Finite Group Databasebeta

← #25070650

Subgroups — #25070650

Order 11008.

908 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145736C212yesmaximal, complemented
2#19140361C211yesmaximal, characteristic
3#19133603C214yesmaximal, complemented
4#19133586C214yesmaximal
5#19133159C212yesmaximal, complemented
6#19132909C211yesmaximal, characteristic
7C43×#3458C211yesmaximal, characteristic
8C2×#13063325C2211yescharacteristic
9C2×#13063304—21no—
10#14583295—22no—
11#14583249—22no—
12#14583227C2218yes—
13#14583184—24no—
14#14582952C2212yes—
15#14582829—21no—
16#14582829C2212yes—
17#14582824—21no—
18#14582824C2212yes—
19#14582805—21no—
20#14582765C2211yescharacteristic
21#14582636C2218yes—
22#14582625C2212yes—
23#14582623C2212yes—
24C43×#544—22no—
25C43×#544—22no—
26C43×#544—21no—
27C43×#544C2212yes—
28C43×#543—21no—
29C43×#543C2212yes—
30C43×#533—24no—
31C43×#533—21no—
32C43×#533C2212yes—
33C2×#117×C43—21no—
34C2×#117×C43C2211yescharacteristic
35C22×Dic86—21no—
36#13063325—22no—
37#13063325—22no—
38#13063304—44no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43C2312yes—
42C2×Dic43⋊C4—22no—
43C2×C22⋊Dic43—22no—
44#13063256—28no—
45C4⋊(C43⋊C8)—22no—
46#13063249—28no—
47C22⋊(C43⋊C8)C2314yes—
48C4×C43⋊C8—22no—
49C43⋊#95—22no—
50C43⋊#95—22no—
51C43⋊#95—21no—
52C43⋊#95C2312yes—
53C23×C4×C43D411yescharacteristic
54C4⋊Q8×C43—24no—
55C4⋊Q8×C43—21no—
56C4⋊Q8×C43—21no—
57C4⋊Q8×C43—24no—
58C4⋊Q8×C43D412yes—
59C4⋊Q8×C43D412yes—
60#125×C43—24no—
61#125×C43—22no—
62#125×C43—24no—
63#125×C43—22no—
64C22⋊Q8×C43—24no—
65C22⋊Q8×C43—24no—
66C22⋊Q8×C43—24no—
67C22⋊Q8×C43—22no—
68C22⋊Q8×C43—22no—
69C22⋊Q8×C43—22no—
70C22⋊Q8×C43—24no—
71C22⋊Q8×C43C2314yes—
72C4×Q8×C43—22no—
73C4×Q8×C43—22no—
74C4×Q8×C43—22no—
75C4×Q8×C43D414yes—
76#117×C43—22no—
77#117×C43—22no—
78#117×C43—22no—
79#117×C43—22no—
80#117×C43—22no—
81#117×C43—22no—
82C2×C4⋊C4×C43—21no—
83C2×C4⋊C4×C43—21no—
84C2×C4⋊C4×C43D411yescharacteristic
85C2×C4⋊C4×C43C2311yescharacteristic
86C2×C22⋊C4×C43—22no—
87C2×C22⋊C4×C43D411yescharacteristic
88C2×C22⋊C4×C43C2311yescharacteristic
89C2×C42×C43—22no—
90C2×C42×C43D411yescharacteristic
91C2×C42×C43C2311yescharacteristic
92C24×C43C2×D411yescharacteristic
93C2×Q8×C43—22no—
94C2×Q8×C43—22no—
95C2×Q8×C43—22no—
96C2×Q8×C43C2×D414yes—
97C22×C4×C43—21no—
98C22×C4×C43—21no—
99C22×C4×C43—22no—
100C22×C4×C43—22no—
101C22×C4×C43—22no—
102C22×C4×C43SD1614yes—
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2411yescharacteristic
109C22×Dic43—22no—
110C22×Dic43—22no—
111C2×Dic86—41no—
112C2×Dic86—41no—
113C2×Dic86—42no—
114C2×Dic86—42no—
115C4⋊C4×C43—22no—
116C4⋊C4×C43—22no—
117C4⋊C4×C43—22no—
118C4⋊C4×C43—24no—
119C4⋊C4×C43—24no—
120C4⋊C4×C43—22no—
121C4⋊C4×C43—22no—
122C4⋊C4×C43—22no—
123C4⋊C4×C43—22no—
124C4⋊C4×C43—22no—
125C4⋊C4×C43—24no—
126C4⋊C4×C43—22no—
127C4⋊C4×C43—24no—
128C4⋊C4×C43C2×D414yes—
129C22⋊C4×C43—24no—
130C22⋊C4×C43—22no—
131C22⋊C4×C43—22no—
132C22⋊C4×C43—24no—
133C42×C43—24no—
134C42×C43—24no—
135C42×C43—21no—
136C42×C43—21no—
137C42×C43C2×D412yes—
138C42×C43C2×D412yes—
139C22⋊Dic43—44no—
140C4⋊Dic43—24no—
141C4⋊Dic43—42no—
142C4⋊Dic43—42no—
143Dic43⋊C4—44no—
144C2×C43⋊C8—24no—
145C23×C43—21no—
146C23×C43—21no—
147C23×C43—41no—
148C23×C43—41no—
149C23×C43C2×SD1612yes—
150C23×C43C22×D411yescharacteristic
151Q8×C43—44no—
152Q8×C43—82no—
153Q8×C43—82no—
154Q8×C43—82no—
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43—24no—
158C2×C4×C43—24no—
159C2×C4×C43—24no—
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—24no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—82no—
168C2×C4×C43—82no—
169C2×C4×C43#12012yes—
170C2×C4×C43#12011yescharacteristic
171C2×C4×C43#12011yescharacteristic
172C2×C4×C43C2×SD1612yes—
173C2×C4×C43C2×SD1612yes—
174C2×C4×C43#13712yes—
175C2×C4×C43C22×D412yes—
176C2×Dic43—42no—
177C2×Dic43—42no—
178C2×Dic43—42no—
179C2×Dic43—42no—
180C2×Dic43—42no—
181C2×Dic43—42no—
182Dic86—82no—
183Dic86—82no—
184C43⋊C8—44no—
185#18310—431nomaximal, Sylow
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—22no—
189C22×C43—42no—
190C22×C43—41no—
191C22×C43—41no—
192C22×C43—81no—
193C22×C43C2×#12011yescharacteristic
194C22×C43C22×SD1611yescharacteristic
195C22×C43C2×#13711yescharacteristic
196C4×C43—22no—
197C4×C43—22no—
198C4×C43—22no—
199C4×C43—41no—
200C4×C43—44no—
201C4×C43—41no—
202C4×C43—44no—
203C4×C43#44812yes—
204C4×C43#44812yes—
205Dic43—82no—
206Dic43—82no—
207#3458D4311yescharacteristic
208#3229—432no—
209#2621—431no—
210#1611—434no—
211#1608—434no—
212#1518—432no—
213#1458—431no—
214C2×C43—21no—
215C2×C43—21no—
216C2×C43—42no—
217C2×C43C2×#44811yescharacteristic
218C2×C43#302211yescharacteristic
219C2×C43#302811yescharacteristic
220#544—22no—
221#544—22no—
222#544—21no—
223#544C2×D4312yes—
224#543—21no—
225#543C2×D4312yes—
226#533—24no—
227#533—21no—
228#533C2×D4312yes—
229C2×C4⋊Q8—431no—
230C2×C22⋊Q8—861no—
231C2×#117—21no—
232C2×#117C2×D4311yescharacteristic
233#498—862no—
234#487—862no—
235#483—438no—
236#475—864no—
237#431—432no—
238#398—432no—
239#398—861no—
240#397—432no—
241#397—861no—
242#391—861no—
243#382—431no—
244#328—438no—
245#324—432no—
246#323—432no—
247C43#1831011yescharacteristic, complemented, Sylow
248C22×Q8—861no—
249C23×C4C22⋊D4311yescharacteristic
250C4⋊Q8—24no—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8—24no—
254C4⋊Q8—862no—
255C4⋊Q8—862no—
256C4⋊Q8C22⋊D4312yes—
257C4⋊Q8C22⋊D4312yes—
258#125—24no—
259#125—22no—
260#125—24no—
261#125—22no—
262C22⋊Q8—24no—
263C22⋊Q8—24no—
264C22⋊Q8—24no—
265C22⋊Q8—22no—
266C22⋊Q8—22no—
267C22⋊Q8—22no—
268C22⋊Q8—24no—
269C22⋊Q8—1724no—
270C22⋊Q8C22×D4314yes—
271C4×Q8—22no—
272C4×Q8—22no—
273C4×Q8—22no—
274C4×Q8C22⋊D4314yes—
275#117—22no—
276#117—22no—
277#117—22no—
278#117—22no—
279#117—22no—
280#117—22no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—432no—
284C2×C4⋊C4—862no—
285C2×C4⋊C4—861no—
286C2×C4⋊C4—861no—
287C2×C4⋊C4C22⋊D4311yescharacteristic
288C2×C4⋊C4C22×D4311yescharacteristic
289C2×C22⋊C4—22no—
290C2×C22⋊C4—862no—
291C2×C22⋊C4C22⋊D4311yescharacteristic
292C2×C22⋊C4C22×D4311yescharacteristic
293C2×C42—22no—
294C2×C42C22⋊D4311yescharacteristic
295C2×C42C22×D4311yescharacteristic
296#106—868no—
297C4⋊C8—862no—
298#103—868no—
299C22⋊C8—434no—
300C4×C8—862no—
301#95—432no—
302#95—861no—
303#95—862no—
304#95—862no—
305C24C2×C22⋊D4311yescharacteristic
306C2×Q8—22no—
307C2×Q8—22no—
308C2×Q8—22no—
309C2×Q8—1721no—
310C2×Q8—1721no—
311C2×Q8—1722no—
312C2×Q8—1722no—
313C2×Q8C2×C22⋊D4314yes—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—862no—
320C22×C4—862no—
321C22×C4#1062188414yes—
322C22×C4C2×C22⋊D4311yescharacteristic
323C22×C4C2×C22⋊D4311yescharacteristic
324C22×C4C2×C22⋊D4311yescharacteristic
325C22×C4C2×C22⋊D4311yescharacteristic
326C22×C4C2×C22⋊D4311yescharacteristic
327C22×C4C23×D4311yescharacteristic
328C2×C8—864no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—24no—
333C4⋊C4—24no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—24no—
340C4⋊C4—22no—
341C4⋊C4—24no—
342C4⋊C4—864no—
343C4⋊C4—1722no—
344C4⋊C4—1724no—
345C4⋊C4—1722no—
346C4⋊C4C2×C22⋊D4314yes—
347C22⋊C4—24no—
348C22⋊C4—24no—
349C22⋊C4—22no—
350C22⋊C4—22no—
351C22⋊C4—1724no—
352C42—24no—
353C42—24no—
354C42—21no—
355C42—21no—
356C42C2×C22⋊D4312yes—
357C42C2×C22⋊D4312yes—
358C23—21no—
359C23—21no—
360C23—41no—
361C23—41no—
362C23C2×#1062188412yes—
363C23C22×C22⋊D4311yescharacteristic
364Q8—44no—
365Q8—82no—
366Q8—82no—
367Q8—82no—
368Q8—3442no—
369Q8—3442no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—24no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4—1722no—
385C2×C4—1722no—
386C2×C4—1722no—
387C2×C4—1722no—
388C2×C4—1722no—
389C2×C4—1722no—
390C2×C4#1306329412yes—
391C2×C4#1306329411yescharacteristic
392C2×C4#1306329411yescharacteristic
393C2×C4C2×#1062188412yes—
394C2×C4C2×#1062188412yes—
395C2×C4#1306335612yes—
396C2×C4C22×C22⋊D4312yes—
397C8—1724no—
398C22—21no—
399C22—21no—
400C22—22no—
401C22—42no—
402C22—41no—
403C22—41no—
404C22—81no—
405C22C2×#1306329411yescharacteristic
406C22C22×#1062188411yescharacteristic
407C22C2×#1306335611yescharacteristic
408C4—22no—
409C4—22no—
410C4—22no—
411C4—41no—
412C4—44no—
413C4—41no—
414C4—44no—
415C4—3442no—
416C4—3442no—
417C4#1458303812yes—
418C4#1458303812yes—
419C2—21no—
420C2—21no—
421C2—42no—
422C2C2×#1458303811yescharacteristic
423C2#1914397411yescharacteristic
424C2#1914400111yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3458C2
socleC22×C43C2×#120
prime radicalC24×C43C2×D4
hypercenter#3458D43
hypocenterC43#18310
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3458

Complements

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

NH ≅ G/Ntype
1. #19145736C2semidirect
3. #19133603C2semidirect
5. #19133159C2semidirect
247. C43#18310semidirect

Maximal subgroups

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

subgroupindex
#191457362
#191403612
#191336032
#191335862
#191331592
#191329092
C43×#34582
#1831043