Finite Group Databasebeta

← C2×#10592473 #11869327

Subgroups — C2×#10592473 #11869327

Order 1152.

1536 conjugacy classes of subgroups.

The subgroup lattice has 351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64147C211yesmaximal, characteristic
2C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×C32×#102C211yesmaximal, characteristic, complemented
4C2×#63659C211yesmaximal, characteristic, complemented
5C2×#63647C211yesmaximal, characteristic, complemented
6C2×#63645C211yesmaximal, characteristic, complemented
7C2×#63634C211yesmaximal, characteristic, complemented
8#10592473C218yesmaximal, direct product factor
9C2×#4774—34nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×#638—21no—
12C22×C4×C3⋊D3—21no—
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×#3757—21no—
17#64147—22no—
18#64147C2214yes—
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×#3750—21no—
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C4⋊C4×C3⋊D3—22no—
24C4⋊C4×C3⋊D3C2214yescomplemented
25C32×#102C2214yescomplemented
26#63659C2214yescomplemented
27#63647C2214yescomplemented
28#63645C2214yescomplemented
29#63634C2214yescomplemented
30C2×#938—34no—
31C2×D3×C4⋊C4—34no—
32C2×C3×#102D314yescomplemented
33C2×#832—34no—
34C2×(C2×D3)⋊C8—34no—
35C2×#818—34no—
36C2×#807—34no—
37#4774—332no—
38C24×C32—21no—
39C23×C3⋊D3D411yescharacteristic
40C2×C32×D4—21no—
41C2×C32×D4—22no—
42C2×C32×D4—22no—
43C2×C32×D4C2312yes—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C2×#638—24no—
47C2×#638—44no—
48C22×C3⋊Dic3—21no—
49C22×C3⋊Dic3—21no—
50C22×C3⋊Dic3D411yescharacteristic
51C2×C4×C3⋊D3—22no—
52C2×C4×C3⋊D3—22no—
53C2×C4×C3⋊D3—24no—
54C2×C4×C3⋊D3—44no—
55C2×C4×C3⋊D3D412yes—
56C2×C4×C3⋊D3C2312yes—
57C2×C32×C8—22no—
58C2×C32×C8C2312yes—
59C32×C4⋊C4—21no—
60C32×C4⋊C4C2312yes—
61#3757—24no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)C2312yes—
65C4⋊(C3⋊Dic3)C2312yes—
66#3750—24no—
67C2×C3⋊(C3⋊C8)—22no—
68C2×C3⋊(C3⋊C8)C2312yes—
69C2×#480—91noSylow
70C22×C3×D4C2×D314yes—
71C22×#67—64no—
72C22×C4×D3—34no—
73C22×C4×D3—64no—
74C22×C3×C8C2×D314yes—
75C2×C3×C4⋊C4C2×D314yes—
76C2×#217—64no—
77#938—316no—
78#938—68no—
79C2×C4⋊Dic3—34no—
80C2×C4⋊Dic3—34no—
81C2×Dic3⋊C4—64no—
82C22×C3⋊C8—34no—
83D3×C4⋊C4—316no—
84D3×C4⋊C4—68no—
85C3×#102C2×D3116yescomplemented
86#832—316no—
87(C2×D3)⋊C8—316no—
88#818—316no—
89#807—316no—
90C23×C32—22no—
91C23×C32—42no—
92C23×C32—42no—
93C23×C32—42no—
94C23×C32C2×D411yescharacteristic
95C22×C3⋊D3—22no—
96C22×C3⋊D3—22no—
97C22×C3⋊D3D814yes—
98C22×C3⋊D3C2×D412yes—
99C32×D4—22no—
100C32×D4—22no—
101C32×D4—42no—
102C2×C32×C4—22no—
103C2×C32×C4—42no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4#4112yes—
106C2×C32×C4#4112yes—
107C2×C32×C4C2411yescharacteristic
108#638—48no—
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3—22no—
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—42no—
113C2×C3⋊Dic3—42no—
114C2×C3⋊Dic3C2×D412yes—
115C4×C3⋊D3—24no—
116C4×C3⋊D3—22no—
117C4×C3⋊D3—22no—
118C4×C3⋊D3—48no—
119C32×C8—22no—
120C3⋊(C3⋊C8)—22no—
121C2×#121—91no—
122C22×C4⋊C4—91no—
123#480—98no—
124C2×#107—91no—
125C2×#107—91no—
126C2×#102—91no—
127C2×#102C3⋊D311yescharacteristic, complemented
128C2×C22⋊C8—91no—
129C24×C3—24no—
130C23×D3—34no—
131C2×C3×D4—28no—
132C2×C3×D4—24no—
133C2×C3×D4—28no—
134C2×C3×D4C22×D318yes—
135C22×C3×C4—24no—
136C22×C3×C4C22×D314yes—
137C2×#67—616no—
138C2×#67—1216no—
139C22×Dic3—34no—
140C22×Dic3—64no—
141C22×Dic3—64no—
142C2×C4×D3—38no—
143C2×C4×D3—38no—
144C2×C4×D3—68no—
145C2×C4×D3—68no—
146C2×C4×D3—616no—
147C2×C4×D3—1216no—
148C2×C3×C8—28no—
149C2×C3×C8C22×D318yes—
150C3×C4⋊C4—24no—
151C3×C4⋊C4C22×D318yes—
152#217—616no—
153C4⋊Dic3—38no—
154C4⋊Dic3—38no—
155C4⋊Dic3—64no—
156C4⋊Dic3—64no—
157Dic3⋊C4—616no—
158C2×C3⋊C8—38no—
159C2×C3⋊C8—68no—
160C22×C32—42no—
161C22×C32—42no—
162C22×C32—42no—
163C22×C32—84no—
164C22×C32#12312yes—
165C22×C32C2×D812yes—
166C22×C32#13712yes—
167C22×C32C22×D411yescharacteristic
168C2×C3⋊D3—22no—
169C2×C3⋊D3—22no—
170C2×C3⋊D3—28no—
171C2×C3⋊D3C2×D814yes—
172C32×C4—42no—
173C32×C4#12312yes—
174C32×C4C2×#4111yescharacteristic
175C32×C4C2×#4111yescharacteristic
176C3⋊Dic3—22no—
177C3⋊Dic3—42no—
178C3⋊Dic3—42no—
179C22×D4—181no—
180C22×D4C2×C3⋊D311yescharacteristic
181C23×C4—91no—
182C23×C4—181no—
183C22×C8—91no—
184C22×C8C2×C3⋊D311yescharacteristic
185#121—94no—
186#121—182no—
187C2×C4⋊C4—91no—
188C2×C4⋊C4—91no—
189C2×C4⋊C4—94no—
190C2×C4⋊C4—182no—
191C2×C4⋊C4—181no—
192C2×C4⋊C4C2×C3⋊D311yescharacteristic
193C2×C22⋊C4—181no—
194#107—94no—
195#107—94no—
196#102—94no—
197#102C2×C3⋊D314yescomplemented
198C22⋊C8—94no—
199C23×C3—28no—
200C23×C3—48no—
201C23×C3—48no—
202C23×C3—48no—
203C23×C3D3×D414yes—
204C22×D3—316no—
205C22×D3—38no—
206C22×D3—68no—
207C22×D3—68no—
208C3×D4—28no—
209C3×D4—28no—
210C3×D4—48no—
211C2×C3×C4—28no—
212C2×C3×C4—48no—
213C2×C3×C4#23518yes—
214C2×C3×C4D3×D414yes—
215C2×C3×C4#23718yes—
216C2×C3×C4C23×D314yes—
217#67—1232no—
218C2×Dic3—38no—
219C2×Dic3—68no—
220C2×Dic3—68no—
221C2×Dic3—68no—
222C2×Dic3—128no—
223C2×Dic3—128no—
224C4×D3—616no—
225C4×D3—68no—
226C4×D3—68no—
227C4×D3—1232no—
228C3×C8—28no—
229C3⋊C8—68no—
230C2×C32—82no—
231C2×C32#48014yescomplemented
232C2×C32C2×#12311yescharacteristic
233C2×C32C22×D811yescharacteristic
234C2×C32C2×#13711yescharacteristic
235C3⋊D3—24no—
236C24—21no—
237C24—91no—
238C2×D4—22no—
239C2×D4—21no—
240C2×D4—22no—
241C2×D4—184no—
242C2×D4—364no—
243C2×D4C22×C3⋊D312yes—
244C22×C4—21no—
245C22×C4—91no—
246C22×C4—92no—
247C22×C4—92no—
248C22×C4—184no—
249C22×C4—182no—
250C22×C4—182no—
251C22×C4—181no—
252C22×C4—181no—
253C22×C4—364no—
254C22×C4C22×C3⋊D311yescharacteristic
255C2×C8—22no—
256C2×C8—92no—
257C2×C8—182no—
258C2×C8C22×C3⋊D312yes—
259C4⋊C4—21no—
260C4⋊C4—92no—
261C4⋊C4—92no—
262C4⋊C4—184no—
263C4⋊C4—181no—
264C4⋊C4—181no—
265C4⋊C4C22×C3⋊D312yes—
266C22⋊C4—184no—
267C22×C3—48no—
268C22×C3—48no—
269C22×C3—48no—
270C22×C3—816no—
271C22×C3#88318yes—
272C22×C3D3×D818yes—
273C22×C3#91518yes—
274C22×C3C2×D3×D414yes—
275C2×D3—316no—
276C2×D3—68no—
277C2×D3—68no—
278C2×D3—632no—
279C3×C4—48no—
280C3×C4#88318yes—
281C3×C4C2×#23514yes—
282C3×C4C2×#23714yes—
283Dic3—68no—
284Dic3—128no—
285Dic3—128no—
286C32C2×#48011yescharacteristic, complemented, Sylow
287C23—22no—
288C23—42no—
289C23—42no—
290C23—42no—
291C23—92no—
292C23—94no—
293C23—182no—
294C23—182no—
295C23D4×C3⋊D311yescharacteristic
296D4—22no—
297D4—22no—
298D4—42no—
299D4—368no—
300C2×C4—22no—
301C2×C4—42no—
302C2×C4—92no—
303C2×C4—182no—
304C2×C4—184no—
305C2×C4—182no—
306C2×C4—182no—
307C2×C4—182no—
308C2×C4—182no—
309C2×C4—368no—
310C2×C4—362no—
311C2×C4—362no—
312C2×C4#382812yes—
313C2×C4D4×C3⋊D311yescharacteristic
314C2×C4#383012yes—
315C2×C4C23×C3⋊D311yescharacteristic
316C8—22no—
317C8—182no—
318C2×C3—88no—
319C2×C3#4774116yescomplemented
320C2×C3C2×#88314yes—
321C2×C3C2×D3×D814yes—
322C2×C3C2×#91514yes—
323D3—616no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22—84no—
328C22—94no—
329C22—182no—
330C22—182no—
331C22—188no—
332C22#6409212yes—
333C22D8×C3⋊D312yes—
334C22#6412412yes—
335C22C2×D4×C3⋊D311yescharacteristic
336C4—42no—
337C4—182no—
338C4—362no—
339C4—362no—
340C4#6409212yes—
341C4C2×#382811yescharacteristic
342C4C2×#383011yescharacteristic
343C3C2×#477414yescomplemented
344C2—82no—
345C2—184no—
346C2#1059247314yesdirect product factor
347C2C2×#6409211yescharacteristic
348C2C2×D8×C3⋊D311yescharacteristic
349C2C2×#6412411yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC2×#64147C2
hypercenterC2×#102C3⋊D3
hypocenterC32C2×#480
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×C3⋊D3C2semidirect
3. C2×C32×#102C2semidirect
4. C2×#63659C2semidirect
5. C2×#63647C2semidirect
6. C2×#63645C2semidirect
7. C2×#63634C2semidirect
8. #10592473C2direct (N × H)
24. C4⋊C4×C3⋊D3C22semidirect
25. C32×#102C22semidirect
26. #63659C22semidirect
27. #63647C22semidirect
28. #63645C22semidirect
29. #63634C22semidirect
32. C2×C3×#102D3semidirect
85. C3×#102C2×D3semidirect
127. C2×#102C3⋊D3semidirect
197. #102C2×C3⋊D3semidirect
231. C2×C32#480semidirect
286. C32C2×#480semidirect
319. C2×C3#4774semidirect
343. C3C2×#4774semidirect
346. C2#10592473direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641472
C2×C4⋊C4×C3⋊D32
C2×C32×#1022
C2×#636592
C2×#636472
C2×#636452
C2×#636342
#105924732
C2×#47743