Finite Group Databasebeta

← #11870457

Subgroups — #11870457

Order 1152.

1139 conjugacy classes of subgroups; only the 172 normal subgroups are shown.

normal subgroups only

This group has 1139 conjugacy classes of subgroups — too many to draw. Only its 172 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#10596196C211yesmaximal, characteristic, complemented
2C4×#3802C211yesmaximal, characteristic, complemented
3C3×#5087C212yesmaximal, complemented
4#10590598C212yesmaximal, complemented
5#10590459C214yesmaximal, complemented
6#10590442C212yesmaximal, complemented
7#10590349C212yesmaximal, complemented
8#10590256C211yesmaximal, characteristic, complemented
9#80948—32nomaximal
10C2×#3832—21no—
11C2×#3802C2211yescharacteristic
12C2×C4×D32—21no—
13C32×C4⋊Q8C2211yescharacteristic, complemented
14#64156—21no—
15#64104—21no—
16#64104C2212yes—
17#64102—21no—
18#64102C2212yescomplemented
19#64083C2211yescharacteristic, complemented
20C42×C3⋊D3C2211yescharacteristic
21C3×C4×D12C2212yes—
22#63921—21no—
23#63902—21no—
24C4×#625—21no—
25#63900C2211yescharacteristic
26#63898C2212yes—
27C2×#3714C2214yes—
28C3×#809C2214yes—
29C3×#807C2214yescomplemented
30C3×C4⋊(C3⋊C8)C2212yescomplemented
31#63564C2214yescomplemented
32#63557C2212yes—
33#63553C2212yescomplemented
34#5725—32no—
35#5725—61no—
36C4×D3×D4—32no—
37C3×#474—32no—
38#5087D312yescomplemented
39#5015—32no—
40#4882—34no—
41#4872—34no—
42#4843—32no—
43#4833—32no—
44#4773—34no—
45#4756—34no—
46C22×D32—21no—
47C2×C32×Q8—21no—
48#3832—44no—
49C2×C4⋊(C3⋊D3)—22no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)C2312yes—
53C2×C4×C3⋊D3—22no—
54C2×C4×C3⋊D3D411yescharacteristic
55C2×C4×C3⋊D3D411yescharacteristic
56C2×C4×C3⋊D3C2311yescharacteristic
57C2×C3×D12C2312yes—
58C2×C3×C4×D3—22no—
59C2×#625—21no—
60C2×#624—21no—
61C2×D3×Dic3—22no—
62#3802—24no—
63C4×D32—44no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4C2312yes—
66C32×C42C2311yescharacteristic
67#3752—22no—
68#3752—22no—
69C4×C3⋊Dic3D411yescharacteristic
70C4×C3⋊Dic3D411yescharacteristic
71C4×C3⋊Dic3C2311yescharacteristic
72C3×(C2×D3)⋊C4—22no—
73C3×C4⋊Dic3C2312yes—
74C2×C3×C3⋊C8C2314yes—
75#3724—21no—
76(C2×D3)⋊Dic3—22no—
77#3714—28no—
78#3100—91noSylow
79C2×#239—62no—
80C2×#239—62no—
81C2×D3×D4—32no—
82C22×C4×D3—62no—
83C3×C4⋊Q8—21no—
84C3×C4⋊Q8C2×D312yescomplemented
85C3×C4×D4—32no—
86#947—62no—
87#947—62no—
88D4×Dic3—32no—
89C2×#213—34no—
90C4×#67—62no—
91C2×D24—34no—
92#895—34no—
93#895—62no—
94#895—62no—
95#895—62no—
96#893—32no—
97#893—34no—
98#893—62no—
99#893—62no—
100#893—62no—
101D3×C4⋊C4—32no—
102#67⋊C4—62no—
103D3×C22⋊C4—62no—
104#874—32no—
105#874—61no—
106C4×D12C2×D312yes—
107C42×D3—32no—
108C42×D3—61no—
109C3×#107—34no—
110C3×C4⋊C8—32no—
111C3×#102—34no—
112#821—34no—
113(C2×D3)⋊C8—34no—
114C8×Dic3—34no—
115#809—34no—
116#809C2×D314yes—
117#807C2×D314yescomplemented
118C4⋊(C3⋊C8)C2×D312yescomplemented
119C22×C3⋊D3—22no—
120C22×C3⋊D3C2×D411yescharacteristic
121C22×C3×D3—22no—
122C2×D32—24no—
123C2×D32—42no—
124C2×D32—42no—
125C32×Q8—42no—
126C2×C32×C4—22no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2411yescharacteristic
130C2×C3⋊Dic3C2×D411yescharacteristic
131C2×C3⋊Dic3C2×D411yescharacteristic
132C2×C3⋊Dic3C2×D411yescharacteristic
133C4⋊(C3⋊D3)—24no—
134C4⋊(C3⋊D3)—42no—
135C4⋊(C3⋊D3)—44no—
136C4⋊(C3⋊D3)—42no—
137C4×C3⋊D3—22no—
138C4×C3⋊D3—41no—
139C4×C3⋊D3—44no—
140C4×C3⋊D3D814yescomplemented
141C2×C3×Dic3—22no—
142C3×D12—22no—
143C3×D12#4114yescomplemented
144C3×C4×D3—44no—
145#625—24no—
146#624—42no—
147D3×Dic3—44no—
148C3×C3⋊C8—24no—
149#532—91no—
150C2×C4×D4—91no—
151#480—92no—
152#474—32no—
153#459—92no—
154#447—92no—
155C4×D8—94no—
156#431—91no—
157C23×D3—62no—
158C2×C3×Q8—22no—
159C2×C3×Q8—22no—
160C2×C3×D4—32no—
161C22×C3×C4—62no—
162C2×#67—62no—
163C22×Dic3—62no—
164#239—128no—
165#239—128no—
166D3×D4—64no—
167D3×D4—64no—
168C2×D12—34no—
169C2×D12—62no—
170C2×D12—64no—
171C2×D12—62no—
172C2×D12—62no—
173C2×D12—64no—
174C2×D12—62no—
175C2×D12—62no—
176C2×D12C22×D312yes—
177C2×C4×D3—22no—
178C2×C4×D3—32no—
179C2×C4×D3—32no—
180C2×C4×D3—32no—
181C2×C4×D3—61no—
182C2×C4×D3—61no—
183C2×C4×D3—61no—
184C2×C4×D3—62no—
185C2×C4×D3—64no—
186C2×C4×D3—62no—
187C2×C4×D3—64no—
188C2×C4×D3—128no—
189C2×C3×C8—34no—
190C3×C4⋊C4—22no—
191C3×C4⋊C4—22no—
192C3×C4⋊C4—22no—
193C3×C4⋊C4—32no—
194C3×C4⋊C4C22×D314yes—
195C3×C22⋊C4—62no—
196C3×C42—21no—
197C3×C42C22×D312yes—
198#217—62no—
199#213—68no—
200(C2×D3)⋊C4—22no—
201(C2×D3)⋊C4—64no—
202(C2×D3)⋊C4—64no—
203(C2×D3)⋊C4—62no—
204(C2×D3)⋊C4—64no—
205(C2×D3)⋊C4—64no—
206C4⋊Dic3C22×D312yes—
207Dic3⋊C4—62no—
208C4×Dic3—32no—
209C4×Dic3—32no—
210C4×Dic3—32no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213C4×Dic3—61no—
214C2×C3⋊C8C22×D314yes—
215D24—68no—
216C22×C32C22×D411yescharacteristic
217C2×C3⋊D3—21no—
218C2×C3⋊D3—21no—
219C2×C3⋊D3—42no—
220C2×C3⋊D3—42no—
221C2×C3⋊D3—42no—
222C2×C3⋊D3C2×D812yes—
223C2×C3×D3—24no—
224C2×C3×D3—42no—
225C2×C3×D3—42no—
226D32—48no—
227C32×C4—21no—
228C32×C4—42no—
229C32×C4C2×D812yes—
230C32×C4C2×#4112yes—
231C3⋊Dic3—21no—
232C3⋊Dic3—21no—
233C3⋊Dic3C2×D812yes—
234C3×Dic3—42no—
235C2×#41—181no—
236C22×D4—91no—
237C23×C4—181no—
238C2×D8—94no—
239C4⋊Q8D3211yescharacteristic, complemented
240#127—91no—
241#124—181no—
242#121—92no—
243#121—181no—
244C4×D4—32no—
245C4×D4—92no—
246C4×D4—92no—
247C4×D4—181no—
248C4×D4—181no—
249C4×D4—181no—
250C2×C4⋊C4—91no—
251C2×C22⋊C4—181no—
252C2×C42—91no—
253#107—34no—
254C4⋊C8—32no—
255#102—34no—
256#102—94no—
257C22⋊C8—92no—
258C4×C8—92no—
259C23×C3—62no—
260C22×D3—22no—
261C22×D3—32no—
262C22×D3—61no—
263C22×D3—68no—
264C22×D3—64no—
265C22×D3—64no—
266C22×D3—124no—
267C22×D3—124no—
268C3×Q8—44no—
269C3×Q8—44no—
270C3×D4—34no—
271C3×D4—62no—
272C2×C3×C4—24no—
273C2×C3×C4—24no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—62no—
278C2×C3×C4—124no—
279C2×C3×C4D3×D412yes—
280C2×C3×C4D3×D412yes—
281C2×C3×C4C23×D312yes—
282#67—68no—
283C2×Dic3—22no—
284C2×Dic3—32no—
285C2×Dic3—32no—
286C2×Dic3—32no—
287C2×Dic3—61no—
288C2×Dic3—61no—
289C2×Dic3—61no—
290C2×Dic3—124no—
291D12—22no—
292D12—64no—
293D12—64no—
294D12—124no—
295D12—124no—
296D12—124no—
297D12—124no—
298D12—128no—
299D12—128no—
300D12—124no—
301D12#23914yescomplemented
302C4×D3—38no—
303C4×D3—44no—
304C4×D3—64no—
305C4×D3—62no—
306C4×D3—62no—
307C4×D3—122no—
308C4×D3—128no—
309C4×D3—124no—
310C4×D3—124no—
311C4×D3—122no—
312C4×D3—128no—
313C4×D3—122no—
314C3×C8—64no—
315C3⋊C8—24no—
316C2×C32#52511yescharacteristic
317C2×C32C22×D811yescharacteristic
318C2×C32#57511yescharacteristic
319C3⋊D3—22no—
320C3⋊D3—82no—
321C3×D3—44no—
322C24—181no—
323#41—364no—
324C2×Q8—21no—
325C2×D4—32no—
326C2×D4—92no—
327C2×D4—182no—
328C2×D4—181no—
329C2×D4—184no—
330C2×D4—181no—
331C2×D4—181no—
332C22×C4—62no—
333C22×C4—91no—
334C22×C4—91no—
335C22×C4—91no—
336C22×C4—182no—
337C22×C4—181no—
338C22×C4—182no—
339C22×C4—364no—
340D8—188no—
341C2×C8—34no—
342C4⋊C4—21no—
343C4⋊C4—32no—
344C4⋊C4—181no—
345C4⋊C4C2×D3212yes—
346C22⋊C4—62no—
347C22⋊C4—182no—
348C22⋊C4—182no—
349C22⋊C4—182no—
350C42—91no—
351C42—91no—
352C42—91no—
353C42C2×D3211yescharacteristic
354C22×C3—21no—
355C22×C3—64no—
356C22×C3—122no—
357C22×C3—122no—
358C22×C3C2×D3×D412yes—
359C2×D3—24no—
360C2×D3—34no—
361C2×D3—42no—
362C2×D3—42no—
363C2×D3—62no—
364C2×D3—62no—
365C2×D3—62no—
366C2×D3—121no—
367C2×D3—121no—
368C2×D3—1216no—
369C2×D3—124no—
370C2×D3—124no—
371C2×D3—124no—
372C2×D3—124no—
373C2×D3—124no—
374C2×D3—124no—
375C3×C4—22no—
376C3×C4—22no—
377C3×C4—22no—
378C3×C4—22no—
379C3×C4—44no—
380C3×C4—44no—
381C3×C4—122no—
382C3×C4D3×D814yes—
383C3×C4C2×#23912yes—
384C3×C4D3×#4112yes—
385Dic3—34no—
386Dic3—42no—
387Dic3—62no—
388Dic3—62no—
389Dic3—62no—
390Dic3—121no—
391Dic3—121no—
392C32#310011yescharacteristic, complemented, Sylow
393C23—62no—
394C23—91no—
395C23—184no—
396C23—182no—
397C23—362no—
398C23—362no—
399Q8—42no—
400D4—34no—
401D4—62no—
402D4—184no—
403D4—184no—
404D4—362no—
405D4—364no—
406D4—362no—
407C2×C4—22no—
408C2×C4—62no—
409C2×C4—91no—
410C2×C4—94no—
411C2×C4—91no—
412C2×C4—91no—
413C2×C4—124no—
414C2×C4—182no—
415C2×C4—361no—
416C2×C4—364no—
417C2×C4—364no—
418C2×C4—362no—
419C2×C4#381111yescharacteristic
420C2×C4#381111yescharacteristic
421C2×C4C22×D3211yescharacteristic
422C8—64no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—124no—
427C2×C3#562712yes—
428C2×C3C2×D3×D812yes—
429C2×C3#577712yes—
430D3—44no—
431D3—64no—
432D3—122no—
433D3—244no—
434D3—244no—
435C22—64no—
436C22—92no—
437C22—122no—
438C22—122no—
439C22—181no—
440C22—181no—
441C22—368no—
442C22—362no—
443C22—362no—
444C22—362no—
445C22C2×#381111yescharacteristic
446C4—21no—
447C4—42no—
448C4—92no—
449C4—122no—
450C4—181no—
451C4—181no—
452C4#6392612yes—
453C4D3×#23912yes—
454C3—21no—
455C3#8094812yescomplemented
456C2—124no—
457C2—182no—
458C2—722no—
459C2C2×#6392611yescharacteristic
460C2#1059532311yescharacteristic
461C2#1059543011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
hypercenterC4⋊Q8D32
hypocenterC32#3100
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. #10596196C2semidirect
2. C4×#3802C2semidirect
3. C3×#5087C2semidirect
4. #10590598C2semidirect
5. #10590459C2semidirect
6. #10590442C2semidirect
7. #10590349C2semidirect
8. #10590256C2semidirect
13. C32×C4⋊Q8C22semidirect
18. #64102C22semidirect
19. #64083C22semidirect
29. C3×#807C22semidirect
30. C3×C4⋊(C3⋊C8)C22semidirect
31. #63564C22semidirect
33. #63553C22semidirect
38. #5087D3semidirect
84. C3×C4⋊Q8C2×D3semidirect
117. #807C2×D3semidirect
118. C4⋊(C3⋊C8)C2×D3semidirect
140. C4×C3⋊D3D8semidirect
143. C3×D12#41semidirect
239. C4⋊Q8D32semidirect
301. D12#239semidirect
392. C32#3100semidirect
455. C3#80948semidirect

Maximal subgroups

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

subgroupindex
#105961962
C4×#38022
C3×#50872
#105905982
#105904592
#105904422
#105903492
#105902562
#809483