Finite Group Databasebeta

← C2×#19134238 #25084342

Subgroups — C2×#19134238 #25084342

Order 11008.

734 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583302C211yesmaximal, characteristic
2C2×#14583295C211yesmaximal, characteristic
3C2×#14583251C211yesmaximal, characteristic
4C2×#14583250C211yesmaximal, characteristic
5C2×#14583249C211yesmaximal, characteristic
6#19134238C218yesmaximal, direct product factor
7C2×#14582620C211yesmaximal, characteristic
8C2×C43×#487C211yesmaximal, characteristic
9C2×#13063325C2211yescharacteristic
10C2×#13063325C2211yescharacteristic
11#14583302—22no—
12#14583302C2214yes—
13#14583295—22no—
14#14583295C2214yes—
15#14583251—22no—
16#14583251C2214yes—
17#14583250—22no—
18#14583250C2214yes—
19#14583249—22no—
20#14583249C2214yes—
21C2×#13063258—22no—
22C2×#13063256—22no—
23C2×#13063250—22no—
24C2×#13063249—22no—
25C2×#13063248—22no—
26C2×C4×C43⋊C8C2211yescharacteristic
27C2×C4×C43⋊C8C2211yescharacteristic
28#14582620C2214yes—
29C2×C4⋊Q8×C43C2211yescharacteristic
30C2×C4⋊Q8×C43C2211yescharacteristic
31C43×#487—22no—
32C43×#487C2214yes—
33C2×#103×C43—22no—
34C2×C4×C8×C43C2211yescharacteristic
35C22×Dic86—21no—
36C22×Dic86—21no—
37C22×C43⋊C8D412yes—
38C22×C43⋊C8D412yes—
39#13063325—21no—
40#13063325—21no—
41#13063325—21no—
42#13063325—21no—
43#13063325—21no—
44#13063325—21no—
45#13063325C2312yes—
46#13063325C2312yes—
47C2×C4⋊Dic43—21no—
48C2×C4⋊Dic43—21no—
49C2×C4⋊Dic43—21no—
50C2×C4⋊Dic43—21no—
51#13063258—28no—
52#13063256—28no—
53#13063250—28no—
54#13063249—28no—
55#13063248—28no—
56C4×C43⋊C8D412yes—
57C4×C43⋊C8D412yes—
58C4×C43⋊C8C2312yes—
59C4×C43⋊C8C2312yes—
60C22×Q8×C43—21no—
61C22×Q8×C43—21no—
62C22×C8×C43D412yes—
63C4⋊Q8×C43—21no—
64C4⋊Q8×C43—21no—
65C4⋊Q8×C43—21no—
66C4⋊Q8×C43—21no—
67C4⋊Q8×C43—21no—
68C4⋊Q8×C43—21no—
69C4⋊Q8×C43C2312yes—
70C4⋊Q8×C43C2312yes—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43—21no—
74C2×C4⋊C4×C43—21no—
75C2×C42×C43C2311yescharacteristic
76#103×C43—28no—
77C4×C8×C43D412yes—
78C4×C8×C43C2312yes—
79C2×Q8×C43—22no—
80C2×Q8×C43—22no—
81C2×Q8×C43—41no—
82C2×Q8×C43—41no—
83C2×Q8×C43—44no—
84C2×Q8×C43—44no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×Dic43—41no—
91C22×Dic43—41no—
92C2×Dic86—22no—
93C2×Dic86—22no—
94C2×Dic86—44no—
95C2×Dic86—44no—
96C2×Dic86—41no—
97C2×Dic86—41no—
98C2×C8×C43—24no—
99C2×C8×C43C2×D414yes—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—22no—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—22no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—41no—
108C42×C43C2×D411yescharacteristic
109C42×C43C2×D411yescharacteristic
110C42×C43C2×D411yescharacteristic
111C42×C43C2411yescharacteristic
112C4⋊Dic43—22no—
113C4⋊Dic43—22no—
114C4⋊Dic43—22no—
115C4⋊Dic43—22no—
116C4⋊Dic43—41no—
117C4⋊Dic43—41no—
118C4⋊Dic43—41no—
119C4⋊Dic43—41no—
120C2×C43⋊C8—24no—
121C2×C43⋊C8—24no—
122C2×C43⋊C8C2×D414yes—
123C2×C43⋊C8C2×D414yes—
124C23×C43#12711yescharacteristic
125Q8×C43—44no—
126Q8×C43—44no—
127Q8×C43—82no—
128Q8×C43—82no—
129C2×C4×C43—42no—
130C2×C4×C43—42no—
131C2×C4×C43—82no—
132C2×C4×C43—82no—
133C2×C4×C43#12711yescharacteristic
134C2×C4×C43#12711yescharacteristic
135C2×C4×C43#12711yescharacteristic
136C2×C4×C43#13514yes—
137C2×C4×C43#13714yes—
138C2×C4×C43#13714yes—
139C2×C4×C43C22×D411yescharacteristic
140C2×C4×C43C22×D411yescharacteristic
141C2×C4×C43C22×D411yescharacteristic
142C2×Dic43—42no—
143C2×Dic43—42no—
144C2×Dic43—82no—
145C2×Dic43—82no—
146Dic86—44no—
147Dic86—44no—
148Dic86—82no—
149Dic86—82no—
150C8×C43—24no—
151C43⋊C8—24no—
152C43⋊C8—24no—
153C2×#1718—431nomaximal, Sylow
154C22×C43#49512yes—
155C22×C43#49712yes—
156C22×C43#49712yes—
157C22×C43C2×#12711yescharacteristic
158C4×C43—82no—
159C4×C43—82no—
160C4×C43#49512yes—
161C4×C43#49712yes—
162C4×C43#49712yes—
163C4×C43C2×#13512yes—
164C4×C43C2×#13712yes—
165C4×C43C2×#13712yes—
166Dic43—82no—
167Dic43—82no—
168C2×#500—431no—
169C2×#498—431no—
170C2×#487—431no—
171C2×#487—431no—
172C2×#487—431no—
173C2×#487D4311yescharacteristic
174#1718—438no—
175C2×#322—431no—
176C2×C43#171814yescomplemented
177C2×C43C2×#49511yescharacteristic
178C2×C43C2×#49711yescharacteristic
179C2×C43C2×#49711yescharacteristic
180C2×C4⋊Q8—431no—
181C2×C4⋊Q8—431no—
182C2×C4⋊Q8C2×D4311yescharacteristic
183C2×C4⋊Q8C2×D4311yescharacteristic
184#500—434no—
185#500—862no—
186#498—434no—
187#498—862no—
188#487—22no—
189#487—434no—
190#487—434no—
191#487—434no—
192#487—862no—
193#487—862no—
194#487—862no—
195#487C2×D4314yes—
196C2×#107—862no—
197C2×#106—862no—
198C2×#103—22no—
199C2×#103—862no—
200C2×#103—862no—
201C2×#103—862no—
202C2×C4×C8—431no—
203C2×C4×C8—431no—
204C2×C4×C8C2×D4311yescharacteristic
205#322—434no—
206C43C2×#171811yescharacteristic, complemented, Sylow
207C22×Q8—21no—
208C22×Q8—21no—
209C22×Q8—861no—
210C22×Q8—861no—
211C22×C8—432no—
212C22×C8—432no—
213C22×C8C22⋊D4312yes—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—432no—
221C4⋊Q8—432no—
222C4⋊Q8—861no—
223C4⋊Q8—861no—
224C4⋊Q8—861no—
225C4⋊Q8—861no—
226C4⋊Q8—861no—
227C4⋊Q8—861no—
228C4⋊Q8C22×D4312yes—
229C4⋊Q8C22×D4312yes—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—861no—
235C2×C4⋊C4—861no—
236C2×C4⋊C4—861no—
237C2×C4⋊C4—861no—
238C2×C42C22×D4311yescharacteristic
239#107—868no—
240#106—868no—
241#103—28no—
242#103—868no—
243#103—868no—
244#103—868no—
245C4×C8—432no—
246C4×C8—432no—
247C4×C8—432no—
248C4×C8—432no—
249C4×C8C22⋊D4312yes—
250C4×C8C22×D4312yes—
251C2×Q8—22no—
252C2×Q8—22no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—44no—
256C2×Q8—44no—
257C2×Q8—862no—
258C2×Q8—862no—
259C2×Q8—1724no—
260C2×Q8—1724no—
261C2×Q8—1721no—
262C2×Q8—1721no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—1721no—
266C22×C4—1721no—
267C22×C4D4×D4311yescharacteristic
268C22×C4D4×D4311yescharacteristic
269C22×C4C2×C22⋊D4311yescharacteristic
270C2×C8—24no—
271C2×C8—434no—
272C2×C8—434no—
273C2×C8—864no—
274C2×C8—864no—
275C2×C8C2×C22⋊D4314yes—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—22no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—862no—
285C4⋊C4—862no—
286C4⋊C4—862no—
287C4⋊C4—862no—
288C4⋊C4—1721no—
289C4⋊C4—1721no—
290C4⋊C4—1721no—
291C4⋊C4—1721no—
292C42D4×D4311yescharacteristic
293C42D4×D4311yescharacteristic
294C42C2×C22⋊D4311yescharacteristic
295C42C23×D4311yescharacteristic
296C23#1306332111yescharacteristic
297Q8—44no—
298Q8—44no—
299Q8—82no—
300Q8—82no—
301Q8—3442no—
302Q8—3442no—
303Q8—1724no—
304Q8—1724no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—82no—
308C2×C4—82no—
309C2×C4—3442no—
310C2×C4—3442no—
311C2×C4—1722no—
312C2×C4—1722no—
313C2×C4#1306332111yescharacteristic
314C2×C4#1306332111yescharacteristic
315C2×C4#1306332111yescharacteristic
316C2×C4#1306334514yes—
317C2×C4#1306335414yes—
318C2×C4#1306335714yes—
319C2×C4C2×D4×D4311yescharacteristic
320C2×C4C2×D4×D4311yescharacteristic
321C2×C4C22×C22⋊D4311yescharacteristic
322C8—24no—
323C8—864no—
324C8—864no—
325C22#1458328112yes—
326C22#1458329012yes—
327C22#1458329212yes—
328C22C2×#1306332111yescharacteristic
329C4—82no—
330C4—82no—
331C4—3442no—
332C4—3442no—
333C4#1458328112yes—
334C4#1458329012yes—
335C4#1458329212yes—
336C4C2×#1306334512yes—
337C4C2×#1306335412yes—
338C4C2×#1306335712yes—
339C2#1913423814yesdirect product factor
340C2C2×#1458328111yescharacteristic
341C2C2×#1458329011yescharacteristic
342C2C2×#1458329211yescharacteristic
subgroupG/H
centerC23#13063321
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#487C2
socle, prime radicalC23×C43#127
hypercenterC2×#487D43
hypocenterC43C2×#1718
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
6. #19134238C2direct (N × H)
176. C2×C43#1718semidirect
206. C43C2×#1718semidirect
339. C2#19134238direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145833022
C2×#145832952
C2×#145832512
C2×#145832502
C2×#145832492
#191342382
C2×#145826202
C2×C43×#4872
C2×#171843