Finite Group Databasebeta

← C2×#19136040 #25125493

Subgroups — C2×#19136040 #25125493

Order 11008.

950 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063257C211yesmaximal, characteristic, complemented
2C2×#14582900C212yesmaximal
3#19136040C218yesmaximal, direct product factor
4C2×#14582667C212yesmaximal, complemented
5C2×#14582664C211yesmaximal, characteristic, complemented
6C2×C43×#408C211yesmaximal, characteristic
7C22×#10621877C2212yes—
8C22×C4⋊Dic43C2212yes—
9C2×#13063257—22no—
10C2×#13063257—22no—
11C2×#13063257C2214yescomplemented
12#14582900—24no—
13#14582900C2218yes—
14C2×#13063249—22no—
15C2×#13063246—22no—
16#14582667C2218yescomplemented
17#14582664C2214yescomplemented
18C22×#41×C43C2211yescharacteristic
19C22×M16×C43C2211yescharacteristic
20C23×C8×C43C2211yescharacteristic
21C43×#408—22no—
22C43×#408C2214yes—
23C2×C22⋊C8×C43—22no—
24C23×Dic43—22no—
25C2×#10621877—22no—
26C2×#10621877—24no—
27C2×#10621877—24no—
28C2×#10621877C2314yes—
29C22×C43⋊C8—22no—
30C2×C4⋊Dic43—22no—
31C2×C4⋊Dic43—22no—
32C2×C4⋊Dic43—22no—
33C2×C4⋊Dic43—22no—
34C2×C4⋊Dic43—22no—
35C2×C4⋊Dic43C2314yes—
36#13063257—28no—
37#13063249—28no—
38#13063246—28no—
39C2×#41×C43—21no—
40C2×#41×C43—21no—
41C2×#41×C43—24no—
42C2×#41×C43—24no—
43C2×#41×C43D412yes—
44C2×#41×C43C2312yes—
45C22×Q8×C43D411yescharacteristic
46C22×D4×C43—21no—
47C22×D4×C43D411yescharacteristic
48C23×C4×C43—21no—
49C23×C4×C43C2311yescharacteristic
50C2×M16×C43—21no—
51C2×M16×C43—24no—
52C2×M16×C43C2312yes—
53C22×C8×C43—24no—
54C22×C8×C43—21no—
55C22×C8×C43D412yes—
56C22×C8×C43D412yes—
57C22×C8×C43C2312yes—
58C22⋊C8×C43—28no—
59C24×C43—21no—
60C24×C43#4111yescharacteristic
61#41×C43—28no—
62#41×C43—24no—
63#41×C43—24no—
64#41×C43—42no—
65#41×C43—42no—
66#41×C43—44no—
67C2×Q8×C43—21no—
68C2×Q8×C43—24no—
69C2×Q8×C43C2×D412yes—
70C2×D4×C43—21no—
71C2×D4×C43—22no—
72C2×D4×C43—22no—
73C2×D4×C43—24no—
74C2×D4×C43—44no—
75C2×D4×C43C2×D412yes—
76C22×C4×C43—22no—
77C22×C4×C43—22no—
78C22×C4×C43—21no—
79C22×C4×C43—42no—
80C22×C4×C43—42no—
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43#4114yes—
86C22×C4×C43#4114yes—
87C22×C4×C43#4111yescharacteristic
88C22×C4×C43C2411yescharacteristic
89C22×Dic43—24no—
90C22×Dic43—42no—
91C22×Dic43—42no—
92C22×Dic43—84no—
93M16×C43—24no—
94M16×C43—42no—
95C2×C8×C43—24no—
96C2×C8×C43—24no—
97C2×C8×C43—24no—
98C2×C8×C43—22no—
99C2×C8×C43—42no—
100C2×C8×C43C2×D414yes—
101C4⋊Dic43—24no—
102C4⋊Dic43—24no—
103C4⋊Dic43—42no—
104C4⋊Dic43—42no—
105#10621877—24no—
106#10621877—24no—
107#10621877—44no—
108C2×C43⋊C8—24no—
109C2×C43⋊C8—44no—
110C23×C43—24no—
111C23×C43—22no—
112C23×C43—42no—
113C23×C43—44no—
114C23×C43#12111yescharacteristic
115C23×C43#12111yescharacteristic
116C23×C43#12614yes—
117C23×C43C2×#4111yescharacteristic
118Q8×C43—24no—
119Q8×C43—42no—
120D4×C43—24no—
121D4×C43—44no—
122D4×C43—44no—
123D4×C43—42no—
124C2×C4×C43—22no—
125C2×C4×C43—42no—
126C2×C4×C43—42no—
127C2×C4×C43—42no—
128C2×C4×C43—44no—
129C2×C4×C43#12111yescharacteristic
130C2×C4×C43#12111yescharacteristic
131C2×C4×C43#12312yes—
132C2×C4×C43#12312yes—
133C2×C4×C43#12314yes—
134C2×C4×C43#12314yes—
135C2×C4×C43#12412yes—
136C2×C4×C43#12412yes—
137C2×C4×C43#12614yes—
138C2×C4×C43C22×D411yescharacteristic
139C2×C4×C43C22×D411yescharacteristic
140C2×C4×C43C2×#4112yes—
141C2×C4×C43C2×#4112yes—
142C2×Dic43—44no—
143C2×Dic43—84no—
144C2×Dic43—84no—
145C2×Dic43—84no—
146C8×C43—24no—
147C8×C43—42no—
148C43⋊C8—44no—
149C2×#2079—431nomaximal, Sylow
150C22×C43—28no—
151C22×C43—22no—
152C22×C43—22no—
153C22×C43—42no—
154C22×C43—44no—
155C22×C43—84no—
156C22×C43#39712yes—
157C22×C43#39712yes—
158C22×C43#47114yes—
159C22×C43C2×#12111yescharacteristic
160C22×C43C2×#12612yes—
161C4×C43—42no—
162C4×C43#39712yes—
163C4×C43#39712yes—
164C4×C43C2×#12311yescharacteristic
165C4×C43C2×#12312yes—
166C4×C43C2×#12411yescharacteristic
167Dic43—84no—
168C22×#106—431no—
169C2×#417—432no—
170C2×#408D4311yescharacteristic
171#2079—438no—
172C2×#343—432no—
173C2×#341—431no—
174C2×C43—22no—
175C2×C43—22no—
176C2×C43—82no—
177C2×C43#207914yescomplemented
178C2×C43C2×#39711yescharacteristic
179C2×C43C2×#47112yes—
180C22×#41C2×D4311yescharacteristic
181C22×M16—432no—
182C22×M16C2×D4311yescharacteristic
183C23×C8C2×D4311yescharacteristic
184C22×C4⋊C4—432no—
185C2×#106—434no—
186C2×#106—862no—
187C2×#106—862no—
188#417—438no—
189#417—864no—
190C2×#103—862no—
191C2×#102—862no—
192#408—22no—
193#408C2×D4314yes—
194C2×C22⋊C8—22no—
195#343—438no—
196#341—434no—
197C43C2×#207911yescharacteristic, complemented, Sylow
198C2×#41—21no—
199C2×#41—21no—
200C2×#41—24no—
201C2×#41—24no—
202C2×#41D17212yes—
203C2×#41C22×D4312yes—
204C22×Q8D17211yescharacteristic
205C22×D4—21no—
206C22×D4D17211yescharacteristic
207C23×C4—21no—
208C23×C4—862no—
209C23×C4C22×D4311yescharacteristic
210C2×M16—21no—
211C2×M16—24no—
212C2×M16—434no—
213C2×M16—862no—
214C2×M16—864no—
215C2×M16—864no—
216C2×M16C22×D4312yes—
217C22×C8—24no—
218C22×C8—21no—
219C22×C8—862no—
220C22×C8C22⋊D4312yes—
221C22×C8C22⋊D4312yes—
222C22×C8C22×D4312yes—
223C2×C4⋊C4—434no—
224C2×C4⋊C4—862no—
225C2×C4⋊C4—862no—
226C2×C4⋊C4—862no—
227C2×C4⋊C4—862no—
228C2×C4⋊C4—862no—
229#106—868no—
230#103—868no—
231#102—868no—
232C22⋊C8—28no—
233C24—21no—
234C24#1062189811yescharacteristic
235#41—28no—
236#41—24no—
237#41—24no—
238#41—42no—
239#41—42no—
240#41—44no—
241C2×Q8—21no—
242C2×Q8—24no—
243C2×Q8C2×D17212yes—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—24no—
248C2×D4—44no—
249C2×D4C2×D17212yes—
250C22×C4—21no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—864no—
256C22×C4—3444no—
257C22×C4—1722no—
258C22×C4—1722no—
259C22×C4C2×D17211yescharacteristic
260C22×C4C2×D17211yescharacteristic
261C22×C4#1062189811yescharacteristic
262C22×C4#1062190014yes—
263C22×C4#1062190014yes—
264C22×C4C2×C22⋊D4311yescharacteristic
265C22×C4C2×C22⋊D4311yescharacteristic
266C22×C4C23×D4311yescharacteristic
267M16—24no—
268M16—42no—
269M16—864no—
270M16—864no—
271M16—1724no—
272C2×C8—24no—
273C2×C8—24no—
274C2×C8—24no—
275C2×C8—22no—
276C2×C8—42no—
277C2×C8—864no—
278C2×C8—1724no—
279C2×C8C2×C22⋊D4314yes—
280C4⋊C4—864no—
281C4⋊C4—864no—
282C4⋊C4—1722no—
283C4⋊C4—1722no—
284C23—24no—
285C23—22no—
286C23—42no—
287C23—44no—
288C23#1306329911yescharacteristic
289C23#1306329911yescharacteristic
290C23#1306331814yes—
291C23C2×#1062189811yescharacteristic
292Q8—24no—
293Q8—42no—
294D4—24no—
295D4—44no—
296D4—44no—
297D4—42no—
298C2×C4—22no—
299C2×C4—42no—
300C2×C4—44no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—3444no—
304C2×C4—3444no—
305C2×C4—3444no—
306C2×C4—1724no—
307C2×C4#1306329911yescharacteristic
308C2×C4#1306329911yescharacteristic
309C2×C4#1306330612yes—
310C2×C4#1306330612yes—
311C2×C4#1306330914yes—
312C2×C4#1306330914yes—
313C2×C4#1306331212yes—
314C2×C4#1306331212yes—
315C2×C4#1306331814yes—
316C2×C4C22×C22⋊D4311yescharacteristic
317C2×C4C22×D17211yescharacteristic
318C2×C4C2×#1062190012yes—
319C2×C4C2×#1062190012yes—
320C8—24no—
321C8—42no—
322C8—1724no—
323C22—28no—
324C22—22no—
325C22—22no—
326C22—42no—
327C22—44no—
328C22—84no—
329C22#1458282412yes—
330C22#1458282412yes—
331C22#1458316214yes—
332C22C2×#1306329911yescharacteristic
333C22C2×#1306331812yes—
334C4—42no—
335C4—3444no—
336C4#1458282412yes—
337C4#1458282412yes—
338C4C2×#1306330611yescharacteristic
339C4C2×#1306330912yes—
340C4C2×#1306331211yescharacteristic
341C2—22no—
342C2—22no—
343C2—82no—
344C2#1913604014yesdirect product factor
345C2C2×#1458282411yescharacteristic
346C2C2×#1458316212yes—
subgroupG/H
centerC23#13063299
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#408C2
socleC23×C43#121
prime radicalC22×#41×C43C22
hypercenterC2×#408D43
hypocenterC43C2×#2079
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
1. C22×#13063257C2semidirect
3. #19136040C2direct (N × H)
4. C2×#14582667C2semidirect
5. C2×#14582664C2semidirect
11. C2×#13063257C22semidirect
16. #14582667C22semidirect
17. #14582664C22semidirect
177. C2×C43#2079semidirect
197. C43C2×#2079semidirect
344. C2#19136040direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130632572
C2×#145829002
#191360402
C2×#145826672
C2×#145826642
C2×C43×#4082
C2×#207943