Finite Group Databasebeta

← #11921919

Subgroups — #11921919

Order 1152.

740 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 740 conjugacy classes of subgroups — too many to draw. Only its 71 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×#64259C211yesmaximal, characteristic, complemented
2C2×C3×C4⋊S4C211yesmaximal, characteristic
3C4×Dic3×A4C211yesmaximal, characteristic, complemented
4(C2×S4)⋊Dic3C214yesmaximal, complemented
5#85290—31nomaximal
6#82698—31nomaximal
7C22×C3×S4C2212yes—
8C2×C3×C4×A4C2211yescharacteristic
9C2×Dic3×A4C2212yes—
10C2×C3⋊SL(2,ℤ/4)C2212yes—
11#64259—22no—
12C3×C4⋊S4—22no—
13#63860—41nomaximal
14C2×C4⋊S4D311yescharacteristic
15C2×A4⋊Q8—31no—
16C2×A4⋊Q8—61no—
17C2×C3×#121—31no—
18C2×#936—31no—
19C2×#924—31no—
20C22×C4×Dic3D311yescharacteristic, complemented
21C42×A4—31no—
22(C2×S4)⋊C4—34no—
23#5221—31no—
24#5220—34no—
25#4977—31no—
26#4973—31no—
27#4945—34no—
28C22×C3×A4C2311yescharacteristic
29C2×C3×S4—22no—
30C2×C3×S4—24no—
31C2×#634—41no—
32C2×C3×D12—41no—
33C3×C4×A4D412yes—
34Dic3×A4—22no—
35C3⋊SL(2,ℤ/4)—22no—
36C3×C4×Dic3—41no—
37(C2×D3)⋊Dic3—44no—
38#2850—91noSylow
39C22×S4C2×D312yes—
40C22×C3×D4—31no—
41C22×C3×D4—32no—
42C23×C3×C4C2×D311yescharacteristic
43C23×Dic3C2×D312yes—
44C22×Dic6—31no—
45C2×C4×A4—21no—
46C2×C4×A4—32no—
47C2×C4×A4C2×D311yescharacteristic
48C2×SL(2,ℤ/4)—32no—
49C2×SL(2,ℤ/4)—62no—
50C4⋊S4—22no—
51A4⋊Q8—64no—
52A4⋊Q8—62no—
53C3×#121—62no—
54C3×#121—62no—
55C2×C3×C4⋊C4—31no—
56C2×C3×C22⋊C4—32no—
57C2×#217—34no—
58C2×#217—34no—
59C2×#217—32no—
60#936—61no—
61#936—62no—
62#936—61no—
63C2×C4⋊Dic3—31no—
64#924—62no—
65#924—62no—
66C2×Dic3⋊C4—32no—
67C2×C4×Dic3—31no—
68C2×C4×Dic3—32no—
69C2×C4×Dic3—31no—
70#875—121no—
71C3⋊#95—34no—
72C3⋊#95—34no—
73C22×C3×D3—42no—
74C2×C3×A4C2×D411yescharacteristic
75C2×C3×A4#4112yes—
76C3×S4—42no—
77C2×C32×C4—41no—
78C2×C3⋊Dic3—42no—
79#634—82no—
80C2×C3×Dic3—42no—
81C3×D12—82no—
82C2×#124—91no—
83C2×C22⋊Q8—91no—
84C2×#121—31no—
85C22×C42—31no—
86#391—91no—
87#390—91no—
88#388—94no—
89#386—94no—
90#382—91no—
91C24×C3—32no—
92C24×C3C22×D311yescharacteristic
93C22×A4—21no—
94C22×A4C22×D311yescharacteristic
95C2×S4—24no—
96C2×S4—22no—
97C2×C3×D4—61no—
98C2×C3×D4—62no—
99C2×C3×D4—62no—
100C2×C3×D4—62no—
101C2×C3×D4—64no—
102C2×C3×D4—62no—
103C2×C3×D4—64no—
104C2×C3×D4—61no—
105C22×C3×C4—31no—
106C22×C3×C4—31no—
107C22×C3×C4—32no—
108C22×C3×C4—32no—
109C22×C3×C4D1212yes—
110C22×Dic3—22no—
111C22×Dic3—32no—
112C22×Dic3—32no—
113C22×Dic3—32no—
114C22×Dic3—32no—
115C22×Dic3—62no—
116C2×D12—41no—
117C2×Dic6—62no—
118C2×Dic6—61no—
119C2×Dic6—62no—
120C2×Dic6—61no—
121C2×Dic6—121no—
122C2×Dic6—241no—
123C4×A4—22no—
124C4×A4—62no—
125C4×A4#6712yes—
126SL(2,ℤ/4)—64no—
127SL(2,ℤ/4)—62no—
128C3×C4⋊C4—62no—
129C3×C22⋊C4—64no—
130C3×C42—121no—
131#217—64no—
132#217—68no—
133#217—62no—
134#217—62no—
135#217—64no—
136(C2×D3)⋊C4—124no—
137C4⋊Dic3—62no—
138Dic3⋊C4—64no—
139C4×Dic3—31no—
140C4×Dic3—32no—
141C4×Dic3—61no—
142C4×Dic3S411yescharacteristic, complemented
143C22×C32—41no—
144C2×C3×D3—82no—
145C2×C3×D3—84no—
146C3×A4#12411yescharacteristic, complemented
147C32×C4—42no—
148C3⋊Dic3—82no—
149C3×Dic3—82no—
150C22×Q8—91no—
151C22×D4—31no—
152C22×D4—32no—
153C23×C4—32no—
154C23×C4D3211yescharacteristic
155#124—181no—
156#124—182no—
157#124—181no—
158C22⋊Q8—182no—
159C22⋊Q8—182no—
160#121—62no—
161#121—62no—
162C2×C4⋊C4—31no—
163C2×C4⋊C4—91no—
164C2×C4⋊C4—92no—
165C2×C22⋊C4—32no—
166C2×C22⋊C4—94no—
167C2×C22⋊C4—94no—
168C2×C22⋊C4—92no—
169C2×C42—91no—
170C2×C42—92no—
171C2×C42—91no—
172#95—94no—
173#95—94no—
174C23×C3—31no—
175C23×C3—31no—
176C23×C3—32no—
177C23×C3—64no—
178C23×C3—62no—
179C23×C3—62no—
180C23×C3—64no—
181C23×C3—62no—
182C23×C3C2×D1211yescharacteristic
183C23×C3#23512yes—
184C22×D3—42no—
185C2×A4—22no—
186C2×A4—21no—
187C2×A4#23712yes—
188C2×A4C2×#6711yescharacteristic
189S4—42no—
190C3×D4—122no—
191C3×D4—122no—
192C3×D4—124no—
193C3×D4—122no—
194C3×D4—122no—
195C2×C3×C4—31no—
196C2×C3×C4—32no—
197C2×C3×C4—32no—
198C2×C3×C4—32no—
199C2×C3×C4—41no—
200C2×C3×C4—61no—
201C2×C3×C4—62no—
202C2×C3×C4—64no—
203C2×C3×C4—81no—
204C2×C3×C4—122no—
205C2×C3×C4C2×S411yescharacteristic
206C2×Dic3—34no—
207C2×Dic3—32no—
208C2×Dic3—62no—
209C2×Dic3—62no—
210C2×Dic3—62no—
211C2×Dic3—62no—
212C2×Dic3—62no—
213C2×Dic3—64no—
214C2×Dic3—62no—
215C2×Dic3—62no—
216C2×Dic3—122no—
217C2×Dic3—242no—
218C2×Dic3C2×S412yes—
219D12—82no—
220Dic6—122no—
221Dic6—122no—
222Dic6—242no—
223Dic6—244no—
224C2×C32—41no—
225C2×C32—42no—
226C3×D3—162no—
227C24—32no—
228C24C2×D3211yescharacteristic
229C2×Q8—182no—
230C2×Q8—181no—
231C2×Q8—182no—
232C2×Q8—181no—
233C2×D4—62no—
234C2×D4—61no—
235C2×D4—62no—
236C2×D4—62no—
237C2×D4—64no—
238C2×D4—64no—
239C2×D4—62no—
240C2×D4—61no—
241C22×C4—31no—
242C22×C4—31no—
243C22×C4—32no—
244C22×C4—32no—
245C22×C4—62no—
246C22×C4—92no—
247C22×C4—92no—
248C22×C4—92no—
249C22×C4—92no—
250C22×C4—182no—
251C22×C4#62612yes—
252C4⋊C4—62no—
253C4⋊C4—184no—
254C4⋊C4—182no—
255C22⋊C4—64no—
256C22⋊C4—184no—
257C22⋊C4—184no—
258C22⋊C4—188no—
259C22⋊C4—182no—
260C22⋊C4—182no—
261C42—31no—
262C42—92no—
263C42—91no—
264C42—181no—
265C22×C3—31no—
266C22×C3—32no—
267C22×C3—31no—
268C22×C3—31no—
269C22×C3—32no—
270C22×C3—32no—
271C22×C3—41no—
272C22×C3—61no—
273C22×C3—81no—
274C22×C3—122no—
275C22×C3—122no—
276C22×C3—124no—
277C22×C3—122no—
278C22×C3—124no—
279C22×C3#87511yescharacteristic, complemented
280C22×C3C22×S411yescharacteristic
281C2×D3—82no—
282C2×D3—84no—
283A4—21no—
284A4#93611yescharacteristic, complemented
285C3×C4—32no—
286C3×C4—42no—
287C3×C4—82no—
288C3×C4—122no—
289C3×C4—242no—
290C3×C4C4⋊S412yes—
291Dic3—22no—
292Dic3—62no—
293Dic3—122no—
294Dic3—122no—
295Dic3—242no—
296Dic3—244no—
297C32—41noSylow
298C23—31no—
299C23—31no—
300C23—32no—
301C23—62no—
302C23—64no—
303C23—64no—
304C23—62no—
305C23—62no—
306C23#379512yes—
307C23C2×#62611yescharacteristic
308Q8—362no—
309Q8—362no—
310D4—122no—
311D4—124no—
312D4—122no—
313D4—122no—
314D4—122no—
315C2×C4—31no—
316C2×C4—32no—
317C2×C4—32no—
318C2×C4—32no—
319C2×C4—32no—
320C2×C4—61no—
321C2×C4—62no—
322C2×C4—64no—
323C2×C4—94no—
324C2×C4—92no—
325C2×C4—182no—
326C2×C4—182no—
327C2×C4—182no—
328C2×C4—182no—
329C2×C4—182no—
330C2×C4—184no—
331C2×C4—182no—
332C2×C4—182no—
333C2×C4D3×S411yescharacteristic
334C2×C3—31no—
335C2×C3—31no—
336C2×C3—32no—
337C2×C3—42no—
338C2×C3—41no—
339C2×C3—82no—
340C2×C3—81no—
341C2×C3—242no—
342C2×C3C2×C4⋊S411yescharacteristic
343C2×C3#591212yes—
344D3—162no—
345C22—32no—
346C22—31no—
347C22—32no—
348C22—32no—
349C22—31no—
350C22—31no—
351C22—61no—
352C22—122no—
353C22—122no—
354C22—124no—
355C22—124no—
356C22—122no—
357C22#6386011yescharacteristic, complemented
358C22C2×D3×S411yescharacteristic
359C4—32no—
360C4—62no—
361C4—122no—
362C4—182no—
363C4—362no—
364C4—362no—
365C4#6420712yes—
366C3—41no—
367C3—81no—
368C3#8529011yescharacteristic, complemented
369C2—31no—
370C2—31no—
371C2—32no—
372C2—242no—
373C2#1059642712yes—
374C2C2×#6420711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutator, cosocleC22×C3×A4C23
FittingC23×C3×C4C2×D3
socleC24×C3C22×D3
prime radicalC2×C3×C4⋊S4C2
hypercenterC2×C4D3×S4
hypocenterC3×A4#124
LCSG ▷ C22×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64259C2semidirect
3. C4×Dic3×A4C2semidirect
4. (C2×S4)⋊Dic3C2semidirect
20. C22×C4×Dic3D3semidirect
142. C4×Dic3S4semidirect
146. C3×A4#124semidirect
279. C22×C3#875semidirect
284. A4#936semidirect
357. C22#63860semidirect
368. C3#85290semidirect

Maximal subgroups

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

subgroupindex
C2×#642592
C2×C3×C4⋊S42
C4×Dic3×A42
(C2×S4)⋊Dic32
#852903
#826983
#638604