Finite Group Databasebeta

← #25964498

Subgroups — #25964498

Order 11008.

2106 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147798C211yesmaximal, characteristic
2#19144558C2116yesmaximal, complemented
3#19144539C218yesmaximal, complemented
4#19143184C212yesmaximal, complemented
5C2×#14582908C212yesmaximal, complemented
6#19143040C211yesmaximal, characteristic
7C2×C43×#536C211yesmaximal, characteristic
8C22×#10621877C2212yes—
9#14583382C2218yes—
10#14583377—21no—
11#14583374—22no—
12#14583374—21no—
13#41×Dic43—24no—
14C2×#13063284C2212yes—
15C2×#13063284C2214yes—
16#14583237C22132yescomplemented
17#14583232C22116yescomplemented
18#14583227C22116yescomplemented
19#14582942C2218yescomplemented
20#14582939C2218yes—
21#14582935C2218yescomplemented
22#14582908C2218yes—
23#14582908C2218yescomplemented
24C2×#13063249C2218yescomplemented
25#14582866C2218yes—
26#14582863C2214yes—
27C22×#41×C43C2211yescharacteristic
28C23×Q8×C43C2211yescharacteristic
29C43×#536—24no—
30C43×#536C2218yes—
31C2×C4⋊Q8×C43—21no—
32C2×#124×C43—21no—
33C2×#123×C43—22no—
34C2×C22⋊Q8×C43C2214yes—
35C2×#117×C43C2211yescharacteristic
36C2×#10621877—28no—
37C2×#10621877C2314yes—
38C2×#10621877C2314yes—
39C22×C43⋊C8C2314yes—
40Q8×Dic43—28no—
41D4×Dic43—216no—
42D4×Dic43—28no—
43#13063284—24no—
44#13063284—22no—
45#13063284—24no—
46#13063284—22no—
47#13063284C2314yes—
48#13063284C2314yes—
49#13063284C2318yes—
50C2×C4⋊Dic43C2314yes—
51C2×C4⋊Dic43C2318yes—
52C2×C22⋊Dic43—24no—
53C2×C22⋊Dic43—22no—
54C2×C4×Dic43—24no—
55C2×C4×Dic43—22no—
56#13063258C23116yes—
57#13063256C23116yes—
58#13063249C23132yes—
59C22⋊(C43⋊C8)C23116yes—
60C2×#41×C43—28no—
61C2×#41×C43D414yes—
62C2×#41×C43C2314yes—
63C22×Q8×C43—21no—
64C22×Q8×C43—22no—
65C22×Q8×C43—28no—
66C22×Q8×C43D411yescharacteristic
67C22×Q8×C43C2312yes—
68C22×Q8×C43C2314yes—
69C22×D4×C43D412yes—
70C22×D4×C43D411yescharacteristic
71C23×C4×C43—21no—
72C23×C4×C43C2312yes—
73C23×C4×C43C2311yescharacteristic
74C4⋊Q8×C43—28no—
75#124×C43—28no—
76#123×C43—216no—
77C22⋊Q8×C43—28no—
78C22⋊Q8×C43C23116yes—
79#117×C43—22no—
80#117×C43C2314yes—
81C2×C4⋊C4×C43—24no—
82C2×C4⋊C4×C43C2312yes—
83C2×C22⋊C4×C43—21no—
84C2×C22⋊C4×C43—24no—
85C2×C42×C43—21no—
86C24×C43C2×D412yes—
87C24×C43C2×D411yescharacteristic
88#41×C43—216no—
89#41×C43—28no—
90#41×C43—28no—
91C2×Q8×C43—24no—
92C2×Q8×C43—22no—
93C2×Q8×C43—24no—
94C2×Q8×C43—28no—
95C2×Q8×C43—28no—
96C2×Q8×C43—28no—
97C2×Q8×C43—44no—
98C2×Q8×C43—48no—
99C2×Q8×C43C2×D414yes—
100C2×Q8×C43C2414yes—
101C2×D4×C43—24no—
102C2×D4×C43—28no—
103C2×D4×C43C2×D418yes—
104C2×D4×C43C2×D414yes—
105C22×C4×C43—28no—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—24no—
109C22×C4×C43—44no—
110C22×C4×C43C2×D412yes—
111C22×C4×C43C2×D414yes—
112C22×C4×C43C2×D411yescharacteristic
113C22×C4×C43C2×D412yes—
114C22×C4×C43#4118yes—
115C22×C4×C43C2414yes—
116C22×C4×C43C2411yescharacteristic
117C22×C4×C43C2412yes—
118C22×Dic43—28no—
119C22×Dic43—24no—
120C4⋊C4×C43—216no—
121C4⋊C4×C43—22no—
122C4⋊C4×C43C2414yes—
123C22⋊C4×C43—24no—
124C22⋊C4×C43—216no—
125C42×C43—24no—
126C22⋊Dic43—24no—
127C22⋊Dic43—28no—
128C22⋊Dic43—24no—
129C4⋊Dic43—28no—
130C4⋊Dic43—24no—
131C4⋊Dic43C2418yes—
132C4×Dic43—24no—
133C4×Dic43—28no—
134C4×Dic43—24no—
135#10621877—28no—
136#10621877—28no—
137C2×C43⋊C8—28no—
138C2×C43⋊C8C2418yes—
139C23×C43—24no—
140C23×C43—42no—
141C23×C43—44no—
142C23×C43#12314yes—
143C23×C43C22×D414yes—
144C23×C43C22×D411yescharacteristic
145C23×C43C22×D412yes—
146Q8×C43—28no—
147Q8×C43—28no—
148Q8×C43—44no—
149Q8×C43—48no—
150D4×C43—216no—
151D4×C43—28no—
152C2×C4×C43—24no—
153C2×C4×C43—28no—
154C2×C4×C43—28no—
155C2×C4×C43—24no—
156C2×C4×C43—24no—
157C2×C4×C43—44no—
158C2×C4×C43—44no—
159C2×C4×C43—48no—
160C2×C4×C43#12314yes—
161C2×C4×C43#12318yes—
162C2×C4×C43C22×D414yes—
163C2×C4×C43C22×D411yescharacteristic
164C2×C4×C43C22×D412yes—
165C2×C4×C43C2×#4114yes—
166C2×C4×C43C2×#4114yes—
167C2×C4×C43C2×#4114yes—
168C2×C4×C43C2511yescharacteristic
169C2×Dic43—28no—
170C2×Dic43—84no—
171C2×Dic43—88no—
172C43⋊C8—28no—
173#60519—431nomaximal, Sylow
174C22×C43—22no—
175C22×C43—24no—
176C22×C43—28no—
177C22×C43—24no—
178C22×C43—44no—
179C22×C43—84no—
180C22×C43C2×#12312yes—
181C22×C43C2×#12314yes—
182C22×C43C23×D411yescharacteristic
183C4×C43—24no—
184C4×C43—44no—
185C4×C43—44no—
186C4×C43C2×#12312yes—
187C4×C43C2×#12314yes—
188C4×C43C22×#4112yes—
189Dic43—48no—
190C2×#536D4311yescharacteristic
191#3428—431no—
192#3097—4316no—
193#3095—438no—
194#2911—432no—
195C2×#419—432no—
196#2879—431no—
197C2×C43—22no—
198C2×C43—24no—
199C2×C43—44no—
200C2×C43C22×#12311yescharacteristic
201C2×C43#358612yes—
202C22×#41C2×D4311yescharacteristic
203C23×Q8C2×D4311yescharacteristic
204C22×M16—432no—
205#536—24no—
206#536C2×D4318yes—
207C2×C4⋊Q8—21no—
208C2×#124—21no—
209C2×#123—22no—
210C2×C22⋊Q8C2×D4314yes—
211#520—438no—
212#519—861no—
213#518—862no—
214#518—861no—
215C4×#41—864no—
216C2×#117—434no—
217C2×#117—432no—
218C2×#117C2×D4311yescharacteristic
219#485—4332no—
220#484—4316no—
221#483—4316no—
222#428—438no—
223#428—438no—
224#427—438no—
225#419—438no—
226#419—438no—
227C2×#103—438no—
228#408—438no—
229#407—434no—
230C43#6051911yescharacteristic, complemented, Sylow
231C2×#41—28no—
232C2×#41C22⋊D4314yes—
233C2×#41C22×D4314yes—
234C22×Q8—21no—
235C22×Q8—22no—
236C22×Q8—28no—
237C22×Q8C22⋊D4311yescharacteristic
238C22×Q8C22×D4312yes—
239C22×Q8C22×D4314yes—
240C22×D4C22⋊D4312yes—
241C22×D4C22⋊D4311yescharacteristic
242C23×C4—21no—
243C23×C4C22×D4312yes—
244C23×C4C22×D4311yescharacteristic
245C2×M16—434no—
246C2×M16—434no—
247C2×M16—868no—
248C22×C8—434no—
249C4⋊Q8—28no—
250#124—28no—
251#123—216no—
252C22⋊Q8—28no—
253C22⋊Q8C22×D43116yes—
254C4×Q8—868no—
255C4×D4—8616no—
256C4×D4—868no—
257#117—22no—
258#117—434no—
259#117—434no—
260#117—438no—
261#117—864no—
262#117—862no—
263#117—864no—
264#117—862no—
265#117C22×D4314yes—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—434no—
268C2×C4⋊C4—438no—
269C2×C4⋊C4C22×D4312yes—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—24no—
272C2×C22⋊C4—864no—
273C2×C22⋊C4—862no—
274C2×C42—21no—
275C2×C42—864no—
276C2×C42—862no—
277#107—4316no—
278#106—4316no—
279#103—4332no—
280C22⋊C8—4316no—
281C24C2×C22⋊D4312yes—
282C24C2×C22⋊D4311yescharacteristic
283#41—216no—
284#41—28no—
285#41—28no—
286C2×Q8—24no—
287C2×Q8—22no—
288C2×Q8—24no—
289C2×Q8—28no—
290C2×Q8—28no—
291C2×Q8—28no—
292C2×Q8—44no—
293C2×Q8—48no—
294C2×Q8C2×C22⋊D4314yes—
295C2×Q8C23×D4314yes—
296C2×D4—28no—
297C2×D4—24no—
298C2×D4C2×C22⋊D4318yes—
299C2×D4C2×C22⋊D4314yes—
300C22×C4—28no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—24no—
304C22×C4—44no—
305C22×C4—868no—
306C22×C4—864no—
307C22×C4#1062190018yes—
308C22×C4C2×C22⋊D4314yes—
309C22×C4C2×C22⋊D4312yes—
310C22×C4C2×C22⋊D4311yescharacteristic
311C22×C4C2×C22⋊D4312yes—
312C22×C4C23×D4314yes—
313C22×C4C23×D4312yes—
314C22×C4C23×D4311yescharacteristic
315M16—868no—
316M16—868no—
317C2×C8—438no—
318C2×C8—868no—
319C4⋊C4—216no—
320C4⋊C4—22no—
321C4⋊C4—438no—
322C4⋊C4—868no—
323C4⋊C4—864no—
324C4⋊C4C23×D4314yes—
325C22⋊C4—24no—
326C22⋊C4—216no—
327C22⋊C4—864no—
328C22⋊C4—868no—
329C22⋊C4—864no—
330C42—24no—
331C42—864no—
332C42—868no—
333C42—864no—
334C23—24no—
335C23—42no—
336C23—44no—
337C23#1306330614yes—
338C23C22×C22⋊D4314yes—
339C23C22×C22⋊D4312yes—
340C23C22×C22⋊D4311yescharacteristic
341Q8—28no—
342Q8—28no—
343Q8—44no—
344Q8—48no—
345D4—216no—
346D4—28no—
347C2×C4—24no—
348C2×C4—28no—
349C2×C4—28no—
350C2×C4—24no—
351C2×C4—24no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—48no—
355C2×C4—868no—
356C2×C4—3444no—
357C2×C4—3448no—
358C2×C4#1306330614yes—
359C2×C4#1306330618yes—
360C2×C4C22×C22⋊D4314yes—
361C2×C4C22×C22⋊D4312yes—
362C2×C4C22×C22⋊D4311yescharacteristic
363C2×C4C2×#1062190014yes—
364C2×C4C2×#1062190014yes—
365C2×C4C2×#1062190014yes—
366C2×C4C24×D4311yescharacteristic
367C8—868no—
368C22—22no—
369C22—24no—
370C22—24no—
371C22—28no—
372C22—44no—
373C22—84no—
374C22C2×#1306330612yes—
375C22C2×#1306330614yes—
376C22C23×C22⋊D4311yescharacteristic
377C4—24no—
378C4—44no—
379C4—44no—
380C4—1728no—
381C4C2×#1306330612yes—
382C4C2×#1306330614yes—
383C4C22×#1062190012yes—
384C2—22no—
385C2—24no—
386C2—44no—
387C2C22×#1306330611yescharacteristic
388C2#1914938212yes—
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#536C2
socleC22×C43C23×D4
prime radicalC22×#41×C43C22
hypercenterC2×#536D43
hypocenterC43#60519
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×#41 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
2. #19144558C2semidirect
3. #19144539C2semidirect
4. #19143184C2semidirect
5. C2×#14582908C2semidirect
16. #14583237C22semidirect
17. #14583232C22semidirect
18. #14583227C22semidirect
19. #14582942C22semidirect
21. #14582935C22semidirect
23. #14582908C22semidirect
24. C2×#13063249C22semidirect
230. C43#60519semidirect

Maximal subgroups

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

subgroupindex
#191477982
#191445582
#191445392
#191431842
C2×#145829082
#191430402
C2×C43×#5362
#6051943