Finite Group Databasebeta

← #11794656

Subgroups — #11794656

Order 1152.

677 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 677 conjugacy classes of subgroups — too many to draw. Only its 146 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#10592920C211yesmaximal, characteristic
2C2×C3×#832C212yesmaximal
3#10591359C211yesmaximal, characteristic, complemented
4#10589164C212yesmaximal, complemented
5#10589156C211yesmaximal, characteristic, complemented
6#70165—32nomaximal
7C22×C32×D4C2211yescharacteristic
8C2×#3757—21no—
9C2×#3757—21no—
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C3×C4⋊Dic3C2212yes—
13C22×C3×C3⋊C8C2212yes—
14C2×#3724—21no—
15C2×#3724—21no—
16C3×#832—24no—
17C2×C3×#102—32no—
18#5221—32no—
19#5221—61no—
20C2×#832D312yes—
21#4975—32no—
22#4551—32no—
23#4550—32no—
24#4529—32no—
25C24×C32—21no—
26C2×C32×D4—22no—
27C2×C32×D4—22no—
28C2×C32×D4—21no—
29C2×C32×D4D412yes—
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3—21no—
32C22×C3⋊Dic3D411yescharacteristic
33C22×C3⋊Dic3D411yescharacteristic
34C22×C3×Dic3—22no—
35#3757—42no—
36#3757—42no—
37C4⋊(C3⋊Dic3)—22no—
38C4×C3⋊Dic3—22no—
39C3×C4⋊Dic3—22no—
40C3×C4⋊Dic3—22no—
41C2×C3×C3⋊C8—22no—
42C2×C3×C3⋊C8—22no—
43C2×C3×C3⋊C8—22no—
44#3724—42no—
45#3724—42no—
46#2071—91noSylow
47C22×C3×D4—21no—
48C22×C3×D4C2×D312yes—
49C22×C3×C8—32no—
50C2×C3×C4⋊C4—32no—
51C2×#217—62no—
52C2×#217—62no—
53C2×#217—62no—
54C2×#217—62no—
55C2×C4⋊Dic3—32no—
56C2×C4⋊Dic3—61no—
57C2×C4⋊Dic3C2×D312yes—
58C2×Dic3⋊C4—62no—
59C2×Dic3⋊C4—62no—
60C2×C4×Dic3—32no—
61C2×C4×Dic3—61no—
62C22×C3⋊C8C2×D312yes—
63C3×#102—64no—
64#832—24no—
65C23×C32—22no—
66C23×C32—41no—
67C23×C32—41no—
68C23×C32—41no—
69C23×C32—41no—
70C23×C32—41no—
71C23×C32—41no—
72C23×C32C2×D411yescharacteristic
73C32×D4—24no—
74C32×D4—42no—
75C2×C32×C4C2×D411yescharacteristic
76C2×C32×C4#4112yes—
77C2×C32×C4#4112yes—
78C2×C32×C4#4111yescharacteristic
79C2×C3⋊Dic3—21no—
80C2×C3⋊Dic3—21no—
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—41no—
84C2×C3⋊Dic3—41no—
85C2×C3⋊Dic3—41no—
86C2×C3⋊Dic3D812yes—
87C2×C3⋊Dic3SD1612yes—
88C2×C3×Dic3—42no—
89C2×C3×Dic3—42no—
90C2×C3×Dic3—42no—
91C3×C3⋊C8—42no—
92C2×#102—32no—
93#390—91no—
94#384—91no—
95#340—92no—
96#336—91no—
97C24×C3—22no—
98C24×C3—22no—
99C2×C3×D4—22no—
100C2×C3×D4—22no—
101C2×C3×D4—22no—
102C2×C3×D4—22no—
103C2×C3×D4—22no—
104C2×C3×D4—22no—
105C2×C3×D4—22no—
106C2×C3×D4—42no—
107C2×C3×D4—42no—
108C2×C3×D4#6714yes—
109C22×C3×C4—21no—
110C22×C3×C4—62no—
111C22×C3×C4C22×D312yes—
112C22×Dic3—22no—
113C22×Dic3—32no—
114C22×Dic3—32no—
115C22×Dic3—61no—
116C22×Dic3—61no—
117C22×Dic3—62no—
118C22×Dic3—62no—
119C2×C3×C8—62no—
120C2×C3×C8—62no—
121C2×C3×C8—62no—
122C3×C4⋊C4—62no—
123C3×C4⋊C4—62no—
124#217—124no—
125#217—124no—
126#217—124no—
127#217—124no—
128C4⋊Dic3—22no—
129C4⋊Dic3—22no—
130C4⋊Dic3—62no—
131C4⋊Dic3—62no—
132C4⋊Dic3—122no—
133Dic3⋊C4—124no—
134Dic3⋊C4—124no—
135C4×Dic3—62no—
136C4×Dic3—62no—
137C4×Dic3—122no—
138C2×C3⋊C8—22no—
139C2×C3⋊C8—22no—
140C2×C3⋊C8—22no—
141C22×C32—42no—
142C22×C32—42no—
143C22×C32—42no—
144C22×C32—81no—
145C22×C32—81no—
146C22×C32—81no—
147C22×C32—81no—
148C22×C32#12111yescharacteristic
149C22×C32#12311yescharacteristic
150C22×C32#12411yescharacteristic
151C22×C32C2×D811yescharacteristic
152C22×C32C2×SD1611yescharacteristic
153C22×C32AGL(1,ℤ/8)11yescharacteristic
154C22×C32#13711yescharacteristic
155C32×C4#12312yes—
156C32×C4#12612yes—
157C3⋊Dic3—22no—
158C3⋊Dic3—22no—
159C3⋊Dic3—81no—
160C3×Dic3—82no—
161C22×D4D3211yescharacteristic
162C22×C8—32no—
163C2×C4⋊C4—32no—
164C2×C4⋊C4—91no—
165C2×C4⋊C4—181no—
166C2×C4⋊C4—181no—
167C2×C22⋊C4—181no—
168C2×C22⋊C4—181no—
169C2×C42—91no—
170#102—64no—
171C23×C3—24no—
172C23×C3—24no—
173C23×C3—21no—
174C23×C3—42no—
175C23×C3—42no—
176C23×C3—42no—
177C23×C3—42no—
178C23×C3—42no—
179C23×C3—42no—
180C23×C3—42no—
181C23×C3—42no—
182C23×C3—42no—
183C23×C3—42no—
184C23×C3—42no—
185C23×C3—42no—
186C23×C3D3×D412yes—
187C3×D4—24no—
188C3×D4—24no—
189C3×D4—44no—
190C3×D4—44no—
191C3×D4—42no—
192C3×D4—42no—
193C2×C3×C4—22no—
194C2×C3×C4—22no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—122no—
198C2×C3×C4—122no—
199C2×C3×C4—122no—
200C2×C3×C4#23512yes—
201C2×C3×C4#23512yes—
202C2×C3×C4#23712yes—
203C2×C3×C4#23712yes—
204C2×C3×C4#23712yes—
205C2×C3×C4C2×#6712yes—
206C2×Dic3—34no—
207C2×Dic3—34no—
208C2×Dic3—42no—
209C2×Dic3—42no—
210C2×Dic3—42no—
211C2×Dic3—62no—
212C2×Dic3—62no—
213C2×Dic3—62no—
214C2×Dic3—62no—
215C2×Dic3—62no—
216C2×Dic3—62no—
217C2×Dic3—121no—
218C2×Dic3—121no—
219C2×Dic3—121no—
220C2×Dic3—121no—
221C2×Dic3—122no—
222C2×Dic3—122no—
223C2×Dic3—122no—
224C2×Dic3—122no—
225C2×Dic3—122no—
226C2×Dic3—122no—
227C3×C8—122no—
228C3⋊C8—42no—
229C2×C32—82no—
230C2×C32#39711yescharacteristic
231C2×C32#45911yescharacteristic
232C2×C32#46111yescharacteristic
233C2×C32#48011yescharacteristic
234C2×C32#48111yescharacteristic
235C2×C32#48611yescharacteristic
236C2×C32#48911yescharacteristic
237C24—21no—
238C2×D4—22no—
239C2×D4—22no—
240C2×D4—21no—
241C2×D4#62512yes—
242C22×C4—62no—
243C22×C4—91no—
244C22×C4—91no—
245C22×C4—181no—
246C22×C4C2×D3211yescharacteristic
247C2×C8—62no—
248C2×C8—62no—
249C2×C8—62no—
250C4⋊C4—62no—
251C4⋊C4—62no—
252C4⋊C4—182no—
253C4⋊C4—362no—
254C4⋊C4—362no—
255C22⋊C4—362no—
256C22⋊C4—362no—
257C42—182no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—44no—
266C22×C3—44no—
267C22×C3—44no—
268C22×C3—44no—
269C22×C3—44no—
270C22×C3—44no—
271C22×C3—82no—
272C22×C3—82no—
273C22×C3—82no—
274C22×C3—82no—
275C22×C3—82no—
276C22×C3—82no—
277C22×C3—82no—
278C22×C3—82no—
279C22×C3#88312yes—
280C22×C3#88512yes—
281C22×C3D3×D812yes—
282C22×C3#91112yes—
283C22×C3D3×SD1612yes—
284C22×C3#91512yes—
285C22×C3#93912yes—
286C3×C4—22no—
287C3×C4—22no—
288C3×C4—242no—
289C3×C4#87912yes—
290C3×C4#87912yes—
291C3×C4#92912yes—
292C3×C4#93512yes—
293Dic3—64no—
294Dic3—64no—
295Dic3—82no—
296Dic3—122no—
297Dic3—122no—
298Dic3—242no—
299Dic3—242no—
300C32#207111yescharacteristic, complemented, Sylow
301C23—22no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23#381111yescharacteristic
309D4—24no—
310D4—42no—
311C2×C4—92no—
312C2×C4—92no—
313C2×C4—122no—
314C2×C4—122no—
315C2×C4—122no—
316C2×C4—181no—
317C2×C4—181no—
318C2×C4—181no—
319C2×C4—181no—
320C2×C4—361no—
321C2×C4—361no—
322C2×C4—361no—
323C2×C4#380412yes—
324C2×C4#380412yes—
325C2×C4#380511yescharacteristic
326C2×C4C2×#62511yescharacteristic
327C8—122no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—84no—
336C2×C3—84no—
337C2×C3#476012yes—
338C2×C3#476512yes—
339C2×C3#477412yes—
340C2×C3#477712yes—
341C2×C3#495212yes—
342C2×C3#515012yes—
343C2×C3#516212yes—
344C22—42no—
345C22—42no—
346C22—42no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22#6392611yescharacteristic
352C22#6392711yescharacteristic
353C22#6393011yescharacteristic
354C22#6393111yescharacteristic
355C22#6395311yescharacteristic
356C22#6397511yescharacteristic
357C22#6398011yescharacteristic
358C4—182no—
359C4—182no—
360C4—242no—
361C4—721no—
362C4#6395612yes—
363C4#6396112yes—
364C3—21no—
365C3#7016512yescomplemented
366C2—82no—
367C2#1059140211yescharacteristic
368C2#1059141711yescharacteristic
369C2#1059141911yescharacteristic
370C2#1059148611yescharacteristic
371C2#1059149611yescharacteristic
372C2#1059149711yescharacteristic
373C2#1059169411yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32#2071
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
3. #10591359C2semidirect
4. #10589164C2semidirect
5. #10589156C2semidirect
300. C32#2071semidirect
365. C3#70165semidirect

Maximal subgroups

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

subgroupindex
#105929202
C2×C3×#8322
#105913592
#105891642
#105891562
#701653