Finite Group Databasebeta

← #24985147

Subgroups — #24985147

Order 11008.

470 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 107 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#19142934C211yesmaximal, characteristic
2#19134575C211yesmaximal, characteristic
3#19132420C212yesmaximal, complemented
4#19132417C212yesmaximal, complemented
5C43×#1749C211yesmaximal, characteristic
6C2×#13063304C411yescharacteristic
7C2×C4⋊(C43⋊C8)—21no—
8C2×C22⋊(C43⋊C8)—21no—
9#14582805C411yescharacteristic
10#14582805C2211yescharacteristic
11#14582797C411yescharacteristic
12#14582797C2211yescharacteristic
13#14582783—21no—
14#14582783—21no—
15#14582772—21no—
16#14582762—21no—
17#14582759C411yescharacteristic
18#14582654C2212yes—
19C22×C42×C43C2211yescharacteristic
20C2×C22⋊C8×C43—21no—
21C2×#97×C43—21no—
22C43×#336C2212yes—
23C22×Dic86C2×C411yescharacteristic
24C22×C43⋊C8—22no—
25#13063304—42no—
26C2×C4⋊Dic43C2×C411yescharacteristic
27C2×C4⋊Dic43C2×C411yescharacteristic
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×Dic43⋊C4—21no—
30C2×Dic43⋊C4—21no—
31C2×Dic43⋊C4—21no—
32C2×C22⋊Dic43—21no—
33C2×C22⋊Dic43—21no—
34C4⋊(C43⋊C8)—42no—
35C22⋊(C43⋊C8)—42no—
36C43⋊#95—21no—
37C43⋊#95—21no—
38C43⋊#95—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C23×C4×C43C2×C411yescharacteristic
44C23×C4×C43D411yescharacteristic
45C23×C4×C43D411yescharacteristic
46C22×C8×C43—22no—
47C2×C42×C43—42no—
48C2×C42×C43C2×C411yescharacteristic
49C2×C42×C43D411yescharacteristic
50C2×C42×C43D411yescharacteristic
51C2×C42×C43C2311yescharacteristic
52C22⋊C8×C43—24no—
53#97×C43—42no—
54C24×C43C22⋊C411yescharacteristic
55C22×C4×C43—22no—
56C22×C4×C43—22no—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—22no—
60C22×C4×C43—22no—
61C22×C4×C43—41no—
62C22×C4×C43—41no—
63C22×C4×C43—41no—
64C22×C4×C43—41no—
65C22×C4×C43C22⋊C411yescharacteristic
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C2×Dic86—22no—
76C2×Dic86—41no—
77C2×Dic86—41no—
78C2×C8×C43—24no—
79C2×C8×C43—42no—
80C2×C8×C43—42no—
81C42×C43—22no—
82C42×C43—22no—
83C42×C43—41no—
84C42×C43—41no—
85C22⋊Dic43—42no—
86C22⋊Dic43—42no—
87C4⋊Dic43—22no—
88C4⋊Dic43—41no—
89C4⋊Dic43—41no—
90Dic43⋊C4—42no—
91Dic43⋊C4—42no—
92Dic43⋊C4—41no—
93Dic43⋊C4—41no—
94C2×C43⋊C8—42no—
95C2×C43⋊C8—42no—
96C2×C43⋊C8—42no—
97C23×C43—21no—
98C23×C43—21no—
99C23×C43—21no—
100C23×C43—21no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43#10412yes—
104C23×C43C2×C22⋊C411yescharacteristic
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—44no—
120C2×C4×C43—44no—
121C2×C4×C43—42no—
122C2×C4×C43—42no—
123C2×C4×C43#9912yes—
124C2×C4×C43#13112yes—
125C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C43#13712yes—
127C2×C4×C43#13711yescharacteristic
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
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—
140Dic86—82no—
141C8×C43—44no—
142C43⋊C8—82no—
143#7701—431nomaximal, Sylow
144C22×C43—22no—
145C22×C43—22no—
146C22×C43—22no—
147C22×C43—41no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43#40811yescharacteristic
152C22×C43C2×#9911yescharacteristic
153C22×C43#41311yescharacteristic
154C22×C43#41711yescharacteristic
155C22×C43#41911yescharacteristic
156C22×C43C2×#10411yescharacteristic
157C22×C43#42111yescharacteristic
158C4×C43—22no—
159C4×C43—22no—
160C4×C43—22no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—41no—
164C4×C43—41no—
165Dic43—81no—
166Dic43—81no—
167Dic43—81no—
168Dic43—81no—
169#2855—431no—
170#1797—431no—
171#1749D4311yescharacteristic
172#1272—432no—
173#1271—432no—
174C2×C43—42no—
175C2×C43#146811yescharacteristic
176C2×C43#148311yescharacteristic
177C2×C43#149711yescharacteristic
178C2×C43#150811yescharacteristic
179C2×C43#151311yescharacteristic
180C2×C43#153211yescharacteristic
181C2×C43#155911yescharacteristic
182C2×C22⋊Q8—431no—
183C22×C42C2×D4311yescharacteristic
184C2×C4⋊C8—861no—
185C2×C22⋊C8—21no—
186C2×C22⋊C8—861no—
187C2×#97—21no—
188#391—431no—
189#391—431no—
190#389—431no—
191#389—431no—
192#387—861no—
193#387—861no—
194#385—861no—
195#381—861no—
196#380—431no—
197#336—432no—
198#336C2×D4312yes—
199C43#770111yescharacteristic, complemented, Sylow
200C22×Q8—431no—
201C23×C4C4×D4311yescharacteristic
202C23×C4D17211yescharacteristic
203C23×C4C22⋊D4311yescharacteristic
204C22×C8—22no—
205C22×C8—862no—
206C22⋊Q8—1722no—
207C2×C4⋊C4—431no—
208C2×C4⋊C4—431no—
209C2×C4⋊C4—431no—
210C2×C4⋊C4—861no—
211C2×C4⋊C4—861no—
212C2×C4⋊C4—861no—
213C2×C22⋊C4—861no—
214C2×C22⋊C4—861no—
215C2×C42—42no—
216C2×C42C4×D4311yescharacteristic
217C2×C42D17211yescharacteristic
218C2×C42C22⋊D4311yescharacteristic
219C2×C42C22×D4311yescharacteristic
220C4⋊C8—1722no—
221C22⋊C8—24no—
222C22⋊C8—1722no—
223#97—42no—
224#95—861no—
225#95—861no—
226#95—861no—
227#95—861no—
228#95—861no—
229#95—861no—
230#95—861no—
231C24(C2×D43)⋊C411yescharacteristic
232C2×Q8—862no—
233C2×Q8—1721no—
234C2×Q8—1721no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—861no—
246C22×C4—861no—
247C22×C4—861no—
248C22×C4—861no—
249C22×C4(C2×D43)⋊C411yescharacteristic
250C22×C4(C2×D43)⋊C411yescharacteristic
251C22×C4(C2×D43)⋊C411yescharacteristic
252C22×C4C2×C4×D4311yescharacteristic
253C22×C4C2×D17211yescharacteristic
254C22×C4C2×C22⋊D4311yescharacteristic
255C2×C8—24no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—1722no—
259C2×C8—1722no—
260C2×C8—1722no—
261C4⋊C4—862no—
262C4⋊C4—1721no—
263C4⋊C4—1721no—
264C4⋊C4—1722no—
265C4⋊C4—1722no—
266C4⋊C4—1721no—
267C4⋊C4—1721no—
268C22⋊C4—1722no—
269C22⋊C4—1722no—
270C42—22no—
271C42—22no—
272C42—41no—
273C42—41no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23#1306325312yes—
281C23C2×(C2×D43)⋊C411yescharacteristic
282Q8—3442no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—1721no—
302C2×C4—1721no—
303C2×C4—1721no—
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#1306323912yes—
314C2×C4#1306333312yes—
315C2×C4#1306335311yescharacteristic
316C2×C4#1306335512yes—
317C2×C4#1306335811yescharacteristic
318C8—44no—
319C8—3442no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22#1458286711yescharacteristic
328C22C2×#1306323911yescharacteristic
329C22#1458288111yescharacteristic
330C22#1458290111yescharacteristic
331C22#1458290711yescharacteristic
332C22C2×#1306325311yescharacteristic
333C22#1458291511yescharacteristic
334C4—22no—
335C4—22no—
336C4—22no—
337C4—21no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—3441no—
342C4—3441no—
343C4—3441no—
344C4—3441no—
345C2—42no—
346C2#1913294411yescharacteristic
347C2#1913300911yescharacteristic
348C2#1913306711yescharacteristic
349C2#1913311411yescharacteristic
350C2#1913313911yescharacteristic
351C2#1913321311yescharacteristic
352C2#1913332611yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1749C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1749D43
hypocenterC43#7701
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
3. #19132420C2semidirect
4. #19132417C2semidirect
199. C43#7701semidirect

Maximal subgroups

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

subgroupindex
#191429342
#191345752
#191324202
#191324172
C43×#17492
#770143