Finite Group Databasebeta

← #11872855

Subgroups — #11872855

Order 1152.

957 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 957 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595992C211yesmaximal, characteristic
2#10594826C211yesmaximal, characteristic, complemented
3C3×#4996C212yesmaximal, complemented
4#10591183C212yesmaximal
5#10591062C211yesmaximal, characteristic, complemented
6#10590565C212yesmaximal, complemented
7#10590484C212yesmaximal, complemented
8#10590483C212yesmaximal, complemented
9#10590435C212yesmaximal, complemented
10#81498—32nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C32×#117C2211yescharacteristic
13#64135C2211yescharacteristic
14#64102C2212yes—
15#64102C2212yes—
16C22⋊C4×C3⋊D3—22no—
17C4×C4⋊(C3⋊D3)—22no—
18C3×#924C2212yes—
19#63956—22no—
20#63873C2211yescharacteristic, complemented
21#63872C2211yescharacteristic, complemented
22#63845—22no—
23#63843C2212yescomplemented
24C2×#3717C2212yes—
25C2×#3717C2212yes—
26C3×#830C2212yes—
27C3×#810C2212yescomplemented
28C3×#810C2212yescomplemented
29C3×#808C2212yescomplemented
30C3×#807C2212yescomplemented
31#63572C2212yescomplemented
32#63564C2212yes—
33#63564C2212yes—
34#63555C2211yescharacteristic, complemented
35#63553C2211yescharacteristic, complemented
36#5625—32no—
37#5521—32no—
38#5521—61no—
39C3×#485—32no—
40#5046—32no—
41#4996D312yescomplemented
42#4891—32no—
43#4889—32no—
44#4871—32no—
45#4852—32no—
46#4818—32no—
47#4818—32no—
48#4817—32no—
49#4788—32no—
50#4731—32no—
51#4720—32no—
52C23×C3⋊D3—21no—
53C22×C32×C4C2311yescharacteristic
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)—24no—
56C2×C4⋊(C3⋊D3)C2312yes—
57C2×C4×C3⋊D3—22no—
58C2×C4×C3⋊D3—22no—
59C2×C3×Dic6C2312yes—
60C32×C4⋊C4C2312yes—
61C32×C22⋊C4—21no—
62C32×C42—21no—
63#3757D412yes—
64#3752—22no—
65#3752—22no—
66C4⋊(C3⋊Dic3)D412yes—
67C4×C3⋊Dic3C2311yescharacteristic
68C4×C3⋊Dic3C2311yescharacteristic
69C3×#217—22no—
70C3×C4⋊Dic3C2312yes—
71C3×Dic3⋊C4—22no—
72C2×C3×C3⋊C8C2312yes—
73C2×C3×C3⋊C8C2312yes—
74#3724—22no—
75Dic3⋊Dic3—22no—
76Dic3⋊Dic3—22no—
77Dic32—22no—
78#3717—24no—
79#3717—24no—
80#3123—91noSylow
81C22×D12—32no—
82C22×D12—61no—
83C3×C22⋊Q8—32no—
84C3×#117—21no—
85C3×#117C2×D312yes—
86Q8×Dic3—32no—
87#944—32no—
88C2×#215—32no—
89C2×#215—32no—
90#926—32no—
91#926—61no—
92#924C2×D312yes—
93C2×#204—32no—
94C2×#204—32no—
95#893—32no—
96#893—32no—
97#893—32no—
98#893—32no—
99#893—62no—
100#893—62no—
101#890—32no—
102#890—62no—
103#889—62no—
104#887—32no—
105D3×C22⋊C4—62no—
106D3×C22⋊C4—62no—
107D3×C22⋊C4—64no—
108#879—62no—
109#879—62no—
110C4×D12—62no—
111C4×D12—62no—
112C4×D12—64no—
113C3×#107—32no—
114C3×#106—32no—
115C3×#103—32no—
116C3×#103—32no—
117C3×C22⋊C8—32no—
118#830C2×D312yes—
119#821—32no—
120#821—32no—
121#815—32no—
122Dic3⋊C8—32no—
123Dic3⋊C8—32no—
124C8×Dic3—32no—
125#810C2×D312yescomplemented
126#810C2×D312yescomplemented
127#809—32no—
128#809—32no—
129#808C2×D312yescomplemented
130#807C2×D312yescomplemented
131C23×C32C2×D411yescharacteristic
132C22×C3⋊D3—22no—
133C22×C3⋊D3—24no—
134C22×C3⋊D3—82no—
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2411yescharacteristic
139C2×C3⋊Dic3C2×D412yes—
140C2×C3⋊Dic3C2×D412yes—
141C4⋊(C3⋊D3)—24no—
142C4⋊(C3⋊D3)—22no—
143C4⋊(C3⋊D3)#4114yes—
144C4×C3⋊D3—82no—
145C4×C3⋊D3—82no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C3×Dic6—22no—
149C3×Dic6—22no—
150C3×C3⋊C8—22no—
151C3×C3⋊C8—22no—
152#541—91no—
153#518—91no—
154#485—32no—
155#478—92no—
156#461—92no—
157#450—92no—
158#440—92no—
159C4×SD16—92no—
160#433—91no—
161C23×D3—62no—
162C23×D3—62no—
163C2×C3×Q8—32no—
164C22×C3×C4—21no—
165C22×C3×C4C22×D312yes—
166C2×D12—32no—
167C2×D12—32no—
168C2×D12—62no—
169C2×D12—64no—
170C2×D12—64no—
171C2×D12—62no—
172C2×D12—68no—
173C2×D12—62no—
174C2×C4×D3—62no—
175C2×C4×D3—62no—
176C2×C4×D3—62no—
177C2×C4×D3—62no—
178C2×C4×D3—64no—
179C2×C4×D3—64no—
180C2×Dic6C22×D312yes—
181C2×C3×C8—32no—
182C2×C3×C8—32no—
183C3×C4⋊C4—22no—
184C3×C4⋊C4—32no—
185C3×C4⋊C4—62no—
186C3×C4⋊C4C22×D312yes—
187C3×C4⋊C4C22×D312yes—
188C3×C22⋊C4—22no—
189C3×C22⋊C4—22no—
190C3×C22⋊C4—62no—
191C3×C42—22no—
192C3×C42—22no—
193#217—22no—
194#217—32no—
195#217—32no—
196#217—62no—
197#215—64no—
198#215—64no—
199(C2×D3)⋊C4—62no—
200(C2×D3)⋊C4—62no—
201(C2×D3)⋊C4—62no—
202(C2×D3)⋊C4—62no—
203(C2×D3)⋊C4—64no—
204(C2×D3)⋊C4—64no—
205C4⋊Dic3—32no—
206C4⋊Dic3—32no—
207C4⋊Dic3—62no—
208C4⋊Dic3—62no—
209C4⋊Dic3—62no—
210C4⋊Dic3C22×D312yes—
211Dic3⋊C4—22no—
212Dic3⋊C4—62no—
213Dic3⋊C4—62no—
214Dic3⋊C4—62no—
215Dic3⋊C4—62no—
216C4×Dic3—32no—
217C4×Dic3—32no—
218C4×Dic3—61no—
219C4×Dic3—61no—
220C4×Dic3—62no—
221C4×Dic3—62no—
222C2×C3⋊C8C22×D312yes—
223C2×C3⋊C8C22×D312yes—
224#204—64no—
225#204—64no—
226C22×C32—21no—
227C22×C32—22no—
228C22×C32C22×D411yescharacteristic
229C2×C3⋊D3—24no—
230C2×C3⋊D3—42no—
231C2×C3⋊D3—42no—
232C2×C3⋊D3—84no—
233C32×C4—21no—
234C32×C4—42no—
235C32×C4C2×#4112yes—
236C3⋊Dic3—22no—
237C3⋊Dic3—22no—
238C3×Dic3—42no—
239C3×Dic3—42no—
240C22×D4—91no—
241C2×SD16—92no—
242C2×SD16—92no—
243C4⋊Q8—91no—
244#126—182no—
245#125—91no—
246#125—182no—
247C22⋊Q8—32no—
248C4×Q8—92no—
249C4×D4—92no—
250C4×D4—92no—
251C4×D4—182no—
252#117—91no—
253#117D3211yescharacteristic
254C2×C22⋊C4—182no—
255#107—32no—
256#106—32no—
257C4⋊C8—92no—
258#103—32no—
259#103—32no—
260#102—92no—
261#102—92no—
262C22⋊C8—32no—
263#97—91no—
264C4×C8—91no—
265C23×C3—21no—
266C23×C3D3×D412yes—
267C22×D3—64no—
268C22×D3—62no—
269C22×D3—62no—
270C22×D3—68no—
271C22×D3—68no—
272C22×D3—242no—
273C22×D3—242no—
274C22×D3—244no—
275C3×Q8—62no—
276C3×Q8—62no—
277C2×C3×C4—24no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—24no—
281C2×C3×C4—22no—
282C2×C3×C4—22no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4D3×D412yes—
288C2×C3×C4C23×D312yes—
289C2×Dic3—22no—
290C2×Dic3—22no—
291C2×Dic3—32no—
292C2×Dic3—32no—
293C2×Dic3—32no—
294C2×Dic3—32no—
295C2×Dic3—62no—
296C2×Dic3—62no—
297D12—34no—
298D12—34no—
299D12—64no—
300D12—68no—
301D12—68no—
302D12—64no—
303D12—62no—
304D12—62no—
305C4×D3—242no—
306C4×D3—242no—
307C4×D3—242no—
308C4×D3—242no—
309C4×D3—244no—
310C4×D3—244no—
311Dic6—22no—
312Dic6—22no—
313C3×C8—62no—
314C3×C8—62no—
315C3⋊C8—22no—
316C3⋊C8—22no—
317C2×C32—41no—
318C2×C32#52511yescharacteristic
319C2×C32#57712yes—
320C3⋊D3—44no—
321C24—181no—
322C2×Q8—32no—
323C2×D4—92no—
324C2×D4—184no—
325C2×D4—181no—
326C22×C4—182no—
327C22×C4—182no—
328C22×C4C2×D3211yescharacteristic
329SD16—184no—
330SD16—184no—
331C2×C8—32no—
332C2×C8—32no—
333C4⋊C4—32no—
334C4⋊C4—62no—
335C4⋊C4—92no—
336C4⋊C4—182no—
337C4⋊C4—182no—
338C4⋊C4—182no—
339C4⋊C4C2×D3212yes—
340C22⋊C4—21no—
341C22⋊C4—62no—
342C22⋊C4—92no—
343C22⋊C4—182no—
344C22⋊C4—182no—
345C42—21no—
346C42—91no—
347C42—91no—
348C42—182no—
349C22×C3—22no—
350C22×C3—22no—
351C22×C3—22no—
352C22×C3—22no—
353C22×C3—21no—
354C22×C3—42no—
355C22×C3C2×D3×D412yes—
356C2×D3—68no—
357C2×D3—64no—
358C2×D3—64no—
359C2×D3—124no—
360C2×D3—124no—
361C2×D3—122no—
362C2×D3—122no—
363C2×D3—122no—
364C2×D3—122no—
365C2×D3—248no—
366C2×D3—248no—
367C3×C4—22no—
368C3×C4—22no—
369C3×C4—22no—
370C3×C4—44no—
371C3×C4—42no—
372C3×C4—42no—
373C3×C4—122no—
374C3×C4—122no—
375C3×C4D3×#4112yes—
376C3×C4D3×#4112yes—
377Dic3—42no—
378Dic3—42no—
379Dic3—62no—
380Dic3—62no—
381Dic3—62no—
382Dic3—62no—
383Dic3—122no—
384Dic3—122no—
385C32#312311yescharacteristic, complemented, Sylow
386C23—184no—
387C23—182no—
388C23—722no—
389C23#381111yescharacteristic
390Q8—62no—
391Q8—62no—
392D4—94no—
393D4—184no—
394D4—182no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—62no—
398C2×C4—62no—
399C2×C4—92no—
400C2×C4—92no—
401C2×C4—722no—
402C2×C4—722no—
403C2×C4#381111yescharacteristic
404C2×C4C22×D3211yescharacteristic
405C8—62no—
406C8—62no—
407C2×C3—21no—
408C2×C3—22no—
409C2×C3—42no—
410C2×C3—42no—
411C2×C3#565612yes—
412C2×C3#577012yes—
413C2×C3#577812yes—
414D3—128no—
415D3—124no—
416D3—124no—
417C22—21no—
418C22—22no—
419C22—184no—
420C22—362no—
421C22—362no—
422C22—724no—
423C22C2×#381111yescharacteristic
424C4—21no—
425C4—42no—
426C4—122no—
427C4—122no—
428C4—182no—
429C4—182no—
430C4#6430612yes—
431C3—21no—
432C3#8149812yescomplemented
433C2—41no—
434C2—364no—
435C2#1059492011yescharacteristic
436C2#1059547312yes—
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenter#117D32
hypocenterC32#3123
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10594826C2semidirect
3. C3×#4996C2semidirect
5. #10591062C2semidirect
6. #10590565C2semidirect
7. #10590484C2semidirect
8. #10590483C2semidirect
9. #10590435C2semidirect
20. #63873C22semidirect
21. #63872C22semidirect
23. #63843C22semidirect
27. C3×#810C22semidirect
28. C3×#810C22semidirect
29. C3×#808C22semidirect
30. C3×#807C22semidirect
31. #63572C22semidirect
34. #63555C22semidirect
35. #63553C22semidirect
41. #4996D3semidirect
125. #810C2×D3semidirect
126. #810C2×D3semidirect
129. #808C2×D3semidirect
130. #807C2×D3semidirect
385. C32#3123semidirect
432. C3#81498semidirect

Maximal subgroups

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

subgroupindex
#105959922
#105948262
C3×#49962
#105911832
#105910622
#105905652
#105904842
#105904832
#105904352
#814983