Finite Group Databasebeta

← #24987943

Subgroups — #24987943

Order 11008.

1238 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 1238 conjugacy classes of subgroups — too many to draw. Only its 147 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×#13063308C211yesmaximal, characteristic
2#19134505C211yesmaximal, characteristic, complemented
3C2×#14582624C212yesmaximal, complemented
4C2×#14582622C212yesmaximal, complemented
5C43×#1779C211yesmaximal, characteristic, complemented
6C23×C22⋊D43C411yescharacteristic
7C2×#13063308—24no—
8C2×#13063308—24no—
9C2×#13063308—22no—
10C2×#13063308—22no—
11C22×Dic43⋊C4C411yescharacteristic
12C22×Dic43⋊C4C2211yescharacteristic
13C22×C22⋊Dic43C411yescharacteristic
14C22×(C2×D43)⋊C4C411yescharacteristic
15C22×(C2×D43)⋊C4C2211yescharacteristic
16C2×C22⋊(C43⋊C8)—22no—
17C2×C22⋊(C43⋊C8)C2212yes—
18#14582624—24no—
19#14582622—24no—
20C24×C4×C43C2211yescharacteristic
21C2×C22⋊C8×C43—22no—
22C2×C22⋊C8×C43C2212yes—
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×C43⋊C8—22no—
32#13063308—216no—
33#13063308—216no—
34C2×Dic43⋊C4—22no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—22no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—22no—
39C2×Dic43⋊C4—22no—
40C2×Dic43⋊C4D414yes—
41C2×C22⋊Dic43—22no—
42C2×C22⋊Dic43—22no—
43C2×C22⋊Dic43—22no—
44C2×(C2×D43)⋊C4—22no—
45C2×(C2×D43)⋊C4—22no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—22no—
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—22no—
50C2×(C2×D43)⋊C4D414yes—
51C22⋊(C43⋊C8)—22no—
52C22⋊(C43⋊C8)—22no—
53C22⋊(C43⋊C8)—44no—
54C25×C43C2×C411yescharacteristic
55C23×C4×C43—22no—
56C23×C4×C43—22no—
57C23×C4×C43—44no—
58C23×C4×C43C2×C411yescharacteristic
59C23×C4×C43D412yes—
60C23×C4×C43D412yes—
61C23×C4×C43C2311yescharacteristic
62C22×C8×C43—22no—
63C22⋊C8×C43—22no—
64C22⋊C8×C43—22no—
65C22⋊C8×C43—44no—
66C24×C43—24no—
67C24×C43—21no—
68C24×C43—21no—
69C24×C43—22no—
70C24×C43—22no—
71C24×C43—42no—
72C24×C43C22⋊C412yes—
73C24×C43C22×C411yescharacteristic
74C23×D43—21no—
75C23×D43—21no—
76C23×D43—22no—
77C23×D43—22no—
78C23×D43—42no—
79C23×D43—42no—
80C23×D43C22⋊C412yes—
81C22×C4×C43—24no—
82C22×C4×C43—24no—
83C22×C4×C43—24no—
84C22×C4×C43—24no—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—42no—
88C22×C4×C43—42no—
89C22×C4×C43—42no—
90C22×C4×C43—42no—
91C22×C4×C43—48no—
92C22×C4×C43—48no—
93C22×C4×C43C22⋊C412yes—
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D412yes—
96C22×C4×C43C2×D412yes—
97C22×C4×C43C2×D411yescharacteristic
98C2×C22⋊D43—28no—
99C2×C22⋊D43—48no—
100C2×C22⋊D43—44no—
101C2×C22⋊D43—48no—
102C2×C22⋊D43—44no—
103C22×Dic43—21no—
104C22×Dic43—21no—
105C22×Dic43—21no—
106C22×Dic43—21no—
107C22×Dic43—21no—
108C22×Dic43—21no—
109C22×Dic43—22no—
110C22×Dic43—22no—
111C22×Dic43—42no—
112C22×Dic43—42no—
113C22×Dic43C22⋊C412yes—
114C22×Dic43C22⋊C412yes—
115C22×Dic43C22⋊C412yes—
116C2×C8×C43—44no—
117C2×C8×C43—42no—
118C22⋊Dic43—28no—
119(C2×D43)⋊C4—28no—
120(C2×D43)⋊C4—24no—
121(C2×D43)⋊C4—24no—
122Dic43⋊C4—28no—
123Dic43⋊C4—24no—
124Dic43⋊C4—24no—
125C2×C43⋊C8—44no—
126C2×C43⋊C8—42no—
127C23×C43—22no—
128C23×C43—22no—
129C23×C43—24no—
130C23×C43—24no—
131C23×C43—22no—
132C23×C43—22no—
133C23×C43—22no—
134C23×C43—22no—
135C23×C43—22no—
136C23×C43—22no—
137C23×C43—48no—
138C23×C43—48no—
139C23×C43—42no—
140C23×C43—42no—
141C23×C43—42no—
142C23×C43—42no—
143C23×C43#9914yes—
144C23×C43C2×C22⋊C411yescharacteristic
145C23×C43C2×C22⋊C411yescharacteristic
146C23×C43C2×C22⋊C411yescharacteristic
147C23×C43#13112yes—
148C23×C43#13112yes—
149C22×D43—22no—
150C22×D43—24no—
151C22×D43—42no—
152C22×D43—42no—
153C22×D43—42no—
154C22×D43—41no—
155C22×D43—41no—
156C22×D43—42no—
157C22×D43—42no—
158C22×D43—42no—
159C22×D43—42no—
160C22×D43—84no—
161C22×D43—84no—
162C2×C4×C43—22no—
163C2×C4×C43—22no—
164C2×C4×C43—22no—
165C2×C4×C43—22no—
166C2×C4×C43—22no—
167C2×C4×C43—42no—
168C2×C4×C43—42no—
169C2×C4×C43—48no—
170C2×C4×C43—48no—
171C2×C4×C43—42no—
172C2×C4×C43—42no—
173C2×C4×C43#12012yes—
174C2×C4×C43#12012yes—
175C22⋊D43—416no—
176C2×Dic43—22no—
177C2×Dic43—22no—
178C2×Dic43—22no—
179C2×Dic43—24no—
180C2×Dic43—42no—
181C2×Dic43—42no—
182C2×Dic43—42no—
183C2×Dic43—41no—
184C2×Dic43—41no—
185C2×Dic43—42no—
186C2×Dic43—42no—
187C2×Dic43—42no—
188C2×Dic43—42no—
189C8×C43—82no—
190C43⋊C8—82no—
191#8304—431nomaximal, Sylow
192C22×C43—24no—
193C22×C43—24no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—21no—
198C22×C43—24no—
199C22×C43—24no—
200C22×C43—24no—
201C22×C43—48no—
202C22×C43—48no—
203C22×C43—42no—
204C22×C43—42no—
205C22×C43—42no—
206C22×C43—42no—
207C22×C43#37911yescharacteristic
208C22×C43#40812yes—
209C22×C43#40812yes—
210C22×C43#40811yescharacteristic
211C22×C43#40811yescharacteristic
212C22×C43C2×#9912yes—
213C22×C43#41312yes—
214C2×D43—42no—
215C2×D43—42no—
216C2×D43—42no—
217C2×D43—84no—
218C2×D43—82no—
219C2×D43—82no—
220C2×D43—84no—
221C4×C43—22no—
222C4×C43—22no—
223C4×C43—42no—
224Dic43—42no—
225Dic43—42no—
226Dic43—42no—
227C22×#123—431no—
228#1779—431no—
229#1779D4311yescharacteristic, complemented
230C2×#324—432no—
231C2×#323—432no—
232C2×C43—22no—
233C2×C43—22no—
234C2×C43—44no—
235C2×C43#146812yes—
236C2×C43#146812yes—
237C2×C43#178011yescharacteristic
238C2×C43#178111yescharacteristic
239C2×C43#178511yescharacteristic
240D43—82no—
241C23×D4—431no—
242C24×C4C2×D4311yescharacteristic
243C2×#123—864no—
244C2×#123—864no—
245C2×#123—862no—
246C2×#123—862no—
247C22×C4⋊C4—431no—
248C22×C4⋊C4—431no—
249C22×C22⋊C4—431no—
250C22×C22⋊C4—431no—
251C22×C22⋊C4—431no—
252C2×C22⋊C8—22no—
253C2×C22⋊C8—432no—
254C2×C22⋊C8—862no—
255C2×C22⋊C8C2×D4312yes—
256#324—864no—
257#323—864no—
258C43#830411yescharacteristic, complemented, Sylow
259C25—431no—
260C25C4×D4311yescharacteristic
261C22×D4—862no—
262C22×D4—862no—
263C22×D4—862no—
264C22×D4—1724no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—44no—
268C23×C4—431no—
269C23×C4—431no—
270C23×C4—431no—
271C23×C4C4×D4311yescharacteristic
272C23×C4D17212yes—
273C23×C4C22⋊D4312yes—
274C23×C4C22×D4311yescharacteristic
275C22×C8—22no—
276C22×C8—862no—
277#123—8616no—
278#123—8616no—
279C2×C4⋊C4—434no—
280C2×C4⋊C4—862no—
281C2×C4⋊C4—862no—
282C2×C4⋊C4—862no—
283C2×C4⋊C4—861no—
284C2×C4⋊C4—862no—
285C2×C4⋊C4—861no—
286C2×C22⋊C4—434no—
287C2×C22⋊C4—862no—
288C2×C22⋊C4—862no—
289C2×C22⋊C4—862no—
290C2×C22⋊C4—862no—
291C2×C22⋊C4—862no—
292C2×C22⋊C4—862no—
293C2×C22⋊C4—861no—
294C2×C22⋊C4—862no—
295C2×C22⋊C4—861no—
296C22⋊C8—22no—
297C22⋊C8—22no—
298C22⋊C8—44no—
299C22⋊C8—862no—
300C22⋊C8—862no—
301C22⋊C8—1724no—
302C24—24no—
303C24—21no—
304C24—21no—
305C24—22no—
306C24—22no—
307C24—42no—
308C24—432no—
309C24—862no—
310C24—862no—
311C24—861no—
312C24—861no—
313C24—1722no—
314C24—1722no—
315C24(C2×D43)⋊C412yes—
316C24C2×C4×D4311yescharacteristic
317C2×D4—868no—
318C2×D4—1728no—
319C2×D4—1724no—
320C2×D4—1728no—
321C2×D4—1724no—
322C22×C4—24no—
323C22×C4—24no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—24no—
327C22×C4—24no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4—48no—
333C22×C4—48no—
334C22×C4—432no—
335C22×C4—432no—
336C22×C4—432no—
337C22×C4—861no—
338C22×C4—861no—
339C22×C4—861no—
340C22×C4—861no—
341C22×C4—861no—
342C22×C4—861no—
343C22×C4—862no—
344C22×C4—862no—
345C22×C4—1722no—
346C22×C4—1722no—
347C22×C4(C2×D43)⋊C412yes—
348C22×C4C2×D17211yescharacteristic
349C22×C4D4×D4312yes—
350C22×C4D4×D4312yes—
351C22×C4C2×C22⋊D4311yescharacteristic
352C2×C8—44no—
353C2×C8—42no—
354C2×C8—1724no—
355C2×C8—1722no—
356C4⋊C4—868no—
357C4⋊C4—864no—
358C4⋊C4—864no—
359C22⋊C4—868no—
360C22⋊C4—868no—
361C22⋊C4—864no—
362C22⋊C4—864no—
363C23—22no—
364C23—22no—
365C23—24no—
366C23—24no—
367C23—22no—
368C23—22no—
369C23—22no—
370C23—22no—
371C23—22no—
372C23—22no—
373C23—48no—
374C23—48no—
375C23—42no—
376C23—42no—
377C23—42no—
378C23—42no—
379C23—864no—
380C23—862no—
381C23—3444no—
382C23—3444no—
383C23—1722no—
384C23—1722no—
385C23—1722no—
386C23—1722no—
387C23—1722no—
388C23—1721no—
389C23—1721no—
390C23—1722no—
391C23—1722no—
392C23#1306323914yes—
393C23C22⋊C4×D4311yescharacteristic
394C23C22⋊C4×D4311yescharacteristic
395C23C2×(C2×D43)⋊C411yescharacteristic
396C23#1306333112yes—
397C23#1306333312yes—
398D4—17216no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—48no—
407C2×C4—48no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—864no—
411C2×C4—862no—
412C2×C4—862no—
413C2×C4—862no—
414C2×C4—1722no—
415C2×C4—1722no—
416C2×C4—1722no—
417C2×C4—1721no—
418C2×C4—1721no—
419C2×C4—1722no—
420C2×C4—1722no—
421C2×C4—1722no—
422C2×C4—1722no—
423C2×C4#1306329312yes—
424C2×C4#1306329512yes—
425C8—82no—
426C8—3442no—
427C22—24no—
428C22—24no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—24no—
434C22—24no—
435C22—24no—
436C22—48no—
437C22—48no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—42no—
442C22—3444no—
443C22—3444no—
444C22—3442no—
445C22—3442no—
446C22—1722no—
447C22—1722no—
448C22—1722no—
449C22#1458275411yescharacteristic
450C22#1458286412yes—
451C22#1458286412yes—
452C22#1458286511yescharacteristic
453C22#1458286711yescharacteristic
454C22C2×#1306323912yes—
455C22#1458288112yes—
456C4—22no—
457C4—22no—
458C4—42no—
459C4—1722no—
460C4—1722no—
461C4—1722no—
462C2—22no—
463C2—22no—
464C2—44no—
465C2—3442no—
466C2#1913294112yes—
467C2#1913294412yes—
468C2#1913450611yescharacteristic
469C2#1913450911yescharacteristic
470C2#1913452111yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1779C2
socleC23×C43C2×C22⋊C4
prime radicalC23×C22⋊D43C4
cosocleC23×C4×C43C23
hypercenter#1779D43
hypocenterC43#8304
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
2. #19134505C2semidirect
3. C2×#14582624C2semidirect
4. C2×#14582622C2semidirect
5. C43×#1779C2semidirect
229. #1779D43semidirect
258. C43#8304semidirect

Maximal subgroups

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

subgroupindex
C22×#130633082
#191345052
C2×#145826242
C2×#145826222
C43×#17792
#830443