Finite Group Databasebeta

← C2×#19143058 #25960070

Subgroups — C2×#19143058 #25960070

Order 11008.

4818 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
1C22×#13063373C211yesmaximal, characteristic
2C2×#14583377C211yesmaximal, characteristic, complemented
3#19143058C2116yesmaximal, direct product factor
4C2×#14582872C2112yesmaximal, complemented
5C2×C43×#519C211yesmaximal, characteristic, complemented
6C2×#13063373—24no—
7C2×#13063373—24no—
8C2×#13063373—24no—
9C2×#13063373—24no—
10C2×#13063373C418yescomplemented
11C2×#13063373C2218yes—
12C22×#10621902C414yescomplemented
13C22×#10621898C2216yes—
14C22×Q8×D43C414yescomplemented
15#14583377—24no—
16#14583377C2218yescomplemented
17C2×Q8×Dic43—24no—
18C2×#13063284C2216yes—
19#14582872C22196yescomplemented
20C2×#13063239C22116yes—
21C23×Q8×C43C2211yescharacteristic
22C43×#519—24no—
23C43×#519C2218yescomplemented
24C2×C4×Q8×C43—24no—
25C2×#117×C43C2216yes—
26#13063373—232no—
27#13063373—232no—
28#13063373—232no—
29#13063373—232no—
30C2×#10621902—216no—
31C2×#10621902—216no—
32C2×#10621902C2×C4132yescomplemented
33C2×#10621898—212no—
34C2×#10621898—212no—
35C2×#10621898—212no—
36C2×#10621898—212no—
37C2×#10621898C2×C4124yes—
38C2×#10621898C23124yes—
39C22×Dic86C2×C416yes—
40C2×Q8×D43—216no—
41C2×Q8×D43—216no—
42C2×Q8×D43C2×C4132yescomplemented
43C22×D172C2×C416yes—
44C22×C22⋊D43C2314yes—
45C22×C4×D43C2×C4112yes—
46Q8×Dic43—232no—
47#13063284—212no—
48#13063284C23124yes—
49C2×C4⋊Dic43—26no—
50C2×C22⋊Dic43C2314yes—
51C2×C4×Dic43—26no—
52#13063239C23164yes—
53C22×Q8×C43C2×C414yes—
54C22×Q8×C43C2×C414yes—
55C22×Q8×C43D414yes—
56C22×Q8×C43D414yes—
57C22×Q8×C43D414yes—
58C22×Q8×C43D414yes—
59C22×Q8×C43C2314yes—
60C23×C4×C43C2313yes—
61C4×Q8×C43—232no—
62#117×C43—212no—
63#117×C43C23124yes—
64C2×C4⋊C4×C43—26no—
65C2×C22⋊C4×C43C2314yes—
66C2×C42×C43—26no—
67C24×C43C2411yescharacteristic
68C23×D43C22×C414yes—
69C2×Q8×C43C22⋊C4116yes—
70C2×Q8×C43C22⋊C4116yes—
71C2×Q8×C43C22⋊C4116yes—
72C2×Q8×C43C22⋊C4116yes—
73C2×Q8×C43C22×C4116yes—
74C2×Q8×C43C2×D4116yes—
75C2×Q8×C43C2×D4116yes—
76C22×C4×C43—24no—
77C22×C4×C43C22×C416yes—
78C22×C4×C43C22×C416yes—
79C22×C4×C43C2×D416yes—
80C22×C4×C43C2×D416yes—
81C22×C4×C43C2×D416yes—
82C22×C4×C43C2×D416yes—
83C22×C4×C43C2416yes—
84C2×C22⋊D43—24no—
85C2×C22⋊D43—24no—
86C2×C22⋊D43—24no—
87C2×C22⋊D43—24no—
88C2×C22⋊D43C22×C418yes—
89C2×C22⋊D43C2418yes—
90C22×Dic43—24no—
91C22×Dic43C22×C414yes—
92#10621902—2128no—
93Q8×D43—2128no—
94#10621898—248no—
95#10621898—248no—
96#10621898—248no—
97#10621898—248no—
98C2×D172—212no—
99C2×D172—212no—
100C2×D172C22×C4124yes—
101C2×C4×D43—224no—
102C2×C4×D43—224no—
103C2×C4×D43C22×C4148yes—
104C2×Dic86—212no—
105C2×Dic86—212no—
106C2×Dic86C22×C4124yes—
107C4⋊C4×C43—224no—
108C22⋊C4×C43—24no—
109C22⋊C4×C43C2418yes—
110C42×C43—224no—
111C22⋊Dic43—24no—
112C22⋊Dic43C2418yes—
113C4⋊Dic43—224no—
114C4×Dic43—224no—
115C23×C43—42no—
116C23×C43C23×C411yescharacteristic
117C23×C43C23×C411yescharacteristic
118C23×C43C22×D411yescharacteristic
119C23×C43C22×D411yescharacteristic
120C23×C43C22×D411yescharacteristic
121C23×C43C22×D411yescharacteristic
122C23×C43C2511yescharacteristic
123C22×D43—24no—
124C22×D43—24no—
125C22×D43—48no—
126C22×D43C23×C418yes—
127Q8×C43C2×C22⋊C4164yes—
128C2×C4×C43—28no—
129C2×C4×C43—48no—
130C2×C4×C43C2×C22⋊C4112yes—
131C2×C4×C43C2×C22⋊C4112yes—
132C2×C4×C43C2×C22⋊C4112yes—
133C2×C4×C43C2×C22⋊C4112yes—
134C2×C4×C43C23×C4112yes—
135C2×C4×C43C22×D4112yes—
136C2×C4×C43C22×D4112yes—
137C22⋊D43—28no—
138C22⋊D43—28no—
139C22⋊D43—28no—
140C22⋊D43—28no—
141C2×Dic43—24no—
142C2×Dic43—24no—
143C2×Dic43—28no—
144C2×Dic43—48no—
145C2×Dic43C23×C418yes—
146D172—248no—
147C4×D43—296no—
148Dic86—248no—
149C2×#2884—431nomaximal, Sylow
150C22×C43—22no—
151C22×C43—22no—
152C22×C43—22no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43C22×C22⋊C411yescharacteristic
158C22×C43C22×C22⋊C411yescharacteristic
159C22×C43C22×C22⋊C411yescharacteristic
160C22×C43C22×C22⋊C411yescharacteristic
161C22×C43C24×C411yescharacteristic
162C22×C43C23×D411yescharacteristic
163C22×C43C23×D411yescharacteristic
164C2×D43—28no—
165C2×D43—48no—
166C2×D43—48no—
167C2×D43—48no—
168C4×C43—48no—
169C4×C43C22×C22⋊C4124yes—
170Dic43—28no—
171Dic43—48no—
172C22×2−1+4—431no—
173C2×#519—431no—
174C2×#519D4311yescharacteristic, complemented
175#2884—4316no—
176C2×#410—4312no—
177C2×C43—21no—
178C2×C43—21no—
179C2×C43—21no—
180C2×C43—21no—
181C2×C43—21no—
182C2×C43—21no—
183C2×C43#288412yescomplemented
184C2×C43C23×C22⋊C411yescharacteristic
185D43—48no—
186C2×2−1+4—438no—
187C2×2−1+4—438no—
188C2×2−1+4—864no—
189C2×2−1+4—864no—
190C2×2−1+4—864no—
191C2×2−1+4—864no—
192C22×#41—434no—
193C22×#41—436no—
194C23×Q8—434no—
195C23×Q8C2×D4311yescharacteristic
196#519—24no—
197#519—438no—
198#519—864no—
199#519C2×D4318yescomplemented
200C2×C4×Q8—24no—
201C2×C4×Q8—864no—
202C2×#117—436no—
203C2×#117C2×D4316yes—
204#410—4396no—
205C2×#99—4316no—
206C43C2×#288411yescharacteristic, complemented, Sylow
2072−1+4—8632no—
2082−1+4—8632no—
2092−1+4—8632no—
2102−1+4—8632no—
211C2×#41—4332no—
212C2×#41—4324no—
213C2×#41—4324no—
214C2×#41—8616no—
215C2×#41—8616no—
216C2×#41—8612no—
217C2×#41—8612no—
218C2×#41—8612no—
219C2×#41—8612no—
220C22×Q8—4332no—
221C22×Q8—436no—
222C22×Q8—8616no—
223C22×Q8—8616no—
224C22×Q8C4×D4314yes—
225C22×Q8C4×D4314yes—
226C22×Q8D17214yes—
227C22×Q8D17214yes—
228C22×Q8C22⋊D4314yes—
229C22×Q8C22⋊D4314yes—
230C22×Q8C22×D4314yes—
231C22×D4—434no—
232C22×D4—436no—
233C23×C4—4312no—
234C23×C4C22×D4313yes—
235C4×Q8—232no—
236C4×Q8—8632no—
237#117—212no—
238#117—4324no—
239#117—8612no—
240#117C22×D43124yes—
241C2×C4⋊C4—26no—
242C2×C4⋊C4—866no—
243C2×C22⋊C4—434no—
244C2×C22⋊C4C22×D4314yes—
245C2×C42—26no—
246C2×C42—866no—
247#99—4364no—
248C24—434no—
249C24C23×D4311yescharacteristic
250#41—86128no—
251#41—8648no—
252#41—8648no—
253#41—8648no—
254#41—8648no—
255C2×Q8—4324no—
256C2×Q8—86128no—
257C2×Q8—8612no—
258C2×Q8—8612no—
259C2×Q8(C2×D43)⋊C4116yes—
260C2×Q8(C2×D43)⋊C4116yes—
261C2×Q8(C2×D43)⋊C4116yes—
262C2×Q8(C2×D43)⋊C4116yes—
263C2×Q8C2×C4×D43116yes—
264C2×Q8C2×D172116yes—
265C2×Q8C2×C22⋊D43116yes—
266C2×D4—438no—
267C2×D4—438no—
268C2×D4—4324no—
269C2×D4—864no—
270C2×D4—864no—
271C2×D4—864no—
272C2×D4—864no—
273C2×D4—8612no—
274C2×D4—8612no—
275C22×C4—24no—
276C22×C4—434no—
277C22×C4—4348no—
278C22×C4—8624no—
279C22×C4—8624no—
280C22×C4—864no—
281C22×C4C2×C4×D4316yes—
282C22×C4C2×C4×D4316yes—
283C22×C4C2×D17216yes—
284C22×C4C2×D17216yes—
285C22×C4C2×C22⋊D4316yes—
286C22×C4C2×C22⋊D4316yes—
287C22×C4C23×D4316yes—
288C4⋊C4—224no—
289C4⋊C4—8624no—
290C22⋊C4—24no—
291C22⋊C4—438no—
292C22⋊C4—864no—
293C22⋊C4C23×D4318yes—
294C42—224no—
295C42—8624no—
296C23—42no—
297C23—438no—
298C23—864no—
299C23—864no—
300C23—1728no—
301C23C22×C4×D4311yescharacteristic
302C23C22×C4×D4311yescharacteristic
303C23C22×C22⋊D4311yescharacteristic
304C23C22×C22⋊D4311yescharacteristic
305C23C22×D17211yescharacteristic
306C23C22×D17211yescharacteristic
307C23C24×D4311yescharacteristic
308Q8—8648no—
309Q8C2×(C2×D43)⋊C4164yes—
310D4—868no—
311D4—868no—
312D4—868no—
313D4—868no—
314D4—8648no—
315C2×C4—28no—
316C2×C4—48no—
317C2×C4—438no—
318C2×C4—864no—
319C2×C4—864no—
320C2×C4—8696no—
321C2×C4—868no—
322C2×C4—1728no—
323C2×C4C2×(C2×D43)⋊C4112yes—
324C2×C4C2×(C2×D43)⋊C4112yes—
325C2×C4C2×(C2×D43)⋊C4112yes—
326C2×C4C2×(C2×D43)⋊C4112yes—
327C2×C4C22×C4×D43112yes—
328C2×C4C22×C22⋊D43112yes—
329C2×C4C22×D172112yes—
330C22—22no—
331C22—22no—
332C22—22no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—868no—
338C22—1728no—
339C22—1728no—
340C22—1728no—
341C22C22×(C2×D43)⋊C411yescharacteristic
342C22C22×(C2×D43)⋊C411yescharacteristic
343C22C22×(C2×D43)⋊C411yescharacteristic
344C22C22×(C2×D43)⋊C411yescharacteristic
345C22C23×C4×D4311yescharacteristic
346C22C23×C22⋊D4311yescharacteristic
347C22C23×D17211yescharacteristic
348C4—48no—
349C4—868no—
350C4—1728no—
351C4C22×(C2×D43)⋊C4124yes—
352C2—21no—
353C2—21no—
354C2—21no—
355C2—21no—
356C2—21no—
357C2—21no—
358C2—1728no—
359C2#1914305812yesdirect product factor
360C2C23×(C2×D43)⋊C411yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#519C2
socleC22×C43C22×C22⋊C4
prime radicalC22×#13063373C2
cosocleC23×C43C25
hypercenterC2×#519D43
hypocenterC43C2×#2884
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×Q8 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
2. C2×#14583377C2semidirect
3. #19143058C2direct (N × H)
4. C2×#14582872C2semidirect
5. C2×C43×#519C2semidirect
10. C2×#13063373C4semidirect
12. C22×#10621902C4semidirect
14. C22×Q8×D43C4semidirect
16. #14583377C22semidirect
19. #14582872C22semidirect
23. C43×#519C22semidirect
32. C2×#10621902C2×C4semidirect
42. C2×Q8×D43C2×C4semidirect
174. C2×#519D43semidirect
183. C2×C43#2884semidirect
199. #519C2×D43semidirect
206. C43C2×#2884semidirect
359. C2#19143058direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633732
C2×#145833772
#191430582
C2×#145828722
C2×C43×#5192
C2×#288443