Finite Group Databasebeta

← #24994250

Subgroups — #24994250

Order 11008.

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

normal subgroups only

This group has 516 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, complemented
2#19139057C211yesmaximal, characteristic
3#19134670C211yesmaximal, characteristic, complemented
4#19133125C211yesmaximal, characteristic
5#19133123C211yesmaximal, characteristic
6#19132448C211yesmaximal, characteristic, complemented
7C43×#1284C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9C2×#13063284C2211yescharacteristic
10#14582957—22no—
11#14582957—22no—
12#14582922—21no—
13#14582863C2211yescharacteristic
14M16×Dic43—21no—
15#14582815—21no—
16#14582815—21no—
17#14582801C411yescharacteristic, complemented
18#14582801C411yescharacteristic, complemented
19#14582791—21no—
20#14582791—21no—
21#14582769C411yescharacteristic, complemented
22#14582765C411yescharacteristic, complemented
23#14582762C2211yescharacteristic
24#14582665—21no—
25#14582665—21no—
26#14582634—22no—
27#14582632—22no—
28C43×#407C2211yescharacteristic
29C43×#381C2211yescharacteristic
30C4×C22⋊C4×C43C2211yescharacteristic
31C22×D172C2×C411yescharacteristic
32C22×C22⋊D43—21no—
33C2×#10621877—21no—
34#13063299—21no—
35#13063299—21no—
36#13063299—21no—
37#13063299—21no—
38#13063284—21no—
39#13063284—21no—
40#13063284—21no—
41#13063284—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43—21no—
44C2×C4⋊Dic43C2×C411yescharacteristic
45C2×C4⋊Dic43C2×C411yescharacteristic
46C2×C4⋊Dic43C2×C411yescharacteristic
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43D411yescharacteristic
49C2×C22⋊Dic43D411yescharacteristic
50C2×(C2×D43)⋊C4—21no—
51C2×(C2×D43)⋊C4—21no—
52C2×(C2×D43)⋊C4—21no—
53C2×(C2×D43)⋊C4—21no—
54C2×(C2×D43)⋊C4—21no—
55C2×C4×Dic43D411yescharacteristic
56C2×C4×Dic43D411yescharacteristic
57Dic43⋊C8—24no—
58C22⋊(C43⋊C8)—21no—
59C22⋊(C43⋊C8)D412yes—
60#13063235—22no—
61C8×Dic43—22no—
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
78C23×D43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43—41no—
82C22×C4×C43—41no—
83C22×C4×C43—41no—
84C22×C4×C43C22×C411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43#4111yescharacteristic
89C22×C4×C43#4111yescharacteristic
90C2×C22⋊D43—41no—
91C2×C22⋊D43—41no—
92C2×C22⋊D43—81no—
93C2×C22⋊D43—81no—
94C22×Dic43—21no—
95C22×Dic43—41no—
96C22×Dic43C22⋊C411yescharacteristic
97C22×Dic43C22⋊C411yescharacteristic
98C22×Dic43C22⋊C411yescharacteristic
99C22×Dic43C22⋊C411yescharacteristic
100C2×D172—21no—
101C2×D172—21no—
102C2×D172—41no—
103C2×D172—41no—
104M16×C43—41no—
105M16×C43—41no—
106C2×C8×C43—22no—
107C22⋊C4×C43—41no—
108C22⋊C4×C43—41no—
109C22⋊C4×C43—42no—
110C42×C43—41no—
111C42×C43—41no—
112C22⋊Dic43—21no—
113C22⋊Dic43—21no—
114C22⋊Dic43—21no—
115C22⋊Dic43—21no—
116C22⋊Dic43—41no—
117C22⋊Dic43—41no—
118(C2×D43)⋊C4—42no—
119(C2×D43)⋊C4—42no—
120(C2×D43)⋊C4—41no—
121(C2×D43)⋊C4—41no—
122(C2×D43)⋊C4—81no—
123(C2×D43)⋊C4—81no—
124C4⋊Dic43—21no—
125C4⋊Dic43—21no—
126C4⋊Dic43—21no—
127C4⋊Dic43—21no—
128C4⋊Dic43—21no—
129C4⋊Dic43—21no—
130C4⋊Dic43—81no—
131C4⋊Dic43—81no—
132C4×Dic43—21no—
133C4×Dic43—21no—
134C4×Dic43—21no—
135C4×Dic43—21no—
136#10621877—41no—
137#10621877—41no—
138C2×C43⋊C8—22no—
139C23×C43—21no—
140C23×C43—21no—
141C23×C43—41no—
142C23×C43—41no—
143C23×C43C2×C22⋊C411yescharacteristic
144C23×C43#12111yescharacteristic
145C23×C43#12111yescharacteristic
146C22×D43—41no—
147C22×D43—41no—
148C22×D43—41no—
149C22×D43—41no—
150C22×D43—41no—
151C22×D43—41no—
152C22×D43—41no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43—22no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—81no—
168C2×C4×C43—81no—
169C2×C4×C43—81no—
170C2×C4×C43C4×D411yescharacteristic
171C2×C4×C43C4×D411yescharacteristic
172C2×C4×C43#12011yescharacteristic
173C2×C4×C43#12311yescharacteristic
174C22⋊D43—82no—
175C22⋊D43—82no—
176C2×Dic43—21no—
177C2×Dic43—21no—
178C2×Dic43—21no—
179C2×Dic43—21no—
180C2×Dic43—41no—
181C2×Dic43—41no—
182C2×Dic43—41no—
183C2×Dic43—41no—
184C2×Dic43—41no—
185C2×Dic43—41no—
186C2×Dic43—41no—
187C2×Dic43—81no—
188C2×Dic43—81no—
189C2×Dic43—81no—
190D172—81no—
191D172—81no—
192C8×C43—42no—
193C43⋊C8—42no—
194#9446—431nomaximal, Sylow
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—21no—
200C22×C43—21no—
201C22×C43—21no—
202C22×C43—21no—
203C22×C43—81no—
204C22×C43—81no—
205C22×C43#38611yescharacteristic
206C22×C43#41011yescharacteristic
207C22×C43#41011yescharacteristic
208C2×D43—81no—
209C2×D43—81no—
210C2×D43—81no—
211C2×D43—81no—
212C2×D43—81no—
213C2×D43—81no—
214C2×D43—81no—
215C4×C43—21no—
216C4×C43—21no—
217C4×C43—21no—
218C4×C43—21no—
219C4×C43—42no—
220C4×C43—81no—
221C4×C43—161no—
222Dic43—41no—
223Dic43—41no—
224Dic43—41no—
225Dic43—41no—
226Dic43—81no—
227Dic43—161no—
228#2921—431no—
229#2500—431no—
230#1820—431no—
231#1510—431no—
232#1510—431no—
233#1284—431no—
234#1284D4311yescharacteristic, complemented
235C2×C43—21no—
236C2×C43—21no—
237C2×C43—41no—
238C2×C43—41no—
239C2×C43#188411yescharacteristic
240C2×C43#189911yescharacteristic
241C2×C43#191011yescharacteristic
242D43—161no—
243C2×#121—431no—
244C2×#117—431no—
245#433—862no—
246#433—862no—
247#423—861no—
248#407—431no—
249#407C2×D4311yescharacteristic
250C4×M16—861no—
251#394—861no—
252#394—861no—
253#390—431no—
254#390—431no—
255#388—861no—
256#388—861no—
257#384—431no—
258#382—431no—
259#381—431no—
260#381C2×D4311yescharacteristic
261C4×C22⋊C4C2×D4311yescharacteristic
262#342—861no—
263#342—861no—
264#327—862no—
265#327—862no—
266C43#944611yescharacteristic, complemented, Sylow
267C22×D4—431no—
268C22×D4—861no—
269C23×C4C22×D4311yescharacteristic
270C2×M16—21no—
271C2×M16—861no—
272#121—861no—
273#121—861no—
274#121—861no—
275#121—861no—
276#117—861no—
277#117—861no—
278#117—861no—
279#117—861no—
280C2×C4⋊C4—431no—
281C2×C4⋊C4—431no—
282C2×C4⋊C4—431no—
283C2×C4⋊C4—861no—
284C2×C4⋊C4—861no—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—431no—
288C2×C22⋊C4—431no—
289C2×C22⋊C4—861no—
290C2×C22⋊C4—861no—
291C2×C22⋊C4—861no—
292C2×C22⋊C4—861no—
293C2×C22⋊C4—861no—
294C2×C22⋊C4—861no—
295C2×C42—431no—
296C2×C42—431no—
297C2×C42C4×D4311yescharacteristic
298C2×C42C4×D4311yescharacteristic
299C4⋊C8—864no—
300C22⋊C8—21no—
301C22⋊C8—432no—
302C22⋊C8—861no—
303C22⋊C8D17212yes—
304#97—862no—
305C4×C8—862no—
306#95—21no—
307#95—21no—
308#95—21no—
309#95—861no—
310#95—861no—
311#95—861no—
312#95—861no—
313C24—861no—
314C24D4×D4311yescharacteristic
315C2×D4—861no—
316C2×D4—861no—
317C2×D4—3441no—
318C2×D4—3441no—
319C2×D4—1721no—
320C2×D4—1721no—
321C2×D4—1721no—
322C2×D4—1721no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—431no—
329C22×C4—431no—
330C22×C4—431no—
331C22×C4—431no—
332C22×C4—861no—
333C22×C4—1721no—
334C22×C4C2×C4×D4311yescharacteristic
335C22×C4C2×D17211yescharacteristic
336C22×C4#1062189811yescharacteristic
337C22×C4D4×D4311yescharacteristic
338C22×C4D4×D4311yescharacteristic
339C22×C4#1062190211yescharacteristic
340M16—41no—
341M16—41no—
342M16—1721no—
343M16—1721no—
344C2×C8—22no—
345C2×C8—862no—
346C4⋊C4—861no—
347C4⋊C4—861no—
348C4⋊C4—861no—
349C4⋊C4—861no—
350C4⋊C4—861no—
351C4⋊C4—861no—
352C4⋊C4—3441no—
353C4⋊C4—3441no—
354C22⋊C4—42no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—861no—
358C22⋊C4—861no—
359C22⋊C4—861no—
360C22⋊C4—861no—
361C22⋊C4—3441no—
362C22⋊C4—3441no—
363C22⋊C4—1722no—
364C22⋊C4—1722no—
365C22⋊C4—1721no—
366C22⋊C4—1721no—
367C22⋊C4—1721no—
368C22⋊C4—1721no—
369C42—41no—
370C42—41no—
371C42—861no—
372C42—861no—
373C42—861no—
374C42—861no—
375C23—21no—
376C23—21no—
377C23—41no—
378C23—41no—
379C23—1721no—
380C23—1721no—
381C23—1721no—
382C23—1721no—
383C23—1721no—
384C23—1721no—
385C23—1721no—
386C23C22⋊C4×D4311yescharacteristic
387C23#1306329811yescharacteristic
388C23#1306330011yescharacteristic
389D4—3441no—
390D4—3441no—
391D4—3442no—
392D4—3442no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4—861no—
411C2×C4—861no—
412C2×C4—861no—
413C2×C4—861no—
414C2×C4—3441no—
415C2×C4—3441no—
416C2×C4—3441no—
417C2×C4—1721no—
418C2×C4—1721no—
419C2×C4—1721no—
420C2×C4—1721no—
421C2×C4—1721no—
422C2×C4—1721no—
423C2×C4—1721no—
424C2×C4#1306328711yescharacteristic
425C2×C4C4×D17211yescharacteristic
426C2×C4#1306329511yescharacteristic
427C2×C4#1306331011yescharacteristic
428C8—42no—
429C8—1722no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—81no—
439C22—81no—
440C22—3441no—
441C22—3441no—
442C22—3441no—
443C22—3441no—
444C22—3441no—
445C22—3441no—
446C22—3441no—
447C22#1458277711yescharacteristic
448C22#1458287111yescharacteristic
449C22#1458287111yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—42no—
455C4—81no—
456C4—161no—
457C4—3441no—
458C4—1721no—
459C4—1721no—
460C4—1721no—
461C4—1721no—
462C4—6881no—
463C2—21no—
464C2—21no—
465C2—41no—
466C2—41no—
467C2—6881no—
468C2#1913497711yescharacteristic
469C2#1913505211yescharacteristic
470C2#1913512111yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1284C2
socleC22×C43#386
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1284D43
hypocenterC43#9446
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
1. #19143230C2semidirect
3. #19134670C2semidirect
6. #19132448C2semidirect
7. C43×#1284C2semidirect
17. #14582801C4semidirect
18. #14582801C4semidirect
21. #14582769C4semidirect
22. #14582765C4semidirect
234. #1284D43semidirect
266. C43#9446semidirect

Maximal subgroups

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

subgroupindex
#191432302
#191390572
#191346702
#191331252
#191331232
#191324482
C43×#12842
#944643