Finite Group Databasebeta

← #11866819

Subgroups — #11866819

Order 1152.

1560 conjugacy classes of subgroups.

The subgroup lattice has 447 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#525C211yesmaximal, characteristic, complemented
2C2×#64159C211yesmaximal, characteristic, complemented
3#10596262C211yesmaximal, characteristic, complemented
4C23×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
5#10592932C211yesmaximal, characteristic, complemented
6#10592750C212yesmaximal, complemented
7#10592747C212yesmaximal, complemented
8#10592740C212yesmaximal, complemented
9#10592737C212yesmaximal, complemented
10#10592701C211yesmaximal, characteristic, complemented
11#10592697C211yesmaximal, characteristic, complemented
12#82922—34nomaximal
13C2×C32×#41C2211yescharacteristic
14C23×C32×C4C2211yescharacteristic
15C2×#3828C2211yescharacteristic
16C32×#123—21no—
17C32×C22⋊Q8C2212yes—
18C32×#121C2212yes—
19C32×#120—21no—
20C32×C4×D4—22no—
21C32×#117C2211yescharacteristic
22#64162—21no—
23#64159—24no—
24C2×#3756C2211yescharacteristic, complemented
25C2×#3755C2211yescharacteristic, complemented
26C2×#3754C2211yescharacteristic, complemented
27C2×#3753C2211yescharacteristic, complemented
28#64139C2212yes—
29#64138—21no—
30C4×#638—22no—
31#64135C2211yescharacteristic
32#64133C2212yes—
33C22×C3⋊(C3⋊C8)—24no—
34C22×C3⋊(C3⋊C8)C2211yescharacteristic
35C22×C3⋊(C3⋊C8)C2212yes—
36C22×C3⋊(C3⋊C8)C2212yes—
37C22×C3⋊(C3⋊C8)C2211yescharacteristic
38#63662C2212yescomplemented
39#63659C2212yescomplemented
40#63637C2212yescomplemented
41#63636C2212yescomplemented
42#63635C2212yescomplemented
43#63634C2212yescomplemented
44C3×#525D314yescomplemented
45C2×#950—34no—
46#5791—34no—
47C23×C3⋊C8—34no—
48#5233—34no—
49#5051—38no—
50#5048—38no—
51#5041—38no—
52#5038—38no—
53#5002—34no—
54#4998—34no—
55C24×C32D411yescharacteristic
56C32×#41—22no—
57C32×#41—22no—
58C2×C32×Q8C2311yescharacteristic
59C2×C32×D4—21no—
60C2×C32×D4—22no—
61C2×C32×D4C2311yescharacteristic
62C22×C32×C4—22no—
63C22×C32×C4—22no—
64C22×C32×C4—21no—
65C22×C32×C4D412yes—
66C22×C32×C4D411yescharacteristic
67C22×C32×C4C2312yes—
68C22×C32×C4C2311yescharacteristic
69C2×#638—21no—
70C2×#638—22no—
71#3828—22no—
72#3828—22no—
73C2×C4⋊(C3⋊D3)C2311yescharacteristic
74C2×C4×C3⋊D3—21no—
75C2×#634C2311yescharacteristic
76C32×C4⋊C4—22no—
77C32×C4⋊C4C2312yes—
78C32×C22⋊C4—21no—
79C32×C22⋊C4—22no—
80C32×C22⋊C4—22no—
81C32×C42—21no—
82#3757—22no—
83#3757—21no—
84#3756—22no—
85#3755—22no—
86#3754—22no—
87#3753—22no—
88#3752—22no—
89C4⋊(C3⋊Dic3)C2312yes—
90#3750—22no—
91C4×C3⋊Dic3—21no—
92C2×C3⋊(C3⋊C8)—22no—
93C2×C3⋊(C3⋊C8)—24no—
94C2×C3⋊(C3⋊C8)—24no—
95C2×C3⋊(C3⋊C8)D414yescomplemented
96C2×C3⋊(C3⋊C8)C2312yes—
97C2×C3⋊(C3⋊C8)C2311yescharacteristic
98C2×C3⋊(C3⋊C8)C2311yescharacteristic
99#3050—91noSylow
100C2×C3×#41C2×D314yes—
101C23×C3×C4C2×D314yes—
102C2×#235—34no—
103C3×#123—24no—
104C3×C22⋊Q8C2×D318yes—
105C3×#121C2×D318yes—
106C3×#120—24no—
107C3×C4×D4—28no—
108C3×#117C2×D314yes—
109#953—64no—
110#950—616no—
111C2×#216—34no—
112C2×#215—34no—
113C2×#214—34no—
114C2×#213—34no—
115#930—38no—
116#929—64no—
117C4×#67—68no—
118#926—34no—
119#924—38no—
120C22×C3⋊C8—34no—
121C22×C3⋊C8—34no—
122C22×C3⋊C8—38no—
123C22×C3⋊C8—38no—
124C22×C3⋊C8—616no—
125#835—38no—
126#832—38no—
127#810—38no—
128#809—38no—
129#808—38no—
130#807—38no—
131C23×C32—22no—
132C23×C32—24no—
133C23×C32—21no—
134C23×C32C2×D411yescharacteristic
135C23×C32C2×D412yes—
136C22×C3⋊D3—21no—
137C32×Q8—21no—
138C32×Q8—21no—
139C32×D4—21no—
140C32×D4—21no—
141C32×D4—42no—
142C32×D4—44no—
143C2×C32×C4—22no—
144C2×C32×C4—24no—
145C2×C32×C4—22no—
146C2×C32×C4—22no—
147C2×C32×C4—22no—
148C2×C32×C4—21no—
149C2×C32×C4—42no—
150C2×C32×C4C2×D412yes—
151C2×C32×C4C2×D412yes—
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4#4112yes—
154C2×C32×C4C2411yescharacteristic
155#638—42no—
156#638—44no—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—21no—
159C4⋊(C3⋊D3)—21no—
160C4⋊(C3⋊D3)—21no—
161C4×C3⋊D3—42no—
162#634—21no—
163#634—21no—
164C3⋊(C3⋊C8)—22no—
165C3⋊(C3⋊C8)C2×D412yes—
166C3⋊(C3⋊C8)C2×D412yes—
167C2×#135—91no—
168C23×C8—91no—
169#525—91no—
170#525C3⋊D311yescharacteristic, complemented
171#467—92no—
172#466—92no—
173#465—92no—
174#465—92no—
175#427—91no—
176#416—91no—
177#416—91no—
178C24×C3#6714yes—
179C3×#41—28no—
180C3×#41—28no—
181C2×C3×Q8C22×D314yes—
182C2×C3×D4—28no—
183C2×C3×D4—24no—
184C2×C3×D4C22×D314yes—
185C22×C3×C4—28no—
186C22×C3×C4—28no—
187C22×C3×C4—24no—
188C22×C3×C4#6718yes—
189C22×C3×C4#6714yes—
190C22×C3×C4C22×D318yes—
191C22×C3×C4C22×D314yes—
192C2×#67—68no—
193C2×#67—64no—
194#235—68no—
195#235—68no—
196C2×D12—34no—
197C2×C4×D3—64no—
198C2×Dic6—34no—
199C3×C4⋊C4—28no—
200C3×C4⋊C4C22×D318yes—
201C3×C22⋊C4—24no—
202C3×C22⋊C4—28no—
203C3×C22⋊C4—28no—
204C3×C42—24no—
205#217—68no—
206#217—64no—
207#216—68no—
208#215—68no—
209#214—68no—
210#213—68no—
211(C2×D3)⋊C4—68no—
212C4⋊Dic3—38no—
213Dic3⋊C4—68no—
214C4×Dic3—64no—
215C2×C3⋊C8—316no—
216C2×C3⋊C8—34no—
217C2×C3⋊C8—34no—
218C2×C3⋊C8—38no—
219C2×C3⋊C8—616no—
220C2×C3⋊C8—616no—
221C2×C3⋊C8—68no—
222C22×C32—28no—
223C22×C32—22no—
224C22×C32—22no—
225C22×C32—22no—
226C22×C32—41no—
227C22×C32—42no—
228C22×C32#12112yes—
229C22×C32#13514yescomplemented
230C22×C32C22×D411yescharacteristic
231C2×C3⋊D3—41no—
232C2×C3⋊D3—42no—
233C32×C4—22no—
234C32×C4—41no—
235C32×C4—42no—
236C32×C4#12112yes—
237C32×C4C22×D411yescharacteristic
238C32×C4C2×#4111yescharacteristic
239C3⋊Dic3—41no—
240C3⋊Dic3—42no—
241C2×#41—91no—
242C2×#41C2×C3⋊D311yescharacteristic
243C23×C4C2×C3⋊D311yescharacteristic
244#135—184no—
245C2×Q16—91no—
246C2×SD16—91no—
247C2×SD16—91no—
248C2×D8—91no—
249C22×C8—91no—
250C22×C8—91no—
251C22×C8—92no—
252C22×C8—92no—
253C22×C8—184no—
254#123—21no—
255#123—181no—
256C22⋊Q8—92no—
257C22⋊Q8C2×C3⋊D312yes—
258#121—92no—
259#121C2×C3⋊D312yes—
260#120—21no—
261#120—181no—
262C4×D4—22no—
263C4×D4—182no—
264#117—91no—
265#117C2×C3⋊D311yescharacteristic
266#107—92no—
267#106—92no—
268#103—92no—
269#103—92no—
270#102—92no—
271#102—92no—
272C23×C3—28no—
273C23×C3—216no—
274C23×C3—24no—
275C23×C3C2×#6714yes—
276C23×C3C2×#6718yes—
277C22×D3—64no—
278C3×Q8—24no—
279C3×Q8—24no—
280C3×D4—24no—
281C3×D4—24no—
282C3×D4—48no—
283C3×D4—416no—
284C2×C3×C4—28no—
285C2×C3×C4—216no—
286C2×C3×C4—28no—
287C2×C3×C4—28no—
288C2×C3×C4—28no—
289C2×C3×C4—24no—
290C2×C3×C4—48no—
291C2×C3×C4D3×D418yes—
292C2×C3×C4#23718yes—
293C2×C3×C4C2×#6718yes—
294C2×C3×C4C2×#6714yes—
295C2×C3×C4C23×D314yes—
296#67—128no—
297#67—1216no—
298C2×Dic3—68no—
299C2×Dic3—64no—
300D12—64no—
301D12—64no—
302C4×D3—128no—
303Dic6—64no—
304Dic6—64no—
305C3⋊C8—38no—
306C3⋊C8—38no—
307C3⋊C8—68no—
308C2×C32—22no—
309C2×C32—24no—
310C2×C32—81no—
311C2×C32C2×#12111yescharacteristic
312C2×C32C2×#13512yes—
313C3⋊D3—81no—
314C24#63811yescharacteristic
315#41—22no—
316#41—22no—
317#41—182no—
318#41—182no—
319C2×Q8—91no—
320C2×Q8C22×C3⋊D311yescharacteristic
321C2×D4—22no—
322C2×D4—21no—
323C2×D4—91no—
324C2×D4—182no—
325C2×D4—181no—
326C2×D4C22×C3⋊D311yescharacteristic
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—21no—
330C22×C4—181no—
331C22×C4#63811yescharacteristic
332C22×C4#63812yes—
333C22×C4C22×C3⋊D312yes—
334C22×C4C22×C3⋊D311yescharacteristic
335Q16—182no—
336SD16—182no—
337SD16—182no—
338D8—182no—
339C2×C8—91no—
340C2×C8—91no—
341C2×C8—94no—
342C2×C8—92no—
343C2×C8—184no—
344C2×C8—184no—
345C2×C8—182no—
346C4⋊C4—22no—
347C4⋊C4—92no—
348C4⋊C4—182no—
349C4⋊C4C22×C3⋊D312yes—
350C22⋊C4—21no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—181no—
354C22⋊C4—182no—
355C22⋊C4—182no—
356C42—21no—
357C42—181no—
358C22×C3—232no—
359C22×C3—28no—
360C22×C3—28no—
361C22×C3—28no—
362C22×C3—44no—
363C22×C3—48no—
364C22×C3#93918yes—
365C22×C3#950116yescomplemented
366C22×C3C22×#6714yes—
367C2×D3—124no—
368C2×D3—128no—
369C3×C4—28no—
370C3×C4—44no—
371C3×C4—48no—
372C3×C4#93918yes—
373C3×C4C2×D3×D414yes—
374C3×C4C2×#23714yes—
375Dic3—124no—
376Dic3—128no—
377C32#305011yescharacteristic, complemented, Sylow
378C23—22no—
379C23—24no—
380C23—21no—
381C23—181no—
382C23C2×#63811yescharacteristic
383C23C2×#63812yes—
384Q8—21no—
385Q8—21no—
386Q8—181no—
387Q8—181no—
388D4—21no—
389D4—21no—
390D4—42no—
391D4—44no—
392D4—181no—
393D4—181no—
394D4—362no—
395D4—364no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—24no—
400C2×C4—22no—
401C2×C4—21no—
402C2×C4—42no—
403C2×C4—182no—
404C2×C4—181no—
405C2×C4—362no—
406C2×C4D4×C3⋊D312yes—
407C2×C4#383012yes—
408C2×C4C2×#63812yes—
409C2×C4C2×#63811yescharacteristic
410C2×C4C23×C3⋊D311yescharacteristic
411C8—92no—
412C8—92no—
413C8—182no—
414C2×C3—28no—
415C2×C3—216no—
416C2×C3—84no—
417C2×C3C2×#93914yes—
418C2×C3C2×#95018yes—
419D3—244no—
420C22—28no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—41no—
425C22—42no—
426C22—361no—
427C22—362no—
428C22#6414812yes—
429C22#6415914yescomplemented
430C22C22×#63811yescharacteristic
431C4—22no—
432C4—41no—
433C4—42no—
434C4—361no—
435C4—362no—
436C4#6414812yes—
437C4C2×D4×C3⋊D311yescharacteristic
438C4C2×#383011yescharacteristic
439C3#8292214yescomplemented
440C2—22no—
441C2—24no—
442C2—81no—
443C2—721no—
444C2C2×#6414811yescharacteristic
445C2C2×#6415912yes—
subgroupG/H
centerC2×C4C2×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#525C2
socleC22×C32C22×D4
hypercenter#525C3⋊D3
hypocenterC32#3050
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C32×#525C2semidirect
2. C2×#64159C2semidirect
3. #10596262C2semidirect
4. C23×C3⋊(C3⋊C8)C2semidirect
5. #10592932C2semidirect
6. #10592750C2semidirect
7. #10592747C2semidirect
8. #10592740C2semidirect
9. #10592737C2semidirect
10. #10592701C2semidirect
11. #10592697C2semidirect
24. C2×#3756C22semidirect
25. C2×#3755C22semidirect
26. C2×#3754C22semidirect
27. C2×#3753C22semidirect
38. #63662C22semidirect
39. #63659C22semidirect
40. #63637C22semidirect
41. #63636C22semidirect
42. #63635C22semidirect
43. #63634C22semidirect
44. C3×#525D3semidirect
95. C2×C3⋊(C3⋊C8)D4semidirect
170. #525C3⋊D3semidirect
229. C22×C32#135semidirect
365. C22×C3#950semidirect
377. C32#3050semidirect
429. C22#64159semidirect
439. C3#82922semidirect

Maximal subgroups

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

subgroupindex
C32×#5252
C2×#641592
#105962622
C23×C3⋊(C3⋊C8)2
#105929322
#105927502
#105927472
#105927402
#105927372
#105927012
#105926972
#829223