Finite Group Databasebeta

← #24990504

Subgroups — #24990504

Order 11008.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143713C211yesmaximal, characteristic
2#19134711C211yesmaximal, 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×#13063251C411yescharacteristic
17C2×#13063251C411yescharacteristic
18C42×Dic43C2211yescharacteristic
19#14582660C411yescharacteristic
20#14582660C411yescharacteristic
21#14582653—22no—
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—
50#13063251—22no—
51#13063251—22no—
52C22⋊(C43⋊C8)—21no—
53(C2×D43)⋊C8—22no—
54#13063235—22no—
55C4×C43⋊C8—21no—
56C2×M16×C43C2×C411yescharacteristic
57C2×M16×C43C2×C411yescharacteristic
58C22×C8×C43D412yes—
59C2×C42×C43C2311yescharacteristic
60C4⋊C8×C43—21no—
61C4⋊C8×C43—21no—
62C4⋊C8×C43—21no—
63C22⋊C8×C43—21no—
64#97×C43—21no—
65C4×C8×C43—21no—
66C4×C8×C43—21no—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43#4111yescharacteristic
70C2×C22⋊D43—21no—
71C22×Dic43—21no—
72C22×Dic43—21no—
73#10621898—21no—
74#10621898—21no—
75#10621898—21no—
76#10621898—21no—
77C2×D172C4⋊C411yescharacteristic
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×Dic86C4⋊C411yescharacteristic
82M16×C43—21no—
83M16×C43—21no—
84M16×C43—21no—
85M16×C43M1612yescomplemented
86C2×C8×C43—21no—
87C2×C8×C43—21no—
88C2×C8×C43—22no—
89C2×C8×C43—42no—
90C2×C8×C43—41no—
91C42×C43C2×D411yescharacteristic
92C42×C43C2×D411yescharacteristic
93C42×C43C2×Q811yescharacteristic
94C42×C43#4111yescharacteristic
95C22⋊Dic43—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98C4⋊Dic43C4⋊C411yescharacteristic
99C4⋊Dic43C4⋊C411yescharacteristic
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43—21no—
107C4×Dic43—21no—
108C4×Dic43—42no—
109C4×Dic43—41no—
110C4×Dic43—41no—
111C4×Dic43M1612yescomplemented
112C2×C43⋊C8—21no—
113C2×C43⋊C8—21no—
114C2×C43⋊C8—42no—
115C2×C43⋊C8—41no—
116#10621872—82no—
117C23×C43C4×D411yescharacteristic
118C22×D43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—41no—
122C2×C4×C43C2×C4⋊C411yescharacteristic
123C2×C4×C43C4×D411yescharacteristic
124C2×C4×C43#12011yescharacteristic
125C2×C4×C43C22⋊Q811yescharacteristic
126C2×C4×C43C22⋊Q811yescharacteristic
127C2×C4×C43#12311yescharacteristic
128C2×C4×C43C2×M1611yescharacteristic
129C2×C4×C43C2×M1611yescharacteristic
130C2×C4×C43#13111yescharacteristic
131C2×C4×C43#13111yescharacteristic
132C22⋊D43—41no—
133C22⋊D43—41no—
134C2×Dic43—22no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—22no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143D172—21no—
144D172—21no—
145C4×D43—41no—
146C4×D43—41no—
147C4×D43—41no—
148C4×D43—41no—
149C4×D43—81no—
150Dic86—21no—
151Dic86—21no—
152C8×C43—22no—
153C8×C43—41no—
154C8×C43—42no—
155C8×C43—81no—
156C43⋊C8—41no—
157C43⋊C8—41no—
158C43⋊C8—81no—
159#8842—431nomaximal, Sylow
160C22×C43—21no—
161C22×C43—21no—
162C22×C43#38511yescharacteristic
163C22×C43#43511yescharacteristic
164C22×C43#43611yescharacteristic
165C2×D43—41no—
166C2×D43—41no—
167C2×D43—41no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—21no—
171C4×C43#42311yescharacteristic
172C4×C43#42411yescharacteristic
173C4×C43#43511yescharacteristic
174C4×C43#43611yescharacteristic
175C4×C43#45411yescharacteristic
176C4×C43#45511yescharacteristic
177Dic43—42no—
178Dic43—42no—
179Dic43—41no—
180Dic43—41no—
181Dic43—41no—
182#2989—431no—
183#1831—431no—
184C4×#104—431no—
185#1565—431no—
186#1477—431no—
187#1283D4311yescharacteristic, complemented
188#1276—431no—
189C2×C43—21no—
190C2×C43—21no—
191C2×C43#185111yescharacteristic
192C2×C43#186011yescharacteristic
193C2×C43#186111yescharacteristic
194D43—81no—
195C4×#41—431no—
196#446—861no—
197#436—861no—
198#435—862no—
199#432—861no—
200#431—431no—
201#431C2×D4311yescharacteristic
202#423—861no—
203C2×C4⋊C8—431no—
204C2×C4⋊C8C2×D4311yescharacteristic
205C2×#104—431no—
206C2×#104—431no—
207C4×M16C2×D4311yescharacteristic
208C43—431no—
209#339—431no—
210#339—431no—
211#336—862no—
212#335—861no—
213#334—861no—
214Q8⋊C8—861no—
215D4⋊C8—861no—
216C43#884211yescharacteristic, complemented, Sylow
217C2×#41—431no—
218C2×M16—862no—
219C2×M16C4×D4311yescharacteristic
220C2×M16C4×D4311yescharacteristic
221C22×C8—861no—
222C22×C8D17212yes—
223C4×Q8—431no—
224C4×Q8—431no—
225C4×D4—431no—
226C4×D4—431no—
227C4×D4—861no—
228C4×D4—861no—
229#117—431no—
230#117—861no—
231C2×C42—431no—
232C2×C42—431no—
233C2×C42—861no—
234C2×C42—861no—
235C2×C42—861no—
236C2×C42C22×D4311yescharacteristic
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—431no—
241C4⋊C8—431no—
242C4⋊C8—862no—
243C4⋊C8—861no—
244C4⋊C8—861no—
245#104—862no—
246#104—862no—
247C22⋊C8—21no—
248C22⋊C8—862no—
249C22⋊C8—861no—
250#97—21no—
251#97—862no—
252C4×C8—21no—
253C4×C8—21no—
254C4×C8—861no—
255#41—861no—
256#41—861no—
257#41—861no—
258#41—861no—
259C2×Q8—431no—
260C2×D4—431no—
261C2×D4—861no—
262C22×C4—861no—
263C22×C4—861no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4C2×C4×D4311yescharacteristic
268C22×C4C2×D17211yescharacteristic
269C22×C4#1062189811yescharacteristic
270M16—21no—
271M16—21no—
272M16—21no—
273M16—3442no—
274M16#1062187212yescomplemented
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—22no—
278C2×C8—42no—
279C2×C8—41no—
280C2×C8—861no—
281C2×C8—861no—
282C2×C8—1722no—
283C2×C8—1721no—
284C4⋊C4—431no—
285C4⋊C4—431no—
286C4⋊C4—861no—
287C4⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C42—432no—
292C42—861no—
293C42—861no—
294C42—861no—
295C42—861no—
296C42—861no—
297C42—861no—
298C42—1721no—
299C42—1721no—
300C42—1722no—
301C42D4×D4311yescharacteristic
302C42D4×D4311yescharacteristic
303C42#1062190011yescharacteristic
304C42Q8×D4311yescharacteristic
305C23—861no—
306C23C4×D17211yescharacteristic
307Q8—861no—
308Q8—861no—
309D4—861no—
310D4—861no—
311D4—1721no—
312D4—1721no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—862no—
317C2×C4—862no—
318C2×C4—861no—
319C2×C4—861no—
320C2×C4—861no—
321C2×C4—3441no—
322C2×C4—1721no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4—1721no—
326C2×C4—1721no—
327C2×C4—1721no—
328C2×C4—1721no—
329C2×C4—1721no—
330C2×C4C4⋊C4×D4311yescharacteristic
331C2×C4(C22⋊D43)⋊C411yescharacteristic
332C2×C4#1306329511yescharacteristic
333C2×C4#1306330311yescharacteristic
334C2×C4#1306330511yescharacteristic
335C2×C4#1306330711yescharacteristic
336C2×C4M16×D4311yescharacteristic
337C2×C4C2×#1062187211yescharacteristic
338C2×C4#1306333111yescharacteristic
339C2×C4#1306333311yescharacteristic
340C8—22no—
341C8—42no—
342C8—41no—
343C8—81no—
344C8—3441no—
345C8—1721no—
346C8—1721no—
347C22—21no—
348C22—21no—
349C22—1721no—
350C22—1721no—
351C22—1721no—
352C22#1458277311yescharacteristic
353C22#1458297211yescharacteristic
354C22#1458297811yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—1722no—
359C4—1722no—
360C4—1721no—
361C4—1721no—
362C4—1721no—
363C4#1458292111yescharacteristic
364C4#1458292411yescharacteristic
365C4#1458296711yescharacteristic
366C4#1458297411yescharacteristic
367C4#1458307411yescharacteristic
368C4#1458307911yescharacteristic
369C2—21no—
370C2—21no—
371C2—3441no—
372C2#1913477911yescharacteristic
373C2#1913483111yescharacteristic
374C2#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#8842
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. #19134711C2semidirect
4. #19133347C2semidirect
6. #19132427C2semidirect
7. C43×#1283C2semidirect
85. M16×C43M16semidirect
111. C4×Dic43M16semidirect
187. #1283D43semidirect
216. C43#8842semidirect
274. M16#10621872semidirect

Maximal subgroups

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

subgroupindex
#191437132
#191347112
C4×#130632512
#191333472
#191329832
#191324272
C43×#12832
#884243