Finite Group Databasebeta

← #11779976

Subgroups — #11779976

Order 1152.

457 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 457 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C3×#5543C211yesmaximal, characteristic
2C3×#5007C211yesmaximal, characteristic
3#10590384C211yesmaximal, characteristic, complemented
4#10590290C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic
6#10589095C211yesmaximal, characteristic, complemented
7#10589083C211yesmaximal, characteristic, complemented
8#71926—31nomaximal
9#71113—31nomaximal
10C32×C4×D4C2211yescharacteristic
11C3×D4×Dic3—21no—
12C2×C3×C4⋊Dic3—21no—
13C3×#924—21no—
14C3×#890—21no—
15C3×#878—22no—
16C3×#869C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C2×#3718—21no—
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#832—21no—
23C3×#807—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63565—22no—
26#63565—21no—
27C3×#554—31no—
28#5543D311yescharacteristic
29C3×#474—31no—
30#5093—31no—
31#5090—31no—
32#5079—31no—
33#5031—31no—
34#5007D311yescharacteristic
35#4546—31no—
36#4535—31no—
37D4⋊(C3⋊C8)—31no—
38D4⋊(C3⋊C8)—31no—
39D4⋊(C3⋊C8)—61no—
40#4484—31no—
41#4481—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C22×C3×Dic3—22no—
45C2×C3×Dic6—21no—
46C2×C3×Dic6D411yescharacteristic
47C2×C3×Dic6D412yes—
48C32×C4⋊C4D411yescharacteristic
49C32×C22⋊C4—21no—
50C32×C42C2311yescharacteristic
51C2×C3⋊(C3⋊C8)—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C3×#217—22no—
54C3×C4⋊Dic3—22no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—22no—
61C3×Dic3⋊C4—21no—
62C3×C4×Dic3—21no—
63C2×C3×C3⋊C8—21no—
64#3718—42no—
65#1644—91noSylow
66C3×C4⋊Q8—31no—
67C3×C4⋊Q8—31no—
68C3×#125—61no—
69C3×C22⋊Q8—62no—
70C3×C22⋊Q8—61no—
71C3×C4×Q8—31no—
72C3×C4×D4—21no—
73C3×C4×D4—61no—
74C3×C4×D4C2×D311yescharacteristic
75C3×C4×D4C2×D311yescharacteristic
76C2×C3×C4⋊C4—61no—
77C2×#216—61no—
78C2×#216—61no—
79D4×Dic3—21no—
80C2×C4⋊Dic3—21no—
81#924—21no—
82#890—21no—
83#878—22no—
84#869C2×D311yescharacteristic
85#869C2×D311yescharacteristic
86C4×Dic6C2×D311yescharacteristic
87C3×#107—61no—
88C3×C4⋊C8—31no—
89C3×#102—61no—
90#835—62no—
91#835—61no—
92#832—21no—
93#810—61no—
94#810—62no—
95#807—21no—
96C4⋊(C3⋊C8)—31no—
97C4⋊(C3⋊C8)—31no—
98C4⋊(C3⋊C8)—61no—
99C4⋊(C3⋊C8)C2×D311yescharacteristic
100C4×C3⋊C8—31no—
101C4×C3⋊C8—31no—
102C4×C3⋊C8—61no—
103C23×C32—21no—
104C32×D4—21no—
105C32×D4Q1612yescomplemented
106C2×C32×C4—21no—
107C2×C32×C4—41no—
108C2×C32×C4—41no—
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3×Dic3—21no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—41no—
116C2×C3×Dic3—82no—
117C3×Dic6—21no—
118C3×Dic6—21no—
119C3×Dic6—42no—
120C3×Dic6—41no—
121C3×Dic6—41no—
122C3⋊(C3⋊C8)—41no—
123C3⋊(C3⋊C8)—41no—
124C3×C3⋊C8—41no—
125#554—31no—
126#487—91no—
127#474—31no—
128#462—91no—
129#333—91no—
130Q8⋊C8—91no—
131D4⋊C8—91no—
132C2×C3×Q8—31no—
133C2×C3×Q8—32no—
134C2×C3×Q8—61no—
135C2×C3×D4—21no—
136C2×C3×D4#6711yescharacteristic
137C2×C3×D4#6711yescharacteristic
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—41no—
141C22×C3×C4—62no—
142C22×Dic3—22no—
143C2×Dic6—21no—
144C2×Dic6#6711yescharacteristic
145C2×Dic6#6712yes—
146C2×C3×C8—61no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—31no—
149C3×C4⋊C4—62no—
150C3×C4⋊C4—62no—
151C3×C4⋊C4—61no—
152C3×C4⋊C4—61no—
153C3×C4⋊C4—61no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4#6711yescharacteristic
157C3×C4⋊C4#6711yescharacteristic
158C3×C22⋊C4—21no—
159C3×C22⋊C4—21no—
160C3×C22⋊C4—41no—
161C3×C22⋊C4—62no—
162C3×C42—21no—
163C3×C42—61no—
164C3×C42C22×D311yescharacteristic
165C3×C42C22×D311yescharacteristic
166#217—22no—
167#216—122no—
168#216—122no—
169C4⋊Dic3—22no—
170C4⋊Dic3—21no—
171C4⋊Dic3—21no—
172C4⋊Dic3—21no—
173C4⋊Dic3—21no—
174C4⋊Dic3#6711yescharacteristic
175Dic3⋊C4—22no—
176Dic3⋊C4—21no—
177C4×Dic3—21no—
178C2×C3⋊C8—21no—
179C2×C3⋊C8—61no—
180C2×C3⋊C8—61no—
181C2×C3⋊C8—61no—
182C2×C3⋊C8—61no—
183C2×C3⋊C8—121no—
184C2×C3⋊C8—121no—
185C22×C32—22no—
186C22×C32—41no—
187C22×C32—41no—
188C22×C32#12011yescharacteristic
189C32×C4—21no—
190C32×C4—41no—
191C32×C4C2×Q1611yescharacteristic
192C32×C4#13511yescharacteristic
193C32×C4AGL(1,ℤ/8)11yescharacteristic
194C32×C4#13711yescharacteristic
195C3×Dic3—41no—
196C3×Dic3—42no—
197C3×Dic3—41no—
198C3×Dic3—81no—
199C2×Q16—181no—
200C4⋊Q8—31no—
201C4⋊Q8—31no—
202#125—61no—
203C22⋊Q8—62no—
204C22⋊Q8—61no—
205C4×Q8—31no—
206C4×D4—61no—
207C4×D4D3211yescharacteristic
208C2×C4⋊C4—61no—
209#107—61no—
210C4⋊C8—31no—
211C4⋊C8—91no—
212#103—181no—
213#103—182no—
214#102—61no—
215C4×C8—91no—
216C23×C3—21no—
217C23×C3—21no—
218C23×C3—41no—
219C3×Q8—61no—
220C3×Q8—61no—
221C3×Q8—122no—
222C3×Q8—121no—
223C3×Q8—121no—
224C3×D4—21no—
225C3×D4—21no—
226C3×D4—22no—
227C3×D4—41no—
228C3×D4#21612yescomplemented
229C3×D4#21612yescomplemented
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—41no—
236C2×C3×C4—41no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—61no—
241C2×C3×C4—61no—
242C2×C3×C4—62no—
243C2×C3×C4—81no—
244C2×C3×C4—81no—
245C2×C3×C4—121no—
246C2×C3×C4—242no—
247C2×C3×C4D3×D411yescharacteristic
248C2×C3×C4D3×D411yescharacteristic
249C2×C3×C4C2×#6711yescharacteristic
250C2×C3×C4C2×#6711yescharacteristic
251C2×C3×C4C2×#6711yescharacteristic
252C2×C3×C4C2×#6711yescharacteristic
253C2×Dic3—21no—
254C2×Dic3—21no—
255C2×Dic3—22no—
256C2×Dic3—41no—
257C2×Dic3—82no—
258Dic6—21no—
259Dic6—21no—
260Dic6—42no—
261Dic6—41no—
262Dic6—41no—
263C3×C8—121no—
264C3⋊C8—41no—
265C3⋊C8—121no—
266C3⋊C8—121no—
267C3⋊C8—122no—
268C3⋊C8—121no—
269C3⋊C8—121no—
270C3⋊C8—241no—
271C2×C32—42no—
272C2×C32#44911yescharacteristic
273C2×C32#45111yescharacteristic
274C2×C32#45511yescharacteristic
275C2×Q8—31no—
276C2×Q8—32no—
277C2×Q8—61no—
278C2×D4#62511yescharacteristic
279C22×C4—21no—
280C22×C4—62no—
281Q16—362no—
282C2×C8—61no—
283C2×C8—181no—
284C2×C8—181no—
285C4⋊C4—31no—
286C4⋊C4—62no—
287C4⋊C4—62no—
288C4⋊C4—61no—
289C4⋊C4—61no—
290C4⋊C4—61no—
291C4⋊C4—61no—
292C4⋊C4—61no—
293C4⋊C4#62511yescharacteristic
294C22⋊C4—21no—
295C22⋊C4—62no—
296C42—61no—
297C42C2×D3211yescharacteristic
298C22×C3—22no—
299C22×C3—22no—
300C22×C3—21no—
301C22×C3—42no—
302C22×C3—41no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3—41no—
306C22×C3—81no—
307C22×C3—81no—
308C22×C3#93711yescharacteristic
309C22×C3#95311yescharacteristic
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—41no—
317C3×C4—41no—
318C3×C4—41no—
319C3×C4—81no—
320C3×C4—121no—
321C3×C4—121no—
322C3×C4—122no—
323C3×C4—241no—
324C3×C4#91111yescharacteristic
325C3×C4#91211yescharacteristic
326C3×C4#94211yescharacteristic
327C3×C4C2×#21611yescharacteristic
328C3×C4C2×#21611yescharacteristic
329C3×C4#94911yescharacteristic
330C3×C4#95011yescharacteristic
331C3×C4#95111yescharacteristic
332Dic3—41no—
333Dic3—42no—
334Dic3—41no—
335Dic3—81no—
336C32#164411yescharacteristic, complemented, Sylow
337C23—21no—
338Q8—61no—
339Q8—61no—
340Q8—122no—
341Q8—121no—
342Q8—121no—
343D4—21no—
344D4#371812yescomplemented
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—61no—
349C2×C4—61no—
350C2×C4—62no—
351C2×C4—121no—
352C2×C4—242no—
353C2×C4C2×#62511yescharacteristic
354C2×C4D3×#6711yescharacteristic
355C2×C4D3×#6711yescharacteristic
356C8—121no—
357C8—361no—
358C8—361no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—42no—
363C2×C3—42no—
364C2×C3—82no—
365C2×C3#505011yescharacteristic
366C2×C3#515811yescharacteristic
367C2×C3#520211yescharacteristic
368C2×C3#522811yescharacteristic
369C2×C3#523811yescharacteristic
370C2×C3#524211yescharacteristic
371C22—22no—
372C22—41no—
373C22—41no—
374C22#6397611yescharacteristic
375C4—21no—
376C4—41no—
377C4—121no—
378C4—122no—
379C4—121no—
380C4—241no—
381C4#6382711yescharacteristic
382C4C2×#371811yescharacteristic
383C4#6392511yescharacteristic
384C4#6393311yescharacteristic
385C3—21no—
386C3#7111311yescharacteristic, complemented
387C3#7192611yescharacteristic, complemented
388C2—42no—
389C2#1059118511yescharacteristic
390C2#1059145011yescharacteristic
391C2#1059166411yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#1644
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #10590384C2semidirect
4. #10590290C2semidirect
6. #10589095C2semidirect
7. #10589083C2semidirect
105. C32×D4Q16semidirect
228. C3×D4#216semidirect
229. C3×D4#216semidirect
336. C32#1644semidirect
344. D4#3718semidirect
386. C3#71113semidirect
387. C3#71926semidirect

Maximal subgroups

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

subgroupindex
C3×#55432
C3×#50072
#105903842
#105902902
D4⋊(C3⋊(C3⋊C8))2
#105890952
#105890832
#719263
#711133