Finite Group Databasebeta

← C2×#19133566 #25068771

Subgroups — C2×#19133566 #25068771

Order 11008.

1480 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1480 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×#14583040C212yesmaximal, complemented
3C2×#14582819C211yesmaximal, characteristic, complemented
4#19133566C218yesmaximal, direct product factor
5C2×#14582634C212yesmaximal, complemented
6C2×C43×#324C211yesmaximal, characteristic, complemented
7C22×#10621898—21no—
8C23×Dic86C2211yescharacteristic
9C22×#10621873—22no—
10#14583480—24no—
11#14583480—22no—
12#14583480C2214yes—
13C2×#13063305—22no—
14C2×#13063300—22no—
15C2×#13063299—21no—
16C2×#13063299C2212yes—
17C22×Dic43⋊C4—21no—
18#14583040—24no—
19#14583040C2218yescomplemented
20C2×#13063250—22no—
21#14582819—22no—
22#14582819C2214yescomplemented
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—22no—
34C22×Dic86—21no—
35C22×Dic86—22no—
36C22×Dic86—21no—
37C22×Dic86—44no—
38C22×Dic86C2312yes—
39C22×D172—21no—
40C22×D172—21no—
41C22×D172D412yes—
42C22×C22⋊D43—22no—
43C23×Dic43—21no—
44C23×Dic43—21no—
45C22×C4×D43—22no—
46C2×#10621873—28no—
47C2×#10621873—48no—
48#13063305—28no—
49#13063305—28no—
50#13063300—28no—
51#13063300—28no—
52#13063299—24no—
53#13063299—24no—
54#13063299—22no—
55#13063299—22no—
56#13063299D414yes—
57#13063299C2314yes—
58C2×C4⋊Dic43—21no—
59C2×C4⋊Dic43D412yes—
60C2×Dic43⋊C4—24no—
61C2×Dic43⋊C4—44no—
62C2×(C2×D43)⋊C4—22no—
63C2×(C2×D43)⋊C4—22no—
64#13063250—28no—
65C43⋊#95—21no—
66C43⋊#95—24no—
67C43⋊#95C2312yes—
68C23×C4×C43D411yescharacteristic
69C23×C4×C43D411yescharacteristic
70C23×C4×C43C2311yescharacteristic
71C22×C8×C43—22no—
72C2×C4⋊C4×C43—22no—
73C2×C4⋊C4×C43—22no—
74C2×C4⋊C4×C43D412yes—
75C2×C4⋊C4×C43C2312yes—
76C22⋊C8×C43—22no—
77C22⋊C8×C43C2314yes—
78C24×C43C2×D411yescharacteristic
79C23×D43—22no—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43—22no—
85C22×C4×C43—42no—
86C22×C4×C43—42no—
87C22×C4×C43SD1614yescomplemented
88C22×C4×C43C2×D412yes—
89C22×C4×C43C2×D412yes—
90C22×C4×C43C2×D412yes—
91C22×C4×C43C2×D412yes—
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2411yescharacteristic
94C2×C22⋊D43—24no—
95C2×C22⋊D43—24no—
96C2×C22⋊D43—44no—
97C2×C22⋊D43—44no—
98C22×Dic43—24no—
99C22×Dic43—24no—
100C22×Dic43—22no—
101C22×Dic43—22no—
102C22×Dic43—22no—
103C22×Dic43—42no—
104C22×Dic43—42no—
105C22×Dic43—41no—
106C22×Dic43—41no—
107C22×Dic43—42no—
108#10621898—48no—
109#10621898—416no—
110#10621898—48no—
111C2×D172—24no—
112C2×D172—24no—
113C2×D172—22no—
114C2×D172—44no—
115C2×D172—44no—
116C2×D172—82no—
117C2×D172C2×D414yes—
118C2×C4×D43—28no—
119C2×C4×D43—48no—
120C2×Dic86—28no—
121C2×Dic86—24no—
122C2×Dic86—24no—
123C2×Dic86—44no—
124C2×Dic86—48no—
125C2×Dic86—44no—
126C2×Dic86—44no—
127C2×Dic86—44no—
128C2×Dic86—42no—
129C2×C8×C43—24no—
130C2×C8×C43—44no—
131C4⋊C4×C43—24no—
132C4⋊C4×C43—24no—
133(C2×D43)⋊C4—28no—
134(C2×D43)⋊C4—24no—
135(C2×D43)⋊C4—24no—
136C4⋊Dic43—24no—
137C4⋊Dic43—22no—
138C4⋊Dic43C2×D414yes—
139Dic43⋊C4—48no—
140#10621873—416no—
141C23×C43—22no—
142C23×C43—22no—
143C23×C43#12011yescharacteristic
144C23×C43#12011yescharacteristic
145C23×C43C2×SD1612yes—
146C23×C43AGL(1,ℤ/8)12yes—
147C23×C43C22×D411yescharacteristic
148C22×D43—24no—
149C22×D43—44no—
150C22×D43—44no—
151C22×D43—44no—
152C2×C4×C43—22no—
153C2×C4×C43—22no—
154C2×C4×C43—24no—
155C2×C4×C43—24no—
156C2×C4×C43—24no—
157C2×C4×C43—22no—
158C2×C4×C43—41no—
159C2×C4×C43—42no—
160C2×C4×C43—41no—
161C2×C4×C43—42no—
162C2×C4×C43—42no—
163C2×C4×C43—81no—
164C2×C4×C43#12012yes—
165C2×C4×C43C2×SD1614yescomplemented
166C2×C4×C43C22×D412yes—
167C22⋊D43—44no—
168C22⋊D43—44no—
169C22⋊D43—48no—
170C2×Dic43—24no—
171C2×Dic43—24no—
172C2×Dic43—24no—
173C2×Dic43—42no—
174C2×Dic43—44no—
175C2×Dic43—42no—
176C2×Dic43—48no—
177C2×Dic43—42no—
178C2×Dic43—42no—
179C2×Dic43—44no—
180C2×Dic43—44no—
181D172—44no—
182D172—48no—
183D172—82no—
184D172—84no—
185C4×D43—416no—
186Dic86—28no—
187Dic86—44no—
188Dic86—48no—
189Dic86—48no—
190C8×C43—44no—
191C2×#1604—431nomaximal, Sylow
192C22×C43—24no—
193C22×C43—24no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—21no—
198C22×C43#45012yes—
199C22×C43#45012yes—
200C22×C43#45612yes—
201C22×C43B(4,𝔽2)12yes—
202C22×C43C2×#12011yescharacteristic
203C22×C43C22×SD1611yescharacteristic
204C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
205C2×D43—44no—
206C2×D43—44no—
207C2×D43—44no—
208C2×D43—88no—
209C4×C43—24no—
210C4×C43—22no—
211C4×C43—22no—
212C4×C43—42no—
213Dic43—44no—
214Dic43—44no—
215Dic43—44no—
216C2×#537—431no—
217C2×#448—432no—
218C2×#395—431no—
219#1604—438no—
220C2×#327—432no—
221C2×#324D4311yescharacteristic, complemented
222C2×C43—21no—
223C2×C43—21no—
224C2×C43—22no—
225C2×C43#160414yescomplemented
226C2×C43C2×#45011yescharacteristic
227C2×C43C2×#45611yescharacteristic
228C2×C43C2×B(4,𝔽2)11yescharacteristic
229D43—84no—
230C22×#41—861no—
231C23×Q8—431no—
232C22×SD16—862no—
233#537—434no—
234#537—864no—
235#537—862no—
236C2×C22⋊Q8—862no—
237C2×#121—432no—
238C2×#121—862no—
239C2×#121—861no—
240C22×C4⋊C4—861no—
241C22×C4⋊C4C2×D4311yescharacteristic
242#448—438no—
243#448—864no—
244C2×#103—862no—
245C2×C22⋊C8C2×D4312yes—
246#395—434no—
247#395—862no—
248C2×#95—431no—
249C2×#95—861no—
250#327—438no—
251#324C2×D4314yescomplemented
252C43C2×#160411yescharacteristic, complemented, Sylow
253C2×#41—864no—
254C2×#41—864no—
255C2×#41—1724no—
256C2×#41—1724no—
257C22×Q8—432no—
258C22×Q8—861no—
259C22×Q8—861no—
260C22×Q8—862no—
261C22×Q8—862no—
262C22×Q8—1724no—
263C22×D4—432no—
264C22×D4—861no—
265C22×D4—861no—
266C22×D4—862no—
267C23×C4—862no—
268C23×C4—861no—
269C23×C4—861no—
270C23×C4D17211yescharacteristic
271C23×C4D17211yescharacteristic
272C23×C4C22×D4311yescharacteristic
273C2×SD16—868no—
274C2×SD16—1728no—
275C22×C8—22no—
276C22⋊Q8—868no—
277C22⋊Q8—868no—
278#121—434no—
279#121—434no—
280#121—868no—
281#121—868no—
282#121—864no—
283#121—862no—
284#121—864no—
285#121—862no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—432no—
289C2×C4⋊C4—861no—
290C2×C4⋊C4—864no—
291C2×C4⋊C4—1724no—
292C2×C4⋊C4D17212yes—
293C2×C4⋊C4C22×D4312yes—
294C2×C22⋊C4—862no—
295C2×C22⋊C4—862no—
296#103—868no—
297C22⋊C8—22no—
298C22⋊C8C22×D4314yes—
299#95—432no—
300#95—861no—
301#95—864no—
302C24—862no—
303C24C2×D17211yescharacteristic
304#41—17216no—
305#41—1728no—
306#41—1728no—
307C2×Q8—864no—
308C2×Q8—868no—
309C2×Q8—864no—
310C2×Q8—1724no—
311C2×Q8—1724no—
312C2×Q8—1724no—
313C2×Q8—1724no—
314C2×Q8—1728no—
315C2×Q8—1722no—
316C2×D4—434no—
317C2×D4—864no—
318C2×D4—864no—
319C2×D4—864no—
320C2×D4—864no—
321C2×D4—862no—
322C2×D4—3442no—
323C2×D4—1724no—
324C2×D4—1724no—
325C2×D4—1724no—
326C2×D4—1724no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—22no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—868no—
335C22×C4—864no—
336C22×C4—864no—
337C22×C4—862no—
338C22×C4—862no—
339C22×C4—862no—
340C22×C4—1728no—
341C22×C4—1722no—
342C22×C4—1722no—
343C22×C4—1721no—
344C22×C4—1721no—
345C22×C4—1722no—
346C22×C4#1062187314yescomplemented
347C22×C4C2×D17212yes—
348C22×C4C2×D17212yes—
349C22×C4C2×D17211yescharacteristic
350C22×C4D4×D4312yes—
351C22×C4D4×D4312yes—
352C22×C4C23×D4311yescharacteristic
353SD16—17216no—
354C2×C8—24no—
355C2×C8—44no—
356C4⋊C4—24no—
357C4⋊C4—24no—
358C4⋊C4—434no—
359C4⋊C4—864no—
360C4⋊C4—862no—
361C4⋊C4—1728no—
362C22⋊C4—868no—
363C22⋊C4—864no—
364C22⋊C4—864no—
365C23—22no—
366C23—22no—
367C23—864no—
368C23—1724no—
369C23—1724no—
370C23—1724no—
371C23#1306329511yescharacteristic
372C23#1306329511yescharacteristic
373C23C2×#1062187312yes—
374C23#1306335312yes—
375C23C22×D17211yescharacteristic
376Q8—868no—
377Q8—1724no—
378Q8—1728no—
379Q8—1728no—
380D4—3442no—
381D4—3444no—
382D4—1724no—
383D4—1728no—
384D4—1728no—
385D4—1724no—
386D4—1724no—
387C2×C4—24no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—81no—
399C2×C4—864no—
400C2×C4—864no—
401C2×C4—864no—
402C2×C4—17216no—
403C2×C4—1722no—
404C2×C4—1722no—
405C2×C4—1724no—
406C2×C4—1728no—
407C2×C4—1724no—
408C2×C4—1724no—
409C2×C4—1722no—
410C2×C4—1722no—
411C2×C4#1306329512yes—
412C2×C4C2×#1062187314yescomplemented
413C2×C4C2×D4×D4312yes—
414C8—44no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—24no—
420C22—24no—
421C22—3448no—
422C22—1724no—
423C22—1724no—
424C22—1724no—
425C22#1458305212yes—
426C22#1458305212yes—
427C22#1458308412yes—
428C22#1458308712yes—
429C22C2×#1306329511yescharacteristic
430C22C22×#1062187311yescharacteristic
431C22C2×#1306335311yescharacteristic
432C4—22no—
433C4—22no—
434C4—24no—
435C4—42no—
436C4—1724no—
437C4—1724no—
438C4—1724no—
439C2—21no—
440C2—22no—
441C2—21no—
442C2—3444no—
443C2#1913356614yesdirect product factor
444C2C2×#1458305211yescharacteristic
445C2C2×#1458308411yescharacteristic
446C2C2×#1458308711yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#324C2
socleC23×C43#120
prime radicalC2×#14583480C2
hypercenterC2×#324D43
hypocenterC43C2×#1604
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×#14583040C2semidirect
3. C2×#14582819C2semidirect
4. #19133566C2direct (N × H)
5. C2×#14582634C2semidirect
6. C2×C43×#324C2semidirect
19. #14583040C22semidirect
22. #14582819C22semidirect
25. #14582634C22semidirect
28. C43×#324C22semidirect
87. C22×C4×C43SD16semidirect
165. C2×C4×C43C2×SD16semidirect
221. C2×#324D43semidirect
225. C2×C43#1604semidirect
251. #324C2×D43semidirect
252. C43C2×#1604semidirect
346. C22×C4#10621873semidirect
412. C2×C4C2×#10621873semidirect
443. C2#19133566direct (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×#145830402
C2×#145828192
#191335662
C2×#145826342
C2×C43×#3242
C2×#160443