Finite Group Databasebeta

← #24993442

Subgroups — #24993442

Order 11008.

512 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144083C211yesmaximal, characteristic
2#19143704C211yesmaximal, characteristic
3#19135546C211yesmaximal, characteristic, complemented
4#19134612C211yesmaximal, characteristic
5#19133268C211yesmaximal, characteristic, complemented
6#19132496C211yesmaximal, characteristic, complemented
7C43×#1292C211yesmaximal, characteristic, complemented
8C2×#13063358—21no—
9C2×#13063325C2211yescharacteristic
10C4×#10621898C2211yescharacteristic
11#14583110—21no—
12#14583110C412yescomplemented
13#14583105—21no—
14#14583105C412yescomplemented
15#14583023—21no—
16#14582964—21no—
17C8×C22⋊D43—22no—
18#14582952C2211yescharacteristic
19#14582951—21no—
20C4⋊C8×D43—21no—
21C2×#13063251—21no—
22#14582909—21no—
23C4×C4⋊Dic43C2211yescharacteristic
24#14582662—22no—
25#14582660—21no—
26#14582646—21no—
27#14582646—21no—
28C43×#423C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C2×C4⋊C8×C43C2211yescharacteristic
31C2×#10621898D411yescharacteristic
32C22×Dic86—21no—
33#13063358—42no—
34#13063358—42no—
35C2×Dic172—22no—
36C2×#10621873—22no—
37C2×C8×D43—22no—
38#13063325—21no—
39#13063325—21no—
40#13063325—21no—
41#13063325C2×C412yes—
42C4×Dic86C2×C411yescharacteristic
43C4×Dic86D411yescharacteristic
44C4×D172C2×C411yescharacteristic
45C4×D172D411yescharacteristic
46C4×C22⋊D43—21no—
47C4×C22⋊D43—21no—
48#13063284D411yescharacteristic
49#13063282—21no—
50C2×C4⋊Dic43—21no—
51C2×C4⋊Dic43—21no—
52C2×C4⋊Dic43—21no—
53C2×C4×Dic43—21no—
54C42×D43—21no—
55C4⋊(C43⋊C8)D411yescharacteristic
56C4⋊(C43⋊C8)D411yescharacteristic
57Dic43⋊C8—22no—
58#13063251—42no—
59#13063250—22no—
60#13063250—22no—
61C22⋊(C43⋊C8)—21no—
62(C2×D43)⋊C8—22no—
63C4×C43⋊C8—21no—
64C8×Dic43—22no—
65C43⋊#95—21no—
66C2×M16×C43—21no—
67C2×M16×C43—21no—
68C22×C8×C43D412yes—
69C2×C42×C43C2311yescharacteristic
70C4⋊C8×C43—21no—
71C4⋊C8×C43—21no—
72C4⋊C8×C43—21no—
73C4⋊C8×C43—21no—
74C4⋊C8×C43—21no—
75C4⋊C8×C43C2×C412yes—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43#4111yescharacteristic
79C2×C22⋊D43—21no—
80C22×Dic43—41no—
81C22×Dic43—41no—
82#10621898—21no—
83#10621898—21no—
84#10621898D812yes—
85#10621898SD1612yes—
86C2×D172C22⋊C411yescharacteristic
87C2×C4×D43—21no—
88C2×C4×D43—21no—
89C2×C4×D43—21no—
90C2×Dic86—22no—
91C2×Dic86—41no—
92C2×Dic86—41no—
93C2×Dic86—41no—
94C2×Dic86—41no—
95C2×Dic86—41no—
96C2×Dic86C22⋊C411yescharacteristic
97M16×C43—41no—
98M16×C43—41no—
99M16×C43—41no—
100M16×C43—41no—
101C2×C8×C43—22no—
102C2×C8×C43—22no—
103C2×C8×C43—42no—
104C2×C8×C43—41no—
105C42×C43C22×C411yescharacteristic
106C42×C43C2×D411yescharacteristic
107C42×C43C2×D411yescharacteristic
108C42×C43#4111yescharacteristic
109C22⋊Dic43—21no—
110(C2×D43)⋊C4—21no—
111(C2×D43)⋊C4—21no—
112C4⋊Dic43—22no—
113C4⋊Dic43—22no—
114C4⋊Dic43—22no—
115C4⋊Dic43—41no—
116C4⋊Dic43—41no—
117C4⋊Dic43—41no—
118C4⋊Dic43C22⋊C411yescharacteristic
119C4⋊Dic43C22⋊C411yescharacteristic
120Dic43⋊C4—21no—
121Dic43⋊C4—21no—
122C4×Dic43—21no—
123C4×Dic43—21no—
124C4×Dic43—21no—
125C4×Dic43—41no—
126C4×Dic43—41no—
127C2×C43⋊C8—21no—
128C2×C43⋊C8—21no—
129Dic172—44no—
130#10621873—44no—
131C8×D43—82no—
132C23×C43#12111yescharacteristic
133C22×D43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—41no—
137C2×C4×C43C2×C22⋊C411yescharacteristic
138C2×C4×C43C4×D411yescharacteristic
139C2×C4×C43C4×D411yescharacteristic
140C2×C4×C43#12011yescharacteristic
141C2×C4×C43#12111yescharacteristic
142C2×C4×C43#12311yescharacteristic
143C2×C4×C43C2×D811yescharacteristic
144C2×C4×C43C2×SD1611yescharacteristic
145C2×C4×C43#13511yescharacteristic
146C2×C4×C43#13511yescharacteristic
147C22⋊D43—22no—
148C22⋊D43—22no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—21no—
152C2×Dic43—42no—
153C2×Dic43—42no—
154C2×Dic43—81no—
155C2×Dic43—81no—
156C2×Dic43—81no—
157C2×Dic43—81no—
158D172—21no—
159D172#10212yes—
160C4×D43—22no—
161C4×D43—22no—
162C4×D43—41no—
163C4×D43—41no—
164C4×D43—81no—
165Dic86—21no—
166Dic86—42no—
167Dic86—42no—
168Dic86—81no—
169Dic86—81no—
170Dic86#10212yes—
171C8×C43—42no—
172C8×C43—42no—
173C8×C43—81no—
174C43⋊C8—41no—
175C43⋊C8—41no—
176#9316—431nomaximal, Sylow
177C22×C43—21no—
178C22×C43—21no—
179C22×C43#38611yescharacteristic
180C22×C43#46511yescharacteristic
181C22×C43#46611yescharacteristic
182C2×D43—22no—
183C2×D43—41no—
184C2×D43—41no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—21no—
188C4×C43C2×#10211yescharacteristic
189C4×C43#41611yescharacteristic
190C4×C43#45511yescharacteristic
191C4×C43#45611yescharacteristic
192C4×C43#46511yescharacteristic
193C4×C43#46611yescharacteristic
194Dic43—22no—
195Dic43—41no—
196Dic43—41no—
197Dic43—82no—
198Dic43—82no—
199#3039—431no—
200#2988—431no—
201#1988—431no—
202#1806—431no—
203#1546—431no—
204#1303—431no—
205#1292D4311yescharacteristic, complemented
206C2×C43—21no—
207C2×C43—21no—
208C2×C43#188211yescharacteristic
209C2×C43#189311yescharacteristic
210C2×C43#190211yescharacteristic
211D43—42no—
212C2×#137—861no—
213C2×C4⋊Q8—431no—
214C4×#41—431no—
215#462—432no—
216#462—861no—
217#461—432no—
218#461—861no—
219C8×Q8—861no—
220C8×D4—861no—
221C8×D4—862no—
222#431—431no—
223#431—861no—
224#423C2×D4311yescharacteristic
225#423C2×D4311yescharacteristic
226C2×C4⋊C8—861no—
227C2×C4⋊C8C2×D4311yescharacteristic
228C2×#104—861no—
229#419—861no—
230C4×C4⋊C4—431no—
231#340—862no—
232#339—861no—
233#332—861no—
234#332—861no—
235C43#931611yescharacteristic, complemented, Sylow
236C2×#41—431no—
237C22×Q8—861no—
238#137—1722no—
239#137—1722no—
240C2×Q16—862no—
241C2×SD16—862no—
242C2×M16—21no—
243C2×M16—21no—
244C22×C8—862no—
245C22×C8D17212yes—
246C4⋊Q8—432no—
247C4⋊Q8—861no—
248C4⋊Q8—861no—
249C4⋊Q8—861no—
250C4×Q8—431no—
251C4×Q8—431no—
252C4×D4—431no—
253C4×D4—431no—
254C4×D4—861no—
255C4×D4—861no—
256#117—431no—
257#117—861no—
258C2×C4⋊C4—861no—
259C2×C4⋊C4—861no—
260C2×C4⋊C4—861no—
261C2×C42—861no—
262C2×C42—861no—
263C2×C42C22×D4311yescharacteristic
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—431no—
270C4⋊C8—431no—
271C4⋊C8—862no—
272C4⋊C8C4×D4312yes—
273#104—1722no—
274#103—862no—
275#103—862no—
276C22⋊C8—862no—
277C22⋊C8—861no—
278C4×C8—862no—
279C4×C8—861no—
280#95—861no—
281#41—432no—
282#41—432no—
283#41—861no—
284#41—861no—
285C2×Q8—431no—
286C2×Q8—862no—
287C2×Q8—1721no—
288C2×Q8—1721no—
289C2×Q8—1721no—
290C2×Q8—1721no—
291C2×Q8—1721no—
292C2×D4—431no—
293C2×D4—861no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4—861no—
297C22×C4—1721no—
298C22×C4—1721no—
299C22×C4C2×D17211yescharacteristic
300C22×C4D4×D4311yescharacteristic
301C22×C4#1062190211yescharacteristic
302Q16—1724no—
303SD16—1724no—
304M16—41no—
305M16—41no—
306M16—41no—
307M16—41no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—42no—
311C2×C8—41no—
312C2×C8—861no—
313C2×C8—861no—
314C2×C8—3442no—
315C4⋊C4—431no—
316C4⋊C4—431no—
317C4⋊C4—862no—
318C4⋊C4—861no—
319C4⋊C4—861no—
320C4⋊C4—862no—
321C4⋊C4—862no—
322C4⋊C4—1721no—
323C4⋊C4—1721no—
324C4⋊C4—1721no—
325C22⋊C4—861no—
326C22⋊C4—861no—
327C22⋊C4—861no—
328C42—861no—
329C42—861no—
330C42—861no—
331C42—1721no—
332C42—1721no—
333C42C2×C4×D4311yescharacteristic
334C42#1062189811yescharacteristic
335C42D4×D4311yescharacteristic
336C42D4×D4311yescharacteristic
337C23—861no—
338C23#1306330011yescharacteristic
339Q8—432no—
340Q8—861no—
341Q8—3441no—
342Q8—3441no—
343Q8—1722no—
344Q8—1722no—
345D4—432no—
346D4—862no—
347D4—862no—
348D4—861no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—41no—
352C2×C4—861no—
353C2×C4—862no—
354C2×C4—862no—
355C2×C4—861no—
356C2×C4—861no—
357C2×C4—3441no—
358C2×C4—3441no—
359C2×C4—3441no—
360C2×C4—3441no—
361C2×C4—3441no—
362C2×C4—1722no—
363C2×C4—1722no—
364C2×C4—1721no—
365C2×C4—1721no—
366C2×C4C22⋊C4×D4311yescharacteristic
367C2×C4#1306328711yescharacteristic
368C2×C4C4×D17211yescharacteristic
369C2×C4#1306329511yescharacteristic
370C2×C4#1306329811yescharacteristic
371C2×C4#1306331011yescharacteristic
372C2×C4D8×D4311yescharacteristic
373C2×C4SD16×D4311yescharacteristic
374C2×C4#1306334611yescharacteristic
375C2×C4#1306334811yescharacteristic
376C8—42no—
377C8—42no—
378C8—81no—
379C8—1721no—
380C8—1721no—
381C22—21no—
382C22—21no—
383C22—862no—
384C22—1721no—
385C22—1721no—
386C22#1458277711yescharacteristic
387C22#1458312911yescharacteristic
388C22#1458313611yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—862no—
393C4—3442no—
394C4—3442no—
395C4—1721no—
396C4—1721no—
397C4#102×D4311yescharacteristic
398C4#1458289411yescharacteristic
399C4#1458307911yescharacteristic
400C4#1458308411yescharacteristic
401C4#1458313111yescharacteristic
402C4#1458313411yescharacteristic
403C2—21no—
404C2—21no—
405C2—1722no—
406C2#1913496311yescharacteristic
407C2#1913502211yescharacteristic
408C2#1913506911yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1292C2
socleC22×C43#386
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenter#1292D43
hypocenterC43#9316
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
3. #19135546C2semidirect
5. #19133268C2semidirect
6. #19132496C2semidirect
7. C43×#1292C2semidirect
12. #14583110C4semidirect
14. #14583105C4semidirect
205. #1292D43semidirect
235. C43#9316semidirect

Maximal subgroups

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

subgroupindex
#191440832
#191437042
#191355462
#191346122
#191332682
#191324962
C43×#12922
#931643