Finite Group Databasebeta

← #25009532

Subgroups — #25009532

Order 11008.

368 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 55 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#19142428C211yesmaximal, characteristic
2#19135937C211yesmaximal, characteristic, complemented
3#19133637C211yesmaximal, characteristic, complemented
4#19132623C211yesmaximal, characteristic, complemented
5#19132598C211yesmaximal, characteristic
6#19132540C211yesmaximal, characteristic, complemented
7C43×#1599C211yesmaximal, characteristic
8#14583232—21no—
9#14582942—21no—
10#14582838C2211yescharacteristic
11#14582822—21no—
12#14582813—21no—
13#14582792—21no—
14#14582787—21no—
15#14582787—21no—
16#14582781—21no—
17#14582768C2211yescharacteristic
18#14582668C2211yescharacteristic
19#14582658—21no—
20#14582636—21no—
21#14582625C2211yescharacteristic
22C43×#544C2211yescharacteristic
23C43×#450—21no—
24C43×#394C2211yescharacteristic
25C43×#328—21no—
26C43×#324C2211yescharacteristic
27C2×#10621877—21no—
28C2×C4⋊Dic43D411yescharacteristic
29C2×C4⋊Dic43D411yescharacteristic
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43—21no—
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37C2×C4×Dic43—21no—
38C2×C4×Dic43D411yescharacteristic
39#13063258—41no—
40#13063258—41no—
41#13063256—41no—
42#13063249—41no—
43C22⋊(C43⋊C8)—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95D411yescharacteristic
49C22×D4×C43D411yescharacteristic
50C2×SD16×C43—41no—
51C4⋊Q8×C43—41no—
52#125×C43—41no—
53C22⋊Q8×C43—21no—
54C22⋊Q8×C43—21no—
55#117×C43—21no—
56C2×C4⋊C4×C43C2311yescharacteristic
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43—21no—
59#102×C43—41no—
60C22⋊C8×C43—21no—
61#95×C43D411yescharacteristic
62C24×C43—21no—
63C2×Q8×C43—21no—
64C2×Q8×C43—21no—
65C2×D4×C43—41no—
66C2×D4×C43—81no—
67C22×C4×C43—21no—
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75SD16×C43—82no—
76C2×C8×C43—41no—
77C4⋊C4×C43—21no—
78C4⋊C4×C43—21no—
79C4⋊C4×C43—21no—
80C4⋊C4×C43—21no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—41no—
84C22⋊C4×C43—41no—
85C22⋊C4×C43—41no—
86C22⋊C4×C43—41no—
87C22⋊C4×C43—81no—
88C42×C43—41no—
89C22⋊Dic43—42no—
90C22⋊Dic43—42no—
91C22⋊Dic43—81no—
92C22⋊Dic43—81no—
93C4⋊Dic43—41no—
94C4⋊Dic43—41no—
95Dic43⋊C4—42no—
96Dic43⋊C4—81no—
97Dic43⋊C4—81no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43—81no—
101#10621877—22no—
102#10621877—41no—
103C2×C43⋊C8—41no—
104C2×C43⋊C8—41no—
105C23×C43—41no—
106C23×C43—41no—
107C23×C43—41no—
108C23×C43—41no—
109C23×C43—41no—
110C23×C43—41no—
111C23×C43—41no—
112C23×C43#12011yescharacteristic
113Q8×C43—81no—
114Q8×C43—81no—
115D4×C43—42no—
116D4×C43—81no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43#13511yescharacteristic
129C2×C4×C43#13711yescharacteristic
130C2×Dic43—22no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C8×C43—81no—
143C43⋊C8—42no—
144C43⋊C8—81no—
145#12238—431nomaximal, Sylow
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—81no—
149C22×C43—81no—
150C22×C43—81no—
151C22×C43—81no—
152C22×C43—81no—
153C22×C43—81no—
154C22×C43—81no—
155C22×C43#45211yescharacteristic
156C22×C43#45611yescharacteristic
157C22×C43B(4,𝔽2)11yescharacteristic
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—81no—
163C4×C43—81no—
164C4×C43—81no—
165Dic43—42no—
166Dic43—81no—
167Dic43—81no—
168Dic43—81no—
169#2795—431no—
170#2060—431no—
171#1617—431no—
172#1599D4311yescharacteristic
173#1353—431no—
174#1345—431no—
175#1325—431no—
176C2×C43—21no—
177C2×C43—21no—
178C2×C43—161no—
179C2×C43#160311yescharacteristic
180C2×C43#220011yescharacteristic
181C2×C43#220411yescharacteristic
182#544C2×D4311yescharacteristic
183#484—861no—
184#450—21no—
185#428—861no—
186#400—431no—
187#396—861no—
188#394—861no—
189#394C2×D4311yescharacteristic
190#388—861no—
191#388—861no—
192#388—861no—
193#387—861no—
194#384—431no—
195#343—431no—
196#339—861no—
197#328—21no—
198#328—861no—
199#324—431no—
200#324C2×D4311yescharacteristic
201C43#1223811yescharacteristic, complemented, Sylow
202C22×D4C22⋊D4311yescharacteristic
203C2×SD16—41no—
204C2×M16—861no—
205C4⋊Q8—41no—
206#125—41no—
207C22⋊Q8—21no—
208C22⋊Q8—21no—
209#117—21no—
210C2×C4⋊C4—431no—
211C2×C4⋊C4—431no—
212C2×C4⋊C4—861no—
213C2×C4⋊C4—861no—
214C2×C4⋊C4—861no—
215C2×C4⋊C4C22×D4311yescharacteristic
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—861no—
219C2×C22⋊C4—861no—
220C2×C22⋊C4—861no—
221C2×C22⋊C4—861no—
222C2×C42—431no—
223C2×C42—861no—
224#107—1721no—
225#107—1721no—
226#106—1721no—
227#103—1721no—
228#102—41no—
229C22⋊C8—21no—
230C22⋊C8—861no—
231#95—431no—
232#95—861no—
233#95—861no—
234#95—861no—
235#95—861no—
236#95C22⋊D4311yescharacteristic
237C24—21no—
238C2×Q8—21no—
239C2×Q8—21no—
240C2×D4—41no—
241C2×D4—81no—
242C22×C4—21no—
243C22×C4—861no—
244C22×C4—861no—
245C22×C4—861no—
246C22×C4—861no—
247C22×C4D4×D4311yescharacteristic
248C22×C4D4×D4311yescharacteristic
249C22×C4C2×C22⋊D4311yescharacteristic
250SD16—82no—
251M16—862no—
252M16—1721no—
253C2×C8—41no—
254C2×C8—1721no—
255C2×C8—1721no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—3441no—
264C4⋊C4—3441no—
265C4⋊C4—1721no—
266C4⋊C4—1721no—
267C4⋊C4—1722no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—81no—
272C22⋊C4—3441no—
273C22⋊C4—3441no—
274C22⋊C4—1722no—
275C22⋊C4—1722no—
276C42—41no—
277C42—861no—
278C42—861no—
279C42—3441no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23#1306329311yescharacteristic
288Q8—81no—
289Q8—81no—
290D4—42no—
291D4—81no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—862no—
304C2×C4—1721no—
305C2×C4—1721no—
306C2×C4—1721no—
307C2×C4—1721no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4—1721no—
312C2×C4—1721no—
313C2×C4—1721no—
314C2×C4—1721no—
315C2×C4#1306334611yescharacteristic
316C2×C4#1306335411yescharacteristic
317C8—81no—
318C8—3441no—
319C8—1722no—
320C22—21no—
321C22—21no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22—81no—
328C22—81no—
329C22#1458305811yescharacteristic
330C22#1458308011yescharacteristic
331C22#1458308511yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—81no—
338C4—81no—
339C4—3441no—
340C4—3441no—
341C4—3441no—
342C4—1722no—
343C2—21no—
344C2—21no—
345C2—161no—
346C2#1913355511yescharacteristic
347C2#1913660011yescharacteristic
348C2#1913661911yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1599C2
socleC22×C43B(4,𝔽2)
prime radicalC22×D4×C43D4
hypercenter#1599D43
hypocenterC43#12238
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1599

Complements

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

NH ≅ G/Ntype
2. #19135937C2semidirect
3. #19133637C2semidirect
4. #19132623C2semidirect
6. #19132540C2semidirect
201. C43#12238semidirect

Maximal subgroups

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

subgroupindex
#191424282
#191359372
#191336372
#191326232
#191325982
#191325402
C43×#15992
#1223843