Finite Group Databasebeta

← C2×#19137197 #25255184

Subgroups — C2×#19137197 #25255184

Order 11008.

2894 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic43⋊C4C211yesmaximal, characteristic
2#19137197C2116yesmaximal, direct product factor
3C2×#14582786C214yesmaximal, complemented
4C2×#14582780C214yesmaximal, complemented
5C2×#14582760C212yesmaximal
6C2×#14582759C211yesmaximal, characteristic
7C2×C22⋊C4×Dic43C212yesmaximal
8C2×C43×#380C211yesmaximal, characteristic
9C24×Dic43C2211yescharacteristic
10C24×Dic43C2211yescharacteristic
11C22×C4⋊Dic43C2212yes—
12C22×Dic43⋊C4C4116yescomplemented
13C22×Dic43⋊C4C2212yes—
14C22×Dic43⋊C4C2212yes—
15C22×Dic43⋊C4C2218yes—
16C22×C22⋊Dic43C2212yes—
17C22×C4×Dic43C2214yes—
18#14582786C22132yescomplemented
19#14582780C22132yescomplemented
20#14582760C22116yes—
21#14582759C2218yes—
22C22⋊C4×Dic43C22116yes—
23C2×C43⋊#95C2214yes—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2218yes—
26C24×C4×C43C2211yescharacteristic
27C22×C4⋊C4×C43C2212yes—
28C22×C22⋊C4×C43C2212yes—
29C43×#380C2218yes—
30C2×#95×C43C2212yes—
31C23×Dic43—24no—
32C23×Dic43—24no—
33C23×Dic43—44no—
34C23×Dic43C2×C418yes—
35C23×Dic43C2×C418yes—
36C23×Dic43C2314yes—
37C23×Dic43C2312yes—
38C23×Dic43C2312yes—
39C23×Dic43C2314yes—
40C23×Dic43C2314yes—
41C2×C4⋊Dic43—44no—
42C2×C4⋊Dic43C2318yes—
43C2×Dic43⋊C4C2×C4116yes—
44C2×Dic43⋊C4C2×C4116yes—
45C2×Dic43⋊C4C2×C4164yescomplemented
46C2×Dic43⋊C4C2318yes—
47C2×Dic43⋊C4C2318yes—
48C2×C22⋊Dic43—28no—
49C2×C22⋊Dic43C2318yes—
50C2×C4×Dic43—48no—
51C2×C4×Dic43C23116yes—
52C43⋊#95C23116yes—
53C43⋊#95C23132yes—
54C43⋊#95C2318yes—
55C25×C43C2311yescharacteristic
56C23×C4×C43—44no—
57C23×C4×C43C2×C418yes—
58C23×C4×C43C2314yes—
59C23×C4×C43C2311yescharacteristic
60C23×C4×C43C2311yescharacteristic
61C23×C4×C43C2314yes—
62C2×C4⋊C4×C43—44no—
63C2×C4⋊C4×C43C2318yes—
64C2×C22⋊C4×C43—28no—
65C2×C22⋊C4×C43C2318yes—
66#95×C43C2318yes—
67C24×C43—24no—
68C24×C43—24no—
69C24×C43C22×C414yes—
70C24×C43#4114yes—
71C24×C43#4114yes—
72C24×C43C2412yes—
73C24×C43C2411yescharacteristic
74C22×C4×C43—28no—
75C22×C4×C43—24no—
76C22×C4×C43—24no—
77C22×C4×C43—28no—
78C22×C4×C43—28no—
79C22×C4×C43—416no—
80C22×C4×C43—48no—
81C22×C4×C43C22×C414yes—
82C22×C4×C43C22×C414yes—
83C22×C4×C43C22×C4116yes—
84C22×C4×C43C2418yes—
85C22×C4×C43C2412yes—
86C22×C4×C43C2412yes—
87C22×Dic43—232no—
88C22×Dic43—28no—
89C22×Dic43—24no—
90C22×Dic43—28no—
91C22×Dic43—24no—
92C22×Dic43—28no—
93C22×Dic43—28no—
94C22×Dic43—28no—
95C22×Dic43—28no—
96C22×Dic43—416no—
97C22×Dic43—48no—
98C22×Dic43C22×C418yes—
99C22×Dic43C22×C418yes—
100C22×Dic43C22×C4116yes—
101C22×Dic43C22×C4116yes—
102C22×Dic43C2418yes—
103C22×Dic43C2414yes—
104C22×Dic43C2414yes—
105C4⋊C4×C43—48no—
106C22⋊C4×C43—216no—
107C22⋊Dic43—216no—
108C4⋊Dic43—48no—
109Dic43⋊C4C22×C4132yes—
110Dic43⋊C4C22×C4132yes—
111C4×Dic43—416no—
112C23×C43—28no—
113C23×C43—28no—
114C23×C43—216no—
115C23×C43—216no—
116C23×C43—24no—
117C23×C43—24no—
118C23×C43#117116yes—
119C23×C43C23×C414yes—
120C23×C43C23×C412yes—
121C23×C43C2×#4114yes—
122C23×C43C2×#4112yes—
123C23×C43C2×#4114yes—
124C23×C43C2×#4112yes—
125C23×C43H(5,𝔽2)14yes—
126C23×C432−1+414yes—
127C23×C43C2511yescharacteristic
128C2×C4×C43—28no—
129C2×C4×C43—28no—
130C2×C4×C43—24no—
131C2×C4×C43—24no—
132C2×C4×C43—28no—
133C2×C4×C43—28no—
134C2×C4×C43—28no—
135C2×C4×C43—416no—
136C2×C4×C43—416no—
137C2×C4×C43C23×C414yes—
138C2×C4×C43C23×C414yes—
139C2×Dic43—232no—
140C2×Dic43—216no—
141C2×Dic43—216no—
142C2×Dic43—24no—
143C2×Dic43—24no—
144C2×Dic43—28no—
145C2×Dic43—28no—
146C2×Dic43—28no—
147C2×Dic43—28no—
148C2×Dic43—416no—
149C2×Dic43—416no—
150C2×Dic43C23×C418yes—
151C2×Dic43C23×C418yes—
152C2×#2313—431nomaximal, Sylow
153C22×C43—232no—
154C22×C43—24no—
155C22×C43—24no—
156C22×C43—28no—
157C22×C43—28no—
158C22×C43C2×#11718yes—
159C22×C43C2×#11714yes—
160C22×C43#51814yes—
161C22×C43#51914yes—
162C22×C43#53918yes—
163C22×C43#53918yes—
164C22×C43C24×C411yescharacteristic
165C22×C43C22×#4111yescharacteristic
166C22×C43C22×#4111yescharacteristic
167C22×C43C2×H(5,𝔽2)12yes—
168C22×C43C2×2−1+412yes—
169C4×C43—24no—
170C4×C43—24no—
171C4×C43—48no—
172Dic43—28no—
173Dic43—28no—
174Dic43—48no—
175C23×C4⋊C4—431no—
176#2313—4316no—
177C2×#387—434no—
178C2×#387—434no—
179C2×#381—432no—
180C2×#380—431no—
181C2×#380D4311yescharacteristic
182C2×C4×C22⋊C4—432no—
183C2×C43—28no—
184C2×C43#231318yescomplemented
185C2×C43C22×#11711yescharacteristic
186C2×C43C2×#51811yescharacteristic
187C2×C43C2×#51911yescharacteristic
188C2×C43C2×#53912yes—
189C2×C43C2×#53912yes—
190C24×C4—431no—
191C24×C4—431no—
192C24×C4C2×D4311yescharacteristic
193C22×C4⋊C4—438no—
194C22×C4⋊C4—432no—
195C22×C4⋊C4—432no—
196C22×C4⋊C4—4316no—
197C22×C4⋊C4—432no—
198C22×C4⋊C4C2×D4312yes—
199C22×C22⋊C4—432no—
200C22×C22⋊C4C2×D4312yes—
201C22×C42—434no—
202#387—4332no—
203#387—4332no—
204#381—4316no—
205#380—438no—
206#380C2×D4318yes—
207C4×C22⋊C4—4316no—
208C2×#95—434no—
209C2×#95—432no—
210C2×#95—438no—
211C2×#95C2×D4312yes—
212C43C2×#231311yescharacteristic, complemented, Sylow
213C25C22×D4311yescharacteristic
214C23×C4—44no—
215C23×C4—438no—
216C23×C4—434no—
217C23×C4—432no—
218C23×C4—432no—
219C23×C4—438no—
220C23×C4—434no—
221C23×C4—434no—
222C23×C4—864no—
223C23×C4—864no—
224C23×C4—1724no—
225C23×C4C4×D4318yes—
226C23×C4C22×D4314yes—
227C23×C4C22×D4311yescharacteristic
228C23×C4C22×D4311yescharacteristic
229C23×C4C22×D4314yes—
230C2×C4⋊C4—44no—
231C2×C4⋊C4—4316no—
232C2×C4⋊C4—4316no—
233C2×C4⋊C4—4364no—
234C2×C4⋊C4—438no—
235C2×C4⋊C4—438no—
236C2×C4⋊C4—438no—
237C2×C4⋊C4—1724no—
238C2×C4⋊C4C22×D4318yes—
239C2×C22⋊C4—28no—
240C2×C22⋊C4—438no—
241C2×C22⋊C4—868no—
242C2×C22⋊C4C22×D4318yes—
243C2×C42—4316no—
244C2×C42—1728no—
245#95—4316no—
246#95—438no—
247#95—4332no—
248#95C22×D4318yes—
249C24—24no—
250C24—24no—
251C24C2×C4×D4314yes—
252C24#1062190014yes—
253C24#1062190214yes—
254C24C23×D4312yes—
255C24C23×D4311yescharacteristic
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—28no—
259C22×C4—28no—
260C22×C4—28no—
261C22×C4—48no—
262C22×C4—416no—
263C22×C4—4316no—
264C22×C4—438no—
265C22×C4—438no—
266C22×C4—434no—
267C22×C4—434no—
268C22×C4—4316no—
269C22×C4—438no—
270C22×C4—8632no—
271C22×C4—868no—
272C22×C4—864no—
273C22×C4—868no—
274C22×C4—864no—
275C22×C4—868no—
276C22×C4—868no—
277C22×C4—868no—
278C22×C4—868no—
279C22×C4—17216no—
280C22×C4—1728no—
281C22×C4C2×C4×D4314yes—
282C22×C4C2×C4×D4314yes—
283C22×C4C2×C4×D43116yes—
284C22×C4C23×D4318yes—
285C22×C4C23×D4312yes—
286C22×C4C23×D4312yes—
287C4⋊C4—48no—
288C4⋊C4—4332no—
289C4⋊C4—4332no—
290C4⋊C4—1728no—
291C22⋊C4—216no—
292C22⋊C4—8616no—
293C42—17216no—
294C23—28no—
295C23—28no—
296C23—24no—
297C23—24no—
298C23—216no—
299C23—216no—
300C23#13063283116yes—
301C23C22×C4×D4314yes—
302C23C22×C4×D4312yes—
303C23C2×#1062190014yes—
304C23C2×#1062190012yes—
305C23C2×#1062190214yes—
306C23C2×#1062190212yes—
307C23#1306337014yes—
308C23#1306337214yes—
309C23C24×D4311yescharacteristic
310C2×C4—28no—
311C2×C4—28no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—28no—
315C2×C4—28no—
316C2×C4—28no—
317C2×C4—416no—
318C2×C4—416no—
319C2×C4—438no—
320C2×C4—438no—
321C2×C4—8632no—
322C2×C4—8616no—
323C2×C4—8616no—
324C2×C4—864no—
325C2×C4—864no—
326C2×C4—868no—
327C2×C4—868no—
328C2×C4—868no—
329C2×C4—868no—
330C2×C4—17216no—
331C2×C4—17216no—
332C2×C4C22×C4×D4314yes—
333C2×C4C22×C4×D4314yes—
334C22—24no—
335C22—24no—
336C22—28no—
337C22—28no—
338C22—232no—
339C22C2×#1306328318yes—
340C22C2×#1306328314yes—
341C22#1458337214yes—
342C22#1458337614yes—
343C22#1458349418yes—
344C22#1458349818yes—
345C22C23×C4×D4311yescharacteristic
346C22C22×#1062190011yescharacteristic
347C22C22×#1062190211yescharacteristic
348C22C2×#1306337012yes—
349C22C2×#1306337212yes—
350C4—24no—
351C4—24no—
352C4—48no—
353C4—868no—
354C4—868no—
355C4—1728no—
356C2—28no—
357C2#1913719718yesdirect product factor
358C2C22×#1306328311yescharacteristic
359C2C2×#1458337211yescharacteristic
360C2C2×#1458337611yescharacteristic
361C2C2×#1458349412yes—
362C2C2×#1458349812yes—
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#380C2
socleC24×C43C24
prime radicalC25×C43C23
cosocleC23×C43C25
hypercenterC2×#380D43
hypocenterC43C2×#2313
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. #19137197C2direct (N × H)
3. C2×#14582786C2semidirect
4. C2×#14582780C2semidirect
12. C22×Dic43⋊C4C4semidirect
18. #14582786C22semidirect
19. #14582780C22semidirect
45. C2×Dic43⋊C4C2×C4semidirect
184. C2×C43#2313semidirect
212. C43C2×#2313semidirect
357. C2#19137197direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Dic43⋊C42
#191371972
C2×#145827862
C2×#145827802
C2×#145827602
C2×#145827592
C2×C22⋊C4×Dic432
C2×C43×#3802
C2×#231343