Finite Group Databasebeta

← #24987942

Subgroups — #24987942

Order 11008.

1238 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 1238 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×#13063307C211yesmaximal, characteristic
2#19134504C212yesmaximal, complemented
3C2×#14582624C212yesmaximal, complemented
4C2×#14582623C211yesmaximal, characteristic, complemented
5C2×C43×#323C211yesmaximal, characteristic, complemented
6C23×C22⋊D43C411yescharacteristic
7C23×C4×D43C2211yescharacteristic
8C2×#13063307—24no—
9C2×#13063307—24no—
10C2×#13063307—22no—
11C2×#13063307—22no—
12C22×C4⋊Dic43C411yescharacteristic
13C22×Dic43⋊C4C2211yescharacteristic
14C22×C22⋊Dic43C411yescharacteristic
15C22×(C2×D43)⋊C4C411yescharacteristic
16C2×C22⋊(C43⋊C8)C2212yes—
17C2×(C2×D43)⋊C8—24no—
18#14582624—24no—
19#14582623—22no—
20C22×C22⋊C4×C43C2211yescharacteristic
21C2×C22⋊C8×C43C2212yes—
22C43×#323—22no—
23C24×D43C2×C411yescharacteristic
24C22×C22⋊D43—22no—
25C22×C22⋊D43—22no—
26C22×C22⋊D43—22no—
27C22×C22⋊D43—44no—
28C23×Dic43C2×C411yescharacteristic
29C23×Dic43C2×C411yescharacteristic
30C23×Dic43C2×C411yescharacteristic
31C22×C4×D43—21no—
32C22×C4×D43—22no—
33C22×C4×D43—21no—
34C22×C4×D43—44no—
35C22×C4×D43D414yes—
36C22×C43⋊C8—22no—
37#13063307—216no—
38#13063307—216no—
39C2×C4⋊Dic43—22no—
40C2×C4⋊Dic43—22no—
41C2×C4⋊Dic43—22no—
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4—22no—
44C2×Dic43⋊C4—21no—
45C2×Dic43⋊C4D414yes—
46C2×C22⋊Dic43—22no—
47C2×C22⋊Dic43—22no—
48C2×C22⋊Dic43—22no—
49C2×(C2×D43)⋊C4—22no—
50C2×(C2×D43)⋊C4—22no—
51C2×(C2×D43)⋊C4—22no—
52C22⋊(C43⋊C8)—22no—
53C22⋊(C43⋊C8)—22no—
54(C2×D43)⋊C8—48no—
55C25×C43C2×C411yescharacteristic
56C23×C4×C43C2×C411yescharacteristic
57C23×C4×C43C2311yescharacteristic
58C22×C8×C43—22no—
59C2×C22⋊C4×C43—22no—
60C2×C22⋊C4×C43—22no—
61C2×C22⋊C4×C43D412yes—
62C2×C22⋊C4×C43D412yes—
63C22⋊C8×C43—22no—
64C22⋊C8×C43—22no—
65C24×C43—21no—
66C24×C43—21no—
67C24×C43—22no—
68C24×C43—22no—
69C24×C43—42no—
70C24×C43—42no—
71C24×C43C22⋊C412yes—
72C24×C43C22×C411yescharacteristic
73C23×D43—21no—
74C23×D43—21no—
75C23×D43—24no—
76C23×D43—22no—
77C23×D43—22no—
78C23×D43—42no—
79C23×D43C22⋊C412yes—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—42no—
83C22×C4×C43—42no—
84C22×C4×C43C22⋊C412yes—
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D412yes—
87C22×C4×C43C2×D412yes—
88C22×C4×C43C2×D411yescharacteristic
89C2×C22⋊D43—28no—
90C2×C22⋊D43—48no—
91C2×C22⋊D43—48no—
92C2×C22⋊D43—44no—
93C2×C22⋊D43—44no—
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×Dic43—42no—
104C22×Dic43C22⋊C412yes—
105C22×Dic43C22⋊C412yes—
106C22×Dic43C22⋊C412yes—
107C2×C4×D43—24no—
108C2×C4×D43—24no—
109C2×C4×D43—28no—
110C2×C4×D43—44no—
111C2×C4×D43—44no—
112C2×C4×D43—48no—
113C2×C4×D43—44no—
114C2×C8×C43—44no—
115C2×C8×C43—42no—
116C22⋊C4×C43—24no—
117C22⋊C4×C43—24no—
118C22⋊Dic43—28no—
119(C2×D43)⋊C4—28no—
120C4⋊Dic43—28no—
121Dic43⋊C4—24no—
122Dic43⋊C4—24no—
123C2×C43⋊C8—44no—
124C2×C43⋊C8—42no—
125C23×C43—22no—
126C23×C43—22no—
127C23×C43—22no—
128C23×C43—22no—
129C23×C43—22no—
130C23×C43—42no—
131C23×C43—42no—
132C23×C43—42no—
133C23×C43—42no—
134C23×C43—42no—
135C23×C43—42no—
136C23×C43—42no—
137C23×C43—42no—
138C23×C43—84no—
139C23×C43—84no—
140C23×C43C2×C22⋊C411yescharacteristic
141C23×C43C2×C22⋊C411yescharacteristic
142C23×C43C2×C22⋊C411yescharacteristic
143C23×C43#13112yes—
144C23×C43#13112yes—
145C22×D43—24no—
146C22×D43—24no—
147C22×D43—22no—
148C22×D43—24no—
149C22×D43—22no—
150C22×D43—24no—
151C22×D43—48no—
152C22×D43—48no—
153C22×D43—42no—
154C22×D43—42no—
155C22×D43—42no—
156C22×D43—41no—
157C22×D43—41no—
158C22×D43#9914yes—
159C2×C4×C43—24no—
160C2×C4×C43—22no—
161C2×C4×C43—41no—
162C2×C4×C43—42no—
163C2×C4×C43—41no—
164C2×C4×C43—42no—
165C2×C4×C43—42no—
166C2×C4×C43—42no—
167C2×C4×C43#12012yes—
168C2×C4×C43#12012yes—
169C22⋊D43—416no—
170C2×Dic43—22no—
171C2×Dic43—22no—
172C2×Dic43—22no—
173C2×Dic43—24no—
174C2×Dic43—24no—
175C2×Dic43—42no—
176C2×Dic43—42no—
177C2×Dic43—42no—
178C2×Dic43—42no—
179C2×Dic43—41no—
180C2×Dic43—41no—
181C2×Dic43—42no—
182C2×Dic43—42no—
183C4×D43—48no—
184C4×D43—48no—
185C8×C43—82no—
186C43⋊C8—82no—
187#8304—431nomaximal, Sylow
188C22×C43—24no—
189C22×C43—24no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—42no—
195C22×C43—42no—
196C22×C43—42no—
197C22×C43—82no—
198C22×C43—82no—
199C22×C43—84no—
200C22×C43—84no—
201C22×C43#37911yescharacteristic
202C22×C43#40812yes—
203C22×C43#40812yes—
204C22×C43#40811yescharacteristic
205C22×C43#40811yescharacteristic
206C22×C43C2×#9912yes—
207C22×C43#41312yes—
208C2×D43—28no—
209C2×D43—24no—
210C2×D43—48no—
211C2×D43—44no—
212C2×D43—44no—
213C2×D43—44no—
214C2×D43—42no—
215C2×D43—42no—
216C4×C43—22no—
217C4×C43—22no—
218C4×C43—42no—
219Dic43—42no—
220Dic43—42no—
221Dic43—42no—
222C22×#123—431no—
223#1779—432no—
224C2×#324—432no—
225C2×#323—431no—
226C2×#323D4311yescharacteristic, complemented
227C2×C43—22no—
228C2×C43—21no—
229C2×C43—21no—
230C2×C43—82no—
231C2×C43#146814yes—
232C2×C43#178011yescharacteristic
233C2×C43#178111yescharacteristic
234C2×C43#178511yescharacteristic
235D43—44no—
236C23×D4—431no—
237C24×C4—431no—
238C2×#123—864no—
239C2×#123—864no—
240C2×#123—862no—
241C2×#123—862no—
242C22×C4⋊C4—431no—
243C22×C4⋊C4—431no—
244C22×C22⋊C4—431no—
245C22×C22⋊C4—431no—
246C22×C22⋊C4C2×D4311yescharacteristic
247C2×C22⋊C8—432no—
248C2×C22⋊C8—864no—
249C2×C22⋊C8C2×D4312yes—
250#324—864no—
251#323—22no—
252#323—862no—
253C43#830411yescharacteristic, complemented, Sylow
254C25—431no—
255C25C4×D4311yescharacteristic
256C22×D4—862no—
257C22×D4—862no—
258C22×D4—862no—
259C22×D4—1724no—
260C23×C4—431no—
261C23×C4—431no—
262C23×C4—431no—
263C23×C4—434no—
264C23×C4—861no—
265C23×C4—862no—
266C23×C4—861no—
267C23×C4—1724no—
268C23×C4C4×D4311yescharacteristic
269C23×C4C22×D4311yescharacteristic
270C22×C8—22no—
271C22×C8—862no—
272#123—8616no—
273#123—8616no—
274C2×C4⋊C4—434no—
275C2×C4⋊C4—862no—
276C2×C4⋊C4—862no—
277C2×C4⋊C4—862no—
278C2×C4⋊C4—861no—
279C2×C4⋊C4—862no—
280C2×C4⋊C4—861no—
281C2×C22⋊C4—22no—
282C2×C22⋊C4—22no—
283C2×C22⋊C4—862no—
284C2×C22⋊C4—862no—
285C2×C22⋊C4—862no—
286C2×C22⋊C4—862no—
287C2×C22⋊C4—862no—
288C2×C22⋊C4—862no—
289C2×C22⋊C4D17212yes—
290C2×C22⋊C4C22⋊D4312yes—
291C22⋊C8—22no—
292C22⋊C8—22no—
293C22⋊C8—862no—
294C22⋊C8—862no—
295C22⋊C8—1728no—
296C24—21no—
297C24—21no—
298C24—22no—
299C24—22no—
300C24—42no—
301C24—42no—
302C24—432no—
303C24—864no—
304C24—861no—
305C24—861no—
306C24—862no—
307C24—862no—
308C24—1722no—
309C24(C2×D43)⋊C412yes—
310C24C2×C4×D4311yescharacteristic
311C2×D4—868no—
312C2×D4—1724no—
313C2×D4—1728no—
314C2×D4—1724no—
315C2×D4—1728no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—432no—
321C22×C4—432no—
322C22×C4—432no—
323C22×C4—868no—
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—864no—
333C22×C4—864no—
334C22×C4—1724no—
335C22×C4—1724no—
336C22×C4—1728no—
337C22×C4—1724no—
338C22×C4—1722no—
339C22×C4—1722no—
340C22×C4(C2×D43)⋊C412yes—
341C22×C4C2×D17211yescharacteristic
342C22×C4D4×D4312yes—
343C22×C4D4×D4312yes—
344C22×C4C2×C22⋊D4311yescharacteristic
345C2×C8—44no—
346C2×C8—42no—
347C2×C8—1724no—
348C2×C8—1722no—
349C4⋊C4—868no—
350C4⋊C4—864no—
351C4⋊C4—864no—
352C22⋊C4—24no—
353C22⋊C4—24no—
354C22⋊C4—868no—
355C22⋊C4—868no—
356C23—22no—
357C23—22no—
358C23—22no—
359C23—22no—
360C23—22no—
361C23—42no—
362C23—42no—
363C23—42no—
364C23—42no—
365C23—42no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23—84no—
370C23—84no—
371C23—434no—
372C23—864no—
373C23—864no—
374C23—864no—
375C23—862no—
376C23—864no—
377C23—862no—
378C23—1728no—
379C23—1728no—
380C23—1722no—
381C23—1722no—
382C23—1722no—
383C23—1721no—
384C23—1721no—
385C23C22⋊C4×D4311yescharacteristic
386C23C22⋊C4×D4311yescharacteristic
387C23C2×(C2×D43)⋊C411yescharacteristic
388C23#1306333112yes—
389C23#1306333312yes—
390D4—17216no—
391C2×C4—24no—
392C2×C4—22no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—864no—
400C2×C4—864no—
401C2×C4—862no—
402C2×C4—862no—
403C2×C4—862no—
404C2×C4—1728no—
405C2×C4—1728no—
406C2×C4—1722no—
407C2×C4—1722no—
408C2×C4—1722no—
409C2×C4—1722no—
410C2×C4—1721no—
411C2×C4—1721no—
412C2×C4—1722no—
413C2×C4—1722no—
414C2×C4#1306329312yes—
415C2×C4#1306329512yes—
416C8—82no—
417C8—3442no—
418C22—24no—
419C22—24no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—42no—
425C22—42no—
426C22—42no—
427C22—82no—
428C22—82no—
429C22—84no—
430C22—84no—
431C22—868no—
432C22—864no—
433C22—1728no—
434C22—1724no—
435C22—1724no—
436C22—1724no—
437C22—1722no—
438C22—1722no—
439C22#1458275411yescharacteristic
440C22#1458286412yes—
441C22#1458286412yes—
442C22#1458286511yescharacteristic
443C22#1458286711yescharacteristic
444C22#99×D4312yes—
445C22#1458288012yes—
446C4—22no—
447C4—22no—
448C4—42no—
449C4—1722no—
450C4—1722no—
451C4—1722no—
452C2—22no—
453C2—21no—
454C2—21no—
455C2—82no—
456C2—1724no—
457C2#1913294014yes—
458C2#1913450611yescharacteristic
459C2#1913450811yescharacteristic
460C2#1913452011yescharacteristic
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#8304
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. #19134504C2semidirect
3. C2×#14582624C2semidirect
4. C2×#14582623C2semidirect
5. C2×C43×#323C2semidirect
226. C2×#323D43semidirect
253. C43#8304semidirect

Maximal subgroups

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

subgroupindex
C22×#130633072
#191345042
C2×#145826242
C2×#145826232
C2×C43×#3232
#830443