Finite Group Databasebeta

← #11785769

Subgroups — #11785769

Order 1152.

897 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 897 conjugacy classes of subgroups — too many to draw. Only its 164 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×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2#10591325C211yesmaximal, characteristic
3C2×#63557C211yesmaximal, characteristic
4C3×#4529C212yesmaximal, complemented
5#10589164C212yesmaximal, complemented
6#68871—32nomaximal
7C22×C4×C3⋊D3—21no—
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11C2×#3750—21no—
12C4⋊C4×C3⋊D3—22no—
13C4⋊C4×C3⋊D3C414yescomplemented
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16C2×#3722—21no—
17#63579—21no—
18#63557—22no—
19C2×D3×C4⋊C4—32no—
20C2×D3×C4⋊C4—61no—
21C2×(C2×D3)⋊C8—32no—
22#4987—32no—
23C3×#340—32no—
24#4551—32no—
25#4529—32no—
26#4529D312yescomplemented
27C23×C3⋊D3D411yescharacteristic
28C22×C32×C4—21no—
29C22×C32×C4C2311yescharacteristic
30C22×C3⋊Dic3—21no—
31C22×C3⋊Dic3D411yescharacteristic
32C2×C4×C3⋊D3—22no—
33C2×C4×C3⋊D3—22no—
34C2×C4×C3⋊D3—24no—
35C2×C4×C3⋊D3—42no—
36C2×C4×C3⋊D3—42no—
37C2×C4×C3⋊D3C2×C412yes—
38C2×C4×C3⋊D3D412yes—
39C22×C3×Dic3—22no—
40C32×C4⋊C4—21no—
41C32×C4⋊C4C2×C412yes—
42C4⋊(C3⋊Dic3)—21no—
43C4⋊(C3⋊Dic3)C2×C412yes—
44#3750—24no—
45C3×C4⋊Dic3—22no—
46C3×C4⋊Dic3—22no—
47C2×C3×C3⋊C8—22no—
48C2×C3×C3⋊C8—22no—
49C2×C3×C3⋊C8—22no—
50#3722—42no—
51#1823—91noSylow
52C22×C4×D3—32no—
53C22×C4×D3—61no—
54C22×C4×D3—62no—
55C22×C4×D3—62no—
56C22×C3×C8—32no—
57C2×C3×C4⋊C4—21no—
58C2×C3×C4⋊C4—32no—
59C2×C3×C4⋊C4C2×D312yes—
60C2×(C2×D3)⋊C4—62no—
61C2×C4⋊Dic3—32no—
62C2×C4⋊Dic3—61no—
63C2×C4⋊Dic3C2×D312yes—
64C2×Dic3⋊C4—62no—
65C2×Dic3⋊C4—62no—
66C22×C3⋊C8C2×D312yes—
67D3×C4⋊C4—38no—
68D3×C4⋊C4—64no—
69D3×C4⋊C4—64no—
70D3×C4⋊C4—64no—
71C3⋊#95—62no—
72(C2×D3)⋊C8—64no—
73C23×C32C2×D411yescharacteristic
74C22×C3⋊D3—22no—
75C22×C3⋊D3—22no—
76C22×C3⋊D3C22⋊C412yes—
77C22×C3⋊D3D812yes—
78C22×C3⋊D3SD1612yes—
79C2×C32×C4—22no—
80C2×C32×C4—41no—
81C2×C32×C4—41no—
82C2×C32×C4C22×C411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C2×C32×C4#4112yes—
85C2×C32×C4#4112yes—
86C2×C3⋊Dic3—22no—
87C2×C3⋊Dic3—22no—
88C2×C3⋊Dic3—41no—
89C2×C3⋊Dic3—41no—
90C2×C3⋊Dic3C22⋊C412yes—
91C4×C3⋊D3—22no—
92C4×C3⋊D3—22no—
93C4×C3⋊D3—24no—
94C4×C3⋊D3—48no—
95C2×C3×Dic3—42no—
96C2×C3×Dic3—42no—
97C2×C3×Dic3—42no—
98C3×C3⋊C8—42no—
99C22×C4⋊C4—91no—
100C2×C22⋊C8—91no—
101#380—91no—
102#340—32no—
103#340—92no—
104C23×D3—32no—
105C23×D3—61no—
106C22×C3×C4—22no—
107C22×C3×C4—22no—
108C22×C3×C4—21no—
109C22×C3×C4—62no—
110C22×C3×C4C22×D312yes—
111C22×Dic3—22no—
112C22×Dic3—32no—
113C22×Dic3—61no—
114C22×Dic3—62no—
115C22×Dic3—62no—
116C2×C4×D3—34no—
117C2×C4×D3—34no—
118C2×C4×D3—62no—
119C2×C4×D3—62no—
120C2×C4×D3—64no—
121C2×C4×D3—64no—
122C2×C4×D3—62no—
123C2×C4×D3—62no—
124C2×C4×D3—62no—
125C2×C4×D3—62no—
126C2×C4×D3—68no—
127C2×C4×D3—68no—
128C2×C4×D3—124no—
129C2×C4×D3—124no—
130C2×C4×D3—124no—
131C2×C4×D3—124no—
132C2×C3×C8—62no—
133C2×C3×C8—62no—
134C2×C3×C8—62no—
135C3×C4⋊C4—22no—
136C3×C4⋊C4—22no—
137C3×C4⋊C4—22no—
138C3×C4⋊C4—62no—
139C3×C4⋊C4—62no—
140C3×C4⋊C4C4×D314yes—
141(C2×D3)⋊C4—124no—
142C4⋊Dic3—22no—
143C4⋊Dic3—22no—
144C4⋊Dic3—34no—
145C4⋊Dic3—62no—
146C4⋊Dic3—62no—
147C4⋊Dic3—62no—
148Dic3⋊C4—68no—
149Dic3⋊C4—68no—
150C2×C3⋊C8—22no—
151C2×C3⋊C8—22no—
152C2×C3⋊C8—22no—
153C22×C32C2×C22⋊C411yescharacteristic
154C22×C32#12312yes—
155C22×C32C2×D811yescharacteristic
156C22×C32C2×SD1611yescharacteristic
157C22×C32#13712yes—
158C2×C3⋊D3—22no—
159C2×C3⋊D3—22no—
160C2×C3⋊D3—24no—
161C2×C3⋊D3—24no—
162C2×C3⋊D3#10214yes—
163C32×C4—42no—
164C32×C4#11711yescharacteristic
165C32×C4#11711yescharacteristic
166C32×C4#12312yes—
167C3⋊Dic3—22no—
168C3⋊Dic3—42no—
169C3×Dic3—82no—
170C23×C4—91no—
171C23×C4—181no—
172C22×C8—32no—
173C2×C4⋊C4—32no—
174C2×C4⋊C4—91no—
175C2×C4⋊C4—94no—
176C2×C4⋊C4—182no—
177C2×C4⋊C4—181no—
178C2×C4⋊C4D3211yescharacteristic
179C2×C22⋊C4—181no—
180C22⋊C8—182no—
181#95—181no—
182C23×C3—21no—
183C23×C3D3×D412yes—
184C22×D3—34no—
185C22×D3—34no—
186C22×D3—34no—
187C22×D3—62no—
188C22×D3—62no—
189C22×D3—62no—
190C22×D3—64no—
191C22×D3—64no—
192C22×D3—62no—
193C22×D3—62no—
194C22×D3—62no—
195C22×D3—62no—
196C2×C3×C4—24no—
197C2×C3×C4—24no—
198C2×C3×C4—22no—
199C2×C3×C4—22no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—42no—
203C2×C3×C4—42no—
204C2×C3×C4—42no—
205C2×C3×C4—42no—
206C2×C3×C4—122no—
207C2×C3×C4—122no—
208C2×C3×C4—122no—
209C2×C3×C4C2×C4×D312yes—
210C2×C3×C4#23512yes—
211C2×C3×C4#23512yes—
212C2×C3×C4D3×D412yes—
213C2×C3×C4#23712yes—
214C2×C3×C4#23912yes—
215C2×Dic3—34no—
216C2×Dic3—42no—
217C2×Dic3—42no—
218C2×Dic3—42no—
219C2×Dic3—62no—
220C2×Dic3—64no—
221C2×Dic3—62no—
222C2×Dic3—62no—
223C2×Dic3—64no—
224C2×Dic3—64no—
225C2×Dic3—122no—
226C2×Dic3—122no—
227C2×Dic3—122no—
228C2×Dic3—122no—
229C4×D3—64no—
230C4×D3—68no—
231C4×D3—64no—
232C4×D3—64no—
233C4×D3—64no—
234C4×D3—64no—
235C4×D3—64no—
236C4×D3—1216no—
237C4×D3—1216no—
238C3×C8—122no—
239C3⋊C8—42no—
240C2×C32#38111yescharacteristic
241C2×C32C2×#10211yescharacteristic
242C2×C32#41911yescharacteristic
243C2×C32#48012yes—
244C2×C32#48312yes—
245C3⋊D3—24no—
246C24—91no—
247C22×C4—21no—
248C22×C4—62no—
249C22×C4—91no—
250C22×C4—92no—
251C22×C4—92no—
252C22×C4—184no—
253C22×C4—182no—
254C22×C4—182no—
255C22×C4—181no—
256C22×C4—362no—
257C22×C4—362no—
258C22×C4C2×D3211yescharacteristic
259C2×C8—62no—
260C2×C8—62no—
261C2×C8—62no—
262C4⋊C4—21no—
263C4⋊C4—62no—
264C4⋊C4—62no—
265C4⋊C4—92no—
266C4⋊C4—184no—
267C4⋊C4—181no—
268C4⋊C4#62412yes—
269C22⋊C4—362no—
270C22×C3—22no—
271C22×C3—21no—
272C22×C3—21no—
273C22×C3—22no—
274C22×C3—21no—
275C22×C3D3×C22⋊C412yes—
276C22×C3#88312yes—
277C22×C3#89412yes—
278C22×C3D3×D812yes—
279C22×C3D3×SD1612yes—
280C22×C3#91512yes—
281C22×C3#91812yes—
282C2×D3—38no—
283C2×D3—64no—
284C2×D3—64no—
285C2×D3—68no—
286C2×D3—68no—
287C2×D3—64no—
288C2×D3—64no—
289C2×D3—64no—
290C2×D3—64no—
291C2×D3—64no—
292C2×D3—64no—
293C2×D3—64no—
294C3×C4—21no—
295C3×C4—22no—
296C3×C4—21no—
297C3×C4—44no—
298C3×C4—44no—
299C3×C4—242no—
300C3×C4#87212yes—
301C3×C4#88312yes—
302C3×C4#89212yes—
303C3×C4#89412yes—
304Dic3—64no—
305Dic3—64no—
306Dic3—82no—
307Dic3—124no—
308Dic3—124no—
309C32#182311yescharacteristic, complemented, Sylow
310C23—92no—
311C23—92no—
312C23—92no—
313C23—182no—
314C23—182no—
315C23#381111yescharacteristic
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—92no—
320C2×C4—122no—
321C2×C4—122no—
322C2×C4—122no—
323C2×C4—182no—
324C2×C4—182no—
325C2×C4—184no—
326C2×C4—182no—
327C2×C4—182no—
328C2×C4—368no—
329C2×C4—361no—
330C2×C4—361no—
331C2×C4#379612yes—
332C2×C4#379812yes—
333C2×C4C2×#62411yescharacteristic
334C2×C4#381111yescharacteristic
335C8—122no—
336C2×C3—22no—
337C2×C3—22no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3#466412yes—
342C2×C3D3×#10212yes—
343C2×C3#477412yes—
344C2×C3#480212yes—
345C2×C3#480512yes—
346C2×C3#486212yes—
347C2×C3#488212yes—
348D3—68no—
349D3—68no—
350C22—94no—
351C22—184no—
352C22—184no—
353C22—182no—
354C22—182no—
355C22#6385312yes—
356C22#6392611yescharacteristic
357C22#6393011yescharacteristic
358C22#6395112yes—
359C22#6397411yescharacteristic
360C4—42no—
361C4—182no—
362C4—242no—
363C4—362no—
364C4#6384911yescharacteristic
365C4#6385312yes—
366C4#6387411yescharacteristic
367C3—21no—
368C3#6887112yescomplemented
369C2—184no—
370C2#1059051012yes—
371C2#1059052912yes—
372C2#1059121911yescharacteristic
373C2#1059141611yescharacteristic
374C2#1059156211yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1823
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C3×#4529C2semidirect
5. #10589164C2semidirect
13. C4⋊C4×C3⋊D3C4semidirect
26. #4529D3semidirect
309. C32#1823semidirect
368. C3#68871semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
#105913252
C2×#635572
C3×#45292
#105891642
#688713