Finite Group Databasebeta

← #25006930

Subgroups — #25006930

Order 11008.

456 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 73 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#19137860C211yesmaximal, characteristic
2#19134382C211yesmaximal, characteristic
3#19132914C211yesmaximal, characteristic
4#19132619C211yesmaximal, characteristic, complemented
5#19132596C211yesmaximal, characteristic, complemented
6#19132594C211yesmaximal, characteristic, complemented
7C43×#1352C211yesmaximal, characteristic, complemented
8C2×(C22⋊D43)⋊C4C2211yescharacteristic
9C2×#13063283C411yescharacteristic, complemented
10#14582949—21no—
11C2×#13063239—21no—
12#14582837C411yescharacteristic, complemented
13#14582831C411yescharacteristic, complemented
14#14582825—21no—
15#14582824C2211yescharacteristic
16#14582815—21no—
17C4⋊C4×Dic43—21no—
18C22⋊C4×Dic43—21no—
19C22⋊C4×Dic43—21no—
20#14582746C411yescharacteristic, complemented
21#14582666C2211yescharacteristic
22#14582623C2211yescharacteristic
23#14582622—21no—
24C43×#399C2211yescharacteristic
25C43×#342C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C22×C22⋊D43D411yescharacteristic
28C23×Dic43D411yescharacteristic
29C22×C4×D43C2×C411yescharacteristic
30(C22⋊D43)⋊C4—41no—
31(C22⋊D43)⋊C4—41no—
32#13063283—41no—
33#13063283—41no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43C2×C411yescharacteristic
36C2×Dic43⋊C4C2×C411yescharacteristic
37C2×C22⋊Dic43—21no—
38C2×C22⋊Dic43—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4D411yescharacteristic
42C2×C4×Dic43—21no—
43C2×C4×Dic43—21no—
44C2×C4×Dic43—41no—
45C2×C4×Dic43D411yescharacteristic
46Dic43⋊C8—41no—
47#13063239—24no—
48C22⋊(C43⋊C8)—21no—
49C8×Dic43—41no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—41no—
55C43⋊#95C2×C411yescharacteristic
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43C2×C411yescharacteristic
58C2×C22⋊C4×C43—21no—
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43C2311yescharacteristic
61C22⋊C8×C43—21no—
62#95×C43C2×C411yescharacteristic
63C24×C43C2×D411yescharacteristic
64C23×D43C22⋊C411yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—41no—
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C2×C22⋊D43—22no—
71C2×C22⋊D43—21no—
72C2×C22⋊D43—21no—
73C2×C22⋊D43—41no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—41no—
79C22×Dic43—42no—
80C22×Dic43C22⋊C411yescharacteristic
81C22×Dic43C22⋊C411yescharacteristic
82C22×Dic43C22⋊C411yescharacteristic
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43—42no—
86C2×C8×C43—41no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—42no—
89C22⋊C4×C43—22no—
90C22⋊C4×C43—41no—
91C22⋊C4×C43—42no—
92C22⋊C4×C43—41no—
93C22⋊Dic43—22no—
94C22⋊Dic43—41no—
95C22⋊Dic43—41no—
96C22⋊Dic43—41no—
97(C2×D43)⋊C4—41no—
98(C2×D43)⋊C4—42no—
99(C2×D43)⋊C4—42no—
100C4⋊Dic43—42no—
101C4⋊Dic43—41no—
102Dic43⋊C4—41no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C4×Dic43—42no—
106C4×Dic43—41no—
107C4×Dic43—41no—
108C4×Dic43—82no—
109C2×C43⋊C8—41no—
110C23×C43—21no—
111C23×C43—21no—
112C23×C43—41no—
113C23×C43—41no—
114C23×C43C2×C22⋊C411yescharacteristic
115C23×C43#13511yescharacteristic
116C23×C43#13511yescharacteristic
117C22×D43—21no—
118C22×D43—21no—
119C22×D43—21no—
120C22×D43—41no—
121C22×D43—41no—
122C2×C4×C43—22no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—42no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—81no—
134C2×C4×C43—81no—
135C22⋊D43—42no—
136C22⋊D43—42no—
137C2×Dic43—21no—
138C2×Dic43—21no—
139C2×Dic43—22no—
140C2×Dic43—21no—
141C2×Dic43—42no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—42no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—81no—
151C2×Dic43—81no—
152C2×Dic43—81no—
153C2×Dic43#9911yescharacteristic
154C2×Dic43#9911yescharacteristic
155C2×Dic43#10412yes—
156C4×D43—42no—
157C4×D43—42no—
158C8×C43—81no—
159C43⋊C8—81no—
160#11727—431nomaximal, Sylow
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—81no—
170C22×C43C2×#9911yescharacteristic
171C22×C43#41611yescharacteristic
172C22×C43C2×#10411yescharacteristic
173C2×D43—41no—
174C2×D43—41no—
175C2×D43—41no—
176C2×D43—81no—
177C2×D43—81no—
178C4×C43—42no—
179C4×C43—41no—
180C4×C43—41no—
181C4×C43—82no—
182C4×C43—81no—
183Dic43—21no—
184Dic43—22no—
185Dic43—41no—
186Dic43—81no—
187Dic43—82no—
188Dic43—81no—
189Dic43#35212yes—
190#2395—431no—
191C4×#99—431no—
192#1460—431no—
193#1352—431no—
194#1352D4311yescharacteristic, complemented
195#1344—431no—
196#1344—431no—
197C2×C43—21no—
198C2×C43—21no—
199C2×C43—41no—
200C2×C43—41no—
201C2×C43#150111yescharacteristic
202C2×C43C2×#35211yescharacteristic
203C2×C43#212611yescharacteristic
204D43—81no—
205C2×C4×D4—431no—
206C2×#117—431no—
207#431—861no—
208C2×#99—861no—
209#400—431no—
210#399C2×D4311yescharacteristic
211#398—431no—
212#397—431no—
213#397—861no—
214#394—861no—
215C4×C4⋊C4—861no—
216C4×C22⋊C4—431no—
217C4×C22⋊C4—861no—
218C4×C22⋊C4—861no—
219#342—431no—
220#342C2×D4311yescharacteristic
221#323—431no—
222#323—861no—
223#323C2×D4311yescharacteristic
224C43#1172711yescharacteristic, complemented, Sylow
225C22×D4—431no—
226C23×C4—431no—
227C23×C4—431no—
228C4×D4—1721no—
229C4×D4—1721no—
230#117—1721no—
231#117—1721no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—431no—
234C2×C4⋊C4—431no—
235C2×C4⋊C4—861no—
236C2×C4⋊C4C4×D4311yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—431no—
240C2×C22⋊C4—861no—
241C2×C22⋊C4—861no—
242C2×C22⋊C4—861no—
243C2×C22⋊C4—861no—
244C2×C22⋊C4C22×D4311yescharacteristic
245C2×C42—431no—
246C2×C42—861no—
247C2×C42—861no—
248C2×C42—1721no—
249C4⋊C8—1721no—
250#99—864no—
251C22⋊C8—21no—
252C22⋊C8—861no—
253C4×C8—1721no—
254#95—431no—
255#95—861no—
256#95—861no—
257#95—861no—
258#95—861no—
259#95—1721no—
260#95C4×D4311yescharacteristic
261C24—431no—
262C24D4×D4311yescharacteristic
263C2×D4—862no—
264C2×D4—861no—
265C2×D4—861no—
266C2×D4—1721no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—41no—
270C22×C4—431no—
271C22×C4—431no—
272C22×C4—431no—
273C22×C4—861no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4—861no—
278C22×C4—861no—
279C22×C4—1722no—
280C22×C4—1722no—
281C22×C4—1721no—
282C22×C4C2×C4×D4311yescharacteristic
283C22×C4D4×D4311yescharacteristic
284C2×C8—41no—
285C2×C8—1721no—
286C4⋊C4—41no—
287C4⋊C4—42no—
288C4⋊C4—1721no—
289C4⋊C4—1721no—
290C4⋊C4—1722no—
291C22⋊C4—22no—
292C22⋊C4—41no—
293C22⋊C4—42no—
294C22⋊C4—41no—
295C22⋊C4—862no—
296C22⋊C4—1721no—
297C22⋊C4—1722no—
298C22⋊C4—1722no—
299C22⋊C4—1721no—
300C22⋊C4—1721no—
301C22⋊C4—1721no—
302C42—861no—
303C42—861no—
304C42—3442no—
305C42—1721no—
306C42—1721no—
307C42—1722no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23—861no—
313C23—861no—
314C23—861no—
315C23—1721no—
316C23—1721no—
317C23C22⋊C4×D4311yescharacteristic
318C23#1306334611yescharacteristic
319C23#1306334811yescharacteristic
320D4—1722no—
321D4—1722no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—431no—
336C2×C4—431no—
337C2×C4—432no—
338C2×C4—862no—
339C2×C4—861no—
340C2×C4—861no—
341C2×C4—861no—
342C2×C4—3441no—
343C2×C4—3441no—
344C2×C4—3441no—
345C2×C4—1722no—
346C2×C4—1722no—
347C2×C4—1722no—
348C2×C4—1721no—
349C2×C4—1722no—
350C2×C4—1721no—
351C2×C4—1721no—
352C2×C4—1721no—
353C2×C4—1721no—
354C2×C4—1721no—
355C2×C4—1721no—
356C8—81no—
357C8—3441no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—81no—
367C22—3441no—
368C22—3441no—
369C22—1721no—
370C22—1721no—
371C22—1721no—
372C22#99×D4311yescharacteristic
373C22#1458289411yescharacteristic
374C22#104×D4311yescharacteristic
375C4—42no—
376C4—41no—
377C4—41no—
378C4—82no—
379C4—81no—
380C4—432no—
381C4—862no—
382C4—861no—
383C4—3441no—
384C4—3442no—
385C4—3441no—
386C4—1721no—
387C2—21no—
388C2—21no—
389C2—41no—
390C2—41no—
391C2—3441no—
392C2#1913308511yescharacteristic
393C2#352×D4311yescharacteristic
394C2#1913625711yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1352C2
socleC22×C43C2×#99
prime radicalC22×C22⋊D43D4
cosocleC2×C22⋊C4×C43C23
hypercenter#1352D43
hypocenterC43#11727
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

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

NH ≅ G/Ntype
4. #19132619C2semidirect
5. #19132596C2semidirect
6. #19132594C2semidirect
7. C43×#1352C2semidirect
9. C2×#13063283C4semidirect
12. #14582837C4semidirect
13. #14582831C4semidirect
20. #14582746C4semidirect
194. #1352D43semidirect
224. C43#11727semidirect

Maximal subgroups

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

subgroupindex
#191378602
#191343822
#191329142
#191326192
#191325962
#191325942
C43×#13522
#1172743