Finite Group Databasebeta

← #24992067

Subgroups — #24992067

Order 11008.

546 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
1C8×#10621898C211yesmaximal, characteristic, complemented
2C4×#13063351C211yesmaximal, characteristic
3#19132980C211yesmaximal, characteristic, complemented
4#19132916C211yesmaximal, characteristic, complemented
5#19132445C211yesmaximal, characteristic, complemented
6#19132432C211yesmaximal, characteristic, complemented
7C2×C43×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#13063351C411yescharacteristic
9C4×#10621898C2211yescharacteristic
10C8×Dic86—21no—
11#14583009—21no—
12#14582999—21no—
13C4×#10621883—21no—
14C4×#10621882—21no—
15C8×D172—21no—
16C8×C22⋊D43—22no—
17#14582952C2211yescharacteristic
18#14582952C2211yescharacteristic
19#14582950—21no—
20#14582939C411yescharacteristic
21#14582904C411yescharacteristic
22#14582898C411yescharacteristic
23C4×#10621877C2211yescharacteristic
24C4×C8×D43—21no—
25#14582629—21no—
26#14582626—21no—
27#14582623—22no—
28C2×C4×D4×C43C2211yescharacteristic
29C2×C4⋊C8×C43C2211yescharacteristic
30C2×C4×C8×C43C2211yescharacteristic
31C43×D4⋊C8—21no—
32C43×D4⋊C8—21no—
33C2×#10621898C2×C411yescharacteristic
34#13063351—22no—
35#13063351C814yescomplemented
36C2×#10621883—21no—
37C2×#10621882—21no—
38C2×#10621877C2×C411yescharacteristic
39C2×#10621877C2×C411yescharacteristic
40C2×C8×D43—22no—
41C4×Dic86D411yescharacteristic
42C4×Dic86D411yescharacteristic
43C4×D172D411yescharacteristic
44C4×D172D411yescharacteristic
45C4×C22⋊D43—21no—
46C4×C22⋊D43—21no—
47#13063284C2×C411yescharacteristic
48#13063282—21no—
49C42×D43—21no—
50#13063258—21no—
51#13063256—21no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)—21no—
54Dic43⋊C8—22no—
55#13063248—21no—
56#13063246—21no—
57#13063246—21no—
58#13063245—21no—
59C22⋊(C43⋊C8)—21no—
60C22⋊(C43⋊C8)D412yes—
61(C2×D43)⋊C8—22no—
62#13063236—21no—
63C4×C43⋊C8—21no—
64C4×C43⋊C8—21no—
65C4×C43⋊C8—21no—
66C8×Dic43—22no—
67C22×D4×C43C2×C411yescharacteristic
68C23×C4×C43—21no—
69C22×C8×C43—21no—
70C22×C8×C43—21no—
71C4×D4×C43—21no—
72C4×D4×C43—21no—
73C4×D4×C43—21no—
74C4×D4×C43—21no—
75C2×C4⋊C4×C43C2×C411yescharacteristic
76C2×C22⋊C4×C43—21no—
77C2×C42×C43C2311yescharacteristic
78C4⋊C8×C43—21no—
79C4⋊C8×C43—21no—
80C4×C8×C43—21no—
81C4×C8×C43D411yescharacteristic
82C4×C8×C43D411yescharacteristic
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×C43C2×C812yescomplemented
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#10621898C2×C812yes—
102#10621898M1612yes—
103C2×D172C22⋊C411yescharacteristic
104C2×C4×D43—21no—
105C2×C4×D43—21no—
106C2×C4×D43—21no—
107C2×Dic86C22⋊C411yescharacteristic
108C2×C8×C43—21no—
109C2×C8×C43—21no—
110C2×C8×C43—42no—
111C2×C8×C43—41no—
112C2×C8×C43—81no—
113C4⋊C4×C43—21no—
114C4⋊C4×C43—21no—
115C22⋊C4×C43—41no—
116C22⋊C4×C43—41no—
117C42×C43C2×D411yescharacteristic
118C42×C43C2×D411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43#4111yescharacteristic
121C22⋊Dic43—21no—
122#10621883—24no—
123#10621882—24no—
124(C2×D43)⋊C4—21no—
125(C2×D43)⋊C4—21no—
126C4⋊Dic43C22⋊C411yescharacteristic
127C4⋊Dic43C22⋊C411yescharacteristic
128Dic43⋊C4—21no—
129Dic43⋊C4—21no—
130C4×Dic43—21no—
131C4×Dic43—21no—
132C4×Dic43—21no—
133#10621877—21no—
134#10621877—21no—
135#10621877—21no—
136#10621877C2×C812yescomplemented
137C2×C43⋊C8—21no—
138C2×C43⋊C8—21no—
139C2×C43⋊C8—22no—
140C2×C43⋊C8—41no—
141C8×D43—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×C43C22×C811yescharacteristic
168C2×C4×C43C2×M1611yescharacteristic
169C2×C4×C43#13111yescharacteristic
170C2×C4×C43#13111yescharacteristic
171C22⋊D43—22no—
172C22⋊D43—22no—
173C2×Dic43—21no—
174C2×Dic43—21no—
175C2×Dic43—21no—
176D172—21no—
177D172C22⋊C812yes—
178C4×D43—22no—
179C4×D43—22no—
180C4×D43—42no—
181C4×D43—41no—
182C4×D43—41no—
183Dic86—21no—
184Dic86C22⋊C812yes—
185C8×C43—22no—
186C8×C43—41no—
187C8×C43—81no—
188C43⋊C8—22no—
189C43⋊C8—42no—
190C43⋊C8—41no—
191C43⋊C8—81no—
192#9095—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×C43C8×D411yescharacteristic
202C22×C43#43511yescharacteristic
203C2×D43—22no—
204C2×D43—41no—
205C2×D43—41no—
206C4×C43—21no—
207C4×C43—21no—
208C4×C43—21no—
209C4×C43—81no—
210C4×C43C2×C22⋊C811yescharacteristic
211C4×C43#40811yescharacteristic
212C4×C43C8×D411yescharacteristic
213C4×C43#43511yescharacteristic
214C4×C43#47111yescharacteristic
215C4×C43#47211yescharacteristic
216Dic43—22no—
217Dic43—41no—
218Dic43—41no—
219C8×#41—431no—
220C4×AGL(1,ℤ/8)—431no—
221#1477—431no—
222C2×D4⋊C8D4311yescharacteristic, complemented
223#1460—431no—
224#1283—431no—
225#1278—431no—
226C2×C43—21no—
227C2×C43—21no—
228C2×C43—82no—
229C2×C43#186911yescharacteristic
230C2×C43#190611yescharacteristic
231C2×C43#190711yescharacteristic
232D43—42no—
233C2×AGL(1,ℤ/8)—431no—
234C4×#41—431no—
235C2×C4×D4C2×D4311yescharacteristic
236C8×Q8—861no—
237#442—861no—
238#440—861no—
239C4×SD16—861no—
240C4×D8—861no—
241C8×D4—861no—
242C8×D4—862no—
243#431—431no—
244#431—431no—
245#431—861no—
246#428—431no—
247C2×C4⋊C8C2×D4311yescharacteristic
248#418—431no—
249#417—431no—
250C4×M16—431no—
251C2×C4×C8—861no—
252C2×C4×C8C2×D4311yescharacteristic
253Q8⋊C8—861no—
254D4⋊C8—21no—
255D4⋊C8—21no—
256D4⋊C8—861no—
257#323—862no—
258C43#909511yescharacteristic, complemented, Sylow
259C2×#41—431no—
260C22×D4C4×D4311yescharacteristic
261C23×C4—21no—
262AGL(1,ℤ/8)—434no—
263AGL(1,ℤ/8)—862no—
264C2×SD16—861no—
265C2×D8—861no—
266C2×M16—431no—
267C2×M16—431no—
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—862no—
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—432no—
299C22⋊C8—862no—
300C22⋊C8—861no—
301#97—861no—
302C4×C8—21no—
303C4×C8—862no—
304C4×C8—861no—
305C4×C8—861no—
306C4×C8—861no—
307C4×C8C22⋊D4311yescharacteristic
308C4×C8C22⋊D4311yescharacteristic
309C24—21no—
310#41—432no—
311#41—432no—
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×D4C8×D4312yescomplemented
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×C4D4×D4311yescharacteristic
333C22×C4#1062190011yescharacteristic
334SD16—864no—
335D8—864no—
336M16—432no—
337M16—861no—
338M16—861no—
339M16—861no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—42no—
343C2×C8—41no—
344C2×C8—81no—
345C2×C8—861no—
346C2×C8—861no—
347C2×C8—862no—
348C2×C8—1724no—
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—
364C42#1062189811yescharacteristic
365C42D4×D4311yescharacteristic
366C42D4×D4311yescharacteristic
367C42C2×C22⋊D4311yescharacteristic
368C23—22no—
369C23—41no—
370C23—41no—
371C23—81no—
372C23—81no—
373C23—861no—
374C23(C22⋊D43)⋊C411yescharacteristic
375Q8—432no—
376Q8—861no—
377D4—22no—
378D4—22no—
379D4—41no—
380D4—41no—
381D4—432no—
382D4—862no—
383D4—862no—
384D4—861no—
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—862no—
395C2×C4—862no—
396C2×C4—861no—
397C2×C4—861no—
398C2×C4—1722no—
399C2×C4—1721no—
400C2×C4—1721no—
401C2×C4C22⋊C4×D4311yescharacteristic
402C2×C4C4×C22⋊D4311yescharacteristic
403C2×C4#1306329311yescharacteristic
404C2×C4#1306329611yescharacteristic
405C2×C4#1306329811yescharacteristic
406C2×C4#1306330711yescharacteristic
407C2×C4C2×C8×D4311yescharacteristic
408C2×C4M16×D4311yescharacteristic
409C2×C4#1306333111yescharacteristic
410C2×C4#1306333311yescharacteristic
411C8—22no—
412C8—41no—
413C8—81no—
414C8—862no—
415C8—3441no—
416C8—1722no—
417C8—1721no—
418C22—21no—
419C22—21no—
420C22—42no—
421C22—82no—
422C22—82no—
423C22—81no—
424C22—81no—
425C22—862no—
426C22—1721no—
427C22—1721no—
428C22#1458277511yescharacteristic
429C22(C22⋊D43)⋊C811yescharacteristic
430C22#1458297311yescharacteristic
431C4—21no—
432C4—21no—
433C4—21no—
434C4—81no—
435C4—862no—
436C4—1721no—
437C4—1721no—
438C4C22⋊C8×D4311yescharacteristic
439C4#1458286411yescharacteristic
440C4C8×C22⋊D4311yescharacteristic
441C4#1458296811yescharacteristic
442C4#1458315911yescharacteristic
443C4#1458316611yescharacteristic
444C2—21no—
445C2—21no—
446C2—82no—
447C2—1722no—
448C2#1913488411yescharacteristic
449C2#1913509911yescharacteristic
450C2#1913510611yescharacteristic
subgroupG/H
centerC2×C4#13063296
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC2×C43×D4⋊C8C2
socleC22×C43#386
prime radicalC2×#13063351C4
cosocleC2×C42×C43C23
hypercenterC2×D4⋊C8D43
hypocenterC43#9095
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
1. C8×#10621898C2semidirect
3. #19132980C2semidirect
4. #19132916C2semidirect
5. #19132445C2semidirect
6. #19132432C2semidirect
7. C2×C43×D4⋊C8C2semidirect
35. #13063351C8semidirect
89. C2×D4×C43C2×C8semidirect
136. #10621877C2×C8semidirect
222. C2×D4⋊C8D43semidirect
258. C43#9095semidirect
322. C2×D4C8×D43semidirect

Maximal subgroups

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

subgroupindex
C8×#106218982
C4×#130633512
#191329802
#191329162
#191324452
#191324322
C2×C43×D4⋊C82
#909543