Finite Group Databasebeta

← #25000211

Subgroups — #25000211

Order 11008.

408 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 97 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×#14583106C211yesmaximal, characteristic
2#19134588C211yesmaximal, characteristic
3#19133366C211yesmaximal, characteristic
4#19133267C211yesmaximal, characteristic
5#19132989C211yesmaximal, characteristic
6#19132490C211yesmaximal, characteristic
7C43×#1546C211yesmaximal, characteristic
8C22×#10621885—21no—
9C2×C4×Dic86C2211yescharacteristic
10#14583106—22no—
11#14583106—22no—
12#14582952C2211yescharacteristic
13#14582923C2211yescharacteristic
14C2×C4⋊(C43⋊C8)C2211yescharacteristic
15C2×#13063249—21no—
16C2×#13063243—21no—
17#14582667—21no—
18#14582650—22no—
19#14582645—22no—
20#14582629—22no—
21C2×C4⋊Q8×C43C2211yescharacteristic
22C43×#431C2211yescharacteristic
23C43×#423C2211yescharacteristic
24C43×#332—22no—
25C22×Dic86D411yescharacteristic
26C2×#10621885—24no—
27C2×#10621885—42no—
28C2×#10621885—42no—
29C2×#10621877—21no—
30C22×C43⋊C8—21no—
31C4×Dic86—21no—
32C4×Dic86—21no—
33C4×Dic86—21no—
34C4×Dic86—21no—
35C2×C4⋊Dic43D411yescharacteristic
36C2×Dic43⋊C4—21no—
37C2×C4×Dic43—21no—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)D412yes—
43#13063249—24no—
44#13063243—42no—
45C22⋊(C43⋊C8)—21no—
46C4×C43⋊C8—21no—
47C22×Q8×C43—21no—
48C2×M16×C43—21no—
49C4⋊Q8×C43—21no—
50C4⋊Q8×C43—21no—
51C4⋊Q8×C43—21no—
52C4⋊Q8×C43D412yes—
53C2×C4⋊C4×C43—21no—
54C2×C4⋊C4×C43—21no—
55C2×C42×C43C2311yescharacteristic
56C4⋊C8×C43—21no—
57C4⋊C8×C43—21no—
58C4⋊C8×C43D412yes—
59C22⋊C8×C43—21no—
60C4×C8×C43—21no—
61C2×Q8×C43—22no—
62C2×Q8×C43—41no—
63C2×Q8×C43—41no—
64C2×Q8×C43—41no—
65C2×Q8×C43—41no—
66C2×Q8×C43—41no—
67C22×C4×C43—41no—
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43#4111yescharacteristic
70C22×C4×C43#4111yescharacteristic
71C22×Dic43—21no—
72C22×Dic43—21no—
73C2×Dic86—21no—
74C2×Dic86—21no—
75C2×Dic86—21no—
76C2×Dic86—21no—
77C2×Dic86—21no—
78C2×Dic86SD1612yes—
79M16×C43—41no—
80M16×C43—41no—
81C2×C8×C43—22no—
82C2×C8×C43—41no—
83C4⋊C4×C43—22no—
84C4⋊C4×C43—22no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C42×C43C2×D411yescharacteristic
88C42×C43C2×D411yescharacteristic
89C42×C43C2×D411yescharacteristic
90C42×C43#4111yescharacteristic
91#10621885—48no—
92C4⋊Dic43—21no—
93C4⋊Dic43—21no—
94Dic43⋊C4—41no—
95Dic43⋊C4—41no—
96C4×Dic43—41no—
97C4×Dic43—41no—
98#10621877—41no—
99#10621877—41no—
100C2×C43⋊C8—22no—
101C2×C43⋊C8—41no—
102C2×C43⋊C8—41no—
103C2×C43⋊C8—41no—
104C2×C43⋊C8—41no—
105C23×C43#12311yescharacteristic
106Q8×C43—42no—
107Q8×C43—42no—
108Q8×C43—81no—
109Q8×C43—81no—
110C2×C4×C43—22no—
111C2×C4×C43—41no—
112C2×C4×C43—42no—
113C2×C4×C43—81no—
114C2×C4×C43—81no—
115C2×C4×C43#12011yescharacteristic
116C2×C4×C43#12111yescharacteristic
117C2×C4×C43#12111yescharacteristic
118C2×C4×C43#12111yescharacteristic
119C2×C4×C43#12311yescharacteristic
120C2×C4×C43#12411yescharacteristic
121C2×C4×C43C2×SD1611yescharacteristic
122C2×C4×C43#13511yescharacteristic
123C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
125C2×Dic43—22no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—81no—
130Dic86—22no—
131Dic86—22no—
132Dic86—41no—
133Dic86—41no—
134C8×C43—42no—
135C8×C43—81no—
136C43⋊C8—42no—
137C43⋊C8—81no—
138C43⋊C8—81no—
139#10447—431nomaximal, Sylow
140C22×C43—21no—
141C22×C43—21no—
142C22×C43#39411yescharacteristic
143C22×C43#48111yescharacteristic
144C22×C43#48211yescharacteristic
145C4×C43—21no—
146C4×C43—21no—
147C4×C43—21no—
148C4×C43—82no—
149C4×C43#44911yescharacteristic
150C4×C43#45011yescharacteristic
151C4×C43#46511yescharacteristic
152C4×C43#46911yescharacteristic
153C4×C43#47312yes—
154Dic43—42no—
155Dic43—81no—
156C2×#462—431no—
157#1801—431no—
158#1570—431no—
159#1546—431no—
160#1546D4311yescharacteristic
161#1479—431no—
162#1301—431no—
163C2×C43—21no—
164C2×C43—21no—
165C2×C43#203411yescharacteristic
166C2×C43#204711yescharacteristic
167C2×C43#204911yescharacteristic
168C22×Q16—861no—
169C2×C4⋊Q8C2×D4311yescharacteristic
170C2×C4×Q8—431no—
171#462—862no—
172#462—862no—
173#431—431no—
174#431C2×D4311yescharacteristic
175#423—431no—
176#423C2×D4311yescharacteristic
177C2×C4⋊C8—431no—
178C2×#103—861no—
179C2×#101—861no—
180#343—861no—
181#334—862no—
182#332—22no—
183#332—862no—
184Q8⋊C8—862no—
185C43#1044711yescharacteristic, complemented, Sylow
186C22×Q8—21no—
187C22×Q8—431no—
188C2×Q16—864no—
189C2×Q16—1722no—
190C2×Q16—1722no—
191C2×M16—21no—
192C2×M16—861no—
193C22×C8—861no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8D17212yes—
198C4×Q8—861no—
199C4×Q8—861no—
200C4×Q8—861no—
201C4×Q8—861no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—431no—
205C2×C4⋊C4—861no—
206C2×C42—861no—
207C2×C42C22×D4311yescharacteristic
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—432no—
211C4⋊C8—861no—
212C4⋊C8—861no—
213C4⋊C8—861no—
214C4⋊C8—861no—
215C4⋊C8C22⋊D4312yes—
216#103—864no—
217#101—1722no—
218C22⋊C8—21no—
219C22⋊C8—861no—
220C4×C8—21no—
221C4×C8—861no—
222C2×Q8—22no—
223C2×Q8—41no—
224C2×Q8—41no—
225C2×Q8—41no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—432no—
229C2×Q8—861no—
230C2×Q8—861no—
231C2×Q8—861no—
232C2×Q8—861no—
233C2×Q8—861no—
234C22×C4—41no—
235C22×C4—861no—
236C22×C4—861no—
237C22×C4#1062189811yescharacteristic
238C22×C4D4×D4311yescharacteristic
239C22×C4#1062190011yescharacteristic
240Q16—1728no—
241M16—41no—
242M16—41no—
243M16—1721no—
244M16—1721no—
245C2×C8—22no—
246C2×C8—41no—
247C2×C8—862no—
248C2×C8—1721no—
249C2×C8—1721no—
250C2×C8—1721no—
251C2×C8—1721no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—861no—
257C4⋊C4—861no—
258C4⋊C4—1721no—
259C4⋊C4—1721no—
260C42—1721no—
261C42—1721no—
262C42C2×D17211yescharacteristic
263C42D4×D4311yescharacteristic
264C42#1062190011yescharacteristic
265C42C2×C22⋊D4311yescharacteristic
266C23#1306330711yescharacteristic
267Q8—42no—
268Q8—42no—
269Q8—81no—
270Q8—81no—
271Q8—862no—
272Q8—862no—
273Q8—1721no—
274Q8—1721no—
275C2×C4—22no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—862no—
281C2×C4—3441no—
282C2×C4—1721no—
283C2×C4—1721no—
284C2×C4—1721no—
285C2×C4#1306329511yescharacteristic
286C2×C4#1306329611yescharacteristic
287C2×C4#1306329711yescharacteristic
288C2×C4#1306329911yescharacteristic
289C2×C4#1306330911yescharacteristic
290C2×C4#1306331111yescharacteristic
291C2×C4SD16×D4311yescharacteristic
292C2×C4#1306334611yescharacteristic
293C2×C4#1306334911yescharacteristic
294C2×C4#1306334911yescharacteristic
295C8—42no—
296C8—81no—
297C8—3441no—
298C8—3441no—
299C8—1722no—
300C22—21no—
301C22—21no—
302C22#1458281511yescharacteristic
303C22#1458321611yescharacteristic
304C22#1458322211yescharacteristic
305C4—21no—
306C4—21no—
307C4—21no—
308C4—82no—
309C4—3441no—
310C4—1722no—
311C4#1458304511yescharacteristic
312C4#1458305111yescharacteristic
313C4#1458312511yescharacteristic
314C4#1458314911yescharacteristic
315C4#1458317212yes—
316C2—21no—
317C2—21no—
318C2#1913578311yescharacteristic
319C2#1913586211yescharacteristic
320C2#1913587411yescharacteristic
subgroupG/H
centerC22#14582815
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1546C2
socleC22×C43#394
prime radicalC23×C43#123
hypercenter#1546D43
hypocenterC43#10447
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
185. C43#10447semidirect

Maximal subgroups

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

subgroupindex
C2×#145831062
#191345882
#191333662
#191332672
#191329892
#191324902
C43×#15462
#1044743