Finite Group Databasebeta

← #11921098

Subgroups — #11921098

Order 1152.

974 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 974 conjugacy classes of subgroups — too many to draw. Only its 159 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
1C22×C3×C4×A4C211yesmaximal, characteristic
2C22×C3⋊SL(2,ℤ/4)C212yesmaximal
3A4⋊#95—33nomaximal
4#72127—31nomaximal
5C23×C3×A4C2211yescharacteristic
6C2×C3×C4×A4—22no—
7C2×C3×C4×A4C412yescomplemented
8C2×C3⋊SL(2,ℤ/4)—22no—
9C2×C3⋊SL(2,ℤ/4)—22no—
10C2×C3⋊SL(2,ℤ/4)C414yescomplemented
11#63658—41nomaximal
12C24×C3×C4D311yescharacteristic
13C22×C4×A4D313yes—
14C22×SL(2,ℤ/4)—36no—
15C22×#217—32no—
16C2×C3⋊#95—32no—
17C2×C3⋊#95—31no—
18C2×C3⋊#95—31no—
19C22×C3×A4C2×C412yes—
20C22×C3×A4C2×C411yescharacteristic
21C22×C3×A4D411yescharacteristic
22C22×C3×A4D412yes—
23C22×C3×A4Q811yescharacteristic
24C22×C32×C4—41no—
25C22×C3⋊Dic3—42no—
26C3×C4×A4—22no—
27C3⋊SL(2,ℤ/4)—24no—
28C22⋊#95—91noSylow
29C25×C3C2×D311yescharacteristic
30C23×A4C2×D313yes—
31C23×C3×C4—22no—
32C23×C3×C4—31no—
33C23×C3×C4—31no—
34C23×C3×C4—32no—
35C23×C3×C4—62no—
36C23×C3×C4Dic312yescomplemented
37C23×Dic3—32no—
38C23×Dic3—32no—
39C2×C4×A4—26no—
40C2×C4×A4Dic316yescomplemented
41C2×SL(2,ℤ/4)—312no—
42C2×SL(2,ℤ/4)—66no—
43C2×SL(2,ℤ/4)—66no—
44C2×#217—34no—
45C2×#217—34no—
46C2×#217—62no—
47C2×#217—62no—
48C2×#217—62no—
49C2×#217—62no—
50C3⋊#95—64no—
51C3⋊#95—62no—
52C3⋊#95—61no—
53C3⋊#95—61no—
54C3⋊#95—123no—
55C23×C32—41no—
56C2×C3×A4C4211yescharacteristic
57C2×C3×A4C22⋊C412yes—
58C2×C3×A4C22⋊C411yescharacteristic
59C2×C3×A4C4⋊C412yes—
60C2×C3×A4C4⋊C411yescharacteristic
61C2×C32×C4—42no—
62C2×C32×C4—82no—
63C2×C3⋊Dic3—44no—
64C2×C3⋊Dic3—82no—
65C2×C3⋊Dic3—82no—
66C24×C4C3⋊D311yescharacteristic
67C22×C22⋊C4—92no—
68C2×#95—92no—
69C2×#95—91no—
70C2×#95—91no—
71C24×C3—31no—
72C24×C3—31no—
73C24×C3—32no—
74C24×C3—31no—
75C24×C3—32no—
76C24×C3—31no—
77C24×C3Dic611yescharacteristic
78C24×C3C4×D312yes—
79C24×C3D1211yescharacteristic
80C24×C3C2×Dic311yescharacteristic
81C24×C3#6712yes—
82C22×A4Dic613yes—
83C22×A4C4×D316yes—
84C22×A4D1213yes—
85C22×A4C2×Dic313yes—
86C22×A4#6716yes—
87C22×C3×C4—22no—
88C22×C3×C4—32no—
89C22×C3×C4—34no—
90C22×C3×C4—31no—
91C22×C3×C4—32no—
92C22×C3×C4—32no—
93C22×C3×C4—43no—
94C22×C3×C4—62no—
95C22×C3×C4—62no—
96C22×C3×C4—61no—
97C22×C3×C4—62no—
98C22×C3×C4—64no—
99C22×C3×C4—64no—
100C22×C3×C4—62no—
101C22×C3×C4S411yescharacteristic
102C22×Dic3—34no—
103C22×Dic3—34no—
104C22×Dic3—62no—
105C22×Dic3—62no—
106C22×Dic3—62no—
107C22×Dic3—62no—
108C22×Dic3—62no—
109C22×Dic3—62no—
110C22×Dic3—62no—
111C22×Dic3—62no—
112C22×Dic3—62no—
113C22×Dic3—62no—
114C22×Dic3—62no—
115C22×Dic3—62no—
116C22×Dic3—126no—
117C4×A4—26no—
118SL(2,ℤ/4)—612no—
119#217—64no—
120#217—64no—
121#217—64no—
122#217—64no—
123C22×C32—41no—
124C22×C32—42no—
125C22×C32—41no—
126C22×C32—41no—
127C22×C32—42no—
128C3×A4#9511yescharacteristic, complemented
129C32×C4—82no—
130C3⋊Dic3—84no—
131C25C2×C3⋊D311yescharacteristic
132C23×C4—22no—
133C23×C4—31no—
134C23×C4—31no—
135C23×C4—32no—
136C23×C4—62no—
137C23×C4—92no—
138C23×C4—92no—
139C23×C4C3⋊Dic312yescomplemented
140C2×C22⋊C4—94no—
141C2×C22⋊C4—94no—
142C2×C22⋊C4—182no—
143C2×C22⋊C4—182no—
144C2×C22⋊C4—182no—
145C2×C22⋊C4—182no—
146#95—184no—
147#95—181no—
148#95—182no—
149#95—181no—
150C23×C3—31no—
151C23×C3—31no—
152C23×C3—32no—
153C23×C3—32no—
154C23×C3—31no—
155C23×C3—31no—
156C23×C3—31no—
157C23×C3—31no—
158C23×C3—32no—
159C23×C3—32no—
160C23×C3—32no—
161C23×C3—32no—
162C23×C3—32no—
163C23×C3—31no—
164C23×C3—32no—
165C23×C3—31no—
166C23×C3—32no—
167C23×C3—32no—
168C23×C3—32no—
169C23×C3—31no—
170C23×C3—31no—
171C23×C3—31no—
172C23×C3—32no—
173C23×C3—43no—
174C23×C3—61no—
175C23×C3—61no—
176C23×C3—62no—
177C23×C3—61no—
178C23×C3—62no—
179C23×C3C4×Dic311yescharacteristic
180C23×C3Dic3⋊C412yes—
181C23×C3C4⋊Dic311yescharacteristic
182C23×C3(C2×D3)⋊C412yes—
183C23×C3#21711yescharacteristic
184C23×C3C2×S411yescharacteristic
185C2×A4C4×Dic313yes—
186C2×A4Dic3⋊C416yes—
187C2×A4C4⋊Dic313yes—
188C2×A4(C2×D3)⋊C416yes—
189C2×A4#21713yes—
190C2×C3×C4—22no—
191C2×C3×C4—34no—
192C2×C3×C4—32no—
193C2×C3×C4—46no—
194C2×C3×C4—62no—
195C2×C3×C4—64no—
196C2×C3×C4—62no—
197C2×C3×C4—64no—
198C2×C3×C4—62no—
199C2×C3×C4—62no—
200C2×C3×C4—86no—
201C2×C3×C4SL(2,ℤ/4)12yescomplemented
202C2×Dic3—64no—
203C2×Dic3—64no—
204C2×Dic3—64no—
205C2×Dic3—64no—
206C2×Dic3—64no—
207C2×Dic3—64no—
208C2×Dic3—1212no—
209C2×Dic3—122no—
210C2×Dic3—122no—
211C2×Dic3—122no—
212C2×Dic3—122no—
213C2×Dic3—122no—
214C2×Dic3—122no—
215C2×Dic3—122no—
216C2×Dic3—122no—
217C2×Dic3—246no—
218C2×Dic3—246no—
219C2×C32—41no—
220C2×C32—42no—
221C2×C32—41no—
222C2×C32—42no—
223C2×C32—41no—
224C24—31no—
225C24—32no—
226C24—31no—
227C24—32no—
228C24—31no—
229C24—31no—
230C24#63411yescharacteristic
231C24C4×C3⋊D312yes—
232C24C4⋊(C3⋊D3)11yescharacteristic
233C24C2×C3⋊Dic311yescharacteristic
234C24#63812yes—
235C22×C4—22no—
236C22×C4—32no—
237C22×C4—34no—
238C22×C4—31no—
239C22×C4—32no—
240C22×C4—32no—
241C22×C4—62no—
242C22×C4—62no—
243C22×C4—61no—
244C22×C4—62no—
245C22×C4—64no—
246C22×C4—64no—
247C22×C4—62no—
248C22×C4—94no—
249C22×C4—94no—
250C22×C4—182no—
251C22×C4—182no—
252C22×C4—182no—
253C22×C4—182no—
254C22×C4—182no—
255C22×C4—182no—
256C22×C4—182no—
257C22×C4—182no—
258C22×C4—182no—
259C22×C4—182no—
260C22×C4—182no—
261C22×C4—182no—
262C22×C4C3⋊S411yescharacteristic
263C22⋊C4—184no—
264C22⋊C4—184no—
265C22⋊C4—184no—
266C22⋊C4—184no—
267C22×C3—31no—
268C22×C3—32no—
269C22×C3—31no—
270C22×C3—32no—
271C22×C3—31no—
272C22×C3—32no—
273C22×C3—31no—
274C22×C3—31no—
275C22×C3—32no—
276C22×C3—32no—
277C22×C3—32no—
278C22×C3—32no—
279C22×C3—31no—
280C22×C3—31no—
281C22×C3—31no—
282C22×C3—31no—
283C22×C3—32no—
284C22×C3—32no—
285C22×C3—32no—
286C22×C3—32no—
287C22×C3—32no—
288C22×C3—31no—
289C22×C3—31no—
290C22×C3—43no—
291C22×C3—46no—
292C22×C3—43no—
293C22×C3—43no—
294C22×C3—46no—
295C22×C3—61no—
296C22×C3—62no—
297C22×C3—62no—
298C22×C3—61no—
299C22×C3—61no—
300C22×C3C3⋊#9511yescharacteristic, complemented
301C22×C3A4⋊Q811yescharacteristic
302C22×C3C4×S412yes—
303C22×C3C4⋊S411yescharacteristic
304C22×C3C2×SL(2,ℤ/4)11yescharacteristic
305C22×C3GL(2,ℤ/4)12yes—
306A4C3⋊#9513yescomplemented
307C3×C4—22no—
308C3×C4—62no—
309C3×C4—86no—
310Dic3—124no—
311Dic3—124no—
312Dic3—2412no—
313C32—41noSylow
314C23—31no—
315C23—31no—
316C23—32no—
317C23—32no—
318C23—31no—
319C23—31no—
320C23—31no—
321C23—31no—
322C23—32no—
323C23—32no—
324C23—32no—
325C23—32no—
326C23—32no—
327C23—31no—
328C23—32no—
329C23—31no—
330C23—32no—
331C23—32no—
332C23—32no—
333C23—31no—
334C23—31no—
335C23—31no—
336C23—32no—
337C23—61no—
338C23—61no—
339C23—62no—
340C23—61no—
341C23—62no—
342C23C4×C3⋊Dic311yescharacteristic
343C23#375012yes—
344C23C4⋊(C3⋊Dic3)11yescharacteristic
345C23#375212yes—
346C23#375711yescharacteristic
347C23C2×C3⋊S411yescharacteristic
348C2×C4—22no—
349C2×C4—34no—
350C2×C4—32no—
351C2×C4—62no—
352C2×C4—62no—
353C2×C4—64no—
354C2×C4—64no—
355C2×C4—62no—
356C2×C4—62no—
357C2×C4—184no—
358C2×C4—184no—
359C2×C4—184no—
360C2×C4—184no—
361C2×C4—184no—
362C2×C4—184no—
363C2×C4—362no—
364C2×C4—362no—
365C2×C4—362no—
366C2×C4—362no—
367C2×C4—362no—
368C2×C4—362no—
369C2×C4—362no—
370C2×C4—362no—
371C2×C4C3⋊SL(2,ℤ/4)12yescomplemented
372C2×C3—32no—
373C2×C3—31no—
374C2×C3—31no—
375C2×C3—32no—
376C2×C3—31no—
377C2×C3—31no—
378C2×C3—43no—
379C2×C3—46no—
380C2×C3—43no—
381C2×C3—46no—
382C2×C3—43no—
383C2×C3C4×SL(2,ℤ/4)11yescharacteristic
384C2×C3SL(2,ℤ/4)⋊C412yes—
385C2×C3C4⋊SL(2,ℤ/4)11yescharacteristic
386C2×C3(C2×S4)⋊C412yes—
387C2×C3#543211yescharacteristic
388C22—31no—
389C22—32no—
390C22—31no—
391C22—32no—
392C22—31no—
393C22—32no—
394C22—31no—
395C22—31no—
396C22—32no—
397C22—32no—
398C22—32no—
399C22—32no—
400C22—31no—
401C22—31no—
402C22—31no—
403C22—31no—
404C22—32no—
405C22—32no—
406C22—32no—
407C22—32no—
408C22—31no—
409C22—32no—
410C22—31no—
411C22—61no—
412C22—62no—
413C22—62no—
414C22—61no—
415C22—61no—
416C22#6365811yescharacteristic, complemented
417C22#6425911yescharacteristic
418C22C4×C3⋊S412yes—
419C22C4⋊(C3⋊S4)11yescharacteristic
420C22C2×C3⋊SL(2,ℤ/4)11yescharacteristic
421C22#6426912yes—
422C4—22no—
423C4—62no—
424C4—364no—
425C4—364no—
426C3—43no—
427C3A4⋊#9511yescharacteristic, complemented
428C2—32no—
429C2—31no—
430C2—31no—
431C2—32no—
432C2—31no—
433C2—31no—
434C2C4×C3⋊SL(2,ℤ/4)11yescharacteristic
435C2#1059364512yes—
436C2C4⋊(C3⋊SL(2,ℤ/4))11yescharacteristic
437C2#1059364712yes—
438C2#1059366611yescharacteristic
subgroupG/H
center, FrattiniC23C2×C3⋊S4
commutatorC2×C3×A4C42
FittingC24×C3×C4D3
socleC25×C3C2×D3
prime radical, cosocleC23×C3×A4C22
hypercenterC22×C4C3⋊S4
hypocenterC3×A4#95
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
7. C2×C3×C4×A4C4semidirect
10. C2×C3⋊SL(2,ℤ/4)C4semidirect
36. C23×C3×C4Dic3semidirect
40. C2×C4×A4Dic3semidirect
128. C3×A4#95semidirect
139. C23×C4C3⋊Dic3semidirect
201. C2×C3×C4SL(2,ℤ/4)semidirect
300. C22×C3C3⋊#95semidirect
306. A4C3⋊#95semidirect
371. C2×C4C3⋊SL(2,ℤ/4)semidirect
416. C22#63658semidirect
427. C3A4⋊#95semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×A42
C22×C3⋊SL(2,ℤ/4)2
A4⋊#953
#721273
#636584