Finite Group Databasebeta

← C2×#19136724 #25251165

Subgroups — C2×#19136724 #25251165

Order 11008.

658 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063269C211yesmaximal, characteristic, complemented
2C2×#14583317C211yesmaximal, characteristic, complemented
3C2×#14583175C211yesmaximal, characteristic, complemented
4C2×#14583166C211yesmaximal, characteristic
5#19136724C218yesmaximal, direct product factor
6C2×#14582728C211yesmaximal, characteristic, complemented
7C2×#14582716C211yesmaximal, characteristic, complemented
8C2×C43×#361C211yesmaximal, characteristic, complemented
9C2×#13063358—21no—
10C2×#13063351—21no—
11C22×Dic172C2211yescharacteristic
12C2×#13063331C2211yescharacteristic
13C2×#13063269—21no—
14C2×#13063269—21no—
15C2×#13063269—22no—
16C2×#13063269C2214yescomplemented
17#14583317—22no—
18#14583317C2214yescomplemented
19C2×#13063264—21no—
20C22×C43⋊C16C2211yescharacteristic
21C2×C16×D43—21no—
22#14583175—22no—
23#14583175C2214yescomplemented
24#14583166—22no—
25#14583166C2214yes—
26C2×#13063261C2211yescharacteristic
27C2×#13063243—21no—
28C2×#13063242—21no—
29#14582728C2214yescomplemented
30#14582716C2214yescomplemented
31C22×D8×C43C2211yescharacteristic
32C2×M32×C43C2211yescharacteristic
33C2×#108×C43C2211yescharacteristic
34C43×#361C2214yescomplemented
35C2×#10621898D411yescharacteristic
36C22×Dic86—21no—
37#13063358—24no—
38#13063358—42no—
39#13063351—24no—
40#13063351—42no—
41C2×Dic172—21no—
42C2×Dic172—21no—
43C2×Dic172—21no—
44C2×Dic172—21no—
45C2×Dic172—21no—
46C2×Dic172—41no—
47C2×Dic172C2312yes—
48C2×#10621873—41no—
49C2×#10621883—41no—
50C2×#10621882—41no—
51#13063331—21no—
52#13063331—21no—
53#13063331D412yes—
54#13063331C2312yes—
55C2×#10621877—21no—
56C2×#10621877D411yescharacteristic
57C2×#10621872—21no—
58C2×C8×D43—21no—
59#13063269—24no—
60#13063269—24no—
61#13063264—24no—
62C2×C43⋊C16D411yescharacteristic
63C2×C43⋊C16D411yescharacteristic
64C2×C43⋊C16D412yes—
65C2×C43⋊C16C2312yes—
66C16×D43—24no—
67#13063261—21no—
68#13063261C2312yes—
69#13063243—24no—
70#13063242—24no—
71C22×D4×C43—21no—
72C2×D8×C43—21no—
73C2×D8×C43—21no—
74C2×D8×C43—21no—
75C2×D8×C43—21no—
76C2×D8×C43—21no—
77C2×D8×C43C2312yes—
78C2×M16×C43—21no—
79C22×C8×C43C2311yescharacteristic
80M32×C43—21no—
81M32×C43C2312yes—
82C2×C16×C43—21no—
83#108×C43—21no—
84#108×C43C2312yes—
85C24×C43—41no—
86C2×D4×C43—22no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C2×D4×C43—41no—
90C2×D4×C43—41no—
91C2×D4×C43—41no—
92C22×C4×C43C2×D411yescharacteristic
93C2×C22⋊D43—21no—
94C22×Dic43—41no—
95#10621898—21no—
96#10621898—21no—
97#10621898D812yes—
98#10621898C2×D412yes—
99C2×D172D811yescharacteristic
100C2×C4×D43—21no—
101C2×Dic86—22no—
102C2×Dic86—41no—
103C2×Dic86—41no—
104C2×Dic86—41no—
105C2×Dic86—41no—
106C2×Dic86—41no—
107C2×Dic86D811yescharacteristic
108D8×C43—22no—
109D8×C43—22no—
110D8×C43—41no—
111D8×C43—41no—
112M16×C43—22no—
113M16×C43—41no—
114C2×C8×C43—41no—
115C2×C8×C43C2×D411yescharacteristic
116C2×C8×C43C2×D411yescharacteristic
117C2×C8×C43C2×D411yescharacteristic
118C2×C8×C43#4111yescharacteristic
119C2×C8×C43#4111yescharacteristic
120C2×C8×C43C2411yescharacteristic
121#10621883—44no—
122#10621882—44no—
123#10621877—21no—
124#10621877—22no—
125#10621877—41no—
126#10621877C2×D412yes—
127C2×C43⋊C8—21no—
128C2×C43⋊C8—41no—
129Dic172—22no—
130Dic172—22no—
131Dic172—44no—
132Dic172—41no—
133Dic172—41no—
134#10621873—44no—
135#10621872—22no—
136#10621872—22no—
137C8×D43—22no—
138C8×D43—22no—
139C16×C43—22no—
140C43⋊C16C2×D412yes—
141C43⋊C16C2×D412yes—
142C23×C43—42no—
143C23×C43—81no—
144C23×C43—81no—
145C23×C43—162no—
146C23×C43#13511yescharacteristic
147C22×D43—21no—
148D4×C43—42no—
149D4×C43—42no—
150D4×C43—81no—
151D4×C43—81no—
152C2×C4×C43#12111yescharacteristic
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43C2×D811yescharacteristic
155C2×C4×C43C2×D811yescharacteristic
156C2×C4×C43#13511yescharacteristic
157C2×C4×C43C22×D411yescharacteristic
158C22⋊D43—22no—
159C22⋊D43—22no—
160C2×Dic43—21no—
161C2×Dic43—42no—
162C2×Dic43—81no—
163C2×Dic43—81no—
164D172—21no—
165D172C2×D812yes—
166C4×D43—22no—
167C4×D43—22no—
168Dic86—21no—
169Dic86—42no—
170Dic86—42no—
171Dic86—81no—
172Dic86—81no—
173Dic86C2×D812yes—
174C8×C43—42no—
175C8×C43#12111yescharacteristic
176C8×C43#12111yescharacteristic
177C8×C43C22×D411yescharacteristic
178C8×C43C2×#4111yescharacteristic
179C43⋊C8—22no—
180C43⋊C8—42no—
181C2×#2223—431nomaximal, Sylow
182C22×C43—22no—
183C22×C43—82no—
184C22×C43—162no—
185C22×C43—162no—
186C22×C43—162no—
187C22×C43#46611yescharacteristic
188C22×C43#46611yescharacteristic
189C22×C43C2×#13511yescharacteristic
190C2×D43—22no—
191C2×D43—42no—
192C4×C43#46611yescharacteristic
193C4×C43#46611yescharacteristic
194C4×C43C2×#12111yescharacteristic
195C4×C43C22×D811yescharacteristic
196Dic43—22no—
197Dic43—82no—
198C22×SD32—431no—
199C2×#504—431no—
200C2×#473—431no—
201C2×#472—431no—
202#2223—438no—
203C2×#368—431no—
204C2×#362—431no—
205C2×#361D4311yescharacteristic, complemented
206C2×C43—21no—
207C2×C43—21no—
208C2×C43—162no—
209C2×C43#222312yescomplemented
210C2×C43C2×#46611yescharacteristic
211D43—42no—
212C2×#137—861no—
213C2×AGL(1,ℤ/8)—861no—
214C22×Q16—431no—
215C22×D8C2×D4311yescharacteristic
216C2×#131—431no—
217C2×SD32—434no—
218C2×SD32—861no—
219C2×SD32—861no—
220C2×SD32—862no—
221#504—434no—
222#504—862no—
223C2×M32—861no—
224C2×M32C2×D4311yescharacteristic
225C22×C16—431no—
226C22×C16—861no—
227#473—434no—
228#473—862no—
229#472—434no—
230#472—862no—
231C2×#108—431no—
232C2×#108C2×D4311yescharacteristic
233C2×#101—861no—
234C2×#100—861no—
235#368—434no—
236#362—434no—
237#361C2×D4314yescomplemented
238C43C2×#222311yescharacteristic, complemented, Sylow
239C2×#41—431no—
240C22×Q8—861no—
241C22×D4—21no—
242#137—864no—
243#137—1722no—
244AGL(1,ℤ/8)—864no—
245AGL(1,ℤ/8)—1722no—
246C2×Q16—432no—
247C2×Q16—861no—
248C2×Q16—861no—
249C2×Q16—861no—
250C2×Q16—861no—
251C2×Q16—861no—
252C2×Q16—1721no—
253C2×SD16—1721no—
254C2×SD16—1721no—
255C2×D8—21no—
256C2×D8—21no—
257C2×D8—21no—
258C2×D8—21no—
259C2×D8—21no—
260C2×D8—1721no—
261C2×D8C22×D4312yes—
262#131—432no—
263#131—432no—
264#131—861no—
265#131—861no—
266C2×M16—21no—
267C2×M16—431no—
268C2×M16—861no—
269C2×M16—861no—
270C22×C8—861no—
271C22×C8C22×D4311yescharacteristic
272SD32—864no—
273SD32—864no—
274M32—21no—
275M32—864no—
276M32C22×D4312yes—
277C2×C16—21no—
278C2×C16—431no—
279C2×C16—431no—
280C2×C16—432no—
281C2×C16—432no—
282C2×C16—864no—
283#108—21no—
284#108—432no—
285#108—861no—
286#108C22×D4312yes—
287#101—864no—
288#100—864no—
289C24—41no—
290#41—432no—
291#41—432no—
292#41—861no—
293#41—861no—
294C2×Q8—431no—
295C2×Q8—862no—
296C2×Q8—1721no—
297C2×Q8—1721no—
298C2×Q8—1721no—
299C2×Q8—1721no—
300C2×Q8—1721no—
301C2×D4—22no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—431no—
308C2×D4—861no—
309C22×C4—861no—
310C22×C4—1721no—
311C22×C4D4×D4311yescharacteristic
312Q16—862no—
313Q16—862no—
314Q16—1724no—
315Q16—1721no—
316Q16—1721no—
317SD16—1724no—
318SD16—1724no—
319D8—22no—
320D8—22no—
321D8—41no—
322D8—41no—
323D8—1724no—
324M16—22no—
325M16—41no—
326M16—432no—
327M16—861no—
328M16—862no—
329M16—862no—
330M16—862no—
331M16—1721no—
332C2×C8—41no—
333C2×C8—861no—
334C2×C8—862no—
335C2×C8—862no—
336C2×C8—1721no—
337C2×C8#1062189811yescharacteristic
338C2×C8#1062189811yescharacteristic
339C2×C8D4×D4311yescharacteristic
340C2×C8D4×D4311yescharacteristic
341C2×C8D4×D4311yescharacteristic
342C2×C8C23×D4311yescharacteristic
343C16—22no—
344C16—432no—
345C16—432no—
346C23—42no—
347C23—81no—
348C23—81no—
349C23—162no—
350C23—861no—
351C23#1306334611yescharacteristic
352Q8—432no—
353Q8—861no—
354Q8—3441no—
355Q8—3441no—
356Q8—1722no—
357Q8—1722no—
358D4—42no—
359D4—42no—
360D4—81no—
361D4—81no—
362D4—432no—
363D4—862no—
364D4—862no—
365D4—861no—
366C2×C4—861no—
367C2×C4—862no—
368C2×C4—862no—
369C2×C4—3441no—
370C2×C4—3441no—
371C2×C4—1722no—
372C2×C4#1306329811yescharacteristic
373C2×C4#1306329811yescharacteristic
374C2×C4D8×D4311yescharacteristic
375C2×C4D8×D4311yescharacteristic
376C2×C4#1306334611yescharacteristic
377C2×C4C2×D4×D4311yescharacteristic
378C8—42no—
379C8—862no—
380C8—1722no—
381C8#1306329811yescharacteristic
382C8#1306329811yescharacteristic
383C8C2×D4×D4311yescharacteristic
384C8C2×#1062189811yescharacteristic
385C22—22no—
386C22—82no—
387C22—162no—
388C22—162no—
389C22—162no—
390C22—862no—
391C22—1722no—
392C22#1458313411yescharacteristic
393C22#1458313411yescharacteristic
394C22C2×#1306334611yescharacteristic
395C4—862no—
396C4—3442no—
397C4#1458313411yescharacteristic
398C4#1458313411yescharacteristic
399C4C2×#1306329811yescharacteristic
400C4C2×D8×D4311yescharacteristic
401C2—21no—
402C2—21no—
403C2—162no—
404C2—1722no—
405C2#1913672412yesdirect product factor
406C2C2×#1458313411yescharacteristic
subgroupG/H
centerC22#14583134
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC2×C43×#361C2
socleC22×C43#466
prime radicalC2×#14583166C2
hypercenterC2×#361D43
hypocenterC43C2×#2223
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

Complements

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

NH ≅ G/Ntype
1. C22×#13063269C2semidirect
2. C2×#14583317C2semidirect
3. C2×#14583175C2semidirect
5. #19136724C2direct (N × H)
6. C2×#14582728C2semidirect
7. C2×#14582716C2semidirect
8. C2×C43×#361C2semidirect
16. C2×#13063269C22semidirect
18. #14583317C22semidirect
23. #14583175C22semidirect
29. #14582728C22semidirect
30. #14582716C22semidirect
34. C43×#361C22semidirect
205. C2×#361D43semidirect
209. C2×C43#2223semidirect
237. #361C2×D43semidirect
238. C43C2×#2223semidirect
405. C2#19136724direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130632692
C2×#145833172
C2×#145831752
C2×#145831662
#191367242
C2×#145827282
C2×#145827162
C2×C43×#3612
C2×#222343