Finite Group Databasebeta

← #25070716

Subgroups — #25070716

Order 11008.

1172 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 1172 conjugacy classes of subgroups — too many to draw. Only its 167 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×#14583525C211yesmaximal, characteristic, complemented
2#19145401C212yesmaximal, complemented
3#19133619C214yesmaximal, complemented
4#19133517C214yesmaximal, complemented
5#19133114C212yesmaximal, complemented
6#19132922C211yesmaximal, characteristic, complemented
7C43×#2539C211yesmaximal, characteristic
8#14583525—24no—
9#14583525—22no—
10#14583525C2214yes—
11C2×#13063304—21no—
12C2×#13063304C2212yes—
13C2×#13063302—22no—
14C2×#13063302—22no—
15C22×C22⋊Dic43—21no—
16#14583234C2214yescomplemented
17#14583210—22no—
18#14583143—24no—
19#14583050C2214yescomplemented
20#14583037—22no—
21#14582863C2212yes—
22#14582635C2218yescomplemented
23#14582623C2214yes—
24C2×#123×C43—21no—
25C2×#121×C43C2211yescharacteristic
26C2×#120×C43—21no—
27C22×C22⋊C4×C43C2211yescharacteristic
28C43×#399C2212yes—
29C43×#392C2212yes—
30C43×#390—22no—
31C4×C22⋊C4×C43C2211yescharacteristic
32C22×Dic86—21no—
33C22×Dic86D412yescomplemented
34C23×Dic43—21no—
35C23×Dic43—21no—
36C2×#10621883—24no—
37C2×#10621877—22no—
38#13063304—24no—
39#13063304—24no—
40#13063304—22no—
41#13063304—22no—
42#13063304D414yescomplemented
43#13063304C2314yes—
44#13063302—28no—
45#13063302—28no—
46#13063302—28no—
47#13063302—28no—
48C2×C4⋊Dic43—21no—
49C2×C4⋊Dic43D412yescomplemented
50C2×Dic43⋊C4—22no—
51C2×Dic43⋊C4—22no—
52C2×C22⋊Dic43—22no—
53C2×C22⋊Dic43—24no—
54C2×C22⋊Dic43—22no—
55C2×C22⋊Dic43—24no—
56#13063258—24no—
57#13063248—24no—
58#13063246—24no—
59C22⋊(C43⋊C8)—22no—
60C22⋊(C43⋊C8)C2314yes—
61C25×C43D411yescharacteristic
62C22×D4×C43—21no—
63C22×D4×C43—22no—
64C22×D4×C43C2311yescharacteristic
65C23×C4×C43D411yescharacteristic
66C23×C4×C43C2311yescharacteristic
67#123×C43—44no—
68#121×C43—22no—
69#121×C43—22no—
70#120×C43—44no—
71C2×C4⋊C4×C43—22no—
72C2×C4⋊C4×C43C2311yescharacteristic
73C2×C22⋊C4×C43—21no—
74C2×C22⋊C4×C43—22no—
75C2×C22⋊C4×C43—22no—
76C2×C22⋊C4×C43—22no—
77C2×C22⋊C4×C43—21no—
78C2×C22⋊C4×C43—22no—
79C2×C22⋊C4×C43D412yes—
80C2×C22⋊C4×C43C2312yes—
81C2×C42×C43—21no—
82#95×C43C2312yes—
83C24×C43—21no—
84C24×C43—21no—
85C24×C43—24no—
86C24×C43—21no—
87C24×C43—42no—
88C24×C43—81no—
89C24×C43C2×D411yescharacteristic
90C24×C43C2×D412yes—
91C2×D4×C43—22no—
92C2×D4×C43—42no—
93C2×D4×C43—42no—
94C2×D4×C43—44no—
95C2×D4×C43—41no—
96C2×D4×C43—41no—
97C2×D4×C43—44no—
98C2×D4×C43—81no—
99C2×D4×C43—82no—
100C22×C4×C43—21no—
101C22×C4×C43—21no—
102C22×C4×C43—22no—
103C22×C4×C43—21no—
104C22×C4×C43—42no—
105C22×C4×C43—81no—
106C22×C4×C43C2×D412yes—
107C22×C4×C43C2×D412yes—
108C22×C4×C43C2×D412yes—
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2411yescharacteristic
111C22×Dic43—24no—
112C22×Dic43—24no—
113C22×Dic43—22no—
114C22×Dic43—22no—
115C22×Dic43—82no—
116C22×Dic43—82no—
117C2×Dic86—24no—
118C2×Dic86—22no—
119C2×Dic86—82no—
120C2×Dic86—82no—
121C2×Dic86C2×D414yes—
122C4⋊C4×C43—22no—
123C4⋊C4×C43—44no—
124C22⋊C4×C43—24no—
125C22⋊C4×C43—24no—
126C22⋊C4×C43—24no—
127C22⋊C4×C43—44no—
128C22⋊C4×C43—44no—
129C22⋊C4×C43—42no—
130C42×C43—81no—
131C22⋊Dic43—28no—
132C22⋊Dic43—24no—
133C22⋊Dic43—24no—
134#10621883—84no—
135C4⋊Dic43—24no—
136C4⋊Dic43—22no—
137C4⋊Dic43C2×D414yes—
138Dic43⋊C4—28no—
139Dic43⋊C4—24no—
140Dic43⋊C4—24no—
141#10621877—82no—
142C2×C43⋊C8—24no—
143C23×C43—24no—
144C23×C43—24no—
145C23×C43—22no—
146C23×C43—22no—
147C23×C43—22no—
148C23×C43—22no—
149C23×C43—41no—
150C23×C43—42no—
151C23×C43—42no—
152C23×C43—42no—
153C23×C43—41no—
154C23×C43—41no—
155C23×C43—42no—
156C23×C43—42no—
157C23×C43—41no—
158C23×C43—42no—
159C23×C43—81no—
160C23×C43—81no—
161C23×C43—88no—
162C23×C43#12011yescharacteristic
163C23×C43#12011yescharacteristic
164C23×C43#13714yes—
165C23×C43C22×D411yescharacteristic
166D4×C43—44no—
167D4×C43—88no—
168D4×C43—82no—
169D4×C43—82no—
170C2×C4×C43—24no—
171C2×C4×C43—22no—
172C2×C4×C43—42no—
173C2×C4×C43—41no—
174C2×C4×C43—42no—
175C2×C4×C43—41no—
176C2×C4×C43—42no—
177C2×C4×C43—42no—
178C2×C4×C43—42no—
179C2×C4×C43—42no—
180C2×C4×C43—41no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43—81no—
184C2×C4×C43#12012yes—
185C2×C4×C43C22×D412yes—
186C2×Dic43—24no—
187C2×Dic43—24no—
188C2×Dic43—44no—
189C2×Dic43—44no—
190C2×Dic43—84no—
191C2×Dic43—84no—
192Dic86—44no—
193Dic86—82no—
194Dic86—84no—
195C43⋊C8—44no—
196#18318—431nomaximal, Sylow
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—21no—
200C22×C43—21no—
201C22×C43—21no—
202C22×C43—24no—
203C22×C43—21no—
204C22×C43—21no—
205C22×C43—44no—
206C22×C43—44no—
207C22×C43—48no—
208C22×C43—42no—
209C22×C43—42no—
210C22×C43—82no—
211C22×C43—82no—
212C22×C43—82no—
213C22×C43—84no—
214C22×C43—81no—
215C22×C43—81no—
216C22×C43—81no—
217C22×C43#45312yes—
218C22×C43C2×#12011yescharacteristic
219C22×C43C2×#13712yes—
220C4×C43—22no—
221C4×C43—22no—
222C4×C43—44no—
223C4×C43—42no—
224C4×C43—81no—
225Dic43—44no—
226Dic43—44no—
227C2×#543—431no—
228#3193—432no—
229#2539D4311yescharacteristic
230#1614—434no—
231#1596—434no—
232#1508—432no—
233#1462—431no—
234C2×C43—22no—
235C2×C43—22no—
236C2×C43—41no—
237C2×C43—44no—
238C2×C43—161no—
239C2×C43#300411yescharacteristic
240C2×C43C2×#45311yescharacteristic
241C2×C43#302611yescharacteristic
242#543—434no—
243#543—864no—
244#543—862no—
245C2×#123—21no—
246C2×C22⋊Q8—432no—
247C2×C22⋊Q8—862no—
248C2×C22⋊Q8—862no—
249C2×C22⋊Q8—861no—
250C2×#121C2×D4311yescharacteristic
251C2×#120—21no—
252C22×C22⋊C4—861no—
253C22×C22⋊C4C2×D4311yescharacteristic
254#484—434no—
255#480—862no—
256#468—864no—
257#450—434no—
258#448—862no—
259#407—432no—
260#399C2×D4312yes—
261#392C2×D4312yes—
262#390—22no—
263C4×C22⋊C4C2×D4311yescharacteristic
264#328—438no—
265#323—434no—
266C43#1831811yescharacteristic, complemented, Sylow
267C25C22⋊D4311yescharacteristic
268C22×Q8—432no—
269C22×Q8—861no—
270C22×D4—21no—
271C22×D4—22no—
272C22×D4C22×D4311yescharacteristic
273C23×C4—861no—
274C23×C4—861no—
275C23×C4C22⋊D4311yescharacteristic
276C23×C4C22×D4311yescharacteristic
277C2×SD16—864no—
278C2×M16—862no—
279#123—44no—
280C22⋊Q8—434no—
281C22⋊Q8—434no—
282C22⋊Q8—868no—
283C22⋊Q8—868no—
284C22⋊Q8—868no—
285C22⋊Q8—868no—
286C22⋊Q8—864no—
287C22⋊Q8—862no—
288C22⋊Q8—862no—
289C22⋊Q8—864no—
290#121—22no—
291#121—22no—
292#120—44no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—432no—
295C2×C4⋊C4—862no—
296C2×C4⋊C4—861no—
297C2×C4⋊C4—862no—
298C2×C4⋊C4C22×D4311yescharacteristic
299C2×C22⋊C4—21no—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—862no—
306C2×C22⋊C4—864no—
307C2×C22⋊C4—862no—
308C2×C22⋊C4—864no—
309C2×C22⋊C4C22⋊D4312yes—
310C2×C22⋊C4C22×D4312yes—
311C2×C42—21no—
312#107—864no—
313#103—864no—
314#102—864no—
315C22⋊C8—434no—
316C22⋊C8—862no—
317#95C22×D4312yes—
318C24—21no—
319C24—21no—
320C24—24no—
321C24—21no—
322C24—42no—
323C24—81no—
324C24C2×C22⋊D4311yescharacteristic
325C24C2×C22⋊D4312yes—
326C2×Q8—434no—
327C2×Q8—864no—
328C2×Q8—862no—
329C2×Q8—3442no—
330C2×Q8—3442no—
331C2×D4—22no—
332C2×D4—44no—
333C2×D4—42no—
334C2×D4—42no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—44no—
338C2×D4—81no—
339C2×D4—82no—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—42no—
345C22×C4—81no—
346C22×C4—864no—
347C22×C4—864no—
348C22×C4—862no—
349C22×C4—862no—
350C22×C4—3442no—
351C22×C4—3442no—
352C22×C4D4×D4312yes—
353C22×C4D4×D4312yes—
354C22×C4C2×C22⋊D4312yes—
355C22×C4C2×C22⋊D4311yescharacteristic
356C22×C4C23×D4311yescharacteristic
357SD16—3444no—
358M16—3442no—
359C2×C8—864no—
360C4⋊C4—22no—
361C4⋊C4—44no—
362C4⋊C4—434no—
363C4⋊C4—868no—
364C4⋊C4—864no—
365C4⋊C4—862no—
366C4⋊C4—864no—
367C4⋊C4—864no—
368C22⋊C4—24no—
369C22⋊C4—24no—
370C22⋊C4—24no—
371C22⋊C4—44no—
372C22⋊C4—44no—
373C22⋊C4—42no—
374C22⋊C4—868no—
375C22⋊C4—864no—
376C22⋊C4—864no—
377C42—81no—
378C23—24no—
379C23—24no—
380C23—22no—
381C23—22no—
382C23—22no—
383C23—22no—
384C23—41no—
385C23—42no—
386C23—42no—
387C23—42no—
388C23—41no—
389C23—41no—
390C23—42no—
391C23—42no—
392C23—41no—
393C23—42no—
394C23—81no—
395C23—81no—
396C23—88no—
397C23#1306329311yescharacteristic
398C23#1306329311yescharacteristic
399C23#1306335514yes—
400C23C22×C22⋊D4311yescharacteristic
401Q8—3442no—
402Q8—3444no—
403Q8—1724no—
404D4—44no—
405D4—88no—
406D4—82no—
407D4—82no—
408C2×C4—24no—
409C2×C4—22no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—81no—
422C2×C4—864no—
423C2×C4—864no—
424C2×C4—3444no—
425C2×C4—3444no—
426C2×C4—1724no—
427C2×C4—1724no—
428C2×C4#1306329312yes—
429C2×C4C2×D4×D4312yes—
430C8—1724no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—24no—
438C22—21no—
439C22—44no—
440C22—44no—
441C22—48no—
442C22—42no—
443C22—42no—
444C22—82no—
445C22—82no—
446C22—82no—
447C22—84no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22#1458306612yes—
452C22C2×#1306329311yescharacteristic
453C22C2×#1306335512yes—
454C4—22no—
455C4—22no—
456C4—44no—
457C4—42no—
458C4—81no—
459C4—1724no—
460C4—1724no—
461C2—22no—
462C2—22no—
463C2—41no—
464C2—44no—
465C2—161no—
466C2#1914382811yescharacteristic
467C2C2×#1458306611yescharacteristic
468C2#1914399111yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#2539C2
socleC22×C43C2×#120
hypercenter#2539D43
hypocenterC43#18318
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2539

Complements

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

NH ≅ G/Ntype
1. C2×#14583525C2semidirect
2. #19145401C2semidirect
3. #19133619C2semidirect
4. #19133517C2semidirect
5. #19133114C2semidirect
6. #19132922C2semidirect
16. #14583234C22semidirect
19. #14583050C22semidirect
22. #14582635C22semidirect
33. C22×Dic86D4semidirect
42. #13063304D4semidirect
49. C2×C4⋊Dic43D4semidirect
266. C43#18318semidirect

Maximal subgroups

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

subgroupindex
C2×#145835252
#191454012
#191336192
#191335172
#191331142
#191329222
C43×#25392
#1831843