Finite Group Databasebeta

← #11775430

Subgroups — #11775430

Order 1152.

659 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 659 conjugacy classes of subgroups — too many to draw. Only its 92 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#10596067C211yesmaximal, characteristic
2#10591229C211yesmaximal, characteristic, complemented
3#10591066C211yesmaximal, characteristic, complemented
4C3×#4537C212yesmaximal, complemented
5#10589151C212yesmaximal, complemented
6#68281—32nomaximal
7C2×#3830—21no—
8C32×#121C2211yescharacteristic
9#64149C411yescharacteristic, complemented
10#64148—21no—
11D4×C3⋊Dic3C411yescharacteristic, complemented
12#64139C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14#64102C411yescharacteristic, complemented
15#64097C411yescharacteristic, complemented
16#64094—21no—
17#64090—21no—
18C3×C3⋊#95C2212yes—
19C3×#830C2212yes—
20#63579—21no—
21#63579—21no—
22#63572—21no—
23#63555—21no—
24#5596—32no—
25#5596—61no—
26#4719—32no—
27#4651—32no—
28C3×#327—32no—
29#4537D312yescomplemented
30#4470—32no—
31#4451—32no—
32C2×C32×D4—21no—
33C2×C32×D4C2×C411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C2×#638—21no—
36C2×#638—21no—
37C2×#638—21no—
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3D411yescharacteristic
40C22×C3⋊Dic3D411yescharacteristic
41#3830—44no—
42C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
43C2×C4×C3⋊D3—21no—
44C2×#634—21no—
45C22×C3×Dic3—22no—
46C32×C4⋊C4C2×C411yescharacteristic
47C32×C22⋊C4—21no—
48#3757—21no—
49#3752—21no—
50#3752—21no—
51C4⋊(C3⋊Dic3)C2×C411yescharacteristic
52#3750—21no—
53C4×C3⋊Dic3C2×C411yescharacteristic
54C4×C3⋊Dic3C2×C411yescharacteristic
55C4×C3⋊Dic3D411yescharacteristic
56C4×C3⋊Dic3D411yescharacteristic
57C2×C3×C3⋊C8—22no—
58#1514—91noSylow
59C2×#237—62no—
60C2×#237—62no—
61C3×#121—21no—
62C3×#121C2×D312yes—
63#940—32no—
64#940—61no—
65#939—62no—
66#939—62no—
67D4×Dic3—32no—
68D4×Dic3—61no—
69#930—32no—
70#930—61no—
71C2×C4×Dic3—32no—
72C2×C4×Dic3—61no—
73#893—32no—
74#893—61no—
75#888—32no—
76#888—61no—
77#885—62no—
78#885—62no—
79#67⋊C4—62no—
80#67⋊C4—62no—
81C3×C22⋊C8—32no—
82C3×#95—32no—
83C3⋊#95—62no—
84C3⋊#95—62no—
85C3⋊#95C2×D312yes—
86#830C2×D312yes—
87#815—62no—
88Dic3⋊C8—62no—
89C23×C32—21no—
90C23×C32C2×D411yescharacteristic
91C22×C3⋊D3—21no—
92C32×D4—41no—
93C32×D4—42no—
94C2×C32×C4—21no—
95C2×C32×C4—41no—
96C2×C32×C4C22×C411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98#638—42no—
99#638—42no—
100#638—42no—
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—21no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3—42no—
105C2×C3⋊Dic3C22⋊C411yescharacteristic
106C2×C3⋊Dic3C22⋊C411yescharacteristic
107C2×C3⋊Dic3C22⋊C411yescharacteristic
108C2×C3⋊Dic3C22⋊C411yescharacteristic
109C4⋊(C3⋊D3)—41no—
110C4×C3⋊D3—42no—
111#634—42no—
112C2×C3×Dic3—42no—
113C2×C3×Dic3—42no—
114C2×C3×Dic3—42no—
115C3×C3⋊C8—42no—
116#532—91no—
117#432—91no—
118#383—91no—
119#327—32no—
120#327—92no—
121C2×C3×D4—22no—
122C2×C3×D4—22no—
123C2×C3×D4—21no—
124C2×C3×D4C4×D312yes—
125C22×C3×C4—21no—
126C22×C3×C4—62no—
127C22×C3×C4C22×D312yes—
128C2×#67—62no—
129C2×#67—62no—
130C2×#67—62no—
131C2×#67—62no—
132C2×#67—62no—
133C2×#67—62no—
134C22×Dic3—22no—
135C22×Dic3—32no—
136C22×Dic3—32no—
137C22×Dic3—61no—
138C22×Dic3—61no—
139C22×Dic3—62no—
140C22×Dic3—62no—
141#237—128no—
142#237—124no—
143#237—124no—
144C2×D12—32no—
145C2×D12—61no—
146C2×C4×D3—62no—
147C2×C4×D3—62no—
148C2×Dic6—62no—
149C2×Dic6—62no—
150C2×C3×C8—62no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4C4×D312yes—
153C3×C22⋊C4—22no—
154C3×C22⋊C4—22no—
155#217—62no—
156#217—62no—
157(C2×D3)⋊C4—62no—
158(C2×D3)⋊C4—62no—
159(C2×D3)⋊C4—62no—
160(C2×D3)⋊C4—62no—
161C4⋊Dic3—32no—
162C4⋊Dic3—61no—
163Dic3⋊C4—62no—
164Dic3⋊C4—62no—
165C4×Dic3—32no—
166C4×Dic3—32no—
167C4×Dic3—32no—
168C4×Dic3—32no—
169C4×Dic3—61no—
170C4×Dic3—61no—
171C4×Dic3—61no—
172C4×Dic3—61no—
173C2×C3⋊C8—22no—
174C22×C32—21no—
175C22×C32—21no—
176C22×C32—41no—
177C22×C32—41no—
178C22×C32—41no—
179C22×C32C2×C22⋊C411yescharacteristic
180C22×C32AGL(1,ℤ/8)12yes—
181C2×C3⋊D3—41no—
182C2×C3⋊D3—41no—
183C2×C3⋊D3—41no—
184C32×C4—21no—
185C32×C4—21no—
186C32×C4—41no—
187C3⋊Dic3—21no—
188C3⋊Dic3—21no—
189C3⋊Dic3—21no—
190C3⋊Dic3—21no—
191C3⋊Dic3—41no—
192C3×Dic3—82no—
193C2×#41—181no—
194C4⋊Q8—91no—
195#127—91no—
196#124—181no—
197#121—91no—
198#121—181no—
199#121D3211yescharacteristic
200C4×D4—91no—
201C4×D4—91no—
202C4×D4—181no—
203C2×C42—91no—
204C4⋊C8—181no—
205C22⋊C8—32no—
206#97—181no—
207#95—32no—
208#95—181no—
209#95—181no—
210C23×C3—22no—
211C23×C3—22no—
212C23×C3—21no—
213C23×C3D3×D412yes—
214C22×D3—62no—
215C22×D3—62no—
216C3×D4—42no—
217C3×D4—42no—
218C3×D4—44no—
219C3×D4—42no—
220C3×D4—42no—
221C2×C3×C4—22no—
222C2×C3×C4—22no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—42no—
226C2×C3×C4—42no—
227C2×C3×C4—122no—
228C2×C3×C4—122no—
229C2×C3×C4—122no—
230C2×C3×C4C2×C4×D312yes—
231C2×C3×C4D3×D412yes—
232#67—124no—
233#67—124no—
234#67—124no—
235#67—124no—
236#67—124no—
237#67—122no—
238#67—122no—
239C2×Dic3—32no—
240C2×Dic3—32no—
241C2×Dic3—32no—
242C2×Dic3—32no—
243C2×Dic3—42no—
244C2×Dic3—42no—
245C2×Dic3—42no—
246C2×Dic3—61no—
247C2×Dic3—61no—
248C2×Dic3—61no—
249C2×Dic3—61no—
250C2×Dic3—64no—
251C2×Dic3—62no—
252C2×Dic3—62no—
253C2×Dic3—62no—
254C2×Dic3—62no—
255C2×Dic3—122no—
256C2×Dic3—124no—
257C2×Dic3—124no—
258C2×Dic3—122no—
259D12—122no—
260D12—122no—
261C4×D3—124no—
262C4×D3—124no—
263Dic6—124no—
264Dic6—124no—
265C3×C8—122no—
266C3⋊C8—42no—
267C2×C32—22no—
268C2×C32—81no—
269C2×C32#41011yescharacteristic
270C2×C32#41811yescharacteristic
271C2×C32#42111yescharacteristic
272C3⋊D3—81no—
273#41—364no—
274C2×Q8—181no—
275C2×D4—21no—
276C2×D4—91no—
277C2×D4—181no—
278C2×D4—181no—
279C2×D4—181no—
280C2×D4#62411yescharacteristic
281C22×C4—62no—
282C22×C4—91no—
283C22×C4—91no—
284C22×C4—181no—
285C22×C4—181no—
286C22×C4C2×D3211yescharacteristic
287C2×C8—62no—
288C4⋊C4—91no—
289C4⋊C4—181no—
290C4⋊C4#62411yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—181no—
293C22⋊C4—181no—
294C22⋊C4—181no—
295C42—91no—
296C42—91no—
297C42—91no—
298C42—91no—
299C22×C3—22no—
300C22×C3—22no—
301C22×C3—22no—
302C22×C3—21no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3—42no—
306C22×C3—42no—
307C22×C3—42no—
308C22×C3—42no—
309C22×C3—42no—
310C22×C3—42no—
311C22×C3D3×C22⋊C412yes—
312C22×C3#91112yes—
313C22×C3#91412yes—
314C2×D3—122no—
315C2×D3—122no—
316C2×D3—122no—
317C2×D3—122no—
318C2×D3—122no—
319C2×D3—122no—
320C3×C4—22no—
321C3×C4—22no—
322C3×C4—22no—
323C3×C4—41no—
324C3×C4—42no—
325C3×C4—42no—
326C3×C4—242no—
327Dic3—62no—
328Dic3—62no—
329Dic3—62no—
330Dic3—62no—
331Dic3—62no—
332Dic3—62no—
333Dic3—62no—
334Dic3—82no—
335Dic3—121no—
336Dic3—122no—
337Dic3—122no—
338C32#151411yescharacteristic, complemented, Sylow
339C23—21no—
340C23—181no—
341C23#381111yescharacteristic
342Q8—362no—
343D4—41no—
344D4—42no—
345D4—361no—
346D4—362no—
347D4—362no—
348D4—362no—
349C2×C4—21no—
350C2×C4—41no—
351C2×C4—91no—
352C2×C4—91no—
353C2×C4—91no—
354C2×C4—91no—
355C2×C4—122no—
356C2×C4—122no—
357C2×C4—122no—
358C2×C4—182no—
359C2×C4—181no—
360C2×C4—362no—
361C2×C4—361no—
362C2×C4—362no—
363C2×C4C2×#62411yescharacteristic
364C2×C4#381111yescharacteristic
365C8—122no—
366C2×C3—22no—
367C2×C3—22no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—42no—
372C2×C3—82no—
373C2×C3—82no—
374C2×C3#474012yes—
375C2×C3#477012yes—
376C2×C3#482112yes—
377D3—242no—
378D3—242no—
379C22—21no—
380C22—21no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—361no—
385C22—361no—
386C22—361no—
387C22#6393712yes—
388C22#6397411yescharacteristic
389C4—21no—
390C4—21no—
391C4—41no—
392C4—181no—
393C4—181no—
394C4—181no—
395C4—181no—
396C4—242no—
397C4—361no—
398C3—21no—
399C3#6828112yescomplemented
400C2—22no—
401C2—81no—
402C2—721no—
403C2#1059142611yescharacteristic
404C2#1059152911yescharacteristic
405C2#1059167211yescharacteristic
subgroupG/H
centerC22#63974
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#121C22
socleC22×C32C2×C22⋊C4
prime radical#10596067C2
cosocleC22×C32×C4C23
hypercenter#121D32
hypocenterC32#1514
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #10591229C2semidirect
3. #10591066C2semidirect
4. C3×#4537C2semidirect
5. #10589151C2semidirect
9. #64149C4semidirect
11. D4×C3⋊Dic3C4semidirect
14. #64102C4semidirect
15. #64097C4semidirect
29. #4537D3semidirect
338. C32#1514semidirect
399. C3#68281semidirect

Maximal subgroups

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

subgroupindex
#105960672
#105912292
#105910662
C3×#45372
#105891512
#682813