Finite Group Databasebeta

← #24991231

Subgroups — #24991231

Order 11008.

488 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#19143713C211yesmaximal, characteristic
2C4×#13063356C211yesmaximal, characteristic
3#19132990C211yesmaximal, characteristic, complemented
4#19132978C211yesmaximal, characteristic
5#19132445C211yesmaximal, characteristic, complemented
6#19132432C211yesmaximal, characteristic, complemented
7C43×#1984C211yesmaximal, characteristic, complemented
8C2×#13063356C411yescharacteristic
9C4×#10621898C2211yescharacteristic
10#14583026—21no—
11#14583004—21no—
12#14582997—21no—
13C4×#10621885—21no—
14C4×#10621884—21no—
15#14582976—21no—
16#14582970—22no—
17#14582955—21no—
18#14582952C2211yescharacteristic
19#14582952C2211yescharacteristic
20#14582939C411yescharacteristic
21#14582921—21no—
22#14582908C411yescharacteristic
23#14582898C411yescharacteristic
24C4×#10621877C2211yescharacteristic
25#14582631—21no—
26Q8⋊(C43⋊C8)—21no—
27Q8⋊(C43⋊C8)—21no—
28#14582628—21no—
29C2×C4×Q8×C43C2211yescharacteristic
30C2×C4⋊C8×C43C2211yescharacteristic
31C2×C4×C8×C43C2211yescharacteristic
32C43×#336—22no—
33C2×#10621898C2×C411yescharacteristic
34#13063356—22no—
35#13063356—22no—
36C2×#10621885—21no—
37C2×#10621884—21no—
38C2×#10621877C2×C411yescharacteristic
39C2×#10621877C2×C411yescharacteristic
40C2×#10621872—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)D411yescharacteristic
54C4⋊(C43⋊C8)D411yescharacteristic
55Dic43⋊C8—22no—
56#13063249—21no—
57#13063249—21no—
58#13063248—21no—
59#13063245—21no—
60C22⋊(C43⋊C8)—21no—
61C22⋊(C43⋊C8)—21no—
62(C2×D43)⋊C8—22no—
63#13063236—21no—
64#13063235—22no—
65C4×C43⋊C8—21no—
66C4×C43⋊C8—21no—
67C4×C43⋊C8—21no—
68C22×Q8×C43C2×C411yescharacteristic
69C22×C8×C43—21no—
70C22×C8×C43D412yes—
71C4×Q8×C43—21no—
72C4×Q8×C43—21no—
73C4×Q8×C43—21no—
74C4×Q8×C43—21no—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43C2×C411yescharacteristic
77C2×C42×C43—21no—
78C2×C42×C43C2311yescharacteristic
79C4⋊C8×C43—21no—
80C4⋊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×C43M1612yescomplemented
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#10621898—21no—
98#10621898—21no—
99C2×D172C22⋊C411yescharacteristic
100C2×C4×D43—21no—
101C2×C4×D43—21no—
102C2×C4×D43—21no—
103C2×Dic86C22⋊C411yescharacteristic
104C2×C8×C43—22no—
105C2×C8×C43—22no—
106C2×C8×C43—41no—
107C2×C8×C43—41no—
108C2×C8×C43—42no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—41no—
112C4⋊C4×C43—41no—
113C42×C43—41no—
114C42×C43—41no—
115C42×C43C2×D411yescharacteristic
116C42×C43C2×D411yescharacteristic
117C42×C43C2×D411yescharacteristic
118C42×C43#4111yescharacteristic
119C22⋊Dic43—21no—
120#10621885—24no—
121#10621884—24no—
122(C2×D43)⋊C4—21no—
123(C2×D43)⋊C4—21no—
124C4⋊Dic43C22⋊C411yescharacteristic
125C4⋊Dic43C22⋊C411yescharacteristic
126Dic43⋊C4—21no—
127Dic43⋊C4—21no—
128C4×Dic43—21no—
129C4×Dic43—21no—
130C4×Dic43—21no—
131#10621877—21no—
132#10621877—21no—
133#10621877—21no—
134#10621877M1612yescomplemented
135C2×C43⋊C8—21no—
136C2×C43⋊C8—21no—
137C2×C43⋊C8—21no—
138C2×C43⋊C8—21no—
139C2×C43⋊C8—41no—
140#10621872—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×C43C2×M1611yescharacteristic
162C2×C4×C43C2×M1611yescharacteristic
163C2×C4×C43#13111yescharacteristic
164C2×C4×C43#13111yescharacteristic
165C22⋊D43—41no—
166C22⋊D43—41no—
167C2×Dic43—21no—
168C2×Dic43—21no—
169C2×Dic43—21no—
170D172—21no—
171D172—21no—
172C4×D43—41no—
173C4×D43—41no—
174C4×D43—41no—
175C4×D43—41no—
176C4×D43—81no—
177Dic86—21no—
178Dic86—21no—
179C8×C43—42no—
180C8×C43—42no—
181C43⋊C8—22no—
182C43⋊C8—41no—
183C43⋊C8—41no—
184C43⋊C8—41no—
185C43⋊C8—81no—
186#8955—431nomaximal, Sylow
187C22×C43—21no—
188C22×C43—21no—
189C22×C43#38611yescharacteristic
190C22×C43#43511yescharacteristic
191C22×C43#43611yescharacteristic
192C2×D43—41no—
193C2×D43—41no—
194C2×D43—41no—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—42no—
199C4×C43—81no—
200C4×C43#40711yescharacteristic
201C4×C43#40811yescharacteristic
202C4×C43#43511yescharacteristic
203C4×C43#43611yescharacteristic
204C4×C43#45511yescharacteristic
205C4×C43#45611yescharacteristic
206Dic43—41no—
207Dic43—41no—
208Dic43—41no—
209#2989—431no—
210C4×#137—431no—
211#1984D4311yescharacteristic, complemented
212#1479—431no—
213#1476—431no—
214#1283—431no—
215#1278—431no—
216C2×C43—21no—
217C2×C43—21no—
218C2×C43#187011yescharacteristic
219C2×C43#188111yescharacteristic
220C2×C43#188211yescharacteristic
221D43—81no—
222C2×#137—431no—
223C4×#41—431no—
224C2×C4×Q8C2×D4311yescharacteristic
225#446—861no—
226#441—861no—
227#440—861no—
228C4×Q16—861no—
229C4×SD16—861no—
230#436—861no—
231#435—862no—
232#432—861no—
233#431—431no—
234#431—431no—
235#428—431no—
236#423—861no—
237C2×C4⋊C8C2×D4311yescharacteristic
238#419—431no—
239#417—431no—
240C4×M16—431no—
241C2×C4×C8C2×D4311yescharacteristic
242#336—22no—
243Q8⋊C8—861no—
244Q8⋊C8—861no—
245Q8⋊C8—861no—
246D4⋊C8—861no—
247C43#895511yescharacteristic, complemented, Sylow
248C2×#41—431no—
249C22×Q8C4×D4311yescharacteristic
250#137—862no—
251#137—862no—
252C2×Q16—861no—
253C2×SD16—861no—
254C2×M16—431no—
255C2×M16—431no—
256C2×M16—862no—
257C22×C8—21no—
258C22×C8C22⋊D4312yes—
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—21no—
280C4⋊C8—431no—
281C4⋊C8—431no—
282C4⋊C8—862no—
283C4⋊C8—861no—
284#103—861no—
285#103—861no—
286#103—861no—
287#102—861no—
288C22⋊C8—862no—
289C22⋊C8—861no—
290C22⋊C8—861no—
291#97—862no—
292#97—861no—
293C4×C8—21no—
294C4×C8—21no—
295C4×C8—861no—
296C4×C8—861no—
297C4×C8—861no—
298#41—861no—
299#41—861no—
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×Q8#1062187212yescomplemented
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×C4#1062189811yescharacteristic
318C22×C4C2×C22⋊D4311yescharacteristic
319Q16—864no—
320SD16—864no—
321M16—432no—
322M16—861no—
323M16—861no—
324M16—861no—
325M16—3442no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—42no—
331C2×C8—861no—
332C2×C8—861no—
333C2×C8—861no—
334C2×C8—861no—
335C2×C8—1721no—
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—
352C42D4×D4311yescharacteristic
353C42D4×D4311yescharacteristic
354C42D4×D4311yescharacteristic
355C42#1062190011yescharacteristic
356C23—861no—
357C23C4×C22⋊D4311yescharacteristic
358Q8—22no—
359Q8—22no—
360Q8—41no—
361Q8—41no—
362Q8—861no—
363Q8—861no—
364D4—861no—
365D4—861no—
366D4—1721no—
367D4—1721no—
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—861no—
378C2×C4—861no—
379C2×C4—3441no—
380C2×C4—1721no—
381C2×C4—1721no—
382C2×C4—1721no—
383C2×C4—1721no—
384C2×C4C22⋊C4×D4311yescharacteristic
385C2×C4(C22⋊D43)⋊C411yescharacteristic
386C2×C4#1306329311yescharacteristic
387C2×C4#1306329611yescharacteristic
388C2×C4#1306329811yescharacteristic
389C2×C4#1306330711yescharacteristic
390C2×C4M16×D4311yescharacteristic
391C2×C4C2×#1062187211yescharacteristic
392C2×C4#1306333111yescharacteristic
393C2×C4#1306333311yescharacteristic
394C8—42no—
395C8—42no—
396C8—862no—
397C8—3441no—
398C8—1721no—
399C8—1721no—
400C8—1721no—
401C22—21no—
402C22—21no—
403C22—1721no—
404C22—1721no—
405C22—1721no—
406C22#1458277511yescharacteristic
407C22#1458297011yescharacteristic
408C22#1458297511yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—42no—
413C4—81no—
414C4—1721no—
415C4—1721no—
416C4—1721no—
417C4#1458286111yescharacteristic
418C4#1458286411yescharacteristic
419C4#1458296711yescharacteristic
420C4#1458297411yescharacteristic
421C4#1458307611yescharacteristic
422C4#1458308111yescharacteristic
423C2—21no—
424C2—21no—
425C2—3441no—
426C2#1913488911yescharacteristic
427C2#1913496011yescharacteristic
428C2#1913496711yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1984C2
socleC22×C43#386
prime radicalC2×#10621898C2×C4
cosocleC2×C42×C43C23
hypercenter#1984D43
hypocenterC43#8955
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1984

Complements

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

NH ≅ G/Ntype
3. #19132990C2semidirect
5. #19132445C2semidirect
6. #19132432C2semidirect
7. C43×#1984C2semidirect
88. C2×Q8×C43M16semidirect
134. #10621877M16semidirect
211. #1984D43semidirect
247. C43#8955semidirect
308. C2×Q8#10621872semidirect

Maximal subgroups

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

subgroupindex
#191437132
C4×#130633562
#191329902
#191329782
#191324452
#191324322
C43×#19842
#895543