Finite Group Databasebeta

← #24994240

Subgroups — #24994240

Order 11008.

474 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 89 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#19143230C211yesmaximal, characteristic
2#19139048C211yesmaximal, characteristic
3#19134670C211yesmaximal, characteristic
4#19133129C211yesmaximal, characteristic
5#19133127C211yesmaximal, characteristic
6#19132448C211yesmaximal, characteristic
7C43×#1284C211yesmaximal, characteristic
8C2×#13063304C2211yescharacteristic
9C2×#13063284C2211yescharacteristic
10#14582957—22no—
11#14582957—22no—
12#14582922—21no—
13#14582863C2211yescharacteristic
14M16×Dic43—21no—
15#14582824—21no—
16#14582824—21no—
17#14582805C411yescharacteristic, complemented
18#14582805C411yescharacteristic, complemented
19#14582784—21no—
20#14582784—21no—
21#14582769C411yescharacteristic, complemented
22#14582765C411yescharacteristic, complemented
23#14582762C2211yescharacteristic
24#14582665—21no—
25#14582665—21no—
26#14582637—22no—
27#14582635—22no—
28C43×#407C2211yescharacteristic
29C43×#381C2211yescharacteristic
30C4×C22⋊C4×C43C2211yescharacteristic
31C22×Dic86C2×C411yescharacteristic
32C2×#10621877—21no—
33#13063304—21no—
34#13063304—21no—
35#13063304—21no—
36#13063304—21no—
37#13063284—21no—
38#13063284—21no—
39#13063284—21no—
40#13063284—21no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43C2×C411yescharacteristic
44C2×C4⋊Dic43C2×C411yescharacteristic
45C2×C4⋊Dic43C2×C411yescharacteristic
46C2×Dic43⋊C4—21no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43—21no—
49C2×C22⋊Dic43D411yescharacteristic
50C2×C22⋊Dic43D411yescharacteristic
51C2×C4×Dic43D411yescharacteristic
52C2×C4×Dic43D411yescharacteristic
53Dic43⋊C8—24no—
54C22⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)D412yes—
56#13063235—22no—
57C8×Dic43—22no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95—21no—
63C43⋊#95—21no—
64C43⋊#95—21no—
65C43⋊#95—21no—
66C23×C4×C43C2311yescharacteristic
67C2×M16×C43—21no—
68C2×C22⋊C4×C43—21no—
69C2×C22⋊C4×C43—21no—
70C2×C42×C43C2×C411yescharacteristic
71C2×C42×C43C2×C411yescharacteristic
72C22⋊C8×C43—21no—
73C22⋊C8×C43D412yes—
74#95×C43—21no—
75#95×C43—21no—
76#95×C43—21no—
77C24×C43C2×D411yescharacteristic
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—41no—
81C22×C4×C43—41no—
82C22×C4×C43—41no—
83C22×C4×C43C22×C411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43#4111yescharacteristic
88C22×C4×C43#4111yescharacteristic
89C22×Dic43—21no—
90C22×Dic43—21no—
91C22×Dic43—41no—
92C22×Dic43C22⋊C411yescharacteristic
93C22×Dic43C22⋊C411yescharacteristic
94C22×Dic43C22⋊C411yescharacteristic
95C22×Dic43C22⋊C411yescharacteristic
96C2×Dic86—21no—
97C2×Dic86—21no—
98C2×Dic86—41no—
99C2×Dic86—41no—
100M16×C43—41no—
101M16×C43—41no—
102C2×C8×C43—22no—
103C22⋊C4×C43—41no—
104C22⋊C4×C43—41no—
105C22⋊C4×C43—42no—
106C42×C43—41no—
107C42×C43—41no—
108C22⋊Dic43—21no—
109C22⋊Dic43—21no—
110C22⋊Dic43—21no—
111C22⋊Dic43—21no—
112C22⋊Dic43—41no—
113C22⋊Dic43—41no—
114C22⋊Dic43—41no—
115C22⋊Dic43—41no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118C4⋊Dic43—21no—
119C4⋊Dic43—21no—
120C4⋊Dic43—21no—
121C4⋊Dic43—21no—
122C4⋊Dic43—42no—
123C4⋊Dic43—42no—
124Dic43⋊C4—41no—
125Dic43⋊C4—41no—
126C4×Dic43—21no—
127C4×Dic43—21no—
128C4×Dic43—21no—
129C4×Dic43—21no—
130#10621877—41no—
131#10621877—41no—
132C2×C43⋊C8—22no—
133C23×C43—21no—
134C23×C43—21no—
135C23×C43—41no—
136C23×C43—41no—
137C23×C43C2×C22⋊C411yescharacteristic
138C23×C43#12111yescharacteristic
139C23×C43#12111yescharacteristic
140C2×C4×C43—21no—
141C2×C4×C43—21no—
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×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—81no—
155C2×C4×C43—81no—
156C2×C4×C43—81no—
157C2×C4×C43C4×D411yescharacteristic
158C2×C4×C43C4×D411yescharacteristic
159C2×C4×C43#12011yescharacteristic
160C2×C4×C43#12311yescharacteristic
161C2×Dic43—21no—
162C2×Dic43—21no—
163C2×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—81no—
176C2×Dic43—81no—
177C2×Dic43—81no—
178Dic86—81no—
179Dic86—81no—
180C8×C43—42no—
181C43⋊C8—42no—
182#9444—431nomaximal, Sylow
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—81no—
192C22×C43—81no—
193C22×C43#38611yescharacteristic
194C22×C43#41011yescharacteristic
195C22×C43#41011yescharacteristic
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—42no—
201C4×C43—81no—
202C4×C43—161no—
203Dic43—41no—
204Dic43—41no—
205Dic43—41no—
206Dic43—41no—
207Dic43—81no—
208Dic43—81no—
209Dic43—161no—
210#2921—431no—
211#2499—431no—
212#1820—431no—
213#1511—431no—
214#1511—431no—
215#1284—431no—
216#1284D4311yescharacteristic
217C2×C43—21no—
218C2×C43—21no—
219C2×C43—41no—
220C2×C43—41no—
221C2×C43#188411yescharacteristic
222C2×C43#189911yescharacteristic
223C2×C43#190911yescharacteristic
224C2×C22⋊Q8—431no—
225C2×#117—431no—
226#433—862no—
227#433—862no—
228#423—861no—
229#407—431no—
230#407C2×D4311yescharacteristic
231C4×M16—861no—
232#397—861no—
233#397—861no—
234#391—431no—
235#391—431no—
236#387—861no—
237#387—861no—
238#384—431no—
239#382—431no—
240#381—431no—
241#381C2×D4311yescharacteristic
242C4×C22⋊C4C2×D4311yescharacteristic
243#342—861no—
244#342—861no—
245#328—862no—
246#328—862no—
247C43#944411yescharacteristic, complemented, Sylow
248C22×Q8—431no—
249C23×C4C22×D4311yescharacteristic
250C2×M16—21no—
251C2×M16—861no—
252C22⋊Q8—861no—
253C22⋊Q8—861no—
254C22⋊Q8—861no—
255C22⋊Q8—861no—
256#117—861no—
257#117—861no—
258#117—861no—
259#117—861no—
260C2×C4⋊C4—431no—
261C2×C4⋊C4—431no—
262C2×C4⋊C4—431no—
263C2×C4⋊C4—861no—
264C2×C4⋊C4—861no—
265C2×C4⋊C4—861no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—431no—
269C2×C22⋊C4—431no—
270C2×C22⋊C4—861no—
271C2×C22⋊C4—861no—
272C2×C42—431no—
273C2×C42—431no—
274C2×C42C4×D4311yescharacteristic
275C2×C42C4×D4311yescharacteristic
276C4⋊C8—864no—
277C22⋊C8—21no—
278C22⋊C8—432no—
279C22⋊C8—861no—
280C22⋊C8D17212yes—
281#97—862no—
282C4×C8—862no—
283#95—21no—
284#95—21no—
285#95—21no—
286#95—861no—
287#95—861no—
288#95—861no—
289#95—861no—
290#95—861no—
291#95—861no—
292#95—861no—
293#95—861no—
294C24D4×D4311yescharacteristic
295C2×Q8—861no—
296C2×Q8—861no—
297C2×Q8—1721no—
298C2×Q8—1721no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—431no—
305C22×C4—431no—
306C22×C4—431no—
307C22×C4—431no—
308C22×C4—861no—
309C22×C4—861no—
310C22×C4—1721no—
311C22×C4C2×C4×D4311yescharacteristic
312C22×C4C2×D17211yescharacteristic
313C22×C4#1062189811yescharacteristic
314C22×C4D4×D4311yescharacteristic
315C22×C4D4×D4311yescharacteristic
316C22×C4#1062190211yescharacteristic
317M16—41no—
318M16—41no—
319M16—1721no—
320M16—1721no—
321C2×C8—22no—
322C2×C8—862no—
323C4⋊C4—861no—
324C4⋊C4—861no—
325C4⋊C4—861no—
326C4⋊C4—861no—
327C4⋊C4—861no—
328C4⋊C4—861no—
329C4⋊C4—1722no—
330C4⋊C4—1722no—
331C4⋊C4—1721no—
332C4⋊C4—1721no—
333C22⋊C4—42no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—861no—
337C22⋊C4—861no—
338C22⋊C4—861no—
339C22⋊C4—861no—
340C22⋊C4—1721no—
341C22⋊C4—1721no—
342C22⋊C4—1721no—
343C22⋊C4—1721no—
344C42—41no—
345C42—41no—
346C42—861no—
347C42—861no—
348C42—861no—
349C42—861no—
350C23—21no—
351C23—21no—
352C23—41no—
353C23—41no—
354C23C22⋊C4×D4311yescharacteristic
355C23#1306329811yescharacteristic
356C23#1306330011yescharacteristic
357Q8—3441no—
358Q8—3441no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—861no—
377C2×C4—861no—
378C2×C4—861no—
379C2×C4—861no—
380C2×C4—3441no—
381C2×C4—3441no—
382C2×C4—3441no—
383C2×C4—1721no—
384C2×C4—1721no—
385C2×C4—1721no—
386C2×C4—1721no—
387C2×C4—1721no—
388C2×C4—1721no—
389C2×C4—1721no—
390C2×C4—1721no—
391C2×C4—1721no—
392C2×C4—1721no—
393C2×C4#1306328711yescharacteristic
394C2×C4C4×D17211yescharacteristic
395C2×C4#1306329511yescharacteristic
396C2×C4#1306331011yescharacteristic
397C8—42no—
398C8—1722no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—81no—
408C22—81no—
409C22#1458277711yescharacteristic
410C22#1458287111yescharacteristic
411C22#1458287111yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—21no—
416C4—42no—
417C4—81no—
418C4—161no—
419C4—3441no—
420C4—3441no—
421C4—1721no—
422C4—1721no—
423C4—1721no—
424C4—1721no—
425C4—6881no—
426C2—21no—
427C2—21no—
428C2—41no—
429C2—41no—
430C2#1913497711yescharacteristic
431C2#1913505211yescharacteristic
432C2#1913511611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1284C2
socleC22×C43#386
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#1284D43
hypocenterC43#9444
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
17. #14582805C4semidirect
18. #14582805C4semidirect
21. #14582769C4semidirect
22. #14582765C4semidirect
247. C43#9444semidirect

Maximal subgroups

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

subgroupindex
#191432302
#191390482
#191346702
#191331292
#191331272
#191324482
C43×#12842
#944443