Finite Group Databasebeta

← #25082095

Subgroups — #25082095

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#19145743C211yesmaximal, characteristic, complemented
2#19144411C211yesmaximal, characteristic
3#19144377C211yesmaximal, characteristic
4#19143704C211yesmaximal, characteristic
5#19134052C212yesmaximal, complemented
6#19134045C212yesmaximal, complemented
7#19133998C212yesmaximal, complemented
8#19133993C212yesmaximal, complemented
9#19133371C211yesmaximal, characteristic, complemented
10C2×#14582647C211yesmaximal, characteristic, complemented
11C43×#1550C211yesmaximal, characteristic, complemented
12C2×#13063325C2211yescharacteristic
13C4×#10621898C2211yescharacteristic
14#14583302C2212yes—
15#14583249C2212yes—
16#14583232—22no—
17#14583203—21no—
18#14583196—21no—
19#14583195C2212yes—
20#14583194—21no—
21#14583194—21no—
22#14583191C2211yescharacteristic
23#14583190C2212yes—
24#14583186C2211yescharacteristic
25#14583185—21no—
26#14583181C2211yescharacteristic
27#14583180—21no—
28#14583176C2211yescharacteristic
29#14583023C2212yes—
30#14582964C2212yes—
31C8×C22⋊D43—22no—
32#14582952C2211yescharacteristic
33#14582951—21no—
34#14582941—21no—
35#14582935—21no—
36C2×C4⋊(C43⋊C8)C2211yescharacteristic
37C4⋊C8×D43—21no—
38#14582901—21no—
39#14582893—21no—
40#14582651C2212yes—
41#14582651C2212yes—
42#14582647C2212yes—
43#14582647C2212yes—
44C43×#533C2211yescharacteristic
45C43×#423C2211yescharacteristic
46C2×C4⋊C8×C43C2211yescharacteristic
47C43×#333C2212yes—
48C43×#332C2212yes—
49C2×#10621898D411yescharacteristic
50C22×Dic86—21no—
51C22×C43⋊C8—21no—
52C2×C8×D43—22no—
53#13063325—21no—
54#13063325—21no—
55#13063325—21no—
56#13063325C2312yes—
57C4×Dic86D411yescharacteristic
58C4×Dic86C2311yescharacteristic
59C4×D172D411yescharacteristic
60C4×D172C2311yescharacteristic
61C4×C22⋊D43—21no—
62C4×C22⋊D43—21no—
63#13063284D411yescharacteristic
64#13063282—21no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—21no—
67C42×D43—21no—
68#13063259—22no—
69#13063258—21no—
70#13063258—21no—
71#13063258—22no—
72#13063258—22no—
73#13063257—22no—
74#13063256—21no—
75#13063256—21no—
76C4⋊(C43⋊C8)—21no—
77C4⋊(C43⋊C8)D411yescharacteristic
78C4⋊(C43⋊C8)D411yescharacteristic
79C4⋊(C43⋊C8)C2311yescharacteristic
80C4⋊(C43⋊C8)C2311yescharacteristic
81Dic43⋊C8—22no—
82#13063250—22no—
83#13063249—22no—
84#13063249—22no—
85#13063248—21no—
86#13063248—21no—
87#13063247—22no—
88#13063245—21no—
89#13063245—21no—
90C22⋊(C43⋊C8)D412yes—
91(C2×D43)⋊C8—22no—
92C4×C43⋊C8C2312yes—
93C8×Dic43—22no—
94C2×M16×C43—21no—
95C22×C8×C43—21no—
96C4⋊Q8×C43C2311yescharacteristic
97C4⋊Q8×C43C2311yescharacteristic
98#125×C43—21no—
99C22⋊Q8×C43—21no—
100C22⋊Q8×C43—21no—
101C4×Q8×C43—21no—
102C4×Q8×C43—21no—
103#117×C43—21no—
104C2×C42×C43C2311yescharacteristic
105C4⋊C8×C43—21no—
106C4⋊C8×C43—21no—
107C4⋊C8×C43C2312yes—
108C4⋊C8×C43C2312yes—
109C2×Q8×C43—21no—
110C2×Q8×C43—21no—
111C22×C4×C43C2×D411yescharacteristic
112C22×C4×C43C2×D411yescharacteristic
113C22×C4×C43#4111yescharacteristic
114C2×C22⋊D43—21no—
115C22×Dic43—41no—
116#10621898—22no—
117#10621898Q1614yes—
118C2×D172C2×D411yescharacteristic
119C2×C4×D43—21no—
120C2×C4×D43—21no—
121C2×C4×D43—21no—
122C2×Dic86—22no—
123C2×Dic86—41no—
124C2×Dic86—82no—
125C2×Dic86C2×D411yescharacteristic
126M16×C43—42no—
127C2×C8×C43—22no—
128C2×C8×C43—22no—
129C2×C8×C43—81no—
130C4⋊C4×C43—21no—
131C4⋊C4×C43—21no—
132C4⋊C4×C43—21no—
133C4⋊C4×C43—21no—
134C4⋊C4×C43—41no—
135C4⋊C4×C43—41no—
136C22⋊C4×C43—41no—
137C42×C43—41no—
138C42×C43C2×D411yescharacteristic
139C42×C43C2×D411yescharacteristic
140C42×C43#4111yescharacteristic
141C42×C43C2411yescharacteristic
142C22⋊Dic43—21no—
143(C2×D43)⋊C4—21no—
144(C2×D43)⋊C4—21no—
145C4⋊Dic43—22no—
146C4⋊Dic43—22no—
147C4⋊Dic43—41no—
148C4⋊Dic43—41no—
149C4⋊Dic43C2×D411yescharacteristic
150C4⋊Dic43C2×D411yescharacteristic
151Dic43⋊C4—21no—
152Dic43⋊C4—21no—
153C4×Dic43—21no—
154C4×Dic43—21no—
155C4×Dic43—21no—
156C2×C43⋊C8—21no—
157C2×C43⋊C8—21no—
158C2×C43⋊C8—42no—
159C2×C43⋊C8C2×D412yes—
160C2×C43⋊C8C2×D412yes—
161C8×D43—82no—
162C23×C43#12111yescharacteristic
163C22×D43—21no—
164Q8×C43—41no—
165Q8×C43—41no—
166Q8×C43—81no—
167C2×C4×C43—21no—
168C2×C4×C43—21no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—41no—
172C2×C4×C43#12111yescharacteristic
173C2×C4×C43#12111yescharacteristic
174C2×C4×C43#12111yescharacteristic
175C2×C4×C43C2×Q1612yes—
176C2×C4×C43#13512yes—
177C2×C4×C43C22×D411yescharacteristic
178C2×C4×C43C22×D411yescharacteristic
179C2×C4×C43C2×#4111yescharacteristic
180C22⋊D43—24no—
181C2×Dic43—21no—
182C2×Dic43—21no—
183C2×Dic43—21no—
184C2×Dic43—42no—
185C2×Dic43—82no—
186D172—21no—
187D172C2×Q1612yes—
188C4×D43—24no—
189C4×D43—41no—
190C4×D43—41no—
191C4×D43—81no—
192Dic86—21no—
193Dic86—82no—
194Dic86—82no—
195Dic86C2×Q1612yes—
196C8×C43—42no—
197C8×C43—42no—
198C43⋊C8—22no—
199C43⋊C8—22no—
200C43⋊C8—41no—
201C43⋊C8—41no—
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—81no—
215C4×C43#46712yes—
216C4×C43C22×Q1611yescharacteristic
217C4×C43C2×#13511yescharacteristic
218C4×C43#57711yescharacteristic
219C4×C43#57811yescharacteristic
220Dic43—22no—
221Dic43—41no—
222Dic43—41no—
223Dic43—82no—
224#3230—431no—
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#1550D4311yescharacteristic, complemented
234C2×#333—431no—
235C2×C43—22no—
236C2×C43#304611yescharacteristic
237C2×C43C2×#46711yescharacteristic
238C2×C43#306811yescharacteristic
239D43—42no—
240#533C2×D4311yescharacteristic
241C2×C4⋊Q8—431no—
242C4×#41—431no—
243#500—432no—
244#487—432no—
245#484—862no—
246#479—861no—
247#478—861no—
248#477—431no—
249#477—432no—
250#477—861no—
251#477—861no—
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—431no—
262#431—861no—
263#428—861no—
264#427—861no—
265#423C2×D4311yescharacteristic
266C2×C4⋊C8—431no—
267C2×C4⋊C8—861no—
268C2×C4⋊C8C2×D4311yescharacteristic
269#417—861no—
270#416—861no—
271#335—432no—
272#335—432no—
273#333—432no—
274#333—432no—
275#333C2×D4312yes—
276#332C2×D4312yes—
277C43#1941711yescharacteristic, complemented, Sylow
278C2×#41—431no—
279C22×Q8—861no—
280C2×M16—21no—
281C22×C8—21no—
282C22×C8—862no—
283C22×C8—861no—
284C4⋊Q8—432no—
285C4⋊Q8—861no—
286C4⋊Q8—861no—
287C4⋊Q8—861no—
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—861no—
305C2×C4⋊C4—861no—
306C2×C42—861no—
307C2×C42C22×D4311yescharacteristic
308#107—861no—
309#107—861no—
310#107—862no—
311#107—862no—
312#107—862no—
313#106—861no—
314#106—861no—
315#106—862no—
316C4⋊C8—21no—
317C4⋊C8—21no—
318C4⋊C8—431no—
319C4⋊C8—431no—
320C4⋊C8—431no—
321C4⋊C8—431no—
322C4⋊C8—862no—
323C4⋊C8—861no—
324C4⋊C8C22×D4312yes—
325C4⋊C8C22×D4312yes—
326#103—861no—
327#103—861no—
328#103—862no—
329#103—862no—
330#103—862no—
331#102—861no—
332#102—861no—
333#102—862no—
334C22⋊C8—432no—
335C22⋊C8—862no—
336C4×C8—432no—
337C4×C8—862no—
338#41—434no—
339#41—862no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—431no—
343C2×Q8—862no—
344C2×Q8—3442no—
345C2×Q8—1721no—
346C2×D4—431no—
347C2×D4—861no—
348C22×C4—861no—
349C22×C4—861no—
350C22×C4—861no—
351C22×C4—1721no—
352C22×C4#1062189811yescharacteristic
353C22×C4D4×D4311yescharacteristic
354C22×C4D4×D4311yescharacteristic
355M16—42no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—81no—
359C2×C8—432no—
360C2×C8—432no—
361C2×C8—861no—
362C2×C8—861no—
363C2×C8—3442no—
364C2×C8—1722no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—431no—
372C4⋊C4—431no—
373C4⋊C4—861no—
374C4⋊C4—861no—
375C4⋊C4—862no—
376C4⋊C4—862no—
377C4⋊C4—1721no—
378C4⋊C4—1721no—
379C22⋊C4—41no—
380C22⋊C4—861no—
381C22⋊C4—861no—
382C22⋊C4—861no—
383C42—41no—
384C42—861no—
385C42—861no—
386C42—861no—
387C42#1062189811yescharacteristic
388C42D4×D4311yescharacteristic
389C42D4×D4311yescharacteristic
390C42C23×D4311yescharacteristic
391C23—861no—
392C23#1306329811yescharacteristic
393Q8—41no—
394Q8—41no—
395Q8—81no—
396Q8—432no—
397Q8—861no—
398Q8—3442no—
399Q8—3442no—
400D4—432no—
401D4—864no—
402D4—861no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—861no—
409C2×C4—864no—
410C2×C4—861no—
411C2×C4—861no—
412C2×C4—3441no—
413C2×C4—3442no—
414C2×C4—1722no—
415C2×C4—1721no—
416C2×C4—1721no—
417C2×C4#1306329811yescharacteristic
418C2×C4#1306329811yescharacteristic
419C2×C4#1306329811yescharacteristic
420C2×C4Q16×D4312yes—
421C2×C4#1306334612yes—
422C2×C4C2×D4×D4311yescharacteristic
423C2×C4C2×D4×D4311yescharacteristic
424C2×C4C2×#1062189811yescharacteristic
425C8—42no—
426C8—42no—
427C8—862no—
428C8—862no—
429C8—1721no—
430C8—1721no—
431C22—21no—
432C22—21no—
433C22—862no—
434C22—1721no—
435C22—1721no—
436C22#1458313912yes—
437C22C2×#1306329811yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—81no—
442C4—81no—
443C4—862no—
444C4—3442no—
445C4—1721no—
446C4—1721no—
447C4#1458313912yes—
448C4C2×Q16×D4311yescharacteristic
449C4C2×#1306334611yescharacteristic
450C4#1458370911yescharacteristic
451C4#1458371511yescharacteristic
452C2—22no—
453C2—1722no—
454C2#1914414411yescharacteristic
455C2C2×#1458313911yescharacteristic
456C2#1914432611yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1550C2
socleC22×C43C2×#121
prime radicalC2×#10621898D4
hypercenter#1550D43
hypocenterC43#19417
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1550

Complements

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

NH ≅ G/Ntype
1. #19145743C2semidirect
5. #19134052C2semidirect
6. #19134045C2semidirect
7. #19133998C2semidirect
8. #19133993C2semidirect
9. #19133371C2semidirect
10. C2×#14582647C2semidirect
11. C43×#1550C2semidirect
233. #1550D43semidirect
277. C43#19417semidirect

Maximal subgroups

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

subgroupindex
#191457432
#191444112
#191443772
#191437042
#191340522
#191340452
#191339982
#191339932
#191333712
C2×#145826472
C43×#15502
#1941743