Finite Group Databasebeta

← #24992539

Subgroups — #24992539

Order 11008.

544 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144067C211yesmaximal, characteristic
2#19133154C211yesmaximal, characteristic
3#19133089C211yesmaximal, characteristic
4#19132990C211yesmaximal, characteristic, complemented
5#19132498C211yesmaximal, characteristic, complemented
6#19132453C211yesmaximal, characteristic, complemented
7C43×#2351C211yesmaximal, characteristic, complemented
8C2×#13063356—21no—
9#14583449C2211yescharacteristic
10#14583121—22no—
11#14583109C412yescomplemented
12#14583099C412yescomplemented
13#14582952C2211yescharacteristic
14#14582952C2211yescharacteristic
15#14582923C2211yescharacteristic
16#14582898—21no—
17#14582632—21no—
18#14582632—21no—
19#14582632—22no—
20Q8⋊(C43⋊C8)—22no—
21C2×C4×Q8×C43—21no—
22C2×C4×Q8×C43C2211yescharacteristic
23C43×#389—21no—
24C43×#389—22no—
25C43×#382—21no—
26C43×#382C2211yescharacteristic
27C4×C4⋊C4×C43—21no—
28C4×C4⋊C4×C43C2211yescharacteristic
29C2×#10621898—21no—
30#13063356—42no—
31#13063356—42no—
32C2×#10621885—22no—
33C2×#10621884—22no—
34C2×#10621877—21no—
35#13063325C2×C411yescharacteristic
36#13063322C2×C411yescharacteristic
37#13063313—21no—
38#13063299—21no—
39#13063299—21no—
40C4×D172—21no—
41C4×D172—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)C2×C412yes—
46#13063248—22no—
47#13063245—22no—
48C22⋊(C43⋊C8)—21no—
49C22⋊(C43⋊C8)—21no—
50C4×C43⋊C8—21no—
51C4×C43⋊C8—21no—
52C22×Q8×C43D411yescharacteristic
53C4×Q8×C43—21no—
54C4×Q8×C43—21no—
55C4×Q8×C43—42no—
56C4×Q8×C43—42no—
57C4×Q8×C43C2×C412yes—
58C4×Q8×C43D412yes—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43—22no—
61C2×C4⋊C4×C43—22no—
62C2×C4⋊C4×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43D411yescharacteristic
65C2×C42×C43—21no—
66C2×C42×C43—22no—
67C2×C42×C43—21no—
68C2×C42×C43C2311yescharacteristic
69#95×C43—22no—
70#95×C43—21no—
71#95×C43D411yescharacteristic
72#95×C43D411yescharacteristic
73#95×C43D412yes—
74C2×Q8×C43—21no—
75C2×Q8×C43—21no—
76C2×Q8×C43—21no—
77C2×Q8×C43C22⋊C412yes—
78C2×Q8×C43D812yes—
79C2×Q8×C43SD1612yes—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43—22no—
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C2×C22⋊D43—41no—
89#10621898—41no—
90#10621898—41no—
91#10621898—41no—
92#10621898—41no—
93C2×D172—21no—
94C2×D172—21no—
95C2×D172—21no—
96C2×C4×D43—41no—
97C2×Dic86—21no—
98C4⋊C4×C43—22no—
99C4⋊C4×C43—22no—
100C4⋊C4×C43—21no—
101C4⋊C4×C43—42no—
102C4⋊C4×C43—44no—
103C4⋊C4×C43—44no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43C22⋊C412yes—
107C42×C43—22no—
108C42×C43—22no—
109C42×C43—44no—
110C42×C43—41no—
111C42×C43—41no—
112C42×C43C22×C411yescharacteristic
113C42×C43C2×D411yescharacteristic
114C42×C43#4111yescharacteristic
115C42×C43#4111yescharacteristic
116#10621885—44no—
117#10621884—44no—
118(C2×D43)⋊C4—41no—
119(C2×D43)⋊C4—41no—
120C4⋊Dic43—21no—
121C4⋊Dic43—21no—
122#10621877—41no—
123#10621877—41no—
124C2×C43⋊C8—22no—
125C2×C43⋊C8—41no—
126C2×C43⋊C8—41no—
127C23×C43#12011yescharacteristic
128C22×D43—41no—
129Q8×C43—22no—
130Q8×C43—22no—
131Q8×C43—22no—
132Q8×C43#10214yes—
133C2×C4×C43—22no—
134C2×C4×C43—22no—
135C2×C4×C43—22no—
136C2×C4×C43—22no—
137C2×C4×C43—22no—
138C2×C4×C43—41no—
139C2×C4×C43—41no—
140C2×C4×C43—42no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—42no—
145C2×C4×C43—41no—
146C2×C4×C43—42no—
147C2×C4×C43—42no—
148C2×C4×C43—41no—
149C2×C4×C43C2×C22⋊C411yescharacteristic
150C2×C4×C43C4×D411yescharacteristic
151C2×C4×C43C4×D411yescharacteristic
152C2×C4×C43#12111yescharacteristic
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43#12311yescharacteristic
155C2×C4×C43C2×D811yescharacteristic
156C2×C4×C43C2×SD1611yescharacteristic
157C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C43#13711yescharacteristic
159C22⋊D43—81no—
160C22⋊D43—81no—
161C2×Dic43—41no—
162D172—41no—
163D172—41no—
164D172—81no—
165D172—81no—
166C4×D43—81no—
167C4×D43—81no—
168Dic86—41no—
169Dic86—41no—
170C43⋊C8—42no—
171C43⋊C8—81no—
172C43⋊C8—81no—
173#9180—431nomaximal, Sylow
174C22×C43—21no—
175C22×C43—21no—
176C22×C43#38611yescharacteristic
177C22×C43#44711yescharacteristic
178C22×C43#44811yescharacteristic
179C2×D43—81no—
180C2×D43—81no—
181C2×D43—81no—
182C4×C43—24no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—42no—
188C4×C43—42no—
189C4×C43—82no—
190C4×C43—81no—
191C4×C43C2×#10211yescharacteristic
192C4×C43#41711yescharacteristic
193C4×C43#48011yescharacteristic
194C4×C43#48111yescharacteristic
195Dic43—81no—
196#3037—431no—
197#2351D4311yescharacteristic, complemented
198#1517—431no—
199#1502—431no—
200#1479—431no—
201#1303—431no—
202#1286—431no—
203C2×C43—21no—
204C2×C43—21no—
205C2×C43#187411yescharacteristic
206C2×C43#190511yescharacteristic
207C2×C43#190611yescharacteristic
208D43—161no—
209C2×#137—861no—
210#532—431no—
211C2×C4×Q8—21no—
212C2×C4×Q8C2×D4311yescharacteristic
213#464—862no—
214#462—432no—
215#460—432no—
216#431—431no—
217#431—431no—
218#423—431no—
219#417—861no—
220#389—21no—
221#389—22no—
222#382—21no—
223#382C2×D4311yescharacteristic
224C4×C4⋊C4—21no—
225C4×C4⋊C4C2×D4311yescharacteristic
226#327—861no—
227#327—861no—
228#327—862no—
229Q8⋊C8—862no—
230C43#918011yescharacteristic, complemented, Sylow
231C2×#41—861no—
232C22×Q8C22⋊D4311yescharacteristic
233#137—1722no—
234#137—1722no—
235C2×Q16—862no—
236C2×SD16—862no—
237C2×M16—861no—
238C4⋊Q8—431no—
239#127—431no—
240#124—861no—
241#121—861no—
242#121—861no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—42no—
246C4×Q8—42no—
247C4×Q8C4×D4312yes—
248C4×Q8D17212yes—
249C4×D4—861no—
250C4×D4—861no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4C22⋊D4311yescharacteristic
257C2×C42—21no—
258C2×C42—22no—
259C2×C42—21no—
260C2×C42C22×D4311yescharacteristic
261C4⋊C8—432no—
262C4⋊C8—861no—
263C4⋊C8—861no—
264C4⋊C8—861no—
265#103—862no—
266#102—862no—
267C22⋊C8—861no—
268C22⋊C8—861no—
269C4×C8—861no—
270C4×C8—861no—
271#95—22no—
272#95—21no—
273#95C22⋊D4311yescharacteristic
274#95C22⋊D4311yescharacteristic
275#95C22⋊D4312yes—
276#41—1721no—
277#41—1721no—
278#41—1721no—
279#41—1721no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—861no—
284C2×Q8(C2×D43)⋊C412yes—
285C2×Q8#1062188212yes—
286C2×Q8#1062188412yes—
287C2×D4—861no—
288C2×D4—861no—
289C2×D4—861no—
290C2×D4—1721no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—22no—
296C22×C4—1721no—
297C22×C4C2×C22⋊D4311yescharacteristic
298C22×C4C2×C22⋊D4311yescharacteristic
299C22×C4C2×C22⋊D4311yescharacteristic
300Q16—1724no—
301SD16—1724no—
302M16—1721no—
303M16—1721no—
304C2×C8—862no—
305C2×C8—1721no—
306C2×C8—1721no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—21no—
310C4⋊C4—44no—
311C4⋊C4—42no—
312C4⋊C4—44no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—861no—
316C4⋊C4—861no—
317C4⋊C4(C2×D43)⋊C412yes—
318C22⋊C4—1721no—
319C22⋊C4—1721no—
320C42—22no—
321C42—22no—
322C42—44no—
323C42—41no—
324C42—41no—
325C42C2×C4×D4311yescharacteristic
326C42C2×D17211yescharacteristic
327C42#1062189811yescharacteristic
328C42#1062189811yescharacteristic
329C23—1721no—
330C23#1306329411yescharacteristic
331Q8—22no—
332Q8—22no—
333Q8—22no—
334Q8—1721no—
335Q8—1721no—
336Q8#1306324514yes—
337D4—3441no—
338D4—3441no—
339D4—3441no—
340D4—3441no—
341D4—1721no—
342D4—1721no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—3441no—
360C2×C4—3441no—
361C2×C4—1721no—
362C2×C4C2×(C2×D43)⋊C411yescharacteristic
363C2×C4C4×C22⋊D4311yescharacteristic
364C2×C4C4×C22⋊D4311yescharacteristic
365C2×C4#1306329911yescharacteristic
366C2×C4#1306329911yescharacteristic
367C2×C4#1306330811yescharacteristic
368C2×C4C2×#1062188211yescharacteristic
369C2×C4C2×#1062188411yescharacteristic
370C2×C4#1306335111yescharacteristic
371C2×C4#1306335611yescharacteristic
372C8—3441no—
373C8—3441no—
374C8—1722no—
375C22—21no—
376C22—21no—
377C22—3441no—
378C22—3441no—
379C22—3441no—
380C22#1458277811yescharacteristic
381C22#1458303311yescharacteristic
382C22#1458303811yescharacteristic
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—24no—
388C4—42no—
389C4—42no—
390C4—82no—
391C4—81no—
392C4—3441no—
393C4C2×#1306324511yescharacteristic
394C4#1458289811yescharacteristic
395C4#1458321211yescharacteristic
396C4#1458321711yescharacteristic
397C2—21no—
398C2—21no—
399C2—6881no—
400C2#1913491211yescharacteristic
401C2#1913508911yescharacteristic
402C2#1913509611yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2351C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#2351D43
hypocenterC43#9180
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2351

Complements

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

NH ≅ G/Ntype
4. #19132990C2semidirect
5. #19132498C2semidirect
6. #19132453C2semidirect
7. C43×#2351C2semidirect
11. #14583109C4semidirect
12. #14583099C4semidirect
197. #2351D43semidirect
230. C43#9180semidirect

Maximal subgroups

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

subgroupindex
#191440672
#191331542
#191330892
#191329902
#191324982
#191324532
C43×#23512
#918043