Finite Group Databasebeta

← #25196887

Subgroups — #25196887

Order 11008.

658 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142980C211yesmaximal, characteristic
2#19137162C211yesmaximal, characteristic
3#19136098C212yesmaximal
4#19136087C212yesmaximal
5#19135568C211yesmaximal, characteristic
6#19135567C211yesmaximal, characteristic
7#19135185C212yesmaximal
8#19135171C212yesmaximal
9#19134761C211yesmaximal, characteristic
10#19134449C211yesmaximal, characteristic
11C43×#1836C211yesmaximal, characteristic
12C2×#13063325C2211yescharacteristic
13C2×#13063290—21no—
14C2×#13063258C2212yes—
15C2×#13063256C2212yes—
16C2×Dic43⋊C8C2212yes—
17C2×#13063236C2211yescharacteristic
18#14582804—21no—
19#14582798C2211yescharacteristic
20#14582798C2211yescharacteristic
21#14582795—21no—
22#14582795C2211yescharacteristic
23#14582795C2211yescharacteristic
24#14582795C2212yes—
25#14582786—21no—
26#14582786—21no—
27#14582782—21no—
28#14582782—21no—
29#14582765C2211yescharacteristic
30C4⋊C4×Dic43—21no—
31C4⋊C4×Dic43C2212yes—
32C42×Dic43C2211yescharacteristic
33#14582662C2212yes—
34#14582662C2212yes—
35#14582661C2212yes—
36#14582661C2212yes—
37#14582653C2212yes—
38C2×#97×C43C2211yescharacteristic
39C43×#384C2211yescharacteristic
40C43×#382C2211yescharacteristic
41C43×#340C2212yes—
42C43×#340C2212yes—
43C22×Dic86—21no—
44C22×C43⋊C8C2312yes—
45#13063325—22no—
46#13063325Q814yes—
47#13063290—44no—
48C2×C4⋊Dic43—21no—
49C2×C4⋊Dic43—21no—
50C2×C4⋊Dic43—21no—
51C2×C4⋊Dic43C2311yescharacteristic
52C2×C4⋊Dic43C2311yescharacteristic
53C2×C4⋊Dic43C2312yes—
54C2×Dic43⋊C4—21no—
55C2×Dic43⋊C4—21no—
56C2×Dic43⋊C4—22no—
57C2×C4×Dic43—22no—
58C2×C4×Dic43D411yescharacteristic
59C2×C4×Dic43D411yescharacteristic
60C2×C4×Dic43D411yescharacteristic
61C2×C4×Dic43D411yescharacteristic
62C2×C4×Dic43C2311yescharacteristic
63C2×C4×Dic43C2311yescharacteristic
64#13063258—24no—
65#13063256—24no—
66Dic43⋊C8—24no—
67#13063236—22no—
68C43⋊#95—21no—
69C43⋊#95—21no—
70C43⋊#95—21no—
71C43⋊#95—21no—
72C43⋊#95—21no—
73C43⋊#95—21no—
74C43⋊#95—22no—
75C43⋊#95—22no—
76C22×C8×C43C2312yes—
77C2×C4⋊C4×C43—21no—
78C2×C4⋊C4×C43—21no—
79C2×C4⋊C4×C43C2311yescharacteristic
80C2×C4⋊C4×C43C2311yescharacteristic
81C2×C4⋊C4×C43C2312yes—
82C2×C42×C43C2311yescharacteristic
83#97×C43—22no—
84#95×C43—21no—
85#95×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43—22no—
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2411yescharacteristic
92C22×Dic43—22no—
93C22×Dic43—21no—
94C22×Dic43—21no—
95C22×Dic43C2×D411yescharacteristic
96C22×Dic43C2×D411yescharacteristic
97C22×Dic43C2×D411yescharacteristic
98C22×Dic43C2×D411yescharacteristic
99C2×Dic86—24no—
100C2×Dic86—42no—
101C2×Dic86—42no—
102C2×C8×C43—22no—
103C2×C8×C43—22no—
104C2×C8×C43—22no—
105C4⋊C4×C43—22no—
106C4⋊C4×C43—22no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43—42no—
110C4⋊C4×C43—42no—
111C42×C43C2×Q812yes—
112C42×C43#4112yes—
113C4⋊Dic43—24no—
114C4⋊Dic43—22no—
115C4⋊Dic43—22no—
116C4⋊Dic43—22no—
117C4⋊Dic43—42no—
118C4⋊Dic43—42no—
119C4⋊Dic43C2×Q814yes—
120Dic43⋊C4—42no—
121Dic43⋊C4—44no—
122Dic43⋊C4—42no—
123C4×Dic43—22no—
124C4×Dic43—22no—
125C4×Dic43—22no—
126C4×Dic43—22no—
127C4×Dic43—41no—
128C4×Dic43—41no—
129C4×Dic43—44no—
130C2×C43⋊C8—22no—
131C2×C43⋊C8—22no—
132C2×C43⋊C8#4114yes—
133C23×C43C22×D411yescharacteristic
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—42no—
139C2×C4×C43—41no—
140C2×C4×C43—41no—
141C2×C4×C43—42no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—42no—
147C2×C4×C43C22⋊Q812yes—
148C2×C4×C43C22⋊Q812yes—
149C2×C4×C43C22×Q811yescharacteristic
150C2×C4×C43C2×#4112yes—
151C2×C4×C43C2×#4111yescharacteristic
152C2×C4×C432−1+412yes—
153C2×Dic43—21no—
154C2×Dic43—21no—
155C2×Dic43—21no—
156C2×Dic43—21no—
157C2×Dic43—24no—
158C2×Dic43—21no—
159C2×Dic43—21no—
160C2×Dic43—21no—
161C2×Dic43—21no—
162C2×Dic43—21no—
163C2×Dic43—21no—
164C2×Dic43—42no—
165C2×Dic43—42no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43AGL(1,ℤ/8)12yes—
173C2×Dic43#13712yes—
174Dic86—48no—
175C8×C43—42no—
176C43⋊C8—24no—
177#29181—431nomaximal, Sylow
178C22×C43C2×C22⋊Q811yescharacteristic
179C22×C43#53211yescharacteristic
180C22×C43#53611yescharacteristic
181C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
182C22×C43C2×#13711yescharacteristic
183C22×C43#57511yescharacteristic
184C22×C43#57511yescharacteristic
185C4×C43—22no—
186C4×C43—22no—
187C4×C43—82no—
188C4×C43—81no—
189C4×C43—81no—
190C4×C43#55212yes—
191C4×C43#55712yes—
192Dic43—22no—
193Dic43—22no—
194Dic43—44no—
195Dic43—41no—
196Dic43—41no—
197Dic43—81no—
198Dic43—81no—
199#2864—431no—
200C4×C4⋊Q8—431no—
201#2088—432no—
202#2086—432no—
203#1993—431no—
204#1993—431no—
205#1921—432no—
206#1919—432no—
207#1847—431no—
208#1836D4311yescharacteristic
209#1767—431no—
210C2×C43#256511yescharacteristic
211C2×C43#307711yescharacteristic
212C2×C43#307811yescharacteristic
213C2×C43#317211yescharacteristic
214C2×C43#318011yescharacteristic
215C2×C43#323911yescharacteristic
216C2×C43#324011yescharacteristic
217C2×C4⋊Q8—431no—
218C2×C4×Q8—861no—
219C2×#107—432no—
220C2×#106—432no—
221C2×C4⋊C8—432no—
222C2×#97—431no—
223C2×#97C2×D4311yescharacteristic
224#391—861no—
225#389—432no—
226#389—431no—
227#389—431no—
228#389—431no—
229#389—431no—
230#389—861no—
231#387—861no—
232#387—861no—
233#387—861no—
234#387—861no—
235#384C2×D4311yescharacteristic
236#382—431no—
237#382C2×D4311yescharacteristic
238C4×C4⋊C4—432no—
239C4×C4⋊C4—861no—
240C43—431no—
241#340—432no—
242#340—432no—
243#340—432no—
244#340—432no—
245#340C2×D4312yes—
246#340C2×D4312yes—
247#336—432no—
248C43#2918111yescharacteristic, complemented, Sylow
249C22×Q8—861no—
250C22×C8—432no—
251C22×C8C22×D4312yes—
252C4⋊Q8—434no—
253C4⋊Q8—862no—
254C4×Q8—1724no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—432no—
258C2×C4⋊C4—431no—
259C2×C4⋊C4—431no—
260C2×C4⋊C4—861no—
261C2×C4⋊C4—862no—
262C2×C4⋊C4—861no—
263C2×C4⋊C4—861no—
264C2×C4⋊C4—861no—
265C2×C4⋊C4—861no—
266C2×C4⋊C4C22×D4311yescharacteristic
267C2×C4⋊C4C22×D4311yescharacteristic
268C2×C4⋊C4C22×D4312yes—
269C2×C42—431no—
270C2×C42—431no—
271C2×C42—431no—
272C2×C42—431no—
273C2×C42—431no—
274C2×C42—431no—
275C2×C42—862no—
276C2×C42C22×D4311yescharacteristic
277#107—864no—
278#106—864no—
279C4⋊C8—864no—
280#97—22no—
281#97—862no—
282#95—21no—
283#95—21no—
284#95—862no—
285#95—862no—
286#95—861no—
287#95—861no—
288#95—861no—
289#95—861no—
290#95—861no—
291#95—861no—
292C2×Q8—864no—
293C2×Q8—1722no—
294C2×Q8—1722no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—431no—
299C22×C4—431no—
300C22×C4—431no—
301C22×C4—431no—
302C22×C4—862no—
303C22×C4—861no—
304C22×C4—861no—
305C22×C4D4×D4311yescharacteristic
306C22×C4D4×D4311yescharacteristic
307C22×C4C23×D4311yescharacteristic
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—434no—
312C2×C8—862no—
313C2×C8—862no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—42no—
319C4⋊C4—42no—
320C4⋊C4—434no—
321C4⋊C4—864no—
322C4⋊C4—862no—
323C4⋊C4—862no—
324C4⋊C4—862no—
325C4⋊C4—1724no—
326C4⋊C4—1722no—
327C4⋊C4—1722no—
328C4⋊C4—1722no—
329C4⋊C4—1722no—
330C42—862no—
331C42—862no—
332C42—862no—
333C42—862no—
334C42—1721no—
335C42—1721no—
336C42—1724no—
337C42#1062189812yes—
338C42Q8×D4312yes—
339C23C2×D4×D4311yescharacteristic
340Q8—1728no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—432no—
355C2×C4—432no—
356C2×C4—861no—
357C2×C4—861no—
358C2×C4—861no—
359C2×C4—861no—
360C2×C4—864no—
361C2×C4—861no—
362C2×C4—861no—
363C2×C4—861no—
364C2×C4—861no—
365C2×C4—861no—
366C2×C4—861no—
367C2×C4—1721no—
368C2×C4—1721no—
369C2×C4—1721no—
370C2×C4—1721no—
371C2×C4—1721no—
372C2×C4—1721no—
373C2×C4—1722no—
374C2×C4—1722no—
375C2×C4#1306330312yes—
376C2×C4#1306330312yes—
377C2×C4C2×Q8×D4311yescharacteristic
378C2×C4#41×D4312yes—
379C2×C4C2×#1062189811yescharacteristic
380C2×C4#1306337212yes—
381C8—42no—
382C8—864no—
383C22C2×#1306330311yescharacteristic
384C22#1458344811yescharacteristic
385C22#1458346911yescharacteristic
386C22AGL(1,ℤ/8)×D4311yescharacteristic
387C22#137×D4311yescharacteristic
388C22#1458369511yescharacteristic
389C22#1458369811yescharacteristic
390C4—22no—
391C4—22no—
392C4—82no—
393C4—81no—
394C4—81no—
395C4—862no—
396C4—862no—
397C4—3441no—
398C4—3441no—
399C4—1721no—
400C4—1724no—
401C4—1721no—
402C4#1458358812yes—
403C4#1458362612yes—
404C2#1913978511yescharacteristic
405C2#1914439111yescharacteristic
406C2#1914439911yescharacteristic
407C2#1914520011yescharacteristic
408C2#1914529211yescharacteristic
409C2#1914582111yescharacteristic
410C2#1914583211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1836C2
socle, prime radicalC23×C43C22×D4
hypercenter#1836D43
hypocenterC43#29181
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1836

Complements

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

NH ≅ G/Ntype
248. C43#29181semidirect

Maximal subgroups

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

subgroupindex
#191429802
#191371622
#191360982
#191360872
#191355682
#191355672
#191351852
#191351712
#191347612
#191344492
C43×#18362
#2918143