Finite Group Databasebeta

← #11786444

Subgroups — #11786444

Order 1152.

686 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 686 conjugacy classes of subgroups — too many to draw. Only its 91 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×#63900C211yesmaximal, characteristic
2C2×#63778C211yesmaximal, characteristic
3C2×#63743C212yesmaximal, complemented
4#10591355C211yesmaximal, characteristic
5#10590075C212yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C22×#624—21no—
8C22×#622C2212yes—
9C2×C3×C4⋊Dic3—21no—
10C2×#3724C2211yescharacteristic
11C2×#3724C2211yescharacteristic
12C2×#3724C2212yes—
13C2×#3722—21no—
14#63900—24no—
15#63778C414yescomplemented
16#63743—24no—
17C3×C3⋊#95—21no—
18C2×D3×C4⋊C4—61no—
19#4667—61no—
20C23×C3⋊D3D411yescharacteristic
21C22×C32×C4D411yescharacteristic
22C22×C3⋊Dic3C2311yescharacteristic
23C2×C4×C3⋊D3—22no—
24C2×C4×C3⋊D3—22no—
25C2×C4×C3⋊D3C2×C412yes—
26C2×C4×C3⋊D3Q812yes—
27C22×C3×Dic3—22no—
28C22×C3×Dic3—21no—
29C22×C3×Dic3—21no—
30C2×#624—24no—
31C2×#624—42no—
32C2×#624—42no—
33C2×#622—22no—
34C2×#622—22no—
35C2×#622C2×C414yescomplemented
36C3×C4⋊Dic3—24no—
37#3724—22no—
38#3724—22no—
39#3724—22no—
40#3724D414yes—
41#3722—42no—
42#1852—91nomaximal, Sylow
43C22×C4×D3—61no—
44C22×C4×D3—61no—
45C22×C4×D3—62no—
46C2×C3×C4⋊C4—61no—
47C2×(C2×D3)⋊C4—61no—
48C2×(C2×D3)⋊C4—61no—
49C2×C4⋊Dic3—21no—
50C2×Dic3⋊C4—62no—
51C2×Dic3⋊C4—61no—
52C2×Dic3⋊C4—61no—
53D3×C4⋊C4—68no—
54C3×#95—61no—
55C3⋊#95—21no—
56C23×C32C2×D411yescharacteristic
57C22×C3⋊D3—21no—
58C22×C3⋊D3—21no—
59C22×C3⋊D3—21no—
60C22×C3⋊D3—21no—
61C22×C3⋊D3C4⋊C412yes—
62C22×C3⋊D3D812yes—
63C22×C3⋊D3Q1612yes—
64C2×C32×C4—21no—
65C2×C32×C4—21no—
66C2×C32×C4C4⋊C412yes—
67C2×C3⋊Dic3C22×C411yescharacteristic
68C2×C3⋊Dic3C2×D412yes—
69C2×C3⋊Dic3C2×Q811yescharacteristic
70C2×C3⋊Dic3#4112yes—
71C4×C3⋊D3—24no—
72C4×C3⋊D3—24no—
73C2×C3×Dic3—24no—
74C2×C3×Dic3—42no—
75C2×C3×Dic3—42no—
76C2×C3×Dic3—41no—
77C2×C3×Dic3—41no—
78C2×C3×Dic3—41no—
79C2×C3×Dic3—41no—
80C2×C3×Dic3—41no—
81C2×C3×Dic3—41no—
82#624—48no—
83#622—24no—
84C22×C4⋊C4—91no—
85C2×#107—92no—
86C2×C22⋊C8—91no—
87#380—91no—
88#340—92no—
89C23×D3—61no—
90C23×D3—61no—
91C22×C3×C4—21no—
92C22×C3×C4—21no—
93C22×C3×C4—62no—
94C22×C3×C4—61no—
95C22×C3×C4—61no—
96C22×Dic3—22no—
97C22×Dic3—21no—
98C22×Dic3—21no—
99C22×Dic3—61no—
100C22×Dic3—61no—
101C2×C4×D3—62no—
102C2×C4×D3—62no—
103C2×C4×D3—62no—
104C2×C4×D3—62no—
105C2×C4×D3—64no—
106C2×C4×D3—64no—
107C2×C4×D3—68no—
108C2×C4×D3—122no—
109C2×C4×D3—122no—
110C2×C4×D3—124no—
111C2×C4×D3—124no—
112C3×C4⋊C4—64no—
113(C2×D3)⋊C4—122no—
114(C2×D3)⋊C4—122no—
115C4⋊Dic3—24no—
116Dic3⋊C4—64no—
117Dic3⋊C4—64no—
118Dic3⋊C4—122no—
119Dic3⋊C4—122no—
120C22×C32C2×C4⋊C411yescharacteristic
121C22×C32#12011yescharacteristic
122C22×C32#12311yescharacteristic
123C22×C32C2×D811yescharacteristic
124C22×C32C2×Q1611yescharacteristic
125C22×C32AGL(1,ℤ/8)11yescharacteristic
126C22×C32#13711yescharacteristic
127C2×C3⋊D3—22no—
128C2×C3⋊D3—22no—
129C2×C3⋊D3—22no—
130C2×C3⋊D3—22no—
131C2×C3⋊D3—22no—
132C2×C3⋊D3—22no—
133C2×C3⋊D3#10714yescomplemented
134C32×C4—22no—
135C3⋊Dic3C4×D412yes—
136C3⋊Dic3C22⋊Q812yes—
137C3×Dic3—44no—
138C3×Dic3—81no—
139C3×Dic3—81no—
140C23×C4—91no—
141C23×C4—181no—
142C22×C8—92no—
143C2×C4⋊C4—61no—
144C2×C4⋊C4—92no—
145C2×C4⋊C4—91no—
146C2×C4⋊C4—91no—
147C2×C4⋊C4—184no—
148C2×C22⋊C4—181no—
149#107—184no—
150C22⋊C8—94no—
151#95—61no—
152C23×C3—21no—
153C23×C3—21no—
154C22×D3—62no—
155C22×D3—62no—
156C22×D3—62no—
157C22×D3—62no—
158C22×D3—62no—
159C22×D3—62no—
160C22×D3—62no—
161C22×D3—62no—
162C22×D3—62no—
163C22×D3—62no—
164C22×D3—121no—
165C22×D3—121no—
166C22×D3—121no—
167C22×D3—121no—
168C2×C3×C4—22no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—22no—
172C2×C3×C4—41no—
173C2×C3×C4—41no—
174C2×C3×C4—64no—
175C2×C3×C4—122no—
176C2×C3×C4—122no—
177C2×C3×C4—121no—
178C2×C3×C4—121no—
179C2×C3×C4—121no—
180C2×C3×C4—121no—
181C2×C3×C4—121no—
182C2×C3×C4—121no—
183C2×Dic3—24no—
184C2×Dic3—42no—
185C2×Dic3—42no—
186C2×Dic3—41no—
187C2×Dic3—41no—
188C2×Dic3—41no—
189C2×Dic3—41no—
190C2×Dic3—41no—
191C2×Dic3—41no—
192C2×Dic3—61no—
193C2×Dic3—61no—
194C2×Dic3—62no—
195C2×Dic3—62no—
196C2×Dic3—61no—
197C2×Dic3—61no—
198C2×Dic3—62no—
199C2×Dic3—62no—
200C4×D3—68no—
201C4×D3—68no—
202C4×D3—124no—
203C4×D3—124no—
204C4×D3—1216no—
205C2×C32#38511yescharacteristic
206C2×C32C2×#10711yescharacteristic
207C2×C32#42811yescharacteristic
208C2×C32#44711yescharacteristic
209C2×C32#45111yescharacteristic
210C2×C32#48011yescharacteristic
211C2×C32#48411yescharacteristic
212C3⋊D3—24no—
213C24—91no—
214C22×C4—62no—
215C22×C4—61no—
216C22×C4—61no—
217C22×C4—91no—
218C22×C4—92no—
219C22×C4—92no—
220C22×C4—182no—
221C22×C4—182no—
222C22×C4—184no—
223C22×C4—362no—
224C22×C4—362no—
225C22×C4GO+(4,𝔽2)11yescharacteristic
226C2×C8—94no—
227C2×C8—182no—
228C2×C8—182no—
229C4⋊C4—64no—
230C4⋊C4—94no—
231C4⋊C4—182no—
232C4⋊C4—182no—
233C4⋊C4—182no—
234C22⋊C4—362no—
235C22×C3—21no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—21no—
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—21no—
249C2×D3—64no—
250C2×D3—64no—
251C2×D3—64no—
252C2×D3—64no—
253C2×D3—64no—
254C2×D3—64no—
255C2×D3—64no—
256C2×D3—64no—
257C2×D3—122no—
258C2×D3—122no—
259C2×D3—122no—
260C2×D3—122no—
261C2×D3—122no—
262C2×D3—122no—
263C3×C4—24no—
264C3×C4—42no—
265C3×C4—124no—
266C3×C4—241no—
267C3×C4—241no—
268Dic3—44no—
269Dic3—62no—
270Dic3—62no—
271Dic3—62no—
272Dic3—62no—
273Dic3—81no—
274Dic3—81no—
275C32#185211yescharacteristic, complemented, Sylow
276C23—92no—
277C23—92no—
278C23—92no—
279C23—181no—
280C23—181no—
281C23—181no—
282C23—181no—
283C23C2×GO+(4,𝔽2)11yescharacteristic
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—64no—
287C2×C4—92no—
288C2×C4—91no—
289C2×C4—91no—
290C2×C4—92no—
291C2×C4—122no—
292C2×C4—122no—
293C2×C4—121no—
294C2×C4—121no—
295C2×C4—121no—
296C2×C4—121no—
297C2×C4—121no—
298C2×C4—121no—
299C2×C4—184no—
300C2×C4—184no—
301C2×C4—368no—
302C2×C4#377312yes—
303C8—184no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318D3—68no—
319D3—124no—
320C22—94no—
321C22—182no—
322C22—182no—
323C22—182no—
324C22—182no—
325C22—182no—
326C22—182no—
327C22#6422411yescharacteristic
328C22#6422511yescharacteristic
329C22#6422611yescharacteristic
330C22#6422811yescharacteristic
331C22#6423311yescharacteristic
332C22C2×#377311yescharacteristic
333C22#6424111yescharacteristic
334C4—22no—
335C4—92no—
336C4—92no—
337C4—124no—
338C4—241no—
339C4—241no—
340C3—21no—
341C3—21no—
342C2—184no—
343C2#1059336811yescharacteristic
344C2#1059337111yescharacteristic
345C2#1059337211yescharacteristic
346C2#1059339411yescharacteristic
347C2#1059339611yescharacteristic
348C2#1059342511yescharacteristic
349C2#1059348511yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1852
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
3. C2×#63743C2semidirect
5. #10590075C2semidirect
15. #63778C4semidirect
35. C2×#622C2×C4semidirect
133. C2×C3⋊D3#107semidirect
275. C32#1852semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
C2×#637782
C2×#637432
#105913552
#105900752
#18529