Finite Group Databasebeta

← C4×#14582688 #25011735

Subgroups — C4×#14582688 #25011735

Order 11008.

576 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C4×#13063306C211yesmaximal, characteristic
2C2×#14582688C212yesmaximal
3C4×#13063242C211yesmaximal, characteristic
4#19132712C212yesmaximal
5C4×#99×C43C211yesmaximal, characteristic
6C2×#13063306C2211yescharacteristic
7C22×C4×Dic43C411yescharacteristic, complemented
8C2×#13063242C2212yes—
9C4×#10621877—21no—
10#14582787—21no—
11#14582780—21no—
12#14582779C2211yescharacteristic
13#14582771C411yescharacteristic, complemented
14#14582760C411yescharacteristic, complemented
15C4×Dic43⋊C4—21no—
16C4×C22⋊Dic43—21no—
17C4×C22⋊Dic43C411yescharacteristic, complemented
18#14582688C418yesdirect product factor
19#14582668—21no—
20C2×C4×D4×C43C2211yescharacteristic
21C2×#99×C43C2212yes—
22C4×C22⋊C4×C43—21no—
23C43×#342—21no—
24C23×Dic43C2×C411yescharacteristic
25C23×Dic43C2×C411yescharacteristic
26C2×#10621877—22no—
27#13063306—22no—
28#13063306C2×C414yes—
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×C22⋊Dic43—21no—
32C2×C22⋊Dic43—21no—
33C2×C22⋊Dic43C2×C411yescharacteristic
34C2×C22⋊Dic43C2×C411yescharacteristic
35C2×C4×Dic43—21no—
36C2×C4×Dic43—21no—
37C2×C4×Dic43—21no—
38C2×C4×Dic43—41no—
39C2×C4×Dic43—41no—
40#13063242—22no—
41#13063242C2×C414yes—
42#13063236—41no—
43C4×C43⋊C8—41no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C22×D4×C43C2311yescharacteristic
50C23×C4×C43C2×C411yescharacteristic
51C23×C4×C43D411yescharacteristic
52C4×D4×C43—41no—
53C4×D4×C43—41no—
54C2×C4⋊C4×C43D411yescharacteristic
55C2×C22⋊C4×C43—22no—
56C2×C22⋊C4×C43C2×C411yescharacteristic
57C2×C22⋊C4×C43D411yescharacteristic
58C2×C42×C43—41no—
59C2×C42×C43D411yescharacteristic
60#99×C43—22no—
61#99×C43C2×C414yes—
62#95×C43—41no—
63C24×C43C22×C411yescharacteristic
64C24×C43C2×D411yescharacteristic
65C2×D4×C43—41no—
66C2×D4×C43—41no—
67C2×D4×C43C22×C412yes—
68C2×D4×C43#4112yes—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—42no—
74C22×C4×C43—42no—
75C22×C4×C43—42no—
76C22×C4×C43C22⋊C411yescharacteristic
77C22×C4×C43C22⋊C411yescharacteristic
78C22×C4×C43C22⋊C411yescharacteristic
79C22×C4×C43C22⋊C411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×Dic43—21no—
82C22×Dic43—21no—
83C22×Dic43—21no—
84C22×Dic43—21no—
85C22×Dic43—21no—
86C22×Dic43—41no—
87C22×Dic43—41no—
88C22×Dic43—41no—
89C22×Dic43—42no—
90C22×Dic43C4212yescomplemented
91C4⋊C4×C43—41no—
92C22⋊C4×C43—24no—
93C22⋊C4×C43—41no—
94C22⋊C4×C43—41no—
95C22⋊C4×C43—42no—
96C42×C43—21no—
97C42×C43—21no—
98C42×C43—82no—
99C22⋊Dic43—21no—
100C22⋊Dic43—24no—
101C22⋊Dic43—41no—
102C22⋊Dic43—42no—
103C22⋊Dic43C4212yescomplemented
104Dic43⋊C4—24no—
105Dic43⋊C4—42no—
106C4×Dic43—42no—
107C4×Dic43—42no—
108C4×Dic43—41no—
109C4×Dic43—41no—
110#10621877—24no—
111#10621877—42no—
112C2×C43⋊C8—42no—
113C23×C43—21no—
114C23×C43—21no—
115C23×C43—21no—
116C23×C43—21no—
117C23×C43—41no—
118C23×C43—41no—
119C23×C43—41no—
120C23×C43—41no—
121C23×C43C2×C4211yescharacteristic
122C23×C43C2×C22⋊C411yescharacteristic
123C23×C43#11711yescharacteristic
124C23×C43C4×D412yes—
125D4×C43—42no—
126D4×C43—42no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—22no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—42no—
134C2×C4×C43—42no—
135C2×C4×C43—42no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—44no—
140C2×C4×C43—81no—
141C2×C4×C43—82no—
142C2×C4×C43—82no—
143C2×C4×C43#9911yescharacteristic
144C2×C4×C43#9911yescharacteristic
145C2×C4×C43C4×D412yes—
146C2×Dic43—22no—
147C2×Dic43—22no—
148C2×Dic43—22no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—42no—
153C2×Dic43—42no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—42no—
158C2×Dic43—42no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C43⋊C8—44no—
163C4×#352—431nomaximal, Sylow
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—22no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43—42no—
172C22×C43—42no—
173C22×C43—41no—
174C22×C43—41no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43—81no—
178C22×C43C4×C22⋊C411yescharacteristic
179C22×C43C2×#9911yescharacteristic
180C22×C43#41011yescharacteristic
181C4×C43—21no—
182C4×C43—22no—
183C4×C43—41no—
184C4×C43—41no—
185C4×C43—41no—
186C4×C43—84no—
187C4×C43#35212yescomplemented
188Dic43—42no—
189Dic43—42no—
190Dic43—42no—
191Dic43—81no—
192C4×#123—431no—
193C2×#352—432no—
194C4×#100—431no—
195C4×#99D4311yescharacteristic
196#1390—432no—
197C2×C43—21no—
198C2×C43—21no—
199C2×C43—42no—
200C2×C43—41no—
201C2×C43—41no—
202C2×C43C4×#9911yescharacteristic
203C2×C43C2×#35211yescharacteristic
204C2×C43#212011yescharacteristic
205C2×#123—431no—
206C2×C4×D4C2×D4311yescharacteristic
207C22×C42—431no—
208C2×#100—432no—
209C2×#99C2×D4312yes—
210C4×M16—861no—
211#388—861no—
212#387—861no—
213#386—431no—
214#385—431no—
215#381—431no—
216C4×C4⋊C4—861no—
217C4×C22⋊C4—21no—
218C4×C22⋊C4—431no—
219C4×C22⋊C4—861no—
220#352—438no—
221#343—861no—
222#342—21no—
223C43C4×#35211yescharacteristic, complemented, Sylow
224C22×D4C22×D4311yescharacteristic
225C23×C4—431no—
226C23×C4—431no—
227C23×C4C4×D4311yescharacteristic
228C23×C4C22⋊D4311yescharacteristic
229C2×M16—862no—
230#123—434no—
231#123—862no—
232C4×D4—41no—
233C4×D4—41no—
234C2×C4⋊C4—861no—
235C2×C4⋊C4—861no—
236C2×C4⋊C4D17211yescharacteristic
237C2×C22⋊C4—22no—
238C2×C22⋊C4—431no—
239C2×C22⋊C4—431no—
240C2×C22⋊C4—861no—
241C2×C22⋊C4—861no—
242C2×C22⋊C4C4×D4311yescharacteristic
243C2×C22⋊C4C22⋊D4311yescharacteristic
244C2×C42—41no—
245C2×C42—861no—
246C2×C42—861no—
247C2×C42—861no—
248C2×C42—1721no—
249C2×C42—1721no—
250C2×C42D17211yescharacteristic
251#100—434no—
252#100—862no—
253#99—22no—
254#99C4×D4314yes—
255#97—1721no—
256C4×C8—1721no—
257#95—41no—
258#95—861no—
259#95—861no—
260#95—861no—
261#95—861no—
262#95—861no—
263C24C2×C4×D4311yescharacteristic
264C24C2×C22⋊D4311yescharacteristic
265C2×D4—41no—
266C2×D4—41no—
267C2×D4C2×C4×D4312yes—
268C2×D4#1062189812yes—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—432no—
277C22×C4—861no—
278C22×C4—861no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4—1722no—
283C22×C4—1721no—
284C22×C4—1721no—
285C22×C4—1721no—
286C22×C4(C2×D43)⋊C411yescharacteristic
287C22×C4(C2×D43)⋊C411yescharacteristic
288C22×C4(C2×D43)⋊C411yescharacteristic
289C22×C4(C2×D43)⋊C411yescharacteristic
290C22×C4C2×D17211yescharacteristic
291M16—864no—
292M16—1722no—
293C2×C8—1722no—
294C4⋊C4—41no—
295C4⋊C4—864no—
296C4⋊C4—1722no—
297C22⋊C4—24no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—42no—
301C22⋊C4—432no—
302C22⋊C4—861no—
303C22⋊C4—864no—
304C22⋊C4—1722no—
305C22⋊C4—1721no—
306C42—21no—
307C42—21no—
308C42—82no—
309C42—1722no—
310C42—1722no—
311C42—1721no—
312C42—1721no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23C42×D4311yescharacteristic
322C23C2×(C2×D43)⋊C411yescharacteristic
323C23#1306328211yescharacteristic
324C23C4×C22⋊D4312yes—
325D4—42no—
326D4—42no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—44no—
340C2×C4—81no—
341C2×C4—82no—
342C2×C4—82no—
343C2×C4—862no—
344C2×C4—862no—
345C2×C4—862no—
346C2×C4—1721no—
347C2×C4—1721no—
348C2×C4—1721no—
349C2×C4—1721no—
350C2×C4—1721no—
351C2×C4—1722no—
352C2×C4—1721no—
353C2×C4—1722no—
354C2×C4—1721no—
355C2×C4—1721no—
356C2×C4—1721no—
357C2×C4—1722no—
358C2×C4—1722no—
359C2×C4#1306323911yescharacteristic
360C2×C4#1306323911yescharacteristic
361C2×C4C4×D17212yes—
362C8—1724no—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—42no—
371C22—42no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—81no—
377C22C4×(C2×D43)⋊C411yescharacteristic
378C22C2×#1306323911yescharacteristic
379C22#1458287211yescharacteristic
380C4—22no—
381C4—21no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—84no—
386C4—3441no—
387C4—1722no—
388C4—1722no—
389C4—1722no—
390C4#1458268812yesdirect product factor
391C2—21no—
392C2—21no—
393C2—42no—
394C2—41no—
395C2—41no—
396C2C4×#1306323911yescharacteristic
397C2C2×#1458268811yescharacteristic
398C2#1913623411yescharacteristic
subgroupG/H
centerC2×C4#13063239
commutatorC23×C43C2×C42
FrattiniC22×D4C22×D43
FittingC4×#99×C43C2
socleC22×C43C2×#99
prime radical, cosocleC22×D4×C43C23
hypercenterC4×#99D43
hypocenterC43C4×#352
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
7. C22×C4×Dic43C4semidirect
13. #14582771C4semidirect
14. #14582760C4semidirect
17. C4×C22⋊Dic43C4semidirect
18. #14582688C4direct (N × H)
90. C22×Dic43C42semidirect
103. C22⋊Dic43C42semidirect
187. C4×C43#352semidirect
223. C43C4×#352semidirect
390. C4#14582688direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#130633062
C2×#145826882
C4×#130632422
#191327122
C4×#99×C432
C4×#35243