Finite Group Databasebeta

← #24993886

Subgroups — #24993886

Order 11008.

492 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 103 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#19137410C211yesmaximal, characteristic
2#19135540C211yesmaximal, characteristic, complemented
3#19133193C211yesmaximal, characteristic
4#19133146C211yesmaximal, characteristic, complemented
5#19132461C211yesmaximal, characteristic, complemented
6#19132450C211yesmaximal, characteristic, complemented
7C43×#3215C211yesmaximal, characteristic
8#14582956C2211yescharacteristic
9C4×#10621877C2211yescharacteristic
10#14582806—21no—
11#14582792—21no—
12#14582792—21no—
13#14582779—21no—
14#14582774—21no—
15#14582767C2211yescharacteristic
16C4×C4⋊Dic43C2211yescharacteristic
17C22⋊C4×Dic43—21no—
18#14582658—21no—
19#14582658—21no—
20#14582639—22no—
21#14582636—21no—
22#14582636—21no—
23C43×#533C2211yescharacteristic
24C2×#124×C43C2211yescharacteristic
25C43×#497C412yescomplemented
26C43×#489C412yescomplemented
27C43×#464—22no—
28C43×#451—21no—
29C43×#450—21no—
30C43×#432C2211yescharacteristic
31C23×Dic43—21no—
32C2×#10621877—21no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43—21no—
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37C2×C22⋊Dic43—21no—
38C2×C4×Dic43—21no—
39C2×C4×Dic43D411yescharacteristic
40C2×C4×Dic43D411yescharacteristic
41C4⋊(C43⋊C8)—21no—
42C22⋊(C43⋊C8)—21no—
43#13063236—21no—
44#13063236—21no—
45C4×C43⋊C8—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95D411yescharacteristic
52C43⋊#95D411yescharacteristic
53C22×Q8×C43D411yescharacteristic
54C22×D4×C43D411yescharacteristic
55C2×Q16×C43—22no—
56C2×SD16×C43—22no—
57C4⋊Q8×C43C2×C411yescharacteristic, complemented
58C4⋊Q8×C43C2×C411yescharacteristic, complemented
59#125×C43—21no—
60#124×C43—21no—
61#124×C43—21no—
62#124×C43C2×C412yes—
63#124×C43D412yes—
64C22⋊Q8×C43—21no—
65C22⋊Q8×C43—21no—
66C4×Q8×C43—21no—
67C4×Q8×C43—21no—
68#117×C43—21no—
69C2×C22⋊C4×C43—21no—
70C2×C22⋊C4×C43—21no—
71C2×C42×C43C2311yescharacteristic
72C4⋊C8×C43—21no—
73#103×C43—22no—
74#102×C43—22no—
75C22⋊C8×C43—21no—
76#97×C43C2×C412yescomplemented
77C24×C43—21no—
78C2×Q8×C43—21no—
79C2×Q8×C43—21no—
80C2×Q8×C43—21no—
81C2×Q8×C43—81no—
82C2×Q8×C43C22⋊C412yes—
83C2×D4×C43—21no—
84C2×D4×C43—81no—
85C2×D4×C43C22⋊C412yes—
86C22×C4×C43—21no—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×Dic43—21no—
91C22×Dic43—21no—
92C22×Dic43—21no—
93C22×Dic43—21no—
94C22×Dic43—42no—
95C22×Dic43—81no—
96C22×Dic43—81no—
97Q16×C43—82no—
98SD16×C43—82no—
99C2×C8×C43—22no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—41no—
106C22⋊C4×C43—22no—
107C22⋊C4×C43—22no—
108C22⋊C4×C43—22no—
109C22⋊C4×C43—22no—
110C22⋊C4×C43—41no—
111C42×C43—41no—
112C42×C43C22×C411yescharacteristic
113C42×C43C2×D411yescharacteristic
114C42×C43#4111yescharacteristic
115C42×C43#4111yescharacteristic
116C22⋊Dic43—42no—
117C22⋊Dic43—81no—
118C22⋊Dic43—81no—
119C4⋊Dic43—42no—
120C4⋊Dic43—81no—
121C4×Dic43—41no—
122C4×Dic43—41no—
123C4×Dic43—81no—
124#10621877—22no—
125#10621877—41no—
126C2×C43⋊C8—41no—
127C2×C43⋊C8—41no—
128C23×C43—22no—
129C23×C43—41no—
130C23×C43—41no—
131C23×C43—41no—
132C23×C43—41no—
133C23×C43—41no—
134C23×C43—41no—
135C23×C43#12011yescharacteristic
136Q8×C43—42no—
137Q8×C43—42no—
138Q8×C43—81no—
139Q8×C43—81no—
140D4×C43—42no—
141D4×C43—81no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—22no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43C2×C22⋊C411yescharacteristic
152C2×C4×C43C4×D411yescharacteristic
153C2×C4×C43C4×D411yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43#12311yescharacteristic
157C2×Dic43—22no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—84no—
170C8×C43—42no—
171C43⋊C8—42no—
172C43⋊C8—81no—
173#9379—431nomaximal, Sylow
174C22×C43—21no—
175C22×C43—21no—
176C22×C43—42no—
177C22×C43—42no—
178C22×C43—42no—
179C22×C43—81no—
180C22×C43—81no—
181C22×C43—81no—
182C22×C43—81no—
183C22×C43#38611yescharacteristic
184C22×C43#45511yescharacteristic
185C22×C43#45611yescharacteristic
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—42no—
193C4×C43—81no—
194C4×C43—81no—
195Dic43—42no—
196Dic43—81no—
197Dic43—81no—
198Dic43—81no—
199#3215D4311yescharacteristic
200#2337—431no—
201#1986—431no—
202#1527—431no—
203#1515—431no—
204#1288—431no—
205#1285—431no—
206C2×C43—21no—
207C2×C43—21no—
208C2×C43—82no—
209C2×C43#188211yescharacteristic
210C2×C43#190611yescharacteristic
211C2×C43#191111yescharacteristic
212#533C2×D4311yescharacteristic
213C2×#124C2×D4311yescharacteristic
214#497Dic4312yescomplemented
215#489Dic4312yescomplemented
216#464—22no—
217#451—21no—
218#450—21no—
219#432—431no—
220#432C2×D4311yescharacteristic
221C4×M16—431no—
222#391—861no—
223#388—861no—
224#388—861no—
225#386—861no—
226#385—861no—
227#383—431no—
228C4×C4⋊C4—431no—
229C4×C22⋊C4—861no—
230#339—861no—
231#339—861no—
232#329—862no—
233#328—861no—
234#328—861no—
235C43#937911yescharacteristic, complemented, Sylow
236C22×Q8C22⋊D4311yescharacteristic
237C22×D4C22⋊D4311yescharacteristic
238C23×C4—861no—
239C2×Q16—22no—
240C2×SD16—22no—
241C2×M16—861no—
242C4⋊Q8C2×Dic4311yescharacteristic, complemented
243C4⋊Q8C2×Dic4311yescharacteristic, complemented
244#125—21no—
245#124—21no—
246#124—21no—
247#124C2×Dic4312yes—
248#124C22⋊D4312yes—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C4×Q8—21no—
252C4×Q8—21no—
253#117—21no—
254C2×C4⋊C4—861no—
255C2×C4⋊C4—861no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—861no—
259C2×C22⋊C4—861no—
260C2×C22⋊C4—861no—
261C2×C42—431no—
262C2×C42—431no—
263C2×C42—861no—
264C2×C42C22×D4311yescharacteristic
265C4⋊C8—21no—
266C4⋊C8—861no—
267#103—22no—
268#102—22no—
269C22⋊C8—21no—
270C22⋊C8—861no—
271#97—861no—
272#97—861no—
273#97C2×Dic4312yescomplemented
274C4×C8—861no—
275#95—431no—
276#95—431no—
277#95—861no—
278#95—861no—
279#95—861no—
280#95—861no—
281#95—861no—
282C24—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8—81no—
287C2×Q8C22⋊Dic4312yes—
288C2×D4—21no—
289C2×D4—81no—
290C2×D4C22⋊Dic4312yes—
291C22×C4—21no—
292C22×C4—861no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4—3441no—
297C22×C4—3441no—
298C22×C4—1722no—
299C22×C4D4×D4311yescharacteristic
300C22×C4D4×D4311yescharacteristic
301C22×C4C2×C22⋊D4311yescharacteristic
302Q16—82no—
303SD16—82no—
304M16—862no—
305M16—1721no—
306C2×C8—22no—
307C2×C8—1721no—
308C2×C8—1721no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—3441no—
316C4⋊C4—1722no—
317C22⋊C4—22no—
318C22⋊C4—22no—
319C22⋊C4—22no—
320C22⋊C4—22no—
321C22⋊C4—41no—
322C22⋊C4—3441no—
323C22⋊C4—3441no—
324C22⋊C4—1722no—
325C42—41no—
326C42—3441no—
327C42—1721no—
328C42—1721no—
329C42#1062190011yescharacteristic
330C42#1062190011yescharacteristic
331C42C22×Dic4311yescharacteristic
332C42C2×C22⋊D4311yescharacteristic
333C23—22no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23#1306329311yescharacteristic
341Q8—42no—
342Q8—42no—
343Q8—81no—
344Q8—81no—
345D4—42no—
346D4—81no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—862no—
357C2×C4—3444no—
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×C4—1721no—
367C2×C4—1721no—
368C2×C4—1721no—
369C2×C4C2×C22⋊Dic4311yescharacteristic
370C2×C4D4×Dic4311yescharacteristic
371C2×C4D4×Dic4311yescharacteristic
372C2×C4#1306329711yescharacteristic
373C2×C4#1306329711yescharacteristic
374C2×C4#1306330611yescharacteristic
375C8—42no—
376C8—3441no—
377C8—1722no—
378C22—21no—
379C22—21no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22#1458277911yescharacteristic
388C22#1458307511yescharacteristic
389C22#1458308011yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—42no—
397C4—81no—
398C4—81no—
399C4—3441no—
400C4—3441no—
401C4—3441no—
402C4—1722no—
403C2—21no—
404C2—21no—
405C2—82no—
406C2#1913496611yescharacteristic
407C2#1913509811yescharacteristic
408C2#1913512811yescharacteristic
subgroupG/H
centerC22#14582779
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#3215C2
socleC22×C43#386
prime radicalC22×D4×C43D4
cosocleC2×C42×C43C23
hypercenter#3215D43
hypocenterC43#9379
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3215

Complements

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

NH ≅ G/Ntype
2. #19135540C2semidirect
4. #19133146C2semidirect
5. #19132461C2semidirect
6. #19132450C2semidirect
25. C43×#497C4semidirect
26. C43×#489C4semidirect
57. C4⋊Q8×C43C2×C4semidirect
58. C4⋊Q8×C43C2×C4semidirect
76. #97×C43C2×C4semidirect
214. #497Dic43semidirect
215. #489Dic43semidirect
235. C43#9379semidirect
242. C4⋊Q8C2×Dic43semidirect
243. C4⋊Q8C2×Dic43semidirect
273. #97C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
#191374102
#191355402
#191331932
#191331462
#191324612
#191324502
C43×#32152
#937943