Finite Group Databasebeta

← #25070448

Subgroups — #25070448

Order 11008.

1142 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 1142 conjugacy classes of subgroups — too many to draw. Only its 187 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#19145353C212yesmaximal, complemented
3#19140329C211yesmaximal, characteristic
4#19133588C214yesmaximal, complemented
5#19133520C214yesmaximal, complemented
6#19133168C212yesmaximal, complemented
7C2×C43×#323C211yesmaximal, characteristic, complemented
8#14583525—24no—
9#14583525—22no—
10#14583525C2214yes—
11C2×#13063304—21no—
12C2×#13063304C2212yes—
13C2×#13063302—22no—
14C2×#13063302—22no—
15C2×#13063299C2211yescharacteristic
16C2×#13063294—21no—
17C22×C22⋊Dic43—21no—
18#14583230C2214yescomplemented
19#14583218—22no—
20#14583128—24no—
21#14583052C2214yescomplemented
22#14583040—22no—
23#14582824C2212yes—
24#14582815—22no—
25#14582808C2212yes—
26#14582778—21no—
27#14582759C2211yescharacteristic
28#14582637C2218yescomplemented
29C22×C22⋊C4×C43C2211yescharacteristic
30C2×C22⋊C8×C43C2212yes—
31C43×#323C2214yes—
32C22×Dic86—21no—
33C22×Dic86D412yescomplemented
34C22×D172C2311yescharacteristic
35C22×C22⋊D43—21no—
36C22×C22⋊D43—22no—
37C23×Dic43—21no—
38C23×Dic43—21no—
39C2×#10621873—24no—
40#13063304—24no—
41#13063304—24no—
42#13063304—22no—
43#13063304—22no—
44#13063304D414yescomplemented
45#13063304C2314yes—
46#13063302—28no—
47#13063302—28no—
48#13063302—28no—
49#13063302—28no—
50#13063299—22no—
51#13063299—22no—
52#13063294—44no—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43—21no—
55C2×C4⋊Dic43D412yescomplemented
56C2×C4⋊Dic43C2311yescharacteristic
57C2×Dic43⋊C4—22no—
58C2×Dic43⋊C4—22no—
59C2×C22⋊Dic43—22no—
60C2×C22⋊Dic43—24no—
61C2×C22⋊Dic43—22no—
62C2×C22⋊Dic43—24no—
63C2×C22⋊Dic43—22no—
64C2×C22⋊Dic43—21no—
65C2×(C2×D43)⋊C4—21no—
66C2×(C2×D43)⋊C4—22no—
67#13063257—24no—
68#13063250—24no—
69#13063247—24no—
70C43⋊#95—22no—
71C43⋊#95C2312yes—
72C25×C43D411yescharacteristic
73C23×C4×C43D411yescharacteristic
74C23×C4×C43C2311yescharacteristic
75C22×C8×C43—22no—
76C2×C22⋊C4×C43—22no—
77C2×C22⋊C4×C43—22no—
78C2×C22⋊C4×C43D412yes—
79C2×C22⋊C4×C43C2312yes—
80C22⋊C8×C43—22no—
81C22⋊C8×C43C2314yes—
82C24×C43—21no—
83C24×C43—21no—
84C24×C43—22no—
85C24×C43—81no—
86C24×C43—81no—
87C24×C43SD1614yescomplemented
88C24×C43C2×D412yes—
89C24×C43C2×D411yescharacteristic
90C23×D43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—81no—
94C22×C4×C43—81no—
95C22×C4×C43C2×D412yes—
96C22×C4×C43C2×D412yes—
97C22×C4×C43C2×D412yes—
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2411yescharacteristic
100C2×C22⋊D43—41no—
101C2×C22⋊D43—41no—
102C2×C22⋊D43—44no—
103C2×C22⋊D43—42no—
104C2×C22⋊D43—42no—
105C2×C22⋊D43—82no—
106C2×C22⋊D43—82no—
107C22×Dic43—24no—
108C22×Dic43—24no—
109C22×Dic43—22no—
110C22×Dic43—22no—
111C22×Dic43—21no—
112C22×Dic43—22no—
113C22×Dic43—82no—
114C22×Dic43—82no—
115C2×D172—22no—
116C2×D172—81no—
117C2×Dic86—24no—
118C2×Dic86—22no—
119C2×Dic86—82no—
120C2×Dic86—82no—
121C2×Dic86C2×D414yes—
122C2×C8×C43—24no—
123C2×C8×C43—82no—
124C22⋊C4×C43—24no—
125C22⋊C4×C43—24no—
126C22⋊Dic43—28no—
127C22⋊Dic43—24no—
128C22⋊Dic43—24no—
129C22⋊Dic43—44no—
130C22⋊Dic43—42no—
131(C2×D43)⋊C4—42no—
132(C2×D43)⋊C4—82no—
133C4⋊Dic43—24no—
134C4⋊Dic43—22no—
135C4⋊Dic43—22no—
136C4⋊Dic43—81no—
137C4⋊Dic43C2×D414yes—
138Dic43⋊C4—28no—
139Dic43⋊C4—24no—
140Dic43⋊C4—24no—
141#10621873—84no—
142C23×C43—22no—
143C23×C43—24no—
144C23×C43—22no—
145C23×C43—24no—
146C23×C43—41no—
147C23×C43—41no—
148C23×C43—42no—
149C23×C43—42no—
150C23×C43—42no—
151C23×C43—42no—
152C23×C43—81no—
153C23×C43—81no—
154C23×C43—84no—
155C23×C43—84no—
156C23×C43#12011yescharacteristic
157C23×C43#12011yescharacteristic
158C23×C43C2×SD1614yes—
159C23×C43C2×SD1612yes—
160C23×C43#13712yes—
161C23×C43C22×D411yescharacteristic
162C22×D43—42no—
163C22×D43—42no—
164C22×D43—41no—
165C22×D43—41no—
166C22×D43—41no—
167C2×C4×C43—22no—
168C2×C4×C43—41no—
169C2×C4×C43—42no—
170C2×C4×C43—42no—
171C2×C4×C43—41no—
172C2×C4×C43—42no—
173C2×C4×C43—42no—
174C2×C4×C43—81no—
175C2×C4×C43#12012yes—
176C2×C4×C43C22×D412yes—
177C22⋊D43—88no—
178C22⋊D43—82no—
179C22⋊D43—82no—
180C2×Dic43—24no—
181C2×Dic43—24no—
182C2×Dic43—44no—
183C2×Dic43—44no—
184C2×Dic43—42no—
185C2×Dic43—42no—
186C2×Dic43—41no—
187C2×Dic43—42no—
188C2×Dic43—41no—
189C2×Dic43—41no—
190C2×Dic43—84no—
191C2×Dic43—84no—
192D172—44no—
193Dic86—44no—
194Dic86—82no—
195Dic86—84no—
196C8×C43—44no—
197#18286—431nomaximal, Sylow
198C22×C43—21no—
199C22×C43—21no—
200C22×C43—21no—
201C22×C43—21no—
202C22×C43—21no—
203C22×C43—21no—
204C22×C43—24no—
205C22×C43—42no—
206C22×C43—42no—
207C22×C43—44no—
208C22×C43—48no—
209C22×C43—42no—
210C22×C43—42no—
211C22×C43—82no—
212C22×C43—84no—
213C22×C43#44812yes—
214C22×C43#44812yes—
215C22×C43C2×#12011yescharacteristic
216C22×C43C22×SD1611yescharacteristic
217C22×C43C2×#13711yescharacteristic
218C2×D43—82no—
219C2×D43—82no—
220C2×D43—81no—
221C2×D43—81no—
222C2×D43—81no—
223C4×C43—22no—
224C4×C43—22no—
225C4×C43—42no—
226Dic43—44no—
227Dic43—44no—
228Dic43—82no—
229Dic43—81no—
230C2×#543—431no—
231#3187—432no—
232#2617—431no—
233#1608—434no—
234#1596—434no—
235#1520—432no—
236C2×#323D4311yescharacteristic, complemented
237C2×C43—21no—
238C2×C43—21no—
239C2×C43—22no—
240C2×C43—22no—
241C2×C43—44no—
242C2×C43C2×#44811yescharacteristic
243C2×C43#301911yescharacteristic
244C2×C43#302611yescharacteristic
245D43—161no—
246#543—434no—
247#543—864no—
248#543—862no—
249C2×C22⋊Q8—432no—
250C2×C22⋊Q8—862no—
251C2×C22⋊Q8—862no—
252C2×C22⋊Q8—861no—
253C2×#121—431no—
254C2×#120—861no—
255C22×C22⋊C4—861no—
256C22×C22⋊C4C2×D4311yescharacteristic
257#483—434no—
258#481—862no—
259#465—864no—
260#450—434no—
261#448—862no—
262C2×C22⋊C8C2×D4312yes—
263#397—432no—
264#394—862no—
265#392—432no—
266#386—861no—
267#380—431no—
268#328—438no—
269#323C2×D4314yes—
270C43#1828611yescharacteristic, complemented, Sylow
271C25D17211yescharacteristic
272C22×Q8—432no—
273C22×Q8—861no—
274C22×D4—431no—
275C22×D4—862no—
276C22×D4—861no—
277C23×C4—861no—
278C23×C4—861no—
279C23×C4D17211yescharacteristic
280C23×C4C22×D4311yescharacteristic
281C2×SD16—864no—
282C22×C8—22no—
283C22⋊Q8—434no—
284C22⋊Q8—434no—
285C22⋊Q8—868no—
286C22⋊Q8—868no—
287C22⋊Q8—868no—
288C22⋊Q8—868no—
289C22⋊Q8—864no—
290C22⋊Q8—862no—
291C22⋊Q8—864no—
292C22⋊Q8—862no—
293#121—862no—
294#121—862no—
295#120—1724no—
296C2×C4⋊C4—432no—
297C2×C4⋊C4—431no—
298C2×C4⋊C4—862no—
299C2×C4⋊C4—861no—
300C2×C4⋊C4—862no—
301C2×C4⋊C4—861no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—862no—
305C2×C22⋊C4—864no—
306C2×C22⋊C4—862no—
307C2×C22⋊C4—864no—
308C2×C22⋊C4—862no—
309C2×C22⋊C4—861no—
310C2×C22⋊C4—862no—
311C2×C22⋊C4—861no—
312C2×C22⋊C4D17212yes—
313C2×C22⋊C4C22×D4312yes—
314#106—864no—
315#103—864no—
316#102—864no—
317C22⋊C8—22no—
318C22⋊C8C22×D4314yes—
319#95—432no—
320#95—862no—
321C24—21no—
322C24—21no—
323C24—22no—
324C24—81no—
325C24—81no—
326C24—861no—
327C24#1062187314yescomplemented
328C24C2×D17212yes—
329C24C2×D17211yescharacteristic
330C2×Q8—434no—
331C2×Q8—864no—
332C2×Q8—862no—
333C2×Q8—3442no—
334C2×Q8—3442no—
335C2×D4—862no—
336C2×D4—3441no—
337C2×D4—3442no—
338C2×D4—3442no—
339C2×D4—1721no—
340C2×D4—1721no—
341C2×D4—1724no—
342C2×D4—1722no—
343C2×D4—1722no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—81no—
347C22×C4—81no—
348C22×C4—864no—
349C22×C4—864no—
350C22×C4—862no—
351C22×C4—862no—
352C22×C4—862no—
353C22×C4—861no—
354C22×C4—3442no—
355C22×C4—3442no—
356C22×C4C2×D17212yes—
357C22×C4C2×D17211yescharacteristic
358C22×C4D4×D4312yes—
359C22×C4D4×D4312yes—
360C22×C4C23×D4311yescharacteristic
361SD16—3444no—
362C2×C8—24no—
363C2×C8—82no—
364C4⋊C4—434no—
365C4⋊C4—868no—
366C4⋊C4—864no—
367C4⋊C4—862no—
368C4⋊C4—864no—
369C4⋊C4—864no—
370C4⋊C4—862no—
371C4⋊C4—3441no—
372C22⋊C4—24no—
373C22⋊C4—24no—
374C22⋊C4—868no—
375C22⋊C4—864no—
376C22⋊C4—864no—
377C22⋊C4—3442no—
378C22⋊C4—1724no—
379C22⋊C4—1722no—
380C22⋊C4—1722no—
381C23—24no—
382C23—22no—
383C23—24no—
384C23—22no—
385C23—41no—
386C23—41no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—81no—
392C23—81no—
393C23—84no—
394C23—84no—
395C23—1722no—
396C23—1722no—
397C23—1721no—
398C23—1721no—
399C23—1721no—
400C23#1306329511yescharacteristic
401C23#1306329511yescharacteristic
402C23C2×#1062187314yes—
403C23C2×#1062187312yes—
404C23#1306335812yes—
405C23C22×D17211yescharacteristic
406Q8—3442no—
407Q8—3444no—
408Q8—1724no—
409D4—3448no—
410D4—3442no—
411D4—3442no—
412D4—1724no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—81no—
421C2×C4—864no—
422C2×C4—864no—
423C2×C4—3444no—
424C2×C4—3444no—
425C2×C4—1722no—
426C2×C4—1722no—
427C2×C4—1721no—
428C2×C4—1722no—
429C2×C4—1721no—
430C2×C4—1721no—
431C2×C4—1724no—
432C2×C4—1724no—
433C2×C4#1306329512yes—
434C2×C4C2×D4×D4312yes—
435C8—44no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—24no—
443C22—42no—
444C22—42no—
445C22—44no—
446C22—48no—
447C22—42no—
448C22—42no—
449C22—82no—
450C22—84no—
451C22—3442no—
452C22—3442no—
453C22—3441no—
454C22—3441no—
455C22—3441no—
456C22#1458304012yes—
457C22#1458304012yes—
458C22C2×#1306329511yescharacteristic
459C22C22×#1062187311yescharacteristic
460C22C2×#1306335811yescharacteristic
461C4—22no—
462C4—22no—
463C4—42no—
464C4—3442no—
465C4—3441no—
466C4—1724no—
467C4—1724no—
468C2—21no—
469C2—22no—
470C2—21no—
471C2—22no—
472C2—44no—
473C2—6881no—
474C2C2×#1458304011yescharacteristic
475C2#1914395511yescharacteristic
476C2#1914399411yescharacteristic
subgroupG/H
centerC22C2×#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#323C2
socleC22×C43C2×#120
prime radical#19140329C2
hypercenterC2×#323D43
hypocenterC43#18286
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
1. C2×#14583525C2semidirect
2. #19145353C2semidirect
4. #19133588C2semidirect
5. #19133520C2semidirect
6. #19133168C2semidirect
7. C2×C43×#323C2semidirect
18. #14583230C22semidirect
21. #14583052C22semidirect
28. #14582637C22semidirect
33. C22×Dic86D4semidirect
44. #13063304D4semidirect
55. C2×C4⋊Dic43D4semidirect
87. C24×C43SD16semidirect
236. C2×#323D43semidirect
270. C43#18286semidirect
327. C24#10621873semidirect

Maximal subgroups

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

subgroupindex
C2×#145835252
#191453532
#191403292
#191335882
#191335202
#191331682
C2×C43×#3232
#1828643