Finite Group Databasebeta

← #11794667

Subgroups — #11794667

Order 1152.

496 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 69 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×#63739C212yesmaximal
2#10591385C211yesmaximal, characteristic
3#10591359C211yesmaximal, characteristic, complemented
4#10590207C211yesmaximal, characteristic, complemented
5#10590075C212yesmaximal, complemented
6C22×#625C2211yescharacteristic
7C22×#622C2212yes—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C2×C3×(C2×D3)⋊C4—21no—
10C2×C3×C4⋊Dic3—21no—
11C2×#3724—21no—
12C2×#3724C2211yescharacteristic
13C2×#3724C2212yes—
14C2×(C2×D3)⋊Dic3—21no—
15#63739—24no—
16#4975—61no—
17#4957—61no—
18C23×C3×D3—21no—
19C22×C32×C4D411yescharacteristic
20C22×C3⋊Dic3D411yescharacteristic
21C22×C3⋊Dic3C2311yescharacteristic
22C22×C3×Dic3—22no—
23C22×C3×Dic3—21no—
24C2×#625—22no—
25C2×#625—22no—
26C2×#625—21no—
27C2×#625D412yes—
28C2×#622—22no—
29C2×#622—22no—
30C2×#622—22no—
31C4×C3⋊Dic3—22no—
32C3×(C2×D3)⋊C4—42no—
33C3×C4⋊Dic3—42no—
34#3724—22no—
35#3724—22no—
36#3724—22no—
37#3724—42no—
38(C2×D3)⋊Dic3—42no—
39#2071—91nomaximal, Sylow
40C22×#67—61no—
41C2×C3×C4⋊C4—61no—
42C2×C3×C22⋊C4—61no—
43C2×#217—61no—
44C2×(C2×D3)⋊C4—21no—
45C2×(C2×D3)⋊C4—61no—
46C2×C4⋊Dic3—21no—
47C2×Dic3⋊C4—61no—
48C2×Dic3⋊C4—62no—
49C2×Dic3⋊C4—62no—
50C2×C4×Dic3—61no—
51C2×C4×Dic3—61no—
52C23×C32C2×D411yescharacteristic
53C22×C3×D3—22no—
54C22×C3×D3—41no—
55C22×C3×D3—41no—
56C22×C3×D3—41no—
57C22×C3×D3—41no—
58C22×C3×D3—41no—
59C22×C3×D3—41no—
60C2×C32×C4—21no—
61C2×C32×C4—21no—
62C2×C32×C4SD1612yes—
63C2×C3⋊Dic3—21no—
64C2×C3⋊Dic3—21no—
65C2×C3⋊Dic3D812yes—
66C2×C3⋊Dic3C2×D411yescharacteristic
67C2×C3⋊Dic3#4112yes—
68C2×C3⋊Dic3#4112yes—
69C2×C3⋊Dic3#4111yescharacteristic
70C2×C3×Dic3—42no—
71C2×C3×Dic3—41no—
72C2×C3×Dic3—41no—
73C2×C3×Dic3—42no—
74C2×C3×Dic3—41no—
75C2×C3×Dic3—42no—
76#625—24no—
77#625—42no—
78#622—42no—
79C2×#102—92no—
80#390—91no—
81#384—91no—
82#340—92no—
83#336—91no—
84C24×C3—61no—
85C23×D3—21no—
86C22×C3×C4—21no—
87C22×C3×C4—21no—
88C22×C3×C4—62no—
89C22×C3×C4—61no—
90C2×#67—62no—
91C2×#67—62no—
92C2×#67—122no—
93C2×#67—122no—
94C22×Dic3—22no—
95C22×Dic3—21no—
96C22×Dic3—61no—
97C22×Dic3—61no—
98C22×Dic3—61no—
99C22×Dic3—61no—
100C3×C4⋊C4—122no—
101C3×C22⋊C4—122no—
102#217—122no—
103(C2×D3)⋊C4—42no—
104(C2×D3)⋊C4—122no—
105C4⋊Dic3—42no—
106Dic3⋊C4—122no—
107Dic3⋊C4—122no—
108Dic3⋊C4—122no—
109Dic3⋊C4—124no—
110C4×Dic3—64no—
111C4×Dic3—122no—
112C22×C32#12111yescharacteristic
113C22×C32#12311yescharacteristic
114C22×C32#12411yescharacteristic
115C22×C32C2×D811yescharacteristic
116C22×C32C2×SD1611yescharacteristic
117C22×C32AGL(1,ℤ/8)11yescharacteristic
118C22×C32#13711yescharacteristic
119C2×C3×D3—42no—
120C2×C3×D3—42no—
121C2×C3×D3—42no—
122C2×C3×D3—81no—
123C2×C3×D3—81no—
124C2×C3×D3—81no—
125C2×C3×D3—81no—
126C32×C4—22no—
127C3⋊Dic3—22no—
128C3⋊Dic3#12312yes—
129C3⋊Dic3#12612yes—
130C3×Dic3—82no—
131C3×Dic3—81no—
132C22×D4—91no—
133C22×C8—92no—
134C2×C4⋊C4—61no—
135C2×C4⋊C4—91no—
136C2×C4⋊C4—92no—
137C2×C4⋊C4—181no—
138C2×C22⋊C4—61no—
139C2×C22⋊C4—181no—
140C2×C42—91no—
141#102—184no—
142C23×C3—21no—
143C23×C3—21no—
144C23×C3—62no—
145C23×C3—121no—
146C23×C3—121no—
147C23×C3—121no—
148C23×C3—121no—
149C23×C3—121no—
150C23×C3—121no—
151C22×D3—22no—
152C22×D3—41no—
153C22×D3—41no—
154C22×D3—41no—
155C22×D3—41no—
156C22×D3—41no—
157C22×D3—41no—
158C2×C3×C4—22no—
159C2×C3×C4—22no—
160C2×C3×C4—22no—
161C2×C3×C4—22no—
162C2×C3×C4—41no—
163C2×C3×C4—41no—
164C2×C3×C4—121no—
165C2×C3×C4—122no—
166C2×C3×C4—122no—
167C2×C3×C4—121no—
168C2×C3×C4—121no—
169C2×C3×C4—122no—
170#67—124no—
171#67—124no—
172C2×Dic3—41no—
173C2×Dic3—42no—
174C2×Dic3—42no—
175C2×Dic3—42no—
176C2×Dic3—41no—
177C2×Dic3—41no—
178C2×Dic3—62no—
179C2×Dic3—61no—
180C2×Dic3—61no—
181C2×Dic3—62no—
182C2×Dic3—62no—
183C2×Dic3—61no—
184C2×Dic3—62no—
185C2×Dic3—62no—
186C2×Dic3—61no—
187C2×Dic3—62no—
188C2×Dic3—62no—
189C2×Dic3—62no—
190C2×Dic3—121no—
191C2×Dic3—121no—
192C2×C32#39711yescharacteristic
193C2×C32#45911yescharacteristic
194C2×C32#46111yescharacteristic
195C2×C32#48011yescharacteristic
196C2×C32#48111yescharacteristic
197C2×C32#48611yescharacteristic
198C2×C32#48911yescharacteristic
199C3×D3—82no—
200C24—61no—
201C2×D4—92no—
202C2×D4—182no—
203C2×D4—182no—
204C2×D4—181no—
205C22×C4—61no—
206C22×C4—62no—
207C22×C4—91no—
208C22×C4—91no—
209C22×C4GO+(4,𝔽2)11yescharacteristic
210C2×C8—182no—
211C2×C8—182no—
212C2×C8—182no—
213C4⋊C4—122no—
214C4⋊C4—182no—
215C4⋊C4—182no—
216C4⋊C4—182no—
217C4⋊C4—362no—
218C22⋊C4—122no—
219C22⋊C4—362no—
220C42—182no—
221C22×C3—21no—
222C22×C3—21no—
223C22×C3—21no—
224C22×C3—21no—
225C22×C3—21no—
226C22×C3—21no—
227C22×C3—21no—
228C22×C3—21no—
229C22×C3—21no—
230C22×C3—21no—
231C22×C3—21no—
232C22×C3—21no—
233C22×C3—21no—
234C22×C3—21no—
235C22×C3—122no—
236C22×C3—122no—
237C22×C3—122no—
238C22×C3—241no—
239C22×C3—241no—
240C22×C3—241no—
241C22×C3—241no—
242C2×D3—42no—
243C2×D3—42no—
244C2×D3—42no—
245C2×D3—81no—
246C2×D3—81no—
247C2×D3—81no—
248C2×D3—81no—
249C3×C4—24no—
250C3×C4—42no—
251C3×C4—241no—
252C3×C4—242no—
253Dic3—62no—
254Dic3—62no—
255Dic3—62no—
256Dic3—62no—
257Dic3—64no—
258Dic3—81no—
259Dic3—82no—
260Dic3—122no—
261C32#207111yescharacteristic, complemented, Sylow
262C23—62no—
263C23—121no—
264C23—121no—
265C23—121no—
266C23—121no—
267C23—121no—
268C23—121no—
269C23C2×GO+(4,𝔽2)11yescharacteristic
270D4—184no—
271D4—362no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—92no—
275C2×C4—91no—
276C2×C4—91no—
277C2×C4—92no—
278C2×C4—92no—
279C2×C4—121no—
280C2×C4—121no—
281C2×C4—122no—
282C2×C4—122no—
283C2×C4—122no—
284C2×C4—121no—
285C2×C4—181no—
286C2×C4—181no—
287C2×C4#377512yes—
288C8—362no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—21no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—242no—
304D3—82no—
305C22—122no—
306C22—122no—
307C22—122no—
308C22—241no—
309C22—241no—
310C22—241no—
311C22—241no—
312C22#6422111yescharacteristic
313C22#6422511yescharacteristic
314C22#6422611yescharacteristic
315C22#6423011yescharacteristic
316C22#6423311yescharacteristic
317C22#6423611yescharacteristic
318C22C2×#377511yescharacteristic
319C4—22no—
320C4—92no—
321C4—92no—
322C4—182no—
323C4—241no—
324C4—242no—
325C3—21no—
326C3—21no—
327C2—242no—
328C2#1059335811yescharacteristic
329C2#1059336611yescharacteristic
330C2#1059336811yescharacteristic
331C2#1059340411yescharacteristic
332C2#1059342611yescharacteristic
333C2#1059343711yescharacteristic
334C2#1059349711yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutator, cosocleC22×C3⋊Dic3C23
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC22×#625C22
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2071
LCSG ▷ C22×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. #10591359C2semidirect
4. #10590207C2semidirect
5. #10590075C2semidirect
261. C32#2071semidirect

Maximal subgroups

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

subgroupindex
C2×#637392
#105913852
#105913592
#105902072
#105900752
#20719