Finite Group Databasebeta

← #25084511

Subgroups — #25084511

Order 11008.

708 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145743C211yesmaximal, characteristic, complemented
2#19145716C211yesmaximal, characteristic
3#19145155C211yesmaximal, characteristic
4#19144989C211yesmaximal, characteristic
5C2×#14583251C211yesmaximal, characteristic, complemented
6#19134249C212yesmaximal, complemented
7#19134242C212yesmaximal, complemented
8#19134208C212yesmaximal, complemented
9#19134203C212yesmaximal, complemented
10M16×C43⋊C8C211yesmaximal, characteristic, complemented
11C43×#3139C211yesmaximal, characteristic, complemented
12#14583449C2211yescharacteristic
13C2×#13063325C2211yescharacteristic
14#14583302C2212yes—
15#14583302C2212yes—
16#14583295C2211yescharacteristic
17#14583273C2211yescharacteristic
18#14583259—22no—
19#14583251—22no—
20#14583251C2212yes—
21#14583251C2212yes—
22#14583250C2212yes—
23#14583249C2212yes—
24#14583249C2211yescharacteristic
25#14583247C2211yescharacteristic
26#14583247C2212yes—
27#14583246C2212yes—
28#14583232—22no—
29#14583212—22no—
30#14583194—22no—
31#14583176—22no—
32#14583130—22no—
33C4×#10621884—22no—
34#14582952C2211yescharacteristic
35#14582901—22no—
36C2×#13063248—22no—
37C2×C4×C43⋊C8C2211yescharacteristic
38#14582620C2212yes—
39C8×C43⋊C8C2212yes—
40C43×#533C2211yescharacteristic
41C2×C4⋊Q8×C43C2211yescharacteristic
42C43×#491—22no—
43C43×#487C2212yes—
44C43×#487C2212yes—
45C43×#419—22no—
46C4×M16×C43C2211yescharacteristic
47C2×#10621898—21no—
48C22×Dic86—21no—
49C2×#10621884—22no—
50C22×C43⋊C8D412yes—
51#13063325—21no—
52#13063325—21no—
53#13063325—21no—
54#13063325C2311yescharacteristic
55#13063325C2312yes—
56#13063322C2311yescharacteristic
57#13063313—21no—
58#13063299—21no—
59#13063299—21no—
60C4×D172—21no—
61C4×D172—21no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43—21no—
64#13063258—24no—
65#13063258—24no—
66#13063256—22no—
67C4⋊(C43⋊C8)D412yes—
68#13063250—24no—
69#13063249—22no—
70#13063249—24no—
71#13063248—24no—
72#13063248—24no—
73#13063247—24no—
74#13063245—22no—
75#13063245—24no—
76C22⋊(C43⋊C8)D412yes—
77C4×C43⋊C8D412yes—
78C4×C43⋊C8C2312yes—
79C4×C43⋊C8C2311yescharacteristic
80C4×C43⋊C8C2311yescharacteristic
81C22×Q8×C43—21no—
82C2×M16×C43D412yes—
83C4⋊Q8×C43—21no—
84C4⋊Q8×C43—21no—
85C4⋊Q8×C43—21no—
86C4⋊Q8×C43C2311yescharacteristic
87C4⋊Q8×C43C2312yes—
88C4⋊Q8×C43C2311yescharacteristic
89#125×C43—21no—
90C22⋊Q8×C43—21no—
91C22⋊Q8×C43—21no—
92C4×Q8×C43—21no—
93C4×Q8×C43—21no—
94#117×C43—21no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43—21no—
97C2×C42×C43C2311yescharacteristic
98#103×C43—24no—
99#103×C43—24no—
100#97×C43D412yes—
101C4×C8×C43C2312yes—
102C2×Q8×C43—22no—
103C2×Q8×C43—21no—
104C2×Q8×C43—21no—
105C2×Q8×C43—41no—
106C2×Q8×C43—44no—
107C22×C4×C43—41no—
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C2×C22⋊D43—41no—
112C22×Dic43—41no—
113#10621898—44no—
114C2×D172—21no—
115C2×D172—21no—
116C2×D172—21no—
117C2×C4×D43—41no—
118C2×Dic86—22no—
119C2×Dic86—21no—
120C2×Dic86—44no—
121C2×Dic86—41no—
122M16×C43—24no—
123C2×C8×C43C2×D414yes—
124C4⋊C4×C43—21no—
125C4⋊C4×C43—21no—
126C4⋊C4×C43—22no—
127C4⋊C4×C43—22no—
128C4⋊C4×C43—21no—
129C4⋊C4×C43—21no—
130C4⋊C4×C43—41no—
131C4⋊C4×C43—41no—
132C4⋊C4×C43—41no—
133C4⋊C4×C43—41no—
134C22⋊C4×C43—41no—
135C42×C43—41no—
136C42×C43C2×D411yescharacteristic
137C42×C43C2×D411yescharacteristic
138C42×C43C2×D411yescharacteristic
139C42×C43C2411yescharacteristic
140#10621884—44no—
141(C2×D43)⋊C4—41no—
142(C2×D43)⋊C4—41no—
143C4⋊Dic43—22no—
144C4⋊Dic43—21no—
145C4⋊Dic43—22no—
146C4⋊Dic43—21no—
147C4⋊Dic43—41no—
148C4⋊Dic43—41no—
149C2×C43⋊C8—42no—
150C2×C43⋊C8C2×D412yes—
151C2×C43⋊C8C2×D412yes—
152C2×C43⋊C8C2×D414yes—
153C23×C43#12711yescharacteristic
154C22×D43—41no—
155Q8×C43—44no—
156Q8×C43—42no—
157Q8×C43—42no—
158Q8×C43—82no—
159C2×C4×C43—22no—
160C2×C4×C43—22no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—42no—
164C2×C4×C43—82no—
165C2×C4×C43#12711yescharacteristic
166C2×C4×C43#12711yescharacteristic
167C2×C4×C43#12711yescharacteristic
168C2×C4×C43#13514yes—
169C2×C4×C43C22×D411yescharacteristic
170C2×C4×C43C22×D411yescharacteristic
171C2×C4×C43C22×D411yescharacteristic
172C22⋊D43—82no—
173C2×Dic43—42no—
174C2×Dic43—41no—
175C2×Dic43—82no—
176D172—42no—
177D172—42no—
178D172—42no—
179C4×D43—82no—
180Dic86—42no—
181Dic86—44no—
182Dic86—82no—
183C8×C43—24no—
184C43⋊C8—22no—
185C43⋊C8—22no—
186C43⋊C8—24no—
187#19628—431nomaximal, Sylow
188C22×C43—21no—
189C22×C43—21no—
190C22×C43#49512yes—
191C22×C43C2×#12711yescharacteristic
192C2×D43—81no—
193C2×D43—81no—
194C2×D43—81no—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—82no—
198C4×C43—81no—
199C4×C43—81no—
200C4×C43#49512yes—
201C4×C43C2×#13512yes—
202C4×C43#57512yes—
203C4×C43#57812yes—
204Dic43—81no—
205Dic43—82no—
206#3230—431no—
207#3226—431no—
208#3167—431no—
209#3141—431no—
210#3139D4311yescharacteristic, complemented
211C2×#487—431no—
212#1719—432no—
213#1718—432no—
214#1711—432no—
215#1710—432no—
216C8×M16—431no—
217C2×C43—22no—
218C2×C43C2×#49511yescharacteristic
219C2×C43#315311yescharacteristic
220C2×C43#315611yescharacteristic
221D43—161no—
222#533C2×D4311yescharacteristic
223#532—431no—
224C2×C4⋊Q8—431no—
225C2×C4⋊Q8C2×D4311yescharacteristic
226#500—432no—
227#500—432no—
228#498—431no—
229#492—431no—
230#491—22no—
231#489—862no—
232#487—432no—
233#487—432no—
234#487—431no—
235#487—432no—
236#487—432no—
237#487—862no—
238#487C2×D4312yes—
239#487C2×D4312yes—
240#486—431no—
241#486—432no—
242#486—432no—
243#484—862no—
244#480—862no—
245#477—862no—
246#474—862no—
247#465—862no—
248C4×SD16—862no—
249#431—431no—
250#419—22no—
251#417—862no—
252C2×#103—862no—
253C4×M16C2×D4311yescharacteristic
254C2×C4×C8—431no—
255#322—432no—
256C82—432no—
257C43#1962811yescharacteristic, complemented, Sylow
258C2×#41—861no—
259C22×Q8—21no—
260C22×Q8—861no—
261C2×SD16—862no—
262C2×M16C22⋊D4312yes—
263C22×C8—432no—
264C4⋊Q8—21no—
265C4⋊Q8—21no—
266C4⋊Q8—21no—
267C4⋊Q8—432no—
268C4⋊Q8—431no—
269C4⋊Q8—861no—
270C4⋊Q8—861no—
271C4⋊Q8—861no—
272C4⋊Q8C22×D4312yes—
273C4⋊Q8C22×D4311yescharacteristic
274C4⋊Q8C22×D4311yescharacteristic
275#127—431no—
276#125—21no—
277#124—861no—
278C22⋊Q8—21no—
279C22⋊Q8—21no—
280#121—861no—
281#121—861no—
282C4×Q8—21no—
283C4×Q8—21no—
284C4×D4—861no—
285C4×D4—861no—
286#117—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—861no—
290C2×C4⋊C4—861no—
291C2×C42C22×D4311yescharacteristic
292#107—864no—
293#107—864no—
294#106—862no—
295C4⋊C8—432no—
296#103—24no—
297#103—24no—
298#103—864no—
299#103—864no—
300#103—862no—
301#103—864no—
302#103—864no—
303#102—862no—
304#102—864no—
305#102—864no—
306C22⋊C8—432no—
307#97C22⋊D4312yes—
308C4×C8—432no—
309C4×C8—431no—
310C4×C8—432no—
311C4×C8—431no—
312C4×C8C22×D4312yes—
313#41—1724no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8—22no—
317C2×Q8—41no—
318C2×Q8—44no—
319C2×Q8—862no—
320C2×Q8—861no—
321C2×Q8—1724no—
322C2×Q8—1721no—
323C2×D4—861no—
324C2×D4—861no—
325C2×D4—861no—
326C2×D4—1721no—
327C22×C4—41no—
328C22×C4—1721no—
329C22×C4—1721no—
330C22×C4D4×D4311yescharacteristic
331C22×C4D4×D4311yescharacteristic
332C22×C4C2×C22⋊D4311yescharacteristic
333SD16—1724no—
334M16—24no—
335C2×C8—432no—
336C2×C8—432no—
337C2×C8—434no—
338C2×C8—1722no—
339C2×C8C2×C22⋊D4314yes—
340C4⋊C4—21no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—861no—
351C4⋊C4—862no—
352C4⋊C4—861no—
353C4⋊C4—862no—
354C4⋊C4—1721no—
355C4⋊C4—1721no—
356C22⋊C4—41no—
357C22⋊C4—1721no—
358C22⋊C4—1721no—
359C42—41no—
360C42D4×D4311yescharacteristic
361C42D4×D4311yescharacteristic
362C42C2×C22⋊D4311yescharacteristic
363C42C23×D4311yescharacteristic
364C23—1721no—
365C23#1306332111yescharacteristic
366Q8—44no—
367Q8—42no—
368Q8—42no—
369Q8—82no—
370Q8—3442no—
371Q8—1722no—
372Q8—1724no—
373D4—3442no—
374D4—1722no—
375D4—1722no—
376D4—1722no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—82no—
383C2×C4—3442no—
384C2×C4—3442no—
385C2×C4—1721no—
386C2×C4—1722no—
387C2×C4#1306332111yescharacteristic
388C2×C4#1306332111yescharacteristic
389C2×C4#1306332111yescharacteristic
390C2×C4#1306334514yes—
391C2×C4C2×D4×D4311yescharacteristic
392C2×C4C2×D4×D4311yescharacteristic
393C2×C4C22×C22⋊D4311yescharacteristic
394C8—24no—
395C8—862no—
396C8—862no—
397C8—864no—
398C22—21no—
399C22—21no—
400C22—3441no—
401C22—3441no—
402C22—3441no—
403C22#1458328112yes—
404C22C2×#1306332111yescharacteristic
405C4—21no—
406C4—21no—
407C4—82no—
408C4—81no—
409C4—81no—
410C4—3441no—
411C4—3442no—
412C4#1458328112yes—
413C4C2×#1306334512yes—
414C4#1458369812yes—
415C4#1458371512yes—
416C2—22no—
417C2—6881no—
418C2C2×#1458328111yescharacteristic
419C2#1914506211yescharacteristic
420C2#1914508811yescharacteristic
subgroupG/H
centerC22C2×#13063321
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3139C2
socleC22×C43C2×#127
prime radical#14583449C22
hypercenter#3139D43
hypocenterC43#19628
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3139

Complements

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

NH ≅ G/Ntype
1. #19145743C2semidirect
5. C2×#14583251C2semidirect
6. #19134249C2semidirect
7. #19134242C2semidirect
8. #19134208C2semidirect
9. #19134203C2semidirect
10. M16×C43⋊C8C2semidirect
11. C43×#3139C2semidirect
210. #3139D43semidirect
257. C43#19628semidirect

Maximal subgroups

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

subgroupindex
#191457432
#191457162
#191451552
#191449892
C2×#145832512
#191342492
#191342422
#191342082
#191342032
M16×C43⋊C82
C43×#31392
#1962843