Finite Group Databasebeta

← #24992434

Subgroups — #24992434

Order 11008.

486 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144694C211yesmaximal, characteristic
2#19134420C211yesmaximal, characteristic
3#19133211C211yesmaximal, characteristic, complemented
4#19133095C211yesmaximal, characteristic, complemented
5#19132495C211yesmaximal, characteristic, complemented
6#19132450C211yesmaximal, characteristic, complemented
7C43×#2974C211yesmaximal, characteristic
8#14583456C2211yescharacteristic
9#14583234—21no—
10#14583179C411yescharacteristic, complemented
11#14583179C411yescharacteristic, complemented
12#14583104C411yescharacteristic, complemented
13#14583104C411yescharacteristic, complemented
14#14583050—21no—
15#14582999—21no—
16#14582999—21no—
17#14582956C2211yescharacteristic
18C2×#13063246—21no—
19C2×#13063236C2211yescharacteristic
20C4×C4⋊Dic43C2211yescharacteristic
21#14582661—21no—
22#14582640—22no—
23#14582637—21no—
24#14582637—21no—
25C2×C4×D4×C43C2211yescharacteristic
26C43×#436—21no—
27C43×#435—22no—
28C8×D4×C43—21no—
29C43×#432C2211yescharacteristic
30C43×#431C2211yescharacteristic
31C43×#407—21no—
32C2×C22⋊C8×C43—21no—
33C2×#10621883—21no—
34C2×#10621883—21no—
35C22×C43⋊C8—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—
46#13063258—21no—
47#13063258—21no—
48C4⋊(C43⋊C8)C2×C411yescharacteristic
49C4⋊(C43⋊C8)C2×C411yescharacteristic
50#13063248—21no—
51#13063248—21no—
52#13063246—24no—
53#13063246—21no—
54#13063246—21no—
55C22⋊(C43⋊C8)—21no—
56#13063236—21no—
57#13063236—21no—
58#13063236—21no—
59C43⋊#95—21no—
60C22×D4×C43D411yescharacteristic
61C23×C4×C43—21no—
62C2×M16×C43—22no—
63C22×C8×C43—22no—
64C4×D4×C43—21no—
65C4×D4×C43—21no—
66C4×D4×C43C2×C411yescharacteristic
67C4×D4×C43C2×C411yescharacteristic
68C4×D4×C43D411yescharacteristic
69C4×D4×C43D411yescharacteristic
70C2×C4⋊C4×C43D411yescharacteristic
71C2×C22⋊C4×C43—21no—
72C2×C42×C43C2311yescharacteristic
73C4⋊C8×C43—21no—
74C4⋊C8×C43—21no—
75C22⋊C8×C43—22no—
76C22⋊C8×C43—22no—
77C22⋊C8×C43—21no—
78C22⋊C8×C43D411yescharacteristic
79C22⋊C8×C43D411yescharacteristic
80#97×C43D412yes—
81C4×C8×C43—21no—
82C24×C43—21no—
83C2×D4×C43—21no—
84C2×D4×C43—22no—
85C2×D4×C43—41no—
86C2×D4×C43C22⋊C411yescharacteristic
87C2×D4×C43C22⋊C411yescharacteristic
88C22×C4×C43—21no—
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—82no—
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43#4111yescharacteristic
97C22×Dic43—41no—
98C2×Dic86—21no—
99C2×Dic86—21no—
100M16×C43—82no—
101C2×C8×C43—21no—
102C2×C8×C43—21no—
103C2×C8×C43—22no—
104C2×C8×C43—82no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43C22⋊C411yescharacteristic
107C4⋊C4×C43C22⋊C411yescharacteristic
108C22⋊C4×C43—21no—
109C22⋊C4×C43—21no—
110C22⋊C4×C43—21no—
111C22⋊C4×C43—21no—
112C42×C43C22×C411yescharacteristic
113C42×C43C2×D411yescharacteristic
114C42×C43C2×D411yescharacteristic
115C42×C43#4111yescharacteristic
116C22⋊Dic43—41no—
117#10621883—42no—
118#10621883—42no—
119C4⋊Dic43—22no—
120C4⋊Dic43—21no—
121C4⋊Dic43—21no—
122C4⋊Dic43—21no—
123C4⋊Dic43—21no—
124C4⋊Dic43—41no—
125Dic43⋊C4—41no—
126Dic43⋊C4—41no—
127C4×Dic43—41no—
128C4×Dic43—81no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—21no—
131C2×C43⋊C8—21no—
132C2×C43⋊C8—41no—
133C2×C43⋊C8—41no—
134C23×C43—21no—
135C23×C43—21no—
136C23×C43—42no—
137C23×C43—41no—
138C23×C43—41no—
139C23×C43—81no—
140C23×C43#12111yescharacteristic
141D4×C43—21no—
142D4×C43—21no—
143D4×C43—21no—
144D4×C43—42no—
145D4×C43#10412yes—
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—41no—
153C2×C4×C43—42no—
154C2×C4×C43—42no—
155C2×C4×C43—81no—
156C2×C4×C43—81no—
157C2×C4×C43—81no—
158C2×C4×C43C2×C22⋊C411yescharacteristic
159C2×C4×C43C4×D411yescharacteristic
160C2×C4×C43C4×D411yescharacteristic
161C2×C4×C43#12011yescharacteristic
162C2×C4×C43#12111yescharacteristic
163C2×C4×C43#12311yescharacteristic
164C2×Dic43—42no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—81no—
168C2×Dic43—81no—
169Dic86—41no—
170Dic86—41no—
171Dic86—81no—
172C8×C43—41no—
173C8×C43—42no—
174C8×C43—41no—
175C43⋊C8—42no—
176C43⋊C8—41no—
177C43⋊C8—41no—
178#9165—431nomaximal, Sylow
179C22×C43—21no—
180C22×C43—21no—
181C22×C43—22no—
182C22×C43—41no—
183C22×C43—41no—
184C22×C43—41no—
185C22×C43—41no—
186C22×C43—41no—
187C22×C43—82no—
188C22×C43—82no—
189C22×C43#38611yescharacteristic
190C22×C43#47111yescharacteristic
191C22×C43#47311yescharacteristic
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—21no—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—41no—
198C4×C43—41no—
199C4×C43C2×#10411yescharacteristic
200C4×C43#42111yescharacteristic
201Dic43—82no—
202Dic43—81no—
203Dic43—81no—
204#3110—431no—
205#2974D4311yescharacteristic
206#1762—431no—
207#1531—431no—
208#1503—431no—
209#1302—431no—
210#1285—431no—
211C2×C43—21no—
212C2×C43—21no—
213C2×C43—42no—
214C2×C43—81no—
215C2×C43#187111yescharacteristic
216C2×C43#190411yescharacteristic
217C2×C43#190811yescharacteristic
218#533—431no—
219C2×C4×D4C2×D4311yescharacteristic
220#484—861no—
221#474—431no—
222#474—431no—
223#461—431no—
224#461—431no—
225#450—861no—
226#440—861no—
227#440—861no—
228#436—21no—
229#435—22no—
230C8×D4—21no—
231#432—431no—
232#432C2×D4311yescharacteristic
233#431C2×D4311yescharacteristic
234C2×#102—861no—
235#407—21no—
236C2×C22⋊C8—21no—
237C2×#97—431no—
238C4×C4⋊C4—431no—
239#340—861no—
240#330—862no—
241#328—861no—
242#328—861no—
243C43#916511yescharacteristic, complemented, Sylow
244C22×D4D17211yescharacteristic
245C23×C4—21no—
246C2×SD16—861no—
247C2×SD16—861no—
248C2×M16—22no—
249C22×C8—22no—
250C22×C8—861no—
251C4⋊Q8—431no—
252C4⋊Q8—431no—
253#125—861no—
254C22⋊Q8—861no—
255C22⋊Q8—861no—
256C4×Q8—861no—
257C4×Q8—861no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4C4×D4311yescharacteristic
261C4×D4C4×D4311yescharacteristic
262C4×D4C22⋊D4311yescharacteristic
263C4×D4C22⋊D4311yescharacteristic
264#117—861no—
265C2×C4⋊C4—861no—
266C2×C4⋊C4D17211yescharacteristic
267C2×C22⋊C4—21no—
268C2×C42—861no—
269C2×C42C22×D4311yescharacteristic
270#107—861no—
271#107—861no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—431no—
275C4⋊C8—431no—
276#103—861no—
277#103—861no—
278#102—864no—
279#102—861no—
280#102—861no—
281C22⋊C8—22no—
282C22⋊C8—22no—
283C22⋊C8—21no—
284C22⋊C8—861no—
285C22⋊C8C22⋊D4311yescharacteristic
286C22⋊C8C22⋊D4311yescharacteristic
287#97—861no—
288#97—861no—
289#97—861no—
290#97C22⋊D4312yes—
291C4×C8—21no—
292#95—861no—
293C24—21no—
294C2×Q8—861no—
295C2×Q8—861no—
296C2×D4—22no—
297C2×D4—21no—
298C2×D4—41no—
299C2×D4(C2×D43)⋊C411yescharacteristic
300C2×D4(C2×D43)⋊C411yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—82no—
307C22×C4—1721no—
308C22×C4C2×D17211yescharacteristic
309C22×C4#1062189811yescharacteristic
310C22×C4C2×C22⋊D4311yescharacteristic
311SD16—1722no—
312SD16—1722no—
313M16—82no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—22no—
317C2×C8—82no—
318C2×C8—862no—
319C2×C8—861no—
320C2×C8—861no—
321C2×C8—1721no—
322C2×C8—1721no—
323C4⋊C4—21no—
324C4⋊C4—862no—
325C4⋊C4—861no—
326C4⋊C4—861no—
327C4⋊C4—861no—
328C4⋊C4—861no—
329C4⋊C4—1721no—
330C4⋊C4—1721no—
331C4⋊C4—1721no—
332C4⋊C4(C2×D43)⋊C411yescharacteristic
333C4⋊C4(C2×D43)⋊C411yescharacteristic
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—21no—
337C22⋊C4—21no—
338C22⋊C4—1721no—
339C42—3441no—
340C42—1721no—
341C42C2×C4×D4311yescharacteristic
342C42#1062189811yescharacteristic
343C42C2×C22⋊D4311yescharacteristic
344C42C2×C22⋊D4311yescharacteristic
345C23—21no—
346C23—21no—
347C23—42no—
348C23—41no—
349C23—41no—
350C23—81no—
351C23#1306329911yescharacteristic
352Q8—3441no—
353Q8—1721no—
354Q8—1721no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—42no—
359D4#1306325112yes—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—81no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—3441no—
373C2×C4—3441no—
374C2×C4—1722no—
375C2×C4—1721no—
376C2×C4—1721no—
377C2×C4C2×(C2×D43)⋊C411yescharacteristic
378C2×C4C4×C22⋊D4311yescharacteristic
379C2×C4C4×C22⋊D4311yescharacteristic
380C2×C4#1306329411yescharacteristic
381C2×C4#1306329911yescharacteristic
382C2×C4#1306330811yescharacteristic
383C8—41no—
384C8—42no—
385C8—41no—
386C8—1722no—
387C8—1721no—
388C8—1721no—
389C22—21no—
390C22—21no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—82no—
398C22—82no—
399C22#1458277811yescharacteristic
400C22#1458316211yescharacteristic
401C22#1458317411yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—3442no—
410C4—3441no—
411C4—3441no—
412C4C2×#1306325111yescharacteristic
413C4#1458291511yescharacteristic
414C2—21no—
415C2—21no—
416C2—42no—
417C2—81no—
418C2#1913489711yescharacteristic
419C2#1913508211yescharacteristic
420C2#1913511011yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2974C2
socleC22×C43#386
prime radicalC22×D4×C43D4
cosocleC2×C42×C43C23
hypercenter#2974D43
hypocenterC43#9165
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2974

Complements

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

NH ≅ G/Ntype
3. #19133211C2semidirect
4. #19133095C2semidirect
5. #19132495C2semidirect
6. #19132450C2semidirect
10. #14583179C4semidirect
11. #14583179C4semidirect
12. #14583104C4semidirect
13. #14583104C4semidirect
243. C43#9165semidirect

Maximal subgroups

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

subgroupindex
#191446942
#191344202
#191332112
#191330952
#191324952
#191324502
C43×#29742
#916543