Finite Group Databasebeta

← #24992897

Subgroups — #24992897

Order 11008.

512 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144626C211yesmaximal, characteristic
2#19135423C211yesmaximal, characteristic
3#19133089C211yesmaximal, characteristic
4#19133024C211yesmaximal, characteristic, complemented
5#19132498C211yesmaximal, characteristic, complemented
6#19132428C211yesmaximal, characteristic, complemented
7C43×#2295C211yesmaximal, characteristic, complemented
8#14583449C2211yescharacteristic
9#14583217—21no—
10#14583184C412yescomplemented
11#14583099C412yescomplemented
12#14583038—21no—
13C4×#10621884—22no—
14#14582952C2211yescharacteristic
15#14582952C2211yescharacteristic
16#14582923C2211yescharacteristic
17C2×#13063253—21no—
18C2×#13063253—21no—
19#14582632—22no—
20Q8⋊(C43⋊C8)—22no—
21C2×C4×Q8×C43C2211yescharacteristic
22C43×#391—21no—
23C43×#389—21no—
24C43×#387—22no—
25C4×C4⋊C4×C43—21no—
26C4×C4⋊C4×C43C2211yescharacteristic
27C43×#376—21no—
28C43×C43C2211yescharacteristic
29C2×#10621898—21no—
30C2×#10621884—22no—
31C2×#10621877—21no—
32#13063325C2×C411yescharacteristic
33#13063322C2×C411yescharacteristic
34#13063313—21no—
35#13063299—21no—
36#13063299—21no—
37C4×D172—21no—
38C4×D172—21no—
39#13063256—22no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)C2×C412yes—
44#13063253—42no—
45#13063253—42no—
46#13063249—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—22no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43D411yescharacteristic
61C2×C42×C43—21no—
62C2×C42×C43—21no—
63C2×C42×C43—21no—
64C2×C42×C43—21no—
65C2×C42×C43D411yescharacteristic
66C2×C42×C43D411yescharacteristic
67C2×C42×C43C2311yescharacteristic
68#95×C43—22no—
69#95×C43—22no—
70#95×C43—22no—
71#95×C43D412yes—
72C2×Q8×C43—21no—
73C2×Q8×C43—42no—
74C2×Q8×C43C22⋊C412yes—
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—22no—
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D411yescharacteristic
83C2×C22⋊D43—41no—
84#10621898—41no—
85#10621898—41no—
86#10621898—41no—
87#10621898—41no—
88C2×D172—21no—
89C2×D172—21no—
90C2×D172—21no—
91C2×C4×D43—41no—
92C2×Dic86—21no—
93C4⋊C4×C43—22no—
94C4⋊C4×C43—22no—
95C4⋊C4×C43—21no—
96C4⋊C4×C43—42no—
97C4⋊C4×C43—44no—
98C4⋊C4×C43C22⋊C412yes—
99C42×C43—22no—
100C42×C43—22no—
101C42×C43—21no—
102C42×C43—21no—
103C42×C43—21no—
104C42×C43—42no—
105C42×C43—42no—
106C42×C43—41no—
107C42×C43—41no—
108C42×C43SD1612yescomplemented
109C42×C43C22×C411yescharacteristic
110C42×C43C2×D411yescharacteristic
111C42×C43#4111yescharacteristic
112C42×C43#4111yescharacteristic
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—42no—
128C2×C4×C43—22no—
129C2×C4×C43—22no—
130C2×C4×C43—22no—
131C2×C4×C43—22no—
132C2×C4×C43—22no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—42no—
138C2×C4×C43—42no—
139C2×C4×C43—41no—
140C2×C4×C43—42no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43C2×C22⋊C411yescharacteristic
144C2×C4×C43C4×D411yescharacteristic
145C2×C4×C43C4×D411yescharacteristic
146C2×C4×C43#12111yescharacteristic
147C2×C4×C43#12111yescharacteristic
148C2×C4×C43#12311yescharacteristic
149C2×C4×C43C2×SD1611yescharacteristic
150C2×C4×C43#13511yescharacteristic
151C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C43#13711yescharacteristic
153C22⋊D43—81no—
154C22⋊D43—81no—
155C2×Dic43—41no—
156D172—42no—
157D172—41no—
158D172—41no—
159D172—81no—
160C4×D43—81no—
161C4×D43—81no—
162Dic86—41no—
163Dic86—41no—
164C43⋊C8—42no—
165C43⋊C8—81no—
166C43⋊C8—81no—
167#9238—431nomaximal, Sylow
168C22×C43—21no—
169C22×C43—21no—
170C22×C43#38611yescharacteristic
171C22×C43#44811yescharacteristic
172C22×C43#44911yescharacteristic
173C2×D43—81no—
174C2×D43—81no—
175C2×D43—81no—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—42no—
180C4×C43—42no—
181C4×C43—42no—
182C4×C43—42no—
183C4×C43—82no—
184C4×C43#42112yes—
185C4×C43C4×SD1611yescharacteristic
186C4×C43#44011yescharacteristic
187C4×C43#46011yescharacteristic
188C4×C43#46411yescharacteristic
189Dic43—81no—
190#3103—431no—
191#2295D4311yescharacteristic, complemented
192#1962—431no—
193#1502—431no—
194#1487—431no—
195#1303—431no—
196#1276—431no—
197C2×C43—21no—
198C2×C43—21no—
199C2×C43#188011yescharacteristic
200C2×C43#189711yescharacteristic
201C2×C43#190611yescharacteristic
202D43—161no—
203#532—431no—
204C2×C4×Q8C2×D4311yescharacteristic
205#481—861no—
206#475—432no—
207#460—432no—
208#448—861no—
209C4×SD16—862no—
210#431—431no—
211#431—431no—
212#423—431no—
213C2×#104—861no—
214C2×#104—861no—
215#391—21no—
216#389—21no—
217#387—22no—
218C4×C4⋊C4—21no—
219C4×C4⋊C4C2×D4311yescharacteristic
220#376—21no—
221C43C2×D4311yescharacteristic
222#327—862no—
223Q8⋊C8—862no—
224C43#923811yescharacteristic, complemented, Sylow
225C2×#41—861no—
226C22×Q8C22⋊D4311yescharacteristic
227C2×SD16—862no—
228C2×M16—861no—
229C4⋊Q8—431no—
230#127—431no—
231#124—861no—
232#121—861no—
233#121—861no—
234C4×Q8—21no—
235C4×Q8—21no—
236C4×Q8C4×D4312yes—
237C4×Q8D17212yes—
238C4×D4—861no—
239C4×D4—861no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4C22⋊D4311yescharacteristic
244C2×C42—21no—
245C2×C42—21no—
246C2×C42—21no—
247C2×C42—21no—
248C2×C42C22⋊D4311yescharacteristic
249C2×C42C22⋊D4311yescharacteristic
250C2×C42C22×D4311yescharacteristic
251#106—862no—
252C4⋊C8—432no—
253C4⋊C8—861no—
254C4⋊C8—861no—
255C4⋊C8—861no—
256#104—1722no—
257#104—1722no—
258#103—862no—
259#102—862no—
260C22⋊C8—861no—
261C22⋊C8—861no—
262C4×C8—861no—
263C4×C8—861no—
264#95—22no—
265#95—22no—
266#95—22no—
267#95C22⋊D4312yes—
268#41—1721no—
269#41—1721no—
270#41—1721no—
271#41—1721no—
272C2×Q8—21no—
273C2×Q8—42no—
274C2×Q8—861no—
275C2×Q8(C2×D43)⋊C412yes—
276C2×D4—861no—
277C2×D4—861no—
278C2×D4—861no—
279C2×D4—1721no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—1721no—
286C22×C4C2×C22⋊D4311yescharacteristic
287C22×C4C2×C22⋊D4311yescharacteristic
288C22×C4C2×C22⋊D4311yescharacteristic
289SD16—1724no—
290M16—1721no—
291M16—1721no—
292C2×C8—862no—
293C2×C8—1721no—
294C2×C8—1721no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—42no—
299C4⋊C4—44no—
300C4⋊C4—861no—
301C4⋊C4—861no—
302C4⋊C4(C2×D43)⋊C412yes—
303C22⋊C4—1721no—
304C22⋊C4—1721no—
305C42—22no—
306C42—22no—
307C42—21no—
308C42—21no—
309C42—21no—
310C42—42no—
311C42—42no—
312C42—41no—
313C42—41no—
314C42#1062188412yescomplemented
315C42C2×C4×D4311yescharacteristic
316C42C2×D17211yescharacteristic
317C42#1062189811yescharacteristic
318C42#1062189811yescharacteristic
319C23—1721no—
320C23#1306329411yescharacteristic
321Q8—22no—
322Q8—22no—
323Q8—42no—
324Q8—1721no—
325Q8—1721no—
326D4—3441no—
327D4—3441no—
328D4—3441no—
329D4—1722no—
330D4—1721no—
331D4—1721no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—3441no—
348C2×C4—3441no—
349C2×C4—1721no—
350C2×C4C2×(C2×D43)⋊C411yescharacteristic
351C2×C4C4×C22⋊D4311yescharacteristic
352C2×C4C4×C22⋊D4311yescharacteristic
353C2×C4#1306329911yescharacteristic
354C2×C4#1306329911yescharacteristic
355C2×C4#1306330811yescharacteristic
356C2×C4C2×#1062188411yescharacteristic
357C2×C4#1306334511yescharacteristic
358C2×C4#1306335011yescharacteristic
359C2×C4#1306335611yescharacteristic
360C8—3441no—
361C8—3441no—
362C8—1722no—
363C22—21no—
364C22—21no—
365C22—3441no—
366C22—3441no—
367C22—3441no—
368C22#1458277811yescharacteristic
369C22#1458303811yescharacteristic
370C22#1458304411yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—42no—
375C4—42no—
376C4—42no—
377C4—42no—
378C4—82no—
379C4—3441no—
380C4#1458291712yes—
381C4C4×#1062188411yescharacteristic
382C4#1458299711yescharacteristic
383C4#1458309911yescharacteristic
384C4#1458312111yescharacteristic
385C2—21no—
386C2—21no—
387C2—6881no—
388C2#1913495011yescharacteristic
389C2#1913504311yescharacteristic
390C2#1913509611yescharacteristic
subgroupG/H
centerC2×C4#13063299
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2295C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#2295D43
hypocenterC43#9238
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2295

Complements

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

NH ≅ G/Ntype
4. #19133024C2semidirect
5. #19132498C2semidirect
6. #19132428C2semidirect
7. C43×#2295C2semidirect
10. #14583184C4semidirect
11. #14583099C4semidirect
108. C42×C43SD16semidirect
191. #2295D43semidirect
224. C43#9238semidirect
314. C42#10621884semidirect

Maximal subgroups

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

subgroupindex
#191446262
#191354232
#191330892
#191330242
#191324982
#191324282
C43×#22952
#923843