Finite Group Databasebeta

← #24992075

Subgroups — #24992075

Order 11008.

520 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143556C211yesmaximal, characteristic, complemented
2C4×#13063351C211yesmaximal, characteristic
3#19132983C211yesmaximal, characteristic, complemented
4C2×D4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
5#19132444C211yesmaximal, characteristic, complemented
6#19132431C211yesmaximal, characteristic, complemented
7C43×#1460C211yesmaximal, characteristic, complemented
8C2×#13063351C411yescharacteristic
9C4×#10621898C2211yescharacteristic
10#14583026—21no—
11#14583009—21no—
12#14582999—21no—
13C4×#10621883—21no—
14C4×#10621882—21no—
15#14582976—21no—
16#14582967—22no—
17#14582950—21no—
18#14582939C411yescharacteristic
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20#14582904C411yescharacteristic
21#14582898C411yescharacteristic
22C4×#10621877C2211yescharacteristic
23C4×#10621872—21no—
24C2×C4×C43⋊C8C2211yescharacteristic
25#14582631—21no—
26#14582628—21no—
27D4⋊(C43⋊C8)—21no—
28D4⋊(C43⋊C8)—21no—
29C2×C4×D4×C43C2211yescharacteristic
30C43×#431C2211yescharacteristic
31C43×#431C2211yescharacteristic
32C43×#323—22no—
33C2×#10621898C2×C411yescharacteristic
34#13063351—22no—
35#13063351—22no—
36C2×#10621883—21no—
37C2×#10621882—21no—
38C2×#10621877C2×C411yescharacteristic
39C2×#10621877C2×C411yescharacteristic
40C2×#10621872—22no—
41C22×C43⋊C8—21no—
42C22×C43⋊C8—21no—
43C4×Dic86D411yescharacteristic
44C4×Dic86D411yescharacteristic
45C4×D172D411yescharacteristic
46C4×D172D411yescharacteristic
47C4×C22⋊D43—21no—
48C4×C22⋊D43—21no—
49#13063284C2×C411yescharacteristic
50#13063282—21no—
51C42×D43—21no—
52#13063258—21no—
53#13063256—21no—
54C4⋊(C43⋊C8)—21no—
55C4⋊(C43⋊C8)—21no—
56Dic43⋊C8—22no—
57#13063248—21no—
58#13063246—21no—
59#13063246—21no—
60#13063245—21no—
61(C2×D43)⋊C8—22no—
62#13063236—21no—
63#13063235—22no—
64C4×C43⋊C8—21no—
65C4×C43⋊C8—21no—
66C4×C43⋊C8D411yescharacteristic
67C4×C43⋊C8D411yescharacteristic
68C22×D4×C43C2×C411yescharacteristic
69C23×C4×C43—21no—
70C4×D4×C43—21no—
71C4×D4×C43—21no—
72C4×D4×C43—21no—
73C4×D4×C43—21no—
74C2×C4⋊C4×C43C2×C411yescharacteristic
75C2×C22⋊C4×C43—21no—
76C2×C42×C43C2311yescharacteristic
77C4⋊C8×C43—21no—
78C4⋊C8×C43—21no—
79C22⋊C8×C43—21no—
80C22⋊C8×C43D412yes—
81C4×C8×C43—21no—
82C4×C8×C43—21no—
83C24×C43—21no—
84C2×D4×C43—21no—
85C2×D4×C43—21no—
86C2×D4×C43—21no—
87C2×D4×C43—21no—
88C2×D4×C43—21no—
89C2×D4×C43M1612yescomplemented
90C22×C4×C43—21no—
91C22×C4×C43—41no—
92C22×C4×C43—41no—
93C22×C4×C43—81no—
94C22×C4×C43—81no—
95C22×C4×C43C22×C411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43#4111yescharacteristic
98C2×C22⋊D43—21no—
99#10621898—21no—
100#10621898—21no—
101#10621898—21no—
102#10621898—21no—
103C2×D172C22⋊C411yescharacteristic
104C2×C4×D43—21no—
105C2×C4×D43—21no—
106C2×C4×D43—21no—
107C2×Dic86C22⋊C411yescharacteristic
108C2×C8×C43—22no—
109C2×C8×C43—41no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—21no—
112C22⋊C4×C43—41no—
113C22⋊C4×C43—41no—
114C42×C43C2×D411yescharacteristic
115C42×C43C2×D411yescharacteristic
116C42×C43C2×D411yescharacteristic
117C42×C43#4111yescharacteristic
118C22⋊Dic43—21no—
119#10621883—24no—
120#10621882—24no—
121(C2×D43)⋊C4—21no—
122(C2×D43)⋊C4—21no—
123C4⋊Dic43C22⋊C411yescharacteristic
124C4⋊Dic43C22⋊C411yescharacteristic
125Dic43⋊C4—21no—
126Dic43⋊C4—21no—
127C4×Dic43—21no—
128C4×Dic43—21no—
129C4×Dic43—21no—
130#10621877—21no—
131#10621877—21no—
132#10621877—21no—
133#10621877M1612yescomplemented
134C2×C43⋊C8—21no—
135C2×C43⋊C8—21no—
136C2×C43⋊C8—21no—
137C2×C43⋊C8—21no—
138C2×C43⋊C8—42no—
139C2×C43⋊C8—41no—
140C2×C43⋊C8—81no—
141#10621872—44no—
142C23×C43—22no—
143C23×C43—41no—
144C23×C43—41no—
145C23×C43—81no—
146C23×C43—81no—
147C23×C43C4×D411yescharacteristic
148C22×D43—21no—
149D4×C43—22no—
150D4×C43—22no—
151D4×C43—41no—
152D4×C43—41no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—82no—
158C2×C4×C43—81no—
159C2×C4×C43—81no—
160C2×C4×C43—81no—
161C2×C4×C43C2×C22⋊C411yescharacteristic
162C2×C4×C43C4×D411yescharacteristic
163C2×C4×C43#12011yescharacteristic
164C2×C4×C43#12111yescharacteristic
165C2×C4×C43#12111yescharacteristic
166C2×C4×C43#12311yescharacteristic
167C2×C4×C43C2×M1611yescharacteristic
168C2×C4×C43C2×M1611yescharacteristic
169C2×C4×C43#13111yescharacteristic
170C2×C4×C43#13111yescharacteristic
171C22⋊D43—41no—
172C22⋊D43—41no—
173C2×Dic43—21no—
174C2×Dic43—21no—
175C2×Dic43—21no—
176D172—21no—
177D172—21no—
178C4×D43—42no—
179C4×D43—41no—
180C4×D43—41no—
181C4×D43—41no—
182C4×D43—41no—
183Dic86—21no—
184Dic86—21no—
185C8×C43—42no—
186C8×C43—81no—
187C43⋊C8—22no—
188C43⋊C8—22no—
189C43⋊C8—41no—
190C43⋊C8—41no—
191C43⋊C8—81no—
192#9097—431nomaximal, Sylow
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—42no—
196C22×C43—82no—
197C22×C43—82no—
198C22×C43—81no—
199C22×C43—81no—
200C22×C43#38611yescharacteristic
201C22×C43#43511yescharacteristic
202C22×C43#43611yescharacteristic
203C2×D43—41no—
204C2×D43—41no—
205C2×D43—41no—
206C4×C43—21no—
207C4×C43—21no—
208C4×C43—21no—
209C4×C43—81no—
210C4×C43#40711yescharacteristic
211C4×C43#40811yescharacteristic
212C4×C43#43511yescharacteristic
213C4×C43#43611yescharacteristic
214C4×C43#47111yescharacteristic
215C4×C43#47211yescharacteristic
216Dic43—41no—
217Dic43—41no—
218Dic43—41no—
219#2965—431no—
220C4×AGL(1,ℤ/8)—431no—
221#1477—431no—
222C2×D4⋊C8—431no—
223#1460D4311yescharacteristic, complemented
224#1283—431no—
225#1278—431no—
226C2×C43—21no—
227C2×C43—21no—
228C2×C43—82no—
229C2×C43#187011yescharacteristic
230C2×C43#190611yescharacteristic
231C2×C43#190711yescharacteristic
232D43—81no—
233C2×AGL(1,ℤ/8)—431no—
234C4×#41—431no—
235C2×C4×D4C2×D4311yescharacteristic
236#446—861no—
237#442—861no—
238#440—861no—
239C4×SD16—861no—
240C4×D8—861no—
241#436—861no—
242#435—862no—
243#431—861no—
244#431C2×D4311yescharacteristic
245#431C2×D4311yescharacteristic
246#428—431no—
247C2×C4⋊C8—431no—
248#418—431no—
249#417—431no—
250C4×M16—431no—
251C4×M16—861no—
252C2×C4×C8—431no—
253Q8⋊C8—861no—
254D4⋊C8—861no—
255D4⋊C8—861no—
256D4⋊C8—861no—
257#323—22no—
258C43#909711yescharacteristic, complemented, Sylow
259C2×#41—431no—
260C22×D4C4×D4311yescharacteristic
261C23×C4—21no—
262AGL(1,ℤ/8)—862no—
263AGL(1,ℤ/8)—862no—
264C2×SD16—861no—
265C2×D8—861no—
266C2×M16—431no—
267C2×M16—431no—
268C2×M16—862no—
269C22×C8—861no—
270C22×C8—861no—
271C4×Q8—431no—
272C4×Q8—431no—
273C4×D4—21no—
274C4×D4—21no—
275C4×D4—21no—
276C4×D4—21no—
277C4×D4—431no—
278C4×D4—431no—
279C4×D4—861no—
280C4×D4—861no—
281#117—431no—
282#117—861no—
283C2×C4⋊C4C4×D4311yescharacteristic
284C2×C22⋊C4—21no—
285C2×C42—861no—
286C2×C42C22×D4311yescharacteristic
287#107—861no—
288#106—861no—
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—862no—
292C4⋊C8—861no—
293C4⋊C8—861no—
294#103—861no—
295#102—861no—
296#102—861no—
297#102—861no—
298C22⋊C8—21no—
299C22⋊C8—862no—
300C22⋊C8C22⋊D4312yes—
301#97—862no—
302#97—861no—
303C4×C8—21no—
304C4×C8—21no—
305C4×C8—431no—
306C4×C8—431no—
307C4×C8—861no—
308C4×C8—861no—
309C24—21no—
310#41—861no—
311#41—861no—
312#41—861no—
313#41—861no—
314C2×Q8—431no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—431no—
321C2×D4—861no—
322C2×D4#1062187212yescomplemented
323C22×C4—21no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—81no—
327C22×C4—81no—
328C22×C4—861no—
329C22×C4—861no—
330C22×C4—861no—
331C22×C4C2×C4×D4311yescharacteristic
332C22×C4#1062189811yescharacteristic
333C22×C4C2×C22⋊D4311yescharacteristic
334SD16—864no—
335D8—864no—
336M16—432no—
337M16—861no—
338M16—861no—
339M16—861no—
340M16—1724no—
341C2×C8—22no—
342C2×C8—41no—
343C2×C8—861no—
344C2×C8—861no—
345C2×C8—861no—
346C2×C8—861no—
347C2×C8—3441no—
348C2×C8—1722no—
349C2×C8—1721no—
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—431no—
353C4⋊C4—431no—
354C4⋊C4—861no—
355C4⋊C4—861no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—861no—
359C22⋊C4—861no—
360C22⋊C4—861no—
361C42—861no—
362C42—861no—
363C42—861no—
364C42D4×D4311yescharacteristic
365C42D4×D4311yescharacteristic
366C42D4×D4311yescharacteristic
367C42#1062190011yescharacteristic
368C23—22no—
369C23—41no—
370C23—41no—
371C23—81no—
372C23—81no—
373C23—861no—
374C23C4×C22⋊D4311yescharacteristic
375Q8—861no—
376Q8—861no—
377D4—22no—
378D4—22no—
379D4—41no—
380D4—41no—
381D4—861no—
382D4—861no—
383D4—1721no—
384D4—1721no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—82no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—861no—
394C2×C4—861no—
395C2×C4—861no—
396C2×C4—1722no—
397C2×C4—1721no—
398C2×C4—1721no—
399C2×C4—1721no—
400C2×C4—1721no—
401C2×C4C22⋊C4×D4311yescharacteristic
402C2×C4(C22⋊D43)⋊C411yescharacteristic
403C2×C4#1306329311yescharacteristic
404C2×C4#1306329611yescharacteristic
405C2×C4#1306329811yescharacteristic
406C2×C4#1306330711yescharacteristic
407C2×C4M16×D4311yescharacteristic
408C2×C4C2×#1062187211yescharacteristic
409C2×C4#1306333111yescharacteristic
410C2×C4#1306333311yescharacteristic
411C8—42no—
412C8—81no—
413C8—862no—
414C8—862no—
415C8—3441no—
416C8—1721no—
417C8—1721no—
418C22—21no—
419C22—21no—
420C22—42no—
421C22—82no—
422C22—82no—
423C22—81no—
424C22—81no—
425C22—1721no—
426C22—1721no—
427C22—1721no—
428C22#1458277511yescharacteristic
429C22#1458297011yescharacteristic
430C22#1458297511yescharacteristic
431C4—21no—
432C4—21no—
433C4—21no—
434C4—81no—
435C4—1721no—
436C4—1721no—
437C4—1721no—
438C4#1458286111yescharacteristic
439C4#1458286411yescharacteristic
440C4#1458296711yescharacteristic
441C4#1458297411yescharacteristic
442C4#1458316111yescharacteristic
443C4#1458316811yescharacteristic
444C2—21no—
445C2—21no—
446C2—82no—
447C2—3441no—
448C2#1913488911yescharacteristic
449C2#1913509311yescharacteristic
450C2#1913510011yescharacteristic
subgroupG/H
centerC2×C4#13063298
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1460C2
socleC22×C43#386
prime radicalC2×#13063351C4
cosocleC2×C42×C43C23
hypercenter#1460D43
hypocenterC43#9097
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
1. #19143556C2semidirect
3. #19132983C2semidirect
4. C2×D4⋊(C43⋊C8)C2semidirect
5. #19132444C2semidirect
6. #19132431C2semidirect
7. C43×#1460C2semidirect
89. C2×D4×C43M16semidirect
133. #10621877M16semidirect
223. #1460D43semidirect
258. C43#9097semidirect
322. C2×D4#10621872semidirect

Maximal subgroups

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

subgroupindex
#191435562
C4×#130633512
#191329832
C2×D4⋊(C43⋊C8)2
#191324442
#191324312
C43×#14602
#909743