Finite Group Databasebeta

← #24985412

Subgroups — #24985412

Order 11008.

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

normal subgroups only

This group has 480 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#19142539C211yesmaximal, characteristic
2#19135733C211yesmaximal, characteristic, complemented
3#19135678C211yesmaximal, characteristic
4#19132421C211yesmaximal, characteristic, complemented
5#19132420C211yesmaximal, characteristic, complemented
6#19132415C211yesmaximal, characteristic
7C43×#2024C211yesmaximal, characteristic, complemented
8C22×#10621884—21no—
9C2×#13063249—21no—
10C2×#13063248—21no—
11#14582841—21no—
12#14582812—21no—
13#14582810—21no—
14#14582805C2211yescharacteristic
15#14582801C2211yescharacteristic
16#14582777—21no—
17#14582773—21no—
18#14582770—21no—
19#14582661—21no—
20#14582654C2211yescharacteristic
21#14582654C2211yescharacteristic
22C2×C4⋊Q8×C43C2211yescharacteristic
23C2×#103×C43—21no—
24C43×#391C2211yescharacteristic
25C43×#340—21no—
26C43×#336C2211yescharacteristic
27C22×Dic86D411yescharacteristic
28C22×D172D411yescharacteristic
29C22×C4×D43—21no—
30C2×#10621884—42no—
31C2×#10621884—42no—
32C2×#10621884—42no—
33C22×C43⋊C8—21no—
34C22×C43⋊C8—21no—
35C2×C4⋊Dic43D411yescharacteristic
36C2×C4⋊Dic43D411yescharacteristic
37C2×Dic43⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43#13063249—42no—
44#13063248—42no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C22×Q8×C43—21no—
51C22×Q8×C43D411yescharacteristic
52C22×C8×C43—21no—
53C4⋊Q8×C43—42no—
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C42×C43C2311yescharacteristic
58#103×C43—42no—
59#95×C43—21no—
60#95×C43—21no—
61C23×D43—21no—
62C2×Q8×C43—22no—
63C2×Q8×C43—21no—
64C2×Q8×C43—21no—
65C2×Q8×C43—41no—
66C2×Q8×C43—41no—
67C2×Q8×C43—41no—
68C2×Q8×C43—41no—
69C2×Q8×C43—41no—
70C2×Q8×C43—41no—
71C2×Q8×C43—41no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—41no—
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C2×D172—21no—
82C2×D172—41no—
83C2×D172—41no—
84C2×D172SD1612yes—
85C2×C4×D43—81no—
86C2×C4×D43—81no—
87C2×C4×D43—81no—
88C2×Dic86—21no—
89C2×Dic86—21no—
90C2×Dic86—41no—
91C2×Dic86—41no—
92C2×C8×C43—41no—
93C2×C8×C43—41no—
94C2×C8×C43—41no—
95C4⋊C4×C43—22no—
96C4⋊C4×C43—22no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C42×C43—41no—
101#10621884—48no—
102(C2×D43)⋊C4—41no—
103(C2×D43)⋊C4—41no—
104(C2×D43)⋊C4—41no—
105(C2×D43)⋊C4—41no—
106(C2×D43)⋊C4—81no—
107(C2×D43)⋊C4—81no—
108(C2×D43)⋊C4—81no—
109C4⋊Dic43—41no—
110C4⋊Dic43—41no—
111Dic43⋊C4—81no—
112C2×C43⋊C8—22no—
113C2×C43⋊C8—41no—
114C2×C43⋊C8—41no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—41no—
117C2×C43⋊C8—41no—
118C23×C43#12011yescharacteristic
119C22×D43—22no—
120C22×D43—41no—
121C22×D43—41no—
122C22×D43—41no—
123C22×D43—41no—
124C22×D43—41no—
125C22×D43—41no—
126Q8×C43—42no—
127Q8×C43—42no—
128Q8×C43—42no—
129Q8×C43—81no—
130Q8×C43—81no—
131Q8×C43—81no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—42no—
145C2×C4×C43—81no—
146C2×C4×C43—81no—
147C2×C4×C43C2×SD1611yescharacteristic
148C2×C4×C43#13511yescharacteristic
149C2×C4×C43#13511yescharacteristic
150C2×C4×C43#13711yescharacteristic
151C2×C4×C43#13711yescharacteristic
152C2×C4×C43#13711yescharacteristic
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162D172—42no—
163D172—81no—
164C4×D43—84no—
165Dic86—42no—
166Dic86—81no—
167C8×C43—81no—
168C43⋊C8—42no—
169C43⋊C8—81no—
170#7755—431nomaximal, Sylow
171C22×C43#44811yescharacteristic
172C22×C43#45211yescharacteristic
173C22×C43#45211yescharacteristic
174C22×C43#45311yescharacteristic
175C22×C43#45511yescharacteristic
176C22×C43#45511yescharacteristic
177C22×C43B(4,𝔽2)11yescharacteristic
178C2×D43—42no—
179C2×D43—42no—
180C2×D43—42no—
181C2×D43—81no—
182C2×D43—81no—
183C2×D43—81no—
184C2×D43—81no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—82no—
192C4×C43—81no—
193C4×C43—81no—
194Dic43—81no—
195Dic43—81no—
196Dic43—81no—
197#2804—431no—
198#2024—431no—
199#2024D4311yescharacteristic, complemented
200#2013—431no—
201#1272—431no—
202#1272—431no—
203#1270—431no—
204C2×C43#159611yescharacteristic
205C2×C43#160611yescharacteristic
206C2×C43#160611yescharacteristic
207C2×C43#163011yescharacteristic
208C2×C43#164311yescharacteristic
209C2×C43#164311yescharacteristic
210C2×C43#165911yescharacteristic
211D43—82no—
212C22×SD16—861no—
213C2×C4⋊Q8C2×D4311yescharacteristic
214C2×#103—21no—
215C2×#103—861no—
216C2×#103—861no—
217#400—861no—
218#393—861no—
219#393—861no—
220#391—431no—
221#391C2×D4311yescharacteristic
222#390—431no—
223#386—861no—
224#385—861no—
225#385—861no—
226#340—21no—
227#340—861no—
228#336—431no—
229#336—431no—
230#336C2×D4311yescharacteristic
231C43#775511yescharacteristic, complemented, Sylow
232C22×Q8—21no—
233C22×Q8—431no—
234C22×Q8C22⋊D4311yescharacteristic
235C22×D4—431no—
236C23×C4—861no—
237C2×SD16—1722no—
238C2×SD16—1722no—
239C2×SD16—1722no—
240C22×C8—21no—
241C22×C8—861no—
242C22×C8—861no—
243C4⋊Q8—42no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—431no—
247C2×C4⋊C4—431no—
248C2×C4⋊C4—861no—
249C2×C4⋊C4C22⋊D4311yescharacteristic
250C2×C22⋊C4—861no—
251C2×C22⋊C4—861no—
252C2×C22⋊C4—861no—
253C2×C22⋊C4—861no—
254C2×C22⋊C4—861no—
255C2×C42C22×D4311yescharacteristic
256#103—42no—
257#103—1722no—
258#103—1722no—
259#95—21no—
260#95—21no—
261#95—861no—
262#95—861no—
263#95—861no—
264#95—861no—
265#95—861no—
266C24—861no—
267C2×Q8—22no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—861no—
278C2×Q8—861no—
279C2×Q8—1721no—
280C2×Q8—1721no—
281C2×D4—432no—
282C2×D4—861no—
283C2×D4—1721no—
284C2×D4—1721no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—41no—
288C22×C4—861no—
289C22×C4—861no—
290C22×C4—861no—
291C22×C4—3441no—
292C22×C4—3441no—
293C22×C4—3441no—
294C22×C4D4×D4311yescharacteristic
295C22×C4D4×D4311yescharacteristic
296C22×C4C2×C22⋊D4311yescharacteristic
297SD16—1728no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—862no—
302C2×C8—1721no—
303C2×C8—1721no—
304C2×C8—1721no—
305C2×C8—1721no—
306C2×C8—1721no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—3441no—
313C4⋊C4—1721no—
314C4⋊C4—1721no—
315C22⋊C4—3441no—
316C22⋊C4—3441no—
317C22⋊C4—3441no—
318C22⋊C4—1721no—
319C22⋊C4—1721no—
320C22⋊C4—1721no—
321C22⋊C4—1721no—
322C42—41no—
323C23—862no—
324C23—1721no—
325C23—1721no—
326C23—1721no—
327C23—1721no—
328C23—1721no—
329C23—1721no—
330C23#1306329311yescharacteristic
331Q8—42no—
332Q8—42no—
333Q8—42no—
334Q8—81no—
335Q8—81no—
336Q8—81no—
337Q8—3441no—
338Q8—1722no—
339D4—3441no—
340D4—1722no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—3444no—
357C2×C4—1721no—
358C2×C4—1721no—
359C2×C4—1721no—
360C2×C4—1721no—
361C2×C4—1721no—
362C2×C4—1721no—
363C2×C4—1721no—
364C2×C4—1721no—
365C2×C4—1721no—
366C2×C4SD16×D4311yescharacteristic
367C2×C4#1306334511yescharacteristic
368C2×C4#1306334811yescharacteristic
369C2×C4#1306335411yescharacteristic
370C2×C4#1306335611yescharacteristic
371C2×C4#1306335711yescharacteristic
372C8—81no—
373C8—3441no—
374C8—1722no—
375C22—3441no—
376C22—3441no—
377C22—3441no—
378C22—3441no—
379C22—1722no—
380C22—1722no—
381C22—1722no—
382C22#1458303611yescharacteristic
383C22#1458305911yescharacteristic
384C22#1458306011yescharacteristic
385C22#1458306511yescharacteristic
386C22#1458307511yescharacteristic
387C22#1458307611yescharacteristic
388C22#1458308511yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—82no—
396C4—81no—
397C4—81no—
398C4—3441no—
399C4—3441no—
400C4—3441no—
401C2—3442no—
402C2#1913351611yescharacteristic
403C2#1913357311yescharacteristic
404C2#1913357411yescharacteristic
405C2#1913371511yescharacteristic
406C2#1913379911yescharacteristic
407C2#1913380111yescharacteristic
408C2#1913390011yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2024C2
socleC23×C43#120
prime radicalC22×D172D4
hypercenter#2024D43
hypocenterC43#7755
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
2. #19135733C2semidirect
4. #19132421C2semidirect
5. #19132420C2semidirect
7. C43×#2024C2semidirect
199. #2024D43semidirect
231. C43#7755semidirect

Maximal subgroups

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

subgroupindex
#191425392
#191357332
#191356782
#191324212
#191324202
#191324152
C43×#20242
#775543