Finite Group Databasebeta

← #11922989

Subgroups — #11922989

Order 1152.

670 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 83 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#10596575C212yesmaximal, complemented
2C2×C3×C8×A4C211yesmaximal, characteristic, complemented
3#10593636C211yesmaximal, characteristic, complemented
4#10593635C212yesmaximal, complemented
5#10593632C211yesmaximal, characteristic, complemented
6#85440—33nomaximal
7#83742—31nomaximal
8C2×C3×C4×A4C2211yescharacteristic
9#64269—22no—
10C4⋊(C3⋊S4)C2212yes—
11C4×C3⋊S4—22no—
12#64259C2212yes—
13#64113—41nomaximal
14C3×C8×A4C2211yescharacteristic
15C3×C8×A4C2211yescharacteristic
16#5912—36no—
17C23×C3×C8D311yescharacteristic, complemented
18#5791—32no—
19C2×#904—31no—
20C2×C8×A4D313yescomplemented
21#5402—33no—
22#5401—36no—
23#5398—33no—
24#5116—31no—
25#5116—31no—
26#5115—31no—
27#5115—31no—
28#5114—32no—
29#5114—32no—
30#5113—32no—
31#5106—31no—
32C22×C3×A4D411yescharacteristic
33C2×C3⋊S4—22no—
34#3828—42no—
35C3×C4×A4D411yescharacteristic
36C3×C4×A4C2311yescharacteristic
37C3⋊SL(2,ℤ/4)—22no—
38C2×C32×C8—41no—
39#3746—41no—
40#3745—41no—
41#3744—42no—
42#3050—91noSylow
43C23×C3×C4C2×D311yescharacteristic
44C2×#235—32no—
45C2×C4×A4C2×D313yes—
46GL(2,ℤ/4)—66no—
47C4⋊S4—36no—
48C4×S4—66no—
49A4⋊Q8—36no—
50C22×C3×C8—31no—
51C22×C3×C8—31no—
52C22×C3×C8—31no—
53C22×C3×C8—31no—
54C22×C3×C8C2×D311yescharacteristic
55C22×C3×C8C2×D311yescharacteristic
56#953—62no—
57#930—32no—
58#930—32no—
59#929—62no—
60C4×#67—62no—
61C4×#67—62no—
62#926—32no—
63#924—32no—
64#924—32no—
65C2×Dic12—31no—
66#904—61no—
67#904—61no—
68#904—61no—
69#904—61no—
70#904—123no—
71C2×D24—31no—
72C2×#204—32no—
73C8×A4C2×D313yes—
74C8×A4C2×D313yes—
75#821—32no—
76#821—32no—
77#818—31no—
78#818—31no—
79#817—32no—
80#816—32no—
81#816—32no—
82C2×C3×A4—21no—
83C2×C3×A4C2×D411yescharacteristic
84C3⋊S4—42no—
85C2×C32×C4—41no—
86#638—82no—
87C4⋊(C3⋊D3)—42no—
88C4×C3⋊D3—82no—
89#634—42no—
90C32×C8—41no—
91C32×C8—41no—
92C2×#135—91no—
93C23×C8C3⋊D311yescharacteristic, complemented
94#525—92no—
95#467—91no—
96#467—91no—
97#466—91no—
98#466—91no—
99#465—92no—
100#465—92no—
101#427—91no—
102#416—92no—
103C24×C3D1211yescharacteristic
104C22×A4D1213yes—
105C2×S4—66no—
106C22×C3×C4—31no—
107C22×C3×C4—31no—
108C22×C3×C4—31no—
109C22×C3×C4—31no—
110C22×C3×C4D1211yescharacteristic
111C22×C3×C4C22×D311yescharacteristic
112C2×#67—62no—
113C2×#67—62no—
114C2×#67—62no—
115#235—62no—
116#235—62no—
117#235—62no—
118#235—62no—
119#235—126no—
120C2×D12—32no—
121C2×C4×D3—62no—
122C2×Dic6—32no—
123C4×A4D1213yes—
124C4×A4C22×D313yes—
125SL(2,ℤ/4)—66no—
126C2×C3×C8—31no—
127C2×C3×C8—31no—
128C2×C3×C8—31no—
129C2×C3×C8—31no—
130C2×C3×C8—31no—
131C2×C3×C8—31no—
132C2×C3×C8—31no—
133C2×C3×C8—43no—
134C2×C3×C8—61no—
135C2×C3×C8S411yescharacteristic, complemented
136#217—62no—
137#217—62no—
138#217—62no—
139(C2×D3)⋊C4—62no—
140(C2×D3)⋊C4—62no—
141C4⋊Dic3—32no—
142C4⋊Dic3—32no—
143Dic3⋊C4—62no—
144Dic3⋊C4—62no—
145C4×Dic3—62no—
146Dic12—61no—
147Dic12—61no—
148Dic12—123no—
149D24—61no—
150D24—61no—
151D24—123no—
152#204—62no—
153#204—62no—
154#204—126no—
155C22×C32—41no—
156C2×C3⋊D3—82no—
157C3×A4#13511yescharacteristic, complemented
158C32×C4—41no—
159C32×C4—41no—
160C3⋊Dic3—82no—
161C2×#41—92no—
162C23×C4C2×C3⋊D311yescharacteristic
163#135—181no—
164#135—181no—
165#135—181no—
166#135—181no—
167C2×Q16—91no—
168C2×SD16—92no—
169C2×D8—91no—
170C22×C8—31no—
171C22×C8—31no—
172C22×C8—31no—
173C22×C8—31no—
174C22×C8C2×C3⋊D311yescharacteristic
175C22×C8C2×C3⋊D311yescharacteristic
176#123—182no—
177C22⋊Q8—92no—
178C22⋊Q8—92no—
179#121—92no—
180#121—92no—
181#120—182no—
182C4×D4—182no—
183C4×D4—182no—
184#117—92no—
185#107—91no—
186#107—91no—
187#106—92no—
188#103—92no—
189#103—92no—
190#102—92no—
191#102—92no—
192C23×C3—21no—
193C23×C3—31no—
194C23×C3—31no—
195C23×C3—61no—
196C23×C3C2×D1211yescharacteristic
197C22×D3—62no—
198C2×A4—23no—
199C2×A4C2×D1213yes—
200S4—126no—
201C2×C3×C4—31no—
202C2×C3×C4—31no—
203C2×C3×C4—31no—
204C2×C3×C4—31no—
205C2×C3×C4—31no—
206C2×C3×C4—31no—
207C2×C3×C4—31no—
208C2×C3×C4—43no—
209C2×C3×C4—61no—
210C2×C3×C4C2×S411yescharacteristic
211#67—122no—
212#67—122no—
213#67—124no—
214#67—122no—
215#67—122no—
216#67—246no—
217C2×Dic3—62no—
218C2×Dic3—62no—
219C2×Dic3—62no—
220D12—62no—
221D12—62no—
222D12—126no—
223C4×D3—122no—
224C4×D3—122no—
225C4×D3—246no—
226Dic6—62no—
227Dic6—62no—
228Dic6—126no—
229C3×C8—31no—
230C3×C8—31no—
231C3×C8—43no—
232C3×C8—43no—
233C3×C8C2×S411yescharacteristic
234C3×C8C2×S411yescharacteristic
235C2×C32—41no—
236C2×C32—81no—
237C3⋊D3—162no—
238C24C4⋊(C3⋊D3)11yescharacteristic
239#41—182no—
240#41—182no—
241#41—182no—
242#41—182no—
243C2×Q8—92no—
244C2×D4—92no—
245C2×D4—182no—
246C2×D4—182no—
247C2×D4—182no—
248C22×C4—31no—
249C22×C4—31no—
250C22×C4—31no—
251C22×C4—31no—
252C22×C4—182no—
253C22×C4C4⋊(C3⋊D3)11yescharacteristic
254C22×C4C22×C3⋊D311yescharacteristic
255Q16—181no—
256Q16—181no—
257SD16—182no—
258SD16—182no—
259D8—181no—
260D8—181no—
261C2×C8—31no—
262C2×C8—31no—
263C2×C8—31no—
264C2×C8—31no—
265C2×C8—31no—
266C2×C8—31no—
267C2×C8—31no—
268C2×C8—61no—
269C2×C8C3⋊S411yescharacteristic, complemented
270C4⋊C4—92no—
271C4⋊C4—92no—
272C4⋊C4—182no—
273C4⋊C4—182no—
274C22⋊C4—182no—
275C22⋊C4—182no—
276C22⋊C4—182no—
277C22⋊C4—182no—
278C22⋊C4—182no—
279C42—182no—
280C22×C3—31no—
281C22×C3—31no—
282C22×C3—32no—
283C22×C3—31no—
284C22×C3—43no—
285C22×C3—61no—
286C22×C3—61no—
287C22×C3—61no—
288C22×C3#90411yescharacteristic, complemented
289C22×C3C4⋊S411yescharacteristic
290C2×D3—122no—
291C2×D3—122no—
292C2×D3—122no—
293C2×D3—246no—
294A4#90413yescomplemented
295C3×C4—31no—
296C3×C4—31no—
297C3×C4—43no—
298C3×C4—43no—
299C3×C4C4⋊S411yescharacteristic
300C3×C4C22×S411yescharacteristic
301Dic3—122no—
302Dic3—122no—
303Dic3—122no—
304Dic3—246no—
305C32—41noSylow
306C23—21no—
307C23—31no—
308C23—31no—
309C23—61no—
310C23—182no—
311C23C2×C4⋊(C3⋊D3)11yescharacteristic
312Q8—182no—
313Q8—182no—
314D4—182no—
315D4—182no—
316D4—362no—
317D4—362no—
318D4—364no—
319D4—362no—
320D4—362no—
321C2×C4—31no—
322C2×C4—31no—
323C2×C4—31no—
324C2×C4—31no—
325C2×C4—31no—
326C2×C4—31no—
327C2×C4—31no—
328C2×C4—61no—
329C2×C4—182no—
330C2×C4—182no—
331C2×C4—182no—
332C2×C4—362no—
333C2×C4—362no—
334C2×C4C2×C3⋊S411yescharacteristic
335C8—31no—
336C8—31no—
337C8C2×C3⋊S411yescharacteristic
338C8C2×C3⋊S411yescharacteristic
339C2×C3—21no—
340C2×C3—31no—
341C2×C3—31no—
342C2×C3—43no—
343C2×C3—61no—
344C2×C3—83no—
345C2×C3C2×C4⋊S411yescharacteristic
346D3—242no—
347D3—486no—
348C22—31no—
349C22—31no—
350C22—32no—
351C22—31no—
352C22—61no—
353C22—61no—
354C22—61no—
355C22—362no—
356C22—362no—
357C22—362no—
358C22#6411311yescharacteristic, complemented
359C22C4⋊(C3⋊S4)11yescharacteristic
360C4—31no—
361C4—31no—
362C4—362no—
363C4—362no—
364C4—362no—
365C4C4⋊(C3⋊S4)11yescharacteristic
366C4C22×C3⋊S411yescharacteristic
367C3—43no—
368C3#8544011yescharacteristic, complemented
369C2—21no—
370C2—31no—
371C2—31no—
372C2—61no—
373C2—722no—
374C2C2×C4⋊(C3⋊S4)11yescharacteristic
subgroupG/H
centerC4C4⋊(C3⋊S4)
commutator, cosocleC3×C4×A4C23
FrattiniC4C22×C3⋊S4
FittingC23×C3×C8D3
socleC23×C3C2×D12
hypercenterC2×C8C3⋊S4
hypocenterC3×A4#135
LCSG ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. #10596575C2semidirect
2. C2×C3×C8×A4C2semidirect
3. #10593636C2semidirect
4. #10593635C2semidirect
5. #10593632C2semidirect
17. C23×C3×C8D3semidirect
20. C2×C8×A4D3semidirect
93. C23×C8C3⋊D3semidirect
135. C2×C3×C8S4semidirect
157. C3×A4#135semidirect
269. C2×C8C3⋊S4semidirect
288. C22×C3#904semidirect
294. A4#904semidirect
358. C22#64113semidirect
368. C3#85440semidirect

Maximal subgroups

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

subgroupindex
#105965752
C2×C3×C8×A42
#105936362
#105936352
#105936322
#854403
#837423
#641134