Finite Group Databasebeta

← #24992553

Subgroups — #24992553

Order 11008.

500 conjugacy classes of subgroups.

The subgroup lattice has 396 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×#2356C211yesmaximal, 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×C43C2211yescharacteristic
22C43×#391—21no—
23C43×#387—22no—
24C43×#383—21no—
25C43×#382C2211yescharacteristic
26C4×C4⋊C4×C43—21no—
27C4×C4⋊C4×C43C2211yescharacteristic
28C43×#376—21no—
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×C43C2×C412yes—
56C4×Q8×C43D412yes—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43D411yescharacteristic
61C2×C42×C43—21no—
62C2×C42×C43—22no—
63C2×C42×C43—21no—
64C2×C42×C43C2311yescharacteristic
65#95×C43—22no—
66#95×C43—22no—
67#95×C43—22no—
68#95×C43—21no—
69#95×C43D411yescharacteristic
70#95×C43D411yescharacteristic
71#95×C43D412yes—
72C2×Q8×C43—21no—
73C2×Q8×C43—21no—
74C2×Q8×C43—21no—
75C2×Q8×C43—21no—
76C2×Q8×C43—21no—
77C2×Q8×C43C22⋊C412yes—
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43—22no—
82C22×C4×C43—21no—
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C2×C22⋊D43—41no—
87#10621898—41no—
88#10621898—41no—
89#10621898—41no—
90#10621898—41no—
91C2×D172—21no—
92C2×D172—21no—
93C2×D172—21no—
94C2×C4×D43—41no—
95C2×Dic86—21no—
96C4⋊C4×C43—22no—
97C4⋊C4×C43—22no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—42no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43—41no—
102C4⋊C4×C43C22⋊C412yes—
103C42×C43—22no—
104C42×C43—22no—
105C42×C43—44no—
106C42×C43—41no—
107C42×C43—41no—
108C42×C43C22×C411yescharacteristic
109C42×C43C2×D411yescharacteristic
110C42×C43#4111yescharacteristic
111C42×C43#4111yescharacteristic
112#10621885—44no—
113#10621884—44no—
114(C2×D43)⋊C4—41no—
115(C2×D43)⋊C4—41no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118#10621877—41no—
119#10621877—41no—
120C2×C43⋊C8—22no—
121C2×C43⋊C8—41no—
122C2×C43⋊C8—41no—
123C23×C43#12011yescharacteristic
124C22×D43—41no—
125Q8×C43—22no—
126Q8×C43—22no—
127Q8×C43—41no—
128Q8×C43—41no—
129C2×C4×C43—22no—
130C2×C4×C43—22no—
131C2×C4×C43—22no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—42no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43—41no—
139C2×C4×C43—42no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—42no—
143C2×C4×C43—41no—
144C2×C4×C43—42no—
145C2×C4×C43C2×C22⋊C411yescharacteristic
146C2×C4×C43C4×D411yescharacteristic
147C2×C4×C43C4×D411yescharacteristic
148C2×C4×C43#12111yescharacteristic
149C2×C4×C43#12111yescharacteristic
150C2×C4×C43#12311yescharacteristic
151C2×C4×C43#13511yescharacteristic
152C2×C4×C43#13511yescharacteristic
153C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
155C22⋊D43—81no—
156C22⋊D43—81no—
157C2×Dic43—41no—
158D172—41no—
159D172—41no—
160D172—81no—
161D172—81no—
162C4×D43—81no—
163C4×D43—81no—
164Dic86—41no—
165Dic86—41no—
166C43⋊C8—42no—
167C43⋊C8—81no—
168C43⋊C8—81no—
169#9182—431nomaximal, Sylow
170C22×C43—21no—
171C22×C43—21no—
172C22×C43#38611yescharacteristic
173C22×C43#44911yescharacteristic
174C22×C43#44911yescharacteristic
175C2×D43—81no—
176C2×D43—81no—
177C2×D43—81no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—42no—
183C4×C43—42no—
184C4×C43—42no—
185C4×C43—81no—
186C4×C43—82no—
187C4×C43#41611yescharacteristic
188C4×C43#41811yescharacteristic
189C4×C43#48211yescharacteristic
190C4×C43#48211yescharacteristic
191Dic43—81no—
192#3037—431no—
193#2356D4311yescharacteristic, complemented
194#1517—431no—
195#1502—431no—
196#1479—431no—
197#1303—431no—
198#1286—431no—
199C2×C43—21no—
200C2×C43—21no—
201C2×C43#187511yescharacteristic
202C2×C43#190511yescharacteristic
203C2×C43#190611yescharacteristic
204D43—161no—
205C2×#137—861no—
206#532—431no—
207C2×C4×Q8C2×D4311yescharacteristic
208#464—862no—
209#462—432no—
210#460—432no—
211#431—431no—
212#431—431no—
213#423—431no—
214#417—861no—
215#391—21no—
216#387—22no—
217#383—21no—
218#382C2×D4311yescharacteristic
219C4×C4⋊C4—21no—
220C4×C4⋊C4C2×D4311yescharacteristic
221#376—21no—
222#327—861no—
223#327—861no—
224#327—862no—
225Q8⋊C8—862no—
226C43#918211yescharacteristic, complemented, Sylow
227C2×#41—861no—
228C22×Q8C22⋊D4311yescharacteristic
229#137—1722no—
230#137—1722no—
231C2×Q16—862no—
232C2×SD16—862no—
233C2×M16—861no—
234C4⋊Q8—431no—
235#127—431no—
236#124—861no—
237#121—861no—
238#121—861no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8C4×D4312yes—
242C4×Q8D17212yes—
243C4×D4—861no—
244C4×D4—861no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4C22⋊D4311yescharacteristic
249C2×C42—21no—
250C2×C42—22no—
251C2×C42—21no—
252C2×C42C22×D4311yescharacteristic
253C4⋊C8—432no—
254C4⋊C8—861no—
255C4⋊C8—861no—
256C4⋊C8—861no—
257#103—862no—
258#102—862no—
259C22⋊C8—861no—
260C22⋊C8—861no—
261C4×C8—861no—
262C4×C8—861no—
263#95—22no—
264#95—22no—
265#95—22no—
266#95—21no—
267#95C22⋊D4311yescharacteristic
268#95C22⋊D4311yescharacteristic
269#95C22⋊D4312yes—
270#41—1721no—
271#41—1721no—
272#41—1721no—
273#41—1721no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8—861no—
280C2×Q8(C2×D43)⋊C412yes—
281C2×D4—861no—
282C2×D4—861no—
283C2×D4—861no—
284C2×D4—1721no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—22no—
289C22×C4—21no—
290C22×C4—1721no—
291C22×C4C2×C22⋊D4311yescharacteristic
292C22×C4C2×C22⋊D4311yescharacteristic
293C22×C4C2×C22⋊D4311yescharacteristic
294Q16—1724no—
295SD16—1724no—
296M16—1721no—
297M16—1721no—
298C2×C8—862no—
299C2×C8—1721no—
300C2×C8—1721no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—21no—
304C4⋊C4—42no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—861no—
308C4⋊C4—861no—
309C4⋊C4(C2×D43)⋊C412yes—
310C22⋊C4—1721no—
311C22⋊C4—1721no—
312C42—22no—
313C42—22no—
314C42—44no—
315C42—41no—
316C42—41no—
317C42C2×C4×D4311yescharacteristic
318C42C2×D17211yescharacteristic
319C42#1062189811yescharacteristic
320C42#1062189811yescharacteristic
321C23—1721no—
322C23#1306329411yescharacteristic
323Q8—22no—
324Q8—22no—
325Q8—41no—
326Q8—41no—
327Q8—1721no—
328Q8—1721no—
329D4—3441no—
330D4—3441no—
331D4—3441no—
332D4—3441no—
333D4—1721no—
334D4—1721no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—3441no—
352C2×C4—3441no—
353C2×C4—1721no—
354C2×C4C2×(C2×D43)⋊C411yescharacteristic
355C2×C4C4×C22⋊D4311yescharacteristic
356C2×C4C4×C22⋊D4311yescharacteristic
357C2×C4#1306329911yescharacteristic
358C2×C4#1306329911yescharacteristic
359C2×C4#1306330811yescharacteristic
360C2×C4#1306334511yescharacteristic
361C2×C4#1306334511yescharacteristic
362C2×C4#1306335011yescharacteristic
363C2×C4#1306335011yescharacteristic
364C8—3441no—
365C8—3441no—
366C8—1722no—
367C22—21no—
368C22—21no—
369C22—3441no—
370C22—3441no—
371C22—3441no—
372C22#1458277811yescharacteristic
373C22#1458304411yescharacteristic
374C22#1458304411yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—42no—
380C4—42no—
381C4—42no—
382C4—81no—
383C4—82no—
384C4—3441no—
385C4#1458289311yescharacteristic
386C4#1458290311yescharacteristic
387C4#1458322311yescharacteristic
388C4#1458322311yescharacteristic
389C2—21no—
390C2—21no—
391C2—6881no—
392C2#1913491711yescharacteristic
393C2#1913508911yescharacteristic
394C2#1913509611yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2356C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#2356D43
hypocenterC43#9182
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2356

Complements

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

NH ≅ G/Ntype
4. #19132990C2semidirect
5. #19132498C2semidirect
6. #19132453C2semidirect
7. C43×#2356C2semidirect
11. #14583109C4semidirect
12. #14583099C4semidirect
193. #2356D43semidirect
226. C43#9182semidirect

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×#23562
#918243