Finite Group Databasebeta

← #24991211

Subgroups — #24991211

Order 11008.

514 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143703C211yesmaximal, characteristic
2C4×#13063356C211yesmaximal, characteristic
3#19135532C211yesmaximal, characteristic, complemented
4#19132975C211yesmaximal, characteristic
5#19132444C211yesmaximal, characteristic, complemented
6#19132431C211yesmaximal, characteristic, complemented
7C43×#1479C211yesmaximal, characteristic, complemented
8C2×#13063356C411yescharacteristic
9C4×#10621898C2211yescharacteristic
10C8×Dic86—21no—
11#14583004—21no—
12#14582997—21no—
13C4×#10621885—21no—
14C4×#10621884—21no—
15C8×D172—21no—
16(C22⋊D43)⋊C8—22no—
17#14582951—21no—
18#14582939C411yescharacteristic
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20C4⋊C8×D43—21no—
21#14582908C411yescharacteristic
22#14582898C411yescharacteristic
23C4×#10621877C2211yescharacteristic
24C2×C4×C43⋊C8C2211yescharacteristic
25#14582654—22no—
26#14582629—21no—
27#14582626—21no—
28C2×C4×Q8×C43C2211yescharacteristic
29C43×#431C2211yescharacteristic
30C43×#431C2211yescharacteristic
31C43×Q8⋊C8—21no—
32C43×Q8⋊C8—21no—
33C2×#10621898C2×C411yescharacteristic
34#13063356—22no—
35#13063356C814yescomplemented
36C2×#10621885—21no—
37C2×#10621884—21no—
38C2×#10621877C2×C411yescharacteristic
39C2×#10621877C2×C411yescharacteristic
40C22×C43⋊C8—21no—
41C22×C43⋊C8D412yes—
42C2×C8×D43—22no—
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#13063249—21no—
58#13063249—21no—
59#13063248—21no—
60#13063245—21no—
61(C2×D43)⋊C8—22no—
62#13063236—21no—
63C4×C43⋊C8—21no—
64C4×C43⋊C8—21no—
65C4×C43⋊C8—21no—
66C8×Dic43—22no—
67C22×Q8×C43C2×C411yescharacteristic
68C4×Q8×C43—21no—
69C4×Q8×C43—21no—
70C4×Q8×C43—21no—
71C4×Q8×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43C2×C411yescharacteristic
74C2×C42×C43—21no—
75C2×C42×C43C2311yescharacteristic
76C4⋊C8×C43—21no—
77C4⋊C8×C43D411yescharacteristic
78C4⋊C8×C43D411yescharacteristic
79C22⋊C8×C43—21no—
80C22⋊C8×C43—21no—
81C4×C8×C43—21no—
82C4×C8×C43—21no—
83C2×Q8×C43—21no—
84C2×Q8×C43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43—21no—
87C2×Q8×C43—21no—
88C2×Q8×C43C2×C812yescomplemented
89C22×C4×C43—21no—
90C22×C4×C43—21no—
91C22×C4×C43C22×C411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43#4111yescharacteristic
94C2×C22⋊D43—21no—
95#10621898—21no—
96#10621898—21no—
97#10621898C2×C812yes—
98#10621898M1612yes—
99C2×D172C22⋊C411yescharacteristic
100C2×C4×D43—21no—
101C2×C4×D43—21no—
102C2×C4×D43—21no—
103C2×Dic86C22⋊C411yescharacteristic
104C2×C8×C43—21no—
105C2×C8×C43—21no—
106C2×C8×C43—41no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—41no—
110C4⋊C4×C43—41no—
111C42×C43—41no—
112C42×C43—41no—
113C42×C43C2×D411yescharacteristic
114C42×C43C2×D411yescharacteristic
115C42×C43C2×D411yescharacteristic
116C42×C43#4111yescharacteristic
117C22⋊Dic43—21no—
118#10621885—24no—
119#10621884—24no—
120(C2×D43)⋊C4—21no—
121(C2×D43)⋊C4—21no—
122C4⋊Dic43C22⋊C411yescharacteristic
123C4⋊Dic43C22⋊C411yescharacteristic
124Dic43⋊C4—21no—
125Dic43⋊C4—21no—
126C4×Dic43—21no—
127C4×Dic43—21no—
128C4×Dic43—21no—
129#10621877—21no—
130#10621877—21no—
131#10621877—21no—
132#10621877C2×C812yescomplemented
133C2×C43⋊C8—21no—
134C2×C43⋊C8—22no—
135C2×C43⋊C8—21no—
136C2×C43⋊C8—22no—
137C2×C43⋊C8—41no—
138C2×C43⋊C8—41no—
139C2×C43⋊C8—42no—
140C8×D43—82no—
141C23×C43C4×D411yescharacteristic
142C22×D43—21no—
143Q8×C43—22no—
144Q8×C43—22no—
145Q8×C43—41no—
146Q8×C43—41no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—22no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—42no—
154C2×C4×C43—41no—
155C2×C4×C43C2×C22⋊C411yescharacteristic
156C2×C4×C43C4×D411yescharacteristic
157C2×C4×C43#12011yescharacteristic
158C2×C4×C43#12111yescharacteristic
159C2×C4×C43#12111yescharacteristic
160C2×C4×C43#12311yescharacteristic
161C2×C4×C43C22×C811yescharacteristic
162C2×C4×C43C2×M1611yescharacteristic
163C2×C4×C43#13111yescharacteristic
164C2×C4×C43#13111yescharacteristic
165C22⋊D43—22no—
166C22⋊D43—22no—
167C2×Dic43—21no—
168C2×Dic43—21no—
169C2×Dic43—21no—
170D172—21no—
171D172C22⋊C812yes—
172C4×D43—22no—
173C4×D43—22no—
174C4×D43—41no—
175C4×D43—41no—
176C4×D43—81no—
177Dic86—21no—
178Dic86C22⋊C812yes—
179C8×C43—41no—
180C8×C43—41no—
181C8×C43—81no—
182C43⋊C8—22no—
183C43⋊C8—42no—
184C43⋊C8—41no—
185C43⋊C8—42no—
186#8953—431nomaximal, Sylow
187C22×C43—21no—
188C22×C43—21no—
189C22×C43#38611yescharacteristic
190C22×C43C8×D411yescharacteristic
191C22×C43#43511yescharacteristic
192C2×D43—22no—
193C2×D43—41no—
194C2×D43—41no—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—42no—
199C4×C43—81no—
200C4×C43C2×C22⋊C811yescharacteristic
201C4×C43#40811yescharacteristic
202C4×C43C8×D411yescharacteristic
203C4×C43#43511yescharacteristic
204C4×C43#45511yescharacteristic
205C4×C43#45611yescharacteristic
206Dic43—22no—
207Dic43—41no—
208Dic43—41no—
209#2988—431no—
210C4×#137—431no—
211#1984—431no—
212#1479D4311yescharacteristic, complemented
213#1476—431no—
214#1283—431no—
215#1278—431no—
216C2×C43—21no—
217C2×C43—21no—
218C2×C43#186911yescharacteristic
219C2×C43#188111yescharacteristic
220C2×C43#188211yescharacteristic
221D43—42no—
222C2×#137—431no—
223C4×#41—431no—
224C2×C4×Q8C2×D4311yescharacteristic
225C8×Q8—861no—
226#441—861no—
227#440—861no—
228C4×Q16—861no—
229C4×SD16—861no—
230C8×D4—861no—
231C8×D4—862no—
232#431—861no—
233#431C2×D4311yescharacteristic
234#431C2×D4311yescharacteristic
235#428—431no—
236C2×C4⋊C8—431no—
237C2×C4⋊C8—861no—
238#419—431no—
239#417—431no—
240C4×M16—431no—
241C2×C4×C8—431no—
242#336—862no—
243Q8⋊C8—21no—
244Q8⋊C8—21no—
245Q8⋊C8—861no—
246D4⋊C8—861no—
247C43#895311yescharacteristic, complemented, Sylow
248C2×#41—431no—
249C22×Q8C4×D4311yescharacteristic
250#137—434no—
251#137—862no—
252C2×Q16—861no—
253C2×SD16—861no—
254C2×M16—431no—
255C2×M16—431no—
256C22×C8—432no—
257C22×C8—862no—
258C22×C8—861no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8—21no—
263C4×Q8—431no—
264C4×Q8—431no—
265C4×D4—431no—
266C4×D4—431no—
267C4×D4—861no—
268C4×D4—861no—
269#117—431no—
270#117—861no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4C4×D4311yescharacteristic
273C2×C42—21no—
274C2×C42—861no—
275C2×C42C22×D4311yescharacteristic
276#107—861no—
277#106—861no—
278C4⋊C8—21no—
279C4⋊C8—862no—
280C4⋊C8—861no—
281C4⋊C8—861no—
282C4⋊C8C22⋊D4311yescharacteristic
283C4⋊C8C22⋊D4311yescharacteristic
284#103—861no—
285#103—861no—
286#103—861no—
287#102—861no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290C22⋊C8—862no—
291#97—861no—
292C4×C8—21no—
293C4×C8—21no—
294C4×C8—862no—
295C4×C8—861no—
296C4×C8—861no—
297C4×C8—861no—
298#41—432no—
299#41—432no—
300#41—861no—
301#41—861no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—431no—
308C2×Q8C8×D4312yescomplemented
309C2×D4—431no—
310C2×D4—861no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—861no—
314C22×C4—861no—
315C22×C4—861no—
316C22×C4C2×C4×D4311yescharacteristic
317C22×C4D4×D4311yescharacteristic
318C22×C4#1062190011yescharacteristic
319Q16—864no—
320SD16—864no—
321M16—432no—
322M16—861no—
323M16—861no—
324M16—861no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—41no—
328C2×C8—861no—
329C2×C8—862no—
330C2×C8—861no—
331C2×C8—862no—
332C2×C8—3442no—
333C2×C8—1721no—
334C2×C8—1721no—
335C2×C8—1722no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—431no—
341C4⋊C4—431no—
342C4⋊C4—861no—
343C4⋊C4—861no—
344C22⋊C4—861no—
345C22⋊C4—861no—
346C22⋊C4—861no—
347C42—41no—
348C42—41no—
349C42—861no—
350C42—861no—
351C42—861no—
352C42#1062189811yescharacteristic
353C42D4×D4311yescharacteristic
354C42D4×D4311yescharacteristic
355C42C2×C22⋊D4311yescharacteristic
356C23—861no—
357C23(C22⋊D43)⋊C411yescharacteristic
358Q8—22no—
359Q8—22no—
360Q8—41no—
361Q8—41no—
362Q8—432no—
363Q8—861no—
364D4—432no—
365D4—862no—
366D4—862no—
367D4—861no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—861no—
377C2×C4—862no—
378C2×C4—862no—
379C2×C4—861no—
380C2×C4—861no—
381C2×C4—3441no—
382C2×C4—1721no—
383C2×C4—1721no—
384C2×C4C22⋊C4×D4311yescharacteristic
385C2×C4C4×C22⋊D4311yescharacteristic
386C2×C4#1306329311yescharacteristic
387C2×C4#1306329611yescharacteristic
388C2×C4#1306329811yescharacteristic
389C2×C4#1306330711yescharacteristic
390C2×C4C2×C8×D4311yescharacteristic
391C2×C4M16×D4311yescharacteristic
392C2×C4#1306333111yescharacteristic
393C2×C4#1306333311yescharacteristic
394C8—41no—
395C8—41no—
396C8—81no—
397C8—862no—
398C8—1722no—
399C8—1722no—
400C8—1721no—
401C22—21no—
402C22—21no—
403C22—862no—
404C22—1721no—
405C22—1721no—
406C22#1458277511yescharacteristic
407C22(C22⋊D43)⋊C811yescharacteristic
408C22#1458297311yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—42no—
413C4—81no—
414C4—862no—
415C4—1721no—
416C4—1721no—
417C4C22⋊C8×D4311yescharacteristic
418C4#1458286411yescharacteristic
419C4C8×C22⋊D4311yescharacteristic
420C4#1458296811yescharacteristic
421C4#1458307511yescharacteristic
422C4#1458308011yescharacteristic
423C2—21no—
424C2—21no—
425C2—1722no—
426C2#1913488411yescharacteristic
427C2#1913495411yescharacteristic
428C2#1913496111yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1479C2
socleC22×C43#386
prime radicalC2×#10621898C2×C4
cosocleC2×C42×C43C23
hypercenter#1479D43
hypocenterC43#8953
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
3. #19135532C2semidirect
5. #19132444C2semidirect
6. #19132431C2semidirect
7. C43×#1479C2semidirect
35. #13063356C8semidirect
88. C2×Q8×C43C2×C8semidirect
132. #10621877C2×C8semidirect
212. #1479D43semidirect
247. C43#8953semidirect
308. C2×Q8C8×D43semidirect

Maximal subgroups

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

subgroupindex
#191437032
C4×#130633562
#191355322
#191329752
#191324442
#191324312
C43×#14792
#895343