Finite Group Databasebeta

← #24990497

Subgroups — #24990497

Order 11008.

440 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143713C211yesmaximal, characteristic
2#19134746C211yesmaximal, characteristic, complemented
3C4×#13063251C211yesmaximal, characteristic
4#19133347C211yesmaximal, characteristic, complemented
5#19132983C211yesmaximal, characteristic
6#19132427C211yesmaximal, characteristic, complemented
7C43×#1283C211yesmaximal, characteristic, complemented
8C4×#10621898C2211yescharacteristic
9#14583026—21no—
10#14582976—21no—
11#14582970—22no—
12#14582955—21no—
13#14582952C2211yescharacteristic
14#14582921—21no—
15C2×C4⋊(C43⋊C8)C2211yescharacteristic
16C2×Dic43⋊C8—22no—
17C2×#13063251C411yescharacteristic
18C2×#13063251C411yescharacteristic
19C42×Dic43C2211yescharacteristic
20#14582660C411yescharacteristic
21#14582660C411yescharacteristic
22#14582652—21no—
23#14582650—21no—
24#14582631—21no—
25#14582628—21no—
26C43×#431C2211yescharacteristic
27C2×C4⋊C8×C43C2211yescharacteristic
28C4×M16×C43C2211yescharacteristic
29C2×#10621898C2×C411yescharacteristic
30C2×#10621872—22no—
31C22×C43⋊C8—21no—
32C4×Dic86D411yescharacteristic
33C4×Dic86Q811yescharacteristic
34C4×D172D411yescharacteristic
35C4×D172Q811yescharacteristic
36C4×C22⋊D43—21no—
37C4×C22⋊D43—21no—
38#13063284C2×C411yescharacteristic
39#13063282—21no—
40C2×C4×Dic43—21no—
41C2×C4×Dic43—21no—
42C2×C4×Dic43C2×C411yescharacteristic
43C2×C4×Dic43C2×C411yescharacteristic
44C42×D43—21no—
45C4⋊(C43⋊C8)—21no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)D411yescharacteristic
48C4⋊(C43⋊C8)D411yescharacteristic
49Dic43⋊C8—22no—
50Dic43⋊C8—44no—
51#13063251—22no—
52#13063251—22no—
53C22⋊(C43⋊C8)—21no—
54(C2×D43)⋊C8—22no—
55#13063235—22no—
56C4×C43⋊C8—21no—
57C2×M16×C43C2×C411yescharacteristic
58C2×M16×C43C2×C411yescharacteristic
59C22×C8×C43D412yes—
60C2×C42×C43C2311yescharacteristic
61C4⋊C8×C43—21no—
62C4⋊C8×C43—21no—
63C4⋊C8×C43—21no—
64C22⋊C8×C43—21no—
65#97×C43—21no—
66C4×C8×C43—21no—
67C4×C8×C43—21no—
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43#4111yescharacteristic
71C2×C22⋊D43—21no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74#10621898—21no—
75#10621898—21no—
76#10621898—21no—
77#10621898—21no—
78C2×D172C4⋊C411yescharacteristic
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×Dic86C4⋊C411yescharacteristic
83M16×C43—21no—
84M16×C43—21no—
85M16×C43—21no—
86M16×C43M1612yescomplemented
87C2×C8×C43—21no—
88C2×C8×C43—21no—
89C2×C8×C43—22no—
90C2×C8×C43—42no—
91C2×C8×C43—41no—
92C42×C43C2×D411yescharacteristic
93C42×C43C2×D411yescharacteristic
94C42×C43C2×Q811yescharacteristic
95C42×C43#4111yescharacteristic
96C22⋊Dic43—21no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4—21no—
99C4⋊Dic43C4⋊C411yescharacteristic
100C4⋊Dic43C4⋊C411yescharacteristic
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103C4×Dic43—22no—
104C4×Dic43—22no—
105C4×Dic43—21no—
106C4×Dic43—21no—
107C4×Dic43—21no—
108C4×Dic43—21no—
109C4×Dic43—21no—
110C4×Dic43—21no—
111C4×Dic43—42no—
112C4×Dic43M1612yescomplemented
113C2×C43⋊C8—21no—
114C2×C43⋊C8—21no—
115C2×C43⋊C8—42no—
116C2×C43⋊C8—41no—
117#10621872—82no—
118C23×C43C4×D411yescharacteristic
119C22×D43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—41no—
123C2×C4×C43C2×C4⋊C411yescharacteristic
124C2×C4×C43C4×D411yescharacteristic
125C2×C4×C43#12011yescharacteristic
126C2×C4×C43C22⋊Q811yescharacteristic
127C2×C4×C43C22⋊Q811yescharacteristic
128C2×C4×C43#12311yescharacteristic
129C2×C4×C43C2×M1611yescharacteristic
130C2×C4×C43C2×M1611yescharacteristic
131C2×C4×C43#13111yescharacteristic
132C2×C4×C43#13111yescharacteristic
133C22⋊D43—41no—
134C22⋊D43—41no—
135C2×Dic43—22no—
136C2×Dic43—22no—
137C2×Dic43—22no—
138C2×Dic43—22no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144D172—21no—
145D172—21no—
146C4×D43—41no—
147C4×D43—41no—
148C4×D43—41no—
149C4×D43—41no—
150C4×D43—81no—
151Dic86—21no—
152Dic86—21no—
153C8×C43—22no—
154C8×C43—41no—
155C8×C43—42no—
156C8×C43—81no—
157C43⋊C8—41no—
158C43⋊C8—41no—
159C43⋊C8—81no—
160#8841—431nomaximal, Sylow
161C22×C43—21no—
162C22×C43—21no—
163C22×C43#38511yescharacteristic
164C22×C43#43511yescharacteristic
165C22×C43#43611yescharacteristic
166C2×D43—41no—
167C2×D43—41no—
168C2×D43—41no—
169C4×C43—21no—
170C4×C43—21no—
171C4×C43—21no—
172C4×C43#42311yescharacteristic
173C4×C43#42411yescharacteristic
174C4×C43#43511yescharacteristic
175C4×C43#43611yescharacteristic
176C4×C43#45311yescharacteristic
177C4×C43#45611yescharacteristic
178Dic43—24no—
179Dic43—42no—
180Dic43—41no—
181Dic43—41no—
182Dic43—41no—
183#2989—431no—
184#1842—431no—
185C4×#104—431no—
186#1565—431no—
187#1477—431no—
188#1283D4311yescharacteristic, complemented
189#1276—431no—
190C2×C43—21no—
191C2×C43—21no—
192C2×C43#185111yescharacteristic
193C2×C43#185911yescharacteristic
194C2×C43#186111yescharacteristic
195D43—81no—
196C4×#41—431no—
197#446—861no—
198#436—861no—
199#435—862no—
200#432—861no—
201#431—431no—
202#431C2×D4311yescharacteristic
203#423—861no—
204C2×C4⋊C8—431no—
205C2×C4⋊C8—862no—
206C2×C4⋊C8C2×D4311yescharacteristic
207C2×#104—431no—
208C2×#104—431no—
209C4×M16C2×D4311yescharacteristic
210C43—431no—
211#339—431no—
212#339—431no—
213#335—861no—
214#334—861no—
215Q8⋊C8—861no—
216D4⋊C8—861no—
217C43#884111yescharacteristic, complemented, Sylow
218C2×#41—431no—
219C2×M16—862no—
220C2×M16C4×D4311yescharacteristic
221C2×M16C4×D4311yescharacteristic
222C22×C8—861no—
223C22×C8D17212yes—
224C4×Q8—431no—
225C4×Q8—431no—
226C4×D4—431no—
227C4×D4—431no—
228C4×D4—861no—
229C4×D4—861no—
230#117—431no—
231#117—861no—
232C2×C42—431no—
233C2×C42—431no—
234C2×C42—861no—
235C2×C42—861no—
236C2×C42—861no—
237C2×C42C22×D4311yescharacteristic
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—431no—
242C4⋊C8—431no—
243C4⋊C8—862no—
244C4⋊C8—861no—
245C4⋊C8—861no—
246C4⋊C8—1724no—
247#104—862no—
248#104—862no—
249C22⋊C8—21no—
250C22⋊C8—862no—
251C22⋊C8—861no—
252#97—21no—
253#97—862no—
254C4×C8—21no—
255C4×C8—21no—
256C4×C8—861no—
257#41—861no—
258#41—861no—
259#41—861no—
260#41—861no—
261C2×Q8—431no—
262C2×D4—431no—
263C2×D4—861no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4C2×C4×D4311yescharacteristic
270C22×C4C2×D17211yescharacteristic
271C22×C4#1062189811yescharacteristic
272M16—21no—
273M16—21no—
274M16—21no—
275M16—3442no—
276M16#1062187212yescomplemented
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—22no—
280C2×C8—42no—
281C2×C8—41no—
282C2×C8—861no—
283C2×C8—861no—
284C2×C8—1722no—
285C2×C8—1721no—
286C4⋊C4—431no—
287C4⋊C4—431no—
288C4⋊C4—861no—
289C4⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C42—432no—
294C42—862no—
295C42—862no—
296C42—861no—
297C42—861no—
298C42—861no—
299C42—861no—
300C42—861no—
301C42—861no—
302C42—1722no—
303C42D4×D4311yescharacteristic
304C42D4×D4311yescharacteristic
305C42#1062190011yescharacteristic
306C42Q8×D4311yescharacteristic
307C23—861no—
308C23C4×D17211yescharacteristic
309Q8—861no—
310Q8—861no—
311D4—861no—
312D4—861no—
313D4—1721no—
314D4—1721no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—862no—
319C2×C4—862no—
320C2×C4—862no—
321C2×C4—862no—
322C2×C4—861no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—3441no—
326C2×C4—1721no—
327C2×C4—1721no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4—1721no—
331C2×C4—1721no—
332C2×C4C4⋊C4×D4311yescharacteristic
333C2×C4(C22⋊D43)⋊C411yescharacteristic
334C2×C4#1306329511yescharacteristic
335C2×C4#1306330311yescharacteristic
336C2×C4#1306330511yescharacteristic
337C2×C4#1306330711yescharacteristic
338C2×C4M16×D4311yescharacteristic
339C2×C4C2×#1062187211yescharacteristic
340C2×C4#1306333111yescharacteristic
341C2×C4#1306333311yescharacteristic
342C8—22no—
343C8—42no—
344C8—41no—
345C8—81no—
346C8—3441no—
347C8—1721no—
348C8—1721no—
349C22—21no—
350C22—21no—
351C22—1721no—
352C22—1721no—
353C22—1721no—
354C22#1458277311yescharacteristic
355C22#1458297211yescharacteristic
356C22#1458297811yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—864no—
361C4—1722no—
362C4—1721no—
363C4—1721no—
364C4—1721no—
365C4#1458292111yescharacteristic
366C4#1458292411yescharacteristic
367C4#1458296711yescharacteristic
368C4#1458297411yescharacteristic
369C4#1458306911yescharacteristic
370C4#1458308411yescharacteristic
371C2—21no—
372C2—21no—
373C2—3441no—
374C2#1913477911yescharacteristic
375C2#1913482411yescharacteristic
376C2#1913483811yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1283C2
socleC22×C43#385
prime radicalC2×#10621898C2×C4
cosocleC2×C42×C43C23
hypercenter#1283D43
hypocenterC43#8841
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1283

Complements

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

NH ≅ G/Ntype
2. #19134746C2semidirect
4. #19133347C2semidirect
6. #19132427C2semidirect
7. C43×#1283C2semidirect
86. M16×C43M16semidirect
112. C4×Dic43M16semidirect
188. #1283D43semidirect
217. C43#8841semidirect
276. M16#10621872semidirect

Maximal subgroups

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

subgroupindex
#191437132
#191347462
C4×#130632512
#191333472
#191329832
#191324272
C43×#12832
#884143