Finite Group Databasebeta

← #24997122

Subgroups — #24997122

Order 11008.

552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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#19145367C211yesmaximal, characteristic
2C2×#14583229C211yesmaximal, characteristic
3#19135580C211yesmaximal, characteristic
4#19134681C211yesmaximal, characteristic
5#19133167C211yesmaximal, characteristic
6#19132443C211yesmaximal, characteristic
7C43×#2503C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9#14583234—21no—
10#14583232—21no—
11#14583229—22no—
12#14583229—22no—
13#14583138—22no—
14#14583055—21no—
15#14583054—21no—
16C2×#13063256—21no—
17C2×#13063248—21no—
18C2×C22⋊(C43⋊C8)C2211yescharacteristic
19C2×C22⋊(C43⋊C8)C2211yescharacteristic
20#14582759C2211yescharacteristic
21#14582665—22no—
22#14582661—22no—
23#14582636—22no—
24C2×C22⋊Q8×C43C2211yescharacteristic
25C22×C4⋊C4×C43C2211yescharacteristic
26C43×#400—22no—
27C43×#391—21no—
28C43×#382—21no—
29C43×#381—22no—
30C4×C22⋊C4×C43C2211yescharacteristic
31C22×Dic86D411yescharacteristic
32C2×#10621885—22no—
33C22×C43⋊C8—21no—
34C22×C43⋊C8D412yes—
35#13063304—21no—
36#13063304—21no—
37#13063304—21no—
38#13063304—21no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43D411yescharacteristic
41C2×Dic43⋊C4—21no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44#13063258—22no—
45#13063256—24no—
46#13063249—22no—
47#13063248—22no—
48#13063248—24no—
49C22⋊(C43⋊C8)—21no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)D412yes—
53C43⋊#95—21no—
54C22×Q8×C43D411yescharacteristic
55C23×C4×C43—21no—
56C23×C4×C43C2311yescharacteristic
57C22⋊Q8×C43—21no—
58C22⋊Q8×C43—21no—
59C22⋊Q8×C43—21no—
60C22⋊Q8×C43—21no—
61C2×C4⋊C4×C43—21no—
62C2×C4⋊C4×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43D412yes—
68C2×C4⋊C4×C43D411yescharacteristic
69C2×C22⋊C4×C43—21no—
70C2×C22⋊C4×C43D412yes—
71C2×C42×C43—21no—
72#95×C43—24no—
73#95×C43—24no—
74#95×C43—21no—
75C24×C43C2×D411yescharacteristic
76C2×Q8×C43—21no—
77C2×Q8×C43—21no—
78C2×Q8×C43—42no—
79C22×C4×C43—22no—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—22no—
83C22×C4×C43—42no—
84C22×C4×C43—41no—
85C22×C4×C43—41no—
86C22×C4×C43—42no—
87C22×C4×C43—42no—
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43#4111yescharacteristic
94C22×Dic43—21no—
95C22×Dic43—21no—
96C22×Dic43—41no—
97C2×Dic86—21no—
98C2×Dic86—21no—
99C2×Dic86—42no—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—41no—
108C22⋊C4×C43—22no—
109C22⋊C4×C43—22no—
110C22⋊C4×C43—41no—
111C22⋊C4×C43—41no—
112C42×C43—42no—
113C22⋊Dic43—41no—
114C22⋊Dic43—41no—
115C22⋊Dic43—42no—
116#10621885—82no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119C4⋊Dic43—42no—
120Dic43⋊C4—41no—
121Dic43⋊C4—41no—
122C2×C43⋊C8—22no—
123C2×C43⋊C8—22no—
124C2×C43⋊C8—42no—
125C2×C43⋊C8—42no—
126C23×C43—41no—
127C23×C43—41no—
128C23×C43#12011yescharacteristic
129C23×C43#12111yescharacteristic
130C23×C43#12711yescharacteristic
131C23×C43#13512yes—
132C23×C43#13712yes—
133Q8×C43—42no—
134Q8×C43—81no—
135C2×C4×C43—22no—
136C2×C4×C43—22no—
137C2×C4×C43—22no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—42no—
148C2×C4×C43—42no—
149C2×C4×C43—44no—
150C2×C4×C43—82no—
151C2×C4×C43—81no—
152C2×C4×C43—81no—
153C2×C4×C43#12011yescharacteristic
154C2×C4×C43#12011yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—81no—
160C2×Dic43—81no—
161C2×Dic43—81no—
162C2×Dic43—81no—
163C2×Dic43—81no—
164Dic86—42no—
165Dic86—42no—
166C43⋊C8—42no—
167C43⋊C8—42no—
168#9961—431nomaximal, Sylow
169C22×C43—21no—
170C22×C43—21no—
171C22×C43—21no—
172C22×C43—21no—
173C22×C43—21no—
174C22×C43—21no—
175C22×C43—42no—
176C22×C43—42no—
177C22×C43#39211yescharacteristic
178C22×C43#45212yes—
179C22×C43#46412yes—
180C22×C43#49511yescharacteristic
181C22×C43#49711yescharacteristic
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—82no—
186C4×C43—81no—
187C4×C43—82no—
188C4×C43—81no—
189C4×C43#45812yes—
190Dic43—81no—
191Dic43—81no—
192Dic43—161no—
193#3189—431no—
194C2×#483—431no—
195#2503D4311yescharacteristic
196#1996—431no—
197#1823—431no—
198#1520—431no—
199#1282—431no—
200C2×C43—21no—
201C2×C43—22no—
202C2×C43—22no—
203C2×C43—21no—
204C2×C43#200911yescharacteristic
205C2×C43#201511yescharacteristic
206C2×C43#202211yescharacteristic
207C2×C22⋊Q8—431no—
208C2×C22⋊Q8C2×D4311yescharacteristic
209C22×C4⋊C4C2×D4311yescharacteristic
210#484—861no—
211#484—861no—
212#483—862no—
213#483—862no—
214#467—862no—
215#451—861no—
216#451—861no—
217C2×#106—861no—
218C2×#103—861no—
219C2×C22⋊C8—431no—
220C2×C22⋊C8—431no—
221#400—22no—
222#391—21no—
223#382—21no—
224#381—22no—
225#380—431no—
226C4×C22⋊C4C2×D4311yescharacteristic
227#342—862no—
228#340—862no—
229#328—862no—
230C43#996111yescharacteristic, complemented, Sylow
231C22×Q8—431no—
232C22×Q8C22⋊D4311yescharacteristic
233C23×C4—21no—
234C23×C4C22×D4311yescharacteristic
235C2×Q16—862no—
236C22×C8—432no—
237C22×C8—861no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C22⋊Q8—21no—
241C22⋊Q8—21no—
242C22⋊Q8—861no—
243C22⋊Q8—861no—
244C22⋊Q8—861no—
245C22⋊Q8—861no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—431no—
253C2×C4⋊C4—861no—
254C2×C4⋊C4—861no—
255C2×C4⋊C4C22⋊D4312yes—
256C2×C4⋊C4C22⋊D4311yescharacteristic
257C2×C22⋊C4—21no—
258C2×C22⋊C4—861no—
259C2×C22⋊C4—861no—
260C2×C22⋊C4C22⋊D4312yes—
261C2×C42—21no—
262#107—862no—
263#106—864no—
264#103—864no—
265#103—862no—
266#103—862no—
267C22⋊C8—432no—
268C22⋊C8—861no—
269C22⋊C8—861no—
270C22⋊C8—861no—
271#95—24no—
272#95—24no—
273#95—21no—
274#95—861no—
275C24C2×C22⋊D4311yescharacteristic
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8—42no—
279C2×Q8—861no—
280C2×Q8—861no—
281C2×Q8—1722no—
282C22×C4—22no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—22no—
286C22×C4—42no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—861no—
292C22×C4—861no—
293C22×C4—1721no—
294C22×C4D4×D4311yescharacteristic
295C22×C4D4×D4311yescharacteristic
296C22×C4D4×D4311yescharacteristic
297C22×C4#1062190011yescharacteristic
298C22×C4C2×C22⋊D4311yescharacteristic
299C22×C4C2×C22⋊D4311yescharacteristic
300Q16—3442no—
301C2×C8—862no—
302C2×C8—862no—
303C2×C8—1722no—
304C2×C8—1722no—
305C4⋊C4—22no—
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—861no—
314C4⋊C4—861no—
315C4⋊C4—1722no—
316C4⋊C4—1721no—
317C4⋊C4—1721no—
318C22⋊C4—22no—
319C22⋊C4—22no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—1722no—
323C22⋊C4—1721no—
324C22⋊C4—1721no—
325C42—42no—
326C23—41no—
327C23—41no—
328C23#1306329411yescharacteristic
329C23#1306329611yescharacteristic
330C23#1306332111yescharacteristic
331C23#1306334512yes—
332C23#1306335512yes—
333Q8—42no—
334Q8—81no—
335Q8—1722no—
336Q8—1722no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—44no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—82no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—3441no—
356C2×C4—3441no—
357C2×C4—3441no—
358C2×C4—3441no—
359C2×C4—3441no—
360C2×C4—1721no—
361C2×C4—1721no—
362C2×C4#1306329311yescharacteristic
363C2×C4#1306329311yescharacteristic
364C2×C4#1306329711yescharacteristic
365C2×C4#1306329711yescharacteristic
366C8—1722no—
367C8—1722no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—42no—
375C22—42no—
376C22#1458280711yescharacteristic
377C22#1458306112yes—
378C22#1458311812yes—
379C22#1458328111yescharacteristic
380C22#1458329411yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—82no—
385C4—81no—
386C4—82no—
387C4—81no—
388C4—3441no—
389C4—3441no—
390C4—6881no—
391C4#1458308812yes—
392C2—22no—
393C2—21no—
394C2—22no—
395C2—21no—
396C2#1913565511yescharacteristic
397C2#1913568911yescharacteristic
398C2#1913572311yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#2503C2
socleC22×C43#392
prime radicalC24×C43C2×D4
hypercenter#2503D43
hypocenterC43#9961
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2503

Complements

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

NH ≅ G/Ntype
230. C43#9961semidirect

Maximal subgroups

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

subgroupindex
#191453672
C2×#145832292
#191355802
#191346812
#191331672
#191324432
C43×#25032
#996143