Finite Group Databasebeta

← #11872769

Subgroups — #11872769

Order 1152.

1005 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 1005 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, complemented
2#10595041C211yesmaximal, characteristic, complemented
3C3×#5003C212yesmaximal, complemented
4#10591168C212yesmaximal, complemented
5#10591062C211yesmaximal, characteristic, complemented
6#10590551C212yesmaximal, complemented
7#10590462C212yesmaximal, complemented
8#10590459C212yesmaximal, complemented
9#10590435C212yesmaximal, complemented
10#81354—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×#930C2212yes—
19#63970—22no—
20#63914C2211yescharacteristic, complemented
21#63898C2212yescomplemented
22#63891—22no—
23#63872C2211yescharacteristic, complemented
24C2×#3714C2212yes—
25C2×#3714C2212yes—
26C3×#830C2212yes—
27C3×#809C2212yescomplemented
28C3×#809C2212yescomplemented
29C3×#808C2212yescomplemented
30C3×#807C2212yescomplemented
31#63572C2212yescomplemented
32#63564C2212yes—
33#63564C2212yes—
34#63555C2211yescharacteristic, complemented
35#63553C2211yescharacteristic, complemented
36#5619—32no—
37#5521—32no—
38#5521—61no—
39C3×#482—32no—
40#5036—32no—
41#5003D312yescomplemented
42#4891—32no—
43#4872—32no—
44#4871—32no—
45#4869—32no—
46#4786—32no—
47#4786—32no—
48#4785—32no—
49#4756—32no—
50#4732—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×#67—22no—
60C2×C3×D12C2312yes—
61C2×#625—22no—
62C2×D3×Dic3—22no—
63C32×C4⋊C4C2312yes—
64C32×C22⋊C4—21no—
65C32×C42—21no—
66#3757D412yes—
67#3752—22no—
68#3752—22no—
69C4⋊(C3⋊Dic3)D412yes—
70C4×C3⋊Dic3C2311yescharacteristic
71C4×C3⋊Dic3C2311yescharacteristic
72C3×(C2×D3)⋊C4—22no—
73C3×C4⋊Dic3C2312yes—
74C2×C3×C3⋊C8C2312yes—
75C2×C3×C3⋊C8C2312yes—
76Dic3⋊Dic3—22no—
77(C2×D3)⋊Dic3—22no—
78#3714—24no—
79#3714—24no—
80#3122—91noSylow
81C22×D12—32no—
82C22×D12—61no—
83C3×#121—32no—
84C3×#117—21no—
85C3×#117C2×D312yes—
86#940—32no—
87#939—62no—
88#938—62no—
89D4×Dic3—32no—
90C2×#213—32no—
91C2×#213—32no—
92#930C2×D312yes—
93#926—32no—
94#926—61no—
95C2×D24—32no—
96C2×D24—32no—
97#893—32no—
98#893—32no—
99#893—32no—
100#893—32no—
101#893—32no—
102#893—62no—
103#893—62no—
104#890—32no—
105#886—62no—
106#883—62no—
107D3×C22⋊C4—62no—
108D3×C22⋊C4—62no—
109D3×C22⋊C4—64no—
110C4×D12—62no—
111C4×D12—62no—
112C4×D12—64no—
113C3×#107—32no—
114C3×#106—32no—
115C3×#102—32no—
116C3×#102—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#809—32no—
126#809—32no—
127#809C2×D312yescomplemented
128#809C2×D312yescomplemented
129#808C2×D312yescomplemented
130#807C2×D312yescomplemented
131C23×C32C2×D411yescharacteristic
132C22×C3⋊D3—22no—
133C22×C3⋊D3—24no—
134C22×C3⋊D3—82no—
135C22×C3×D3—22no—
136C2×C32×C4—22no—
137C2×C32×C4—22no—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2411yescharacteristic
140C2×C3⋊Dic3C2×D412yes—
141C2×C3⋊Dic3C2×D412yes—
142C4⋊(C3⋊D3)—24no—
143C4⋊(C3⋊D3)—22no—
144C4⋊(C3⋊D3)#4114yes—
145C4×C3⋊D3—82no—
146C4×C3⋊D3—82no—
147C3×#67—82no—
148C2×C3×Dic3—22no—
149C3×D12—22no—
150C3×D12—22no—
151#625—82no—
152D3×Dic3—82no—
153C3×C3⋊C8—22no—
154C3×C3⋊C8—22no—
155#540—91no—
156#518—91no—
157#482—32no—
158#478—92no—
159#459—92no—
160#447—92no—
161#442—92no—
162C4×D8—92no—
163#433—91no—
164C23×D3—62no—
165C23×D3—62no—
166C2×C3×D4—32no—
167C2×C3×D4—62no—
168C22×C3×C4—21no—
169C22×C3×C4C22×D312yes—
170C2×#67—22no—
171C2×#67—62no—
172C2×#67—62no—
173C22×Dic3—62no—
174C2×D12—32no—
175C2×D12—32no—
176C2×D12—62no—
177C2×D12—64no—
178C2×D12—64no—
179C2×D12—62no—
180C2×D12—68no—
181C2×D12—62no—
182C2×D12C22×D312yes—
183C2×C4×D3—62no—
184C2×C4×D3—62no—
185C2×C4×D3—62no—
186C2×C4×D3—62no—
187C2×C4×D3—62no—
188C2×C4×D3—64no—
189C2×C4×D3—64no—
190C2×C3×C8—32no—
191C2×C3×C8—32no—
192C3×C4⋊C4—22no—
193C3×C4⋊C4—32no—
194C3×C4⋊C4C22×D312yes—
195C3×C4⋊C4C22×D312yes—
196C3×C22⋊C4—22no—
197C3×C22⋊C4—22no—
198C3×C22⋊C4—62no—
199C3×C42—22no—
200C3×C42—22no—
201#217—32no—
202#217—32no—
203#217—62no—
204#217—62no—
205#213—64no—
206#213—64no—
207(C2×D3)⋊C4—22no—
208(C2×D3)⋊C4—62no—
209(C2×D3)⋊C4—62no—
210(C2×D3)⋊C4—62no—
211(C2×D3)⋊C4—62no—
212(C2×D3)⋊C4—62no—
213(C2×D3)⋊C4—64no—
214(C2×D3)⋊C4—64no—
215C4⋊Dic3—32no—
216C4⋊Dic3—32no—
217C4⋊Dic3—62no—
218C4⋊Dic3—62no—
219C4⋊Dic3C22×D312yes—
220Dic3⋊C4—62no—
221C4×Dic3—32no—
222C4×Dic3—32no—
223C4×Dic3—61no—
224C4×Dic3—61no—
225C2×C3⋊C8C22×D312yes—
226C2×C3⋊C8C22×D312yes—
227D24—64no—
228D24—64no—
229C22×C32—21no—
230C22×C32—22no—
231C22×C32C22×D411yescharacteristic
232C2×C3⋊D3—24no—
233C2×C3⋊D3—42no—
234C2×C3⋊D3—42no—
235C2×C3⋊D3—84no—
236C2×C3×D3—42no—
237C2×C3×D3—42no—
238C2×C3×D3—42no—
239C32×C4—21no—
240C32×C4—42no—
241C32×C4C2×#4112yes—
242C3⋊Dic3—22no—
243C3⋊Dic3—22no—
244C3×Dic3—42no—
245C22×D4—91no—
246C2×D8—92no—
247C2×D8—92no—
248#127—91no—
249#125—91no—
250#123—182no—
251#121—32no—
252#121—182no—
253C4×D4—92no—
254C4×D4—92no—
255C4×D4—92no—
256C4×D4—182no—
257#117—91no—
258#117D3211yescharacteristic
259C2×C22⋊C4—182no—
260#107—32no—
261#106—32no—
262C4⋊C8—92no—
263#102—32no—
264#102—32no—
265#102—92no—
266#102—92no—
267C22⋊C8—32no—
268#97—91no—
269C4×C8—91no—
270C23×C3—21no—
271C23×C3—62no—
272C23×C3D3×D412yes—
273C22×D3—22no—
274C22×D3—64no—
275C22×D3—62no—
276C22×D3—62no—
277C22×D3—68no—
278C22×D3—68no—
279C22×D3—242no—
280C22×D3—242no—
281C22×D3—244no—
282C3×D4—62no—
283C3×D4—62no—
284C3×D4—242no—
285C2×C3×C4—24no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—24no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—62no—
294C2×C3×C4D3×D412yes—
295C2×C3×C4C23×D312yes—
296#67—82no—
297#67—242no—
298#67—242no—
299C2×Dic3—22no—
300C2×Dic3—32no—
301C2×Dic3—32no—
302C2×Dic3—32no—
303C2×Dic3—32no—
304C2×Dic3—62no—
305C2×Dic3—62no—
306C2×Dic3—242no—
307D12—22no—
308D12—22no—
309D12—34no—
310D12—34no—
311D12—64no—
312D12—68no—
313D12—68no—
314D12—64no—
315D12—62no—
316D12—62no—
317C4×D3—242no—
318C4×D3—242no—
319C4×D3—242no—
320C4×D3—242no—
321C4×D3—242no—
322C4×D3—244no—
323C4×D3—244no—
324C3×C8—62no—
325C3×C8—62no—
326C3⋊C8—22no—
327C3⋊C8—22no—
328C2×C32—41no—
329C2×C32#52511yescharacteristic
330C2×C32#57612yes—
331C3⋊D3—44no—
332C3×D3—82no—
333C24—181no—
334C2×D4—32no—
335C2×D4—62no—
336C2×D4—92no—
337C2×D4—184no—
338C2×D4—182no—
339C2×D4—181no—
340C22×C4—182no—
341C22×C4—182no—
342C22×C4—182no—
343C22×C4C2×D3211yescharacteristic
344D8—184no—
345D8—184no—
346C2×C8—32no—
347C2×C8—32no—
348C4⋊C4—32no—
349C4⋊C4—92no—
350C4⋊C4—182no—
351C4⋊C4C2×D3212yes—
352C22⋊C4—21no—
353C22⋊C4—62no—
354C22⋊C4—92no—
355C22⋊C4—182no—
356C22⋊C4—182no—
357C22⋊C4—182no—
358C42—21no—
359C42—91no—
360C42—91no—
361C22×C3—22no—
362C22×C3—22no—
363C22×C3—22no—
364C22×C3—22no—
365C22×C3—21no—
366C22×C3—42no—
367C22×C3—122no—
368C22×C3—122no—
369C22×C3—122no—
370C22×C3C2×D3×D412yes—
371C2×D3—42no—
372C2×D3—42no—
373C2×D3—42no—
374C2×D3—68no—
375C2×D3—64no—
376C2×D3—64no—
377C2×D3—124no—
378C2×D3—124no—
379C2×D3—122no—
380C2×D3—122no—
381C2×D3—122no—
382C2×D3—122no—
383C2×D3—248no—
384C2×D3—248no—
385C3×C4—22no—
386C3×C4—22no—
387C3×C4—22no—
388C3×C4—44no—
389C3×C4—42no—
390C3×C4—42no—
391C3×C4—122no—
392C3×C4D3×#4112yes—
393C3×C4D3×#4112yes—
394Dic3—42no—
395Dic3—62no—
396Dic3—62no—
397Dic3—62no—
398Dic3—62no—
399Dic3—122no—
400Dic3—122no—
401C32#312211yescharacteristic, complemented, Sylow
402C23—62no—
403C23—184no—
404C23—182no—
405C23—722no—
406C23#381111yescharacteristic
407D4—62no—
408D4—62no—
409D4—94no—
410D4—184no—
411D4—182no—
412D4—242no—
413D4—722no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—62no—
417C2×C4—92no—
418C2×C4—92no—
419C2×C4—722no—
420C2×C4—722no—
421C2×C4—722no—
422C2×C4#381111yescharacteristic
423C2×C4C22×D3211yescharacteristic
424C8—62no—
425C8—62no—
426C2×C3—21no—
427C2×C3—22no—
428C2×C3—42no—
429C2×C3—42no—
430C2×C3—242no—
431C2×C3#565612yes—
432C2×C3#576912yes—
433C2×C3#577412yes—
434D3—82no—
435D3—128no—
436D3—124no—
437D3—124no—
438C22—21no—
439C22—22no—
440C22—122no—
441C22—122no—
442C22—122no—
443C22—184no—
444C22—362no—
445C22—362no—
446C22—724no—
447C22C2×#381111yescharacteristic
448C4—21no—
449C4—42no—
450C4—122no—
451C4—182no—
452C4—182no—
453C4#6430612yes—
454C3—21no—
455C3#8135412yescomplemented
456C2—41no—
457C2—242no—
458C2—364no—
459C2#1059492011yescharacteristic
460C2#1059546112yes—
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
hypercenter#117D32
hypocenterC32#3122
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
1. #10595992C2semidirect
2. #10595041C2semidirect
3. C3×#5003C2semidirect
4. #10591168C2semidirect
5. #10591062C2semidirect
6. #10590551C2semidirect
7. #10590462C2semidirect
8. #10590459C2semidirect
9. #10590435C2semidirect
20. #63914C22semidirect
21. #63898C22semidirect
23. #63872C22semidirect
27. C3×#809C22semidirect
28. C3×#809C22semidirect
29. C3×#808C22semidirect
30. C3×#807C22semidirect
31. #63572C22semidirect
34. #63555C22semidirect
35. #63553C22semidirect
41. #5003D3semidirect
127. #809C2×D3semidirect
128. #809C2×D3semidirect
129. #808C2×D3semidirect
130. #807C2×D3semidirect
401. C32#3122semidirect
455. C3#81354semidirect

Maximal subgroups

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

subgroupindex
#105959922
#105950412
C3×#50032
#105911682
#105910622
#105905512
#105904622
#105904592
#105904352
#813543