Finite Group Databasebeta

← C2×#19132863 #25018317

Subgroups — C2×#19132863 #25018317

Order 11008.

2942 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C43⋊#95C214yesmaximal
2C22×C43⋊#95C211yesmaximal, characteristic
3C22×C43⋊#95C211yesmaximal, characteristic
4#19132863C218yesmaximal, direct product factor
5C23×C4⋊C4×C43C211yesmaximal, characteristic
6C24×Dic43C2212yes—
7C24×Dic43C2212yes—
8C2×C43⋊#95—216no—
9C2×C43⋊#95—24no—
10C2×C43⋊#95—24no—
11C2×C43⋊#95C22116yes—
12C2×C43⋊#95C2214yes—
13C2×C43⋊#95C2214yes—
14C24×C4×C43C2212yes—
15C24×C4×C43C2211yescharacteristic
16C22×C4⋊C4×C43—24no—
17C22×C4⋊C4×C43—24no—
18C22×C4⋊C4×C43C418yescomplemented
19C22×C4⋊C4×C43C2214yes—
20C23×Dic43—28no—
21C23×Dic43—24no—
22C23×Dic43—24no—
23C23×Dic43—28no—
24C23×Dic43—28no—
25C23×Dic43—24no—
26C23×Dic43—24no—
27C23×Dic43—28no—
28C23×Dic43D418yes—
29C23×Dic43Q818yes—
30C23×Dic43C2314yes—
31C23×Dic43C2314yes—
32C43⋊#95—28no—
33C43⋊#95—28no—
34C43⋊#95—232no—
35C25×C43C2311yescharacteristic
36C23×C4×C43—28no—
37C23×C4×C43—24no—
38C23×C4×C43—24no—
39C23×C4×C43—28no—
40C23×C4×C43—28no—
41C23×C4×C43C2×C418yes—
42C23×C4×C43C2×C414yes—
43C23×C4×C43D414yes—
44C23×C4×C43D414yes—
45C23×C4×C43C2314yes—
46C23×C4×C43C2312yes—
47C2×C4⋊C4×C43—232no—
48C2×C4⋊C4×C43—28no—
49C2×C4⋊C4×C43—28no—
50C2×C4⋊C4×C43C2×C4116yescomplemented
51C24×C43C22×C412yes—
52C24×C43C2×D412yes—
53C24×C43C2×D412yes—
54C24×C43C2×D414yes—
55C24×C43C2×Q814yes—
56C24×C43#4118yes—
57C24×C43#4114yes—
58C24×C43#4114yes—
59C24×C43C2411yescharacteristic
60C22×C4×C43—216no—
61C22×C4×C43—216no—
62C22×C4×C43—232no—
63C22×C4×C43—216no—
64C22×C4×C43—216no—
65C22×C4×C43—24no—
66C22×C4×C43—24no—
67C22×C4×C43—28no—
68C22×C4×C43—28no—
69C22×C4×C43—28no—
70C22×C4×C43—416no—
71C22×C4×C43—48no—
72C22×C4×C43—48no—
73C22×C4×C43C22⋊C4116yes—
74C22×C4×C43C22×C418yes—
75C22×C4×C43C22×C414yes—
76C22×C4×C43C2×D414yes—
77C22×C4×C43C2×D414yes—
78C22×Dic43—216no—
79C22×Dic43—216no—
80C22×Dic43—232no—
81C22×Dic43—232no—
82C22×Dic43—28no—
83C22×Dic43—24no—
84C22×Dic43—24no—
85C22×Dic43—24no—
86C22×Dic43—28no—
87C22×Dic43—28no—
88C22×Dic43—24no—
89C22×Dic43—28no—
90C22×Dic43—48no—
91C22×Dic43—48no—
92C22×Dic43—416no—
93C22×Dic43—48no—
94C22×Dic43—416no—
95C22×Dic43—48no—
96C22×Dic43C2×D418yes—
97C22×Dic43C2×Q818yes—
98C4⋊C4×C43—232no—
99C23×C43C2×C22⋊C414yes—
100C23×C43#11718yes—
101C23×C43C4×D418yes—
102C23×C43C4×Q818yes—
103C23×C43#12118yes—
104C23×C43C22⋊Q818yes—
105C23×C43C22⋊Q8116yes—
106C23×C43#12318yes—
107C23×C43#12318yes—
108C23×C43#123116yes—
109C23×C43#12414yes—
110C23×C43#12414yes—
111C23×C43#125116yes—
112C23×C43#126116yes—
113C23×C43#12714yes—
114C23×C43C4⋊Q814yes—
115C23×C43C23×C411yescharacteristic
116C23×C43C22×D412yes—
117C23×C43C22×D411yescharacteristic
118C23×C43C22×D411yescharacteristic
119C23×C43C22×Q812yes—
120C23×C43C2×#4112yes—
121C23×C43C2×#4114yes—
122C23×C43C2×#4112yes—
123C2×C4×C43—28no—
124C2×C4×C43—28no—
125C2×C4×C43—28no—
126C2×C4×C43—232no—
127C2×C4×C43—28no—
128C2×C4×C43—216no—
129C2×C4×C43—48no—
130C2×C4×C43—44no—
131C2×C4×C43—44no—
132C2×C4×C43—432no—
133C2×C4×C43C2×C22⋊C418yes—
134C2×Dic43—28no—
135C2×Dic43—28no—
136C2×Dic43—216no—
137C2×Dic43—216no—
138C2×Dic43—44no—
139C2×Dic43—44no—
140C2×Dic43—48no—
141C2×Dic43—44no—
142C2×Dic43—48no—
143C2×Dic43—44no—
144C2×Dic43—432no—
145C2×Dic43—432no—
146C2×#1445—431nomaximal, Sylow
147C22×C43#38118yes—
148C22×C43#387132yes—
149C22×C43#39018yes—
150C22×C43#39118yes—
151C22×C43#397116yes—
152C22×C43#398116yes—
153C22×C43#399116yes—
154C22×C43#400116yes—
155C22×C43C22×C22⋊C411yescharacteristic
156C22×C43C2×#11712yes—
157C22×C43C2×C4×D412yes—
158C22×C43C2×C4×Q812yes—
159C22×C43C2×#12112yes—
160C22×C43C2×C22⋊Q812yes—
161C22×C43C2×C22⋊Q814yes—
162C22×C43C2×#12312yes—
163C22×C43C2×#12312yes—
164C22×C43C2×#12314yes—
165C22×C43C2×#12411yescharacteristic
166C22×C43C2×#12411yescharacteristic
167C22×C43C2×#12514yes—
168C22×C43C2×#12614yes—
169C22×C43C2×#12711yescharacteristic
170C22×C43C2×C4⋊Q811yescharacteristic
171C4×C43—28no—
172C4×C43—48no—
173Dic43—48no—
174Dic43—48no—
175C23×C4⋊C4D4311yescharacteristic
176C22×#95—434no—
177C22×#95—431no—
178C22×#95—431no—
179#1445—438no—
180C2×C43#1445116yescomplemented
181C2×C43C2×#38111yescharacteristic
182C2×C43C2×#38714yes—
183C2×C43C2×#39011yescharacteristic
184C2×C43C2×#39111yescharacteristic
185C2×C43C2×#39712yes—
186C2×C43C2×#39812yes—
187C2×C43C2×#39912yes—
188C2×C43C2×#40012yes—
189C24×C4—432no—
190C24×C4—432no—
191C24×C4C2×D4312yes—
192C24×C4C2×D4311yescharacteristic
193C22×C4⋊C4—24no—
194C22×C4⋊C4—24no—
195C22×C4⋊C4Dic4318yescomplemented
196C22×C4⋊C4C2×D4314yes—
197C2×#95—4316no—
198C2×#95—434no—
199C2×#95—434no—
200C2×#95—8616no—
201C2×#95—864no—
202C2×#95—864no—
203C43C2×#144511yescharacteristic, complemented, Sylow
204C25C22×D4311yescharacteristic
205C23×C4—28no—
206C23×C4—28no—
207C23×C4—28no—
208C23×C4—24no—
209C23×C4—24no—
210C23×C4—438no—
211C23×C4—438no—
212C23×C4—434no—
213C23×C4—434no—
214C23×C4—868no—
215C23×C4—868no—
216C23×C4—868no—
217C23×C4—864no—
218C23×C4—864no—
219C23×C4—868no—
220C23×C4—864no—
221C23×C4—864no—
222C23×C4C2×Dic4318yes—
223C23×C4C2×Dic4314yes—
224C23×C4C22⋊D4314yes—
225C23×C4C22⋊D4314yes—
226C23×C4C22×D4314yes—
227C23×C4C22×D4312yes—
228C2×C4⋊C4—232no—
229C2×C4⋊C4—28no—
230C2×C4⋊C4—28no—
231C2×C4⋊C4C2×Dic43116yescomplemented
232#95—8632no—
233#95—868no—
234#95—868no—
235C24#1062189818yes—
236C24D4×D4314yes—
237C24#1062190014yes—
238C24Q8×D4314yes—
239C24#1062190214yes—
240C24C22×Dic4312yes—
241C24C2×C22⋊D4312yes—
242C24C2×C22⋊D4312yes—
243C24C23×D4311yescharacteristic
244C22×C4—216no—
245C22×C4—216no—
246C22×C4—216no—
247C22×C4—28no—
248C22×C4—216no—
249C22×C4—232no—
250C22×C4—28no—
251C22×C4—24no—
252C22×C4—24no—
253C22×C4—28no—
254C22×C4—416no—
255C22×C4—48no—
256C22×C4—48no—
257C22×C4—438no—
258C22×C4—438no—
259C22×C4—8616no—
260C22×C4—8616no—
261C22×C4—8632no—
262C22×C4—8632no—
263C22×C4—868no—
264C22×C4—864no—
265C22×C4—864no—
266C22×C4—864no—
267C22×C4—868no—
268C22×C4—868no—
269C22×C4—864no—
270C22×C4—868no—
271C22×C4—1728no—
272C22×C4—1728no—
273C22×C4—17216no—
274C22×C4—1728no—
275C22×C4—17216no—
276C22×C4—1728no—
277C22×C4C22⋊Dic43116yes—
278C22×C4C22×Dic4318yes—
279C22×C4C22×Dic4314yes—
280C22×C4C2×C22⋊D4314yes—
281C22×C4C2×C22⋊D4314yes—
282C4⋊C4—232no—
283C23C2×C22⋊Dic4314yes—
284C23#1306328418yes—
285C23D4×Dic4318yes—
286C23Q8×Dic4318yes—
287C23#1306329618yes—
288C23#1306330118yes—
289C23#13063303116yes—
290C23#1306330818yes—
291C23#1306330818yes—
292C23#13063310116yes—
293C23#1306331214yes—
294C23#1306331414yes—
295C23#13063315116yes—
296C23#13063320116yes—
297C23#1306332114yes—
298C23#1306332314yes—
299C23C23×Dic4311yescharacteristic
300C23C2×D4×D4312yes—
301C23C22×C22⋊D4311yescharacteristic
302C23C22×C22⋊D4311yescharacteristic
303C23C2×Q8×D4312yes—
304C23C2×#1062190012yes—
305C23C2×#1062189814yes—
306C23C2×#1062190212yes—
307C2×C4—28no—
308C2×C4—28no—
309C2×C4—28no—
310C2×C4—232no—
311C2×C4—28no—
312C2×C4—216no—
313C2×C4—432no—
314C2×C4—48no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—868no—
318C2×C4—868no—
319C2×C4—8616no—
320C2×C4—8616no—
321C2×C4—17232no—
322C2×C4—17232no—
323C2×C4—1724no—
324C2×C4—1724no—
325C2×C4—1728no—
326C2×C4—1724no—
327C2×C4—1728no—
328C2×C4—1724no—
329C2×C4C2×C22⋊Dic4318yes—
330C22#1458276218yes—
331C22#14582785132yes—
332C22#1458280218yes—
333C22#1458280618yes—
334C22#14582825116yes—
335C22#14582830116yes—
336C22#14582834116yes—
337C22#14582837116yes—
338C22C22×C22⋊Dic4311yescharacteristic
339C22C2×#1306328412yes—
340C22C2×D4×Dic4312yes—
341C22C2×Q8×Dic4312yes—
342C22C2×#1306329612yes—
343C22C2×#1306330112yes—
344C22C2×#1306330314yes—
345C22C2×#1306330812yes—
346C22C2×#1306330812yes—
347C22C2×#1306331014yes—
348C22C2×#1306331211yescharacteristic
349C22C2×#1306331411yescharacteristic
350C22C2×#1306331514yes—
351C22C2×#1306332014yes—
352C22C2×#1306332111yescharacteristic
353C22C2×#1306332311yescharacteristic
354C4—28no—
355C4—48no—
356C4—1728no—
357C4—1728no—
358C2#19132863116yesdirect product factor
359C2C2×#1458276211yescharacteristic
360C2C2×#1458278514yes—
361C2C2×#1458280211yescharacteristic
362C2C2×#1458280611yescharacteristic
363C2C2×#1458282512yes—
364C2C2×#1458283012yes—
365C2C2×#1458283412yes—
366C2C2×#1458283712yes—
subgroupG/H
centerC25C22×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC23×C4⋊C4×C43C2
socle, prime radicalC25×C43C23
cosocleC24×C43C24
hypercenterC23×C4⋊C4D43
hypocenterC43C2×#1445
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C25 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #19132863C2direct (N × H)
18. C22×C4⋊C4×C43C4semidirect
50. C2×C4⋊C4×C43C2×C4semidirect
180. C2×C43#1445semidirect
195. C22×C4⋊C4Dic43semidirect
203. C43C2×#1445semidirect
231. C2×C4⋊C4C2×Dic43semidirect
358. C2#19132863direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C43⋊#952
#191328632
C23×C4⋊C4×C432
C2×#144543