Finite Group Databasebeta

← #25069723

Subgroups — #25069723

Order 11008.

958 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 958 conjugacy classes of subgroups — too many to draw. Only its 203 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#19144599C212yesmaximal
2#19139500C211yesmaximal, characteristic
3#19133603C214yesmaximal, complemented
4#19133535C214yesmaximal
5#19133159C212yesmaximal, complemented
6#19132919C211yesmaximal, characteristic, complemented
7C43×#3502C211yesmaximal, characteristic, complemented
8C2×#13063301—21no—
9C2×C4×D172C2211yescharacteristic
10#14583227C2214yes—
11#14583186—22no—
12#14583101—22no—
13#14583049C2214yes—
14C4×#10621884—24no—
15#14582952C2212yes—
16#14582829C2212yes—
17#14582816C2212yes—
18#14582790—22no—
19#14582765C2211yescharacteristic
20#14582756—21no—
21#14582636C2218yes—
22#14582625C2214yes—
23Q82×C43—22no—
24C43×#557—22no—
25C43×#557—24no—
26C43×#544—21no—
27C43×#544C2214yes—
28C43×#533—22no—
29C43×#533C2212yes—
30C43×#519—21no—
31C2×C4×Q8×C43C2211yescharacteristic
32C22×D172C2311yescharacteristic
33C22×C4×D43—21no—
34C2×#10621884—24no—
35#13063301—44no—
36C4×D172—22no—
37C4×D172—22no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43C2311yescharacteristic
40C2×Dic43⋊C4—22no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—22no—
43C2×(C2×D43)⋊C4—22no—
44#13063256—24no—
45C4⋊(C43⋊C8)—22no—
46#13063249—24no—
47#13063245—24no—
48C22⋊(C43⋊C8)C2314yes—
49C4×C43⋊C8—22no—
50C43⋊#95—21no—
51C43⋊#95—22no—
52C43⋊#95C2312yes—
53C22×Q8×C43D411yescharacteristic
54C4⋊Q8×C43—22no—
55C4⋊Q8×C43—22no—
56C4⋊Q8×C43—24no—
57C4⋊Q8×C43—28no—
58C4⋊Q8×C43D412yes—
59C4⋊Q8×C43D412yes—
60#125×C43—24no—
61#125×C43—24no—
62#125×C43—28no—
63#125×C43—22no—
64C22⋊Q8×C43—22no—
65C22⋊Q8×C43—24no—
66C22⋊Q8×C43C2314yes—
67C4×Q8×C43—24no—
68C4×Q8×C43—24no—
69C4×Q8×C43—24no—
70C4×Q8×C43—24no—
71C4×Q8×C43—22no—
72C4×Q8×C43—22no—
73C4×Q8×C43—22no—
74C4×Q8×C43D414yes—
75#117×C43—24no—
76#117×C43—22no—
77C2×C4⋊C4×C43D411yescharacteristic
78C2×C4⋊C4×C43C2312yes—
79C2×C42×C43D412yes—
80C2×C42×C43C2311yescharacteristic
81C23×D43—21no—
82C2×Q8×C43—24no—
83C2×Q8×C43—22no—
84C2×Q8×C43—22no—
85C2×Q8×C43—22no—
86C2×Q8×C43SD1614yescomplemented
87C2×Q8×C43C2×D414yes—
88C22×C4×C43C2×D412yes—
89C22×C4×C43C2×D412yes—
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2411yescharacteristic
93C22×Dic43—22no—
94C22×Dic43—21no—
95C2×D172—22no—
96C2×D172—42no—
97C2×C4×D43—42no—
98C2×C4×D43—42no—
99C2×C4×D43—42no—
100C4⋊C4×C43—24no—
101C4⋊C4×C43—24no—
102C4⋊C4×C43—24no—
103C4⋊C4×C43—28no—
104C4⋊C4×C43—22no—
105C4⋊C4×C43—22no—
106C4⋊C4×C43—22no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—24no—
109C4⋊C4×C43—24no—
110C4⋊C4×C43—24no—
111C4⋊C4×C43C2×D414yes—
112C22⋊C4×C43—24no—
113C42×C43—28no—
114C42×C43—22no—
115C42×C43—22no—
116C42×C43—24no—
117C42×C43C2×D412yes—
118C42×C43C2×D412yes—
119#10621884—48no—
120(C2×D43)⋊C4—44no—
121(C2×D43)⋊C4—41no—
122(C2×D43)⋊C4—41no—
123(C2×D43)⋊C4—44no—
124C4⋊Dic43—22no—
125C4⋊Dic43—42no—
126Dic43⋊C4—44no—
127C2×C43⋊C8—24no—
128C23×C43C22×D411yescharacteristic
129C22×D43—22no—
130C22×D43—41no—
131C22×D43—41no—
132C22×D43—41no—
133C22×D43—41no—
134C22×D43—41no—
135C22×D43—41no—
136Q8×C43—28no—
137Q8×C43—44no—
138Q8×C43—44no—
139Q8×C43—84no—
140C2×C4×C43—22no—
141C2×C4×C43—22no—
142C2×C4×C43—24no—
143C2×C4×C43—24no—
144C2×C4×C43—22no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—42no—
148C2×C4×C43#12011yescharacteristic
149C2×C4×C43#12011yescharacteristic
150C2×C4×C43#12012yes—
151C2×C4×C43C2×SD1614yes—
152C2×C4×C43C2×SD1612yes—
153C2×C4×C43#13712yes—
154C2×C4×C43C22×D412yes—
155C2×Dic43—42no—
156C2×Dic43—42no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—42no—
160C2×Dic43—41no—
161D172—24no—
162D172—42no—
163C4×D43—84no—
164C43⋊C8—44no—
165#18220—431nomaximal, Sylow
166C22×C43—21no—
167C22×C43—21no—
168C22×C43C2×#12011yescharacteristic
169C22×C43C22×SD1611yescharacteristic
170C22×C43C2×#13711yescharacteristic
171C2×D43—42no—
172C2×D43—42no—
173C2×D43—42no—
174C2×D43—81no—
175C2×D43—81no—
176C2×D43—81no—
177C2×D43—81no—
178C4×C43—24no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—22no—
182C4×C43—44no—
183C4×C43—42no—
184C4×C43—44no—
185C4×C43#44814yes—
186Dic43—82no—
187Dic43—81no—
188#3502D4311yescharacteristic, complemented
189#3101—432no—
190#2536—431no—
191#1611—434no—
192#1599—434no—
193#1518—432no—
194#1461—431no—
195C2×C43—21no—
196C2×C43—21no—
197C2×C43C2×#44811yescharacteristic
198C2×C43#302011yescharacteristic
199C2×C43#302511yescharacteristic
200D43—82no—
201Q82—22no—
202#557—22no—
203#557—24no—
204#544—21no—
205#544C2×D4314yes—
206#533—22no—
207#533C2×D4312yes—
208C2×C22⋊Q8—861no—
209#519—21no—
210C2×C4×Q8C2×D4311yescharacteristic
211C2×C4×D4—431no—
212#483—434no—
213#476—862no—
214#461—862no—
215#450—434no—
216C4×SD16—864no—
217#431—432no—
218#398—432no—
219#394—432no—
220#388—862no—
221#382—431no—
222#380—861no—
223#328—438no—
224#324—434no—
225C43#1822011yescharacteristic, complemented, Sylow
226C22×Q8C22⋊D4311yescharacteristic
227C22×D4—431no—
228C23×C4—861no—
229C2×SD16—864no—
230C4⋊Q8—22no—
231C4⋊Q8—22no—
232C4⋊Q8—24no—
233C4⋊Q8—28no—
234C4⋊Q8C22⋊D4312yes—
235C4⋊Q8C22⋊D4312yes—
236#125—24no—
237#125—24no—
238#125—28no—
239#125—22no—
240C22⋊Q8—22no—
241C22⋊Q8—24no—
242C22⋊Q8—1724no—
243C22⋊Q8C22×D4314yes—
244C4×Q8—24no—
245C4×Q8—24no—
246C4×Q8—24no—
247C4×Q8—24no—
248C4×Q8—22no—
249C4×Q8—22no—
250C4×Q8—22no—
251C4×Q8C22⋊D4314yes—
252C4×D4—862no—
253C4×D4—862no—
254#117—24no—
255#117—22no—
256C2×C4⋊C4—431no—
257C2×C4⋊C4—862no—
258C2×C4⋊C4—861no—
259C2×C4⋊C4C22⋊D4311yescharacteristic
260C2×C4⋊C4C22×D4312yes—
261C2×C22⋊C4—861no—
262C2×C22⋊C4—862no—
263C2×C22⋊C4—862no—
264C2×C42C22⋊D4312yes—
265C2×C42C22×D4311yescharacteristic
266#106—864no—
267C4⋊C8—862no—
268#103—864no—
269#102—864no—
270C22⋊C8—434no—
271C4×C8—862no—
272#95—432no—
273#95—862no—
274#95—861no—
275C24—861no—
276C2×Q8—24no—
277C2×Q8—22no—
278C2×Q8—22no—
279C2×Q8—22no—
280C2×Q8#1062188414yescomplemented
281C2×Q8C2×C22⋊D4314yes—
282C2×D4—862no—
283C2×D4—1722no—
284C22×C4—862no—
285C22×C4—861no—
286C22×C4—1722no—
287C22×C4—1722no—
288C22×C4—1722no—
289C22×C4C2×C22⋊D4312yes—
290C22×C4C2×C22⋊D4312yes—
291C22×C4C2×C22⋊D4311yescharacteristic
292C22×C4C2×C22⋊D4311yescharacteristic
293C22×C4C23×D4311yescharacteristic
294SD16—1728no—
295C2×C8—864no—
296C4⋊C4—24no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—28no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—24no—
305C4⋊C4—24no—
306C4⋊C4—24no—
307C4⋊C4—862no—
308C4⋊C4—1724no—
309C4⋊C4—1722no—
310C4⋊C4C2×C22⋊D4314yes—
311C22⋊C4—24no—
312C22⋊C4—1724no—
313C22⋊C4—1721no—
314C22⋊C4—1721no—
315C22⋊C4—1724no—
316C42—28no—
317C42—22no—
318C42—22no—
319C42—24no—
320C42C2×C22⋊D4312yes—
321C42C2×C22⋊D4312yes—
322C23—862no—
323C23—1721no—
324C23—1721no—
325C23—1721no—
326C23—1721no—
327C23—1721no—
328C23—1721no—
329C23C22×C22⋊D4311yescharacteristic
330Q8—28no—
331Q8—44no—
332Q8—44no—
333Q8—84no—
334D4—864no—
335D4—1722no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—22no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—3444no—
345C2×C4—1722no—
346C2×C4—1722no—
347C2×C4—1721no—
348C2×C4—1722no—
349C2×C4—1721no—
350C2×C4—1721no—
351C2×C4#1306329411yescharacteristic
352C2×C4#1306329411yescharacteristic
353C2×C4#1306329412yes—
354C2×C4C2×#1062188414yes—
355C2×C4C2×#1062188412yes—
356C2×C4#1306335612yes—
357C2×C4C22×C22⋊D4312yes—
358C8—1724no—
359C22—21no—
360C22—21no—
361C22—3441no—
362C22—3441no—
363C22—3441no—
364C22—3441no—
365C22—1722no—
366C22—1722no—
367C22—1722no—
368C22C2×#1306329411yescharacteristic
369C22C22×#1062188411yescharacteristic
370C22C2×#1306335611yescharacteristic
371C4—21no—
372C4—21no—
373C4—22no—
374C4—24no—
375C4—44no—
376C4—42no—
377C4—44no—
378C4—3442no—
379C4—3441no—
380C4#1458303814yes—
381C2—21no—
382C2—21no—
383C2—3442no—
384C2C2×#1458303811yescharacteristic
385C2#1914395911yescharacteristic
386C2#1914398711yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3502C2
socleC22×C43C2×#120
prime radicalC22×D172C23
hypercenter#3502D43
hypocenterC43#18220
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3502

Complements

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

NH ≅ G/Ntype
3. #19133603C2semidirect
5. #19133159C2semidirect
6. #19132919C2semidirect
7. C43×#3502C2semidirect
86. C2×Q8×C43SD16semidirect
188. #3502D43semidirect
225. C43#18220semidirect
280. C2×Q8#10621884semidirect

Maximal subgroups

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

subgroupindex
#191445992
#191395002
#191336032
#191335352
#191331592
#191329192
C43×#35022
#1822043