Finite Group Databasebeta

← #24997121

Subgroups — #24997121

Order 11008.

552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 99 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×#14583227C211yesmaximal, characteristic
3#19139080C211yesmaximal, characteristic
4#19134679C211yesmaximal, characteristic
5#19133166C211yesmaximal, characteristic
6#19132443C211yesmaximal, characteristic
7C43×#1996C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9C22×C4⋊Dic43C2211yescharacteristic
10#14583234—21no—
11#14583232—21no—
12#14583227—22no—
13#14583227—22no—
14#14583138—22no—
15#14583055—21no—
16#14583054—21no—
17C2×#13063256—21no—
18C2×#13063249—21no—
19C2×C22⋊(C43⋊C8)C2211yescharacteristic
20C2×C22⋊(C43⋊C8)C2211yescharacteristic
21#14582839—22no—
22#14582805—21no—
23#14582765—21no—
24#14582760—22no—
25#14582661—22no—
26#14582635—22no—
27C2×C22⋊Q8×C43C2211yescharacteristic
28C43×#380C2211yescharacteristic
29C4×C22⋊C4×C43C2211yescharacteristic
30C43×#342—22no—
31C22×Dic86D411yescharacteristic
32C23×Dic43—21no—
33C2×#10621885—22no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8D412yes—
36#13063304—21no—
37#13063304—21no—
38#13063304—21no—
39#13063304—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43D412yes—
46C2×C4⋊Dic43D411yescharacteristic
47C2×Dic43⋊C4—21no—
48C2×C22⋊Dic43—21no—
49#13063258—22no—
50#13063256—24no—
51#13063249—22no—
52#13063249—24no—
53#13063248—22no—
54C22⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)D412yes—
58C43⋊#95—24no—
59C43⋊#95—24no—
60C22×Q8×C43D411yescharacteristic
61C23×C4×C43C2311yescharacteristic
62C22⋊Q8×C43—21no—
63C22⋊Q8×C43—21no—
64C22⋊Q8×C43—21no—
65C22⋊Q8×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43D411yescharacteristic
69C2×C22⋊C4×C43—21no—
70C2×C22⋊C4×C43—21no—
71C2×C22⋊C4×C43D412yes—
72C2×C42×C43—21no—
73#95×C43—21no—
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—42no—
83C22×C4×C43—41no—
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43#4111yescharacteristic
90C22×Dic43—21no—
91C22×Dic43—21no—
92C22×Dic43—22no—
93C22×Dic43—41no—
94C22×Dic43—41no—
95C22×Dic43—42no—
96C22×Dic43—42no—
97C2×Dic86—21no—
98C2×Dic86—21no—
99C2×Dic86—42no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—42no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43—41no—
105C22⋊C4×C43—22no—
106C22⋊C4×C43—22no—
107C22⋊C4×C43—41no—
108C22⋊C4×C43—41no—
109C22⋊C4×C43—42no—
110C42×C43—42no—
111C22⋊Dic43—41no—
112C22⋊Dic43—41no—
113#10621885—82no—
114C4⋊Dic43—22no—
115C4⋊Dic43—21no—
116C4⋊Dic43—22no—
117C4⋊Dic43—21no—
118C4⋊Dic43—41no—
119C4⋊Dic43—41no—
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—42no—
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—41no—
144C2×C4×C43—41no—
145C2×C4×C43—42no—
146C2×C4×C43—81no—
147C2×C4×C43—81no—
148C2×C4×C43—81no—
149C2×C4×C43—81no—
150C2×C4×C43—81no—
151C2×C4×C43#12011yescharacteristic
152C2×C4×C43#12011yescharacteristic
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×Dic43—42no—
156C2×Dic43—42no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—42no—
160C2×Dic43—44no—
161C2×Dic43—82no—
162C2×Dic43—81no—
163C2×Dic43—81no—
164Dic86—42no—
165Dic86—81no—
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—81no—
188C4×C43—161no—
189C4×C43#45812yes—
190Dic43—81no—
191Dic43—82no—
192Dic43—81no—
193#3189—431no—
194C2×#483—431no—
195#2503—431no—
196#1996D4311yescharacteristic
197#1823—431no—
198#1520—431no—
199#1282—431no—
200C2×C43—22no—
201C2×C43—21no—
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⋊C4—431no—
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—862no—
222#391—861no—
223#382—861no—
224#381—862no—
225#380C2×D4311yescharacteristic
226C4×C22⋊C4C2×D4311yescharacteristic
227#342—22no—
228#340—862no—
229#328—862no—
230C43#996111yescharacteristic, complemented, Sylow
231C22×Q8—431no—
232C22×Q8D17211yescharacteristic
233C23×C4—861no—
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—432no—
249C2×C4⋊C4—431no—
250C2×C4⋊C4—861no—
251C2×C4⋊C4—861no—
252C2×C4⋊C4—861no—
253C2×C4⋊C4—861no—
254C2×C4⋊C4—861no—
255C2×C4⋊C4—861no—
256C2×C4⋊C4D17211yescharacteristic
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—861no—
260C2×C22⋊C4C22⋊D4312yes—
261C2×C42—21no—
262#107—862no—
263#106—864no—
264#103—862no—
265#103—864no—
266#103—862no—
267C22⋊C8—432no—
268C22⋊C8—861no—
269C22⋊C8—861no—
270C22⋊C8—861no—
271#95—21no—
272#95—21no—
273#95—864no—
274#95—864no—
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—42no—
286C22×C4—41no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4—862no—
290C22×C4—1721no—
291C22×C4—1721no—
292C22×C4—1722no—
293C22×C4—1722no—
294C22×C4C2×D17211yescharacteristic
295C22×C4#1062189811yescharacteristic
296C22×C4D4×D4311yescharacteristic
297C22×C4D4×D4311yescharacteristic
298C22×C4D4×D4311yescharacteristic
299C22×C4D4×D4311yescharacteristic
300Q16—3442no—
301C2×C8—862no—
302C2×C8—862no—
303C2×C8—1722no—
304C2×C8—1722no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—42no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—862no—
311C4⋊C4—861no—
312C4⋊C4—862no—
313C4⋊C4—861no—
314C4⋊C4—1721no—
315C4⋊C4—1721no—
316C4⋊C4—1721no—
317C4⋊C4—1721no—
318C22⋊C4—22no—
319C22⋊C4—22no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—42no—
323C22⋊C4—1721no—
324C22⋊C4—1721no—
325C42—42no—
326C23—41no—
327C23—41no—
328C23#1306329311yescharacteristic
329C23#1306329911yescharacteristic
330C23#1306332111yescharacteristic
331C23#1306334512yes—
332C23#1306335612yes—
333Q8—42no—
334Q8—42no—
335Q8—3441no—
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—41no—
347C2×C4—41no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—3442no—
354C2×C4—3441no—
355C2×C4—3441no—
356C2×C4—1722no—
357C2×C4—1722no—
358C2×C4—1724no—
359C2×C4—1721no—
360C2×C4—1721no—
361C2×C4—1722no—
362C2×C4#1306329511yescharacteristic
363C2×C4#1306329511yescharacteristic
364C2×C4#1306329811yescharacteristic
365C2×C4#1306329811yescharacteristic
366C8—1722no—
367C8—1722no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—42no—
375C22—42no—
376C22#1458280811yescharacteristic
377C22#1458305912yes—
378C22#1458312112yes—
379C22#1458328111yescharacteristic
380C22#1458329111yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—82no—
385C4—81no—
386C4—81no—
387C4—161no—
388C4—3441no—
389C4—3442no—
390C4—3441no—
391C4#1458309012yes—
392C2—22no—
393C2—21no—
394C2—22no—
395C2—21no—
396C2#1913565411yescharacteristic
397C2#1913568811yescharacteristic
398C2#1913572511yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1996C2
socleC22×C43#392
prime radicalC24×C43C2×D4
hypercenter#1996D43
hypocenterC43#9961
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

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×#145832272
#191390802
#191346792
#191331662
#191324432
C43×#19962
#996143