Finite Group Databasebeta

← #11921101

Subgroups — #11921101

Order 1152.

670 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×C3×D4×A4C211yesmaximal, characteristic
2#10593666C212yesmaximal, complemented
3#73145—33nomaximal
4#72130—31nomaximal
5C23×C3×A4C411yescharacteristic, complemented
6C23×C3×A4C2211yescharacteristic
7C3×D4×A4—22no—
8C2×C3×C4×A4C411yescharacteristic, complemented
9C2×C3⋊SL(2,ℤ/4)—22no—
10#63661—41nomaximal
11C23×C3×D4D311yescharacteristic
12C2×D4×A4D313yes—
13#5432—36no—
14#5247—32no—
15C2×#834—32no—
16C2×#834—31no—
17C2×#834—31no—
18C22×C3×A4—21no—
19C22×C3×A4—41no—
20C22×C3×A4—41no—
21C22×C3×A4C2×C411yescharacteristic
22C22×C3×A4D412yes—
23C2×C32×D4—41no—
24C3×C4×A4—21no—
25C3⋊SL(2,ℤ/4)—42no—
26#3757—42no—
27#1781—91noSylow
28C25×C3Dic311yescharacteristic, complemented
29C25×C3C2×D311yescharacteristic
30C23×A4Dic313yescomplemented
31C23×A4C2×D313yes—
32C22×C3×D4—22no—
33C22×C3×D4—31no—
34C22×C3×D4—31no—
35C22×C3×D4—31no—
36C22×C3×D4—31no—
37C22×C3×D4—62no—
38C23×C3×C4Dic311yescharacteristic, complemented
39D4×A4—26no—
40C2×C4×A4Dic313yescomplemented
41C2×SL(2,ℤ/4)—66no—
42C2×#217—32no—
43C2×#217—32no—
44C2×#217—62no—
45C2×#217—62no—
46#834—64no—
47#834—61no—
48#834—61no—
49#834—61no—
50#834—61no—
51#834—123no—
52C23×C32—41no—
53C23×C32—41no—
54C2×C3×A4—21no—
55C2×C3×A4—22no—
56C2×C3×A4—41no—
57C2×C3×A4C22⋊C411yescharacteristic
58C32×D4—82no—
59C2×C32×C4—41no—
60C2×C3⋊Dic3—82no—
61C23×D4C3⋊D311yescharacteristic
62C2×#99—92no—
63C2×#99—91no—
64C2×#99—91no—
65#379—92no—
66C24×C3—21no—
67C24×C3—31no—
68C24×C3—32no—
69C24×C3—31no—
70C24×C3—31no—
71C24×C3—31no—
72C24×C3—41no—
73C24×C3—41no—
74C24×C3—61no—
75C24×C3—121no—
76C24×C3—121no—
77C24×C3C2×Dic311yescharacteristic
78C24×C3#6712yes—
79C22×A4—23no—
80C22×A4—43no—
81C22×A4—43no—
82C22×A4C2×Dic313yes—
83C22×A4#6716yes—
84C2×C3×D4—34no—
85C2×C3×D4—31no—
86C2×C3×D4—31no—
87C2×C3×D4—31no—
88C2×C3×D4—43no—
89C2×C3×D4—61no—
90C2×C3×D4—62no—
91C2×C3×D4—62no—
92C2×C3×D4—62no—
93C2×C3×D4—62no—
94C2×C3×D4—62no—
95C2×C3×D4—62no—
96C2×C3×D4—62no—
97C2×C3×D4S411yescharacteristic
98C22×C3×C4—21no—
99C22×C3×C4—31no—
100C22×C3×C4—31no—
101C22×C3×C4—61no—
102C22×Dic3—62no—
103C22×Dic3—62no—
104C4×A4—23no—
105SL(2,ℤ/4)—126no—
106#217—62no—
107#217—62no—
108#217—62no—
109#217—62no—
110#217—126no—
111#217—122no—
112#217—122no—
113#217—124no—
114C22×C32—41no—
115C22×C32—42no—
116C22×C32—81no—
117C22×C32—161no—
118C22×C32—161no—
119C3×A4#9911yescharacteristic, complemented
120C32×C4—81no—
121C3⋊Dic3—162no—
122C25C3⋊Dic311yescharacteristic, complemented
123C25C2×C3⋊D311yescharacteristic
124C22×D4—22no—
125C22×D4—31no—
126C22×D4—31no—
127C22×D4—31no—
128C22×D4—31no—
129C22×D4—62no—
130C23×C4C3⋊Dic311yescharacteristic, complemented
131C2×C22⋊C4—92no—
132C2×C22⋊C4—92no—
133C2×C22⋊C4—182no—
134C2×C22⋊C4—182no—
135#99—184no—
136#99—181no—
137#99—181no—
138#99—181no—
139#99—181no—
140C23×C3—22no—
141C23×C3—21no—
142C23×C3—31no—
143C23×C3—32no—
144C23×C3—31no—
145C23×C3—32no—
146C23×C3—31no—
147C23×C3—32no—
148C23×C3—32no—
149C23×C3—31no—
150C23×C3—41no—
151C23×C3—43no—
152C23×C3—43no—
153C23×C3—61no—
154C23×C3—61no—
155C23×C3—61no—
156C23×C3—61no—
157C23×C3—62no—
158C23×C3—64no—
159C23×C3—61no—
160C23×C3—121no—
161C23×C3—122no—
162C23×C3—121no—
163C23×C3—121no—
164C23×C3—121no—
165C23×C3—121no—
166C23×C3—122no—
167C23×C3—121no—
168C23×C3—121no—
169C23×C3—121no—
170C23×C3—121no—
171C23×C3—122no—
172C23×C3#21711yescharacteristic
173C23×C3SL(2,ℤ/4)11yescharacteristic, complemented
174C23×C3C2×S411yescharacteristic
175C2×A4—26no—
176C2×A4—23no—
177C2×A4—43no—
178C2×A4#21713yes—
179C3×D4—22no—
180C3×D4—62no—
181C3×D4—62no—
182C3×D4—64no—
183C3×D4—62no—
184C3×D4—86no—
185C2×C3×C4—32no—
186C2×C3×C4—31no—
187C2×C3×C4—43no—
188C2×C3×C4—61no—
189C2×C3×C4—61no—
190C2×C3×C4—61no—
191C2×C3×C4SL(2,ℤ/4)11yescharacteristic, complemented
192C2×Dic3—122no—
193C2×Dic3—122no—
194C2×Dic3—122no—
195C2×Dic3—122no—
196C2×Dic3—122no—
197C2×Dic3—122no—
198C2×Dic3—246no—
199C2×C32—41no—
200C2×C32—82no—
201C2×C32—81no—
202C2×C32—161no—
203C24—21no—
204C24—31no—
205C24—32no—
206C24—31no—
207C24—31no—
208C24—31no—
209C24—41no—
210C24—41no—
211C24—61no—
212C24—121no—
213C24—121no—
214C24C2×C3⋊Dic311yescharacteristic
215C24#63812yes—
216C2×D4—34no—
217C2×D4—31no—
218C2×D4—31no—
219C2×D4—31no—
220C2×D4—61no—
221C2×D4—62no—
222C2×D4—62no—
223C2×D4—62no—
224C2×D4—62no—
225C2×D4—62no—
226C2×D4—62no—
227C2×D4—62no—
228C2×D4C3⋊S411yescharacteristic
229C22×C4—21no—
230C22×C4—31no—
231C22×C4—31no—
232C22×C4—61no—
233C22×C4—182no—
234C22×C4—182no—
235C22⋊C4—182no—
236C22⋊C4—182no—
237C22⋊C4—182no—
238C22⋊C4—182no—
239C22⋊C4—362no—
240C22⋊C4—362no—
241C22⋊C4—364no—
242C22×C3—21no—
243C22×C3—31no—
244C22×C3—31no—
245C22×C3—32no—
246C22×C3—32no—
247C22×C3—31no—
248C22×C3—41no—
249C22×C3—41no—
250C22×C3—43no—
251C22×C3—46no—
252C22×C3—62no—
253C22×C3—62no—
254C22×C3—61no—
255C22×C3—61no—
256C22×C3—62no—
257C22×C3—61no—
258C22×C3—62no—
259C22×C3—61no—
260C22×C3—83no—
261C22×C3—122no—
262C22×C3—121no—
263C22×C3—121no—
264C22×C3—121no—
265C22×C3—121no—
266C22×C3—121no—
267C22×C3—121no—
268C22×C3—122no—
269C22×C3—122no—
270C22×C3—122no—
271C22×C3—163no—
272C22×C3—163no—
273C22×C3#83411yescharacteristic, complemented
274C22×C3C2×SL(2,ℤ/4)11yescharacteristic
275C22×C3GL(2,ℤ/4)12yes—
276A4#83413yescomplemented
277C3×C4—21no—
278C3×C4—61no—
279C3×C4—83no—
280Dic3—242no—
281Dic3—242no—
282Dic3—486no—
283C32—41noSylow
284C23—22no—
285C23—21no—
286C23—31no—
287C23—32no—
288C23—31no—
289C23—32no—
290C23—31no—
291C23—32no—
292C23—32no—
293C23—31no—
294C23—41no—
295C23—61no—
296C23—61no—
297C23—61no—
298C23—61no—
299C23—62no—
300C23—64no—
301C23—61no—
302C23—121no—
303C23—122no—
304C23—121no—
305C23—121no—
306C23—121no—
307C23—121no—
308C23—122no—
309C23—121no—
310C23—121no—
311C23—121no—
312C23—121no—
313C23—122no—
314C23#375711yescharacteristic
315C23C3⋊SL(2,ℤ/4)11yescharacteristic, complemented
316C23C2×C3⋊S411yescharacteristic
317D4—22no—
318D4—62no—
319D4—62no—
320D4—64no—
321D4—62no—
322C2×C4—32no—
323C2×C4—31no—
324C2×C4—61no—
325C2×C4—61no—
326C2×C4—61no—
327C2×C4—362no—
328C2×C4—362no—
329C2×C4—362no—
330C2×C4—362no—
331C2×C4—362no—
332C2×C4—362no—
333C2×C4C3⋊SL(2,ℤ/4)11yescharacteristic, complemented
334C2×C3—22no—
335C2×C3—21no—
336C2×C3—31no—
337C2×C3—31no—
338C2×C3—41no—
339C2×C3—43no—
340C2×C3—62no—
341C2×C3—61no—
342C2×C3—86no—
343C2×C3—83no—
344C2×C3—121no—
345C2×C3—163no—
346C2×C3#543211yescharacteristic
347C22—21no—
348C22—31no—
349C22—31no—
350C22—32no—
351C22—31no—
352C22—32no—
353C22—41no—
354C22—41no—
355C22—62no—
356C22—62no—
357C22—61no—
358C22—61no—
359C22—61no—
360C22—62no—
361C22—62no—
362C22—61no—
363C22—122no—
364C22—121no—
365C22—121no—
366C22—121no—
367C22—121no—
368C22—121no—
369C22—121no—
370C22—122no—
371C22—122no—
372C22—122no—
373C22#6366111yescharacteristic, complemented
374C22C2×C3⋊SL(2,ℤ/4)11yescharacteristic
375C22#6426912yes—
376C4—21no—
377C4—61no—
378C4—722no—
379C4—722no—
380C3—43no—
381C3#7314511yescharacteristic, complemented
382C2—22no—
383C2—21no—
384C2—31no—
385C2—31no—
386C2—41no—
387C2—62no—
388C2—61no—
389C2—121no—
390C2#1059366611yescharacteristic
subgroupG/H
centerC2#10593666
commutatorC22×C3×A4C2×C4
FrattiniC23C2×C3⋊S4
FittingC23×C3×D4D3
socleC23×C3#217
prime radicalC2×C3×D4×A4C2
cosocleC23×C3×A4C22
hypercenterC2×D4C3⋊S4
hypocenterC3×A4#99
LCSG ▷ C22×C3×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2 ◁ C23 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #10593666C2semidirect
5. C23×C3×A4C4semidirect
8. C2×C3×C4×A4C4semidirect
28. C25×C3Dic3semidirect
30. C23×A4Dic3semidirect
38. C23×C3×C4Dic3semidirect
40. C2×C4×A4Dic3semidirect
119. C3×A4#99semidirect
122. C25C3⋊Dic3semidirect
130. C23×C4C3⋊Dic3semidirect
173. C23×C3SL(2,ℤ/4)semidirect
191. C2×C3×C4SL(2,ℤ/4)semidirect
273. C22×C3#834semidirect
276. A4#834semidirect
315. C23C3⋊SL(2,ℤ/4)semidirect
333. C2×C4C3⋊SL(2,ℤ/4)semidirect
373. C22#63661semidirect
381. C3#73145semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×A42
#105936662
#731453
#721303
#636614