Finite Group Databasebeta

← #24992925

Subgroups — #24992925

Order 11008.

478 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583223C211yesmaximal, characteristic
2#19134694C211yesmaximal, characteristic, complemented
3#19133112C211yesmaximal, characteristic
4#19132954C211yesmaximal, characteristic
5#19132471C211yesmaximal, characteristic, complemented
6#19132441C211yesmaximal, characteristic, complemented
7C43×#2924C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9#14583223—21no—
10#14583223—21no—
11#14583223—21no—
12#14583223—21no—
13C2×#13063258C411yescharacteristic, complemented
14C2×#13063256C411yescharacteristic, complemented
15C2×#13063245C411yescharacteristic, complemented
16C2×#13063245C411yescharacteristic, complemented
17#14582863C2211yescharacteristic
18C2×C22⋊(C43⋊C8)C2211yescharacteristic
19C4×C22⋊Dic43C2211yescharacteristic
20#14582658—21no—
21#14582658—21no—
22#14582634—22no—
23#14582622—21no—
24#14582622—21no—
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×#10621877—21no—
36C22×C43⋊C8C2×C411yescharacteristic
37C22×C43⋊C8C2×C411yescharacteristic
38#13063299—21no—
39#13063299—21no—
40#13063299—21no—
41#13063299—21no—
42C2×C4⋊Dic43C2×C411yescharacteristic
43C2×C22⋊Dic43—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×C4×Dic43—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×C43D411yescharacteristic
65#117×C43D411yescharacteristic
66#117×C43D411yescharacteristic
67#117×C43D411yescharacteristic
68C2×C4⋊C4×C43C2×C411yescharacteristic
69C2×C4⋊C4×C43C2×C411yescharacteristic
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×C43D411yescharacteristic
77C22⋊C8×C43D411yescharacteristic
78C22⋊C8×C43D412yes—
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—82no—
96C22×Dic43—21no—
97C22×Dic43—41no—
98C2×D172—21no—
99C2×D172—21no—
100C2×D172—41no—
101C2×D172—41no—
102M16×C43—41no—
103M16×C43—41no—
104C2×C8×C43—21no—
105C2×C8×C43—22no—
106C2×C8×C43—21no—
107C2×C8×C43—41no—
108C2×C8×C43—41no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43C22⋊C411yescharacteristic
112C4⋊C4×C43C22⋊C411yescharacteristic
113C4⋊C4×C43C22⋊C411yescharacteristic
114C4⋊C4×C43C22⋊C411yescharacteristic
115C22⋊C4×C43—21no—
116C22⋊C4×C43—21no—
117C22⋊C4×C43—21no—
118C22⋊C4×C43—21no—
119C42×C43—21no—
120C42×C43—21no—
121C42×C43—21no—
122C42×C43—21no—
123C22⋊Dic43—22no—
124C22⋊Dic43—41no—
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—41no—
147C22×D43—41no—
148C22×D43—81no—
149C22×D43—81no—
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—21no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—81no—
166C2×C4×C43C2×C22⋊C411yescharacteristic
167C2×C4×C43C4×D411yescharacteristic
168C2×C4×C43#12011yescharacteristic
169C2×C4×C43#12111yescharacteristic
170C22⋊D43—82no—
171C22⋊D43—82no—
172C2×Dic43—42no—
173C2×Dic43—41no—
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#9242—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#44311yescharacteristic
199C22×C43#44411yescharacteristic
200C2×D43—81no—
201C2×D43—81no—
202C2×D43—81no—
203C2×D43—161no—
204C2×D43—161no—
205C4×C43—21no—
206C4×C43—21no—
207C4×C43—21no—
208C4×C43—41no—
209C4×C43—41no—
210C4×C43—41no—
211C4×C43—41no—
212C4×C43#41011yescharacteristic
213C4×C43#41011yescharacteristic
214Dic43—82no—
215Dic43—81no—
216C2×#482—431no—
217#2924D4311yescharacteristic, complemented
218#1826—431no—
219#1507—431no—
220#1471—431no—
221#1293—431no—
222#1282—431no—
223C2×C43—21no—
224C2×C43—21no—
225C2×C43—41no—
226C2×C43—41no—
227C2×C43#187611yescharacteristic
228C2×C43#189911yescharacteristic
229C2×C43#190311yescharacteristic
230D43—161no—
231C2×#121—431no—
232C2×#117C2×D4311yescharacteristic
233#482—861no—
234#482—861no—
235#482—861no—
236#482—861no—
237#433—22no—
238#432—21no—
239#431—21no—
240C2×#107—431no—
241C2×#106—431no—
242#424—21no—
243C2×#102—431no—
244C2×#102—431no—
245#407—431no—
246#407C2×D4311yescharacteristic
247C2×C22⋊C8—431no—
248C2×C22⋊C8C2×D4311yescharacteristic
249#405—21no—
250C4×C22⋊C4—431no—
251#339—861no—
252#339—861no—
253#327—862no—
254#323—861no—
255#323—861no—
256C43#924211yescharacteristic, complemented, Sylow
257C22×D4—431no—
258C22×D4—861no—
259C23×C4C22×D4311yescharacteristic
260C2×M16—21no—
261C2×M16—861no—
262C22×C8—21no—
263C22×C8—431no—
264C22×C8—431no—
265#121—861no—
266#121—861no—
267#121—861no—
268#121—861no—
269#117—21no—
270#117—21no—
271#117D17211yescharacteristic
272#117D17211yescharacteristic
273#117C22⋊D4311yescharacteristic
274#117C22⋊D4311yescharacteristic
275C2×C4⋊C4—431no—
276C2×C4⋊C4C4×D4311yescharacteristic
277C2×C4⋊C4C4×D4311yescharacteristic
278C2×C22⋊C4—21no—
279C2×C22⋊C4—861no—
280C2×C22⋊C4—861no—
281C2×C42—21no—
282C2×C42—861no—
283#107—861no—
284#107—861no—
285#106—861no—
286#106—861no—
287C4⋊C8—22no—
288C4⋊C8—22no—
289#102—861no—
290#102—861no—
291#102—861no—
292#102—861no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C22⋊C8—861no—
296C22⋊C8—861no—
297C22⋊C8—861no—
298C22⋊C8—861no—
299C22⋊C8C22⋊D4311yescharacteristic
300C22⋊C8C22⋊D4311yescharacteristic
301C22⋊C8C22⋊D4312yes—
302#97—22no—
303C4×C8—22no—
304#95—861no—
305C24—861no—
306C24#1062189811yescharacteristic
307C2×D4—861no—
308C2×D4—861no—
309C2×D4—3442no—
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(C2×D43)⋊C411yescharacteristic
345C4⋊C4(C2×D43)⋊C411yescharacteristic
346C4⋊C4(C2×D43)⋊C411yescharacteristic
347C4⋊C4(C2×D43)⋊C411yescharacteristic
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—862no—
353C22⋊C4—1721no—
354C22⋊C4—1721no—
355C22⋊C4—1721no—
356C42—21no—
357C42—21no—
358C42—21no—
359C42—21no—
360C42—1721no—
361C42—1721no—
362C23—21no—
363C23—21no—
364C23—41no—
365C23—41no—
366C23—3441no—
367C23—3441no—
368C23—1721no—
369C23—1721no—
370C23—1721no—
371C23C4×C22⋊D4311yescharacteristic
372C23#1306329911yescharacteristic
373C23#1306330811yescharacteristic
374D4—3441no—
375D4—3442no—
376D4—3442no—
377D4—1721no—
378D4—1721no—
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—21no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—3441no—
396C2×C4—3441no—
397C2×C4—3441no—
398C2×C4—1722no—
399C2×C4—1721no—
400C2×C4C2×(C2×D43)⋊C411yescharacteristic
401C2×C4C4×C22⋊D4311yescharacteristic
402C2×C4#1306329411yescharacteristic
403C2×C4#1306329911yescharacteristic
404C8—41no—
405C8—41no—
406C8—42no—
407C8—3441no—
408C8—1721no—
409C8—1721no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—81no—
419C22—81no—
420C22—3441no—
421C22—3441no—
422C22—3441no—
423C22—6881no—
424C22—6881no—
425C22#1458277811yescharacteristic
426C22#1458301411yescharacteristic
427C22#1458301911yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—41no—
432C4—41no—
433C4—41no—
434C4—41no—
435C4—3442no—
436C4—3441no—
437C4#1458287211yescharacteristic
438C4#1458287211yescharacteristic
439C2—21no—
440C2—21no—
441C2—41no—
442C2—41no—
443C2—6881no—
444C2#1913492211yescharacteristic
445C2#1913505311yescharacteristic
446C2#1913507511yescharacteristic
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#9242
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. #19134694C2semidirect
5. #19132471C2semidirect
6. #19132441C2semidirect
7. C43×#2924C2semidirect
13. C2×#13063258C4semidirect
14. C2×#13063256C4semidirect
15. C2×#13063245C4semidirect
16. C2×#13063245C4semidirect
217. #2924D43semidirect
256. C43#9242semidirect

Maximal subgroups

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

subgroupindex
C2×#145832232
#191346942
#191331122
#191329542
#191324712
#191324412
C43×#29242
#924243