Finite Group Databasebeta

← #24997465

Subgroups — #24997465

Order 11008.

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

normal subgroups only

This group has 528 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#19144630C211yesmaximal, characteristic
2#19137886C211yesmaximal, characteristic
3#19135577C211yesmaximal, characteristic
4#19133025C211yesmaximal, characteristic
5#19133024C211yesmaximal, characteristic
6#19132423C211yesmaximal, characteristic
7C43×#3104C211yesmaximal, characteristic
8C2×C4×Dic86C2211yescharacteristic
9#14583232—21no—
10#14583191—21no—
11#14583106—21no—
12#14583054—21no—
13C4×#10621885—22no—
14#14582952C2211yescharacteristic
15#14582923C2211yescharacteristic
16#14582830—21no—
17#14582829—21no—
18#14582819—21no—
19#14582818—21no—
20C4×Dic43⋊C4—22no—
21#14582745C2211yescharacteristic
22#14582658—22no—
23#14582631—22no—
24Q8⋊(C43⋊C8)—22no—
25C43×#533C2211yescharacteristic
26C2×C4×Q8×C43C2211yescharacteristic
27C43×#484—21no—
28C43×#477—21no—
29C43×#462—21no—
30C43×#451—21no—
31C4×Q16×C43—22no—
32C43×#431C2211yescharacteristic
33C22×Dic86D411yescharacteristic
34C2×#10621885—22no—
35C2×#10621877—21no—
36C4×Dic86—21no—
37C4×Dic86—21no—
38C4×Dic86—21no—
39C4×Dic86—21no—
40C2×C4⋊Dic43D411yescharacteristic
41C2×Dic43⋊C4—22no—
42C2×Dic43⋊C4—22no—
43C2×Dic43⋊C4—21no—
44C2×C4×Dic43—21no—
45C2×C4×Dic43D412yes—
46#13063258—22no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)—21no—
50#13063249—22no—
51#13063248—22no—
52C22⋊(C43⋊C8)—21no—
53C4×C43⋊C8D412yes—
54C43⋊#95—22no—
55C43⋊#95—22no—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C22×Q8×C43D411yescharacteristic
59C2×Q16×C43—22no—
60C4⋊Q8×C43D411yescharacteristic
61C4⋊Q8×C43D411yescharacteristic
62#125×C43—21no—
63C22⋊Q8×C43—21no—
64C22⋊Q8×C43—21no—
65C4×Q8×C43—21no—
66C4×Q8×C43—21no—
67C4×Q8×C43—21no—
68C4×Q8×C43—21no—
69C4×Q8×C43—21no—
70C4×Q8×C43—21no—
71#117×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43D411yescharacteristic
74C2×C42×C43—21no—
75C2×C42×C43C2311yescharacteristic
76#107×C43—22no—
77C4⋊C8×C43—21no—
78#103×C43—22no—
79#103×C43—22no—
80C22⋊C8×C43—21no—
81C4×C8×C43D412yes—
82C2×Q8×C43—21no—
83C2×Q8×C43—21no—
84C2×Q8×C43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43—42no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×Dic43—22no—
93C22×Dic43—21no—
94C22×Dic43—21no—
95C2×Dic86—21no—
96C2×Dic86—21no—
97C2×Dic86—42no—
98Q16×C43—44no—
99C2×C8×C43—22no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—41no—
108C4⋊C4×C43—41no—
109C4⋊C4×C43—41no—
110C22⋊C4×C43—41no—
111C42×C43—41no—
112C42×C43—41no—
113C42×C43—41no—
114C42×C43C2×D411yescharacteristic
115C42×C43C2×D411yescharacteristic
116C42×C43C2×D411yescharacteristic
117C42×C43#4111yescharacteristic
118#10621885—44no—
119C4⋊Dic43—21no—
120C4⋊Dic43—21no—
121Dic43⋊C4—44no—
122Dic43⋊C4—44no—
123Dic43⋊C4—41no—
124Dic43⋊C4—41no—
125C4×Dic43—22no—
126C4×Dic43—41no—
127C4×Dic43—41no—
128C4×Dic43Q1614yescomplemented
129#10621877—42no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8—41no—
132C23×C43#12011yescharacteristic
133Q8×C43—22no—
134Q8×C43—22no—
135Q8×C43—41no—
136Q8×C43—41no—
137Q8×C43—42no—
138Q8×C43—42no—
139C2×C4×C43—22no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—42no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43#12011yescharacteristic
149C2×C4×C43#12011yescharacteristic
150C2×C4×C43#12111yescharacteristic
151C2×C4×C43#12111yescharacteristic
152C2×C4×C43#12111yescharacteristic
153C2×C4×C43#12711yescharacteristic
154C2×C4×C43C2×Q1612yes—
155C2×C4×C43#13712yes—
156C2×Dic43—22no—
157C2×Dic43—24no—
158C2×Dic43—42no—
159C2×Dic43—42no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—42no—
163C2×Dic43—41no—
164Dic86—22no—
165Dic86—22no—
166Dic86—41no—
167Dic86—41no—
168C8×C43—42no—
169C43⋊C8—42no—
170C43⋊C8—81no—
171#10017—431nomaximal, Sylow
172C22×C43—21no—
173C22×C43—21no—
174C22×C43#39211yescharacteristic
175C22×C43#45112yes—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—42no—
181C4×C43—81no—
182C4×C43—81no—
183C4×C43—81no—
184C4×C43#46212yes—
185C4×C43#49411yescharacteristic
186C4×C43#49711yescharacteristic
187Dic43—44no—
188Dic43—42no—
189Dic43—81no—
190#3104—431no—
191#3104D4311yescharacteristic
192#2399—431no—
193#1995—431no—
194#1487—431no—
195#1487—431no—
196#1274—431no—
197C2×C43—22no—
198C2×C43#201011yescharacteristic
199C2×C43#201011yescharacteristic
200C2×C43#201611yescharacteristic
201#533C2×D4311yescharacteristic
202C2×C4×Q8—431no—
203C2×C4×Q8C2×D4311yescharacteristic
204#484—21no—
205#484—861no—
206#477—21no—
207#477—861no—
208#462—21no—
209#462—861no—
210#451—21no—
211#451—861no—
212C4×Q16—22no—
213C4×Q16—862no—
214#431—431no—
215#431C2×D4311yescharacteristic
216#423—431no—
217#398—861no—
218#398—861no—
219#395—861no—
220#395—861no—
221C4×C4⋊C4—862no—
222#376—431no—
223#339—862no—
224Q8⋊C8—862no—
225Q8⋊C8—862no—
226C43#1001711yescharacteristic, complemented, Sylow
227C22×Q8—431no—
228C22×Q8C22⋊D4311yescharacteristic
229C2×Q16—22no—
230C2×Q16—862no—
231C2×M16—861no—
232C4⋊Q8C22⋊D4311yescharacteristic
233C4⋊Q8C22⋊D4311yescharacteristic
234#125—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8—21no—
242C4×Q8—21no—
243C4×Q8—861no—
244C4×Q8—861no—
245C4×Q8—861no—
246C4×Q8—861no—
247#117—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—431no—
250C2×C4⋊C4—862no—
251C2×C4⋊C4—862no—
252C2×C4⋊C4—861no—
253C2×C4⋊C4C22⋊D4311yescharacteristic
254C2×C42—21no—
255C2×C42—432no—
256C2×C42—861no—
257C2×C42C22×D4311yescharacteristic
258#107—22no—
259#107—862no—
260C4⋊C8—21no—
261C4⋊C8—861no—
262C4⋊C8—861no—
263C4⋊C8—861no—
264#103—22no—
265#103—22no—
266#103—862no—
267#103—862no—
268C22⋊C8—21no—
269C22⋊C8—861no—
270C4×C8—432no—
271C4×C8C22⋊D4312yes—
272#95—862no—
273#95—862no—
274#95—861no—
275#95—861no—
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×Q8—42no—
281C2×Q8—861no—
282C2×Q8—861no—
283C2×Q8—1722no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—862no—
287C22×C4—861no—
288C22×C4—861no—
289C22×C4D4×D4311yescharacteristic
290C22×C4D4×D4311yescharacteristic
291C22×C4C2×C22⋊D4311yescharacteristic
292Q16—44no—
293Q16—1724no—
294M16—1722no—
295C2×C8—22no—
296C2×C8—862no—
297C2×C8—1721no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—861no—
309C4⋊C4—861no—
310C4⋊C4—1724no—
311C4⋊C4—1724no—
312C4⋊C4—1721no—
313C4⋊C4—1721no—
314C22⋊C4—41no—
315C42—41no—
316C42—41no—
317C42—41no—
318C42—434no—
319C42—862no—
320C42—1721no—
321C42—1721no—
322C42D4×D4311yescharacteristic
323C42#1062190011yescharacteristic
324C42C2×C22⋊D4311yescharacteristic
325C42C2×C22⋊D4311yescharacteristic
326C23#1306329311yescharacteristic
327Q8—22no—
328Q8—22no—
329Q8—41no—
330Q8—41no—
331Q8—42no—
332Q8—42no—
333Q8—862no—
334Q8—862no—
335Q8—1721no—
336Q8—1721no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—862no—
347C2×C4—864no—
348C2×C4—1722no—
349C2×C4—1721no—
350C2×C4—1722no—
351C2×C4—1722no—
352C2×C4—1721no—
353C2×C4—1721no—
354C2×C4#1306329311yescharacteristic
355C2×C4#1306329411yescharacteristic
356C2×C4#1306329611yescharacteristic
357C2×C4#1306329711yescharacteristic
358C2×C4#1306329711yescharacteristic
359C2×C4#1306332111yescharacteristic
360C2×C4Q16×D4312yes—
361C2×C4#1306335712yes—
362C8—42no—
363C8—3441no—
364C8—1722no—
365C22—21no—
366C22—21no—
367C22#1458280711yescharacteristic
368C22#1458305312yes—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—42no—
374C4—81no—
375C4—81no—
376C4—81no—
377C4—3441no—
378C4—1724no—
379C4—1722no—
380C4#1458310712yes—
381C4#1458327711yescharacteristic
382C4#1458329211yescharacteristic
383C2—22no—
384C2#1913565911yescharacteristic
385C2#1913566011yescharacteristic
386C2#1913569311yescharacteristic
subgroupG/H
centerC2×C4#13063321
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#3104C2
socleC22×C43#392
prime radicalC23×C43#120
hypercenter#3104D43
hypocenterC43#10017
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3104

Complements

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

NH ≅ G/Ntype
128. C4×Dic43Q16semidirect
226. C43#10017semidirect

Maximal subgroups

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

subgroupindex
#191446302
#191378862
#191355772
#191330252
#191330242
#191324232
C43×#31042
#1001743