Finite Group Databasebeta

← #11785795

Subgroups — #11785795

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#68872—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—44no—
36C2×C4×C3⋊D3C2×C412yes—
37C2×C4×C3⋊D3D412yes—
38C22×C3×Dic3—22no—
39C32×C4⋊C4—21no—
40C32×C4⋊C4C2×C412yes—
41C4⋊(C3⋊Dic3)—21no—
42C4⋊(C3⋊Dic3)C2×C412yes—
43#3750—24no—
44C3×C4⋊Dic3—22no—
45C3×C4⋊Dic3—22no—
46C2×C3×C3⋊C8—22no—
47C2×C3×C3⋊C8—22no—
48C2×C3×C3⋊C8—22no—
49#3722—42no—
50#1824—91noSylow
51C22×C4×D3—32no—
52C22×C4×D3—61no—
53C22×C4×D3—62no—
54C22×C4×D3—62no—
55C22×C3×C8—32no—
56C2×C3×C4⋊C4—21no—
57C2×C3×C4⋊C4—32no—
58C2×C3×C4⋊C4C2×D312yes—
59C2×(C2×D3)⋊C4—62no—
60C2×C4⋊Dic3—32no—
61C2×C4⋊Dic3—61no—
62C2×C4⋊Dic3C2×D312yes—
63C2×Dic3⋊C4—62no—
64C2×Dic3⋊C4—62no—
65C22×C3⋊C8C2×D312yes—
66D3×C4⋊C4—38no—
67D3×C4⋊C4—64no—
68D3×C4⋊C4—64no—
69D3×C4⋊C4—64no—
70C3⋊#95—62no—
71(C2×D3)⋊C8—64no—
72C23×C32C2×D411yescharacteristic
73C22×C3⋊D3—22no—
74C22×C3⋊D3—22no—
75C22×C3⋊D3C22⋊C412yes—
76C22×C3⋊D3SD1612yes—
77C22×C3⋊D3Q1612yes—
78C2×C32×C4—22no—
79C2×C32×C4—42no—
80C2×C32×C4C22×C411yescharacteristic
81C2×C32×C4C2×D411yescharacteristic
82C2×C32×C4#4112yes—
83C2×C32×C4#4112yes—
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3—42no—
87C2×C3⋊Dic3C22⋊C412yes—
88C4×C3⋊D3—22no—
89C4×C3⋊D3—22no—
90C4×C3⋊D3—24no—
91C4×C3⋊D3—48no—
92C2×C3×Dic3—42no—
93C2×C3×Dic3—42no—
94C2×C3×Dic3—42no—
95C3×C3⋊C8—42no—
96C22×C4⋊C4—91no—
97C2×C22⋊C8—91no—
98#380—91no—
99#340—32no—
100#340—92no—
101C23×D3—32no—
102C23×D3—61no—
103C22×C3×C4—22no—
104C22×C3×C4—22no—
105C22×C3×C4—21no—
106C22×C3×C4—62no—
107C22×C3×C4C22×D312yes—
108C22×Dic3—22no—
109C22×Dic3—32no—
110C22×Dic3—61no—
111C22×Dic3—62no—
112C22×Dic3—62no—
113C2×C4×D3—34no—
114C2×C4×D3—34no—
115C2×C4×D3—62no—
116C2×C4×D3—62no—
117C2×C4×D3—64no—
118C2×C4×D3—64no—
119C2×C4×D3—62no—
120C2×C4×D3—62no—
121C2×C4×D3—62no—
122C2×C4×D3—62no—
123C2×C4×D3—68no—
124C2×C4×D3—68no—
125C2×C4×D3—128no—
126C2×C4×D3—124no—
127C2×C4×D3—124no—
128C2×C3×C8—62no—
129C2×C3×C8—62no—
130C2×C3×C8—62no—
131C3×C4⋊C4—22no—
132C3×C4⋊C4—22no—
133C3×C4⋊C4—22no—
134C3×C4⋊C4—62no—
135C3×C4⋊C4—62no—
136C3×C4⋊C4C4×D314yes—
137(C2×D3)⋊C4—124no—
138C4⋊Dic3—22no—
139C4⋊Dic3—22no—
140C4⋊Dic3—34no—
141C4⋊Dic3—62no—
142C4⋊Dic3—62no—
143C4⋊Dic3—62no—
144Dic3⋊C4—68no—
145Dic3⋊C4—68no—
146C2×C3⋊C8—22no—
147C2×C3⋊C8—22no—
148C2×C3⋊C8—22no—
149C22×C32C2×C22⋊C411yescharacteristic
150C22×C32#12312yes—
151C22×C32C2×SD1611yescharacteristic
152C22×C32C2×Q1611yescharacteristic
153C22×C32AGL(1,ℤ/8)12yes—
154C2×C3⋊D3—22no—
155C2×C3⋊D3—22no—
156C2×C3⋊D3—24no—
157C2×C3⋊D3—24no—
158C2×C3⋊D3#10314yes—
159C32×C4—42no—
160C32×C4#11711yescharacteristic
161C32×C4#11711yescharacteristic
162C32×C4#12312yes—
163C3⋊Dic3—22no—
164C3⋊Dic3—42no—
165C3×Dic3—82no—
166C23×C4—91no—
167C23×C4—181no—
168C22×C8—32no—
169C2×C4⋊C4—32no—
170C2×C4⋊C4—91no—
171C2×C4⋊C4—94no—
172C2×C4⋊C4—182no—
173C2×C4⋊C4—181no—
174C2×C4⋊C4D3211yescharacteristic
175C2×C22⋊C4—181no—
176C22⋊C8—182no—
177#95—181no—
178C23×C3—21no—
179C23×C3D3×D412yes—
180C22×D3—34no—
181C22×D3—34no—
182C22×D3—34no—
183C22×D3—62no—
184C22×D3—62no—
185C22×D3—62no—
186C22×D3—64no—
187C22×D3—64no—
188C22×D3—62no—
189C22×D3—62no—
190C22×D3—62no—
191C22×D3—62no—
192C2×C3×C4—24no—
193C2×C3×C4—24no—
194C2×C3×C4—22no—
195C2×C3×C4—22no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—44no—
199C2×C3×C4—42no—
200C2×C3×C4—42no—
201C2×C3×C4—122no—
202C2×C3×C4—122no—
203C2×C3×C4—122no—
204C2×C3×C4C2×C4×D312yes—
205C2×C3×C4#23512yes—
206C2×C3×C4#23512yes—
207C2×C3×C4D3×D412yes—
208C2×C3×C4#23712yes—
209C2×C3×C4#23912yes—
210C2×Dic3—34no—
211C2×Dic3—42no—
212C2×Dic3—42no—
213C2×Dic3—42no—
214C2×Dic3—62no—
215C2×Dic3—64no—
216C2×Dic3—62no—
217C2×Dic3—62no—
218C2×Dic3—64no—
219C2×Dic3—64no—
220C2×Dic3—124no—
221C2×Dic3—122no—
222C2×Dic3—122no—
223C4×D3—64no—
224C4×D3—68no—
225C4×D3—64no—
226C4×D3—64no—
227C4×D3—64no—
228C4×D3—64no—
229C4×D3—64no—
230C4×D3—1216no—
231C4×D3—1216no—
232C3×C8—122no—
233C3⋊C8—42no—
234C2×C32#38111yescharacteristic
235C2×C32C2×#10311yescharacteristic
236C2×C32#41811yescharacteristic
237C2×C32#48112yes—
238C2×C32#48412yes—
239C3⋊D3—24no—
240C24—91no—
241C22×C4—21no—
242C22×C4—62no—
243C22×C4—91no—
244C22×C4—92no—
245C22×C4—92no—
246C22×C4—184no—
247C22×C4—182no—
248C22×C4—182no—
249C22×C4—181no—
250C22×C4—364no—
251C22×C4C2×D3211yescharacteristic
252C2×C8—62no—
253C2×C8—62no—
254C2×C8—62no—
255C4⋊C4—21no—
256C4⋊C4—62no—
257C4⋊C4—62no—
258C4⋊C4—92no—
259C4⋊C4—184no—
260C4⋊C4—181no—
261C4⋊C4#62412yes—
262C22⋊C4—362no—
263C22×C3—22no—
264C22×C3—22no—
265C22×C3—21no—
266C22×C3—21no—
267C22×C3—21no—
268C22×C3D3×C22⋊C412yes—
269C22×C3#88312yes—
270C22×C3#89412yes—
271C22×C3#91112yes—
272C22×C3D3×SD1612yes—
273C22×C3#91412yes—
274C22×C3D3×Q1612yes—
275C2×D3—38no—
276C2×D3—64no—
277C2×D3—64no—
278C2×D3—64no—
279C2×D3—68no—
280C2×D3—68no—
281C2×D3—64no—
282C2×D3—64no—
283C2×D3—64no—
284C2×D3—64no—
285C2×D3—64no—
286C2×D3—64no—
287C3×C4—21no—
288C3×C4—22no—
289C3×C4—21no—
290C3×C4—44no—
291C3×C4—44no—
292C3×C4—242no—
293C3×C4#87212yes—
294C3×C4#88312yes—
295C3×C4#89212yes—
296C3×C4#89412yes—
297Dic3—64no—
298Dic3—64no—
299Dic3—82no—
300Dic3—124no—
301Dic3—124no—
302C32#182411yescharacteristic, complemented, Sylow
303C23—92no—
304C23—92no—
305C23—92no—
306C23—182no—
307C23—182no—
308C23#381111yescharacteristic
309C2×C4—22no—
310C2×C4—42no—
311C2×C4—92no—
312C2×C4—122no—
313C2×C4—122no—
314C2×C4—122no—
315C2×C4—182no—
316C2×C4—182no—
317C2×C4—184no—
318C2×C4—182no—
319C2×C4—182no—
320C2×C4—368no—
321C2×C4—362no—
322C2×C4#379612yes—
323C2×C4#379812yes—
324C2×C4C2×#62411yescharacteristic
325C2×C4#381111yescharacteristic
326C8—122no—
327C2×C3—22no—
328C2×C3—22no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3#466412yes—
333C2×C3#477012yes—
334C2×C3#477712yes—
335C2×C3D3×#10312yes—
336C2×C3#481112yes—
337C2×C3#486312yes—
338C2×C3#488412yes—
339D3—68no—
340D3—68no—
341C22—94no—
342C22—184no—
343C22—184no—
344C22—182no—
345C22—182no—
346C22#6385312yes—
347C22#6393712yes—
348C22#6394011yescharacteristic
349C22#6394411yescharacteristic
350C22#6397411yescharacteristic
351C4—42no—
352C4—182no—
353C4—242no—
354C4—362no—
355C4#6384911yescharacteristic
356C4#6385312yes—
357C4#6387411yescharacteristic
358C3—21no—
359C3#6887212yescomplemented
360C2—184no—
361C2#1059051112yes—
362C2#1059052812yes—
363C2#1059121911yescharacteristic
364C2#1059142611yescharacteristic
365C2#1059155211yescharacteristic
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#1824
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
302. C32#1824semidirect
359. C3#68872semidirect

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
#688723