Finite Group Databasebeta

← #25155504

Subgroups — #25155504

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145135C211yesmaximal, characteristic, complemented
2#19144459C212yesmaximal
3#19143192C211yesmaximal, characteristic
4#19136105C212yesmaximal, complemented
5#19135944C212yesmaximal, complemented
6#19135381C211yesmaximal, characteristic, complemented
7#19134829C212yesmaximal
8#19134759C211yesmaximal, characteristic, complemented
9#19134656C211yesmaximal, characteristic
10#19134432C211yesmaximal, characteristic
11C43×#1945C211yesmaximal, characteristic, complemented
12C2×#13063331C2211yescharacteristic
13#14583527C2212yes—
14#14583379C2212yes—
15#14583306—22no—
16#14583303—21no—
17#14583300—21no—
18#14583207—22no—
19#14583200—22no—
20#14583190—22no—
21#14583185—22no—
22#14582942C2212yes—
23#14582942C2212yes—
24#14582941C2212yes—
25#14582938—22no—
26#14582936—21no—
27C2×#13063259C2211yescharacteristic
28C2×#13063259C2211yescharacteristic
29#107×D43—21no—
30C2×#13063257C2212yes—
31C2×#13063253C2211yescharacteristic
32#14582901C2212yes—
33#14582896C2211yescharacteristic
34#14582854C2211yescharacteristic
35#14582765C2212yes—
36#14582667C2212yes—
37#14582667C2212yes—
38#14582664C2211yescharacteristic
39#14582659C2211yescharacteristic
40C2×#108×C43C2211yescharacteristic
41C43×#427C2211yescharacteristic
42C43×#424C2212yes—
43C2×C4×C8×C43C2211yescharacteristic
44C43×#339C2212yes—
45C2×#10621898C2311yescharacteristic
46#13063331—22no—
47#13063331Q814yescomplemented
48C2×#10621877C2311yescharacteristic
49C2×#10621877C2311yescharacteristic
50C2×#10621872—21no—
51C2×C8×D43—21no—
52#13063325—22no—
53#13063324—22no—
54#13063317—22no—
55#13063316—22no—
56#13063302—42no—
57C4×Dic86—22no—
58C4×D172—22no—
59(C22⋊D43)⋊C4—42no—
60#13063284C2311yescharacteristic
61#13063283—22no—
62C2×C4⋊Dic43C2312yes—
63C2×C4⋊Dic43C2312yes—
64C4⋊C4×D43—22no—
65#13063259—21no—
66#13063259—21no—
67#13063259—21no—
68#13063259—21no—
69#13063259—22no—
70#13063258—22no—
71#13063258—22no—
72#13063257—22no—
73#13063257—22no—
74#13063257—22no—
75#13063256—22no—
76#13063256—22no—
77#13063253Q814yescomplemented
78#13063250—22no—
79#13063250D411yescharacteristic
80#13063250D411yescharacteristic
81#13063247—22no—
82#13063247D411yescharacteristic
83#13063247D411yescharacteristic
84#13063235—21no—
85C8×Dic43—21no—
86C43⋊#95—42no—
87C2×M16×C43C2312yes—
88C22×C8×C43C2311yescharacteristic
89C22×C8×C43C2311yescharacteristic
90#117×C43C2312yes—
91C2×C42×C43C2311yescharacteristic
92#108×C43—22no—
93#107×C43D411yescharacteristic
94#107×C43D411yescharacteristic
95#106×C43D412yes—
96C4⋊C8×C43—22no—
97C4⋊C8×C43—22no—
98C4×C8×C43—22no—
99C22×C4×C43—21no—
100C22×C4×C43C2411yescharacteristic
101C2×C22⋊D43—21no—
102C22×Dic43—22no—
103C22×Dic43—22no—
104#10621898—21no—
105#10621898—21no—
106#10621898C2×Q812yes—
107#10621898C2×Q812yes—
108C2×D172C2×D411yescharacteristic
109C2×C4×D43—21no—
110C2×C4×D43—42no—
111C2×Dic86—42no—
112C2×Dic86C2×D411yescharacteristic
113M16×C43—22no—
114M16×C43—22no—
115C2×C8×C43—21no—
116C2×C8×C43—21no—
117C2×C8×C43—22no—
118C2×C8×C43C2×D411yescharacteristic
119C2×C8×C43C2×D411yescharacteristic
120C2×C8×C43C2×D411yescharacteristic
121C2×C8×C43C2×D411yescharacteristic
122C2×C8×C43C2×Q812yes—
123C2×C8×C43#4112yes—
124C4⋊C4×C43C2×D412yes—
125C4⋊C4×C43C2×D412yes—
126C22⋊C4×C43—22no—
127C42×C43—22no—
128C42×C43—21no—
129C42×C43C2×Q812yes—
130C22⋊Dic43—21no—
131(C2×D43)⋊C4—42no—
132C4⋊Dic43—22no—
133C4⋊Dic43—22no—
134C4⋊Dic43—22no—
135C4⋊Dic43—22no—
136C4⋊Dic43—42no—
137C4⋊Dic43C2×D411yescharacteristic
138C4⋊Dic43C2×D411yescharacteristic
139Dic43⋊C4—42no—
140Dic43⋊C4—42no—
141Dic43⋊C4—42no—
142C4×Dic43—21no—
143C4×Dic43—42no—
144#10621877—21no—
145#10621877—21no—
146#10621877C2×Q812yes—
147#10621877C2×Q812yes—
148C2×C43⋊C8—21no—
149C2×C43⋊C8—21no—
150#10621872—24no—
151C8×D43—24no—
152C23×C43H(5,𝔽2)11yescharacteristic
153C22×D43—21no—
154C2×C4×C43—22no—
155C2×C4×C43—22no—
156C2×C4×C43—22no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43C22×D411yescharacteristic
160C2×C4×C43C22×D411yescharacteristic
161C2×C4×C43C22×Q811yescharacteristic
162C2×C4×C43C22×Q811yescharacteristic
163C2×C4×C43C2×#4111yescharacteristic
164C2×C4×C432−1+411yescharacteristic
165C22⋊D43—22no—
166C22⋊D43—22no—
167C2×Dic43—21no—
168C2×Dic43—21no—
169C2×Dic43—21no—
170C2×Dic43—42no—
171C2×Dic43—42no—
172C2×Dic43—82no—
173C2×Dic43—82no—
174D172—21no—
175D172C4⋊Q812yes—
176C4×D43—22no—
177C4×D43—22no—
178C4×D43—162no—
179Dic86—21no—
180Dic86—162no—
181Dic86C4⋊Q812yes—
182C8×C43—21no—
183C8×C43—21no—
184C8×C43—42no—
185C8×C43C22⋊Q812yes—
186C8×C43C22⋊Q812yes—
187C43⋊C8—22no—
188C43⋊C8—22no—
189#26082—431nomaximal, Sylow
190C22×C43—21no—
191C22×C43—21no—
192C22×C43#54411yescharacteristic
193C22×C43D4211yescharacteristic
194C22×C43#55411yescharacteristic
195C2×D43—22no—
196C2×D43—41no—
197C2×D43—41no—
198C4×C43—42no—
199C4×C43—42no—
200C4×C43—42no—
201C4×C43C2×C22⋊Q811yescharacteristic
202C4×C43C2×C4⋊Q811yescharacteristic
203C4×C43#54711yescharacteristic
204C4×C43D4×Q811yescharacteristic
205Dic43—22no—
206Dic43—41no—
207Dic43—41no—
208Dic43—82no—
209Dic43—82no—
210#3164—431no—
211#3084—432no—
212#2913—431no—
213#2090—432no—
214#2061—432no—
215#1952—431no—
216#1945D4311yescharacteristic, complemented
217#1860—432no—
218#1846—431no—
219#1816—431no—
220#1764—431no—
221C2×C43—21no—
222C2×C43—21no—
223C2×C43#244011yescharacteristic
224C2×C43#329011yescharacteristic
225C2×C43#329011yescharacteristic
226D43—42no—
227C2×#131—431no—
228#544—432no—
229#520—432no—
230#501—862no—
231#500—861no—
232#499—861no—
233#479—862no—
234#478—862no—
235#476—862no—
236#475—862no—
237C2×#108C2×D4311yescharacteristic
238#428—432no—
239#428—432no—
240#428—432no—
241#428—862no—
242#427—861no—
243#427C2×D4311yescharacteristic
244C2×#107—431no—
245C2×#107—431no—
246C2×#107—861no—
247C2×#106—432no—
248#424C2×D4312yes—
249C2×#104—431no—
250#417—432no—
251#416—431no—
252#405—431no—
253C2×C4×C8C2×D4311yescharacteristic
254#382—432no—
255#343—432no—
256#343—432no—
257#341—431no—
258#339—431no—
259#339C2×D4312yes—
260C43#2608211yescharacteristic, complemented, Sylow
261C2×#41—431no—
262#131—434no—
263#131—862no—
264C2×M16—431no—
265C2×M16—431no—
266C2×M16—861no—
267C2×M16C22×D4312yes—
268C22×C8—861no—
269C22×C8C22×D4311yescharacteristic
270C22×C8C22×D4311yescharacteristic
271C4⋊Q8—862no—
272C4⋊Q8—862no—
273#125—862no—
274#125—862no—
275C22⋊Q8—1722no—
276C4×Q8—862no—
277C4×D4—862no—
278C4×D4—1722no—
279#117—431no—
280#117—862no—
281#117C22×D4312yes—
282C2×C4⋊C4—432no—
283C2×C4⋊C4—432no—
284C2×C4⋊C4—862no—
285C2×C42C22×D4311yescharacteristic
286#108—22no—
287#107—862no—
288#107—861no—
289#107—861no—
290#107—861no—
291#107—861no—
292#107—862no—
293#107—862no—
294#107D17211yescharacteristic
295#107D17211yescharacteristic
296#106—862no—
297#106—862no—
298#106—862no—
299#106—862no—
300#106—862no—
301#106D17212yes—
302C4⋊C8—22no—
303C4⋊C8—22no—
304#104—434no—
305#103—431no—
306#103—431no—
307#103—862no—
308#102—431no—
309#102—431no—
310#102—862no—
311#97—861no—
312C4×C8—22no—
313C4×C8—861no—
314#95—1722no—
315#41—432no—
316#41—432no—
317#41—861no—
318#41—861no—
319C2×Q8—431no—
320C2×Q8—1722no—
321C2×D4—431no—
322C2×D4—861no—
323C22×C4—21no—
324C22×C4—861no—
325C22×C4—862no—
326C22×C4—862no—
327C22×C4—1722no—
328C22×C4C23×D4311yescharacteristic
329M16—22no—
330M16—22no—
331M16—432no—
332M16—432no—
333M16—861no—
334M16—861no—
335M16—864no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—22no—
339C2×C8—861no—
340C2×C8—861no—
341C2×C8—864no—
342C2×C8C2×D17211yescharacteristic
343C2×C8C2×D17211yescharacteristic
344C2×C8D4×D4311yescharacteristic
345C2×C8D4×D4311yescharacteristic
346C2×C8#1062190012yes—
347C2×C8Q8×D4312yes—
348C4⋊C4—431no—
349C4⋊C4—431no—
350C4⋊C4—862no—
351C4⋊C4—862no—
352C4⋊C4—862no—
353C4⋊C4—862no—
354C4⋊C4—1722no—
355C4⋊C4—1722no—
356C4⋊C4—1722no—
357C4⋊C4—1722no—
358C4⋊C4C2×D17212yes—
359C4⋊C4C2×D17212yes—
360C22⋊C4—22no—
361C22⋊C4—861no—
362C22⋊C4—1722no—
363C42—22no—
364C42—21no—
365C42—861no—
366C42—1722no—
367C42Q8×D4312yes—
368C23—861no—
369C23#1306337111yescharacteristic
370Q8—432no—
371Q8—861no—
372Q8—6882no—
373D4—432no—
374D4—862no—
375D4—862no—
376D4—861no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—861no—
383C2×C4—862no—
384C2×C4—862no—
385C2×C4—861no—
386C2×C4—861no—
387C2×C4—3442no—
388C2×C4—3442no—
389C2×C4—1722no—
390C2×C4—1722no—
391C2×C4—6882no—
392C2×C4C2×D4×D4311yescharacteristic
393C2×C4C22×D17211yescharacteristic
394C2×C4C2×Q8×D4311yescharacteristic
395C2×C4C2×Q8×D4311yescharacteristic
396C2×C4C2×#1062190011yescharacteristic
397C2×C4#1306337211yescharacteristic
398C8—21no—
399C8—21no—
400C8—42no—
401C8—862no—
402C8—862no—
403C8#1306330512yes—
404C8#1306330512yes—
405C22—21no—
406C22—21no—
407C22—862no—
408C22—1721no—
409C22—1721no—
410C22#1458352911yescharacteristic
411C22D4×D17211yescharacteristic
412C22#1458360711yescharacteristic
413C4—42no—
414C4—42no—
415C4—42no—
416C4—862no—
417C4—3442no—
418C4—3442no—
419C4—1721no—
420C4—1721no—
421C4C2×#1306330511yescharacteristic
422C4C4⋊Q8×D4311yescharacteristic
423C4#1458354911yescharacteristic
424C4Q8×D17211yescharacteristic
425C2—21no—
426C2—21no—
427C2—1722no—
428C2#1913829511yescharacteristic
429C2#1914638311yescharacteristic
430C2#1914638311yescharacteristic
subgroupG/H
centerC22D4×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1945C2
socleC22×C43D42
prime radicalC2×#10621898C23
hypercenter#1945D43
hypocenterC43#26082
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1945

Complements

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

NH ≅ G/Ntype
1. #19145135C2semidirect
4. #19136105C2semidirect
5. #19135944C2semidirect
6. #19135381C2semidirect
8. #19134759C2semidirect
11. C43×#1945C2semidirect
47. #13063331Q8semidirect
77. #13063253Q8semidirect
216. #1945D43semidirect
260. C43#26082semidirect

Maximal subgroups

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

subgroupindex
#191451352
#191444592
#191431922
#191361052
#191359442
#191353812
#191348292
#191347592
#191346562
#191344322
C43×#19452
#2608243