Finite Group Databasebeta

← #25114299

Subgroups — #25114299

Order 11008.

810 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×#107×D43C211yesmaximal, characteristic
2#19137468C212yesmaximal
3#19135333C211yesmaximal, characteristic, complemented
4#19135331C211yesmaximal, characteristic, complemented
5#19135166C212yesmaximal, complemented
6#19135164C212yesmaximal, complemented
7#19134684C212yesmaximal
8#19134617C211yesmaximal, characteristic
9#19134494C211yesmaximal, characteristic, complemented
10#19134372C211yesmaximal, characteristic
11C43×#1776C211yesmaximal, characteristic, complemented
12C22×C8×D43C2211yescharacteristic
13C2×C4⋊C4×D43C2212yes—
14C2×#13063259C2211yescharacteristic
15C2×#13063258C2212yes—
16#107×D43C418yescomplemented
17C2×#13063257C2211yescharacteristic
18C2×(C2×D43)⋊C8C2211yescharacteristic
19C2×#13063235C2211yescharacteristic
20#14582797C2212yes—
21#14582795C2212yes—
22#14582783—22no—
23#14582781—22no—
24#14582758—22no—
25#14582756C2212yes—
26C4⋊C4×Dic43C2212yes—
27C4×(C2×D43)⋊C4—22no—
28C4×(C2×D43)⋊C4C2211yescharacteristic
29#14582662C2212yes—
30#14582661C2212yes—
31#14582661C2212yes—
32#14582661C2212yes—
33#14582654C2211yescharacteristic
34#14582653C2211yescharacteristic
35C2×#107×C43C2211yescharacteristic
36C2×#106×C43C2211yescharacteristic
37C2×#97×C43C2211yescharacteristic
38C4×C4⋊C4×C43C2212yes—
39C43×#340C2212yes—
40C22×C4×D43—22no—
41C22×C4×D43C2311yescharacteristic
42C22×C43⋊C8C2311yescharacteristic
43C22×C43⋊C8C2311yescharacteristic
44C2×C8×D43—22no—
45C2×C8×D43—22no—
46C2×C8×D43C2×C414yes—
47C2×C4⋊Dic43C2312yes—
48C2×C4⋊Dic43C2312yes—
49C2×Dic43⋊C4—22no—
50C2×Dic43⋊C4—22no—
51C2×Dic43⋊C4—22no—
52C4⋊C4×D43—24no—
53C4⋊C4×D43C2×C418yes—
54C2×(C2×D43)⋊C4—22no—
55C2×(C2×D43)⋊C4D412yes—
56C2×C4×Dic43—22no—
57C2×C4×Dic43C2311yescharacteristic
58#13063259C2×C414yes—
59#13063258C2×C418yes—
60#13063257—22no—
61(C2×D43)⋊C8—22no—
62#13063235—22no—
63C43⋊#95—22no—
64C43⋊#95—22no—
65C43⋊#95—22no—
66C43⋊#95—22no—
67C43⋊#95D412yes—
68C22×C8×C43C2311yescharacteristic
69C22×C8×C43C2311yescharacteristic
70C2×C4⋊C4×C43C2312yes—
71C2×C4⋊C4×C43C2312yes—
72C2×C42×C43—22no—
73C2×C42×C43C2311yescharacteristic
74#107×C43C2×C414yes—
75#106×C43—22no—
76#97×C43—22no—
77#95×C43—22no—
78C23×D43C2×D411yescharacteristic
79C22×C4×C43—22no—
80C22×C4×C43—22no—
81C22×C4×C43C2×D412yes—
82C22×C4×C43C2411yescharacteristic
83C22×Dic43—22no—
84C22×Dic43—22no—
85C22×Dic43C2×D412yes—
86C22×Dic43C2×D411yescharacteristic
87C2×C4×D43—21no—
88C2×C4×D43—21no—
89C2×C4×D43—21no—
90C2×C4×D43—21no—
91C2×C4×D43—28no—
92C2×C4×D43—82no—
93C2×C4×D43—82no—
94C2×C4×D43C22×C412yes—
95C2×C4×D43#4112yes—
96C2×C8×C43—21no—
97C2×C8×C43—21no—
98C2×C8×C43—21no—
99C2×C8×C43C22×C412yes—
100C2×C8×C43#4112yes—
101C2×C8×C43#4112yes—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—22no—
104C4⋊C4×C43—22no—
105C4⋊C4×C43C22×C414yes—
106C42×C43—21no—
107C42×C43—21no—
108C42×C43—82no—
109(C2×D43)⋊C4—24no—
110(C2×D43)⋊C4—44no—
111C4⋊Dic43—22no—
112C4⋊Dic43—22no—
113C4⋊Dic43—22no—
114C4⋊Dic43C22×C414yes—
115Dic43⋊C4—28no—
116Dic43⋊C4—82no—
117Dic43⋊C4—82no—
118C4×Dic43—21no—
119C4×Dic43—21no—
120C4×Dic43—82no—
121C2×C43⋊C8—21no—
122C2×C43⋊C8—21no—
123C2×C43⋊C8—21no—
124C2×C43⋊C8—21no—
125C2×C43⋊C8—21no—
126C2×C43⋊C8C22×C412yes—
127C8×D43—28no—
128C23×C43C22×D411yescharacteristic
129C22×D43—21no—
130C22×D43—21no—
131C22×D43—22no—
132C22×D43C4×D412yes—
133C22×D43#13714yes—
134C2×C4×C43—24no—
135C2×C4×C43—22no—
136C2×C4×C43—22no—
137C2×C4×C43—22no—
138C2×C4×C43—42no—
139C2×C4×C43—42no—
140C2×C4×C43—42no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43C23×C411yescharacteristic
144C2×C4×C43C2×#4111yescharacteristic
145C2×C4×C43C2×#4111yescharacteristic
146C2×C4×C43C2×#4111yescharacteristic
147C2×C4×C432−1+411yescharacteristic
148C2×C4×C432−1+411yescharacteristic
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—24no—
152C2×Dic43—22no—
153C2×Dic43—22no—
154C2×Dic43—22no—
155C2×Dic43—42no—
156C2×Dic43—42no—
157C2×Dic43—42no—
158C2×Dic43—42no—
159C2×Dic43—42no—
160C2×Dic43C4×D412yes—
161C4×D43—22no—
162C4×D43—22no—
163C4×D43—22no—
164C4×D43—22no—
165C4×D43—88no—
166C8×C43—41no—
167C8×C43#11714yes—
168C43⋊C8—22no—
169C43⋊C8—41no—
170#22618—431nomaximal, Sylow
171C22×C43C2×C4×D411yescharacteristic
172C22×C43#54711yescharacteristic
173C22×C43#54711yescharacteristic
174C22×C43C2×#13712yes—
175C22×C43#57612yes—
176C2×D43—24no—
177C2×D43—24no—
178C2×D43—22no—
179C2×D43—22no—
180C2×D43#44114yes—
181C4×C43—42no—
182C4×C43—44no—
183C4×C43—82no—
184C4×C43C2×#11711yescharacteristic
185C4×C43#51911yescharacteristic
186C4×C43#55211yescharacteristic
187C4×C43#55211yescharacteristic
188Dic43—22no—
189Dic43—42no—
190Dic43—44no—
191Dic43—82no—
192C22×#107—431no—
193#2345—432no—
194#1943—431no—
195#1943—431no—
196#1918—432no—
197#1918—432no—
198#1824—432no—
199#1807—431no—
200#1776—431no—
201#1776D4311yescharacteristic, complemented
202#1752—431no—
203C2×C43#234411yescharacteristic
204C2×C43C2×#44111yescharacteristic
205C2×C43#294811yescharacteristic
206C2×C43#334612yes—
207C2×C43#334612yes—
208D43—24no—
209C23×C8—431no—
210C22×C4⋊C4—432no—
211C2×#107—431no—
212C2×#107—432no—
213C2×#107—438no—
214C2×#107C2×D4311yescharacteristic
215C2×#106—431no—
216C2×#106C2×D4311yescharacteristic
217C2×C22⋊C8—431no—
218C2×#97—431no—
219C2×#97C2×D4311yescharacteristic
220#389—432no—
221#389—432no—
222#387—862no—
223#387—862no—
224#380—432no—
225#380—862no—
226C4×C4⋊C4—432no—
227C4×C4⋊C4C2×D4312yes—
228C4×C22⋊C4—431no—
229C4×C22⋊C4—862no—
230#340—432no—
231#340—432no—
232#340—432no—
233#340—432no—
234#340C2×D4312yes—
235#336—431no—
236#336—431no—
237C43#2261811yescharacteristic, complemented, Sylow
238C23×C4—431no—
239C23×C4—862no—
240C22×C8—431no—
241C22×C8—434no—
242C22×C8—431no—
243C22×C8—862no—
244C22×C8—862no—
245C22×C8C22×D4311yescharacteristic
246C22×C8C22×D4311yescharacteristic
247C2×C4⋊C4—432no—
248C2×C4⋊C4—438no—
249C2×C4⋊C4—432no—
250C2×C4⋊C4—864no—
251C2×C4⋊C4—862no—
252C2×C4⋊C4—862no—
253C2×C4⋊C4—862no—
254C2×C4⋊C4C22×D4312yes—
255C2×C4⋊C4C22×D4312yes—
256C2×C22⋊C4—432no—
257C2×C22⋊C4—862no—
258C2×C42—22no—
259C2×C42—431no—
260C2×C42—862no—
261C2×C42C22×D4311yescharacteristic
262#107—434no—
263#107—438no—
264#107C4×D4314yes—
265#106—22no—
266#106—862no—
267C22⋊C8—862no—
268#97—22no—
269#97—862no—
270#95—22no—
271#95—432no—
272#95—862no—
273#95—862no—
274#95—862no—
275#95—862no—
276C24—431no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—431no—
280C22×C4—432no—
281C22×C4—432no—
282C22×C4—432no—
283C22×C4—868no—
284C22×C4—861no—
285C22×C4—861no—
286C22×C4—861no—
287C22×C4—861no—
288C22×C4—862no—
289C22×C4—862no—
290C22×C4—3442no—
291C22×C4—3442no—
292C22×C4D4×D4312yes—
293C22×C4C23×D4311yescharacteristic
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—432no—
298C2×C8—861no—
299C2×C8—861no—
300C2×C8—868no—
301C2×C8—861no—
302C2×C8—861no—
303C2×C8—861no—
304C2×C8C2×C4×D4312yes—
305C2×C8#1062189812yes—
306C2×C8#1062189812yes—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—434no—
311C4⋊C4—868no—
312C4⋊C4—862no—
313C4⋊C4—862no—
314C4⋊C4—862no—
315C4⋊C4—3442no—
316C4⋊C4—3442no—
317C4⋊C4C2×C4×D4314yes—
318C22⋊C4—864no—
319C22⋊C4—1724no—
320C42—21no—
321C42—21no—
322C42—82no—
323C42—861no—
324C42—861no—
325C42—3442no—
326C23—432no—
327C23—434no—
328C23—861no—
329C23—862no—
330C23—861no—
331C23C2×D4×D4311yescharacteristic
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—432no—
342C2×C4—861no—
343C2×C4—861no—
344C2×C4—862no—
345C2×C4—862no—
346C2×C4—862no—
347C2×C4—862no—
348C2×C4—862no—
349C2×C4—864no—
350C2×C4—862no—
351C2×C4—862no—
352C2×C4—3448no—
353C2×C4—1722no—
354C2×C4—1722no—
355C2×C4—1722no—
356C2×C4—1722no—
357C2×C4—1722no—
358C2×C4C22×C4×D4311yescharacteristic
359C2×C4#41×D4311yescharacteristic
360C2×C4C2×#1062189811yescharacteristic
361C2×C4C2×#1062189811yescharacteristic
362C2×C4#1306337211yescharacteristic
363C2×C4#1306337311yescharacteristic
364C8—41no—
365C8—862no—
366C8—1721no—
367C8#1306328214yes—
368C22—434no—
369C22—862no—
370C22—864no—
371C22—864no—
372C22—862no—
373C22C4×D4×D4311yescharacteristic
374C22#1458355011yescharacteristic
375C22#1458355411yescharacteristic
376C22#137×D4312yes—
377C22#1458370312yes—
378C4—44no—
379C4—42no—
380C4—82no—
381C4—862no—
382C4—3442no—
383C4—1724no—
384C4—1722no—
385C4C2×#1306328211yescharacteristic
386C4#1458337511yescharacteristic
387C4#1458358811yescharacteristic
388C4#1458359011yescharacteristic
389C2—864no—
390C2#1913746011yescharacteristic
391C2#441×D4311yescharacteristic
392C2#1914344411yescharacteristic
393C2#1914708112yes—
394C2#1914708512yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1776C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1776D43
hypocenterC43#22618
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1776

Complements

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

NH ≅ G/Ntype
3. #19135333C2semidirect
4. #19135331C2semidirect
5. #19135166C2semidirect
6. #19135164C2semidirect
9. #19134494C2semidirect
11. C43×#1776C2semidirect
16. #107×D43C4semidirect
201. #1776D43semidirect
237. C43#22618semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D432
#191374682
#191353332
#191353312
#191351662
#191351642
#191346842
#191346172
#191344942
#191343722
C43×#17762
#2261843