Finite Group Databasebeta

← #11773879

Subgroups — #11773879

Order 1152.

833 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 833 conjugacy classes of subgroups — too many to draw. Only its 106 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#10591159C212yesmaximal
3C3×#4528C212yesmaximal, complemented
4#10589148C212yesmaximal, complemented
5#68144—32nomaximal
6C22×C4×C3⋊D3C411yescharacteristic
7C22×C4×C3⋊D3C411yescharacteristic
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×C4⋊(C3⋊Dic3)C411yescharacteristic
11C2×#3750C411yescharacteristic
12C2×#3750C2211yescharacteristic
13C4⋊C4×C3⋊D3—22no—
14C4⋊C4×C3⋊D3—22no—
15C2×#3712—22no—
16C3×#830C2214yes—
17#63557—22no—
18C2×D3×C4⋊C4—32no—
19C2×D3×C4⋊C4—61no—
20#4726—34no—
21C3×#324—32no—
22#4528D312yescomplemented
23#4469—34no—
24C23×C3⋊D3C2×C411yescharacteristic
25C22×C32×C4C2×C411yescharacteristic
26C22×C32×C4C2×C411yescharacteristic
27C22×C32×C4C2311yescharacteristic
28C22×C3⋊Dic3C2×C411yescharacteristic
29C22×C3⋊Dic3C2×C411yescharacteristic
30C22×C3⋊Dic3C2×C411yescharacteristic
31C2×C4×C3⋊D3—21no—
32C2×C4×C3⋊D3—21no—
33C2×C4×C3⋊D3—22no—
34C2×C4×C3⋊D3—22no—
35C2×C4×C3⋊D3—21no—
36C2×C4×C3⋊D3—21no—
37C2×C4×C3⋊D3—42no—
38C2×C4×C3⋊D3—42no—
39C2×C4×C3⋊D3D412yes—
40C2×C4×C3⋊D3D412yes—
41C32×C4⋊C4—22no—
42C4⋊(C3⋊Dic3)—22no—
43#3750—22no—
44#3750—22no—
45C2×C3×C3⋊C8—24no—
46#3712—44no—
47#1463—91noSylow
48C22×C4×D3—32no—
49C22×C4×D3—32no—
50C22×C4×D3—32no—
51C22×C4×D3—61no—
52C22×C4×D3—61no—
53C22×C4×D3—61no—
54C2×C3×C4⋊C4—21no—
55C2×C3×C4⋊C4C2×D312yes—
56C2×C4⋊Dic3—32no—
57C2×C4⋊Dic3—61no—
58C2×Dic3⋊C4—32no—
59C2×Dic3⋊C4—32no—
60C2×Dic3⋊C4—61no—
61C2×Dic3⋊C4—61no—
62C2×ΓL(1,𝔽25)—64no—
63D3×C4⋊C4—64no—
64D3×C4⋊C4—64no—
65D3×C4⋊C4—64no—
66D3×C4⋊C4—64no—
67C3×C22⋊C8—34no—
68#830C2×D314yes—
69(C2×D3)⋊C8—64no—
70C23×C32C22×C411yescharacteristic
71C22×C3⋊D3—21no—
72C22×C3⋊D3—21no—
73C22×C3⋊D3—22no—
74C22×C3⋊D3—22no—
75C22×C3⋊D3C22⋊C411yescharacteristic
76C22×C3⋊D3C22⋊C411yescharacteristic
77C2×C32×C4—21no—
78C2×C32×C4—21no—
79C2×C32×C4—21no—
80C2×C32×C4—41no—
81C2×C32×C4—41no—
82C2×C32×C4M1612yescomplemented
83C2×C32×C4C2×D412yes—
84C2×C3⋊Dic3—21no—
85C2×C3⋊Dic3—21no—
86C2×C3⋊Dic3—21no—
87C2×C3⋊Dic3—41no—
88C2×C3⋊Dic3—41no—
89C2×C3⋊Dic3C22⋊C412yes—
90C2×C3⋊Dic3M1612yescomplemented
91C4×C3⋊D3—24no—
92C4×C3⋊D3—24no—
93C4×C3⋊D3—24no—
94C4×C3⋊D3—42no—
95C4×C3⋊D3—42no—
96C4×C3⋊D3—42no—
97C3×C3⋊C8—44no—
98C22×C4⋊C4—91no—
99#407—92no—
100#324—32no—
101#324—92no—
102C23×D3—32no—
103C23×D3—61no—
104C22×C3×C4—21no—
105C22×C3×C4—21no—
106C22×C3×C4—21no—
107C22×C3×C4C4×D312yes—
108C22×C3×C4C4×D312yes—
109C22×C3×C4C22×D312yes—
110C22×Dic3—32no—
111C22×Dic3—32no—
112C22×Dic3—32no—
113C22×Dic3—61no—
114C22×Dic3—61no—
115C22×Dic3—61no—
116C2×C4×D3—34no—
117C2×C4×D3—34no—
118C2×C4×D3—62no—
119C2×C4×D3—62no—
120C2×C4×D3—64no—
121C2×C4×D3—62no—
122C2×C4×D3—62no—
123C2×C4×D3—62no—
124C2×C4×D3—62no—
125C2×C4×D3—64no—
126C2×C4×D3—64no—
127C2×C4×D3—64no—
128C2×C4×D3—62no—
129C2×C4×D3—62no—
130C2×C4×D3—62no—
131C2×C4×D3—62no—
132C2×C4×D3—124no—
133C2×C4×D3—124no—
134C2×C4×D3—124no—
135C2×C4×D3—124no—
136C2×C3×C8—64no—
137C3×C4⋊C4—24no—
138C3×C4⋊C4—24no—
139C4⋊Dic3—64no—
140C4⋊Dic3—64no—
141Dic3⋊C4—64no—
142Dic3⋊C4—64no—
143Dic3⋊C4—64no—
144Dic3⋊C4—64no—
145C2×C3⋊C8—24no—
146ΓL(1,𝔽25)—128no—
147C22×C32—21no—
148C22×C32—21no—
149C22×C32C2×C22⋊C411yescharacteristic
150C22×C32C2×M1611yescharacteristic
151C22×C32C2×M1611yescharacteristic
152C2×C3⋊D3—24no—
153C2×C3⋊D3—24no—
154C2×C3⋊D3—21no—
155C2×C3⋊D3—21no—
156C2×C3⋊D3—21no—
157C2×C3⋊D3—21no—
158C2×C3⋊D3#9912yes—
159C2×C3⋊D3#10112yes—
160C32×C4—22no—
161C32×C4—22no—
162C32×C4—41no—
163C3⋊Dic3—22no—
164C3⋊Dic3—22no—
165C3⋊Dic3—41no—
166C23×C4—91no—
167C23×C4—91no—
168C23×C4—91no—
169C2×M16—182no—
170C2×C4⋊C4—91no—
171C2×C4⋊C4—91no—
172C2×C4⋊C4—91no—
173C2×C4⋊C4—182no—
174C2×C4⋊C4—182no—
175C2×C4⋊C4D3211yescharacteristic
176C22⋊C8—34no—
177C22⋊C8—182no—
178C23×C3—21no—
179C23×C3C2×C4×D312yes—
180C22×D3—32no—
181C22×D3—32no—
182C22×D3—61no—
183C22×D3—61no—
184C22×D3—64no—
185C22×D3—64no—
186C22×D3—62no—
187C22×D3—62no—
188C22×D3—64no—
189C22×D3—64no—
190C22×D3—62no—
191C22×D3—62no—
192C2×C3×C4—22no—
193C2×C3×C4—22no—
194C2×C3×C4—22no—
195C2×C3×C4—22no—
196C2×C3×C4—22no—
197C2×C3×C4—22no—
198C2×C3×C4—22no—
199C2×C3×C4—22no—
200C2×C3×C4—42no—
201C2×C3×C4—42no—
202C2×C3×C4—42no—
203C2×C3×C4—42no—
204C2×C3×C4ΓL(1,𝔽25)14yescomplemented
205C2×C3×C4D3×D414yes—
206C2×Dic3—34no—
207C2×Dic3—34no—
208C2×Dic3—62no—
209C2×Dic3—62no—
210C2×Dic3—62no—
211C2×Dic3—62no—
212C2×Dic3—62no—
213C2×Dic3—62no—
214C2×Dic3—62no—
215C2×Dic3—62no—
216C2×Dic3—122no—
217C2×Dic3—122no—
218C2×Dic3—122no—
219C2×Dic3—122no—
220C4×D3—68no—
221C4×D3—68no—
222C4×D3—68no—
223C4×D3—68no—
224C4×D3—68no—
225C4×D3—124no—
226C4×D3—124no—
227C4×D3—124no—
228C4×D3—124no—
229C4×D3—124no—
230C4×D3—124no—
231C4×D3—124no—
232C3×C8—124no—
233C3⋊C8—44no—
234C2×C32—21no—
235C2×C32—21no—
236C2×C32#40711yescharacteristic
237C2×C32C2×#9911yescharacteristic
238C2×C32C2×#10111yescharacteristic
239C3⋊D3—22no—
240C3⋊D3—22no—
241C24—91no—
242C22×C4—91no—
243C22×C4—91no—
244C22×C4—92no—
245C22×C4—92no—
246C22×C4—91no—
247C22×C4—182no—
248C22×C4—181no—
249C22×C4—181no—
250C22×C4—181no—
251C22×C4—181no—
252C22×C4—182no—
253C22×C4—362no—
254C22×C4—362no—
255C22×C4#62411yescharacteristic
256C22×C4#62411yescharacteristic
257C22×C4C2×D3211yescharacteristic
258M16—364no—
259C2×C8—64no—
260C4⋊C4—22no—
261C4⋊C4—182no—
262C4⋊C4—182no—
263C4⋊C4—182no—
264C22×C3—22no—
265C22×C3—22no—
266C22×C3—22no—
267C22×C3—22no—
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3D3×C22⋊C412yes—
272C22×C3C2×ΓL(1,𝔽25)12yes—
273C22×C3D3×M1612yes—
274C2×D3—34no—
275C2×D3—34no—
276C2×D3—62no—
277C2×D3—62no—
278C2×D3—62no—
279C2×D3—62no—
280C2×D3—62no—
281C2×D3—68no—
282C2×D3—68no—
283C2×D3—68no—
284C2×D3—68no—
285C2×D3—62no—
286C2×D3—62no—
287C2×D3—62no—
288C2×D3—62no—
289C2×D3—62no—
290C3×C4—24no—
291C3×C4—24no—
292C3×C4—24no—
293C3×C4—42no—
294C3×C4—42no—
295C3×C4—42no—
296Dic3—64no—
297Dic3—64no—
298Dic3—64no—
299Dic3—122no—
300Dic3—122no—
301Dic3—122no—
302C32#146311yescharacteristic, complemented, Sylow
303C23—91no—
304C23—91no—
305C23—182no—
306C23—182no—
307C23—181no—
308C23—181no—
309C23C2×#62411yescharacteristic
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—92no—
316C2×C4—92no—
317C2×C4—184no—
318C2×C4—184no—
319C2×C4—184no—
320C2×C4—181no—
321C2×C4—181no—
322C2×C4—181no—
323C2×C4—362no—
324C2×C4—362no—
325C2×C4—362no—
326C2×C4—361no—
327C2×C4—361no—
328C2×C4#371212yescomplemented
329C2×C4#381112yes—
330C8—124no—
331C2×C3—22no—
332C2×C3—22no—
333C2×C3—22no—
334C2×C3—22no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3#472612yes—
339C2×C3D3×#9912yes—
340C2×C3D3×#10112yes—
341D3—64no—
342D3—64no—
343D3—64no—
344D3—64no—
345C22—21no—
346C22—21no—
347C22—92no—
348C22—92no—
349C22—184no—
350C22—184no—
351C22—181no—
352C22—181no—
353C22—181no—
354C22—181no—
355C22#6381811yescharacteristic
356C22C2×#371211yescharacteristic
357C22#6397411yescharacteristic
358C4—22no—
359C4—22no—
360C4—41no—
361C4—182no—
362C4—182no—
363C4—361no—
364C3—21no—
365C3#6814412yescomplemented
366C2—21no—
367C2—21no—
368C2—182no—
369C2—182no—
370C2#1059115911yescharacteristic
371C2#1059152711yescharacteristic
372C2#1059163911yescharacteristic
subgroupG/H
centerC22#63974
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1463
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×#4528C2semidirect
4. #10589148C2semidirect
22. #4528D3semidirect
82. C2×C32×C4M16semidirect
90. C2×C3⋊Dic3M16semidirect
204. C2×C3×C4ΓL(1,𝔽25)semidirect
302. C32#1463semidirect
328. C2×C4#3712semidirect
365. C3#68144semidirect

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
#105911592
C3×#45282
#105891482
#681443