Finite Group Databasebeta

← #11776198

Subgroups — #11776198

Order 1152.

493 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 493 conjugacy classes of subgroups — too many to draw. Only its 106 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
2C3⋊D3×C4⋊C8C211yesmaximal, characteristic
3#10590256C211yesmaximal, characteristic
4C3×#4486C211yesmaximal, characteristic, complemented
5C3×#4481C211yesmaximal, characteristic, complemented
6#10589095C211yesmaximal, characteristic, complemented
7#10589093C211yesmaximal, characteristic, complemented
8#68481—31nomaximal
9#68418—31nomaximal
10C2×C8×C3⋊D3—21no—
11C42×C3⋊D3C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14#63872—21no—
15#63871—21no—
16#63871C412yes—
17#63849—21no—
18#63843—21no—
19#63843C412yes—
20C32×C4⋊C8C2211yescharacteristic
21#63641—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—
31D3×C4⋊C8—31no—
32D3×C4⋊C8—31no—
33D3×C4⋊C8—61no—
34C3×#333—31no—
35C3×#332—31no—
36#4547—31no—
37#4546—31no—
38#4486D311yescharacteristic, complemented
39#4482—31no—
40#4481—31no—
41#4481D311yescharacteristic, complemented
42C2×C4×C3⋊D3C2×C411yescharacteristic
43C2×C4×C3⋊D3D411yescharacteristic
44C2×C4×C3⋊D3D411yescharacteristic
45C2×C3×Dic6—21no—
46C2×C3×Dic6C2×C412yes—
47C2×C32×C8—21no—
48C32×C42C2311yescharacteristic
49C4×C3⋊Dic3C2×C411yescharacteristic
50C4×C3⋊Dic3D411yescharacteristic
51C4×C3⋊Dic3D411yescharacteristic
52C2×C3⋊(C3⋊C8)—21no—
53C8×C3⋊D3—42no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3C2×C412yes—
58C2×C3×C3⋊C8—21no—
59C2×C3×C3⋊C8—21no—
60Dic3⋊Dic3—22no—
61Dic3⋊Dic3—22no—
62#3722—22no—
63Dic32—22no—
64#1542—91noSylow
65C3×C4⋊Q8—31no—
66C3×C4⋊Q8—31no—
67#946—32no—
68#946—61no—
69Q8×Dic3—32no—
70Q8×Dic3—61no—
71C2×D3×C8—61no—
72C2×D3×C8—61no—
73C2×D3×C8—62no—
74#897—32no—
75#897—61no—
76#892—61no—
77#892—61no—
78#890—61no—
79#890—61no—
80#887—32no—
81#887—61no—
82C42×D3—31no—
83C42×D3—31no—
84C42×D3—61no—
85#869C2×D311yescharacteristic
86#869C2×D311yescharacteristic
87C3×C4⋊C8—21no—
88C3×C4⋊C8—31no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8C2×D311yescharacteristic
91C3×C4⋊C8C2×D311yescharacteristic
92(C2×D3)⋊C8—61no—
93(C2×D3)⋊C8—61no—
94Dic3⋊C8—61no—
95Dic3⋊C8—61no—
96Dic3⋊C8—62no—
97C8×Dic3—61no—
98C8×Dic3—61no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—61no—
102C4⋊(C3⋊C8)C2×D311yescharacteristic
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C22×C3⋊D3C22⋊C411yescharacteristic
105C2×C32×C4C22×C411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C3⋊Dic3C22⋊C411yescharacteristic
109C2×C3⋊Dic3C22⋊C411yescharacteristic
110C2×C3⋊Dic3C22⋊C411yescharacteristic
111C4×C3⋊D3—21no—
112C4×C3⋊D3—21no—
113C4×C3⋊D3—41no—
114C4×C3⋊D3SD1612yes—
115C4×C3⋊D3Q1612yes—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—22no—
118C3×Dic6—41no—
119C3×Dic6—41no—
120C3×Dic6—42no—
121C32×C8—41no—
122C3⋊(C3⋊C8)—41no—
123C3×C3⋊C8—41no—
124C3×C3⋊C8—41no—
125#533—91no—
126#431—91no—
127C2×C4⋊C8—91no—
128#333—31no—
129#333—91no—
130#332—31no—
131#332—91no—
132C2×C3×Q8—32no—
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×Dic6C4×D312yes—
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—61no—
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—21no—
162C4⋊Dic3—62no—
163C4⋊Dic3—62no—
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—
183D3×C8—122no—
184D3×C8—122no—
185D3×C8—124no—
186C22×C32C2×C22⋊C411yescharacteristic
187C2×C3⋊D3—21no—
188C2×C3⋊D3—21no—
189C2×C3⋊D3#10312yes—
190C32×C4—21no—
191C32×C4C2×SD1611yescharacteristic
192C32×C4C2×Q1611yescharacteristic
193C32×C4#13511yescharacteristic
194C32×C4#13511yescharacteristic
195C3⋊Dic3—21no—
196C3⋊Dic3—21no—
197C3⋊Dic3#10312yes—
198C3×Dic3—42no—
199C3×Dic3—42no—
200C22×C8—181no—
201C4⋊Q8—31no—
202C4⋊Q8—31no—
203#125—181no—
204C22⋊Q8—92no—
205C22⋊Q8—181no—
206C4×Q8—92no—
207C4×Q8—181no—
208#117—181no—
209C2×C42—91no—
210C4⋊C8—31no—
211C4⋊C8—31no—
212C4⋊C8—91no—
213C4⋊C8—181no—
214C4⋊C8D3211yescharacteristic
215C22⋊C8—181no—
216C4×C8—181no—
217C22×D3—31no—
218C22×D3—31no—
219C22×D3—61no—
220C3×Q8—122no—
221C3×Q8—121no—
222C3×Q8—121no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—62no—
227C2×C3×C4—62no—
228C2×C3×C4C2×C4×D311yescharacteristic
229C2×C3×C4C2×C4×D311yescharacteristic
230C2×C3×C4D3×D411yescharacteristic
231C2×C3×C4D3×D411yescharacteristic
232C2×C3×C4D3×D411yescharacteristic
233C2×C3×C4D3×D411yescharacteristic
234C2×Dic3—22no—
235C2×Dic3—22no—
236C2×Dic3—31no—
237C2×Dic3—31no—
238C2×Dic3—31no—
239C2×Dic3—31no—
240C2×Dic3—31no—
241C2×Dic3—31no—
242C2×Dic3—61no—
243C2×Dic3—61no—
244C2×Dic3—61no—
245C4×D3—32no—
246C4×D3—32no—
247C4×D3—32no—
248C4×D3—32no—
249C4×D3—62no—
250C4×D3—62no—
251C4×D3—62no—
252C4×D3—62no—
253C4×D3—61no—
254C4×D3—61no—
255C4×D3—61no—
256C4×D3—61no—
257C4×D3—121no—
258C4×D3—121no—
259C4×D3—122no—
260Dic6—41no—
261Dic6—41no—
262Dic6—42no—
263C3×C8—42no—
264C3×C8—41no—
265C3×C8—41no—
266C3×C8—121no—
267C3×C8—121no—
268C3⋊C8—41no—
269C3⋊C8—41no—
270C3⋊C8—122no—
271C3⋊C8—121no—
272C3⋊C8—121no—
273C2×C32#41311yescharacteristic
274C2×C32C2×#10311yescharacteristic
275C2×C32#41611yescharacteristic
276C3⋊D3—22no—
277C2×Q8—32no—
278C2×Q8—61no—
279C22×C4—91no—
280C22×C4—91no—
281C22×C4—91no—
282C2×C8—21no—
283C2×C8—61no—
284C2×C8—61no—
285C2×C8—181no—
286C2×C8—362no—
287C4⋊C4—32no—
288C4⋊C4—61no—
289C4⋊C4—61no—
290C4⋊C4—61no—
291C4⋊C4—182no—
292C4⋊C4—182no—
293C22⋊C4—182no—
294C42—91no—
295C42—91no—
296C42—91no—
297C42—182no—
298C42C2×D3211yescharacteristic
299C22×C3—21no—
300C22×C3D3×C22⋊C411yescharacteristic
301C22×C3D3×C22⋊C411yescharacteristic
302C2×D3—32no—
303C2×D3—32no—
304C2×D3—62no—
305C2×D3—62no—
306C2×D3—62no—
307C2×D3—61no—
308C2×D3—61no—
309C2×D3—61no—
310C2×D3—61no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—41no—
318C3×C4—122no—
319C3×C4—122no—
320C3×C4#91211yescharacteristic
321C3×C4D3×SD1611yescharacteristic
322C3×C4D3×SD1611yescharacteristic
323C3×C4#91611yescharacteristic
324C3×C4#91611yescharacteristic
325C3×C4D3×Q1611yescharacteristic
326C3×C4D3×Q1611yescharacteristic
327C3×C4#91911yescharacteristic
328Dic3—32no—
329Dic3—32no—
330Dic3—42no—
331Dic3—42no—
332Dic3—62no—
333Dic3—62no—
334Dic3—61no—
335Dic3—61no—
336Dic3—61no—
337Dic3—61no—
338Dic3—121no—
339C32#154211yescharacteristic, complemented, Sylow
340C23—91no—
341Q8—122no—
342Q8—121no—
343Q8—121no—
344C2×C4—62no—
345C2×C4—62no—
346C2×C4—91no—
347C2×C4—92no—
348C2×C4—92no—
349C2×C4—91no—
350C2×C4—91no—
351C2×C4—181no—
352C2×C4—181no—
353C2×C4—361no—
354C2×C4C4×D3211yescharacteristic
355C2×C4#380211yescharacteristic
356C2×C4#381111yescharacteristic
357C8—41no—
358C8—121no—
359C8—121no—
360C8—361no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3#474511yescharacteristic
365C2×C3#475111yescharacteristic
366C2×C3#477211yescharacteristic
367C2×C3D3×#10311yescharacteristic
368C2×C3D3×#10311yescharacteristic
369C2×C3#480411yescharacteristic
370D3—64no—
371D3—62no—
372D3—62no—
373C22—92no—
374C22—181no—
375C22—181no—
376C22#6392111yescharacteristic
377C4—21no—
378C4—92no—
379C4—122no—
380C4—122no—
381C4—181no—
382C4—181no—
383C4#6380911yescharacteristic
384C4#6381011yescharacteristic
385C4#6393011yescharacteristic
386C4#6394411yescharacteristic
387C3—21no—
388C3#6841811yescharacteristic, complemented
389C3#6848111yescharacteristic, complemented
390C2—182no—
391C2#1059060111yescharacteristic
392C2#1059095611yescharacteristic
393C2#1059101011yescharacteristic
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#1542
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×#4481C2semidirect
6. #10589095C2semidirect
7. #10589093C2semidirect
38. #4486D3semidirect
41. #4481D3semidirect
339. C32#1542semidirect
388. C3#68418semidirect
389. C3#68481semidirect

Maximal subgroups

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

subgroupindex
#105938662
C3⋊D3×C4⋊C82
#105902562
C3×#44862
C3×#44812
#105890952
#105890932
#684813
#684183