Finite Group Databasebeta

← #11775371

Subgroups — #11775371

Order 1152.

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

normal subgroups only

This group has 561 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#10596095C211yesmaximal, characteristic
2#10591360C211yesmaximal, characteristic, complemented
3#10591066C211yesmaximal, characteristic, complemented
4C3×#4538C212yesmaximal, complemented
5#10589151C212yesmaximal
6#68312—32nomaximal
7C32×C22⋊Q8C2211yescharacteristic
8#64156C411yescharacteristic, complemented
9Q8×C3⋊Dic3C411yescharacteristic, complemented
10#64139C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12#64107—21no—
13#64102C411yescharacteristic, complemented
14#64101—21no—
15#64099C411yescharacteristic, complemented
16#64095—21no—
17#64090—21no—
18C2×#3724—21no—
19C3×C3⋊#95C2212yes—
20C3×#830C2212yes—
21#63579—21no—
22#63572—21no—
23#63555—21no—
24#5624—32no—
25#5624—61no—
26#4719—32no—
27#4650—32no—
28C3×#328—32no—
29#4538D312yescomplemented
30#4470—32no—
31#4451—32no—
32C2×C32×Q8C2×C411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C2×#638—21no—
35C22×C3⋊Dic3D411yescharacteristic
36C22×C3⋊Dic3D411yescharacteristic
37C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
38C2×C4×C3⋊D3—21no—
39C22×C3×Dic3—22no—
40C32×C4⋊C4—21no—
41C32×C4⋊C4C2×C411yescharacteristic
42C32×C22⋊C4—21no—
43#3752—21no—
44#3752—21no—
45#3752—21no—
46#3752—21no—
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)C2×C411yescharacteristic
50#3750—21no—
51C4×C3⋊Dic3—21no—
52C4×C3⋊Dic3C2×C411yescharacteristic
53C4×C3⋊Dic3C2×C411yescharacteristic
54C4×C3⋊Dic3D411yescharacteristic
55C4×C3⋊Dic3D411yescharacteristic
56C2×C3×C3⋊C8—22no—
57#3724—42no—
58#1512—91noSylow
59C3×C22⋊Q8—21no—
60C3×C22⋊Q8C2×D312yes—
61#947—32no—
62#947—61no—
63Q8×Dic3—32no—
64Q8×Dic3—61no—
65#930—32no—
66#930—61no—
67C2×Dic3⋊C4—62no—
68C2×C4×Dic3—32no—
69C2×C4×Dic3—61no—
70#898—62no—
71#898—62no—
72#893—32no—
73#893—61no—
74#892—62no—
75#892—62no—
76#890—32no—
77#890—61no—
78#886—62no—
79#886—62no—
80#67⋊C4—62no—
81#67⋊C4—62no—
82C3×C22⋊C8—32no—
83C3×#95—32no—
84C3⋊#95—62no—
85C3⋊#95C2×D312yes—
86#830C2×D312yes—
87#815—62no—
88Dic3⋊C8—62no—
89C23×C32C2×D411yescharacteristic
90C22×C3⋊D3—21no—
91C32×Q8—41no—
92C2×C32×C4—21no—
93C2×C32×C4—21no—
94C2×C32×C4—41no—
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97#638—41no—
98#638—41no—
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3C22⋊C411yescharacteristic
104C2×C3⋊Dic3C22⋊C411yescharacteristic
105C2×C3⋊Dic3C22⋊C411yescharacteristic
106C2×C3⋊Dic3C22⋊C411yescharacteristic
107C4⋊(C3⋊D3)—41no—
108C4×C3⋊D3—42no—
109C2×C3×Dic3—42no—
110C2×C3×Dic3—42no—
111C2×C3×Dic3—42no—
112C3×C3⋊C8—42no—
113#529—91no—
114#432—91no—
115#382—91no—
116#328—32no—
117#327—92no—
118C2×C3×Q8—21no—
119C2×C3×Q8C4×D312yes—
120C22×C3×C4—21no—
121C22×C3×C4—62no—
122C22×C3×C4C22×D312yes—
123C2×#67—62no—
124C2×#67—62no—
125C22×Dic3—22no—
126C22×Dic3—32no—
127C22×Dic3—32no—
128C22×Dic3—61no—
129C22×Dic3—61no—
130C2×D12—32no—
131C2×D12—61no—
132C2×C4×D3—62no—
133C2×C4×D3—62no—
134C2×C3×C8—62no—
135C3×C4⋊C4—22no—
136C3×C4⋊C4—22no—
137C3×C4⋊C4—21no—
138C3×C4⋊C4C4×D312yes—
139C3×C22⋊C4—22no—
140C3×C22⋊C4—22no—
141(C2×D3)⋊C4—62no—
142(C2×D3)⋊C4—62no—
143(C2×D3)⋊C4—62no—
144(C2×D3)⋊C4—62no—
145(C2×D3)⋊C4—62no—
146(C2×D3)⋊C4—62no—
147(C2×D3)⋊C4—62no—
148(C2×D3)⋊C4—62no—
149C4⋊Dic3—32no—
150C4⋊Dic3—61no—
151C4⋊Dic3—62no—
152C4⋊Dic3—62no—
153C4⋊Dic3—62no—
154C4⋊Dic3—62no—
155Dic3⋊C4—62no—
156Dic3⋊C4—62no—
157Dic3⋊C4—124no—
158C4×Dic3—32no—
159C4×Dic3—32no—
160C4×Dic3—32no—
161C4×Dic3—32no—
162C4×Dic3—61no—
163C4×Dic3—61no—
164C4×Dic3—61no—
165C4×Dic3—61no—
166C4×Dic3—62no—
167C4×Dic3—62no—
168C2×C3⋊C8—22no—
169C22×C32—21no—
170C22×C32—21no—
171C22×C32C2×C22⋊C411yescharacteristic
172C22×C32AGL(1,ℤ/8)11yescharacteristic
173C22×C32#13711yescharacteristic
174C2×C3⋊D3—41no—
175C2×C3⋊D3—41no—
176C2×C3⋊D3—41no—
177C32×C4—21no—
178C32×C4—21no—
179C32×C4—41no—
180C32×C4—41no—
181C3⋊Dic3—21no—
182C3⋊Dic3—21no—
183C3⋊Dic3—21no—
184C3⋊Dic3—21no—
185C3⋊Dic3—41no—
186C3×Dic3—82no—
187#126—181no—
188#125—91no—
189#124—91no—
190#123—181no—
191C22⋊Q8D3211yescharacteristic
192#121—91no—
193C4×Q8—91no—
194C4×D4—91no—
195C4×D4—181no—
196#117—181no—
197C2×C4⋊C4—181no—
198C2×C42—91no—
199C4⋊C8—181no—
200C22⋊C8—32no—
201#97—181no—
202#95—32no—
203#95—181no—
204C23×C3—21no—
205C23×C3D3×D412yes—
206C22×D3—62no—
207C22×D3—62no—
208C3×Q8—42no—
209C3×Q8—42no—
210C2×C3×C4—22no—
211C2×C3×C4—22no—
212C2×C3×C4—22no—
213C2×C3×C4—22no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—42no—
217C2×C3×C4—42no—
218C2×C3×C4—122no—
219C2×C3×C4—122no—
220C2×C3×C4—122no—
221C2×C3×C4C2×C4×D312yes—
222C2×C3×C4D3×D412yes—
223#67—122no—
224#67—122no—
225#67—122no—
226#67—122no—
227C2×Dic3—32no—
228C2×Dic3—32no—
229C2×Dic3—32no—
230C2×Dic3—32no—
231C2×Dic3—42no—
232C2×Dic3—42no—
233C2×Dic3—42no—
234C2×Dic3—61no—
235C2×Dic3—61no—
236C2×Dic3—61no—
237C2×Dic3—61no—
238C2×Dic3—62no—
239C2×Dic3—62no—
240C2×Dic3—62no—
241C2×Dic3—62no—
242C2×Dic3—121no—
243C2×Dic3—121no—
244C2×Dic3—122no—
245C2×Dic3—122no—
246D12—122no—
247D12—122no—
248C4×D3—124no—
249C4×D3—124no—
250C3×C8—122no—
251C3⋊C8—42no—
252C2×C32—21no—
253C2×C32—21no—
254C2×C32#41011yescharacteristic
255C2×C32#41711yescharacteristic
256C2×C32#42111yescharacteristic
257C3⋊D3—81no—
258C2×Q8#62411yescharacteristic
259C2×D4—91no—
260C2×D4—181no—
261C22×C4—62no—
262C22×C4—91no—
263C22×C4—91no—
264C22×C4—181no—
265C22×C4C2×D3211yescharacteristic
266C2×C8—62no—
267C4⋊C4—21no—
268C4⋊C4—91no—
269C4⋊C4—181no—
270C4⋊C4—181no—
271C4⋊C4—181no—
272C4⋊C4—362no—
273C4⋊C4#62411yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—181no—
276C22⋊C4—181no—
277C22⋊C4—181no—
278C22⋊C4—181no—
279C42—91no—
280C42—91no—
281C42—91no—
282C42—91no—
283C42—181no—
284C22×C3—22no—
285C22×C3—22no—
286C22×C3—21no—
287C22×C3—21no—
288C22×C3—21no—
289C22×C3—41no—
290C22×C3—41no—
291C22×C3D3×C22⋊C412yes—
292C22×C3#91412yes—
293C22×C3#91812yes—
294C2×D3—122no—
295C2×D3—122no—
296C2×D3—122no—
297C2×D3—122no—
298C2×D3—122no—
299C2×D3—122no—
300C3×C4—22no—
301C3×C4—22no—
302C3×C4—22no—
303C3×C4—41no—
304C3×C4—42no—
305C3×C4—42no—
306C3×C4—42no—
307C3×C4—42no—
308C3×C4—242no—
309Dic3—62no—
310Dic3—62no—
311Dic3—62no—
312Dic3—62no—
313Dic3—62no—
314Dic3—82no—
315Dic3—121no—
316Dic3—121no—
317Dic3—121no—
318Dic3—122no—
319Dic3—122no—
320C32#151211yescharacteristic, complemented, Sylow
321C23—181no—
322C23#381111yescharacteristic
323Q8—41no—
324D4—361no—
325D4—361no—
326D4—361no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—41no—
330C2×C4—91no—
331C2×C4—91no—
332C2×C4—91no—
333C2×C4—91no—
334C2×C4—122no—
335C2×C4—122no—
336C2×C4—122no—
337C2×C4—181no—
338C2×C4—181no—
339C2×C4—181no—
340C2×C4—362no—
341C2×C4—361no—
342C2×C4C2×#62411yescharacteristic
343C2×C4#381111yescharacteristic
344C8—122no—
345C2×C3—22no—
346C2×C3—22no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—41no—
351C2×C3—41no—
352C2×C3#474012yes—
353C2×C3#480312yes—
354C2×C3#482112yes—
355D3—242no—
356D3—242no—
357C22—21no—
358C22—21no—
359C22—361no—
360C22—361no—
361C22—361no—
362C22#6394111yescharacteristic
363C22#6394511yescharacteristic
364C22#6397411yescharacteristic
365C4—21no—
366C4—21no—
367C4—41no—
368C4—41no—
369C4—181no—
370C4—181no—
371C4—181no—
372C4—181no—
373C4—242no—
374C4—361no—
375C3—21no—
376C3#6831212yescomplemented
377C2—21no—
378C2—21no—
379C2—721no—
380C2#1059152911yescharacteristic
381C2#1059155411yescharacteristic
382C2#1059167211yescharacteristic
subgroupG/H
centerC22#63974
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32C2×C22⋊C4
prime radical#64139C22
cosocleC22×C32×C4C23
hypercenterC22⋊Q8D32
hypocenterC32#1512
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10591360C2semidirect
3. #10591066C2semidirect
4. C3×#4538C2semidirect
8. #64156C4semidirect
9. Q8×C3⋊Dic3C4semidirect
13. #64102C4semidirect
15. #64099C4semidirect
29. #4538D3semidirect
320. C32#1512semidirect
376. C3#68312semidirect

Maximal subgroups

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

subgroupindex
#105960952
#105913602
#105910662
C3×#45382
#105891512
#683123