Finite Group Databasebeta

← #25007056

Subgroups — #25007056

Order 11008.

500 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 83 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#19140161C211yesmaximal, characteristic
2#19132929C211yesmaximal, characteristic, complemented
3#19132618C212yesmaximal, complemented
4#19132591C212yesmaximal
5C43×#1740C211yesmaximal, characteristic, complemented
6C2×C4×D172C411yescharacteristic, complemented
7#14582956—21no—
8#14582838C411yescharacteristic, complemented
9#14582835C2211yescharacteristic
10#14582816C411yescharacteristic, complemented
11#14582808C2211yescharacteristic
12#14582790—21no—
13#14582778—21no—
14#14582775—21no—
15#14582770—21no—
16#14582767C411yescharacteristic, complemented
17#14582625—21no—
18#14582623C2212yes—
19C2×#117×C43—21no—
20C2×#117×C43C2211yescharacteristic
21C43×#342—21no—
22C43×#342C2212yes—
23C22×D172C2×C411yescharacteristic
24C22×C22⋊D43—21no—
25C22×C4×D43—21no—
26C4×D172—41no—
27C4×D172—41no—
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×Dic43⋊C4—21no—
30C2×C22⋊Dic43—21no—
31C2×(C2×D43)⋊C4—21no—
32C2×(C2×D43)⋊C4—21no—
33C2×(C2×D43)⋊C4—21no—
34C2×(C2×D43)⋊C4—21no—
35C4⋊(C43⋊C8)—41no—
36C22⋊(C43⋊C8)—22no—
37#13063236—41no—
38C43⋊#95—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95C2×C411yescharacteristic
43C43⋊#95C2×C411yescharacteristic
44C23×C4×C43D411yescharacteristic
45#117×C43—24no—
46#117×C43—41no—
47#117×C43—41no—
48#117×C43—42no—
49C2×C4⋊C4×C43—41no—
50C2×C4⋊C4×C43C2×C411yescharacteristic
51C2×C4⋊C4×C43D411yescharacteristic
52C2×C22⋊C4×C43—22no—
53C2×C22⋊C4×C43D411yescharacteristic
54C2×C22⋊C4×C43C2311yescharacteristic
55C2×C42×C43—41no—
56C2×C42×C43C2×C411yescharacteristic
57C2×C42×C43D411yescharacteristic
58C24×C43C2×D411yescharacteristic
59C23×D43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—22no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—42no—
66C22×C4×C43C22⋊C411yescharacteristic
67C22×C4×C43C22⋊C411yescharacteristic
68C22×C4×C43C22⋊C411yescharacteristic
69C22×C4×C43C22⋊C411yescharacteristic
70C22×C4×C43C22×C411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C2×C22⋊D43—42no—
73C2×C22⋊D43—41no—
74C2×C22⋊D43—41no—
75C2×C22⋊D43—81no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C2×D172—42no—
80C2×D172—41no—
81C2×C4×D43—42no—
82C2×C4×D43—81no—
83C2×C4×D43—81no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—44no—
87C22⋊C4×C43—24no—
88C22⋊C4×C43—41no—
89C22⋊C4×C43—41no—
90C22⋊C4×C43—42no—
91C42×C43—21no—
92C42×C43—21no—
93C42×C43—21no—
94C42×C43—21no—
95C42×C43—44no—
96C22⋊Dic43—81no—
97(C2×D43)⋊C4—42no—
98(C2×D43)⋊C4—41no—
99(C2×D43)⋊C4—41no—
100(C2×D43)⋊C4—42no—
101(C2×D43)⋊C4—81no—
102C4⋊Dic43—41no—
103Dic43⋊C4—81no—
104C2×C43⋊C8—42no—
105C23×C43—21no—
106C23×C43—21no—
107C23×C43—41no—
108C23×C43—41no—
109C23×C43C2×C22⋊C411yescharacteristic
110C23×C43AGL(1,ℤ/8)11yescharacteristic
111C23×C43#13711yescharacteristic
112C22×D43—22no—
113C22×D43—41no—
114C22×D43—41no—
115C22×D43—41no—
116C22×D43—41no—
117C22×D43—41no—
118C22×D43—41no—
119C2×C4×C43—22no—
120C2×C4×C43—22no—
121C2×C4×C43—22no—
122C2×C4×C43—22no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—44no—
136C2×C4×C43—82no—
137C2×C4×C43—82no—
138C2×C4×C43#9911yescharacteristic
139C2×C4×C43#9911yescharacteristic
140C2×C4×C43#10412yes—
141C22⋊D43—82no—
142C22⋊D43—82no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152D172—42no—
153D172—42no—
154C4×D43—84no—
155C43⋊C8—82no—
156#11754—431nomaximal, Sylow
157C22×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—81no—
166C22×C43C2×#9911yescharacteristic
167C22×C43#41711yescharacteristic
168C22×C43C2×#10411yescharacteristic
169C2×D43—42no—
170C2×D43—42no—
171C2×D43—42no—
172C2×D43—81no—
173C2×D43—81no—
174C2×D43—81no—
175C2×D43—81no—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—22no—
179C4×C43—41no—
180C4×C43—41no—
181C4×C43—41no—
182C4×C43—41no—
183C4×C43—84no—
184Dic43—81no—
185Dic43—81no—
186Dic43—81no—
187#2598—431no—
188#1740D4311yescharacteristic, complemented
189#1464—431no—
190#1352—432no—
191#1343—432no—
192C2×C43—21no—
193C2×C43—21no—
194C2×C43—41no—
195C2×C43—41no—
196C2×C43#150411yescharacteristic
197C2×C43#212011yescharacteristic
198C2×C43#212811yescharacteristic
199D43—82no—
200C2×C4×D4—431no—
201C2×#117—21no—
202C2×#117C2×D4311yescharacteristic
203#432—861no—
204#400—431no—
205#399—431no—
206#394—431no—
207#392—431no—
208#388—861no—
209#386—861no—
210#386—861no—
211#385—861no—
212#383—431no—
213#342—21no—
214#342C2×D4312yes—
215#324—861no—
216#323—432no—
217C43#1175411yescharacteristic, complemented, Sylow
218C22×D4—431no—
219C22×D4—861no—
220C23×C4—861no—
221C23×C4C22⋊D4311yescharacteristic
222C4×D4—1721no—
223C4×D4—1721no—
224#117—24no—
225#117—41no—
226#117—41no—
227#117—42no—
228C2×C4⋊C4—41no—
229C2×C4⋊C4—431no—
230C2×C4⋊C4—861no—
231C2×C4⋊C4C4×D4311yescharacteristic
232C2×C4⋊C4D17211yescharacteristic
233C2×C22⋊C4—22no—
234C2×C22⋊C4—861no—
235C2×C22⋊C4—861no—
236C2×C22⋊C4—861no—
237C2×C22⋊C4—861no—
238C2×C22⋊C4—861no—
239C2×C22⋊C4C22⋊D4311yescharacteristic
240C2×C22⋊C4C22×D4311yescharacteristic
241C2×C42—41no—
242C2×C42C4×D4311yescharacteristic
243C2×C42D17211yescharacteristic
244C4⋊C8—1721no—
245C22⋊C8—862no—
246#97—1721no—
247#95—431no—
248#95—431no—
249#95—861no—
250#95—861no—
251#95—861no—
252#95—861no—
253C24—861no—
254C24C2×C22⋊D4311yescharacteristic
255C2×D4—3441no—
256C2×D4—1721no—
257C2×D4—1722no—
258C2×D4—1722no—
259C2×D4—1721no—
260C2×D4—1721no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—42no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4—861no—
270C22×C4—3441no—
271C22×C4—3441no—
272C22×C4—1722no—
273C22×C4(C2×D43)⋊C411yescharacteristic
274C22×C4(C2×D43)⋊C411yescharacteristic
275C22×C4(C2×D43)⋊C411yescharacteristic
276C22×C4(C2×D43)⋊C411yescharacteristic
277C22×C4C2×C4×D4311yescharacteristic
278C22×C4C2×D17211yescharacteristic
279C2×C8—1722no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—44no—
283C4⋊C4—3441no—
284C4⋊C4—1721no—
285C22⋊C4—24no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—42no—
289C22⋊C4—3441no—
290C22⋊C4—3441no—
291C22⋊C4—1722no—
292C22⋊C4—1721no—
293C22⋊C4—1721no—
294C22⋊C4—1722no—
295C42—21no—
296C42—21no—
297C42—21no—
298C42—21no—
299C42—44no—
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23—862no—
305C23—1721no—
306C23—1721no—
307C23—1721no—
308C23—1721no—
309C23—1721no—
310C23—1721no—
311C23C2×(C2×D43)⋊C411yescharacteristic
312C23#1306335111yescharacteristic
313C23#1306335611yescharacteristic
314D4—3442no—
315D4—3442no—
316D4—1722no—
317D4—1722no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—44no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—3444no—
338C2×C4—1721no—
339C2×C4—1721no—
340C2×C4—1721no—
341C2×C4—1721no—
342C2×C4—1721no—
343C2×C4—1721no—
344C2×C4—1721no—
345C2×C4—1721no—
346C2×C4—1721no—
347C2×C4#1306323911yescharacteristic
348C2×C4#1306323911yescharacteristic
349C2×C4#1306325312yes—
350C8—3442no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—81no—
360C22—3441no—
361C22—3441no—
362C22—3441no—
363C22—3441no—
364C22—1722no—
365C22—1722no—
366C22—1722no—
367C22C2×#1306323911yescharacteristic
368C22#1458289811yescharacteristic
369C22C2×#1306325311yescharacteristic
370C4—21no—
371C4—21no—
372C4—22no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—84no—
378C4—3441no—
379C4—3441no—
380C4—3441no—
381C2—21no—
382C2—21no—
383C2—41no—
384C2—41no—
385C2—3442no—
386C2#1913309711yescharacteristic
387C2#1913623411yescharacteristic
388C2#1913626611yescharacteristic
subgroupG/H
centerC22C2×#13063239
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1740C2
socleC22×C43C2×#99
prime radical#14582808C22
cosocleC2×C22⋊C4×C43C23
hypercenter#1740D43
hypocenterC43#11754
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1740

Complements

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

NH ≅ G/Ntype
2. #19132929C2semidirect
3. #19132618C2semidirect
5. C43×#1740C2semidirect
6. C2×C4×D172C4semidirect
8. #14582838C4semidirect
10. #14582816C4semidirect
16. #14582767C4semidirect
188. #1740D43semidirect
217. C43#11754semidirect

Maximal subgroups

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

subgroupindex
#191401612
#191329292
#191326182
#191325912
C43×#17402
#1175443