Finite Group Databasebeta

← #11776244

Subgroups — #11776244

Order 1152.

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

normal subgroups only

This group has 463 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
1#10593866C211yesmaximal, characteristic
2#10592532C211yesmaximal, characteristic
3#10590256C211yesmaximal, characteristic
4C3×#4486C211yesmaximal, characteristic, complemented
5C3×#4482C211yesmaximal, characteristic, complemented
6#10589093C211yesmaximal, characteristic, complemented
7#10589092C211yesmaximal, characteristic, complemented
8#68419—31nomaximal
9#68419—31nomaximal
10C42×C3⋊D3C2211yescharacteristic
11C3×#869C2211yescharacteristic
12C3×#869C2211yescharacteristic
13#63872C412yes—
14#63871—21no—
15#63871—21no—
16#63849C412yes—
17#63843—21no—
18#63843—21no—
19C32×C4⋊C8C2211yescharacteristic
20#63647—21no—
21C8×C3⋊Dic3—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63557—21no—
26#63553—21no—
27#5728—31no—
28#5728—31no—
29#4833—31no—
30#4833—31no—
31#4833—31no—
32#4833—31no—
33#4833—61no—
34C3×#332—31no—
35C3×#332—31no—
36#4547—31no—
37#4547—31no—
38#4486—31no—
39#4486D311yescharacteristic, complemented
40#4482—31no—
41#4482D311yescharacteristic, complemented
42C2×C4×C3⋊D3C2×C411yescharacteristic
43C2×C4×C3⋊D3D411yescharacteristic
44C2×C4×C3⋊D3D411yescharacteristic
45C2×C3×Dic6—21no—
46C2×C3×Dic6—21no—
47C2×C32×C8—21no—
48C32×C42C2311yescharacteristic
49C4×C3⋊Dic3C2×C411yescharacteristic
50C4×C3⋊Dic3D411yescharacteristic
51C4×C3⋊Dic3D411yescharacteristic
52C2×C3⋊(C3⋊C8)—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3C2×C412yes—
56C3×C4⋊Dic3C2×C412yes—
57C2×C3×C3⋊C8—21no—
58C2×C3×C3⋊C8—21no—
59Dic3⋊Dic3—22no—
60Dic3⋊Dic3—22no—
61#3722—22no—
62Dic32—22no—
63#1544—91noSylow
64C3×C4⋊Q8—31no—
65C3×C4⋊Q8—31no—
66#946—61no—
67#946—61no—
68Q8×Dic3—61no—
69Q8×Dic3—61no—
70#897—61no—
71#897—61no—
72#892—32no—
73#892—32no—
74#890—32no—
75#890—32no—
76#887—61no—
77#887—61no—
78C42×D3—31no—
79C42×D3—31no—
80C42×D3—61no—
81#869C2×D311yescharacteristic
82#869C2×D311yescharacteristic
83C3×C4⋊C8—21no—
84C3×C4⋊C8—31no—
85C3×C4⋊C8—31no—
86C3×C4⋊C8C2×D311yescharacteristic
87C3×C4⋊C8C2×D311yescharacteristic
88(C2×D3)⋊C8—61no—
89(C2×D3)⋊C8—61no—
90(C2×D3)⋊C8—61no—
91(C2×D3)⋊C8—61no—
92(C2×D3)⋊C8—62no—
93C8×Dic3—61no—
94C8×Dic3—61no—
95C8×Dic3—61no—
96C8×Dic3—61no—
97C8×Dic3—62no—
98C4⋊(C3⋊C8)—31no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—61no—
101C4⋊(C3⋊C8)C2×D311yescharacteristic
102C4⋊(C3⋊C8)C2×D311yescharacteristic
103C22×C3⋊D3C22⋊C411yescharacteristic
104C2×C32×C4C22×C411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C3⋊Dic3C22⋊C411yescharacteristic
108C2×C3⋊Dic3C22⋊C411yescharacteristic
109C2×C3⋊Dic3C22⋊C411yescharacteristic
110C4×C3⋊D3—21no—
111C4×C3⋊D3—21no—
112C4×C3⋊D3—21no—
113C4×C3⋊D3—21no—
114C4×C3⋊D3—22no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—22no—
117C3×Dic6—41no—
118C3×Dic6—41no—
119C3×Dic6—41no—
120C3×Dic6—41no—
121C32×C8—41no—
122C3⋊(C3⋊C8)—41no—
123C3×C3⋊C8—41no—
124C3×C3⋊C8—41no—
125#533—91no—
126#431—91no—
127#431—91no—
128#332—31no—
129#332—31no—
130#332—91no—
131#332—91no—
132C2×C3×Q8—61no—
133C2×C3×Q8—61no—
134C2×C4×D3—31no—
135C2×C4×D3—31no—
136C2×C4×D3—31no—
137C2×C4×D3—31no—
138C2×C4×D3—31no—
139C2×C4×D3—31no—
140C2×C4×D3—61no—
141C2×C4×D3—61no—
142C2×C4×D3—61no—
143C2×Dic6—21no—
144C2×Dic6—21no—
145C2×C3×C8—22no—
146C2×C3×C8—21no—
147C2×C3×C8—21no—
148C2×C3×C8—61no—
149C2×C3×C8—61no—
150C3×C4⋊C4—32no—
151C3×C4⋊C4—32no—
152C3×C4⋊C4—61no—
153C3×C4⋊C4—61no—
154C3×C42—21no—
155C3×C42C22×D311yescharacteristic
156C3×C42C22×D311yescharacteristic
157(C2×D3)⋊C4—62no—
158(C2×D3)⋊C4—62no—
159C4⋊Dic3—21no—
160C4⋊Dic3—21no—
161C4⋊Dic3—62no—
162C4⋊Dic3—62no—
163C4⋊Dic3C4×D312yes—
164C4⋊Dic3C4×D312yes—
165Dic3⋊C4—62no—
166Dic3⋊C4—62no—
167C4×Dic3—31no—
168C4×Dic3—31no—
169C4×Dic3—31no—
170C4×Dic3—31no—
171C4×Dic3—31no—
172C4×Dic3—31no—
173C4×Dic3—61no—
174C4×Dic3—61no—
175C4×Dic3—61no—
176C4×Dic3—62no—
177C4×Dic3—62no—
178C2×C3⋊C8—21no—
179C2×C3⋊C8—21no—
180C2×C3⋊C8—62no—
181C2×C3⋊C8—61no—
182C2×C3⋊C8—61no—
183C22×C32C2×C22⋊C411yescharacteristic
184C2×C3⋊D3—21no—
185C2×C3⋊D3—21no—
186C2×C3⋊D3—21no—
187C32×C4—21no—
188C32×C4#13511yescharacteristic
189C32×C4#13511yescharacteristic
190C32×C4#13511yescharacteristic
191C32×C4#13511yescharacteristic
192C3⋊Dic3—21no—
193C3⋊Dic3—21no—
194C3⋊Dic3#10112yes—
195C3×Dic3—42no—
196C3×Dic3—42no—
197C4⋊Q8—31no—
198C4⋊Q8—31no—
199#125—92no—
200C22⋊Q8—181no—
201C22⋊Q8—181no—
202C4×Q8—181no—
203C4×Q8—181no—
204#117—92no—
205C2×C42—91no—
206C4⋊C8—31no—
207C4⋊C8—31no—
208C4⋊C8—91no—
209C4⋊C8D3211yescharacteristic
210C22⋊C8—181no—
211C22⋊C8—181no—
212C4×C8—181no—
213C4×C8—181no—
214C22×D3—31no—
215C22×D3—31no—
216C22×D3—61no—
217C3×Q8—121no—
218C3×Q8—121no—
219C3×Q8—121no—
220C3×Q8—121no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—62no—
225C2×C3×C4—62no—
226C2×C3×C4C2×C4×D311yescharacteristic
227C2×C3×C4C2×C4×D311yescharacteristic
228C2×C3×C4D3×D411yescharacteristic
229C2×C3×C4D3×D411yescharacteristic
230C2×C3×C4D3×D411yescharacteristic
231C2×C3×C4D3×D411yescharacteristic
232C2×Dic3—22no—
233C2×Dic3—22no—
234C2×Dic3—31no—
235C2×Dic3—31no—
236C2×Dic3—31no—
237C2×Dic3—31no—
238C2×Dic3—31no—
239C2×Dic3—31no—
240C2×Dic3—61no—
241C2×Dic3—61no—
242C2×Dic3—61no—
243C4×D3—62no—
244C4×D3—62no—
245C4×D3—62no—
246C4×D3—62no—
247C4×D3—61no—
248C4×D3—61no—
249C4×D3—61no—
250C4×D3—61no—
251C4×D3—61no—
252C4×D3—61no—
253C4×D3—61no—
254C4×D3—61no—
255C4×D3—122no—
256C4×D3—121no—
257C4×D3—121no—
258Dic6—41no—
259Dic6—41no—
260Dic6—41no—
261Dic6—41no—
262C3×C8—42no—
263C3×C8—41no—
264C3×C8—41no—
265C3×C8—121no—
266C3×C8—121no—
267C3⋊C8—41no—
268C3⋊C8—41no—
269C3⋊C8—122no—
270C3⋊C8—121no—
271C3⋊C8—121no—
272C2×C32C2×#10111yescharacteristic
273C2×C32#41611yescharacteristic
274C2×C32#41611yescharacteristic
275C3⋊D3—41no—
276C2×Q8—61no—
277C2×Q8—61no—
278C22×C4—91no—
279C22×C4—91no—
280C22×C4—91no—
281C2×C8—21no—
282C2×C8—61no—
283C2×C8—61no—
284C2×C8—181no—
285C4⋊C4—32no—
286C4⋊C4—32no—
287C4⋊C4—61no—
288C4⋊C4—61no—
289C4⋊C4—182no—
290C4⋊C4—182no—
291C22⋊C4—182no—
292C42—91no—
293C42—91no—
294C42—91no—
295C42—182no—
296C42C2×D3211yescharacteristic
297C22×C3—21no—
298C22×C3D3×C22⋊C411yescharacteristic
299C22×C3D3×C22⋊C411yescharacteristic
300C2×D3—62no—
301C2×D3—61no—
302C2×D3—61no—
303C2×D3—61no—
304C2×D3—61no—
305C2×D3—61no—
306C2×D3—61no—
307C2×D3—121no—
308C2×D3—121no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—41no—
316C3×C4—122no—
317C3×C4—122no—
318C3×C4#91211yescharacteristic
319C3×C4#91211yescharacteristic
320C3×C4#91611yescharacteristic
321C3×C4#91611yescharacteristic
322C3×C4#91611yescharacteristic
323C3×C4#91611yescharacteristic
324C3×C4#91911yescharacteristic
325C3×C4#91911yescharacteristic
326Dic3—32no—
327Dic3—32no—
328Dic3—42no—
329Dic3—42no—
330Dic3—62no—
331Dic3—62no—
332Dic3—61no—
333Dic3—61no—
334Dic3—61no—
335Dic3—61no—
336Dic3—121no—
337C32#154411yescharacteristic, complemented, Sylow
338C23—91no—
339Q8—121no—
340Q8—121no—
341Q8—121no—
342Q8—121no—
343C2×C4—62no—
344C2×C4—62no—
345C2×C4—91no—
346C2×C4—91no—
347C2×C4—91no—
348C2×C4—182no—
349C2×C4—181no—
350C2×C4—181no—
351C2×C4—181no—
352C2×C4—181no—
353C2×C4C4×D3211yescharacteristic
354C2×C4#380211yescharacteristic
355C2×C4#381111yescharacteristic
356C8—41no—
357C8—121no—
358C8—121no—
359C8—361no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3D3×#10111yescharacteristic
364C2×C3D3×#10111yescharacteristic
365C2×C3#477211yescharacteristic
366C2×C3#477211yescharacteristic
367C2×C3#480411yescharacteristic
368C2×C3#480411yescharacteristic
369D3—122no—
370D3—121no—
371D3—121no—
372C22—181no—
373C22—181no—
374C22—181no—
375C22#6392111yescharacteristic
376C4—21no—
377C4—92no—
378C4—122no—
379C4—122no—
380C4—181no—
381C4—181no—
382C4#6380911yescharacteristic
383C4#6381011yescharacteristic
384C4#6393611yescharacteristic
385C4#6395011yescharacteristic
386C3—21no—
387C3#6841911yescharacteristic, complemented
388C3#6841911yescharacteristic, complemented
389C2—361no—
390C2#1059061111yescharacteristic
391C2#1059095611yescharacteristic
392C2#1059100311yescharacteristic
subgroupG/H
centerC22#63921
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1544
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. C3×#4486C2semidirect
5. C3×#4482C2semidirect
6. #10589093C2semidirect
7. #10589092C2semidirect
39. #4486D3semidirect
41. #4482D3semidirect
337. C32#1544semidirect
387. C3#68419semidirect
388. C3#68419semidirect

Maximal subgroups

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

subgroupindex
#105938662
#105925322
#105902562
C3×#44862
C3×#44822
#105890932
#105890922
#684193