—
147C4×C3⋊D3—28no—
148C4×C3⋊D3—28no—
149#634—24no—
150#634—22no—
151#634C2×D414yes—
152C3⋊(C3⋊C8)—24no—
153C22×#41—91no—
154C2×#137—92no—
155C2×C22⋊Q8C3⋊D311yescharacteristic, complemented
156#452—94no—
157#451—92no—
158#450—92no—
159#417—92no—
160#407—91no—
161C24×C3#6714yes—
162C23×D3—64no—
163C2×C3×Q8—24no—
164C2×C3×Q8—216no—
165C2×C3×Q8C22×D318yes—
166C22×C3×C4—216no—
167C22×C3×C4—24no—
168C22×C3×C4—24no—
169C22×C3×C4#6714yes—
170C22×C3×C4#6714yes—
171C22×C3×C4#6714yes—
172C22×C3×C4C22×D314yes—
173C22×C3×C4C22×D314yes—
174C22×C3×C4C22×D314yes—
175C2×#67—632no—
176C2×#67—68no—
177C2×#67—68no—
178C22×Dic3—64no—
179#235—332no—
180#235—616no—
181#235—616no—
182#235—632no—
183#235—632no—
184#235—616no—
185C2×D12—38no—
186C2×D12—616no—
187C2×D12—64no—
188C2×C4×D3—632no—
189C2×C4×D3—68no—
190C2×C4×D3—68no—
191C2×Dic6—38no—
192C2×Dic6—616no—
193C2×Dic6—64no—
194C3×C4⋊C4—28no—
195C3×C4⋊C4—28no—
196C3×C4⋊C4—24no—
197C3×C4⋊C4C22×D318yes—
198C3×C22⋊C4—28no—
199C3×C22⋊C4—28no—
200#216—632no—
201#215—632no—
202#208—616no—
203C2×C3⋊C8—316no—
204C22×C32—21no—
205C22×C32—21no—
206C22×C32—21no—
207C22×C32—21no—
208C22×C32—21no—
209C22×C32—21no—
210C22×C32—21no—
211C22×C32—44no—
212C22×C32#12012yes—
213C22×C32#13712yescomplemented
214C22×C32C22×D411yescharacteristic
215C2×C3⋊D3—24no—
216C2×C3⋊D3—48no—
217C2×C3⋊D3—42no—
218C2×C3⋊D3—42no—
219C32×C4—21no—
220C32×C4—21no—
221C32×C4—42no—
222C32×C4—42no—
223C32×C4#12012yes—
224C32×C4C22×D412yes—
225C3⋊Dic3—24no—
226C2×#41—92no—
227C2×#41—92no—
228C2×#41—188no—
229C2×#41—181no—
230C2×#41—181no—
231C22×Q8—91no—
232C22×Q8C2×C3⋊D311yescharacteristic, complemented
233C22×D4—91no—
234C22×D4—181no—
235C23×C4—181no—
236C23×C4C2×C3⋊D311yescharacteristic
237#137—188no—
238C2×Q16—94no—
239C2×SD16—94no—
240C2×M16—92no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C22⋊Q8C2×C3⋊D312yes—
244C22⋊Q8C2×C3⋊D312yescomplemented
245C2×C4⋊C4—21no—
246C2×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
247C2×C22⋊C4—21no—
248#103—94no—
249#102—94no—
250C22⋊C8—92no—
251C22⋊C8—92no—
252C23×C3—28no—
253C23×C3—28no—
254C23×C3—44no—
255C23×C3C2×#6714yes—
256C23×C3C2×#6714yes—
257C23×C3C2×#6714yes—
258C22×D3—616no—
259C22×D3—68no—
260C22×D3—128no—
261C22×D3—128no—
262C3×Q8—216no—
263C3×Q8—48no—
264C2×C3×C4—28no—
265C2×C3×C4—28no—
266C2×C3×C4—28no—
267C2×C3×C4—28no—
268C2×C3×C4—28no—
269C2×C3×C4—28no—
270C2×C3×C4—28no—
271C2×C3×C4—48no—
272C2×C3×C4—48no—
273C2×C3×C4D3×D4116yes—
274C2×C3×C4C2×#6714yes—
275C2×C3×C4C2×#6714yes—
276C2×C3×C4C2×#6714yes—
277C2×C3×C4C23×D314yes—
278#67—632no—
279#67—632no—
280C2×Dic3—616no—
281C2×Dic3—68no—
282D12—316no—
283D12—616no—
284D12—68no—
285C4×D3—632no—
286C4×D3—632no—
287Dic6—316no—
288Dic6—616no—
289Dic6—68no—
290C3⋊C8—616no—
291C2×C32—22no—
292C2×C32—22no—
293C2×C32—41no—
294C2×C32C2×#12011yescharacteristic
295C2×C32C2×#13711yescharacteristic
296C2×C32#57511yescharacteristic
297C3⋊D3—44no—
298C24—181no—
299C24#63811yescharacteristic
300#41—98no—
301#41—184no—
302#41—184no—
303#41—188no—
304#41—188no—
305#41—184no—
306C2×Q8—21no—
307C2×Q8—24no—
308C2×Q8—92no—
309C2×Q8—184no—
310C2×Q8—181no—
311C2×Q8C22×C3⋊D312yes—
312C2×D4—92no—
313C2×D4—184no—
314C2×D4—188no—
315C2×D4—182no—
316C2×D4—182no—
317C2×D4—181no—
318C22×C4—24no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—188no—
322C22×C4—181no—
323C22×C4—182no—
324C22×C4—182no—
325C22×C4#63811yescharacteristic
326C22×C4#63811yescharacteristic
327C22×C4#63811yescharacteristic
328C22×C4C22×C3⋊D311yescharacteristic
329C22×C4C22×C3⋊D311yescharacteristic
330C22×C4C22×C3⋊D311yescharacteristic
331Q16—188no—
332SD16—188no—
333M16—184no—
334C2×C8—94no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—21no—
338C4⋊C4C22×C3⋊D312yes—
339C22⋊C4—22no—
340C22⋊C4—22no—
341C22×C3—24no—
342C22×C3—24no—
343C22×C3—24no—
344C22×C3—24no—
345C22×C3—24no—
346C22×C3—24no—
347C22×C3—24no—
348C22×C3—416no—
349C22×C3#93718yes—
350C22×C3#94218yescomplemented
351C22×C3C22×#6714yes—
352C2×D3—616no—
353C2×D3—1232no—
354C2×D3—128no—
355C2×D3—128no—
356C3×C4—24no—
357C3×C4—24no—
358C3×C4—48no—
359C3×C4—48no—
360C3×C4#93718yes—
361C3×C4C2×D3×D418yes—
362Dic3—616no—
363C32#300711yescharacteristic, complemented, Sylow
364C23—22no—
365C23—22no—
366C23—41no—
367C23—184no—
368C23—182no—
369C23—362no—
370C23—362no—
371C23C2×#63811yescharacteristic
372C23C2×#63811yescharacteristic
373C23C2×#63811yescharacteristic
374Q8—24no—
375Q8—42no—
376Q8—94no—
377Q8—184no—
378Q8—182no—
379D4—94no—
380D4—184no—
381D4—188no—
382D4—188no—
383D4—182no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—188no—
394C2×C4—184no—
395C2×C4—182no—
396C2×C4—188no—
397C2×C4D4×C3⋊D314yes—
398C2×C4C2×#63811yescharacteristic
399C2×C4C2×#63811yescharacteristic
400C2×C4C2×#63811yescharacteristic
401C2×C4C23×C3⋊D311yescharacteristic
402C8—184no—
403C2×C3—28no—
404C2×C3—28no—
405C2×C3—44no—
406C2×C3C2×#93714yes—
407C2×C3C2×#94214yes—
408C2×C3#582214yes—
409D3—1216no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—44no—
418C22—184no—
419C22—368no—
420C22—362no—
421C22—362no—
422C22#6414612yes—
423C22#6415112yescomplemented
424C22C22×#63811yescharacteristic
425C4—21no—
426C4—21no—
427C4—42no—
428C4—42no—
429C4—184no—
430C4#6414612yes—
431C4C2×D4×C3⋊D312yes—
432C3#8273514yescomplemented
433C2—22no—
434C2—22no—
435C2—41no—
436C2—364no—
437C2C2×#6414611yescharacteristic
438C2C2×#6415111yescharacteristic
439C2#1059629311yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×C22⋊Q8C2
socleC22×C32C22×D4
prime radicalC22×#3828C2
hypercenterC2×C22⋊Q8C3⋊D3
hypocenterC32#3007
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×C32×C22⋊Q8C2semidirect
3. C2×#64151C2semidirect
4. #10592906C2semidirect
5. #10592749C2semidirect
6. #10592746C2semidirect
7. #10592745C2semidirect
8. #10592665C2semidirect
10. C22×C32×Q8C22semidirect
24. C32×C22⋊Q8C22semidirect
26. C2×C32×C4⋊C4C22semidirect
28. C2×#3756C22semidirect
30. C2×#3755C22semidirect
31. C2×#3748C22semidirect
33. #63657C22semidirect
34. #63637C22semidirect
35. #63636C22semidirect
37. C2×C3×C22⋊Q8D3semidirect
88. C22×C3×Q8C2×D3semidirect
102. C3×C22⋊Q8C2×D3semidirect
104. C2×C3×C4⋊C4C2×D3semidirect
155. C2×C22⋊Q8C3⋊D3semidirect
213. C22×C32#137semidirect
232. C22×Q8C2×C3⋊D3semidirect
244. C22⋊Q8C2×C3⋊D3semidirect
246. C2×C4⋊C4C2×C3⋊D3semidirect
350. C22×C3#942semidirect
363. C32#3007semidirect
423. C22#64151semidirect
432. C3#82735semidirect

Maximal subgroups

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

subgroupindex
C22×#38282
C2×C32×C22⋊Q82
C2×#641512
#105929062
#105927492
#105927462
#105927452
#105926652
#827353