Finite Group Databasebeta

← #24988206

Subgroups — #24988206

Order 11008.

1074 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C2×#14583554C211yesmaximal, characteristic
2#19134538C212yesmaximal, complemented
3C4×#13063240C211yesmaximal, characteristic, complemented
4#19133116C212yesmaximal, complemented
5C43×#1465C211yesmaximal, characteristic, complemented
6C22×#10621898C411yescharacteristic, complemented
7C22×#10621898C2211yescharacteristic
8#14583554—24no—
9#14583554—24no—
10C2×#13063325C411yescharacteristic, complemented
11C2×#13063307—21no—
12C2×#13063307—21no—
13C2×#13063304C411yescharacteristic, complemented
14C2×#13063304C2211yescharacteristic
15C2×#13063296—21no—
16C2×C4×D172C411yescharacteristic, complemented
17C2×C4⋊C4×D43—21no—
18C2×#13063251—24no—
19C2×#13063240—21no—
20C4×C22⋊Dic43C2212yes—
21#14582666—21no—
22#14582637—24no—
23C2×C4×D4×C43C2211yescharacteristic
24C43×#407C2212yes—
25C43×#324—21no—
26C43×#323—21no—
27C2×#10621898—22no—
28C2×#10621898—22no—
29C2×#10621898—22no—
30C2×#10621898—44no—
31C2×#10621898—44no—
32C2×#10621898D414yes—
33C22×Dic86C2×C411yescharacteristic
34C22×Dic86C2×C411yescharacteristic
35C22×D172C2×C411yescharacteristic
36C22×C22⋊D43—21no—
37C22×C22⋊D43—21no—
38C22×C4×D43—21no—
39C22×C4×D43—21no—
40C22×C4×D43—21no—
41#13063325—22no—
42#13063325—22no—
43#13063307—28no—
44#13063307—28no—
45#13063304—22no—
46#13063304—22no—
47#13063304—22no—
48#13063304D414yes—
49#13063296—28no—
50C4×D172—22no—
51C4×D172—22no—
52C2×C4⋊Dic43—21no—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43C2×C411yescharacteristic
55C2×Dic43⋊C4—21no—
56C2×Dic43⋊C4—21no—
57C4⋊C4×D43—28no—
58C2×C22⋊Dic43—21no—
59C2×C22⋊Dic43—21no—
60C2×C22⋊Dic43—22no—
61C2×(C2×D43)⋊C4—21no—
62C2×C4×Dic43—22no—
63#13063251—48no—
64#13063240—24no—
65C43⋊#95—22no—
66C22×D4×C43D411yescharacteristic
67C23×C4×C43C2×C411yescharacteristic
68C23×C4×C43C2311yescharacteristic
69C2×M16×C43—22no—
70C4×D4×C43—22no—
71C4×D4×C43—22no—
72C2×C4⋊C4×C43D411yescharacteristic
73C2×C22⋊C4×C43D411yescharacteristic
74C2×C22⋊C4×C43D411yescharacteristic
75C2×C42×C43C2×C411yescharacteristic
76C22⋊C8×C43—22no—
77C22⋊C8×C43—22no—
78C24×C43C22⋊C411yescharacteristic
79C24×C43C2×D411yescharacteristic
80C23×D43—21no—
81C2×D4×C43—22no—
82C2×D4×C43—22no—
83C2×D4×C43—41no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—42no—
87C22×C4×C43—42no—
88C22×C4×C43C22⋊C411yescharacteristic
89C22×C4×C43C22⋊C411yescharacteristic
90C22×C4×C43C22⋊C411yescharacteristic
91C22×C4×C43C22×C411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D412yes—
94C22×C4×C43C2×D412yes—
95C2×C22⋊D43—24no—
96C2×C22⋊D43—24no—
97C2×C22⋊D43—44no—
98C2×C22⋊D43—44no—
99C22×Dic43—21no—
100C22×Dic43—21no—
101C22×Dic43—21no—
102C22×Dic43—42no—
103#10621898—28no—
104#10621898—44no—
105#10621898—48no—
106#10621898—44no—
107#10621898—48no—
108#10621898—44no—
109C2×D172—21no—
110C2×D172—24no—
111C2×D172C22⋊C412yes—
112C2×C4×D43—24no—
113C2×C4×D43—24no—
114C2×C4×D43—24no—
115C2×C4×D43—44no—
116C2×C4×D43—44no—
117C2×C4×D43—42no—
118C2×C4×D43—42no—
119C2×Dic86—21no—
120C2×Dic86—21no—
121C2×Dic86—42no—
122C2×Dic86—42no—
123C2×Dic86C22⋊C412yes—
124C2×Dic86C22⋊C412yes—
125M16×C43—44no—
126C2×C8×C43—42no—
127C4⋊C4×C43—22no—
128C22⋊C4×C43—22no—
129C22⋊C4×C43—22no—
130C42×C43—21no—
131C42×C43—21no—
132C22⋊Dic43—24no—
133C22⋊Dic43—24no—
134C22⋊Dic43—24no—
135C22⋊Dic43—42no—
136(C2×D43)⋊C4—24no—
137C4⋊Dic43—24no—
138C4⋊Dic43—24no—
139C4⋊Dic43—21no—
140C4⋊Dic43C22⋊C412yes—
141Dic43⋊C4—24no—
142Dic43⋊C4—24no—
143C4×Dic43—44no—
144C23×C43—21no—
145C23×C43—21no—
146C23×C43—21no—
147C23×C43—21no—
148C23×C43—21no—
149C23×C43—41no—
150C23×C43—41no—
151C23×C43—41no—
152C23×C43—41no—
153C23×C43C2×C22⋊C411yescharacteristic
154C23×C43#12012yes—
155C22×D43—24no—
156C22×D43—22no—
157C22×D43—42no—
158C22×D43—41no—
159C22×D43—41no—
160D4×C43—44no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—24no—
164C2×C4×C43—22no—
165C2×C4×C43—21no—
166C2×C4×C43—21no—
167C2×C4×C43—41no—
168C2×C4×C43—42no—
169C2×C4×C43—42no—
170C2×C4×C43—42no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43#10412yescomplemented
174C2×C4×C43C2×C22⋊C411yescharacteristic
175C2×C4×C43C2×C22⋊C411yescharacteristic
176C2×C4×C43#12012yes—
177C22⋊D43—48no—
178C22⋊D43—48no—
179C2×Dic43—22no—
180C2×Dic43—22no—
181C2×Dic43—22no—
182C2×Dic43—42no—
183C2×Dic43—42no—
184C2×Dic43—41no—
185C2×Dic43—41no—
186C2×Dic43—44no—
187C2×Dic43—82no—
188C2×Dic43—82no—
189D172—24no—
190D172—22no—
191D172#9914yescomplemented
192C4×D43—48no—
193C4×D43—48no—
194C4×D43—48no—
195Dic86—24no—
196Dic86—42no—
197Dic86—42no—
198Dic86—42no—
199C8×C43—82no—
200#8364—431nomaximal, Sylow
201C22×C43—21no—
202C22×C43—21no—
203C22×C43—22no—
204C22×C43—22no—
205C22×C43—22no—
206C22×C43—41no—
207C22×C43—41no—
208C22×C43—41no—
209C22×C43—81no—
210C22×C43—81no—
211C22×C43—81no—
212C22×C43—81no—
213C22×C43#37911yescharacteristic
214C22×C43C2×#10411yescharacteristic
215C22×C43#42111yescharacteristic
216C2×D43—24no—
217C2×D43—44no—
218C2×D43—44no—
219C2×D43—42no—
220C2×D43—42no—
221C4×C43—22no—
222C4×C43—21no—
223C4×C43—22no—
224C4×C43—41no—
225C4×C43—41no—
226C4×C43C2×#9912yes—
227Dic43—42no—
228Dic43—42no—
229Dic43—42no—
230Dic43—84no—
231C2×#547—431no—
232#1789—432no—
233C4×#99—431no—
234#1508—432no—
235#1465D4311yescharacteristic, complemented
236C2×C43—21no—
237C2×C43—21no—
238C2×C43—42no—
239C2×C43—81no—
240C2×C43#178111yescharacteristic
241C2×C43#178911yescharacteristic
242C2×C43#179611yescharacteristic
243D43—44no—
244C22×#41—431no—
245C22×#41—431no—
246#547—864no—
247#547—864no—
248C2×C4⋊Q8—431no—
249C2×#123—861no—
250C2×#123—861no—
251C2×C22⋊Q8—431no—
252C2×C22⋊Q8—431no—
253C2×#121—861no—
254C2×C4×D4—431no—
255C2×C4×D4C2×D4311yescharacteristic
256C22×C4⋊C4—861no—
257C2×#104—864no—
258C2×#99—861no—
259#407C2×D4312yes—
260C4×C22⋊C4—432no—
261#342—861no—
262#328—864no—
263#324—21no—
264#323—21no—
265C43#836411yescharacteristic, complemented, Sylow
266C2×#41—434no—
267C2×#41—862no—
268C2×#41—862no—
269C2×#41—862no—
270C2×#41—1724no—
271C2×#41—1724no—
272C22×Q8—431no—
273C22×Q8—431no—
274C22×D4—431no—
275C22×D4—861no—
276C22×D4—861no—
277C22×D4D17211yescharacteristic
278C23×C4—861no—
279C23×C4—861no—
280C23×C4—861no—
281C23×C4C4×D4311yescharacteristic
282C23×C4C22×D4311yescharacteristic
283C2×M16—22no—
284C4⋊Q8—862no—
285C4⋊Q8—862no—
286#123—868no—
287#123—868no—
288C22⋊Q8—434no—
289C22⋊Q8—862no—
290C22⋊Q8—862no—
291C22⋊Q8—862no—
292#121—868no—
293C4×D4—22no—
294C4×D4—22no—
295C4×D4—862no—
296C4×D4—862no—
297C2×C4⋊C4—431no—
298C2×C4⋊C4—868no—
299C2×C4⋊C4—861no—
300C2×C4⋊C4—861no—
301C2×C4⋊C4—861no—
302C2×C4⋊C4—861no—
303C2×C4⋊C4C22⋊D4311yescharacteristic
304C2×C22⋊C4—861no—
305C2×C22⋊C4—861no—
306C2×C22⋊C4—861no—
307C2×C22⋊C4—862no—
308C2×C22⋊C4D17211yescharacteristic
309C2×C22⋊C4C22⋊D4311yescharacteristic
310C2×C42—862no—
311C2×C42C4×D4311yescharacteristic
312#104—1728no—
313#99—864no—
314C22⋊C8—22no—
315C22⋊C8—22no—
316#95—862no—
317C24—861no—
318C24(C2×D43)⋊C411yescharacteristic
319C24C2×D17211yescharacteristic
320#41—868no—
321#41—1724no—
322#41—1724no—
323#41—1728no—
324#41—1728no—
325#41—1724no—
326C2×Q8—432no—
327C2×Q8—432no—
328C2×Q8—861no—
329C2×Q8—861no—
330C2×Q8—1722no—
331C2×Q8—1722no—
332C2×D4—22no—
333C2×D4—22no—
334C2×D4—41no—
335C2×D4—432no—
336C2×D4—864no—
337C2×D4—864no—
338C2×D4—864no—
339C2×D4—861no—
340C2×D4—1724no—
341C2×D4—1724no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—864no—
347C22×C4—864no—
348C22×C4—861no—
349C22×C4—861no—
350C22×C4—861no—
351C22×C4—864no—
352C22×C4—1722no—
353C22×C4—1724no—
354C22×C4—1724no—
355C22×C4—1722no—
356C22×C4—1722no—
357C22×C4(C2×D43)⋊C411yescharacteristic
358C22×C4(C2×D43)⋊C411yescharacteristic
359C22×C4(C2×D43)⋊C411yescharacteristic
360C22×C4C2×C4×D4311yescharacteristic
361C22×C4D4×D4312yes—
362C22×C4D4×D4312yes—
363C22×C4C2×C22⋊D4311yescharacteristic
364M16—44no—
365C2×C8—42no—
366C4⋊C4—22no—
367C4⋊C4—432no—
368C4⋊C4—864no—
369C4⋊C4—864no—
370C4⋊C4—864no—
371C4⋊C4—861no—
372C4⋊C4—864no—
373C22⋊C4—22no—
374C22⋊C4—22no—
375C22⋊C4—864no—
376C22⋊C4—864no—
377C22⋊C4—864no—
378C22⋊C4—864no—
379C22⋊C4—1722no—
380C42—21no—
381C42—21no—
382C42—1724no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—864no—
393C23—862no—
394C23—1722no—
395C23—1721no—
396C23—1721no—
397C23C2×(C2×D43)⋊C411yescharacteristic
398C23#1306329512yes—
399Q8—864no—
400Q8—1722no—
401Q8—1722no—
402Q8—1722no—
403D4—44no—
404D4—434no—
405D4—864no—
406D4—862no—
407D4—1728no—
408D4—1728no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—24no—
412C2×C4—22no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—862no—
422C2×C4—862no—
423C2×C4—862no—
424C2×C4—3442no—
425C2×C4—3442no—
426C2×C4—1728no—
427C2×C4—1728no—
428C2×C4—1728no—
429C2×C4—1724no—
430C2×C4—1722no—
431C2×C4—1722no—
432C2×C4—1721no—
433C2×C4—1721no—
434C2×C4#1306325112yescomplemented
435C2×C4C22⋊C4×D4311yescharacteristic
436C2×C4C22⋊C4×D4311yescharacteristic
437C2×C4#1306329312yes—
438C8—82no—
439C22—21no—
440C22—21no—
441C22—22no—
442C22—22no—
443C22—22no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—864no—
452C22—1724no—
453C22—1724no—
454C22—1722no—
455C22—1722no—
456C22#1458275411yescharacteristic
457C22C2×#1306325111yescharacteristic
458C22#1458291511yescharacteristic
459C4—22no—
460C4—21no—
461C4—22no—
462C4—41no—
463C4—41no—
464C4—3444no—
465C4—1722no—
466C4—1722no—
467C4—1722no—
468C4#99×D4312yes—
469C2—21no—
470C2—21no—
471C2—42no—
472C2—81no—
473C2—1724no—
474C2#1913450811yescharacteristic
475C2#1913453811yescharacteristic
476C2#1913457111yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1465C2
socleC22×C43#379
prime radicalC2×#14583554C2
cosocleC23×C4×C43C23
hypercenter#1465D43
hypocenterC43#8364
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1465

Complements

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

NH ≅ G/Ntype
2. #19134538C2semidirect
3. C4×#13063240C2semidirect
4. #19133116C2semidirect
5. C43×#1465C2semidirect
6. C22×#10621898C4semidirect
10. C2×#13063325C4semidirect
13. C2×#13063304C4semidirect
16. C2×C4×D172C4semidirect
173. C2×C4×C43#104semidirect
191. D172#99semidirect
235. #1465D43semidirect
265. C43#8364semidirect
434. C2×C4#13063251semidirect

Maximal subgroups

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

subgroupindex
C2×#145835542
#191345382
C4×#130632402
#191331162
C43×#14652
#836443