Finite Group Databasebeta

← #11872818

Subgroups — #11872818

Order 1152.

957 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 957 conjugacy classes of subgroups — too many to draw. Only its 164 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#10596269C211yesmaximal, characteristic
2#10594826C211yesmaximal, characteristic, complemented
3C3×#5218C212yesmaximal
4#10591497C212yesmaximal, complemented
5#10591479C212yesmaximal, complemented
6#10591446C212yesmaximal, complemented
7#10591445C212yesmaximal, complemented
8#10591127C212yesmaximal, complemented
9#10591062C211yesmaximal, characteristic, complemented
10#80137—32nomaximal
11C22×C32×D4C2211yescharacteristic
12C2×#3757—22no—
13D4×C3⋊Dic3—22no—
14D4×C3⋊Dic3C2212yes—
15D4×C3⋊Dic3C2212yes—
16#64135C2211yescharacteristic
17#64135C2211yescharacteristic
18C2×C3×#214C2212yes—
19C2×C3×#214C2212yes—
20C3×#924C2212yes—
21#63956—22no—
22#63873C2211yescharacteristic, complemented
23#63872C2211yescharacteristic, complemented
24#63845—22no—
25#63843C2212yescomplemented
26C3×#832C2212yes—
27C3×#832C2212yes—
28C3×#830C2212yes—
29#63575C2212yescomplemented
30#63573C2212yescomplemented
31#63572C2212yescomplemented
32#63566C2212yescomplemented
33#63566C2212yescomplemented
34#63555C2211yescharacteristic, complemented
35#63553C2211yescharacteristic, complemented
36#5798—32no—
37#5798—61no—
38#5625—32no—
39C3×#450—32no—
40#5218D312yes—
41#5164—32no—
42#5162—32no—
43#5162—32no—
44Dic3×SD16—32no—
45#5045—32no—
46#4766—32no—
47#4763—32no—
48#4758—32no—
49#4757—32no—
50#4723—32no—
51#4720—32no—
52C24×C32—21no—
53C2×C32×D4—24no—
54C2×C32×D4—21no—
55C2×C32×D4C2312yes—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3—22no—
58C22×C3⋊Dic3—22no—
59C2×C3×Dic6C2312yes—
60#3757—21no—
61#3757—22no—
62#3757—22no—
63#3757D412yes—
64C4⋊(C3⋊Dic3)D412yes—
65C4⋊(C3⋊Dic3)C2312yes—
66C4×C3⋊Dic3—21no—
67C4×C3⋊Dic3C2311yescharacteristic
68C4×C3⋊Dic3C2311yescharacteristic
69C3×#217—22no—
70C3×#214—24no—
71C3×#214—24no—
72C3×C4⋊Dic3C2312yes—
73C3×Dic3⋊C4—22no—
74C2×C3×C3⋊C8C2312yes—
75C2×C3×C3⋊C8C2312yes—
76#3724—22no—
77Dic3⋊Dic3—22no—
78Dic3⋊Dic3—22no—
79Dic32—22no—
80#3123—91noSylow
81C22×C3×D4—21no—
82C22×C3×D4C2×D312yes—
83C2×C3×SD16—32no—
84C2×C3×SD16—32no—
85C3×C22⋊Q8—32no—
86C2×#217—62no—
87C2×#217—62no—
88C2×#217—64no—
89Q8×Dic3—32no—
90#944—32no—
91D4×Dic3—32no—
92D4×Dic3—32no—
93D4×Dic3—32no—
94D4×Dic3—32no—
95D4×Dic3—62no—
96D4×Dic3—62no—
97D4×Dic3—62no—
98D4×Dic3—62no—
99D4×Dic3—64no—
100C2×#214C2×D312yes—
101C2×#214C2×D312yes—
102#926—32no—
103#926—32no—
104#926—61no—
105#926—61no—
106#924C2×D312yes—
107#890—32no—
108#890—62no—
109#889—62no—
110#887—32no—
111#879—62no—
112#879—62no—
113C3×#102—32no—
114C3×#102—32no—
115C3×C22⋊C8—32no—
116#835—32no—
117#835—32no—
118#832C2×D312yes—
119#832C2×D312yes—
120#830C2×D312yes—
121#818—32no—
122#817—32no—
123#816—32no—
124#816—32no—
125#815—32no—
126Dic3⋊C8—32no—
127Dic3⋊C8—32no—
128C8×Dic3—32no—
129#808—32no—
130#807—32no—
131C23×C32—24no—
132C23×C32—22no—
133C23×C32—82no—
134C23×C32C2×D411yescharacteristic
135C32×D4—24no—
136C32×D4—22no—
137C32×D4#4114yes—
138C2×C32×C4—22no—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2411yescharacteristic
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—82no—
143C2×C3⋊Dic3—82no—
144C2×C3⋊Dic3C2×D412yes—
145C2×C3⋊Dic3C2×D412yes—
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—92no—
155#478—92no—
156#461—92no—
157#450—32no—
158#440—92no—
159C4×SD16—92no—
160#433—91no—
161C24×C3—22no—
162C24×C3—22no—
163C2×C3×Q8—32no—
164C2×C3×D4—22no—
165C2×C3×D4—28no—
166C2×C3×D4—24no—
167C2×C3×D4—24no—
168C2×C3×D4—22no—
169C2×C3×D4—22no—
170C2×C3×D4C22×D312yes—
171C2×C3×D4C22×D312yes—
172C22×C3×C4—21no—
173C22×C3×C4C22×D312yes—
174C22×Dic3—62no—
175C22×Dic3—62no—
176C22×Dic3—62no—
177C22×Dic3—62no—
178C22×Dic3—64no—
179C22×Dic3—64no—
180C2×Dic6C22×D312yes—
181C3×SD16—64no—
182C3×SD16—64no—
183C2×C3×C8—32no—
184C2×C3×C8—32no—
185C3×C4⋊C4—32no—
186C3×C4⋊C4—62no—
187C3×C22⋊C4—62no—
188#217—22no—
189#217—32no—
190#217—32no—
191#217—62no—
192#217—62no—
193#217—62no—
194#217—62no—
195#217—62no—
196#217—62no—
197#217—64no—
198#217—64no—
199#217—62no—
200#214—24no—
201#214—24no—
202C4⋊Dic3—32no—
203C4⋊Dic3—32no—
204C4⋊Dic3—32no—
205C4⋊Dic3—32no—
206C4⋊Dic3—62no—
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—
222C4×Dic3—62no—
223C4×Dic3—62no—
224C2×C3⋊C8C22×D312yes—
225C2×C3⋊C8C22×D312yes—
226C22×C32—21no—
227C22×C32—24no—
228C22×C32—22no—
229C22×C32—42no—
230C22×C32—42no—
231C22×C32—84no—
232C22×C32C22×D411yescharacteristic
233C32×C4—21no—
234C32×C4C2×#4112yes—
235C3⋊Dic3—22no—
236C3⋊Dic3—22no—
237C3⋊Dic3—42no—
238C3×Dic3—42no—
239C3×Dic3—42no—
240C22×D4D3211yescharacteristic
241C2×SD16—32no—
242C2×SD16—32no—
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#117—91no—
254C2×C22⋊C4—182no—
255#107—92no—
256#106—92no—
257C4⋊C8—92no—
258#103—92no—
259#103—92no—
260#102—32no—
261#102—32no—
262C22⋊C8—32no—
263#97—91no—
264C4×C8—91no—
265C23×C3—24no—
266C23×C3—28no—
267C23×C3—28no—
268C23×C3—22no—
269C23×C3—22no—
270C23×C3—21no—
271C23×C3—82no—
272C23×C3—82no—
273C23×C3—84no—
274C23×C3D3×D412yes—
275C3×Q8—62no—
276C3×Q8—62no—
277C3×D4—28no—
278C3×D4—28no—
279C3×D4—24no—
280C3×D4—22no—
281C3×D4—22no—
282C3×D4—24no—
283C3×D4#23714yes—
284C3×D4#23714yes—
285C2×C3×C4—24no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4D3×D412yes—
293C2×C3×C4C23×D312yes—
294C2×Dic3—22no—
295C2×Dic3—22no—
296C2×Dic3—32no—
297C2×Dic3—32no—
298C2×Dic3—32no—
299C2×Dic3—32no—
300C2×Dic3—62no—
301C2×Dic3—62no—
302C2×Dic3—64no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—242no—
306C2×Dic3—242no—
307C2×Dic3—242no—
308C2×Dic3—242no—
309C2×Dic3—244no—
310C2×Dic3—244no—
311Dic6—22no—
312Dic6—22no—
313C3×C8—62no—
314C3×C8—62no—
315C3⋊C8—22no—
316C3⋊C8—22no—
317C2×C32—41no—
318C2×C32—44no—
319C2×C32#52511yescharacteristic
320C2×C32#57712yes—
321C24—21no—
322C2×Q8—32no—
323C2×D4—24no—
324C2×D4—21no—
325C2×D4C2×D3212yes—
326C22×C4—182no—
327C22×C4—182no—
328C22×C4C2×D3211yescharacteristic
329SD16—64no—
330SD16—64no—
331C2×C8—32no—
332C2×C8—32no—
333C4⋊C4—32no—
334C4⋊C4—62no—
335C4⋊C4—92no—
336C4⋊C4—92no—
337C4⋊C4—182no—
338C4⋊C4—182no—
339C4⋊C4—182no—
340C22⋊C4—62no—
341C22⋊C4—92no—
342C22⋊C4—182no—
343C22⋊C4—182no—
344C22⋊C4—181no—
345C42—91no—
346C42—91no—
347C42—182no—
348C42—181no—
349C22×C3—22no—
350C22×C3—28no—
351C22×C3—22no—
352C22×C3—22no—
353C22×C3—22no—
354C22×C3—24no—
355C22×C3—24no—
356C22×C3—21no—
357C22×C3—42no—
358C22×C3—44no—
359C22×C3—44no—
360C22×C3—42no—
361C22×C3—42no—
362C22×C3—42no—
363C22×C3—42no—
364C22×C3—88no—
365C22×C3—88no—
366C22×C3C2×D3×D412yes—
367C3×C4—22no—
368C3×C4—22no—
369C3×C4—22no—
370C3×C4—122no—
371C3×C4—122no—
372C3×C4C2×#23712yes—
373C3×C4C2×#23712yes—
374Dic3—42no—
375Dic3—42no—
376Dic3—62no—
377Dic3—62no—
378Dic3—62no—
379Dic3—62no—
380Dic3—122no—
381Dic3—122no—
382Dic3—124no—
383Dic3—122no—
384Dic3—122no—
385C32#312311yescharacteristic, complemented, Sylow
386C23—24no—
387C23—22no—
388C23—82no—
389C23#381111yescharacteristic
390Q8—62no—
391Q8—62no—
392D4—24no—
393D4—22no—
394D4#380514yes—
395C2×C4—22no—
396C2×C4—62no—
397C2×C4—62no—
398C2×C4—92no—
399C2×C4—92no—
400C2×C4—182no—
401C2×C4—722no—
402C2×C4—722no—
403C2×C4#381111yescharacteristic
404C2×C4C22×D3211yescharacteristic
405C8—62no—
406C8—62no—
407C2×C3—22no—
408C2×C3—21no—
409C2×C3—42no—
410C2×C3—48no—
411C2×C3—42no—
412C2×C3—44no—
413C2×C3—44no—
414C2×C3#558612yes—
415C2×C3#576212yes—
416C2×C3#577512yes—
417C22—22no—
418C22—21no—
419C22—24no—
420C22—42no—
421C22—42no—
422C22—84no—
423C22C2×#381111yescharacteristic
424C4—21no—
425C4—122no—
426C4—122no—
427C4—182no—
428C4—182no—
429C4—362no—
430C4C2×#380512yes—
431C3—21no—
432C3#8013712yescomplemented
433C2—41no—
434C2—44no—
435C2#1059511512yes—
436C2#1059550111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3123
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10594826C2semidirect
4. #10591497C2semidirect
5. #10591479C2semidirect
6. #10591446C2semidirect
7. #10591445C2semidirect
8. #10591127C2semidirect
9. #10591062C2semidirect
22. #63873C22semidirect
23. #63872C22semidirect
25. #63843C22semidirect
29. #63575C22semidirect
30. #63573C22semidirect
31. #63572C22semidirect
32. #63566C22semidirect
33. #63566C22semidirect
34. #63555C22semidirect
35. #63553C22semidirect
385. C32#3123semidirect
432. C3#80137semidirect

Maximal subgroups

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

subgroupindex
#105962692
#105948262
C3×#52182
#105914972
#105914792
#105914462
#105914452
#105911272
#105910622
#801373