Finite Group Databasebeta

← #24993667

Subgroups — #24993667

Order 11008.

470 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144535C211yesmaximal, characteristic
2#19134690C211yesmaximal, characteristic, complemented
3#19133164C211yesmaximal, characteristic
4#19132956C211yesmaximal, characteristic
5#19132502C211yesmaximal, characteristic, complemented
6#19132483C211yesmaximal, characteristic, complemented
7C43×#2924C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9#14583223—21no—
10#14583223—21no—
11#14583217—21no—
12#14583212—21no—
13#14582942C411yescharacteristic, complemented
14#14582942C411yescharacteristic, complemented
15#14582903C411yescharacteristic, complemented
16#14582903C411yescharacteristic, complemented
17#14582863C2211yescharacteristic
18C2×C22⋊(C43⋊C8)C2211yescharacteristic
19#14582759C2211yescharacteristic
20#14582661—21no—
21#14582661—21no—
22#14582634—21no—
23#14582634—21no—
24#14582622—22no—
25C2×#117×C43C2211yescharacteristic
26C43×#433—22no—
27C43×#432—21no—
28C43×#431—21no—
29C43×#424—21no—
30C43×#407C2211yescharacteristic
31C2×C22⋊C8×C43C2211yescharacteristic
32C43×#405—21no—
33C22×D172C2×C411yescharacteristic
34C22×C22⋊D43—21no—
35C2×#10621877C2×C411yescharacteristic
36C2×#10621877C2×C411yescharacteristic
37C22×C43⋊C8—21no—
38#13063299—21no—
39#13063299—21no—
40#13063299—21no—
41#13063299—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43C2×C411yescharacteristic
44C2×C22⋊Dic43—21no—
45C2×(C2×D43)⋊C4—21no—
46#13063258—21no—
47#13063258—21no—
48#13063256—21no—
49#13063256—21no—
50#13063245—21no—
51#13063245—21no—
52#13063245—21no—
53#13063245—21no—
54C22⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)—21no—
58C43⋊#95—21no—
59C23×C4×C43C2311yescharacteristic
60C2×M16×C43—21no—
61C22×C8×C43—21no—
62#117×C43—21no—
63#117×C43—21no—
64#117×C43C2×C411yescharacteristic
65#117×C43C2×C411yescharacteristic
66#117×C43D411yescharacteristic
67#117×C43D411yescharacteristic
68C2×C4⋊C4×C43D411yescharacteristic
69C2×C4⋊C4×C43D411yescharacteristic
70C2×C22⋊C4×C43—21no—
71C2×C42×C43—21no—
72C4⋊C8×C43—22no—
73C4⋊C8×C43—22no—
74C22⋊C8×C43—21no—
75C22⋊C8×C43—21no—
76C22⋊C8×C43D412yes—
77C22⋊C8×C43D411yescharacteristic
78C22⋊C8×C43D411yescharacteristic
79#97×C43—22no—
80C4×C8×C43—22no—
81C24×C43#4111yescharacteristic
82C23×D43—21no—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43C22×C411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43#4111yescharacteristic
93C2×C22⋊D43—41no—
94C2×C22⋊D43—41no—
95C2×C22⋊D43—81no—
96C2×C22⋊D43—81no—
97C22×Dic43—21no—
98C22×Dic43—41no—
99C2×D172—21no—
100C2×D172—21no—
101C2×D172—41no—
102C2×D172—41no—
103M16×C43—41no—
104M16×C43—41no—
105C2×C8×C43—21no—
106C2×C8×C43—22no—
107C2×C8×C43—21no—
108C2×C8×C43—41no—
109C2×C8×C43—41no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—21no—
112C4⋊C4×C43C22⋊C411yescharacteristic
113C4⋊C4×C43C22⋊C411yescharacteristic
114C4⋊C4×C43C22⋊C411yescharacteristic
115C4⋊C4×C43C22⋊C411yescharacteristic
116C22⋊C4×C43—21no—
117C22⋊C4×C43—21no—
118C22⋊C4×C43—21no—
119C22⋊C4×C43—21no—
120C42×C43—21no—
121C42×C43—21no—
122C42×C43—21no—
123C42×C43—21no—
124C22⋊Dic43—81no—
125(C2×D43)⋊C4—41no—
126(C2×D43)⋊C4—41no—
127C4⋊Dic43—21no—
128C4⋊Dic43—21no—
129C4⋊Dic43—41no—
130C4⋊Dic43—41no—
131#10621877—41no—
132#10621877—41no—
133C2×C43⋊C8—21no—
134C2×C43⋊C8—21no—
135C2×C43⋊C8—41no—
136C2×C43⋊C8—41no—
137C2×C43⋊C8—41no—
138C23×C43—21no—
139C23×C43—21no—
140C23×C43—41no—
141C23×C43—41no—
142C23×C43C4×D411yescharacteristic
143C23×C43#12111yescharacteristic
144C23×C43#12311yescharacteristic
145C22×D43—41no—
146C22×D43—42no—
147C22×D43—81no—
148C22×D43—81no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43—21no—
158C2×C4×C43—21no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—81no—
165C2×C4×C43C2×C22⋊C411yescharacteristic
166C2×C4×C43C4×D411yescharacteristic
167C2×C4×C43#12011yescharacteristic
168C2×C4×C43#12111yescharacteristic
169C22⋊D43—82no—
170C22⋊D43—81no—
171C22⋊D43—81no—
172C2×Dic43—41no—
173C2×Dic43—81no—
174C2×Dic43—81no—
175C2×Dic43—81no—
176C2×Dic43—81no—
177D172—41no—
178D172—41no—
179D172—81no—
180C8×C43—41no—
181C8×C43—41no—
182C8×C43—42no—
183C43⋊C8—41no—
184C43⋊C8—41no—
185C43⋊C8—81no—
186#9348—431nomaximal, Sylow
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—81no—
196C22×C43—81no—
197C22×C43#38611yescharacteristic
198C22×C43#47111yescharacteristic
199C22×C43#47211yescharacteristic
200C2×D43—81no—
201C2×D43—81no—
202C2×D43—81no—
203C2×D43—162no—
204C4×C43—21no—
205C4×C43—21no—
206C4×C43—21no—
207C4×C43—41no—
208C4×C43—41no—
209C4×C43—41no—
210C4×C43—41no—
211C4×C43#41011yescharacteristic
212C4×C43#41011yescharacteristic
213Dic43—81no—
214Dic43—161no—
215#3094—431no—
216#2924D4311yescharacteristic, complemented
217#1825—431no—
218#1519—431no—
219#1471—431no—
220#1305—431no—
221#1298—431no—
222C2×C43—21no—
223C2×C43—21no—
224C2×C43—41no—
225C2×C43—41no—
226C2×C43#188111yescharacteristic
227C2×C43#189911yescharacteristic
228C2×C43#190711yescharacteristic
229D43—161no—
230C2×#121—431no—
231C2×#117C2×D4311yescharacteristic
232#482—861no—
233#482—861no—
234#481—861no—
235#480—861no—
236#433—22no—
237#432—21no—
238#431—21no—
239#428—431no—
240#428—431no—
241#424—21no—
242#418—431no—
243#418—431no—
244#407—431no—
245#407C2×D4311yescharacteristic
246C2×C22⋊C8—431no—
247C2×C22⋊C8C2×D4311yescharacteristic
248#405—21no—
249#380—431no—
250#340—861no—
251#340—861no—
252#327—861no—
253#327—861no—
254#323—862no—
255C43#934811yescharacteristic, complemented, Sylow
256C22×D4—431no—
257C22×D4—861no—
258C23×C4C22×D4311yescharacteristic
259C2×M16—21no—
260C2×M16—431no—
261C2×M16—431no—
262C22×C8—21no—
263C22×C8—861no—
264#121—861no—
265#121—861no—
266#121—861no—
267#121—861no—
268#117—21no—
269#117—21no—
270#117C4×D4311yescharacteristic
271#117C4×D4311yescharacteristic
272#117C22⋊D4311yescharacteristic
273#117C22⋊D4311yescharacteristic
274C2×C4⋊C4—431no—
275C2×C4⋊C4—861no—
276C2×C4⋊C4D17211yescharacteristic
277C2×C4⋊C4D17211yescharacteristic
278C2×C22⋊C4—21no—
279C2×C22⋊C4—861no—
280C2×C22⋊C4—861no—
281C2×C42—21no—
282#107—861no—
283#107—861no—
284#106—861no—
285#106—861no—
286C4⋊C8—22no—
287C4⋊C8—22no—
288#102—861no—
289#102—861no—
290#102—861no—
291#102—861no—
292C22⋊C8—21no—
293C22⋊C8—21no—
294C22⋊C8—861no—
295C22⋊C8—861no—
296C22⋊C8—861no—
297C22⋊C8—861no—
298C22⋊C8C22⋊D4312yes—
299C22⋊C8C22⋊D4311yescharacteristic
300C22⋊C8C22⋊D4311yescharacteristic
301#97—22no—
302C4×C8—22no—
303#95—861no—
304C24—861no—
305C24#1062189811yescharacteristic
306C2×D4—861no—
307C2×D4—861no—
308C2×D4—3441no—
309C2×D4—3441no—
310C2×D4—1721no—
311C2×D4—1721no—
312C2×D4—1721no—
313C2×D4—1721no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—861no—
319C22×C4—1721no—
320C22×C4C2×C4×D4311yescharacteristic
321C22×C4C2×D17211yescharacteristic
322C22×C4#1062189811yescharacteristic
323C22×C4C2×C22⋊D4311yescharacteristic
324C22×C4C2×C22⋊D4311yescharacteristic
325C22×C4C2×C22⋊D4311yescharacteristic
326M16—41no—
327M16—41no—
328M16—1721no—
329M16—1721no—
330C2×C8—21no—
331C2×C8—22no—
332C2×C8—21no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—861no—
336C2×C8—861no—
337C2×C8—1721no—
338C2×C8—1721no—
339C2×C8—1721no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—861no—
343C4⋊C4—861no—
344C4⋊C4—1721no—
345C4⋊C4—1721no—
346C4⋊C4(C2×D43)⋊C411yescharacteristic
347C4⋊C4(C2×D43)⋊C411yescharacteristic
348C4⋊C4(C2×D43)⋊C411yescharacteristic
349C4⋊C4(C2×D43)⋊C411yescharacteristic
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—21no—
353C22⋊C4—21no—
354C22⋊C4—3441no—
355C22⋊C4—1721no—
356C22⋊C4—1721no—
357C42—21no—
358C42—21no—
359C42—21no—
360C42—21no—
361C23—21no—
362C23—21no—
363C23—41no—
364C23—41no—
365C23—3441no—
366C23—3441no—
367C23—1722no—
368C23—1721no—
369C23C4×C22⋊D4311yescharacteristic
370C23#1306329911yescharacteristic
371C23#1306330811yescharacteristic
372D4—3441no—
373D4—3442no—
374D4—3441no—
375D4—3441no—
376D4—1721no—
377D4—1721no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—81no—
394C2×C4—3441no—
395C2×C4—3441no—
396C2×C4—3441no—
397C2×C4—3441no—
398C2×C4—1721no—
399C2×C4C2×(C2×D43)⋊C411yescharacteristic
400C2×C4C4×C22⋊D4311yescharacteristic
401C2×C4#1306329411yescharacteristic
402C2×C4#1306329911yescharacteristic
403C8—41no—
404C8—41no—
405C8—42no—
406C8—3441no—
407C8—1721no—
408C8—1721no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—81no—
418C22—81no—
419C22—3441no—
420C22—3441no—
421C22—3441no—
422C22—6882no—
423C22#1458277811yescharacteristic
424C22#1458316211yescharacteristic
425C22#1458316911yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—41no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—3441no—
434C4—6881no—
435C4#1458287211yescharacteristic
436C4#1458287211yescharacteristic
437C2—21no—
438C2—21no—
439C2—41no—
440C2—41no—
441C2—6881no—
442C2#1913495711yescharacteristic
443C2#1913505311yescharacteristic
444C2#1913510311yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2924C2
socleC22×C43#386
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#2924D43
hypocenterC43#9348
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #19134690C2semidirect
5. #19132502C2semidirect
6. #19132483C2semidirect
7. C43×#2924C2semidirect
13. #14582942C4semidirect
14. #14582942C4semidirect
15. #14582903C4semidirect
16. #14582903C4semidirect
216. #2924D43semidirect
255. C43#9348semidirect

Maximal subgroups

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

subgroupindex
#191445352
#191346902
#191331642
#191329562
#191325022
#191324832
C43×#29242
#934843