Finite Group Databasebeta

← C2×#19133634 #25068822

Subgroups — C2×#19133634 #25068822

Order 11008.

1264 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1264 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×#14583480C211yesmaximal, characteristic
2C2×#14583218C212yesmaximal, complemented
3C2×#14582838C211yesmaximal, characteristic, complemented
4#19133634C218yesmaximal, direct product factor
5C2×#14582634C212yesmaximal, complemented
6C2×C43×#324C211yesmaximal, characteristic, complemented
7C22×#10621898—21no—
8#14583480—24no—
9#14583480—22no—
10#14583480C2214yes—
11C2×#13063305—22no—
12C2×#13063300—22no—
13C2×#13063299—21no—
14C2×#13063299C2212yes—
15C22×C4⋊Dic43C2211yescharacteristic
16#14583218—24no—
17#14583218C2218yescomplemented
18C2×#13063257—22no—
19C2×#13063247—22no—
20#14582838—22no—
21#14582838C2214yescomplemented
22C2×C43⋊#95—21no—
23C2×C43⋊#95—21no—
24C2×C43⋊#95C2211yescharacteristic
25#14582634C2218yescomplemented
26C22×C4⋊C4×C43C2211yescharacteristic
27C2×C22⋊C8×C43C2212yes—
28C43×#324C2214yescomplemented
29C2×#10621898—24no—
30C2×#10621898—24no—
31C2×#10621898—44no—
32C2×#10621898—44no—
33C22×Dic86—21no—
34C22×D172—21no—
35C22×D172—21no—
36C22×D172D412yes—
37C22×C22⋊D43—22no—
38C23×Dic43—21no—
39C23×Dic43—21no—
40C22×C4×D43—22no—
41#13063305—28no—
42#13063305—28no—
43#13063300—28no—
44#13063300—28no—
45#13063299—24no—
46#13063299—24no—
47#13063299—22no—
48#13063299—22no—
49#13063299D414yes—
50#13063299C2314yes—
51C2×C4⋊Dic43—21no—
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43—21no—
55C2×C4⋊Dic43D412yes—
56C2×C4⋊Dic43C2312yes—
57C2×(C2×D43)⋊C4—22no—
58C2×(C2×D43)⋊C4—22no—
59#13063257—28no—
60#13063247—28no—
61C43⋊#95—21no—
62C43⋊#95—24no—
63C43⋊#95—24no—
64C43⋊#95C2312yes—
65C23×C4×C43D411yescharacteristic
66C23×C4×C43D411yescharacteristic
67C23×C4×C43C2311yescharacteristic
68C22×C8×C43—22no—
69C2×C4⋊C4×C43—22no—
70C2×C4⋊C4×C43—22no—
71C2×C4⋊C4×C43D412yes—
72C2×C4⋊C4×C43C2312yes—
73C22⋊C8×C43—22no—
74C22⋊C8×C43C2314yes—
75C24×C43C2×D411yescharacteristic
76C23×D43—22no—
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×C43SD1614yes—
85C22×C4×C43C2×D412yes—
86C22×C4×C43C2×D412yes—
87C22×C4×C43C2×D412yes—
88C22×C4×C43C2×D412yes—
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2411yescharacteristic
91C2×C22⋊D43—24no—
92C2×C22⋊D43—24no—
93C2×C22⋊D43—44no—
94C2×C22⋊D43—44no—
95C22×Dic43—22no—
96C22×Dic43—22no—
97C22×Dic43—22no—
98C22×Dic43—42no—
99C22×Dic43—44no—
100C22×Dic43—42no—
101C22×Dic43—41no—
102C22×Dic43—41no—
103C22×Dic43—42no—
104#10621898—48no—
105#10621898—416no—
106#10621898—48no—
107C2×D172—24no—
108C2×D172—24no—
109C2×D172—22no—
110C2×D172—44no—
111C2×D172—44no—
112C2×D172—82no—
113C2×D172C2×D414yes—
114C2×C4×D43—28no—
115C2×C4×D43—48no—
116C2×Dic86—24no—
117C2×Dic86—44no—
118C2×C8×C43—24no—
119C2×C8×C43—44no—
120C4⋊C4×C43—24no—
121C4⋊C4×C43—24no—
122(C2×D43)⋊C4—28no—
123(C2×D43)⋊C4—24no—
124(C2×D43)⋊C4—24no—
125C4⋊Dic43—24no—
126C4⋊Dic43—22no—
127C4⋊Dic43—24no—
128C4⋊Dic43—42no—
129C4⋊Dic43C2×D414yes—
130C23×C43—22no—
131C23×C43—22no—
132C23×C43#12011yescharacteristic
133C23×C43#12011yescharacteristic
134C23×C43C2×SD1612yes—
135C23×C43AGL(1,ℤ/8)12yes—
136C23×C43C22×D411yescharacteristic
137C22×D43—24no—
138C22×D43—44no—
139C22×D43—44no—
140C22×D43—44no—
141C2×C4×C43—22no—
142C2×C4×C43—22no—
143C2×C4×C43—24no—
144C2×C4×C43—24no—
145C2×C4×C43—24no—
146C2×C4×C43—22no—
147C2×C4×C43—41no—
148C2×C4×C43—42no—
149C2×C4×C43—41no—
150C2×C4×C43—42no—
151C2×C4×C43—42no—
152C2×C4×C43—81no—
153C2×C4×C43#12012yes—
154C2×C4×C43C2×SD1614yes—
155C2×C4×C43C22×D412yes—
156C22⋊D43—44no—
157C22⋊D43—44no—
158C22⋊D43—48no—
159C2×Dic43—24no—
160C2×Dic43—44no—
161C2×Dic43—42no—
162C2×Dic43—42no—
163C2×Dic43—44no—
164C2×Dic43—42no—
165C2×Dic43—42no—
166C2×Dic43—84no—
167C2×Dic43—82no—
168C2×Dic43—82no—
169D172—44no—
170D172—48no—
171D172—82no—
172D172—84no—
173C4×D43—416no—
174Dic86—48no—
175C8×C43—44no—
176C2×#1616—431nomaximal, Sylow
177C22×C43—24no—
178C22×C43—24no—
179C22×C43—21no—
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—21no—
183C22×C43#45012yes—
184C22×C43#45012yes—
185C22×C43#45412yes—
186C22×C43#45812yes—
187C22×C43C2×#12011yescharacteristic
188C22×C43C22×SD1611yescharacteristic
189C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
190C2×D43—44no—
191C2×D43—44no—
192C2×D43—44no—
193C2×D43—88no—
194C4×C43—24no—
195C4×C43—22no—
196C4×C43—22no—
197C4×C43—42no—
198Dic43—44no—
199Dic43—82no—
200Dic43—82no—
201C2×#537—431no—
202C2×#481—432no—
203C2×#400—431no—
204#1616—438no—
205C2×#327—432no—
206C2×#324D4311yescharacteristic, complemented
207C2×C43—21no—
208C2×C43—21no—
209C2×C43—22no—
210C2×C43#161614yescomplemented
211C2×C43C2×#45011yescharacteristic
212C2×C43C2×#45411yescharacteristic
213C2×C43C2×#45811yescharacteristic
214D43—84no—
215C22×#41—861no—
216#537—434no—
217#537—864no—
218#537—862no—
219C2×C22⋊Q8—862no—
220C2×#121—432no—
221C2×#121—862no—
222C2×#121—861no—
223C22×C4⋊C4—431no—
224C22×C4⋊C4C2×D4311yescharacteristic
225#481—438no—
226#481—864no—
227C2×#106—862no—
228C2×#102—862no—
229C2×C22⋊C8C2×D4312yes—
230#400—434no—
231#400—862no—
232C2×#95—431no—
233C2×#95—861no—
234C2×#95—861no—
235#327—438no—
236#324C2×D4314yescomplemented
237C43C2×#161611yescharacteristic, complemented, Sylow
238C2×#41—864no—
239C2×#41—864no—
240C2×#41—1724no—
241C2×#41—1724no—
242C22×Q8—861no—
243C22×D4—432no—
244C22×D4—861no—
245C22×D4—861no—
246C22×D4—862no—
247C23×C4—862no—
248C23×C4—861no—
249C23×C4—861no—
250C23×C4D17211yescharacteristic
251C23×C4D17211yescharacteristic
252C23×C4C22×D4311yescharacteristic
253C22×C8—22no—
254C22⋊Q8—868no—
255C22⋊Q8—868no—
256#121—434no—
257#121—434no—
258#121—868no—
259#121—868no—
260#121—864no—
261#121—862no—
262#121—864no—
263#121—862no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—432no—
267C2×C4⋊C4—432no—
268C2×C4⋊C4—861no—
269C2×C4⋊C4—862no—
270C2×C4⋊C4—862no—
271C2×C4⋊C4—861no—
272C2×C4⋊C4D17212yes—
273C2×C4⋊C4C22×D4312yes—
274C2×C22⋊C4—862no—
275C2×C22⋊C4—862no—
276#106—868no—
277#102—868no—
278C22⋊C8—22no—
279C22⋊C8C22×D4314yes—
280#95—432no—
281#95—861no—
282#95—864no—
283#95—864no—
284C24—862no—
285C24C2×D17211yescharacteristic
286#41—17216no—
287#41—1728no—
288#41—1728no—
289C2×Q8—864no—
290C2×Q8—1724no—
291C2×D4—434no—
292C2×D4—864no—
293C2×D4—864no—
294C2×D4—864no—
295C2×D4—864no—
296C2×D4—862no—
297C2×D4—3442no—
298C2×D4—1724no—
299C2×D4—1724no—
300C2×D4—1724no—
301C2×D4—1724no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—868no—
310C22×C4—862no—
311C22×C4—862no—
312C22×C4—862no—
313C22×C4—1728no—
314C22×C4—1722no—
315C22×C4—1722no—
316C22×C4—1724no—
317C22×C4—1721no—
318C22×C4—1721no—
319C22×C4—1722no—
320C22×C4#1062187314yes—
321C22×C4C2×D17212yes—
322C22×C4C2×D17212yes—
323C22×C4C2×D17211yescharacteristic
324C22×C4D4×D4312yes—
325C22×C4D4×D4312yes—
326C22×C4C23×D4311yescharacteristic
327C2×C8—24no—
328C2×C8—44no—
329C4⋊C4—24no—
330C4⋊C4—24no—
331C4⋊C4—434no—
332C4⋊C4—864no—
333C4⋊C4—862no—
334C4⋊C4—864no—
335C4⋊C4—1722no—
336C22⋊C4—868no—
337C22⋊C4—864no—
338C22⋊C4—864no—
339C23—22no—
340C23—22no—
341C23—864no—
342C23—1724no—
343C23—1724no—
344C23—1724no—
345C23#1306329511yescharacteristic
346C23#1306329511yescharacteristic
347C23C2×#1062187312yes—
348C23#1306335312yes—
349C23C22×D17211yescharacteristic
350Q8—1728no—
351D4—3442no—
352D4—3444no—
353D4—1724no—
354D4—1728no—
355D4—1728no—
356D4—1724no—
357D4—1724no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—81no—
370C2×C4—864no—
371C2×C4—3444no—
372C2×C4—3442no—
373C2×C4—3442no—
374C2×C4—17216no—
375C2×C4—1722no—
376C2×C4—1722no—
377C2×C4—1724no—
378C2×C4—1722no—
379C2×C4—1722no—
380C2×C4—1724no—
381C2×C4#1306329512yes—
382C2×C4C2×#1062187314yes—
383C2×C4C2×D4×D4312yes—
384C8—44no—
385C22—21no—
386C22—21no—
387C22—24no—
388C22—24no—
389C22—21no—
390C22—21no—
391C22—3448no—
392C22—1724no—
393C22—1724no—
394C22—1724no—
395C22#1458305212yes—
396C22#1458305212yes—
397C22#1458307412yes—
398C22#1458309012yes—
399C22C2×#1306329511yescharacteristic
400C22C22×#1062187311yescharacteristic
401C22C2×#1306335311yescharacteristic
402C4—22no—
403C4—22no—
404C4—24no—
405C4—42no—
406C4—3442no—
407C4—3442no—
408C4—1724no—
409C2—21no—
410C2—22no—
411C2—21no—
412C2—3444no—
413C2#1913363414yesdirect product factor
414C2C2×#1458305211yescharacteristic
415C2C2×#1458307411yescharacteristic
416C2C2×#1458309011yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#324C2
socleC23×C43#120
prime radicalC2×#14583480C2
hypercenterC2×#324D43
hypocenterC43C2×#1616
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
2. C2×#14583218C2semidirect
3. C2×#14582838C2semidirect
4. #19133634C2direct (N × H)
5. C2×#14582634C2semidirect
6. C2×C43×#324C2semidirect
17. #14583218C22semidirect
21. #14582838C22semidirect
25. #14582634C22semidirect
28. C43×#324C22semidirect
206. C2×#324D43semidirect
210. C2×C43#1616semidirect
236. #324C2×D43semidirect
237. C43C2×#1616semidirect
413. C2#19133634direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834802
C2×#145832182
C2×#145828382
#191336342
C2×#145826342
C2×C43×#3242
C2×#161643