Finite Group Databasebeta

← #25009155

Subgroups — #25009155

Order 11008.

422 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 63 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#19135846C211yesmaximal, characteristic
2#19133614C211yesmaximal, characteristic
3#19133546C211yesmaximal, characteristic
4#19132619C211yesmaximal, characteristic, complemented
5#19132616C211yesmaximal, characteristic, complemented
6#19132543C211yesmaximal, characteristic, complemented
7C43×#2742C211yesmaximal, characteristic, complemented
8#14583461C2211yescharacteristic
9#14583217—21no—
10#14583038—21no—
11C2×#13063239—21no—
12#14582778—21no—
13#14582666C2211yescharacteristic
14#14582632—21no—
15#14582632—21no—
16#14582623C2211yescharacteristic
17#14582623C2211yescharacteristic
18C43×#400—21no—
19C43×#399C2211yescharacteristic
20C43×#395—21no—
21C43×#393C2211yescharacteristic
22C43×#389—21no—
23C43×#388—21no—
24C43×#387—21no—
25C43×#385C2211yescharacteristic
26C43×#380—21no—
27C22×C22⋊D43—21no—
28C2×#10621884—41no—
29#13063309—41no—
30#13063299—21no—
31#13063299—21no—
32#13063295—41no—
33C2×C22⋊Dic43—21no—
34C2×(C2×D43)⋊C4—41no—
35#13063256—41no—
36#13063249—41no—
37#13063245—41no—
38#13063239—42no—
39C22⋊(C43⋊C8)—21no—
40C22⋊(C43⋊C8)—21no—
41C43⋊#95—41no—
42C22×Q8×C43D411yescharacteristic
43C23×C4×C43D411yescharacteristic
44C2×C4⋊C4×C43—21no—
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×C22⋊C4×C43—21no—
51C2×C22⋊C4×C43—21no—
52C2×C22⋊C4×C43D411yescharacteristic
53C2×C22⋊C4×C43C2311yescharacteristic
54C2×C42×C43—21no—
55#95×C43—21no—
56#95×C43—21no—
57#95×C43—21no—
58#95×C43—21no—
59#95×C43—21no—
60#95×C43—21no—
61#95×C43D411yescharacteristic
62#95×C43D411yescharacteristic
63C24×C43C2×D411yescharacteristic
64C23×D43—21no—
65C2×Q8×C43—41no—
66C2×Q8×C43—81no—
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—41no—
74C22×C4×C43—42no—
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C2×C22⋊D43—41no—
78C2×C22⋊D43—41no—
79C2×C22⋊D43—41no—
80C2×C22⋊D43—41no—
81C2×C22⋊D43—41no—
82C2×C22⋊D43—41no—
83C22×Dic43—21no—
84C22×Dic43—41no—
85C2×D172—21no—
86C2×D172—21no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—42no—
89C4⋊C4×C43—42no—
90C4⋊C4×C43—81no—
91C4⋊C4×C43—81no—
92C4⋊C4×C43—81no—
93C22⋊C4×C43—21no—
94C22⋊C4×C43—41no—
95C22⋊C4×C43—81no—
96C22⋊C4×C43—81no—
97C22⋊C4×C43SD1612yescomplemented
98C42×C43—81no—
99C22⋊Dic43—41no—
100C22⋊Dic43—41no—
101#10621884—82no—
102(C2×D43)⋊C4—41no—
103(C2×D43)⋊C4—41no—
104(C2×D43)⋊C4—82no—
105C4⋊Dic43—21no—
106C4⋊Dic43—21no—
107C2×C43⋊C8—41no—
108C2×C43⋊C8—41no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—41no—
112C23×C43—41no—
113C23×C43#12011yescharacteristic
114C23×C43C2×SD1611yescharacteristic
115C23×C43#13711yescharacteristic
116C22×D43—41no—
117C22×D43—41no—
118C22×D43—41no—
119C22×D43—81no—
120C22×D43—81no—
121Q8×C43—42no—
122Q8×C43—81no—
123C2×C4×C43—22no—
124C2×C4×C43—22no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—42no—
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—41no—
153C2×Dic43—41no—
154C2×Dic43—81no—
155C2×Dic43—81no—
156C2×Dic43—81no—
157D172—81no—
158D172—81no—
159C43⋊C8—81no—
160C43⋊C8—81no—
161#12178—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#44811yescharacteristic
172C22×C43#45411yescharacteristic
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—42no—
182C4×C43—41no—
183C4×C43—81no—
184C4×C43—81no—
185C4×C43—81no—
186C4×C43—81no—
187Dic43—81no—
188Dic43—161no—
189#2742D4311yescharacteristic, complemented
190#2044—431no—
191#1613—431no—
192#1601—431no—
193#1352—431no—
194#1351—431no—
195#1326—431no—
196C2×C43—21no—
197C2×C43—21no—
198C2×C43—41no—
199C2×C43—41no—
200C2×C43#159911yescharacteristic
201C2×C43#219711yescharacteristic
202C2×C43#220011yescharacteristic
203D43—161no—
204#534—431no—
205#481—861no—
206#448—861no—
207C2×#99—861no—
208#400—21no—
209#399C2×D4311yescharacteristic
210#395—21no—
211#393C2×D4311yescharacteristic
212#389—21no—
213#388—21no—
214#387—21no—
215#386—861no—
216#385C2×D4311yescharacteristic
217#380—21no—
218#342—431no—
219#327—861no—
220#327—861no—
221#323—431no—
222#323—431no—
223C43#1217811yescharacteristic, complemented, Sylow
224C22×Q8C22⋊D4311yescharacteristic
225C22×D4—861no—
226C23×C4C22⋊D4311yescharacteristic
227C2×SD16—1721no—
228#123—1721no—
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—21no—
237C2×C4⋊C4C22⋊D4311yescharacteristic
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—861no—
241C2×C22⋊C4—1721no—
242C2×C22⋊C4C22⋊D4311yescharacteristic
243C2×C22⋊C4C22×D4311yescharacteristic
244C2×C42—21no—
245#106—1721no—
246#103—1721no—
247#102—1721no—
248#99—1722no—
249C22⋊C8—861no—
250C22⋊C8—861no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—21no—
255#95—21no—
256#95—21no—
257#95—1721no—
258#95C22⋊D4311yescharacteristic
259#95C22⋊D4311yescharacteristic
260C24—861no—
261C24C2×C22⋊D4311yescharacteristic
262C2×Q8—41no—
263C2×Q8—81no—
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—42no—
279C22×C4—41no—
280C22×C4—861no—
281C22×C4—1721no—
282C22×C4C2×C22⋊D4311yescharacteristic
283C22×C4C2×C22⋊D4311yescharacteristic
284SD16—3442no—
285C2×C8—1721no—
286C2×C8—1721no—
287C4⋊C4—41no—
288C4⋊C4—42no—
289C4⋊C4—42no—
290C4⋊C4—81no—
291C4⋊C4—81no—
292C4⋊C4—81no—
293C4⋊C4—861no—
294C4⋊C4—861no—
295C22⋊C4—21no—
296C22⋊C4—41no—
297C22⋊C4—81no—
298C22⋊C4—81no—
299C22⋊C4—3442no—
300C22⋊C4—1721no—
301C22⋊C4—1721no—
302C22⋊C4—1721no—
303C22⋊C4—1721no—
304C22⋊C4#1062188412yescomplemented
305C42—81no—
306C23—21no—
307C23—21no—
308C23—41no—
309C23—41no—
310C23—3441no—
311C23—3441no—
312C23—1721no—
313C23—1721no—
314C23—1721no—
315C23#1306329411yescharacteristic
316C23C2×#1062188411yescharacteristic
317C23#1306335611yescharacteristic
318Q8—42no—
319Q8—81no—
320D4—3441no—
321D4—3441no—
322D4—3441no—
323D4—3441no—
324D4—3441no—
325D4—3441no—
326C2×C4—22no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
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—3441no—
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#1458303811yescharacteristic
373C22#1458307211yescharacteristic
374C22#1458308611yescharacteristic
375C4—42no—
376C4—41no—
377C4—42no—
378C4—41no—
379C4—81no—
380C4—81no—
381C4—81no—
382C4—81no—
383C4—3441no—
384C4—6881no—
385C2—21no—
386C2—21no—
387C2—41no—
388C2—41no—
389C2—6881no—
390C2#1913353511yescharacteristic
391C2#1913658511yescharacteristic
392C2#1913660211yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#2742C2
socleC22×C43B(4,𝔽2)
prime radical#14583461C22
hypercenter#2742D43
hypocenterC43#12178
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2742

Complements

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

NH ≅ G/Ntype
4. #19132619C2semidirect
5. #19132616C2semidirect
6. #19132543C2semidirect
7. C43×#2742C2semidirect
97. C22⋊C4×C43SD16semidirect
189. #2742D43semidirect
223. C43#12178semidirect
304. C22⋊C4#10621884semidirect

Maximal subgroups

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

subgroupindex
#191358462
#191336142
#191335462
#191326192
#191326162
#191325432
C43×#27422
#1217843