Finite Group Databasebeta

← #10594380

Subgroups — #10594380

Order 576.

577 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3798C211yesmaximal, characteristic
2C2×D3×Dic6C211yesmaximal, characteristic, complemented
3#64106C211yesmaximal, characteristic, complemented
4C3×#897C211yesmaximal, characteristic, complemented
5C3×#892C211yesmaximal, characteristic, complemented
6#63918C212yesmaximal, complemented
7#63891C212yesmaximal, complemented
8#63890C212yesmaximal, complemented
9#63871C211yesmaximal, characteristic, complemented
10#63857C211yesmaximal, characteristic, complemented
11#63852C212yesmaximal, complemented
12#5628—31nomaximal
13#5526—31nomaximal
14C2×C4×C3⋊D3C2211yescharacteristic
15C2×#634C2211yescharacteristic
16C2×C3×C4×D3C2211yescharacteristic
17C2×C3×C4×D3C2211yescharacteristic
18C2×C3×Dic6C2211yescharacteristic
19C2×#627C2212yes—
20C2×#627C2211yescharacteristic
21C2×#626C2211yescharacteristic
22C2×#626C2211yescharacteristic
23C2×#625C2211yescharacteristic
24C2×D3×Dic3C2212yes—
25#3798—24no—
26D3×Dic6—24no—
27C32×C4⋊C4C2211yescharacteristic
28#3752C2212yes—
29C4⋊(C3⋊Dic3)C2212yes—
30C3×(C2×D3)⋊C4C2212yes—
31C3×(C2×D3)⋊C4C2212yes—
32C3×C4⋊Dic3C2211yescharacteristic
33C3×C4⋊Dic3C2212yes—
34C3×C4×Dic3C2212yes—
35Dic3⋊Dic3C2212yes—
36Dic3⋊Dic3C2212yes—
37#3722C2212yes—
38(C2×D3)⋊Dic3C2212yes—
39C2×D3×Q8—31no—
40C2×#235—31no—
41C2×#235—31no—
42C22×Dic6—31no—
43C3×C22⋊Q8—31no—
44C3×#117—31no—
45#946—31no—
46#924—31no—
47#897—31no—
48#897—31no—
49#897—31no—
50#897—31no—
51#897—61no—
52#897D311yescharacteristic, complemented
53#894—32no—
54#892D311yescharacteristic, complemented
55#888—32no—
56#886—32no—
57#886—32no—
58#885—32no—
59#883—32no—
60#875—32no—
61#869—32no—
62C22×C3⋊D3C2311yescharacteristic
63C22×C3×D3C2311yescharacteristic
64C22×C3×D3C2311yescharacteristic
65C2×C32×C4C2312yes—
66C2×C32×C4C2311yescharacteristic
67C2×C3⋊Dic3C2312yes—
68C2×C3⋊Dic3C2311yescharacteristic
69C4×C3⋊D3—22no—
70#634—22no—
71C2×C3×Dic3C2312yes—
72C2×C3×Dic3C2312yes—
73C2×C3×Dic3C2311yescharacteristic
74C2×C3×Dic3C2311yescharacteristic
75C3×C4×D3—22no—
76C3×C4×D3D414yes—
77C3×Dic6—22no—
78#627—24no—
79#627—22no—
80#626—22no—
81#626—22no—
82#625—22no—
83D3×Dic3—24no—
84#536—91noSylow
85C2×C3×Q8—31no—
86C22×C3×C4—31no—
87C22×C3×C4—31no—
88C2×#67—31no—
89C2×#67—31no—
90C2×#67—31no—
91C2×#67—31no—
92C22×Dic3—32no—
93D3×Q8—64no—
94#235—64no—
95#235—64no—
96C2×D12—31no—
97C2×D12—31no—
98C2×C4×D3—32no—
99C2×C4×D3—31no—
100C2×C4×D3—31no—
101C2×C4×D3—61no—
102C2×C4×D3C2×D311yescharacteristic
103C2×C4×D3C2×D311yescharacteristic
104C2×Dic6—31no—
105C2×Dic6—31no—
106C2×Dic6—31no—
107C2×Dic6—32no—
108C2×Dic6—32no—
109C2×Dic6—31no—
110C2×Dic6—61no—
111C2×Dic6—64no—
112C2×Dic6C2×D311yescharacteristic
113C3×C4⋊C4—21no—
114C3×C4⋊C4—32no—
115C3×C4⋊C4—31no—
116C3×C4⋊C4C2×D311yescharacteristic
117C3×C4⋊C4C2×D311yescharacteristic
118C3×C22⋊C4—32no—
119C3×C22⋊C4—32no—
120C3×C42—32no—
121#217—32no—
122(C2×D3)⋊C4—32no—
123(C2×D3)⋊C4—32no—
124(C2×D3)⋊C4—32no—
125(C2×D3)⋊C4—32no—
126(C2×D3)⋊C4—32no—
127(C2×D3)⋊C4—62no—
128(C2×D3)⋊C4C2×D312yes—
129(C2×D3)⋊C4C2×D312yes—
130C4⋊Dic3—32no—
131C4⋊Dic3—32no—
132C4⋊Dic3—32no—
133C4⋊Dic3—32no—
134C4⋊Dic3—62no—
135C4⋊Dic3C2×D312yes—
136C4⋊Dic3C2×D311yescharacteristic
137Dic3⋊C4—32no—
138Dic3⋊C4—32no—
139C4×Dic3C2×D312yes—
140C22×C32C2411yescharacteristic
141C2×C3⋊D3—21no—
142C2×C3⋊D3—21no—
143C2×C3⋊D3—21no—
144C2×C3×D3—21no—
145C2×C3×D3—21no—
146C2×C3×D3—21no—
147C2×C3×D3—21no—
148C2×C3×D3—21no—
149C2×C3×D3C2×D412yes—
150C32×C4—22no—
151C32×C4C2×D412yes—
152C3⋊Dic3—22no—
153C3⋊Dic3—21no—
154C3×Dic3—22no—
155C3×Dic3—21no—
156C3×Dic3—22no—
157C3×Dic3C2×D412yes—
158C2×#41—91no—
159C22×Q8—91no—
160C4⋊Q8—92no—
161#124—92no—
162#123—92no—
163#123—92no—
164C22⋊Q8—31no—
165C22⋊Q8—91no—
166C22⋊Q8—91no—
167C22⋊Q8—91no—
168#117—31no—
169C23×C3—31no—
170C23×C3—31no—
171C22×D3—31no—
172C22×D3—31no—
173C22×D3—61no—
174C22×D3C22×D311yescharacteristic
175C22×D3C22×D311yescharacteristic
176C3×Q8—62no—
177C2×C3×C4—21no—
178C2×C3×C4—22no—
179C2×C3×C4—31no—
180C2×C3×C4—34no—
181C2×C3×C4—31no—
182C2×C3×C4—32no—
183C2×C3×C4—32no—
184C2×C3×C4—62no—
185C2×C3×C4C22×D312yes—
186C2×C3×C4C22×D312yes—
187C2×C3×C4C22×D311yescharacteristic
188C2×C3×C4C22×D311yescharacteristic
189#67—62no—
190#67—62no—
191#67—62no—
192#67—62no—
193C2×Dic3—31no—
194C2×Dic3—32no—
195C2×Dic3—31no—
196C2×Dic3—32no—
197C2×Dic3—61no—
198C2×Dic3—62no—
199C2×Dic3—64no—
200C2×Dic3C22×D312yes—
201C2×Dic3C22×D311yescharacteristic
202C2×Dic3C22×D312yes—
203C2×Dic3C22×D311yescharacteristic
204D12—62no—
205D12—62no—
206C4×D3—22no—
207C4×D3—64no—
208C4×D3—62no—
209C4×D3—62no—
210C4×D3—122no—
211C4×D3D1214yes—
212Dic6—22no—
213Dic6—64no—
214Dic6—62no—
215Dic6—62no—
216Dic6—62no—
217Dic6—62no—
218Dic6—64no—
219Dic6—122no—
220C2×C32C22×D411yescharacteristic
221C2×C322−1+411yescharacteristic
222C2×C322−1+411yescharacteristic
223C3⋊D3—41no—
224C3×D3—22no—
225C3×D3—41no—
226#41—184no—
227C2×Q8—31no—
228C2×Q8—92no—
229C2×Q8—91no—
230C2×Q8—91no—
231C2×Q8—184no—
232C2×D4—91no—
233C2×D4—91no—
234C2×D4—91no—
235C22×C4—31no—
236C22×C4—31no—
237C22×C4—92no—
238C22×C4—91no—
239C4⋊C4—31no—
240C4⋊C4—32no—
241C4⋊C4—92no—
242C4⋊C4—92no—
243C4⋊C4—92no—
244C4⋊C4D3211yescharacteristic
245C22⋊C4—32no—
246C22⋊C4—32no—
247C22⋊C4—92no—
248C22⋊C4—92no—
249C22⋊C4—92no—
250C42—32no—
251C22×C3—21no—
252C22×C3—32no—
253C22×C3—61no—
254C22×C3—61no—
255C22×C3—61no—
256C22×C3—61no—
257C22×C3—61no—
258C22×C3C23×D311yescharacteristic
259C22×C3C23×D311yescharacteristic
260C2×D3—21no—
261C2×D3—21no—
262C2×D3—21no—
263C2×D3—21no—
264C2×D3—21no—
265C2×D3—62no—
266C2×D3—61no—
267C2×D3—61no—
268C2×D3—61no—
269C2×D3—61no—
270C2×D3—61no—
271C2×D3—61no—
272C2×D3—121no—
273C2×D3—121no—
274C2×D3C2×D1212yes—
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—22no—
278C3×C4—32no—
279C3×C4—42no—
280C3×C4—62no—
281C3×C4—61no—
282C3×C4—62no—
283C3×C4C2×D1212yes—
284C3×C4D3×D412yes—
285Dic3—22no—
286Dic3—21no—
287Dic3—22no—
288Dic3—62no—
289Dic3—61no—
290Dic3—62no—
291Dic3—61no—
292Dic3—122no—
293Dic3—121no—
294Dic3C2×D1212yes—
295C32#53611yescharacteristic, complemented, Sylow
296C23—31no—
297C23—31no—
298C23—91no—
299Q8—62no—
300Q8—184no—
301Q8—182no—
302Q8—182no—
303D4—182no—
304D4—182no—
305D4—182no—
306C2×C4—31no—
307C2×C4—34no—
308C2×C4—32no—
309C2×C4—32no—
310C2×C4—31no—
311C2×C4—62no—
312C2×C4—92no—
313C2×C4—91no—
314C2×C4—184no—
315C2×C4—182no—
316C2×C4C2×D3212yes—
317C2×C4C2×D3211yescharacteristic
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—62no—
322C2×C3—121no—
323C2×C3C22×D1211yescharacteristic
324C2×C3C2×D3×D411yescharacteristic
325C2×C3#100711yescharacteristic
326C2×C3#101011yescharacteristic
327C2×C3#101011yescharacteristic
328C2×C3#101011yescharacteristic
329D3—22no—
330D3—41no—
331D3—122no—
332D3—121no—
333D3—121no—
334C22—32no—
335C22—61no—
336C22—61no—
337C22—61no—
338C22—61no—
339C22—61no—
340C22—181no—
341C22—181no—
342C22—181no—
343C22C22×D3211yescharacteristic
344C4—22no—
345C4—32no—
346C4—61no—
347C4—62no—
348C4—62no—
349C4—181no—
350C4—182no—
351C4D3×D1212yes—
352C3—21no—
353C3#552611yescharacteristic, complemented
354C3#562811yescharacteristic, complemented
355C2—62no—
356C2—121no—
357C2—361no—
358C2C2×D3×D1211yescharacteristic
359C2#6430911yescharacteristic
360C2#6431511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C4⋊C4C22
prime radicalC2×#3798C2
hypercenterC4⋊C4D32
hypocenterC32#536
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×D3×Dic6C2semidirect
3. #64106C2semidirect
4. C3×#897C2semidirect
5. C3×#892C2semidirect
6. #63918C2semidirect
7. #63891C2semidirect
8. #63890C2semidirect
9. #63871C2semidirect
10. #63857C2semidirect
11. #63852C2semidirect
52. #897D3semidirect
54. #892D3semidirect
295. C32#536semidirect
353. C3#5526semidirect
354. C3#5628semidirect

Maximal subgroups

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

subgroupindex
C2×#37982
C2×D3×Dic62
#641062
C3×#8972
C3×#8922
#639182
#638912
#638902
#638712
#638572
#638522
#56283
#55263