Finite Group Databasebeta

← #24987946

Subgroups — #24987946

Order 11008.

1154 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C22×#13063311C211yesmaximal, characteristic
2#19134661C212yesmaximal, complemented
3C2×#14582623C211yesmaximal, characteristic, complemented
4C2×#14582622C212yesmaximal, complemented
5C2×C43×#323C211yesmaximal, characteristic, complemented
6C23×Dic86C411yescharacteristic
7C23×C22⋊D43C411yescharacteristic
8C2×#13063311—24no—
9C2×#13063311—24no—
10C2×#13063311—22no—
11C2×#13063311—22no—
12C22×C22⋊Dic43C411yescharacteristic
13C22×(C2×D43)⋊C4C411yescharacteristic
14C22×(C2×D43)⋊C4C2211yescharacteristic
15C22×C4×Dic43C2211yescharacteristic
16C2×C22⋊(C43⋊C8)C2212yes—
17#14582653—24no—
18#14582623—22no—
19#14582622—24no—
20C22×C22⋊C4×C43C2211yescharacteristic
21C2×C22⋊C8×C43C2212yes—
22C43×#323—22no—
23C24×D43C2×C411yescharacteristic
24C22×Dic86—22no—
25C22×Dic86—22no—
26C22×Dic86—22no—
27C22×Dic86—44no—
28C22×C22⋊D43—22no—
29C22×C22⋊D43—22no—
30C22×C22⋊D43—22no—
31C22×C22⋊D43—44no—
32C23×Dic43C2×C411yescharacteristic
33C23×Dic43C2×C411yescharacteristic
34C23×Dic43C2×C411yescharacteristic
35C22×C43⋊C8—22no—
36#13063311—216no—
37#13063311—216no—
38C2×C22⋊Dic43—22no—
39C2×C22⋊Dic43—22no—
40C2×C22⋊Dic43—22no—
41C2×(C2×D43)⋊C4—22no—
42C2×(C2×D43)⋊C4—22no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—22no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—22no—
47C2×(C2×D43)⋊C4D414yes—
48C2×C4×Dic43—21no—
49C2×C4×Dic43—22no—
50C2×C4×Dic43—21no—
51C2×C4×Dic43D414yes—
52C22⋊(C43⋊C8)—22no—
53C22⋊(C43⋊C8)—22no—
54C25×C43C2×C411yescharacteristic
55C23×C4×C43C2×C411yescharacteristic
56C23×C4×C43C2311yescharacteristic
57C22×C8×C43—22no—
58C2×C22⋊C4×C43—22no—
59C2×C22⋊C4×C43—22no—
60C2×C22⋊C4×C43D412yes—
61C2×C22⋊C4×C43D412yes—
62C22⋊C8×C43—22no—
63C22⋊C8×C43—22no—
64C24×C43—21no—
65C24×C43—21no—
66C24×C43—22no—
67C24×C43—22no—
68C24×C43—42no—
69C24×C43—42no—
70C24×C43C22⋊C412yes—
71C24×C43C22×C411yescharacteristic
72C23×D43—21no—
73C23×D43—21no—
74C23×D43—22no—
75C23×D43—22no—
76C23×D43—42no—
77C23×D43—42no—
78C23×D43C22⋊C412yes—
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43—42no—
82C22×C4×C43—42no—
83C22×C4×C43C22⋊C412yes—
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D412yes—
86C22×C4×C43C2×D412yes—
87C22×C4×C43C2×D411yescharacteristic
88C2×C22⋊D43—28no—
89C2×C22⋊D43—48no—
90C2×C22⋊D43—44no—
91C2×C22⋊D43—48no—
92C2×C22⋊D43—44no—
93C22×Dic43—24no—
94C22×Dic43—21no—
95C22×Dic43—21no—
96C22×Dic43—21no—
97C22×Dic43—21no—
98C22×Dic43—21no—
99C22×Dic43—21no—
100C22×Dic43—22no—
101C22×Dic43—22no—
102C22×Dic43—42no—
103C22×Dic43C22⋊C412yes—
104C22×Dic43C22⋊C412yes—
105C22×Dic43C22⋊C412yes—
106C2×Dic86—28no—
107C2×Dic86—48no—
108C2×Dic86—48no—
109C2×Dic86—44no—
110C2×Dic86—44no—
111C2×C8×C43—44no—
112C2×C8×C43—42no—
113C22⋊C4×C43—24no—
114C22⋊C4×C43—24no—
115C22⋊Dic43—28no—
116(C2×D43)⋊C4—28no—
117(C2×D43)⋊C4—24no—
118(C2×D43)⋊C4—24no—
119C4×Dic43—24no—
120C4×Dic43—24no—
121C2×C43⋊C8—44no—
122C2×C43⋊C8—42no—
123C23×C43—22no—
124C23×C43—22no—
125C23×C43—22no—
126C23×C43—22no—
127C23×C43—22no—
128C23×C43—42no—
129C23×C43—42no—
130C23×C43—42no—
131C23×C43—42no—
132C23×C43—42no—
133C23×C43—42no—
134C23×C43—42no—
135C23×C43—42no—
136C23×C43—84no—
137C23×C43—84no—
138C23×C43C2×C22⋊C411yescharacteristic
139C23×C43C2×C22⋊C411yescharacteristic
140C23×C43C2×C22⋊C411yescharacteristic
141C23×C43#13112yes—
142C23×C43#13112yes—
143C22×D43—22no—
144C22×D43—24no—
145C22×D43—42no—
146C22×D43—42no—
147C22×D43—42no—
148C22×D43—41no—
149C22×D43—41no—
150C22×D43—42no—
151C22×D43—42no—
152C22×D43—42no—
153C22×D43—42no—
154C22×D43—84no—
155C22×D43—84no—
156C2×C4×C43—24no—
157C2×C4×C43—22no—
158C2×C4×C43—41no—
159C2×C4×C43—42no—
160C2×C4×C43—41no—
161C2×C4×C43—42no—
162C2×C4×C43—42no—
163C2×C4×C43—42no—
164C2×C4×C43#12012yes—
165C2×C4×C43#12012yes—
166C22⋊D43—416no—
167C2×Dic43—24no—
168C2×Dic43—24no—
169C2×Dic43—22no—
170C2×Dic43—22no—
171C2×Dic43—22no—
172C2×Dic43—22no—
173C2×Dic43—24no—
174C2×Dic43—42no—
175C2×Dic43—42no—
176C2×Dic43—41no—
177C2×Dic43—41no—
178C2×Dic43—42no—
179C2×Dic43—42no—
180C2×Dic43#10014yes—
181Dic86—416no—
182C8×C43—82no—
183C43⋊C8—82no—
184#8305—431nomaximal, Sylow
185C22×C43—24no—
186C22×C43—24no—
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—42no—
192C22×C43—42no—
193C22×C43—42no—
194C22×C43—82no—
195C22×C43—82no—
196C22×C43—84no—
197C22×C43—84no—
198C22×C43#37911yescharacteristic
199C22×C43#40812yes—
200C22×C43#40812yes—
201C22×C43#40811yescharacteristic
202C22×C43#40811yescharacteristic
203C22×C43#41012yes—
204C22×C43C2×#10012yes—
205C2×D43—42no—
206C2×D43—42no—
207C2×D43—42no—
208C2×D43—82no—
209C2×D43—82no—
210C2×D43—84no—
211C2×D43—84no—
212C4×C43—22no—
213C4×C43—22no—
214C4×C43—42no—
215Dic43—24no—
216Dic43—42no—
217Dic43—42no—
218C22×#124—431no—
219#1817—432no—
220C2×#323—432no—
221C2×#323—431no—
222C2×#323D4311yescharacteristic, complemented
223C2×C43—22no—
224C2×C43—21no—
225C2×C43—21no—
226C2×C43—82no—
227C2×C43#146914yes—
228C2×C43#178011yescharacteristic
229C2×C43#178211yescharacteristic
230C2×C43#178311yescharacteristic
231D43—82no—
232C23×Q8—431no—
233C23×D4—431no—
234C2×#124—864no—
235C2×#124—864no—
236C2×#124—862no—
237C2×#124—862no—
238C22×C22⋊C4—431no—
239C22×C22⋊C4—431no—
240C22×C22⋊C4—431no—
241C22×C22⋊C4C2×D4311yescharacteristic
242C22×C42—431no—
243C2×C22⋊C8—432no—
244C2×C22⋊C8C2×D4312yes—
245#336—864no—
246#323—22no—
247#323—864no—
248#323—862no—
249C43#830511yescharacteristic, complemented, Sylow
250C25—431no—
251C25C4×D4311yescharacteristic
252C22×Q8—862no—
253C22×Q8—862no—
254C22×Q8—862no—
255C22×Q8—1724no—
256C22×D4—862no—
257C22×D4—862no—
258C22×D4—862no—
259C22×D4—1724no—
260C23×C4—431no—
261C23×C4—431no—
262C23×C4—431no—
263C23×C4C4×D4311yescharacteristic
264C23×C4C22×D4311yescharacteristic
265C22×C8—22no—
266C22×C8—862no—
267#124—8616no—
268#124—8616no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—434no—
272C2×C22⋊C4—862no—
273C2×C22⋊C4—862no—
274C2×C22⋊C4—862no—
275C2×C22⋊C4—862no—
276C2×C22⋊C4—862no—
277C2×C22⋊C4—862no—
278C2×C22⋊C4—861no—
279C2×C22⋊C4—862no—
280C2×C22⋊C4—861no—
281C2×C22⋊C4D17212yes—
282C2×C22⋊C4C22⋊D4312yes—
283C2×C42—434no—
284C2×C42—861no—
285C2×C42—862no—
286C2×C42—861no—
287C22⋊C8—22no—
288C22⋊C8—22no—
289C22⋊C8—862no—
290C22⋊C8—862no—
291C24—21no—
292C24—21no—
293C24—22no—
294C24—22no—
295C24—42no—
296C24—42no—
297C24—432no—
298C24—862no—
299C24—862no—
300C24—861no—
301C24—861no—
302C24—1722no—
303C24—1722no—
304C24(C2×D43)⋊C412yes—
305C24C2×C4×D4311yescharacteristic
306C2×Q8—868no—
307C2×Q8—1724no—
308C2×Q8—1728no—
309C2×Q8—1724no—
310C2×Q8—1728no—
311C2×D4—868no—
312C2×D4—1724no—
313C2×D4—1728no—
314C2×D4—1728no—
315C2×D4—1724no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—432no—
321C22×C4—432no—
322C22×C4—432no—
323C22×C4—864no—
324C22×C4—861no—
325C22×C4—861no—
326C22×C4—861no—
327C22×C4—861no—
328C22×C4—861no—
329C22×C4—861no—
330C22×C4—862no—
331C22×C4—862no—
332C22×C4—1722no—
333C22×C4(C2×D43)⋊C412yes—
334C22×C4C2×D17211yescharacteristic
335C22×C4D4×D4312yes—
336C22×C4D4×D4312yes—
337C22×C4C2×C22⋊D4311yescharacteristic
338C2×C8—44no—
339C2×C8—42no—
340C2×C8—1724no—
341C2×C8—1722no—
342C22⋊C4—24no—
343C22⋊C4—24no—
344C22⋊C4—868no—
345C22⋊C4—868no—
346C22⋊C4—864no—
347C22⋊C4—864no—
348C42—864no—
349C42—864no—
350C23—22no—
351C23—22no—
352C23—22no—
353C23—22no—
354C23—22no—
355C23—42no—
356C23—42no—
357C23—42no—
358C23—42no—
359C23—42no—
360C23—42no—
361C23—42no—
362C23—42no—
363C23—84no—
364C23—84no—
365C23—864no—
366C23—862no—
367C23—3444no—
368C23—3444no—
369C23—1722no—
370C23—1722no—
371C23—1722no—
372C23—1722no—
373C23—1722no—
374C23—1721no—
375C23—1721no—
376C23—1722no—
377C23—1722no—
378C23C22⋊C4×D4311yescharacteristic
379C23C22⋊C4×D4311yescharacteristic
380C23C2×(C2×D43)⋊C411yescharacteristic
381C23#1306333112yes—
382C23#1306333312yes—
383Q8—17216no—
384D4—17216no—
385C2×C4—24no—
386C2×C4—22no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—434no—
394C2×C4—864no—
395C2×C4—864no—
396C2×C4—862no—
397C2×C4—862no—
398C2×C4—864no—
399C2×C4—862no—
400C2×C4—862no—
401C2×C4—1722no—
402C2×C4—1722no—
403C2×C4—1721no—
404C2×C4—1721no—
405C2×C4—1722no—
406C2×C4—1722no—
407C2×C4#1306329312yes—
408C2×C4#1306329512yes—
409C8—82no—
410C8—3442no—
411C22—24no—
412C22—24no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—42no—
418C22—42no—
419C22—42no—
420C22—82no—
421C22—82no—
422C22—84no—
423C22—84no—
424C22—3444no—
425C22—3442no—
426C22—3442no—
427C22—3444no—
428C22—1722no—
429C22—1722no—
430C22—1722no—
431C22#1458275411yescharacteristic
432C22#1458286412yes—
433C22#1458286412yes—
434C22#1458286511yescharacteristic
435C22#1458286711yescharacteristic
436C22#1458287112yes—
437C22#100×D4312yes—
438C4—22no—
439C4—22no—
440C4—42no—
441C4—864no—
442C4—1722no—
443C4—1722no—
444C2—22no—
445C2—21no—
446C2—21no—
447C2—82no—
448C2—3442no—
449C2#1913294514yes—
450C2#1913450611yescharacteristic
451C2#1913451111yescharacteristic
452C2#1913451411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#323C2
socleC23×C43C2×C22⋊C4
prime radicalC23×C22⋊D43C4
cosocleC23×C4×C43C23
hypercenterC2×#323D43
hypocenterC43#8305
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. #19134661C2semidirect
3. C2×#14582623C2semidirect
4. C2×#14582622C2semidirect
5. C2×C43×#323C2semidirect
222. C2×#323D43semidirect
249. C43#8305semidirect

Maximal subgroups

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

subgroupindex
C22×#130633112
#191346612
C2×#145826232
C2×#145826222
C2×C43×#3232
#830543