Finite Group Databasebeta

← #24991316

Subgroups — #24991316

Order 11008.

478 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#19144666C211yesmaximal, characteristic
2#19135571C211yesmaximal, characteristic, complemented
3C4×#13063252C211yesmaximal, characteristic
4#19133015C211yesmaximal, characteristic, complemented
5#19132484C211yesmaximal, characteristic, complemented
6#19132427C211yesmaximal, characteristic, complemented
7C43×#2990C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583240—21no—
10#14583184C411yescharacteristic, complemented
11#14583179C411yescharacteristic, complemented
12#14583109C411yescharacteristic, complemented
13#14583104C411yescharacteristic, complemented
14#14583061—21no—
15C4×#10621885—21no—
16C4×#10621883—21no—
17#14582952C2211yescharacteristic
18C2×#13063252—21no—
19C4×#10621877C2211yescharacteristic
20C42×Dic43C2211yescharacteristic
21#14582660—22no—
22#14582658—21no—
23#14582629—21no—
24#14582629—21no—
25C4×#41×C43C2211yescharacteristic
26C43×#446—21no—
27C43×#435—22no—
28C8×D4×C43—21no—
29C43×#432—21no—
30C43×#431C2211yescharacteristic
31C43×#423C2211yescharacteristic
32C2×C4⋊C8×C43—21no—
33C2×#10621885—21no—
34C2×#10621883—21no—
35C2×#10621877—21no—
36#13063325C2×C411yescharacteristic
37#13063325C2×C411yescharacteristic
38#13063317—21no—
39#13063304—21no—
40#13063304—21no—
41C4×Dic86—21no—
42C4×Dic86—21no—
43#13063284—21no—
44C2×C4×Dic43—21no—
45C2×C4×Dic43—21no—
46C2×C4×Dic43—21no—
47#13063258—21no—
48#13063256—21no—
49C4⋊(C43⋊C8)C2×C411yescharacteristic
50C4⋊(C43⋊C8)C2×C411yescharacteristic
51#13063252—24no—
52#13063249—21no—
53#13063248—21no—
54#13063248—21no—
55#13063246—21no—
56C22⋊(C43⋊C8)—21no—
57#13063236—21no—
58C4×C43⋊C8—21no—
59C4×C43⋊C8—21no—
60C2×#41×C43D411yescharacteristic
61C2×M16×C43D412yes—
62C22×C8×C43—22no—
63C4×Q8×C43C2×C411yescharacteristic
64C4×Q8×C43D411yescharacteristic
65C4×D4×C43—21no—
66C4×D4×C43—21no—
67C4×D4×C43C2×C411yescharacteristic
68C4×D4×C43D411yescharacteristic
69#117×C43—21no—
70#117×C43D411yescharacteristic
71C2×C42×C43—21no—
72C2×C42×C43C2311yescharacteristic
73C4⋊C8×C43—22no—
74C4⋊C8×C43—21no—
75C4⋊C8×C43—21no—
76C4⋊C8×C43D411yescharacteristic
77C4⋊C8×C43D411yescharacteristic
78C22⋊C8×C43—22no—
79C22⋊C8×C43—21no—
80#97×C43—22no—
81C4×C8×C43—21no—
82#41×C43—22no—
83#41×C43—41no—
84C2×Q8×C43C22⋊C411yescharacteristic
85C2×D4×C43—21no—
86C2×D4×C43C22⋊C411yescharacteristic
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43#4111yescharacteristic
93C22×Dic43—41no—
94C2×Dic86—21no—
95C2×Dic86—21no—
96M16×C43—42no—
97C2×C8×C43—21no—
98C2×C8×C43—21no—
99C2×C8×C43—22no—
100C2×C8×C43—82no—
101C4⋊C4×C43—21no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43C22⋊C411yescharacteristic
104C4⋊C4×C43C22⋊C411yescharacteristic
105C22⋊C4×C43—21no—
106C22⋊C4×C43—21no—
107C22⋊C4×C43—21no—
108C42×C43—21no—
109C42×C43—21no—
110C42×C43—21no—
111C42×C43C22×C411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C42×C43C2×D411yescharacteristic
114C42×C43#4111yescharacteristic
115C22⋊Dic43—41no—
116#10621885—42no—
117#10621883—42no—
118C4⋊Dic43—21no—
119C4⋊Dic43—21no—
120C4⋊Dic43—21no—
121C4⋊Dic43—21no—
122Dic43⋊C4—41no—
123Dic43⋊C4—41no—
124C4×Dic43—22no—
125C4×Dic43—22no—
126C4×Dic43—22no—
127C4×Dic43—41no—
128C4×Dic43—41no—
129C4×Dic43—41no—
130C4×Dic43—41no—
131#10621877—22no—
132#10621877—41no—
133C2×C43⋊C8—21no—
134C2×C43⋊C8—21no—
135C2×C43⋊C8—41no—
136C23×C43—21no—
137C23×C43#12111yescharacteristic
138Q8×C43—21no—
139Q8×C43—21no—
140D4×C43—21no—
141D4×C43—42no—
142D4×C43#10412yes—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—42no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43C2×C22⋊C411yescharacteristic
158C2×C4×C43C4×D411yescharacteristic
159C2×C4×C43C4×D411yescharacteristic
160C2×C4×C43#12011yescharacteristic
161C2×C4×C43#12111yescharacteristic
162C2×C4×C43#12311yescharacteristic
163C2×Dic43—42no—
164C2×Dic43—42no—
165C2×Dic43—42no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168Dic86—41no—
169Dic86—41no—
170Dic86—41no—
171Dic86—41no—
172C8×C43—41no—
173C8×C43—42no—
174C8×C43—41no—
175C43⋊C8—42no—
176C43⋊C8—41no—
177C43⋊C8—41no—
178#8971—431nomaximal, Sylow
179C22×C43—22no—
180C22×C43—21no—
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—41no—
184C22×C43—41no—
185C22×C43#38611yescharacteristic
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—41no—
190C4×C43—41no—
191C4×C43—41no—
192C4×C43C2×#10411yescharacteristic
193C4×C43#42111yescharacteristic
194C4×C43#44311yescharacteristic
195C4×C43#44411yescharacteristic
196C4×C43#45511yescharacteristic
197C4×C43#45611yescharacteristic
198Dic43—44no—
199Dic43—81no—
200Dic43—81no—
201#3107—431no—
202#2990D4311yescharacteristic
203#1994—431no—
204C4×#104—431no—
205#1485—431no—
206#1299—431no—
207#1276—431no—
208C2×C43—41no—
209C2×C43—42no—
210C2×C43#187111yescharacteristic
211C2×C43#187611yescharacteristic
212C2×C43#188211yescharacteristic
213#533—431no—
214C4×#41C2×D4311yescharacteristic
215#485—861no—
216#475—431no—
217#474—431no—
218#462—431no—
219#461—431no—
220#452—861no—
221#446—21no—
222C4×Q16—861no—
223C4×SD16—861no—
224#435—22no—
225C8×D4—21no—
226#432—21no—
227#431—431no—
228#431C2×D4311yescharacteristic
229#423C2×D4311yescharacteristic
230C2×C4⋊C8—21no—
231C2×#104—861no—
232C4×M16—431no—
233C43—431no—
234#339—862no—
235#339—861no—
236Q8⋊C8—861no—
237Q8⋊C8—861no—
238C43#897111yescharacteristic, complemented, Sylow
239C2×#41D17211yescharacteristic
240C2×Q16—861no—
241C2×SD16—861no—
242C2×M16—861no—
243C2×M16C22⋊D4312yes—
244C22×C8—22no—
245C4⋊Q8—431no—
246C4⋊Q8—431no—
247#125—861no—
248C22⋊Q8—861no—
249C22⋊Q8—861no—
250C4×Q8—861no—
251C4×Q8—861no—
252C4×Q8C4×D4311yescharacteristic
253C4×Q8C22⋊D4311yescharacteristic
254C4×D4—21no—
255C4×D4—21no—
256C4×D4C4×D4311yescharacteristic
257C4×D4C22⋊D4311yescharacteristic
258#117—21no—
259#117—861no—
260#117D17211yescharacteristic
261C2×C42—21no—
262C2×C42—861no—
263C2×C42—861no—
264C2×C42—861no—
265C2×C42C22×D4311yescharacteristic
266#107—861no—
267#106—861no—
268C4⋊C8—22no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—431no—
272C4⋊C8—431no—
273C4⋊C8C22⋊D4311yescharacteristic
274C4⋊C8C22⋊D4311yescharacteristic
275#104—864no—
276#103—861no—
277#103—861no—
278#103—861no—
279#102—861no—
280C22⋊C8—22no—
281C22⋊C8—21no—
282C22⋊C8—861no—
283#97—22no—
284#97—861no—
285C4×C8—21no—
286C4×C8—861no—
287C4×C8—861no—
288#41—22no—
289#41—41no—
290C2×Q8—861no—
291C2×Q8—861no—
292C2×Q8(C2×D43)⋊C411yescharacteristic
293C2×D4—21no—
294C2×D4(C2×D43)⋊C411yescharacteristic
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—1721no—
299C22×C4C2×D17211yescharacteristic
300C22×C4#1062189811yescharacteristic
301C22×C4C2×C22⋊D4311yescharacteristic
302Q16—1722no—
303SD16—1722no—
304M16—42no—
305M16—862no—
306M16—1721no—
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—22no—
310C2×C8—82no—
311C2×C8—861no—
312C2×C8—861no—
313C2×C8—1721no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—861no—
317C4⋊C4—861no—
318C4⋊C4—861no—
319C4⋊C4—861no—
320C4⋊C4—1721no—
321C4⋊C4—1721no—
322C4⋊C4(C2×D43)⋊C411yescharacteristic
323C4⋊C4(C2×D43)⋊C411yescharacteristic
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—1721no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42—862no—
332C42—862no—
333C42—862no—
334C42—1721no—
335C42—1721no—
336C42—1721no—
337C42—1721no—
338C42C2×C4×D4311yescharacteristic
339C42#1062189811yescharacteristic
340C42C2×C22⋊D4311yescharacteristic
341C42C2×C22⋊D4311yescharacteristic
342C23—21no—
343C23#1306329911yescharacteristic
344Q8—21no—
345Q8—21no—
346Q8—1721no—
347Q8—1721no—
348Q8—1721no—
349Q8—1721no—
350D4—21no—
351D4—42no—
352D4#1306325112yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—1721no—
368C2×C4—1721no—
369C2×C4—1722no—
370C2×C4—1722no—
371C2×C4—1722no—
372C2×C4C2×(C2×D43)⋊C411yescharacteristic
373C2×C4C4×C22⋊D4311yescharacteristic
374C2×C4C4×C22⋊D4311yescharacteristic
375C2×C4#1306329411yescharacteristic
376C2×C4#1306329911yescharacteristic
377C2×C4#1306330811yescharacteristic
378C8—41no—
379C8—42no—
380C8—41no—
381C8—1722no—
382C8—1721no—
383C8—1721no—
384C22—21no—
385C22—22no—
386C22—21no—
387C22—21no—
388C22—41no—
389C22—41no—
390C22#1458277811yescharacteristic
391C4—21no—
392C4—21no—
393C4—21no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—3441no—
398C4—3441no—
399C4—1724no—
400C4C2×#1306325111yescharacteristic
401C4#1458291511yescharacteristic
402C4#1458301411yescharacteristic
403C4#1458301911yescharacteristic
404C4#1458307711yescharacteristic
405C4#1458308211yescharacteristic
406C2—41no—
407C2—42no—
408C2#1913489711yescharacteristic
409C2#1913492211yescharacteristic
410C2#1913496411yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2990C2
socleC22×C43#386
prime radicalC2×#41×C43D4
cosocleC2×C42×C43C23
hypercenter#2990D43
hypocenterC43#8971
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2990

Complements

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

NH ≅ G/Ntype
2. #19135571C2semidirect
4. #19133015C2semidirect
5. #19132484C2semidirect
6. #19132427C2semidirect
10. #14583184C4semidirect
11. #14583179C4semidirect
12. #14583109C4semidirect
13. #14583104C4semidirect
238. C43#8971semidirect

Maximal subgroups

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

subgroupindex
#191446662
#191355712
C4×#130632522
#191330152
#191324842
#191324272
C43×#29902
#897143