Finite Group Databasebeta

← C2×#19133571 #25068783

Subgroups — C2×#19133571 #25068783

Order 11008.

1200 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1200 conjugacy classes of subgroups — too many to draw. Only its 203 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583530C211yesmaximal, characteristic
2C2×#14583057C212yesmaximal
3C2×#14582819C211yesmaximal, characteristic
4#19133571C218yesmaximal, direct product factor
5C2×#14582637C212yesmaximal
6C2×C43×#324C211yesmaximal, characteristic
7C23×Dic86C2211yescharacteristic
8C22×Dic172—22no—
9#14583530—24no—
10#14583530—22no—
11#14583530C2214yes—
12C2×#13063324—22no—
13C2×#13063316—22no—
14C2×#13063304—21no—
15C2×#13063304C2212yes—
16C2×#13063284—21no—
17C22×Dic43⋊C4—21no—
18#14583057—24no—
19#14583057C2218yes—
20C2×#13063250—22no—
21#14582819—22no—
22#14582819C2214yes—
23C2×C43⋊#95—21no—
24C2×C43⋊#95C2211yescharacteristic
25#14582637C2218yes—
26C22×C4⋊C4×C43C2211yescharacteristic
27C2×C22⋊C8×C43C2212yes—
28C43×#324C2214yes—
29C22×Dic86—22no—
30C22×Dic86—21no—
31C22×Dic86—22no—
32C22×Dic86—21no—
33C22×Dic86—44no—
34C22×Dic86D412yes—
35C22×Dic86C2312yes—
36C23×Dic43—21no—
37C23×Dic43—21no—
38C2×Dic172—28no—
39C2×Dic172—48no—
40#13063324—28no—
41#13063324—28no—
42#13063316—28no—
43#13063316—28no—
44#13063304—24no—
45#13063304—24no—
46#13063304—22no—
47#13063304—22no—
48#13063304D414yes—
49#13063304C2314yes—
50#13063284—24no—
51#13063284—24no—
52C2×C4⋊Dic43—21no—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43—21no—
55C2×C4⋊Dic43D412yes—
56C2×Dic43⋊C4—22no—
57C2×Dic43⋊C4—22no—
58C2×Dic43⋊C4—24no—
59C2×Dic43⋊C4—44no—
60C2×C22⋊Dic43—22no—
61C2×C4×Dic43—22no—
62#13063250—28no—
63C43⋊#95—21no—
64C43⋊#95—24no—
65C43⋊#95C2312yes—
66C23×C4×C43D411yescharacteristic
67C23×C4×C43D411yescharacteristic
68C23×C4×C43C2311yescharacteristic
69C22×C8×C43—22no—
70C2×C4⋊C4×C43—22no—
71C2×C4⋊C4×C43—22no—
72C2×C4⋊C4×C43D412yes—
73C2×C4⋊C4×C43C2312yes—
74C22⋊C8×C43—22no—
75C22⋊C8×C43C2314yes—
76C24×C43C2×D411yescharacteristic
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43—22no—
82C22×C4×C43—42no—
83C22×C4×C43—42no—
84C22×C4×C43Q1614yescomplemented
85C22×C4×C43C2×D412yes—
86C22×C4×C43C2×D412yes—
87C22×C4×C43C2×D412yes—
88C22×C4×C43C2×D412yes—
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2411yescharacteristic
91C22×Dic43—24no—
92C22×Dic43—24no—
93C22×Dic43—22no—
94C22×Dic43—22no—
95C22×Dic43—22no—
96C22×Dic43—22no—
97C22×Dic43—42no—
98C22×Dic43—42no—
99C22×Dic43—41no—
100C22×Dic43—41no—
101C22×Dic43—42no—
102C2×Dic86—28no—
103C2×Dic86—24no—
104C2×Dic86—24no—
105C2×Dic86—22no—
106C2×Dic86—44no—
107C2×Dic86—48no—
108C2×Dic86—44no—
109C2×Dic86—44no—
110C2×Dic86—42no—
111C2×Dic86—44no—
112C2×Dic86—82no—
113C2×Dic86C2×D414yes—
114C2×C8×C43—24no—
115C2×C8×C43—44no—
116C4⋊C4×C43—24no—
117C4⋊C4×C43—24no—
118C22⋊Dic43—24no—
119C22⋊Dic43—24no—
120C4⋊Dic43—24no—
121C4⋊Dic43—24no—
122C4⋊Dic43—24no—
123C4⋊Dic43—22no—
124C4⋊Dic43C2×D414yes—
125Dic43⋊C4—28no—
126Dic43⋊C4—24no—
127Dic43⋊C4—24no—
128Dic43⋊C4—48no—
129C4×Dic43—28no—
130Dic172—416no—
131C23×C43—22no—
132C23×C43—22no—
133C23×C43#12011yescharacteristic
134C23×C43#12011yescharacteristic
135C23×C43C2×Q1612yes—
136C23×C43#13712yes—
137C23×C43C22×D411yescharacteristic
138C2×C4×C43—22no—
139C2×C4×C43—22no—
140C2×C4×C43—24no—
141C2×C4×C43—24no—
142C2×C4×C43—24no—
143C2×C4×C43—22no—
144C2×C4×C43—41no—
145C2×C4×C43—42no—
146C2×C4×C43—41no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43—81no—
150C2×C4×C43#12012yes—
151C2×C4×C43C2×Q1614yescomplemented
152C2×C4×C43C22×D412yes—
153C2×Dic43—24no—
154C2×Dic43—24no—
155C2×Dic43—24no—
156C2×Dic43—24no—
157C2×Dic43—42no—
158C2×Dic43—44no—
159C2×Dic43—42no—
160C2×Dic43—48no—
161C2×Dic43—42no—
162C2×Dic43—42no—
163C2×Dic43—44no—
164C2×Dic43—44no—
165C2×Dic43—44no—
166Dic86—28no—
167Dic86—44no—
168Dic86—48no—
169Dic86—44no—
170Dic86—82no—
171Dic86—84no—
172C8×C43—44no—
173C2×#1605—431nomaximal, Sylow
174C22×C43—24no—
175C22×C43—24no—
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—21no—
180C22×C43#45112yes—
181C22×C43#45112yes—
182C22×C43#45612yes—
183C22×C43B(4,𝔽2)12yes—
184C22×C43C2×#12011yescharacteristic
185C22×C43C22×Q1611yescharacteristic
186C22×C43C2×#13711yescharacteristic
187C4×C43—24no—
188C4×C43—22no—
189C4×C43—22no—
190C4×C43—42no—
191Dic43—44no—
192Dic43—44no—
193Dic43—44no—
194Dic43—44no—
195C2×#544—431no—
196C2×#451—432no—
197C2×#395—431no—
198#1605—438no—
199C2×#328—432no—
200C2×#324D4311yescharacteristic
201C2×C43—21no—
202C2×C43—21no—
203C2×C43—22no—
204C2×C43#160514yescomplemented
205C2×C43C2×#45111yescharacteristic
206C2×C43C2×#45611yescharacteristic
207C2×C43C2×B(4,𝔽2)11yescharacteristic
208C23×Q8—431no—
209C22×Q16—862no—
210#544—434no—
211#544—864no—
212#544—862no—
213C2×C4⋊Q8—862no—
214C2×#125—862no—
215C2×C22⋊Q8—432no—
216C2×C22⋊Q8—861no—
217C2×#117—861no—
218C22×C4⋊C4—861no—
219C22×C4⋊C4C2×D4311yescharacteristic
220#451—438no—
221#451—864no—
222C2×#103—862no—
223C2×C22⋊C8C2×D4312yes—
224#395—434no—
225#395—862no—
226C2×#95—431no—
227C2×#95—861no—
228#328—438no—
229#324C2×D4314yes—
230C43C2×#160511yescharacteristic, complemented, Sylow
231C22×Q8—432no—
232C22×Q8—432no—
233C22×Q8—861no—
234C22×Q8—861no—
235C22×Q8—862no—
236C22×Q8—862no—
237C22×Q8—1724no—
238C23×C4—861no—
239C23×C4—861no—
240C23×C4D17211yescharacteristic
241C23×C4D17211yescharacteristic
242C23×C4C22×D4311yescharacteristic
243C2×Q16—868no—
244C2×Q16—1728no—
245C22×C8—22no—
246C4⋊Q8—868no—
247C4⋊Q8—868no—
248#125—868no—
249#125—868no—
250C22⋊Q8—434no—
251C22⋊Q8—434no—
252C22⋊Q8—864no—
253C22⋊Q8—862no—
254C22⋊Q8—864no—
255C22⋊Q8—862no—
256#117—864no—
257#117—864no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—432no—
261C2×C4⋊C4—861no—
262C2×C4⋊C4—861no—
263C2×C4⋊C4—861no—
264C2×C4⋊C4—862no—
265C2×C4⋊C4—862no—
266C2×C4⋊C4—864no—
267C2×C4⋊C4—1724no—
268C2×C4⋊C4D17212yes—
269C2×C4⋊C4C22×D4312yes—
270C2×C22⋊C4—862no—
271C2×C42—862no—
272#103—868no—
273C22⋊C8—22no—
274C22⋊C8C22×D4314yes—
275#95—432no—
276#95—861no—
277#95—864no—
278C24C2×D17211yescharacteristic
279C2×Q8—434no—
280C2×Q8—864no—
281C2×Q8—868no—
282C2×Q8—862no—
283C2×Q8—864no—
284C2×Q8—3442no—
285C2×Q8—1724no—
286C2×Q8—1724no—
287C2×Q8—1724no—
288C2×Q8—1724no—
289C2×Q8—1728no—
290C2×Q8—1722no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—22no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—864no—
299C22×C4—864no—
300C22×C4—862no—
301C22×C4—862no—
302C22×C4—862no—
303C22×C4—862no—
304C22×C4—1722no—
305C22×C4—1722no—
306C22×C4—1721no—
307C22×C4—1721no—
308C22×C4—1722no—
309C22×C4Dic17214yescomplemented
310C22×C4C2×D17212yes—
311C22×C4C2×D17212yes—
312C22×C4C2×D17211yescharacteristic
313C22×C4D4×D4312yes—
314C22×C4D4×D4312yes—
315C22×C4C23×D4311yescharacteristic
316Q16—17216no—
317C2×C8—24no—
318C2×C8—44no—
319C4⋊C4—24no—
320C4⋊C4—24no—
321C4⋊C4—434no—
322C4⋊C4—864no—
323C4⋊C4—864no—
324C4⋊C4—864no—
325C4⋊C4—868no—
326C4⋊C4—862no—
327C4⋊C4—864no—
328C4⋊C4—864no—
329C4⋊C4—1728no—
330C22⋊C4—864no—
331C22⋊C4—864no—
332C42—868no—
333C23—22no—
334C23—22no—
335C23#1306329511yescharacteristic
336C23#1306329511yescharacteristic
337C23C2×Dic17212yes—
338C23#1306335812yes—
339C23C22×D17211yescharacteristic
340Q8—868no—
341Q8—3442no—
342Q8—3444no—
343Q8—1724no—
344Q8—1724no—
345Q8—1728no—
346C2×C4—24no—
347C2×C4—24no—
348C2×C4—24no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—81no—
358C2×C4—864no—
359C2×C4—864no—
360C2×C4—864no—
361C2×C4—864no—
362C2×C4—1722no—
363C2×C4—1722no—
364C2×C4—1724no—
365C2×C4—1728no—
366C2×C4—1724no—
367C2×C4—1724no—
368C2×C4—1724no—
369C2×C4—1722no—
370C2×C4—1722no—
371C2×C4#1306329512yes—
372C2×C4C2×Dic17214yescomplemented
373C2×C4C2×D4×D4312yes—
374C8—44no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—24no—
380C22—24no—
381C22#1458305712yes—
382C22#1458305712yes—
383C22#1458308412yes—
384C22#1458308712yes—
385C22C2×#1306329511yescharacteristic
386C22C22×Dic17211yescharacteristic
387C22C2×#1306335811yescharacteristic
388C4—22no—
389C4—22no—
390C4—24no—
391C4—42no—
392C4—1724no—
393C4—1724no—
394C4—1724no—
395C4—1724no—
396C2—21no—
397C2—22no—
398C2—21no—
399C2#1913357114yesdirect product factor
400C2C2×#1458305711yescharacteristic
401C2C2×#1458308411yescharacteristic
402C2C2×#1458308711yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#324C2
socleC23×C43#120
prime radicalC24×C43C2×D4
hypercenterC2×#324D43
hypocenterC43C2×#1605
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
4. #19133571C2direct (N × H)
84. C22×C4×C43Q16semidirect
151. C2×C4×C43C2×Q16semidirect
204. C2×C43#1605semidirect
230. C43C2×#1605semidirect
309. C22×C4Dic172semidirect
372. C2×C4C2×Dic172semidirect
399. C2#19133571direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835302
C2×#145830572
C2×#145828192
#191335712
C2×#145826372
C2×C43×#3242
C2×#160543