Finite Group Databasebeta

← #25082092

Subgroups — #25082092

Order 11008.

608 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144404C211yesmaximal, characteristic
2#19144377C211yesmaximal, characteristic
3#19143703C211yesmaximal, characteristic
4#19134050C212yesmaximal, complemented
5#19134043C212yesmaximal, complemented
6#19133996C212yesmaximal, complemented
7#19133991C212yesmaximal, complemented
8#19133370C211yesmaximal, characteristic, complemented
9#19133285C211yesmaximal, characteristic, complemented
10C2×#14582648C211yesmaximal, characteristic, complemented
11C43×#3230C211yesmaximal, characteristic, complemented
12C4×#10621898C2211yescharacteristic
13#14583203—21no—
14#14583196—21no—
15#14583191C2211yescharacteristic
16#14583191C2212yes—
17#14583186C2211yescharacteristic
18#14583186C2212yes—
19#14583181—21no—
20#14583181C2211yescharacteristic
21#14583176—21no—
22#14583176C2211yescharacteristic
23C8×Dic86C2212yes—
24C8×D172C2212yes—
25(C22⋊D43)⋊C8—22no—
26#14582951—21no—
27#14582939—21no—
28#14582935—21no—
29#14582923C2211yescharacteristic
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C4⋊C8×D43—21no—
33#14582898—21no—
34#14582893—21no—
35#14582652C2212yes—
36#14582652C2212yes—
37#14582648C2212yes—
38#14582648C2212yes—
39#14582648C2212yes—
40#14582645C2212yes—
41C43×#533C2211yescharacteristic
42C2×C4⋊Q8×C43C2211yescharacteristic
43C43×#500C2212yes—
44C43×#487C2212yes—
45C43×#484—22no—
46C43×#477—21no—
47C43×#477—21no—
48C43×#431C2211yescharacteristic
49C2×#10621898D411yescharacteristic
50C2×#10621877—21no—
51C22×C43⋊C8—21no—
52C22×C43⋊C8—21no—
53C2×C8×D43—22no—
54C4×Dic86D411yescharacteristic
55C4×Dic86C2311yescharacteristic
56C4×D172D411yescharacteristic
57C4×D172C2311yescharacteristic
58C4×C22⋊D43—21no—
59C4×C22⋊D43—21no—
60#13063284D411yescharacteristic
61#13063282—21no—
62C42×D43—21no—
63#13063258—22no—
64#13063258—21no—
65#13063258—21no—
66#13063256—22no—
67#13063256—21no—
68#13063256—21no—
69C4⋊(C43⋊C8)—21no—
70C4⋊(C43⋊C8)—21no—
71C4⋊(C43⋊C8)—21no—
72C4⋊(C43⋊C8)C2312yes—
73C4⋊(C43⋊C8)C2312yes—
74C4⋊(C43⋊C8)C2311yescharacteristic
75C4⋊(C43⋊C8)C2311yescharacteristic
76Dic43⋊C8—22no—
77#13063248—21no—
78#13063248—21no—
79#13063248—22no—
80#13063245—21no—
81#13063245—21no—
82#13063245—22no—
83(C2×D43)⋊C8—22no—
84C8×Dic43—22no—
85C22×Q8×C43—21no—
86C4⋊Q8×C43—21no—
87C4⋊Q8×C43—21no—
88C4⋊Q8×C43—21no—
89C4⋊Q8×C43C2311yescharacteristic
90C4⋊Q8×C43C2312yes—
91C4⋊Q8×C43C2311yescharacteristic
92#125×C43—21no—
93C22⋊Q8×C43—21no—
94C22⋊Q8×C43—21no—
95C4×Q8×C43—21no—
96C4×Q8×C43—21no—
97#117×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C42×C43C2311yescharacteristic
101#107×C43—22no—
102#107×C43—22no—
103C4⋊C8×C43D411yescharacteristic
104C4⋊C8×C43D411yescharacteristic
105#103×C43—22no—
106#103×C43—22no—
107C22⋊C8×C43D412yes—
108C4×C8×C43C2312yes—
109C2×Q8×C43—21no—
110C2×Q8×C43—21no—
111C2×Q8×C43—22no—
112C2×Q8×C43—41no—
113C2×Q8×C43—82no—
114C22×C4×C43—41no—
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43#4111yescharacteristic
118C2×C22⋊D43—21no—
119#10621898—22no—
120#10621898Q1614yes—
121C2×D172C2×D411yescharacteristic
122C2×C4×D43—21no—
123C2×C4×D43—21no—
124C2×C4×D43—21no—
125C2×Dic86C2×D411yescharacteristic
126C2×C8×C43C2×D412yes—
127C2×C8×C43C2×D412yes—
128C4⋊C4×C43—22no—
129C4⋊C4×C43—21no—
130C4⋊C4×C43—22no—
131C4⋊C4×C43—21no—
132C4⋊C4×C43—21no—
133C4⋊C4×C43—21no—
134C4⋊C4×C43—41no—
135C4⋊C4×C43—41no—
136C4⋊C4×C43—41no—
137C4⋊C4×C43—41no—
138C22⋊C4×C43—41no—
139C42×C43—41no—
140C42×C43C2×D411yescharacteristic
141C42×C43C2×D411yescharacteristic
142C42×C43#4111yescharacteristic
143C42×C43C2411yescharacteristic
144C22⋊Dic43—21no—
145(C2×D43)⋊C4—21no—
146(C2×D43)⋊C4—21no—
147C4⋊Dic43C2×D411yescharacteristic
148C4⋊Dic43C2×D411yescharacteristic
149Dic43⋊C4—21no—
150Dic43⋊C4—21no—
151C4×Dic43—21no—
152C4×Dic43—21no—
153C4×Dic43—21no—
154#10621877—42no—
155C2×C43⋊C8—22no—
156C2×C43⋊C8—21no—
157C2×C43⋊C8—22no—
158C2×C43⋊C8—21no—
159C2×C43⋊C8—42no—
160C2×C43⋊C8—81no—
161C8×D43—82no—
162C23×C43#12111yescharacteristic
163C22×D43—21no—
164Q8×C43—41no—
165Q8×C43—41no—
166Q8×C43—81no—
167Q8×C43—82no—
168Q8×C43—82no—
169C2×C4×C43—21no—
170C2×C4×C43—21no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—42no—
175C2×C4×C43—82no—
176C2×C4×C43#12111yescharacteristic
177C2×C4×C43#12111yescharacteristic
178C2×C4×C43#12111yescharacteristic
179C2×C4×C43C2×Q1612yes—
180C2×C4×C43#13512yes—
181C2×C4×C43C22×D411yescharacteristic
182C2×C4×C43C22×D411yescharacteristic
183C2×C4×C43C2×#4111yescharacteristic
184C22⋊D43—24no—
185C2×Dic43—21no—
186C2×Dic43—21no—
187C2×Dic43—21no—
188D172—21no—
189D172C2×Q1612yes—
190C4×D43—24no—
191C4×D43—41no—
192C4×D43—41no—
193C4×D43—81no—
194Dic86—21no—
195Dic86C2×Q1612yes—
196C8×C43—22no—
197C8×C43—22no—
198C43⋊C8—41no—
199C43⋊C8—41no—
200C43⋊C8—42no—
201C43⋊C8—42no—
202#19417—431nomaximal, Sylow
203C22×C43—21no—
204C22×C43—21no—
205C22×C43#46712yes—
206C22×C43C2×#12111yescharacteristic
207C2×D43—22no—
208C2×D43—41no—
209C2×D43—41no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—81no—
214C4×C43—82no—
215C4×C43—81no—
216C4×C43#46712yes—
217C4×C43C22×Q1611yescharacteristic
218C4×C43C2×#13511yescharacteristic
219C4×C43#57711yescharacteristic
220C4×C43#57811yescharacteristic
221Dic43—22no—
222Dic43—41no—
223Dic43—41no—
224#3230D4311yescharacteristic, complemented
225#3079—431no—
226#3076—431no—
227#2988—431no—
228#1684—432no—
229#1683—432no—
230#1676—432no—
231#1675—432no—
232#1571—431no—
233#1550—431no—
234C2×#333—431no—
235C2×C43—22no—
236C2×C43#304611yescharacteristic
237C2×C43C2×#46711yescharacteristic
238C2×C43#306811yescharacteristic
239D43—42no—
240#533C2×D4311yescharacteristic
241C2×C4⋊Q8C2×D4311yescharacteristic
242C4×#41—431no—
243#500C2×D4312yes—
244#487C2×D4312yes—
245#484—22no—
246#479—861no—
247#478—861no—
248#477—21no—
249#477—21no—
250#477—431no—
251#477—432no—
252#476—431no—
253#476—432no—
254#475—431no—
255#475—861no—
256#474—431no—
257#474—861no—
258C8×Q8—432no—
259C8×D4—432no—
260C8×D4—862no—
261#431—861no—
262#431C2×D4311yescharacteristic
263#428—861no—
264#427—861no—
265#423—431no—
266C2×C4⋊C8—431no—
267C2×C4⋊C8—431no—
268C2×C4⋊C8—861no—
269#417—861no—
270#416—861no—
271#335—432no—
272#335—432no—
273#333—432no—
274#333—432no—
275#333—432no—
276#332—432no—
277C43#1941711yescharacteristic, complemented, Sylow
278C2×#41—431no—
279C22×Q8—21no—
280C2×M16—861no—
281C22×C8—861no—
282C22×C8—861no—
283C22×C8—862no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8C22×D4312yes—
288C4⋊Q8C22×D4311yescharacteristic
289C4⋊Q8C22×D4311yescharacteristic
290#125—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8—431no—
296C4×Q8—431no—
297C4×D4—431no—
298C4×D4—431no—
299C4×D4—861no—
300C4×D4—861no—
301#117—21no—
302#117—431no—
303#117—861no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C42—861no—
307C2×C42C22×D4311yescharacteristic
308#107—22no—
309#107—22no—
310#107—861no—
311#107—861no—
312#107—862no—
313#106—861no—
314#106—861no—
315#106—862no—
316C4⋊C8—432no—
317C4⋊C8—432no—
318C4⋊C8—431no—
319C4⋊C8—431no—
320C4⋊C8—862no—
321C4⋊C8—861no—
322C4⋊C8—861no—
323C4⋊C8—861no—
324C4⋊C8C22⋊D4311yescharacteristic
325C4⋊C8C22⋊D4311yescharacteristic
326#103—22no—
327#103—22no—
328#103—861no—
329#103—861no—
330#103—862no—
331#102—861no—
332#102—861no—
333#102—862no—
334C22⋊C8—862no—
335C22⋊C8C22⋊D4312yes—
336C4×C8—862no—
337C4×C8C22×D4312yes—
338#41—434no—
339#41—862no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—22no—
343C2×Q8—41no—
344C2×Q8—82no—
345C2×Q8—431no—
346C2×D4—431no—
347C2×D4—861no—
348C22×C4—41no—
349C22×C4—861no—
350C22×C4—861no—
351C22×C4—861no—
352C22×C4D4×D4311yescharacteristic
353C22×C4#1062190011yescharacteristic
354C22×C4C2×C22⋊D4311yescharacteristic
355M16—1722no—
356C2×C8—861no—
357C2×C8—862no—
358C2×C8—861no—
359C2×C8—862no—
360C2×C8—3442no—
361C2×C8—3441no—
362C2×C8—1722no—
363C2×C8C2×C22⋊D4312yes—
364C2×C8C2×C22⋊D4312yes—
365C4⋊C4—22no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—431no—
376C4⋊C4—431no—
377C4⋊C4—861no—
378C4⋊C4—861no—
379C22⋊C4—41no—
380C22⋊C4—861no—
381C22⋊C4—861no—
382C22⋊C4—861no—
383C42—41no—
384C42—861no—
385C42—861no—
386C42—861no—
387C42D4×D4311yescharacteristic
388C42#1062190011yescharacteristic
389C42C2×C22⋊D4311yescharacteristic
390C42C23×D4311yescharacteristic
391C23—861no—
392C23#1306329611yescharacteristic
393Q8—41no—
394Q8—41no—
395Q8—82no—
396Q8—81no—
397Q8—82no—
398Q8—432no—
399Q8—861no—
400D4—432no—
401D4—864no—
402D4—861no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—82no—
410C2×C4—861no—
411C2×C4—864no—
412C2×C4—861no—
413C2×C4—861no—
414C2×C4—3441no—
415C2×C4—1721no—
416C2×C4—1721no—
417C2×C4#1306329611yescharacteristic
418C2×C4#1306329611yescharacteristic
419C2×C4#1306329611yescharacteristic
420C2×C4Q16×D4312yes—
421C2×C4#1306334812yes—
422C2×C4C2×D4×D4311yescharacteristic
423C2×C4C22×C22⋊D4311yescharacteristic
424C2×C4C2×#1062190011yescharacteristic
425C8—22no—
426C8—22no—
427C8—1721no—
428C8—1721no—
429C8—1722no—
430C8—1722no—
431C22—21no—
432C22—21no—
433C22—862no—
434C22—1721no—
435C22—1721no—
436C22#1458313712yes—
437C22C2×#1306329611yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—82no—
442C4—81no—
443C4—81no—
444C4—862no—
445C4—1721no—
446C4—1721no—
447C4#1458313712yes—
448C4C2×Q16×D4311yescharacteristic
449C4C2×#1306334811yescharacteristic
450C4#1458370711yescharacteristic
451C4#1458371411yescharacteristic
452C2—22no—
453C2—1722no—
454C2#1914414111yescharacteristic
455C2C2×#1458313711yescharacteristic
456C2#1914431911yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3230C2
socleC22×C43C2×#121
prime radicalC2×#10621898D4
hypercenter#3230D43
hypocenterC43#19417
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
4. #19134050C2semidirect
5. #19134043C2semidirect
6. #19133996C2semidirect
7. #19133991C2semidirect
8. #19133370C2semidirect
9. #19133285C2semidirect
10. C2×#14582648C2semidirect
11. C43×#3230C2semidirect
224. #3230D43semidirect
277. C43#19417semidirect

Maximal subgroups

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

subgroupindex
#191444042
#191443772
#191437032
#191340502
#191340432
#191339962
#191339912
#191333702
#191332852
C2×#145826482
C43×#32302
#1941743