Finite Group Databasebeta

← #24991213

Subgroups — #24991213

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#19143704C211yesmaximal, characteristic
2C4×#13063358C211yesmaximal, characteristic
3#19135530C211yesmaximal, characteristic, complemented
4#19132991C211yesmaximal, characteristic, complemented
5#19132975C211yesmaximal, characteristic
6#19132433C211yesmaximal, characteristic, complemented
7C43×#1283C211yesmaximal, characteristic, complemented
8C2×#13063358C411yescharacteristic
9C4×#10621898C2211yescharacteristic
10C2×C4×Dic86C2211yescharacteristic
11#14583023—21no—
12#14583007—21no—
13#14583001—21no—
14C4×Dic172—21no—
15C4×#10621873—21no—
16#14582964—21no—
17C8×C22⋊D43—22no—
18#14582952C2211yescharacteristic
19#14582951—21no—
20#14582941C411yescharacteristic
21C4⋊C8×D43—21no—
22#14582909C411yescharacteristic
23#14582901C411yescharacteristic
24C2×C4×C43⋊C8C2211yescharacteristic
25#14582653—22no—
26#14582631—21no—
27#14582631—21no—
28#14582629—21no—
29#14582626—21no—
30C43×#431C2211yescharacteristic
31C2×C4⋊C8×C43C2211yescharacteristic
32C4×M16×C43C2211yescharacteristic
33C2×#10621898C2×C411yescharacteristic
34C22×Dic86C2×C411yescharacteristic
35#13063358—22no—
36#13063358C814yescomplemented
37C2×Dic172—21no—
38C2×#10621873—21no—
39C22×C43⋊C8—21no—
40C2×C8×D43—22no—
41C4×Dic86—21no—
42C4×Dic86—21no—
43C4×Dic86—21no—
44C4×Dic86—21no—
45C4×Dic86D411yescharacteristic
46C4×Dic86D411yescharacteristic
47C4×D172D411yescharacteristic
48C4×D172D411yescharacteristic
49C4×C22⋊D43—21no—
50C4×C22⋊D43—21no—
51#13063284C2×C411yescharacteristic
52#13063282—21no—
53C2×C4⋊Dic43C2×C411yescharacteristic
54C2×Dic43⋊C4—21no—
55C2×C4×Dic43—21no—
56C42×D43—21no—
57#13063259—21no—
58#13063257—21no—
59C4⋊(C43⋊C8)D411yescharacteristic
60C4⋊(C43⋊C8)D411yescharacteristic
61Dic43⋊C8—22no—
62#13063250—21no—
63#13063250—21no—
64#13063250—21no—
65#13063247—21no—
66C22⋊(C43⋊C8)—21no—
67(C2×D43)⋊C8—22no—
68C4×C43⋊C8—21no—
69C4×C43⋊C8—21no—
70C4×C43⋊C8—21no—
71C8×Dic43—22no—
72C2×M16×C43C2×C411yescharacteristic
73C2×M16×C43C2×C411yescharacteristic
74C22×C8×C43D412yes—
75C2×C42×C43C2311yescharacteristic
76C4⋊C8×C43—21no—
77C4⋊C8×C43—21no—
78C4⋊C8×C43—21no—
79C22⋊C8×C43—21no—
80#97×C43—21no—
81C4×C8×C43—21no—
82C4×C8×C43—21no—
83C22×C4×C43C22×C411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43#4111yescharacteristic
86C2×C22⋊D43—21no—
87C22×Dic43—21no—
88C22×Dic43—21no—
89#10621898—21no—
90#10621898—21no—
91#10621898C2×C812yes—
92#10621898M1612yes—
93C2×D172C22⋊C411yescharacteristic
94C2×C4×D43—21no—
95C2×C4×D43—21no—
96C2×C4×D43—21no—
97C2×Dic86—21no—
98C2×Dic86—21no—
99C2×Dic86—21no—
100C2×Dic86—21no—
101C2×Dic86—21no—
102C2×Dic86C22⋊C411yescharacteristic
103C2×Dic86C2×C812yescomplemented
104M16×C43—21no—
105M16×C43—21no—
106M16×C43—21no—
107M16×C43C2×C812yescomplemented
108C2×C8×C43—21no—
109C2×C8×C43—21no—
110C2×C8×C43—22no—
111C2×C8×C43—42no—
112C2×C8×C43—41no—
113C42×C43C2×D411yescharacteristic
114C42×C43C2×D411yescharacteristic
115C42×C43C2×D411yescharacteristic
116C42×C43#4111yescharacteristic
117C22⋊Dic43—21no—
118(C2×D43)⋊C4—21no—
119(C2×D43)⋊C4—21no—
120C4⋊Dic43—21no—
121C4⋊Dic43—21no—
122C4⋊Dic43C22⋊C411yescharacteristic
123C4⋊Dic43C22⋊C411yescharacteristic
124Dic43⋊C4—21no—
125Dic43⋊C4—21no—
126Dic43⋊C4—41no—
127Dic43⋊C4—41no—
128C4×Dic43—21no—
129C4×Dic43—21no—
130C4×Dic43—21no—
131C4×Dic43—41no—
132C4×Dic43—41no—
133C2×C43⋊C8—22no—
134C2×C43⋊C8—21no—
135C2×C43⋊C8—21no—
136C2×C43⋊C8—41no—
137C2×C43⋊C8—41no—
138Dic172—24no—
139#10621873—24no—
140C8×D43—82no—
141C23×C43C4×D411yescharacteristic
142C22×D43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—41no—
146C2×C4×C43C2×C22⋊C411yescharacteristic
147C2×C4×C43C4×D411yescharacteristic
148C2×C4×C43#12011yescharacteristic
149C2×C4×C43#12111yescharacteristic
150C2×C4×C43#12111yescharacteristic
151C2×C4×C43#12311yescharacteristic
152C2×C4×C43C22×C811yescharacteristic
153C2×C4×C43C2×M1611yescharacteristic
154C2×C4×C43#13111yescharacteristic
155C2×C4×C43#13111yescharacteristic
156C22⋊D43—22no—
157C22⋊D43—22no—
158C2×Dic43—21no—
159C2×Dic43—21no—
160C2×Dic43—21no—
161C2×Dic43—22no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164C2×Dic43—42no—
165C2×Dic43—41no—
166D172—21no—
167D172C22⋊C812yes—
168C4×D43—22no—
169C4×D43—22no—
170C4×D43—41no—
171C4×D43—41no—
172C4×D43—81no—
173Dic86—21no—
174Dic86—22no—
175Dic86—22no—
176Dic86—41no—
177Dic86—41no—
178Dic86C22⋊C812yes—
179C8×C43—22no—
180C8×C43—41no—
181C8×C43—42no—
182C8×C43—81no—
183C43⋊C8—42no—
184C43⋊C8—41no—
185C43⋊C8—41no—
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×C43C2×C22⋊C811yescharacteristic
199C4×C43#40811yescharacteristic
200C4×C43C8×D411yescharacteristic
201C4×C43#43511yescharacteristic
202C4×C43#45511yescharacteristic
203C4×C43#45611yescharacteristic
204Dic43—22no—
205Dic43—42no—
206Dic43—41no—
207Dic43—41no—
208Dic43—81no—
209#2988—431no—
210C4×#137—431no—
211#1984—431no—
212#1479—431no—
213#1476—431no—
214#1283D4311yescharacteristic, complemented
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×Q8—431no—
225C8×Q8—861no—
226#441—861no—
227#440—861no—
228C4×Q16—861no—
229C4×SD16—861no—
230C8×D4—861no—
231C8×D4—862no—
232#431—431no—
233#431—861no—
234#431C2×D4311yescharacteristic
235#428—431no—
236C2×C4⋊C8—861no—
237C2×C4⋊C8C2×D4311yescharacteristic
238#419—431no—
239#417—431no—
240C4×M16C2×D4311yescharacteristic
241C2×C4×C8—431no—
242#336—862no—
243Q8⋊C8—861no—
244Q8⋊C8—861no—
245Q8⋊C8—861no—
246D4⋊C8—861no—
247C43#895311yescharacteristic, complemented, Sylow
248C2×#41—431no—
249C22×Q8—431no—
250#137—434no—
251#137—862no—
252C2×Q16—861no—
253C2×SD16—861no—
254C2×M16C4×D4311yescharacteristic
255C2×M16C4×D4311yescharacteristic
256C22×C8—862no—
257C22×C8—861no—
258C22×C8D17212yes—
259C4×Q8—431no—
260C4×Q8—431no—
261C4×Q8—861no—
262C4×Q8—861no—
263C4×Q8—861no—
264C4×Q8—861no—
265C4×D4—431no—
266C4×D4—431no—
267C4×D4—861no—
268C4×D4—861no—
269#117—431no—
270#117—861no—
271C2×C4⋊C4—431no—
272C2×C4⋊C4—861no—
273C2×C42—861no—
274C2×C42—861no—
275C2×C42C22×D4311yescharacteristic
276#107—861no—
277#106—861no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280C4⋊C8—21no—
281C4⋊C8—431no—
282C4⋊C8—431no—
283C4⋊C8—862no—
284#103—861no—
285#103—861no—
286#103—861no—
287#102—861no—
288C22⋊C8—21no—
289C22⋊C8—862no—
290C22⋊C8—861no—
291#97—21no—
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—431no—
303C2×Q8—432no—
304C2×Q8—861no—
305C2×Q8—861no—
306C2×Q8—861no—
307C2×Q8—861no—
308C2×Q8—861no—
309C2×D4—431no—
310C2×D4—861no—
311C22×C4—861no—
312C22×C4—861no—
313C22×C4—861no—
314C22×C4—861no—
315C22×C4—861no—
316C22×C4C2×C4×D4311yescharacteristic
317C22×C4C2×D17211yescharacteristic
318C22×C4#1062189811yescharacteristic
319Q16—864no—
320SD16—864no—
321M16—21no—
322M16—21no—
323M16—21no—
324M16C8×D4312yescomplemented
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—22no—
328C2×C8—42no—
329C2×C8—41no—
330C2×C8—862no—
331C2×C8—861no—
332C2×C8—861no—
333C2×C8—3442no—
334C2×C8—1721no—
335C2×C8—1721no—
336C4⋊C4—431no—
337C4⋊C4—431no—
338C4⋊C4—861no—
339C4⋊C4—861no—
340C4⋊C4—861no—
341C4⋊C4—861no—
342C4⋊C4—1721no—
343C4⋊C4—1721no—
344C22⋊C4—861no—
345C22⋊C4—861no—
346C22⋊C4—861no—
347C42—861no—
348C42—861no—
349C42—861no—
350C42—1721no—
351C42—1721no—
352C42D4×D4311yescharacteristic
353C42D4×D4311yescharacteristic
354C42D4×D4311yescharacteristic
355C42#1062190211yescharacteristic
356C23—861no—
357C23C4×D17211yescharacteristic
358Q8—432no—
359Q8—861no—
360Q8—862no—
361Q8—862no—
362Q8—1721no—
363Q8—1721no—
364D4—432no—
365D4—862no—
366D4—862no—
367D4—861no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—861no—
372C2×C4—862no—
373C2×C4—862no—
374C2×C4—862no—
375C2×C4—861no—
376C2×C4—861no—
377C2×C4—3441no—
378C2×C4—1722no—
379C2×C4—1721no—
380C2×C4—1721no—
381C2×C4—1721no—
382C2×C4—1721no—
383C2×C4—1721no—
384C2×C4C22⋊C4×D4311yescharacteristic
385C2×C4#1306328711yescharacteristic
386C2×C4#1306329511yescharacteristic
387C2×C4#1306329811yescharacteristic
388C2×C4#1306330011yescharacteristic
389C2×C4#1306331011yescharacteristic
390C2×C4C2×C8×D4311yescharacteristic
391C2×C4M16×D4311yescharacteristic
392C2×C4#1306333111yescharacteristic
393C2×C4#1306333311yescharacteristic
394C8—22no—
395C8—42no—
396C8—41no—
397C8—81no—
398C8—1722no—
399C8—1721no—
400C8—1721no—
401C22—21no—
402C22—21no—
403C22—862no—
404C22—1721no—
405C22—1721no—
406C22#1458277711yescharacteristic
407C22C8×D17211yescharacteristic
408C22#1458297211yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—862no—
413C4—3441no—
414C4—1722no—
415C4—1721no—
416C4—1721no—
417C4C22⋊C8×D4311yescharacteristic
418C4#1458286411yescharacteristic
419C4#1458296411yescharacteristic
420C4#1458296911yescharacteristic
421C4#1458307911yescharacteristic
422C4#1458308411yescharacteristic
423C2—21no—
424C2—21no—
425C2—1722no—
426C2#1913488611yescharacteristic
427C2#1913495611yescharacteristic
428C2#1913496311yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1283C2
socleC22×C43#386
prime radicalC2×#10621898C2×C4
cosocleC2×C42×C43C23
hypercenter#1283D43
hypocenterC43#8953
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1283

Complements

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

NH ≅ G/Ntype
3. #19135530C2semidirect
4. #19132991C2semidirect
6. #19132433C2semidirect
7. C43×#1283C2semidirect
36. #13063358C8semidirect
103. C2×Dic86C2×C8semidirect
107. M16×C43C2×C8semidirect
214. #1283D43semidirect
247. C43#8953semidirect
324. M16C8×D43semidirect

Maximal subgroups

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

subgroupindex
#191437042
C4×#130633582
#191355302
#191329912
#191329752
#191324332
C43×#12832
#895343