Finite Group Databasebeta

← #24997363

Subgroups — #24997363

Order 11008.

568 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 97 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
1#19144603C211yesmaximal, characteristic
2#19144402C211yesmaximal, characteristic, complemented
3#19139504C211yesmaximal, characteristic
4#19133160C211yesmaximal, characteristic, complemented
5#19132989C211yesmaximal, characteristic, complemented
6#19132455C211yesmaximal, characteristic, complemented
7C43×#1486C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9C2×#13063304—21no—
10C2×C4×Dic86C2211yescharacteristic
11#14583229—21no—
12#14583207—22no—
13#14583195—21no—
14#14583189—21no—
15#14583185—21no—
16#14583104—21no—
17#14583050—21no—
18C4×#10621883—22no—
19#14582952C2211yescharacteristic
20#14582941—21no—
21#14582909—21no—
22#14582830—21no—
23#14582813—21no—
24#14582787—22no—
25#14582765C2211yescharacteristic
26#14582759—21no—
27#14582637—22no—
28#14582629—22no—
29C2×C4×D4×C43C2211yescharacteristic
30C43×#431C2211yescharacteristic
31C43×#423C2211yescharacteristic
32C43×D4⋊C8—22no—
33C22×Dic86D411yescharacteristic
34C2×#10621883—22no—
35#13063325D411yescharacteristic
36#13063325D411yescharacteristic
37#13063317—21no—
38#13063304—21no—
39#13063304—21no—
40#13063304—42no—
41#13063304—42no—
42C4×Dic86—21no—
43C4×Dic86—21no—
44C4×Dic86—21no—
45C4×Dic86—21no—
46C4×Dic86—21no—
47C4×Dic86—21no—
48#13063284—21no—
49C2×C4⋊Dic43—21no—
50C2×C4⋊Dic43D411yescharacteristic
51C2×Dic43⋊C4—22no—
52C2×Dic43⋊C4—21no—
53C2×C22⋊Dic43—22no—
54C2×C22⋊Dic43—22no—
55C2×C4×Dic43—21no—
56#13063259—22no—
57#13063257—22no—
58#13063256—22no—
59C4⋊(C43⋊C8)—21no—
60#13063250—22no—
61#13063250—22no—
62#13063248—22no—
63#13063246—22no—
64C22⋊(C43⋊C8)—21no—
65C4×C43⋊C8D412yes—
66C43⋊#95—22no—
67C43⋊#95—21no—
68C43⋊#95D412yes—
69C22×D4×C43D411yescharacteristic
70C23×C4×C43—21no—
71C2×M16×C43—21no—
72C4×D4×C43—21no—
73C4×D4×C43—21no—
74C4×D4×C43—21no—
75C4×D4×C43—21no—
76C2×C4⋊C4×C43D411yescharacteristic
77C2×C22⋊C4×C43—21no—
78C2×C42×C43C2311yescharacteristic
79C4⋊C8×C43—21no—
80C4⋊C8×C43—21no—
81C4⋊C8×C43D412yes—
82C22⋊C8×C43—21no—
83C4×C8×C43—21no—
84C24×C43—21no—
85C2×D4×C43—21no—
86C2×D4×C43—21no—
87C2×D4×C43—42no—
88C22×C4×C43—21no—
89C22×C4×C43—41no—
90C22×C4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43—41no—
93C22×C4×C43—41no—
94C22×C4×C43—41no—
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×Dic43—21no—
99C22×Dic43—22no—
100C22×Dic43—21no—
101C2×Dic86—21no—
102C2×Dic86—21no—
103C2×Dic86—21no—
104C2×Dic86—21no—
105C2×Dic86—21no—
106C2×Dic86—21no—
107C2×Dic86—21no—
108C2×Dic86SD1612yescomplemented
109M16×C43—41no—
110M16×C43—41no—
111C2×C8×C43—22no—
112C2×C8×C43—41no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—21no—
115C22⋊C4×C43—41no—
116C22⋊C4×C43—41no—
117C42×C43C2×D411yescharacteristic
118C42×C43C2×D411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43#4111yescharacteristic
121C22⋊Dic43—44no—
122C22⋊Dic43—44no—
123C22⋊Dic43—41no—
124#10621883—44no—
125C4⋊Dic43—21no—
126C4⋊Dic43—21no—
127C4⋊Dic43—21no—
128C4⋊Dic43—21no—
129C4⋊Dic43—21no—
130C4⋊Dic43—21no—
131C4⋊Dic43—41no—
132C4⋊Dic43—41no—
133Dic43⋊C4—44no—
134Dic43⋊C4—41no—
135Dic43⋊C4—41no—
136Dic43⋊C4—41no—
137Dic43⋊C4—41no—
138C4×Dic43—41no—
139C4×Dic43—41no—
140C4×Dic43—41no—
141C2×C43⋊C8—22no—
142C23×C43—22no—
143C23×C43—41no—
144C23×C43—41no—
145C23×C43—41no—
146C23×C43—41no—
147C23×C43—41no—
148C23×C43—41no—
149C23×C43#12011yescharacteristic
150D4×C43—22no—
151D4×C43—22no—
152D4×C43—41no—
153D4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—81no—
160C2×C4×C43—81no—
161C2×C4×C43—81no—
162C2×C4×C43—81no—
163C2×C4×C43#12011yescharacteristic
164C2×C4×C43#12011yescharacteristic
165C2×C4×C43#12111yescharacteristic
166C2×C4×C43#12111yescharacteristic
167C2×C4×C43#12111yescharacteristic
168C2×C4×C43#12711yescharacteristic
169C2×C4×C43C2×SD1611yescharacteristic
170C2×C4×C43#13511yescharacteristic
171C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C43#13711yescharacteristic
173C2×Dic43—22no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176C2×Dic43—42no—
177C2×Dic43—42no—
178C2×Dic43—42no—
179C2×Dic43—41no—
180C2×Dic43—41no—
181C2×Dic43—41no—
182C2×Dic43—42no—
183Dic86—22no—
184Dic86—22no—
185Dic86—41no—
186Dic86—41no—
187Dic86—42no—
188Dic86—81no—
189C8×C43—42no—
190C8×C43—81no—
191C43⋊C8—42no—
192#10001—431nomaximal, Sylow
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—42no—
196C22×C43—42no—
197C22×C43—42no—
198C22×C43—81no—
199C22×C43—81no—
200C22×C43—81no—
201C22×C43—81no—
202C22×C43#39211yescharacteristic
203C22×C43#45011yescharacteristic
204C22×C43#45211yescharacteristic
205C4×C43—21no—
206C4×C43—21no—
207C4×C43—21no—
208C4×C43—21no—
209C4×C43—81no—
210C4×C43#44811yescharacteristic
211C4×C43#44911yescharacteristic
212C4×C43#46511yescharacteristic
213C4×C43#46811yescharacteristic
214Dic43—42no—
215Dic43—82no—
216Dic43—81no—
217Dic43—81no—
218Dic43—81no—
219#3101—431no—
220#3078—431no—
221#2536—431no—
222#1518—431no—
223#1486D4311yescharacteristic
224#1479—431no—
225#1286—431no—
226C2×C43—21no—
227C2×C43—21no—
228C2×C43—82no—
229C2×C43#200011yescharacteristic
230C2×C43#200911yescharacteristic
231C2×C43#201011yescharacteristic
232#533—431no—
233C2×C22⋊Q8—861no—
234C2×C4×Q8—431no—
235C2×C4×D4C2×D4311yescharacteristic
236#483—861no—
237#479—862no—
238#477—861no—
239#476—861no—
240#475—861no—
241#461—861no—
242#450—861no—
243C4×SD16—862no—
244#431—431no—
245#431C2×D4311yescharacteristic
246#428—861no—
247#423C2×D4311yescharacteristic
248#419—861no—
249#398—861no—
250#394—861no—
251#388—862no—
252#382—431no—
253#380—861no—
254#328—862no—
255Q8⋊C8—862no—
256D4⋊C8—22no—
257C43#1000111yescharacteristic, complemented, Sylow
258C22×Q8—431no—
259C22×D4D17211yescharacteristic
260C23×C4—21no—
261C2×SD16—862no—
262C2×M16—21no—
263C4⋊Q8—431no—
264C4⋊Q8—431no—
265#125—861no—
266C22⋊Q8—861no—
267C22⋊Q8—861no—
268C22⋊Q8—1722no—
269C22⋊Q8—1722no—
270C4×Q8—861no—
271C4×Q8—861no—
272C4×Q8—861no—
273C4×Q8—861no—
274C4×Q8—861no—
275C4×Q8—861no—
276C4×D4—21no—
277C4×D4—21no—
278C4×D4—21no—
279C4×D4—21no—
280#117—861no—
281C2×C4⋊C4—431no—
282C2×C4⋊C4—862no—
283C2×C4⋊C4—861no—
284C2×C4⋊C4—861no—
285C2×C4⋊C4D17211yescharacteristic
286C2×C22⋊C4—21no—
287C2×C22⋊C4—862no—
288C2×C22⋊C4—862no—
289C2×C42—861no—
290C2×C42C22×D4311yescharacteristic
291#107—862no—
292#106—862no—
293#106—862no—
294C4⋊C8—21no—
295C4⋊C8—21no—
296C4⋊C8—861no—
297C4⋊C8C22⋊D4312yes—
298#103—862no—
299#103—862no—
300#103—862no—
301#102—862no—
302C22⋊C8—21no—
303C22⋊C8—861no—
304C4×C8—21no—
305C4×C8—432no—
306#95—432no—
307#95—862no—
308#95—861no—
309C24—21no—
310C2×Q8—432no—
311C2×Q8—861no—
312C2×Q8—861no—
313C2×Q8—861no—
314C2×Q8—861no—
315C2×Q8—861no—
316C2×Q8—861no—
317C2×Q8—861no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—42no—
321C22×C4—21no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—861no—
329C22×C4—862no—
330C22×C4—861no—
331C22×C4C2×D17211yescharacteristic
332C22×C4D4×D4311yescharacteristic
333C22×C4D4×D4311yescharacteristic
334SD16—1724no—
335M16—41no—
336M16—41no—
337C2×C8—22no—
338C2×C8—41no—
339C2×C8—862no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—861no—
343C4⋊C4—861no—
344C4⋊C4—861no—
345C4⋊C4—861no—
346C4⋊C4—861no—
347C4⋊C4—861no—
348C4⋊C4—1724no—
349C4⋊C4—1721no—
350C4⋊C4—1721no—
351C4⋊C4—1721no—
352C4⋊C4—1721no—
353C4⋊C4—1721no—
354C4⋊C4—1721no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—1724no—
358C22⋊C4—1724no—
359C22⋊C4—1721no—
360C42—1721no—
361C42—1721no—
362C42—1721no—
363C42#1062189811yescharacteristic
364C42D4×D4311yescharacteristic
365C42D4×D4311yescharacteristic
366C42C2×C22⋊D4311yescharacteristic
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23#1306329511yescharacteristic
375Q8—862no—
376Q8—862no—
377Q8—3441no—
378Q8—1722no—
379Q8—1721no—
380Q8—1721no—
381D4—22no—
382D4—22no—
383D4—41no—
384D4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—862no—
395C2×C4—1722no—
396C2×C4—1722no—
397C2×C4—1722no—
398C2×C4—1722no—
399C2×C4—1721no—
400C2×C4—1721no—
401C2×C4—1721no—
402C2×C4—1721no—
403C2×C4—1721no—
404C2×C4#1306329311yescharacteristic
405C2×C4#1306329511yescharacteristic
406C2×C4#1306329811yescharacteristic
407C2×C4#1306329811yescharacteristic
408C2×C4#1306329911yescharacteristic
409C2×C4#1306332111yescharacteristic
410C2×C4SD16×D4311yescharacteristic
411C2×C4#1306334411yescharacteristic
412C2×C4#1306334911yescharacteristic
413C2×C4#1306335411yescharacteristic
414C8—42no—
415C8—81no—
416C8—1722no—
417C22—21no—
418C22—21no—
419C22—42no—
420C22—42no—
421C22—42no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22#1458280811yescharacteristic
427C22#1458305111yescharacteristic
428C22#1458306211yescharacteristic
429C4—21no—
430C4—21no—
431C4—21no—
432C4—21no—
433C4—81no—
434C4—3442no—
435C4—3441no—
436C4—3441no—
437C4—3441no—
438C4—1722no—
439C4#1458303611yescharacteristic
440C4#1458304111yescharacteristic
441C4#1458312711yescharacteristic
442C4#1458314411yescharacteristic
443C2—21no—
444C2—21no—
445C2—82no—
446C2#1913559911yescharacteristic
447C2#1913565611yescharacteristic
448C2#1913566211yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1486C2
socleC22×C43#392
prime radicalC22×D4×C43D4
hypercenter#1486D43
hypocenterC43#10001
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #19144402C2semidirect
4. #19133160C2semidirect
5. #19132989C2semidirect
6. #19132455C2semidirect
108. C2×Dic86SD16semidirect
257. C43#10001semidirect

Maximal subgroups

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

subgroupindex
#191446032
#191444022
#191395042
#191331602
#191329892
#191324552
C43×#14862
#1000143