Finite Group Databasebeta

← #24997008

Subgroups — #24997008

Order 11008.

574 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 85 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#19144539C211yesmaximal, characteristic
2#19138882C211yesmaximal, characteristic
3#19134695C211yesmaximal, characteristic
4#19133128C211yesmaximal, characteristic
5#19132925C211yesmaximal, characteristic
6#19132448C211yesmaximal, characteristic
7C43×#2583C211yesmaximal, characteristic
8C2×#13063284C2211yescharacteristic
9#14583237—22no—
10#14583232—21no—
11#14583227—21no—
12#14582939—21no—
13#14582908—21no—
14#14582863C2211yescharacteristic
15#14582863C2211yescharacteristic
16#14582838—21no—
17#14582829—21no—
18#14582780—22no—
19#14582772—21no—
20#14582762—21no—
21#14582762C2211yescharacteristic
22#14582659—22no—
23#14582636—22no—
24#14582625—22no—
25C2×C22⋊Q8×C43C2211yescharacteristic
26C22×C4⋊C4×C43C2211yescharacteristic
27C43×#398—21no—
28C43×#395—21no—
29C43×#389—22no—
30C43×#385—21no—
31C43×#385—21no—
32C4×C22⋊C4×C43C2211yescharacteristic
33C2×#10621877—21no—
34C2×#10621877—21no—
35#13063284—21no—
36#13063284—21no—
37#13063284—21no—
38#13063284—21no—
39C2×C4⋊Dic43D411yescharacteristic
40C2×C4⋊Dic43D411yescharacteristic
41C2×Dic43⋊C4—22no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×C4×Dic43—21no—
45#13063258—22no—
46#13063256—22no—
47#13063249—22no—
48#13063249—22no—
49C22⋊(C43⋊C8)—21no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)D412yes—
53C43⋊#95—22no—
54C43⋊#95—22no—
55C43⋊#95—22no—
56C43⋊#95—21no—
57C43⋊#95D412yes—
58C22×Q8×C43D411yescharacteristic
59C23×C4×C43D411yescharacteristic
60C23×C4×C43D411yescharacteristic
61C23×C4×C43C2311yescharacteristic
62C22⋊Q8×C43—21no—
63C22⋊Q8×C43—21no—
64C22⋊Q8×C43—21no—
65C22⋊Q8×C43—21no—
66C2×C4⋊C4×C43—22no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43—21no—
74C2×C4⋊C4×C43—22no—
75C2×C4⋊C4×C43D411yescharacteristic
76C2×C22⋊C4×C43—21no—
77C2×C22⋊C4×C43—21no—
78C2×C42×C43D412yes—
79#95×C43—22no—
80#95×C43—22no—
81#95×C43—21no—
82C24×C43C2×D411yescharacteristic
83C2×Q8×C43—21no—
84C2×Q8×C43—21no—
85C2×Q8×C43—42no—
86C22×C4×C43—22no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—21no—
94C22×C4×C43—21no—
95C22×C4×C43—42no—
96C22×C4×C43—42no—
97C22×C4×C43—42no—
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43#4111yescharacteristic
104C22×Dic43—22no—
105C22×Dic43—21no—
106C22×Dic43—21no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—44no—
110C4⋊C4×C43—41no—
111C4⋊C4×C43—41no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43—41no—
114C4⋊C4×C43—41no—
115C4⋊C4×C43—41no—
116C4⋊C4×C43—82no—
117C22⋊C4×C43—24no—
118C22⋊C4×C43—41no—
119C22⋊C4×C43—41no—
120C42×C43—42no—
121C22⋊Dic43—42no—
122C22⋊Dic43—41no—
123C22⋊Dic43—41no—
124C4⋊Dic43—21no—
125C4⋊Dic43—21no—
126C4⋊Dic43—21no—
127C4⋊Dic43—21no—
128Dic43⋊C4—44no—
129C4×Dic43—41no—
130C4×Dic43—41no—
131#10621877—42no—
132#10621877—42no—
133C2×C43⋊C8—22no—
134C2×C43⋊C8—41no—
135C23×C43—22no—
136C23×C43—22no—
137C23×C43—41no—
138C23×C43#12011yescharacteristic
139C23×C43#12011yescharacteristic
140C23×C43#12111yescharacteristic
141Q8×C43—42no—
142Q8×C43—81no—
143C2×C4×C43—22no—
144C2×C4×C43—22no—
145C2×C4×C43—22no—
146C2×C4×C43—24no—
147C2×C4×C43—22no—
148C2×C4×C43—22no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—42no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—42no—
159C2×C4×C43—42no—
160C2×C4×C43—42no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—42no—
165C2×C4×C43—42no—
166C2×C4×C43—81no—
167C2×C4×C43#12011yescharacteristic
168C2×C4×C43#12111yescharacteristic
169C2×C4×C43#12111yescharacteristic
170C2×C4×C43#12711yescharacteristic
171C2×Dic43—42no—
172C2×Dic43—42no—
173C2×Dic43—42no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43—42no—
177C2×Dic43—42no—
178C43⋊C8—42no—
179C43⋊C8—81no—
180#9945—431nomaximal, Sylow
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—44no—
189C22×C43#39211yescharacteristic
190C22×C43#45612yes—
191C22×C43#45812yes—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—21no—
195C4×C43—21no—
196C4×C43—44no—
197C4×C43—42no—
198C4×C43—81no—
199C4×C43—81no—
200C4×C43—81no—
201Dic43—82no—
202Dic43—81no—
203Dic43—81no—
204#3095—431no—
205#2583D4311yescharacteristic
206#2484—431no—
207#1826—431no—
208#1511—431no—
209#1463—431no—
210#1284—431no—
211C2×C43—22no—
212C2×C43—22no—
213C2×C43—41no—
214C2×C43#200511yescharacteristic
215C2×C43#201011yescharacteristic
216C2×C43#202211yescharacteristic
217C2×C22⋊Q8C2×D4311yescharacteristic
218C2×#117—431no—
219C22×C4⋊C4C2×D4311yescharacteristic
220#485—862no—
221#484—861no—
222#483—861no—
223#428—861no—
224#419—861no—
225#407—431no—
226#407—431no—
227#400—861no—
228#398—21no—
229#398—861no—
230#395—21no—
231#389—22no—
232#387—862no—
233#385—21no—
234#385—21no—
235#385—861no—
236#381—431no—
237#381—861no—
238C4×C22⋊C4C2×D4311yescharacteristic
239#339—862no—
240#328—862no—
241#324—862no—
242C43#994511yescharacteristic, complemented, Sylow
243C22×Q8C22⋊D4311yescharacteristic
244C23×C4C22⋊D4311yescharacteristic
245C23×C4C22⋊D4311yescharacteristic
246C23×C4C22×D4311yescharacteristic
247C2×M16—861no—
248C2×M16—861no—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253#117—861no—
254#117—861no—
255#117—861no—
256#117—861no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—431no—
267C2×C4⋊C4—431no—
268C2×C4⋊C4—862no—
269C2×C4⋊C4C22⋊D4311yescharacteristic
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—861no—
273C2×C22⋊C4—861no—
274C2×C42—861no—
275C2×C42C22⋊D4312yes—
276#107—862no—
277#106—862no—
278#103—862no—
279#103—862no—
280C22⋊C8—432no—
281C22⋊C8—861no—
282C22⋊C8—861no—
283C22⋊C8—861no—
284#95—22no—
285#95—22no—
286#95—21no—
287#95—432no—
288#95—862no—
289#95—862no—
290#95—862no—
291#95—861no—
292C24C2×C22⋊D4311yescharacteristic
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—42no—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—42no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—862no—
309C22×C4—861no—
310C22×C4—861no—
311C22×C4D4×D4311yescharacteristic
312C22×C4D4×D4311yescharacteristic
313C22×C4D4×D4311yescharacteristic
314C22×C4#1062190011yescharacteristic
315C22×C4C2×C22⋊D4311yescharacteristic
316C22×C4C2×C22⋊D4311yescharacteristic
317M16—1722no—
318M16—1722no—
319C2×C8—862no—
320C2×C8—1721no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—44no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—82no—
331C4⋊C4—861no—
332C4⋊C4—861no—
333C4⋊C4—861no—
334C4⋊C4—861no—
335C4⋊C4—1724no—
336C22⋊C4—24no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—1722no—
340C22⋊C4—1721no—
341C22⋊C4—1721no—
342C42—42no—
343C42—1721no—
344C42—1721no—
345C23—22no—
346C23—22no—
347C23—41no—
348C23#1306329311yescharacteristic
349C23#1306329411yescharacteristic
350C23#1306329711yescharacteristic
351Q8—42no—
352Q8—81no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—24no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—81no—
377C2×C4—1722no—
378C2×C4—1722no—
379C2×C4—1722no—
380C2×C4—1721no—
381C2×C4—1721no—
382C2×C4—1722no—
383C2×C4—1722no—
384C2×C4#1306329311yescharacteristic
385C2×C4#1306329611yescharacteristic
386C2×C4#1306329711yescharacteristic
387C2×C4#1306332111yescharacteristic
388C8—3441no—
389C8—1722no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—44no—
398C22#1458280711yescharacteristic
399C22#1458308112yes—
400C22#1458308912yes—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—44no—
406C4—42no—
407C4—81no—
408C4—81no—
409C4—81no—
410C4—3442no—
411C4—3441no—
412C4—3441no—
413C2—22no—
414C2—22no—
415C2—41no—
416C2#1913563111yescharacteristic
417C2#1913566011yescharacteristic
418C2#1913572411yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#2583C2
socleC22×C43#392
prime radicalC24×C43C2×D4
hypercenter#2583D43
hypocenterC43#9945
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2583

Complements

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

NH ≅ G/Ntype
242. C43#9945semidirect

Maximal subgroups

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

subgroupindex
#191445392
#191388822
#191346952
#191331282
#191329252
#191324482
C43×#25832
#994543