Finite Group Databasebeta

← #25114914

Subgroups — #25114914

Order 11008.

914 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583007C211yesmaximal, characteristic
2C2×#14583005C211yesmaximal, characteristic
3C2×#14582993C211yesmaximal, characteristic
4#19137509C212yesmaximal
5#19135334C211yesmaximal, characteristic
6#19134864C212yesmaximal
7#19134862C212yesmaximal
8#19134750C211yesmaximal, characteristic
9#19134599C212yesmaximal
10#19134463C211yesmaximal, characteristic
11C43×#1943C211yesmaximal, characteristic
12C22×Dic172C2211yescharacteristic
13C2×C4×Dic86C2212yes—
14C2×#13063290C2212yes—
15C2×#13063290C2212yes—
16#14583007—24no—
17#14583005—24no—
18#14582993C418yescomplemented
19C2×#13063257C2211yescharacteristic
20C2×#13063256C2212yes—
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063250C2212yes—
23C2×#13063248C2212yes—
24C2×#13063248C2212yes—
25C2×#13063235C2211yescharacteristic
26C2×C8×Dic43C2211yescharacteristic
27#14582798C2212yes—
28#14582796—22no—
29#14582794—22no—
30#14582768—22no—
31#14582768C2212yes—
32C4×Dic43⋊C4C2211yescharacteristic
33#14582750—22no—
34#14582661C2212yes—
35#14582654C2211yescharacteristic
36#14582653C2211yescharacteristic
37C2×#107×C43C2211yescharacteristic
38C2×#106×C43C2211yescharacteristic
39C2×#97×C43C2211yescharacteristic
40C43×#389C2212yes—
41C43×#340C2212yes—
42C22×Dic86C2312yes—
43C2×Dic172C2×C414yes—
44C2×Dic172D414yes—
45C2×Dic172Q814yes—
46C22×C43⋊C8C2311yescharacteristic
47C22×C43⋊C8C2311yescharacteristic
48C4×Dic86—24no—
49C4×Dic86—42no—
50#13063290—24no—
51#13063290—24no—
52#13063290—42no—
53#13063290C2×C418yes—
54C2×C4⋊Dic43—22no—
55C2×C4⋊Dic43C2312yes—
56C2×Dic43⋊C4—22no—
57C2×Dic43⋊C4—22no—
58C2×Dic43⋊C4—22no—
59C2×Dic43⋊C4—22no—
60C2×Dic43⋊C4—22no—
61C2×Dic43⋊C4D412yes—
62C2×C4×Dic43—22no—
63C2×C4×Dic43—22no—
64C2×C4×Dic43—22no—
65C2×C4×Dic43C2311yescharacteristic
66C2×C4×Dic43C2311yescharacteristic
67#13063257—22no—
68#13063256—42no—
69Dic43⋊C8—22no—
70#13063250—24no—
71#13063248—24no—
72#13063248C2×C418yes—
73#13063235—22no—
74C8×Dic43C2×C414yes—
75C43⋊#95—22no—
76C43⋊#95D412yes—
77C22×C8×C43C2311yescharacteristic
78C22×C8×C43C2311yescharacteristic
79C2×C4⋊C4×C43—22no—
80C2×C4⋊C4×C43C2312yes—
81C2×C4⋊C4×C43C2312yes—
82C2×C42×C43C2311yescharacteristic
83#107×C43C2×C414yes—
84#106×C43—22no—
85#97×C43—22no—
86#95×C43—22no—
87C22×C4×C43—22no—
88C22×C4×C43—22no—
89C22×C4×C43C2×D412yes—
90C22×C4×C43C2411yescharacteristic
91C22×Dic43—22no—
92C22×Dic43—22no—
93C22×Dic43C2×D412yes—
94C22×Dic43C2×D411yescharacteristic
95C22×Dic43C2×D411yescharacteristic
96C2×Dic86—22no—
97C2×Dic86—22no—
98C2×Dic86—22no—
99C2×Dic86C22×C414yes—
100C2×Dic86C2×D414yes—
101C2×Dic86C2×Q814yes—
102C2×C8×C43—21no—
103C2×C8×C43—21no—
104C2×C8×C43—21no—
105C2×C8×C43C22×C412yes—
106C2×C8×C43C2×D412yes—
107C2×C8×C43C2×Q812yes—
108C4⋊C4×C43—22no—
109C4⋊C4×C43—22no—
110C4⋊C4×C43—22no—
111C4⋊C4×C43—82no—
112C4⋊C4×C43C22×C414yes—
113C42×C43—21no—
114C42×C43—21no—
115C4⋊Dic43—22no—
116C4⋊Dic43—22no—
117C4⋊Dic43—82no—
118Dic43⋊C4—28no—
119Dic43⋊C4—24no—
120Dic43⋊C4—44no—
121Dic43⋊C4—44no—
122Dic43⋊C4—44no—
123Dic43⋊C4—82no—
124C4×Dic43—21no—
125C4×Dic43—21no—
126C4×Dic43—28no—
127C4×Dic43—44no—
128C4×Dic43—44no—
129C4×Dic43C22×C412yes—
130C4×Dic43#4112yes—
131C2×C43⋊C8—21no—
132C2×C43⋊C8—21no—
133C2×C43⋊C8—21no—
134C2×C43⋊C8—21no—
135C2×C43⋊C8—21no—
136C2×C43⋊C8C22×C412yes—
137Dic172C4⋊C4116yescomplemented
138C23×C43C22×D411yescharacteristic
139C2×C4×C43—24no—
140C2×C4×C43—22no—
141C2×C4×C43—22no—
142C2×C4×C43—22no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43—42no—
146C2×C4×C43—42no—
147C2×C4×C43—42no—
148C2×C4×C43C23×C411yescharacteristic
149C2×C4×C43C22×D411yescharacteristic
150C2×C4×C43C22×Q811yescharacteristic
151C2×C4×C43C2×#4111yescharacteristic
152C2×C4×C43H(5,𝔽2)11yescharacteristic
153C2×C4×C432−1+411yescharacteristic
154C2×Dic43—24no—
155C2×Dic43—24no—
156C2×Dic43—24no—
157C2×Dic43—22no—
158C2×Dic43—22no—
159C2×Dic43—22no—
160C2×Dic43—22no—
161C2×Dic43—42no—
162C2×Dic43—42no—
163C2×Dic43—42no—
164C2×Dic43C4×D412yes—
165C2×Dic43C4×D412yes—
166C2×Dic43#13714yes—
167Dic86—24no—
168Dic86—24no—
169Dic86—24no—
170Dic86C2×C4⋊C418yes—
171C8×C43—41no—
172C8×C43C2×C4⋊C414yes—
173C43⋊C8—22no—
174C43⋊C8—41no—
175#22674—431nomaximal, Sylow
176C22×C43C2×C4×D411yescharacteristic
177C22×C43D4211yescharacteristic
178C22×C43D4×Q811yescharacteristic
179C22×C43C2×#13712yes—
180C22×C43#57712yes—
181C4×C43—44no—
182C4×C43—42no—
183C4×C43—82no—
184C4×C43C22×C4⋊C411yescharacteristic
185C4×C43#52011yescharacteristic
186C4×C43#54711yescharacteristic
187C4×C43#55411yescharacteristic
188Dic43—28no—
189Dic43—22no—
190Dic43—42no—
191Dic43—82no—
192Dic43#44114yescomplemented
193C2×#441—431no—
194C2×#441—431no—
195C2×C4×Q16—431no—
196Q8×C4⋊C4—432no—
197#1943—431no—
198#1943D4311yescharacteristic
199#1865—432no—
200#1865—432no—
201#1844—431no—
202#1803—432no—
203#1770—431no—
204C2×C43D4×C4⋊C411yescharacteristic
205C2×C43C2×#44111yescharacteristic
206C2×C43#295211yescharacteristic
207C2×C43#327812yes—
208C2×C43#338712yes—
209C22×Q16—431no—
210C2×C4×Q8—432no—
211C2×C4×Q8—432no—
212C2×C4×Q8—432no—
213#441—864no—
214#441—864no—
215C4×Q16—438no—
216C2×#107C2×D4311yescharacteristic
217C2×#106—431no—
218C2×#106—432no—
219C2×#106C2×D4311yescharacteristic
220C2×C4⋊C8—431no—
221C2×#103—432no—
222C2×#103—432no—
223C2×#103—432no—
224C2×#97—431no—
225C2×#97C2×D4311yescharacteristic
226C2×C4×C8—431no—
227#389—432no—
228#389—862no—
229#389—862no—
230#389C2×D4312yes—
231#384—432no—
232#384—862no—
233C4×C4⋊C4—431no—
234C4×C4⋊C4—862no—
235#340—432no—
236#340C2×D4312yes—
237#336—431no—
238#336—431no—
239C43#2267411yescharacteristic, complemented, Sylow
240C22×Q8—432no—
241C2×Q16—434no—
242C2×Q16—434no—
243C2×Q16—434no—
244C22×C8—431no—
245C22×C8—431no—
246C22×C8C22×D4311yescharacteristic
247C22×C8C22×D4311yescharacteristic
248C4×Q8—438no—
249C4×Q8—864no—
250C4×Q8—864no—
251C4×Q8—864no—
252C4×Q8—1722no—
253C4×Q8—1722no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—432no—
256C2×C4⋊C4—432no—
257C2×C4⋊C4—862no—
258C2×C4⋊C4—862no—
259C2×C4⋊C4—862no—
260C2×C4⋊C4—862no—
261C2×C4⋊C4—862no—
262C2×C4⋊C4—862no—
263C2×C4⋊C4C22×D4312yes—
264C2×C4⋊C4C22×D4312yes—
265C2×C42—431no—
266C2×C42—431no—
267C2×C42—862no—
268C2×C42—862no—
269C2×C42—862no—
270C2×C42C22×D4311yescharacteristic
271#107C4×D4314yes—
272#106—22no—
273#106—862no—
274#106—1722no—
275C4⋊C8—862no—
276#103—438no—
277#103—864no—
278#103—864no—
279#97—22no—
280#97—862no—
281C4×C8—434no—
282#95—22no—
283#95—432no—
284#95—862no—
285C2×Q8—434no—
286C2×Q8—434no—
287C2×Q8—434no—
288C2×Q8—862no—
289C2×Q8—862no—
290C2×Q8—862no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—431no—
294C22×C4—431no—
295C22×C4—432no—
296C22×C4—862no—
297C22×C4—862no—
298C22×C4D4×D4312yes—
299C22×C4C23×D4311yescharacteristic
300Q16—4316no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—432no—
305C2×C8—861no—
306C2×C8—861no—
307C2×C8—861no—
308C2×C8—861no—
309C2×C8—861no—
310C2×C8C2×C4×D4312yes—
311C2×C8D4×D4312yes—
312C2×C8Q8×D4312yes—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—82no—
317C4⋊C4—864no—
318C4⋊C4—868no—
319C4⋊C4—862no—
320C4⋊C4—862no—
321C4⋊C4—3442no—
322C4⋊C4—3442no—
323C4⋊C4—1724no—
324C4⋊C4—1724no—
325C4⋊C4—1724no—
326C4⋊C4C2×C4×D4314yes—
327C42—21no—
328C42—21no—
329C42—432no—
330C42—432no—
331C42—868no—
332C42—861no—
333C42—861no—
334C42—1724no—
335C42—1724no—
336C23C2×D4×D4311yescharacteristic
337Q8—438no—
338Q8—864no—
339Q8—864no—
340Q8—864no—
341C2×C4—24no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—432no—
351C2×C4—434no—
352C2×C4—432no—
353C2×C4—864no—
354C2×C4—864no—
355C2×C4—862no—
356C2×C4—864no—
357C2×C4—862no—
358C2×C4—862no—
359C2×C4—862no—
360C2×C4—1722no—
361C2×C4—1722no—
362C2×C4—1722no—
363C2×C4C22×C4×D4311yescharacteristic
364C2×C4C2×D4×D4311yescharacteristic
365C2×C4C2×Q8×D4311yescharacteristic
366C2×C4#41×D4311yescharacteristic
367C2×C4#1306337111yescharacteristic
368C2×C4#1306337311yescharacteristic
369C8—41no—
370C8—862no—
371C8—1721no—
372C8C4⋊C4×D4314yes—
373C22C4×D4×D4311yescharacteristic
374C22#1458353311yescharacteristic
375C22#1458356411yescharacteristic
376C22#137×D4312yes—
377C22#1458370912yes—
378C4—42no—
379C4—44no—
380C4—82no—
381C4—434no—
382C4—862no—
383C4—868no—
384C4—3442no—
385C4—1722no—
386C4C2×C4⋊C4×D4311yescharacteristic
387C4#1458338111yescharacteristic
388C4#1458355111yescharacteristic
389C4#1458360511yescharacteristic
390C2#1913749611yescharacteristic
391C2#441×D4311yescharacteristic
392C2#1914347711yescharacteristic
393C2#1914625812yes—
394C2#1914752412yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1943C2
socle, prime radicalC23×C43C22×D4
cosocleC22×C4×C43C24
hypercenter#1943D43
hypocenterC43#22674
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1943

Complements

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

NH ≅ G/Ntype
18. #14582993C4semidirect
137. Dic172C4⋊C4semidirect
192. Dic43#441semidirect
239. C43#22674semidirect

Maximal subgroups

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

subgroupindex
C2×#145830072
C2×#145830052
C2×#145829932
#191375092
#191353342
#191348642
#191348622
#191347502
#191345992
#191344632
C43×#19432
#2267443