Finite Group Databasebeta

← #25012099

Subgroups — #25012099

Order 11008.

990 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 990 conjugacy classes of subgroups — too many to draw. Only its 115 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×#14583470C211yesmaximal, characteristic
2C2×#14582693C214yesmaximal, complemented
3#19134513C211yesmaximal, characteristic
4C43×#1782C211yesmaximal, characteristic
5C23×Dic86C411yescharacteristic, complemented
6#14583470—28no—
7C2×#13063323C412yescomplemented
8C2×#13063312C2212yes—
9C2×#13063306—21no—
10C2×#13063306—21no—
11C2×#13063304—21no—
12C2×#13063304—21no—
13C2×#13063284C411yescharacteristic, complemented
14C2×#13063240—21no—
15C2×#13063240C2212yes—
16#14582762—21no—
17#14582693—28no—
18C22×#41×C43C2211yescharacteristic
19C2×#99×C43—21no—
20C2×#99×C43C2212yes—
21C43×#381—21no—
22C22×Dic86—21no—
23C22×Dic86—24no—
24C22×Dic86—42no—
25C22×Dic86—42no—
26C22×Dic86C2×C412yes—
27C23×Dic43—21no—
28#13063323—24no—
29#13063323—24no—
30#13063312—24no—
31#13063312D418yes—
32#13063306—28no—
33#13063306—28no—
34#13063304—28no—
35#13063304—28no—
36#13063284—24no—
37C2×C4⋊Dic43—21no—
38C2×Dic43⋊C4—22no—
39C2×Dic43⋊C4—22no—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43—22no—
42C2×C22⋊Dic43—22no—
43C2×C22⋊Dic43—22no—
44C2×C4×Dic43C2×C412yes—
45#13063240—24no—
46#13063240—42no—
47C43⋊#95—42no—
48C2×#41×C43—24no—
49C2×#41×C43—42no—
50C2×#41×C43—42no—
51C22×Q8×C43C2×C411yescharacteristic
52C22×D4×C43D411yescharacteristic
53C22×D4×C43D411yescharacteristic
54C22×D4×C43C2311yescharacteristic
55C23×C4×C43C2×C411yescharacteristic
56C23×C4×C43D411yescharacteristic
57C23×C4×C43D411yescharacteristic
58C2×C22⋊C4×C43—22no—
59#99×C43—24no—
60#99×C43—42no—
61#95×C43—42no—
62C24×C43C22⋊C411yescharacteristic
63C24×C43C2×D411yescharacteristic
64C24×C43C2×D411yescharacteristic
65#41×C43—416no—
66C2×Q8×C43—22no—
67C2×Q8×C43—41no—
68C2×Q8×C43—41no—
69C2×D4×C43—22no—
70C2×D4×C43—22no—
71C2×D4×C43—22no—
72C2×D4×C43—22no—
73C2×D4×C43—41no—
74C2×D4×C43—41no—
75C2×D4×C43—41no—
76C2×D4×C43—41no—
77C2×D4×C43C2×D414yes—
78C22×C4×C43—22no—
79C22×C4×C43—22no—
80C22×C4×C43—22no—
81C22×C4×C43—22no—
82C22×C4×C43—22no—
83C22×C4×C43—22no—
84C22×C4×C43—22no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43—42no—
88C22×C4×C43C22⋊C411yescharacteristic
89C22×C4×C43C22⋊C411yescharacteristic
90C22×C4×C43C22⋊C411yescharacteristic
91C22×C4×C43C22×C411yescharacteristic
92C22×Dic43—24no—
93C22×Dic43—22no—
94C22×Dic43—22no—
95C22×Dic43—42no—
96C22×Dic43—42no—
97C22×Dic43—42no—
98C2×Dic86—24no—
99C2×Dic86—22no—
100C2×Dic86—42no—
101C2×Dic86—416no—
102C2×Dic86—42no—
103C2×Dic86—42no—
104C2×Dic86—42no—
105C2×Dic86C22⋊C414yes—
106C22⋊C4×C43—42no—
107C22⋊C4×C43—42no—
108C22⋊Dic43—24no—
109C22⋊Dic43—28no—
110C22⋊Dic43—28no—
111C22⋊Dic43—42no—
112C22⋊Dic43—42no—
113C4⋊Dic43—24no—
114Dic43⋊C4—28no—
115Dic43⋊C4—28no—
116C4×Dic43—22no—
117C4×Dic43C22⋊C414yes—
118C23×C43—21no—
119C23×C43—21no—
120C23×C43—21no—
121C23×C43—21no—
122C23×C43—21no—
123C23×C43—21no—
124C23×C43—42no—
125C23×C43—42no—
126C23×C43—42no—
127C23×C43#9912yes—
128C23×C43C2×C22⋊C411yescharacteristic
129C23×C43#12012yes—
130C23×C43#12012yes—
131Q8×C43—44no—
132D4×C43—44no—
133D4×C43—44no—
134D4×C43—44no—
135C2×C4×C43—28no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—44no—
147C2×C4×C43—44no—
148C2×C4×C43—82no—
149C2×C4×C43—84no—
150C2×C4×C43#9912yes—
151C2×C4×C43C2×C22⋊C412yes—
152C2×Dic43—24no—
153C2×Dic43—24no—
154C2×Dic43—48no—
155C2×Dic43—44no—
156C2×Dic43—42no—
157C2×Dic43—42no—
158C2×Dic43—82no—
159C2×Dic43—84no—
160Dic86—48no—
161Dic86—44no—
162Dic86—44no—
163#12698—431nomaximal, Sylow
164C22×C43—22no—
165C22×C43—22no—
166C22×C43—22no—
167C22×C43—22no—
168C22×C43—42no—
169C22×C43—42no—
170C22×C43—42no—
171C22×C43—42no—
172C22×C43—42no—
173C22×C43—42no—
174C22×C43—42no—
175C22×C43—81no—
176C22×C43—81no—
177C22×C43#37911yescharacteristic
178C22×C43C2×#9911yescharacteristic
179C22×C43C2×#9911yescharacteristic
180C4×C43—22no—
181C4×C43—22no—
182C4×C43—41no—
183C4×C43—41no—
184C4×C43—162no—
185Dic43—44no—
186Dic43—44no—
187Dic43—162no—
188C2×#536—431no—
189C2×#354—434no—
190#1782—431no—
191#1782D4311yescharacteristic
192C2×C43—21no—
193C2×C43—21no—
194C2×C43—42no—
195C2×C43—42no—
196C2×C43—42no—
197C2×C43#178111yescharacteristic
198C2×C43#212912yes—
199C22×#41C2×D4311yescharacteristic
200C23×Q8—431no—
201#536—868no—
202C2×C4⋊Q8—432no—
203C2×#124—432no—
204C2×#123—861no—
205C2×#123—861no—
206C2×C22⋊Q8—861no—
207C2×C22⋊Q8—861no—
208C2×#117—431no—
209C2×#99—21no—
210C2×#99—432no—
211C2×#99—861no—
212C2×#99C2×D4312yes—
213#381—21no—
214#381—861no—
215#354—868no—
216C43#1269811yescharacteristic, complemented, Sylow
217C2×#41—24no—
218C2×#41—42no—
219C2×#41—42no—
220C22×Q8—432no—
221C22×Q8—864no—
222C22×Q8—861no—
223C22×Q8—1722no—
224C22×Q8—1722no—
225C22×Q8C4×D4311yescharacteristic
226C22×D4D17211yescharacteristic
227C22×D4C22⋊D4311yescharacteristic
228C22×D4C22×D4311yescharacteristic
229C23×C4—861no—
230C23×C4C4×D4311yescharacteristic
231C23×C4D17211yescharacteristic
232C23×C4C22⋊D4311yescharacteristic
233C4⋊Q8—864no—
234C4⋊Q8—864no—
235#124—438no—
236#124—864no—
237#123—868no—
238#123—868no—
239C22⋊Q8—868no—
240C22⋊Q8—868no—
241#117—864no—
242C2×C4⋊C4—862no—
243C2×C4⋊C4—862no—
244C2×C4⋊C4—861no—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—861no—
247C2×C22⋊C4—862no—
248C2×C22⋊C4—862no—
249C2×C22⋊C4—862no—
250C2×C42—432no—
251#99—24no—
252#99—42no—
253#99—864no—
254#99—1722no—
255#95—42no—
256#95—1722no—
257C24(C2×D43)⋊C411yescharacteristic
258C24C2×D17211yescharacteristic
259C24C2×C22⋊D4311yescharacteristic
260#41—416no—
261C2×Q8—22no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×Q8—434no—
265C2×Q8—864no—
266C2×Q8—862no—
267C2×Q8—17216no—
268C2×Q8—1722no—
269C2×Q8—1722no—
270C2×Q8—1722no—
271C2×Q8—1722no—
272C2×D4—22no—
273C2×D4—22no—
274C2×D4—22no—
275C2×D4—22no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4D4×D4314yes—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—42no—
291C22×C4—864no—
292C22×C4—862no—
293C22×C4—862no—
294C22×C4—1722no—
295C22×C4—1722no—
296C22×C4—1722no—
297C22×C4(C2×D43)⋊C411yescharacteristic
298C22×C4(C2×D43)⋊C411yescharacteristic
299C22×C4(C2×D43)⋊C411yescharacteristic
300C22×C4C2×C4×D4311yescharacteristic
301C4⋊C4—864no—
302C4⋊C4—868no—
303C4⋊C4—868no—
304C22⋊C4—42no—
305C22⋊C4—42no—
306C22⋊C4—864no—
307C22⋊C4—868no—
308C22⋊C4—868no—
309C22⋊C4—1722no—
310C22⋊C4—1722no—
311C42—434no—
312C42—862no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23#1306323912yes—
323C23C2×(C2×D43)⋊C411yescharacteristic
324C23#1306329312yes—
325C23#1306329512yes—
326Q8—44no—
327Q8—1724no—
328Q8—1728no—
329Q8—1724no—
330D4—44no—
331D4—44no—
332D4—44no—
333C2×C4—28no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—82no—
347C2×C4—84no—
348C2×C4—864no—
349C2×C4—864no—
350C2×C4—3442no—
351C2×C4—3444no—
352C2×C4—1728no—
353C2×C4—1724no—
354C2×C4—1722no—
355C2×C4—1722no—
356C2×C4#1306323912yes—
357C2×C4C22⋊C4×D4312yes—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—42no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—42no—
367C22—42no—
368C22—42no—
369C22—81no—
370C22—81no—
371C22#1458275411yescharacteristic
372C22C2×#1306323911yescharacteristic
373C22C2×#1306323911yescharacteristic
374C4—22no—
375C4—22no—
376C4—41no—
377C4—41no—
378C4—162no—
379C4—1724no—
380C4—1724no—
381C4—6882no—
382C2—21no—
383C2—21no—
384C2—42no—
385C2—42no—
386C2—42no—
387C2#1913450911yescharacteristic
388C2#1913626912yes—
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC22×D4C22×D43
FittingC43×#1782C2
socleC22×C43C2×#99
prime radicalC22×#41×C43C22
cosocleC22×D4×C43C23
hypercenter#1782D43
hypocenterC43#12698
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #1782

Complements

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

NH ≅ G/Ntype
2. C2×#14582693C2semidirect
5. C23×Dic86C4semidirect
7. C2×#13063323C4semidirect
13. C2×#13063284C4semidirect
216. C43#12698semidirect

Maximal subgroups

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

subgroupindex
C2×#145834702
C2×#145826932
#191345132
C43×#17822
#1269843