Finite Group Databasebeta

← #24997049

Subgroups — #24997049

Order 11008.

610 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 105 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#19145352C211yesmaximal, characteristic
2#19139069C211yesmaximal, characteristic, complemented
3#19135432C211yesmaximal, characteristic
4#19134685C211yesmaximal, characteristic, complemented
5#19133168C211yesmaximal, characteristic, complemented
6#19132441C211yesmaximal, characteristic, complemented
7C2×C43×#481C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9#14583229—21no—
10#14583215—21no—
11#14583126—22no—
12#14583050—21no—
13#14583037—21no—
14C2×#13063240—22no—
15C2×C22⋊(C43⋊C8)C2211yescharacteristic
16#14582830—22no—
17#14582804—21no—
18#14582772—22no—
19#14582768—21no—
20#14582759C2211yescharacteristic
21C4×C22⋊Dic43C2211yescharacteristic
22#14582661—22no—
23#14582637—22no—
24C2×#121×C43C2211yescharacteristic
25C22×C4⋊C4×C43C2211yescharacteristic
26C43×#481—22no—
27C43×#481—22no—
28C2×#106×C43—21no—
29C2×#102×C43—21no—
30C2×C22⋊C8×C43C2211yescharacteristic
31C22×Dic86D411yescharacteristic
32C2×#10621883—22no—
33C22×C43⋊C8D412yes—
34#13063304—21no—
35#13063304—21no—
36#13063304—21no—
37#13063304—21no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43D411yescharacteristic
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—24no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43D412yes—
45C2×C4×Dic43—21no—
46#13063256—22no—
47#13063248—22no—
48#13063246—22no—
49#13063240—44no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C43⋊#95—24no—
53C43⋊#95—21no—
54C43⋊#95—21no—
55C22×D4×C43—21no—
56C22×D4×C43D411yescharacteristic
57C23×C4×C43—21no—
58C23×C4×C43C2311yescharacteristic
59C22×C8×C43—21no—
60#121×C43—21no—
61#121×C43—21no—
62#121×C43—21no—
63#121×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43D412yes—
70C2×C4⋊C4×C43D411yescharacteristic
71C2×C22⋊C4×C43—21no—
72#106×C43—24no—
73#102×C43—24no—
74C22⋊C8×C43—21no—
75C22⋊C8×C43D412yes—
76C24×C43—21no—
77C24×C43C2×D411yescharacteristic
78C2×D4×C43—21no—
79C2×D4×C43—21no—
80C2×D4×C43—41no—
81C2×D4×C43—41no—
82C2×D4×C43—42no—
83C2×D4×C43—42no—
84C2×D4×C43—42no—
85C22×C4×C43—22no—
86C22×C4×C43—21no—
87C22×C4×C43—42no—
88C22×C4×C43—41no—
89C22×C4×C43—41no—
90C22×C4×C43—82no—
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43#4111yescharacteristic
97C22×Dic43—22no—
98C22×Dic43—21no—
99C22×Dic43—21no—
100C22×Dic43—41no—
101C2×Dic86—21no—
102C2×Dic86—21no—
103C2×Dic86—42no—
104C2×C8×C43—22no—
105C2×C8×C43—42no—
106C4⋊C4×C43—22no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—22no—
110C4⋊C4×C43—41no—
111C4⋊C4×C43—41no—
112C22⋊C4×C43—41no—
113C22⋊C4×C43—41no—
114C22⋊Dic43—22no—
115C22⋊Dic43—41no—
116C22⋊Dic43—41no—
117C22⋊Dic43—42no—
118C22⋊Dic43SD1614yescomplemented
119#10621883—82no—
120C4⋊Dic43—21no—
121C4⋊Dic43—21no—
122C4⋊Dic43—42no—
123Dic43⋊C4—41no—
124Dic43⋊C4—41no—
125Dic43⋊C4—84no—
126C4×Dic43—42no—
127C2×C43⋊C8—22no—
128C2×C43⋊C8—42no—
129C23×C43—41no—
130C23×C43—41no—
131C23×C43—41no—
132C23×C43—42no—
133C23×C43—81no—
134C23×C43—81no—
135C23×C43#12011yescharacteristic
136C23×C43#12111yescharacteristic
137C23×C43#12711yescharacteristic
138C23×C43C2×SD1612yes—
139C23×C43#13712yes—
140D4×C43—42no—
141D4×C43—42no—
142D4×C43—82no—
143D4×C43—81no—
144D4×C43—81no—
145C2×C4×C43—22no—
146C2×C4×C43—22no—
147C2×C4×C43—22no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—44no—
152C2×C4×C43—41no—
153C2×C4×C43—42no—
154C2×C4×C43—42no—
155C2×C4×C43—82no—
156C2×C4×C43—82no—
157C2×C4×C43#12011yescharacteristic
158C2×C4×C43#12011yescharacteristic
159C2×C4×C43#12111yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C2×Dic43—24no—
162C2×Dic43—42no—
163C2×Dic43—42no—
164C2×Dic43—42no—
165C2×Dic43—42no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—81no—
169C2×Dic43—81no—
170C2×Dic43—81no—
171Dic86—42no—
172Dic86—81no—
173C8×C43—42no—
174C43⋊C8—42no—
175#9951—431nomaximal, Sylow
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—21no—
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—42no—
183C22×C43—42no—
184C22×C43—81no—
185C22×C43—81no—
186C22×C43—81no—
187C22×C43—162no—
188C22×C43#39211yescharacteristic
189C22×C43#44812yes—
190C22×C43#46112yes—
191C22×C43#49211yescharacteristic
192C22×C43#49711yescharacteristic
193C4×C43—21no—
194C4×C43—21no—
195C4×C43—21no—
196C4×C43—82no—
197C4×C43—81no—
198C4×C43#45812yes—
199Dic43—44no—
200Dic43—81no—
201Dic43—81no—
202Dic43—161no—
203#3187—431no—
204C2×#481D4311yescharacteristic
205#2502—431no—
206#1964—431no—
207#1824—431no—
208#1520—431no—
209#1282—431no—
210C2×C43—22no—
211C2×C43—21no—
212C2×C43—22no—
213C2×C43—21no—
214C2×C43—161no—
215C2×C43#200811yescharacteristic
216C2×C43#201311yescharacteristic
217C2×C43#202211yescharacteristic
218C2×C22⋊Q8—431no—
219C2×#121C2×D4311yescharacteristic
220C22×C4⋊C4C2×D4311yescharacteristic
221#483—861no—
222#481—22no—
223#481—22no—
224#481—861no—
225#465—862no—
226#450—861no—
227#448—861no—
228C2×#106—21no—
229C2×#102—21no—
230C2×#99—862no—
231C2×C22⋊C8—431no—
232C2×C22⋊C8C2×D4311yescharacteristic
233#398—862no—
234#391—861no—
235#385—862no—
236#384—861no—
237#380—431no—
238C4×C22⋊C4—431no—
239#340—862no—
240#328—862no—
241C43#995111yescharacteristic, complemented, Sylow
242C22×Q8—431no—
243C22×D4—21no—
244C22×D4C22⋊D4311yescharacteristic
245C23×C4—21no—
246C23×C4C22×D4311yescharacteristic
247C2×SD16—862no—
248C22×C8—21no—
249C22×C8—432no—
250C22⋊Q8—861no—
251C22⋊Q8—861no—
252C22⋊Q8—861no—
253C22⋊Q8—861no—
254#121—21no—
255#121—21no—
256#121—21no—
257#121—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—431no—
264C2×C4⋊C4—864no—
265C2×C4⋊C4—861no—
266C2×C4⋊C4—861no—
267C2×C4⋊C4C22⋊D4312yes—
268C2×C4⋊C4C22⋊D4311yescharacteristic
269C2×C22⋊C4—21no—
270C2×C22⋊C4—432no—
271C2×C22⋊C4—861no—
272C2×C22⋊C4—861no—
273C2×C42—861no—
274#106—24no—
275#106—862no—
276#103—862no—
277#102—24no—
278#102—862no—
279#99—1724no—
280C22⋊C8—21no—
281C22⋊C8—861no—
282C22⋊C8—861no—
283C22⋊C8C22⋊D4312yes—
284#95—864no—
285#95—861no—
286#95—861no—
287C24—21no—
288C24D4×D4311yescharacteristic
289C2×Q8—861no—
290C2×Q8—861no—
291C2×Q8—1722no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—42no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—42no—
298C2×D4—42no—
299C22×C4—22no—
300C22×C4—21no—
301C22×C4—42no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—82no—
305C22×C4—862no—
306C22×C4—861no—
307C22×C4—861no—
308C22×C4—1721no—
309C22×C4D4×D4311yescharacteristic
310C22×C4D4×D4311yescharacteristic
311C22×C4#1062190011yescharacteristic
312C22×C4C2×C22⋊D4311yescharacteristic
313C22×C4C2×C22⋊D4311yescharacteristic
314C22×C4C2×C22⋊D4311yescharacteristic
315SD16—3442no—
316C2×C8—22no—
317C2×C8—42no—
318C2×C8—862no—
319C2×C8—1722no—
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—21no—
323C4⋊C4—22no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—861no—
327C4⋊C4—861no—
328C4⋊C4—3444no—
329C4⋊C4—1722no—
330C4⋊C4—1721no—
331C4⋊C4—1721no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—434no—
335C22⋊C4—862no—
336C22⋊C4—1722no—
337C22⋊C4—1721no—
338C22⋊C4—1721no—
339C42—1722no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—42no—
344C23—81no—
345C23—81no—
346C23#1306329311yescharacteristic
347C23#1306329711yescharacteristic
348C23#1306332111yescharacteristic
349C23SD16×D4312yes—
350C23#1306335412yes—
351Q8—3441no—
352Q8—1722no—
353D4—42no—
354D4—42no—
355D4—81no—
356D4—81no—
357D4—82no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—44no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—864no—
371C2×C4—3441no—
372C2×C4—3441no—
373C2×C4—3441no—
374C2×C4—1722no—
375C2×C4—1722no—
376C2×C4—1721no—
377C2×C4—1721no—
378C2×C4—1722no—
379C2×C4—1722no—
380C2×C4#1306329311yescharacteristic
381C2×C4#1306329411yescharacteristic
382C2×C4#1306329611yescharacteristic
383C2×C4#1306329711yescharacteristic
384C8—42no—
385C8—1722no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—42no—
393C22—42no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22—162no—
398C22#1458280711yescharacteristic
399C22#1458303612yes—
400C22#1458310212yes—
401C22#1458327011yescharacteristic
402C22#1458329011yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—82no—
407C4—81no—
408C4—3441no—
409C4—3441no—
410C4—1724no—
411C4—6881no—
412C4#1458308812yes—
413C2—22no—
414C2—21no—
415C2—22no—
416C2—21no—
417C2—161no—
418C2#1913564611yescharacteristic
419C2#1913567611yescharacteristic
420C2#1913572311yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC2×C43×#481C2
socleC22×C43#392
prime radicalC2×#121×C43C22
hypercenterC2×#481D43
hypocenterC43#9951
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
2. #19139069C2semidirect
4. #19134685C2semidirect
5. #19133168C2semidirect
6. #19132441C2semidirect
118. C22⋊Dic43SD16semidirect
241. C43#9951semidirect

Maximal subgroups

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

subgroupindex
#191453522
#191390692
#191354322
#191346852
#191331682
#191324412
C2×C43×#4812
#995143