Finite Group Databasebeta

← #24993994

Subgroups — #24993994

Order 11008.

466 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 109 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
1#19143678C211yesmaximal, characteristic
2#19139804C211yesmaximal, characteristic
3#19134588C211yesmaximal, characteristic
4#19133276C211yesmaximal, characteristic
5#19132497C211yesmaximal, characteristic
6#19132496C211yesmaximal, characteristic
7C43×#1548C211yesmaximal, characteristic
8C2×C4×Dic86C2211yescharacteristic
9#14583029—22no—
10#14583026—22no—
11#14582953—22no—
12#14582952C2211yescharacteristic
13#14582923C2211yescharacteristic
14C2×#13063243—21no—
15#14582818C414yes—
16#14582804—21no—
17#14582795—22no—
18#14582768—21no—
19C4×C4⋊Dic43C2211yescharacteristic
20#14582667—21no—
21#14582648—22no—
22C2×C4⋊Q8×C43C2211yescharacteristic
23C43×#431C2211yescharacteristic
24C43×#423C2211yescharacteristic
25C43×#333—22no—
26C22×Dic86D411yescharacteristic
27C2×#10621877—21no—
28C4×Dic86—21no—
29C4×Dic86—21no—
30C4×Dic86—21no—
31C4×Dic86—21no—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43D411yescharacteristic
34C2×Dic43⋊C4—24no—
35C2×Dic43⋊C4C2×C412yes—
36C2×C4×Dic43—21no—
37C2×C4×Dic43D412yes—
38C4⋊(C43⋊C8)—21no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)D412yes—
41Dic43⋊C8—24no—
42#13063243—42no—
43C22⋊(C43⋊C8)—21no—
44#13063235—24no—
45C4×C43⋊C8—21no—
46C43⋊#95—24no—
47C43⋊#95C2×C412yes—
48C22×Q8×C43C2×C412yes—
49C2×M16×C43—21no—
50C4⋊Q8×C43—21no—
51C4⋊Q8×C43—21no—
52C4⋊Q8×C43—21no—
53C4⋊Q8×C43—21no—
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C42×C43C2311yescharacteristic
57C4⋊C8×C43—21no—
58C4⋊C8×C43—21no—
59C4⋊C8×C43D412yes—
60C22⋊C8×C43—21no—
61C4×C8×C43—21no—
62C2×Q8×C43—22no—
63C2×Q8×C43—22no—
64C2×Q8×C43—82no—
65C22×C4×C43—22no—
66C22×C4×C43C22×C411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×Dic43—22no—
70C22×Dic43C22⋊C412yes—
71C22×Dic43C22⋊C412yes—
72C2×Dic86—21no—
73C2×Dic86—21no—
74C2×Dic86—21no—
75C2×Dic86—21no—
76C2×Dic86—21no—
77C2×Dic86—21no—
78M16×C43—41no—
79M16×C43—41no—
80C2×C8×C43—22no—
81C2×C8×C43—41no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C42×C43C2×D411yescharacteristic
87C42×C43C2×D411yescharacteristic
88C42×C43#4111yescharacteristic
89C42×C43#4111yescharacteristic
90C4⋊Dic43—24no—
91C4⋊Dic43—21no—
92C4⋊Dic43—21no—
93Dic43⋊C4—22no—
94Dic43⋊C4—22no—
95Dic43⋊C4—84no—
96C4×Dic43—22no—
97C4×Dic43—22no—
98C4×Dic43—41no—
99C4×Dic43—41no—
100#10621877—41no—
101#10621877—41no—
102C2×C43⋊C8—22no—
103C2×C43⋊C8—41no—
104C23×C43C2×C22⋊C411yescharacteristic
105Q8×C43—82no—
106Q8×C43—82no—
107C2×C4×C43—22no—
108C2×C4×C43—41no—
109C2×C4×C43—44no—
110C2×C4×C43—42no—
111C2×C4×C43C4×D411yescharacteristic
112C2×C4×C43C4×D411yescharacteristic
113C2×C4×C43#12011yescharacteristic
114C2×C4×C43#12111yescharacteristic
115C2×C4×C43#12111yescharacteristic
116C2×C4×C43#12311yescharacteristic
117C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C43#13711yescharacteristic
119C2×C4×C43#13711yescharacteristic
120C2×C4×C43#13711yescharacteristic
121C2×Dic43—24no—
122C2×Dic43—22no—
123C2×Dic43—22no—
124C2×Dic43—22no—
125C2×Dic43—22no—
126C2×Dic43—42no—
127C2×Dic43—42no—
128C2×Dic43—42no—
129Dic86—41no—
130Dic86—41no—
131Dic86—41no—
132Dic86—41no—
133C8×C43—42no—
134C8×C43—81no—
135C43⋊C8—42no—
136C43⋊C8—81no—
137#9400—431nomaximal, Sylow
138C22×C43—21no—
139C22×C43—21no—
140C22×C43#38611yescharacteristic
141C22×C43#41711yescharacteristic
142C22×C43#41911yescharacteristic
143C4×C43—21no—
144C4×C43—21no—
145C4×C43—21no—
146C4×C43—82no—
147C4×C43#45612yes—
148C4×C43#46811yescharacteristic
149C4×C43#46811yescharacteristic
150C4×C43#47011yescharacteristic
151C4×C43#47011yescharacteristic
152Dic43—44no—
153Dic43—42no—
154Dic43—42no—
155#2983—431no—
156#2567—431no—
157#1801—431no—
158#1548—431no—
159#1548D4311yescharacteristic
160#1303—431no—
161#1303—431no—
162C2×C43—21no—
163C2×C43—21no—
164C2×C43#188611yescharacteristic
165C2×C43#189411yescharacteristic
166C2×C43#191411yescharacteristic
167C2×C4⋊Q8C2×D4311yescharacteristic
168C2×C4×Q8—431no—
169#446—862no—
170#446—862no—
171#432—862no—
172#431—431no—
173#431C2×D4311yescharacteristic
174#423—431no—
175#423C2×D4311yescharacteristic
176C2×#101—861no—
177#395—434no—
178#391—861no—
179#389—862no—
180#384—861no—
181C4×C4⋊C4—431no—
182#343—861no—
183#333—22no—
184#333—862no—
185C43#940011yescharacteristic, complemented, Sylow
186C22×Q8—431no—
187C22×Q8C4×D4312yes—
188C2×M16—21no—
189C2×M16—861no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4×Q8—861no—
195C4×Q8—861no—
196C4×Q8—861no—
197C4×Q8—861no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—432no—
201C2×C4⋊C4—431no—
202C2×C4⋊C4—861no—
203C2×C4⋊C4—864no—
204C2×C42—432no—
205C2×C42—861no—
206C2×C42C22×D4311yescharacteristic
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—432no—
210C4⋊C8—864no—
211C4⋊C8—861no—
212C4⋊C8—861no—
213C4⋊C8C22⋊D4312yes—
214#101—1722no—
215C22⋊C8—21no—
216C22⋊C8—861no—
217#97—864no—
218C4×C8—21no—
219C4×C8—861no—
220#95—432no—
221#95—864no—
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8—82no—
225C2×Q8—861no—
226C2×Q8—861no—
227C2×Q8—861no—
228C2×Q8—861no—
229C2×Q8—861no—
230C2×Q8—861no—
231C22×C4—22no—
232C22×C4—432no—
233C22×C4—432no—
234C22×C4—862no—
235C22×C4C2×C4×D4311yescharacteristic
236C22×C4D4×D4311yescharacteristic
237C22×C4D4×D4311yescharacteristic
238M16—41no—
239M16—41no—
240M16—1721no—
241M16—1721no—
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—862no—
245C2×C8—1721no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—864no—
251C4⋊C4—862no—
252C4⋊C4—862no—
253C4⋊C4—861no—
254C4⋊C4—861no—
255C4⋊C4—3444no—
256C42—862no—
257C42—862no—
258C42—1721no—
259C42—1721no—
260C42#1062189811yescharacteristic
261C42D4×D4311yescharacteristic
262C42#1062190011yescharacteristic
263C42C2×C22⋊D4311yescharacteristic
264C23C22⋊C4×D4311yescharacteristic
265Q8—82no—
266Q8—82no—
267Q8—1721no—
268Q8—1721no—
269Q8—1721no—
270Q8—1721no—
271C2×C4—22no—
272C2×C4—41no—
273C2×C4—44no—
274C2×C4—42no—
275C2×C4—864no—
276C2×C4—862no—
277C2×C4—862no—
278C2×C4—862no—
279C2×C4—862no—
280C2×C4—1722no—
281C2×C4—1722no—
282C2×C4—1722no—
283C2×C4(C22⋊D43)⋊C411yescharacteristic
284C2×C4C4×C22⋊D4311yescharacteristic
285C2×C4#1306329311yescharacteristic
286C2×C4#1306329611yescharacteristic
287C2×C4#1306329811yescharacteristic
288C2×C4#1306330711yescharacteristic
289C2×C4#1306335211yescharacteristic
290C2×C4#1306335411yescharacteristic
291C2×C4#1306335711yescharacteristic
292C2×C4#1306335711yescharacteristic
293C8—42no—
294C8—81no—
295C8—3441no—
296C8—1722no—
297C22—21no—
298C22—21no—
299C22#1458277511yescharacteristic
300C22#1458289911yescharacteristic
301C22#1458290611yescharacteristic
302C4—21no—
303C4—21no—
304C4—21no—
305C4—82no—
306C4—1724no—
307C4—1722no—
308C4—1722no—
309C4#1458308012yes—
310C4#1458314211yescharacteristic
311C4#1458314811yescharacteristic
312C4#1458315411yescharacteristic
313C4#1458315611yescharacteristic
314C2—21no—
315C2—21no—
316C2#1913498511yescharacteristic
317C2#1913502511yescharacteristic
318C2#1913513911yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1548C2
socleC22×C43#386
prime radicalC23×C43C2×C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1548D43
hypocenterC43#9400
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
185. C43#9400semidirect

Maximal subgroups

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

subgroupindex
#191436782
#191398042
#191345882
#191332762
#191324972
#191324962
C43×#15482
#940043