Finite Group Databasebeta

← #24997508

Subgroups — #24997508

Order 11008.

518 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 81 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#19145144C211yesmaximal, characteristic, complemented
2#19144694C211yesmaximal, characteristic
3#19133222C211yesmaximal, characteristic, complemented
4#19133145C211yesmaximal, characteristic, complemented
5#19133038C211yesmaximal, characteristic
6#19132459C211yesmaximal, characteristic, complemented
7C43×#2633C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583309—21no—
10#14583309—21no—
11#14583298—22no—
12#14583234—21no—
13#14583179—21no—
14#14583104—21no—
15#14583050—21no—
16#14582999—22no—
17#14582956C2211yescharacteristic
18#14582956C2211yescharacteristic
19#14582939—21no—
20#14582939—21no—
21C4×#10621877C2211yescharacteristic
22#14582641—22no—
23#14582635—22no—
24D4⋊(C43⋊C8)—22no—
25C2×#125×C43C2211yescharacteristic
26C2×C4×D4×C43C2211yescharacteristic
27C43×#399—21no—
28C43×#398—21no—
29C43×#397—21no—
30C43×#394—21no—
31C43×#385—22no—
32C43×#383C2211yescharacteristic
33C2×#10621883—22no—
34C2×#10621877—21no—
35#13063325D411yescharacteristic
36#13063325D411yescharacteristic
37#13063317—21no—
38#13063304—21no—
39#13063304—21no—
40C4×Dic86—21no—
41C4×Dic86—21no—
42#13063284—21no—
43#13063258—22no—
44#13063258—22no—
45#13063258—22no—
46#13063256—22no—
47#13063256—22no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)—21no—
50#13063248—22no—
51#13063246—22no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54#13063236—21no—
55#13063236—21no—
56#13063236D412yes—
57C4×C43⋊C8D412yes—
58C22×D4×C43D411yescharacteristic
59C23×C4×C43—21no—
60#125×C43—21no—
61#125×C43—21no—
62#125×C43—21no—
63#125×C43—21no—
64C4×D4×C43—21no—
65C4×D4×C43—21no—
66C4×D4×C43—21no—
67C4×D4×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43—22no—
71C2×C4⋊C4×C43D411yescharacteristic
72C2×C4⋊C4×C43D411yescharacteristic
73C2×C4⋊C4×C43D411yescharacteristic
74C2×C22⋊C4×C43—22no—
75C2×C22⋊C4×C43—21no—
76C2×C22⋊C4×C43—22no—
77C2×C42×C43C2311yescharacteristic
78#95×C43—22no—
79#95×C43—21no—
80#95×C43—21no—
81#95×C43D412yes—
82C24×C43—21no—
83C2×D4×C43—21no—
84C2×D4×C43—21no—
85C2×D4×C43—42no—
86C22×C4×C43—22no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43—82no—
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C2×Dic86—21no—
97C2×Dic86—21no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—21no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—41no—
108C4⋊C4×C43—82no—
109C22⋊C4×C43—44no—
110C22⋊C4×C43—41no—
111C22⋊C4×C43—41no—
112C22⋊C4×C43—82no—
113C42×C43C2×D411yescharacteristic
114C42×C43C2×D411yescharacteristic
115C42×C43C2×D411yescharacteristic
116C42×C43#4111yescharacteristic
117C22⋊Dic43—41no—
118#10621883—44no—
119C4⋊Dic43—21no—
120C4⋊Dic43—21no—
121C4⋊Dic43—21no—
122C4⋊Dic43—21no—
123Dic43⋊C4—41no—
124Dic43⋊C4—41no—
125C4×Dic43—41no—
126#10621877—24no—
127C2×C43⋊C8—22no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—41no—
130C23×C43—22no—
131C23×C43—42no—
132C23×C43—41no—
133C23×C43—41no—
134C23×C43—42no—
135C23×C43#12011yescharacteristic
136D4×C43—22no—
137D4×C43—22no—
138D4×C43—41no—
139D4×C43—41no—
140C2×C4×C43—22no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43—41no—
146C2×C4×C43—42no—
147C2×C4×C43—41no—
148C2×C4×C43—42no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—42no—
153C2×C4×C43—82no—
154C2×C4×C43—82no—
155C2×C4×C43#12011yescharacteristic
156C2×C4×C43#12011yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43#12111yescharacteristic
159C2×C4×C43#12111yescharacteristic
160C2×C4×C43#12711yescharacteristic
161C2×Dic43—41no—
162C2×Dic43—41no—
163Dic86—42no—
164Dic86—81no—
165C43⋊C8—24no—
166C43⋊C8—42no—
167C43⋊C8—81no—
168#10023—431nomaximal, Sylow
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—44no—
172C22×C43—42no—
173C22×C43—82no—
174C22×C43—81no—
175C22×C43—81no—
176C22×C43#39211yescharacteristic
177C22×C43#45612yes—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—82no—
185C4×C43—81no—
186C4×C43—81no—
187C4×C43—81no—
188Dic43—81no—
189Dic43—81no—
190#3166—431no—
191#3110—431no—
192#2633D4311yescharacteristic
193#1534—431no—
194#1515—431no—
195#1490—431no—
196#1288—431no—
197C2×C43—22no—
198C2×C43—82no—
199C2×C43#200511yescharacteristic
200C2×C43#200811yescharacteristic
201C2×C43#201011yescharacteristic
202#533—431no—
203C2×#125C2×D4311yescharacteristic
204C2×C4×D4C2×D4311yescharacteristic
205#501—861no—
206#501—861no—
207#499—862no—
208#484—861no—
209#474—861no—
210#461—861no—
211#450—861no—
212#440—862no—
213#432—431no—
214#432—431no—
215#428—861no—
216#428—861no—
217C4×M16—431no—
218#399—21no—
219#398—21no—
220#397—21no—
221#394—21no—
222#385—22no—
223#383C2×D4311yescharacteristic
224#330—862no—
225#328—862no—
226D4⋊C8—862no—
227C43#1002311yescharacteristic, complemented, Sylow
228C22×D4C22⋊D4311yescharacteristic
229C23×C4—21no—
230C2×SD16—862no—
231C2×M16—861no—
232C4⋊Q8—431no—
233C4⋊Q8—431no—
234#125—21no—
235#125—21no—
236#125—21no—
237#125—21no—
238#125—861no—
239C22⋊Q8—861no—
240C22⋊Q8—861no—
241C4×Q8—861no—
242C4×Q8—861no—
243C4×D4—21no—
244C4×D4—21no—
245C4×D4—21no—
246C4×D4—21no—
247#117—861no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4C22⋊D4311yescharacteristic
252C2×C4⋊C4C22⋊D4311yescharacteristic
253C2×C4⋊C4C22⋊D4311yescharacteristic
254C2×C22⋊C4—22no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—22no—
257C2×C42C22×D4311yescharacteristic
258#107—862no—
259#107—862no—
260#107—862no—
261#106—862no—
262#106—862no—
263C4⋊C8—861no—
264C4⋊C8—861no—
265#103—862no—
266#102—862no—
267C22⋊C8—861no—
268C22⋊C8—861no—
269#97—432no—
270#97—861no—
271#97—861no—
272C4×C8—432no—
273#95—22no—
274#95—21no—
275#95—21no—
276#95C22⋊D4312yes—
277C24—21no—
278C2×Q8—861no—
279C2×Q8—861no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—42no—
283C22×C4—22no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—82no—
290C22×C4C2×C22⋊D4311yescharacteristic
291C22×C4C2×C22⋊D4311yescharacteristic
292C22×C4C2×C22⋊D4311yescharacteristic
293SD16—1724no—
294M16—864no—
295C2×C8—862no—
296C2×C8—862no—
297C2×C8—1721no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—82no—
309C4⋊C4—861no—
310C4⋊C4—861no—
311C4⋊C4—861no—
312C4⋊C4—861no—
313C4⋊C4—1721no—
314C4⋊C4—1721no—
315C22⋊C4—44no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—82no—
319C22⋊C4—1721no—
320C42—1721no—
321C42D4×D4311yescharacteristic
322C42D4×D4311yescharacteristic
323C42D4×D4311yescharacteristic
324C42#1062190011yescharacteristic
325C23—22no—
326C23—42no—
327C23—41no—
328C23—41no—
329C23—42no—
330C23#1306329411yescharacteristic
331Q8—3441no—
332Q8—1722no—
333D4—22no—
334D4—22no—
335D4—41no—
336D4—41no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—82no—
351C2×C4—82no—
352C2×C4—1721no—
353C2×C4—1721no—
354C2×C4#1306329311yescharacteristic
355C2×C4#1306329311yescharacteristic
356C2×C4#1306329611yescharacteristic
357C2×C4#1306329711yescharacteristic
358C2×C4#1306329711yescharacteristic
359C2×C4#1306332111yescharacteristic
360C8—864no—
361C8—3441no—
362C8—1722no—
363C22—21no—
364C22—21no—
365C22—44no—
366C22—42no—
367C22—82no—
368C22—81no—
369C22—81no—
370C22#1458280711yescharacteristic
371C22#1458308212yes—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—82no—
379C4—81no—
380C4—81no—
381C4—81no—
382C4—3441no—
383C4—3441no—
384C2—22no—
385C2—82no—
386C2#1913562911yescharacteristic
387C2#1913564811yescharacteristic
388C2#1913566011yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2633C2
socleC22×C43#392
prime radicalC22×D4×C43D4
hypercenter#2633D43
hypocenterC43#10023
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2633

Complements

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

NH ≅ G/Ntype
1. #19145144C2semidirect
3. #19133222C2semidirect
4. #19133145C2semidirect
6. #19132459C2semidirect
227. C43#10023semidirect

Maximal subgroups

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

subgroupindex
#191451442
#191446942
#191332222
#191331452
#191330382
#191324592
C43×#26332
#1002343