Finite Group Databasebeta

← #25009224

Subgroups — #25009224

Order 11008.

432 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 59 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#19135726C211yesmaximal, characteristic
2#19133614C211yesmaximal, characteristic
3#19133580C211yesmaximal, characteristic
4#19132619C211yesmaximal, characteristic, complemented
5#19132595C211yesmaximal, characteristic, complemented
6#19132525C211yesmaximal, characteristic, complemented
7C43×#2771C211yesmaximal, characteristic, complemented
8#14583461C2211yescharacteristic
9C2×#13063308—21no—
10#14583217—21no—
11#14583212—21no—
12C2×#13063239—21no—
13#14582666C2211yescharacteristic
14#14582632—21no—
15#14582632—21no—
16#14582623C2211yescharacteristic
17#14582623C2211yescharacteristic
18C43×#400—21no—
19C43×#400—21no—
20C43×#399C2211yescharacteristic
21C43×#397C2211yescharacteristic
22C43×#389—21no—
23C43×#388—21no—
24C43×#387—21no—
25C43×#385—21no—
26C43×#381C2211yescharacteristic
27C22×C22⋊D43—21no—
28#13063309—41no—
29#13063308—42no—
30#13063308—42no—
31#13063299—21no—
32#13063299—21no—
33#13063295—41no—
34C2×Dic43⋊C4—41no—
35C2×C22⋊Dic43—21no—
36C2×(C2×D43)⋊C4—41no—
37#13063258—41no—
38#13063256—41no—
39#13063245—41no—
40#13063245—41no—
41#13063239—42no—
42C22⋊(C43⋊C8)—21no—
43C22⋊(C43⋊C8)—21no—
44C23×C4×C43D411yescharacteristic
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43D411yescharacteristic
50C2×C4⋊C4×C43D411yescharacteristic
51C2×C22⋊C4×C43—21no—
52C2×C22⋊C4×C43—21no—
53C2×C22⋊C4×C43D411yescharacteristic
54C2×C22⋊C4×C43C2311yescharacteristic
55C2×C42×C43—21no—
56#95×C43—21no—
57#95×C43—21no—
58#95×C43—21no—
59#95×C43—21no—
60#95×C43—21no—
61#95×C43—21no—
62#95×C43—21no—
63#95×C43D411yescharacteristic
64#95×C43D411yescharacteristic
65C24×C43C2×D411yescharacteristic
66C23×D43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43—41no—
76C22×C4×C43—41no—
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C2×C22⋊D43—41no—
80C2×C22⋊D43—41no—
81C2×C22⋊D43—41no—
82C2×C22⋊D43—41no—
83C2×C22⋊D43—41no—
84C2×C22⋊D43—41no—
85C22×Dic43—21no—
86C22×Dic43—41no—
87C2×D172—21no—
88C2×D172—21no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—42no—
92C4⋊C4×C43—42no—
93C4⋊C4×C43—81no—
94C4⋊C4×C43—81no—
95C22⋊C4×C43—41no—
96C22⋊C4×C43—41no—
97C22⋊C4×C43—42no—
98C22⋊C4×C43—41no—
99C22⋊C4×C43—41no—
100C42×C43—81no—
101C22⋊Dic43—22no—
102C22⋊Dic43—41no—
103(C2×D43)⋊C4—41no—
104(C2×D43)⋊C4—41no—
105(C2×D43)⋊C4—44no—
106C4⋊Dic43—21no—
107C4⋊Dic43—21no—
108Dic43⋊C4—44no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8—41no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43#12011yescharacteristic
116C23×C43#13511yescharacteristic
117C23×C43AGL(1,ℤ/8)11yescharacteristic
118C22×D43—41no—
119C22×D43—41no—
120C22×D43—41no—
121C22×D43—81no—
122C22×D43—81no—
123C2×C4×C43—22no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—42no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—81no—
147C22⋊D43—81no—
148C22⋊D43—81no—
149C22⋊D43—81no—
150C22⋊D43—81no—
151C2×Dic43—41no—
152C2×Dic43—42no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—81no—
156C2×Dic43—81no—
157D172—81no—
158D172—81no—
159C43⋊C8—81no—
160C43⋊C8—81no—
161#12189—431nomaximal, Sylow
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—81no—
171C22×C43#44911yescharacteristic
172C22×C43#45311yescharacteristic
173C22×C43B(4,𝔽2)11yescharacteristic
174C2×D43—82no—
175C2×D43—81no—
176C2×D43—81no—
177C2×D43—81no—
178C2×D43—161no—
179C4×C43—42no—
180C4×C43—41no—
181C4×C43—41no—
182C4×C43—81no—
183C4×C43—81no—
184C4×C43—81no—
185C4×C43—81no—
186C4×C43—81no—
187Dic43—82no—
188Dic43—81no—
189#2771D4311yescharacteristic, complemented
190#2022—431no—
191#1613—431no—
192#1607—431no—
193#1352—431no—
194#1344—431no—
195#1317—431no—
196C2×C43—21no—
197C2×C43—21no—
198C2×C43—41no—
199C2×C43—41no—
200C2×C43#160011yescharacteristic
201C2×C43#219811yescharacteristic
202C2×C43#220111yescharacteristic
203D43—161no—
204#534—431no—
205C2×#123—861no—
206#481—861no—
207#480—861no—
208C2×#99—861no—
209#400—21no—
210#400—21no—
211#399C2×D4311yescharacteristic
212#397C2×D4311yescharacteristic
213#389—21no—
214#388—21no—
215#387—21no—
216#385—21no—
217#381C2×D4311yescharacteristic
218#342—431no—
219#327—861no—
220#327—861no—
221#323—431no—
222#323—431no—
223C43#1218911yescharacteristic, complemented, Sylow
224C22×D4—861no—
225C23×C4C22⋊D4311yescharacteristic
226#123—1721no—
227#123—1722no—
228#123—1722no—
229#121—861no—
230#121—861no—
231#120—1721no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—1721no—
237C2×C4⋊C4C22⋊D4311yescharacteristic
238C2×C4⋊C4C22⋊D4311yescharacteristic
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—861no—
242C2×C22⋊C4—1721no—
243C2×C22⋊C4C22⋊D4311yescharacteristic
244C2×C22⋊C4C22×D4311yescharacteristic
245C2×C42—21no—
246#107—1721no—
247#106—1721no—
248#102—1721no—
249#102—1721no—
250#99—1722no—
251C22⋊C8—861no—
252C22⋊C8—861no—
253#95—21no—
254#95—21no—
255#95—21no—
256#95—21no—
257#95—21no—
258#95—21no—
259#95—21no—
260#95C22⋊D4311yescharacteristic
261#95C22⋊D4311yescharacteristic
262C24—861no—
263C24C2×C22⋊D4311yescharacteristic
264C2×D4—861no—
265C2×D4—861no—
266C2×D4—1721no—
267C2×D4—1721no—
268C2×D4—1721no—
269C2×D4—1721no—
270C2×D4—1721no—
271C2×D4—1721no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—861no—
283C22×C4—1721no—
284C22×C4C2×C22⋊D4311yescharacteristic
285C22×C4C2×C22⋊D4311yescharacteristic
286C2×C8—1721no—
287C2×C8—1721no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—42no—
291C4⋊C4—42no—
292C4⋊C4—81no—
293C4⋊C4—81no—
294C4⋊C4—861no—
295C4⋊C4—861no—
296C4⋊C4—1724no—
297C22⋊C4—41no—
298C22⋊C4—42no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—862no—
303C22⋊C4—1721no—
304C22⋊C4—1721no—
305C22⋊C4—1724no—
306C22⋊C4—1721no—
307C42—81no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23—3441no—
313C23—3441no—
314C23—1721no—
315C23—1721no—
316C23—1721no—
317C23#1306329411yescharacteristic
318C23#1306334511yescharacteristic
319C23#1306335011yescharacteristic
320D4—3441no—
321D4—3441no—
322D4—3441no—
323D4—3441no—
324D4—3441no—
325D4—3441no—
326C2×C4—22no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—3441no—
351C2×C4—3441no—
352C2×C4—1722no—
353C2×C4—1721no—
354C2×C4—1721no—
355C2×C4—1721no—
356C8—3441no—
357C8—3441no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—81no—
367C22—3442no—
368C22—3441no—
369C22—3441no—
370C22—3441no—
371C22—6881no—
372C22#1458304411yescharacteristic
373C22#1458306711yescharacteristic
374C22#1458308611yescharacteristic
375C4—42no—
376C4—41no—
377C4—41no—
378C4—81no—
379C4—81no—
380C4—81no—
381C4—81no—
382C4—81no—
383C4—3442no—
384C4—3441no—
385C2—21no—
386C2—21no—
387C2—41no—
388C2—41no—
389C2—6881no—
390C2#1913354111yescharacteristic
391C2#1913659111yescharacteristic
392C2#1913660811yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#2771C2
socleC22×C43B(4,𝔽2)
prime radical#14583461C22
hypercenter#2771D43
hypocenterC43#12189
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2771

Complements

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

NH ≅ G/Ntype
4. #19132619C2semidirect
5. #19132595C2semidirect
6. #19132525C2semidirect
7. C43×#2771C2semidirect
189. #2771D43semidirect
223. C43#12189semidirect

Maximal subgroups

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

subgroupindex
#191357262
#191336142
#191335802
#191326192
#191325952
#191325252
C43×#27712
#1218943