Finite Group Databasebeta

← #11872845

Subgroups — #11872845

Order 1152.

884 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 884 conjugacy classes of subgroups — too many to draw. Only its 156 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#10596202C211yesmaximal, characteristic, complemented
2#10593996C211yesmaximal, characteristic
3C3×#5083C212yesmaximal, complemented
4#10591652C212yesmaximal
5#10591572C212yesmaximal, complemented
6#10591571C212yesmaximal, complemented
7#10591561C212yesmaximal, complemented
8#10590271C212yesmaximal, complemented
9#10590257C211yesmaximal, characteristic, complemented
10#80413—32nomaximal
11C2×#3802C2211yescharacteristic
12C32×C4⋊Q8C2211yescharacteristic, complemented
13#64155C2212yes—
14Q8×C3⋊Dic3C2212yescomplemented
15#64107—22no—
16#64098—22no—
17#64081C2211yescharacteristic
18#64079C2211yescharacteristic, complemented
19C2×C3×#215C2212yes—
20C2×C3×#215C2212yes—
21C3×C4×D12C2212yes—
22D3×(C2×D3)⋊C4—22no—
23#63898C2212yes—
24#63879—22no—
25#63849C2211yescharacteristic
26C3×#835C2212yescomplemented
27C3×#835C2212yescomplemented
28C3×C4⋊(C3⋊C8)C2212yescomplemented
29#63575C2212yescomplemented
30#63573C2212yescomplemented
31#63563C2212yes—
32#63563C2212yes—
33#63557C2212yes—
34#63555C2211yescharacteristic, complemented
35#63553C2211yescharacteristic, complemented
36#5731—32no—
37#5731—61no—
38#5545—32no—
39C3×#461—32no—
40#5169—32no—
41#5169—32no—
42#5164—32no—
43Dic3×SD16—32no—
44#5083D312yescomplemented
45#5009—32no—
46#4847—32no—
47#4840—32no—
48#4817—32no—
49#4815—32no—
50#4814—32no—
51#4788—32no—
52C22×D32—21no—
53C2×C32×Q8C2312yes—
54C2×C4×C3⋊D3C2311yescharacteristic
55C2×C3×D12C2312yes—
56C2×C3×C4×D3—22no—
57C2×#625—21no—
58C2×D3×Dic3—22no—
59#3802—24no—
60C32×C4⋊C4—22no—
61C32×C42C2311yescharacteristic
62#3752—22no—
63#3752D412yes—
64C4⋊(C3⋊Dic3)—22no—
65C4⋊(C3⋊Dic3)C2312yes—
66#3750—22no—
67#3750—22no—
68#3750D412yes—
69C4×C3⋊Dic3—22no—
70C4×C3⋊Dic3C2311yescharacteristic
71C3×#215—24no—
72C3×#215—24no—
73C3×(C2×D3)⋊C4—22no—
74C3×C4⋊Dic3C2312yes—
75C2×C3×C3⋊C8C2312yes—
76C2×C3×C3⋊C8C2312yes—
77#3722—21no—
78(C2×D3)⋊Dic3—22no—
79Dic32—21no—
80#3123—91noSylow
81C2×D3×D4—32no—
82C2×C3×SD16—32no—
83C2×C3×SD16—32no—
84C3×C4⋊Q8—21no—
85C3×C4⋊Q8C2×D312yescomplemented
86C3×C4×D4—32no—
87#946—32no—
88#946—32no—
89#946—62no—
90Q8×Dic3—32no—
91Q8×Dic3—32no—
92Q8×Dic3—62no—
93C2×#215C2×D312yes—
94C2×#215C2×D312yes—
95D4×Dic3—32no—
96C4×#67—62no—
97C2×(C2×D3)⋊C4—62no—
98#898—62no—
99#898—62no—
100#898—64no—
101#893—32no—
102#892—32no—
103#889—62no—
104#889—62no—
105#889—64no—
106#67⋊C4—62no—
107D3×C22⋊C4—62no—
108C4×D12C2×D312yes—
109#872—32no—
110#872—61no—
111#870—32no—
112#870—61no—
113C3×C4⋊C8—32no—
114C3×#103—32no—
115C3×#103—32no—
116#835C2×D312yescomplemented
117#835C2×D312yescomplemented
118#832—32no—
119#832—32no—
120#821—32no—
121#821—32no—
122(C2×D3)⋊C8—32no—
123(C2×D3)⋊C8—32no—
124#818—32no—
125#817—32no—
126#815—32no—
127C8×Dic3—32no—
128#808—32no—
129#807—32no—
130C4⋊(C3⋊C8)C2×D312yescomplemented
131C22×C3⋊D3C2×D411yescharacteristic
132C22×C3×D3—22no—
133C2×D32—24no—
134C2×D32—82no—
135C32×Q8—22no—
136C32×Q8—22no—
137C2×C32×C4—22no—
138C2×C32×C4C2×D412yes—
139C2×C32×C4C2411yescharacteristic
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3C2×D411yescharacteristic
142C2×C3⋊Dic3C2×D412yes—
143C4×C3⋊D3—22no—
144C2×C3×Dic3—22no—
145C3×D12—22no—
146C3×D12#4114yes—
147C3×C4×D3—82no—
148#625—24no—
149D3×Dic3—82no—
150C3×C3⋊C8—22no—
151C3×C3⋊C8—22no—
152#541—91no—
153#518—91no—
154#485—92no—
155#478—92no—
156#461—32no—
157#450—92no—
158#440—92no—
159C4×SD16—92no—
160#433—91no—
161C23×D3—62no—
162C2×C3×Q8—22no—
163C2×C3×Q8C22×D312yes—
164C2×C3×Q8C22×D312yes—
165C2×C3×D4—32no—
166C22×C3×C4—62no—
167C2×#67—62no—
168C22×Dic3—62no—
169D3×D4—64no—
170D3×D4—64no—
171C2×D12C22×D312yes—
172C2×C4×D3—22no—
173C2×C4×D3—32no—
174C2×C4×D3—61no—
175C2×C4×D3—62no—
176C3×SD16—64no—
177C3×SD16—64no—
178C2×C3×C8—32no—
179C2×C3×C8—32no—
180C3×C4⋊C4—24no—
181C3×C4⋊C4—22no—
182C3×C4⋊C4—22no—
183C3×C4⋊C4—32no—
184C3×C22⋊C4—62no—
185C3×C42—21no—
186C3×C42C22×D312yes—
187#217—62no—
188#215—24no—
189#215—24no—
190(C2×D3)⋊C4—22no—
191(C2×D3)⋊C4—32no—
192(C2×D3)⋊C4—32no—
193(C2×D3)⋊C4—62no—
194(C2×D3)⋊C4—62no—
195(C2×D3)⋊C4—62no—
196(C2×D3)⋊C4—62no—
197(C2×D3)⋊C4—62no—
198(C2×D3)⋊C4—64no—
199C4⋊Dic3—32no—
200C4⋊Dic3—32no—
201C4⋊Dic3—62no—
202C4⋊Dic3—62no—
203C4⋊Dic3—62no—
204C4⋊Dic3—64no—
205C4⋊Dic3C22×D312yes—
206Dic3⋊C4—32no—
207Dic3⋊C4—32no—
208Dic3⋊C4—62no—
209Dic3⋊C4—62no—
210Dic3⋊C4—62no—
211Dic3⋊C4—64no—
212Dic3⋊C4—64no—
213Dic3⋊C4—62no—
214Dic3⋊C4—62no—
215C4×Dic3—32no—
216C4×Dic3—61no—
217C4×Dic3—62no—
218C4×Dic3—62no—
219C4×Dic3—62no—
220C4×Dic3—64no—
221C2×C3⋊C8C22×D312yes—
222C2×C3⋊C8C22×D312yes—
223C22×C32C22×D411yescharacteristic
224C2×C3⋊D3—21no—
225C2×C3⋊D3—22no—
226C2×C3×D3—24no—
227C2×C3×D3—42no—
228C2×C3×D3—42no—
229D32—84no—
230C32×C4—22no—
231C32×C4—42no—
232C32×C4C2×#4112yes—
233C3⋊Dic3—21no—
234C3⋊Dic3—22no—
235C3⋊Dic3—42no—
236C3×Dic3—42no—
237C22×D4—91no—
238C2×SD16—32no—
239C2×SD16—32no—
240C4⋊Q8D3211yescharacteristic, complemented
241#126—182no—
242#125—91no—
243#125—182no—
244C22⋊Q8—92no—
245C4×Q8—92no—
246C4×D4—32no—
247C4×D4—92no—
248C4×D4—182no—
249#117—91no—
250#117—91no—
251C2×C22⋊C4—182no—
252#107—92no—
253#106—92no—
254C4⋊C8—32no—
255#103—32no—
256#103—32no—
257#102—92no—
258#102—92no—
259C22⋊C8—92no—
260#97—91no—
261C4×C8—91no—
262C23×C3—62no—
263C22×D3—22no—
264C22×D3—32no—
265C22×D3—61no—
266C22×D3—68no—
267C22×D3—242no—
268C22×D3—242no—
269C3×Q8—22no—
270C3×Q8—22no—
271C3×Q8—22no—
272C3×Q8—22no—
273C3×Q8—42no—
274C3×Q8—42no—
275C3×D4—34no—
276C3×D4—62no—
277C2×C3×C4—24no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—21no—
281C2×C3×C4—22no—
282C2×C3×C4—62no—
283C2×C3×C4—242no—
284C2×C3×C4D3×D412yes—
285C2×C3×C4D3×D412yes—
286C2×C3×C4C23×D312yes—
287#67—68no—
288C2×Dic3—22no—
289C2×Dic3—32no—
290C2×Dic3—32no—
291C2×Dic3—32no—
292C2×Dic3—62no—
293C2×Dic3—61no—
294C2×Dic3—64no—
295C2×Dic3—62no—
296C2×Dic3—62no—
297C2×Dic3—242no—
298D12—22no—
299D12#23714yes—
300C4×D3—62no—
301C4×D3—62no—
302C4×D3—82no—
303C4×D3—122no—
304C4×D3—242no—
305C3×C8—62no—
306C3×C8—62no—
307C3⋊C8—22no—
308C3⋊C8—22no—
309C2×C32#52511yescharacteristic
310C2×C32#57712yes—
311C3⋊D3—41no—
312C3×D3—44no—
313C24—181no—
314C2×Q8C2×D3212yes—
315C2×D4—32no—
316C2×D4—181no—
317C2×D4—184no—
318C22×C4—62no—
319C22×C4—91no—
320C22×C4—182no—
321SD16—64no—
322SD16—64no—
323C2×C8—32no—
324C2×C8—32no—
325C4⋊C4—22no—
326C4⋊C4—32no—
327C4⋊C4—92no—
328C4⋊C4—92no—
329C4⋊C4—182no—
330C4⋊C4—182no—
331C4⋊C4—182no—
332C22⋊C4—62no—
333C22⋊C4—92no—
334C22⋊C4—182no—
335C22⋊C4—181no—
336C22⋊C4—182no—
337C42—91no—
338C42—182no—
339C42—181no—
340C42C2×D3211yescharacteristic
341C22×C3—21no—
342C22×C3—64no—
343C22×C3—122no—
344C22×C3—122no—
345C22×C3C2×D3×D412yes—
346C2×D3—24no—
347C2×D3—42no—
348C2×D3—42no—
349C2×D3—62no—
350C2×D3—62no—
351C2×D3—62no—
352C2×D3—121no—
353C2×D3—122no—
354C2×D3—248no—
355C3×C4—22no—
356C3×C4—22no—
357C3×C4—22no—
358C3×C4—42no—
359C3×C4—44no—
360C3×C4—42no—
361C3×C4—42no—
362C3×C4—122no—
363C3×C4C2×#23712yes—
364C3×C4D3×#4112yes—
365Dic3—42no—
366Dic3—62no—
367Dic3—62no—
368Dic3—62no—
369Dic3—121no—
370Dic3—122no—
371Dic3—124no—
372Dic3—122no—
373Dic3—122no—
374C32#312311yescharacteristic, complemented, Sylow
375C23—62no—
376C23—91no—
377C23—184no—
378C23—722no—
379Q8—22no—
380Q8—22no—
381D4—34no—
382D4—62no—
383D4—184no—
384C2×C4—22no—
385C2×C4—62no—
386C2×C4—92no—
387C2×C4—91no—
388C2×C4—182no—
389C2×C4—182no—
390C2×C4—242no—
391C2×C4—722no—
392C2×C4#381112yes—
393C2×C4C22×D3211yescharacteristic
394C8—62no—
395C8—62no—
396C2×C3—21no—
397C2×C3—22no—
398C2×C3—124no—
399C2×C3#560612yes—
400C2×C3#576212yes—
401C2×C3#577812yes—
402D3—44no—
403D3—122no—
404D3—241no—
405C22—64no—
406C22—122no—
407C22—122no—
408C22—181no—
409C22—182no—
410C22—724no—
411C22C2×#381111yescharacteristic
412C4—22no—
413C4—42no—
414C4—122no—
415C4—181no—
416C4—182no—
417C4—362no—
418C4D3×#23712yes—
419C3—21no—
420C3#8041312yescomplemented
421C2—124no—
422C2—361no—
423C2#1059530611yescharacteristic
424C2#1059532412yes—
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenterC4⋊Q8D32
hypocenterC32#3123
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596202C2semidirect
3. C3×#5083C2semidirect
5. #10591572C2semidirect
6. #10591571C2semidirect
7. #10591561C2semidirect
8. #10590271C2semidirect
9. #10590257C2semidirect
12. C32×C4⋊Q8C22semidirect
14. Q8×C3⋊Dic3C22semidirect
18. #64079C22semidirect
26. C3×#835C22semidirect
27. C3×#835C22semidirect
28. C3×C4⋊(C3⋊C8)C22semidirect
29. #63575C22semidirect
30. #63573C22semidirect
34. #63555C22semidirect
35. #63553C22semidirect
44. #5083D3semidirect
85. C3×C4⋊Q8C2×D3semidirect
116. #835C2×D3semidirect
117. #835C2×D3semidirect
130. C4⋊(C3⋊C8)C2×D3semidirect
240. C4⋊Q8D32semidirect
374. C32#3123semidirect
420. C3#80413semidirect

Maximal subgroups

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

subgroupindex
#105962022
#105939962
C3×#50832
#105916522
#105915722
#105915712
#105915612
#105902712
#105902572
#804133