Finite Group Databasebeta

← #24992688

Subgroups — #24992688

Order 11008.

532 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144052C211yesmaximal, characteristic
2#19143551C211yesmaximal, characteristic, complemented
3#19134612C211yesmaximal, characteristic, complemented
4#19133091C211yesmaximal, characteristic, complemented
5#19133045C211yesmaximal, characteristic, complemented
6#19132434C211yesmaximal, characteristic, complemented
7C43×#1301C211yesmaximal, characteristic, complemented
8C2×#13063347—21no—
9#14583449C2211yescharacteristic
10C4×#10621898C2211yescharacteristic
11#14583122—21no—
12#14583115—21no—
13#14583110C411yescharacteristic, complemented
14#14583105C411yescharacteristic, complemented
15#14583100C411yescharacteristic, complemented
16#14583095C411yescharacteristic, complemented
17#14583023—21no—
18#14582964—21no—
19(C22⋊D43)⋊C8—22no—
20#14582950—21no—
21C2×#13063251—21no—
22#14582896—21no—
23C2×C4×C43⋊C8C2211yescharacteristic
24C4×C8×D43—21no—
25C4×C4⋊Dic43C2211yescharacteristic
26#14582660—21no—
27#14582634—22no—
28#14582626—21no—
29#14582626—21no—
30C43×#431C2211yescharacteristic
31C43×#423C2211yescharacteristic
32C2×C4⋊C8×C43C2211yescharacteristic
33C2×#10621898—21no—
34C2×#10621898D411yescharacteristic
35#13063347—42no—
36#13063347—42no—
37C2×Dic172—21no—
38C2×#10621873—21no—
39C2×#10621873—21no—
40C2×D344—21no—
41C22×C43⋊C8—21no—
42C2×C8×D43—22no—
43#13063325C2×C411yescharacteristic
44#13063322C2×C411yescharacteristic
45#13063313—21no—
46#13063299—21no—
47#13063299—21no—
48C4×Dic86C2×C411yescharacteristic
49C4×Dic86D411yescharacteristic
50C4×D172—21no—
51C4×D172—21no—
52C4×D172C2×C411yescharacteristic
53C4×D172D411yescharacteristic
54C4×C22⋊D43—21no—
55C4×C22⋊D43—21no—
56#13063284D411yescharacteristic
57#13063282—21no—
58C2×C4⋊Dic43—21no—
59C2×C4×Dic43—21no—
60C42×D43—21no—
61Dic43⋊C8—22no—
62#13063251—42no—
63#13063250—21no—
64#13063250—21no—
65#13063247—21no—
66#13063247—21no—
67(C2×D43)⋊C8—22no—
68C4×C43⋊C8—21no—
69C4×C43⋊C8D411yescharacteristic
70C4×C43⋊C8D411yescharacteristic
71C8×Dic43—22no—
72C43⋊#95—21no—
73C2×M16×C43—21no—
74C22×C8×C43—21no—
75C2×C42×C43C2311yescharacteristic
76C4⋊C8×C43—21no—
77C4⋊C8×C43—21no—
78C4⋊C8×C43—21no—
79C4⋊C8×C43—21no—
80C4⋊C8×C43C2×C411yescharacteristic
81C4⋊C8×C43C2×C411yescharacteristic
82C22⋊C8×C43D412yes—
83C4×C8×C43—21no—
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43#4111yescharacteristic
87C2×C22⋊D43—21no—
88C2×C22⋊D43—41no—
89C22×Dic43—41no—
90#10621898—21no—
91#10621898—21no—
92#10621898—41no—
93#10621898—41no—
94#10621898—41no—
95#10621898—41no—
96#10621898D812yes—
97#10621898SD1612yes—
98C2×D172—21no—
99C2×D172—21no—
100C2×D172—21no—
101C2×D172C22⋊C411yescharacteristic
102C2×C4×D43—21no—
103C2×C4×D43—21no—
104C2×C4×D43—21no—
105C2×C4×D43—41no—
106C2×Dic86—21no—
107C2×Dic86C22⋊C411yescharacteristic
108M16×C43—41no—
109M16×C43—41no—
110C2×C8×C43—21no—
111C2×C8×C43—21no—
112C2×C8×C43—22no—
113C2×C8×C43—41no—
114C2×C8×C43—41no—
115C2×C8×C43—41no—
116C42×C43C22×C411yescharacteristic
117C42×C43C2×D411yescharacteristic
118C42×C43C2×D411yescharacteristic
119C42×C43#4111yescharacteristic
120C22⋊Dic43—21no—
121(C2×D43)⋊C4—21no—
122(C2×D43)⋊C4—21no—
123(C2×D43)⋊C4—41no—
124(C2×D43)⋊C4—41no—
125C4⋊Dic43—22no—
126C4⋊Dic43—21no—
127C4⋊Dic43—21no—
128C4⋊Dic43—41no—
129C4⋊Dic43C22⋊C411yescharacteristic
130C4⋊Dic43C22⋊C411yescharacteristic
131Dic43⋊C4—21no—
132Dic43⋊C4—21no—
133C4×Dic43—21no—
134C4×Dic43—21no—
135C4×Dic43—21no—
136C4×Dic43—41no—
137C4×Dic43—41no—
138C2×C43⋊C8—21no—
139C2×C43⋊C8—21no—
140C2×C43⋊C8—42no—
141Dic172—42no—
142D344—42no—
143#10621873—42no—
144#10621873—42no—
145C8×D43—44no—
146C23×C43#12111yescharacteristic
147C22×D43—21no—
148C22×D43—41no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—41no—
152C2×C4×C43C2×C22⋊C411yescharacteristic
153C2×C4×C43C4×D411yescharacteristic
154C2×C4×C43C4×D411yescharacteristic
155C2×C4×C43#12011yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#12311yescharacteristic
158C2×C4×C43C2×D811yescharacteristic
159C2×C4×C43C2×SD1611yescharacteristic
160C2×C4×C43#13511yescharacteristic
161C2×C4×C43#13511yescharacteristic
162C22⋊D43—22no—
163C22⋊D43—22no—
164C22⋊D43—81no—
165C22⋊D43—81no—
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—21no—
169C2×Dic43—42no—
170C2×Dic43—41no—
171C2×Dic43—81no—
172C2×Dic43—81no—
173D172—21no—
174D172—41no—
175D172—41no—
176D172—41no—
177D172—41no—
178D172—81no—
179D172#10212yes—
180C4×D43—22no—
181C4×D43—22no—
182C4×D43—42no—
183C4×D43—41no—
184C4×D43—41no—
185C4×D43—81no—
186C4×D43—81no—
187Dic86—21no—
188Dic86—41no—
189Dic86—41no—
190Dic86#10212yes—
191C8×C43—42no—
192C8×C43—41no—
193C8×C43—41no—
194C8×C43—81no—
195C43⋊C8—22no—
196C43⋊C8—41no—
197#9208—431nomaximal, Sylow
198C22×C43—21no—
199C22×C43—21no—
200C22×C43#38611yescharacteristic
201C22×C43#46511yescharacteristic
202C22×C43#46611yescharacteristic
203C2×D43—22no—
204C2×D43—41no—
205C2×D43—41no—
206C2×D43—81no—
207C2×D43—81no—
208C2×D43—81no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43C2×#10211yescharacteristic
213C4×C43#41611yescharacteristic
214C4×C43#44311yescharacteristic
215C4×C43#44411yescharacteristic
216C4×C43#46511yescharacteristic
217C4×C43#46611yescharacteristic
218Dic43—22no—
219Dic43—41no—
220Dic43—41no—
221Dic43—82no—
222Dic43—81no—
223#3035—431no—
224C8×#41—431no—
225#1806—431no—
226#1502—431no—
227#1492—431no—
228#1301D4311yescharacteristic, complemented
229#1279—431no—
230C2×C43—21no—
231C2×C43—21no—
232C2×C43#187611yescharacteristic
233C2×C43#189311yescharacteristic
234C2×C43#190611yescharacteristic
235D43—42no—
236D43—161no—
237C2×#135—861no—
238#532—431no—
239C4×#41—431no—
240#464—861no—
241#463—861no—
242#462—431no—
243#461—431no—
244#460—431no—
245#459—431no—
246C8×Q8—861no—
247C8×D4—861no—
248C8×D4—862no—
249#431—861no—
250#431C2×D4311yescharacteristic
251#423C2×D4311yescharacteristic
252C2×C4⋊C8C2×D4311yescharacteristic
253C2×#104—861no—
254#416—861no—
255C2×C4×C8—431no—
256C2×C4×C8—861no—
257C4×C4⋊C4—431no—
258#339—861no—
259#327—862no—
260D4⋊C8—861no—
261D4⋊C8—861no—
262C43#920811yescharacteristic, complemented, Sylow
263C2×#41—431no—
264C2×#41—861no—
265#135—1722no—
266#135—1722no—
267C2×Q16—861no—
268C2×SD16—861no—
269C2×SD16—861no—
270C2×D8—861no—
271C2×M16—21no—
272C22×C8—21no—
273C22×C8—862no—
274C22×C8—861no—
275C4⋊Q8—431no—
276#127—431no—
277#124—861no—
278#121—861no—
279#121—861no—
280C4×Q8—431no—
281C4×Q8—431no—
282C4×D4—431no—
283C4×D4—431no—
284C4×D4—861no—
285C4×D4—861no—
286C4×D4—861no—
287C4×D4—861no—
288#117—431no—
289#117—861no—
290C2×C4⋊C4—861no—
291C2×C42—861no—
292C2×C42—861no—
293C2×C42C22×D4311yescharacteristic
294C4⋊C8—21no—
295C4⋊C8—21no—
296C4⋊C8—21no—
297C4⋊C8—21no—
298C4⋊C8—862no—
299C4⋊C8C4×D4311yescharacteristic
300C4⋊C8C4×D4311yescharacteristic
301#104—1722no—
302#103—861no—
303#103—861no—
304#102—861no—
305#102—861no—
306C22⋊C8—862no—
307C22⋊C8D17212yes—
308C4×C8—21no—
309C4×C8—431no—
310C4×C8—431no—
311C4×C8—862no—
312C4×C8—861no—
313#95—861no—
314#41—432no—
315#41—432no—
316#41—861no—
317#41—861no—
318#41—1721no—
319#41—1721no—
320#41—1721no—
321#41—1721no—
322C2×Q8—431no—
323C2×Q8—861no—
324C2×D4—431no—
325C2×D4—861no—
326C2×D4—861no—
327C2×D4—861no—
328C2×D4—861no—
329C2×D4—1721no—
330C22×C4—861no—
331C22×C4—861no—
332C22×C4—861no—
333C22×C4—1721no—
334C22×C4—1721no—
335C22×C4C2×D17211yescharacteristic
336C22×C4D4×D4311yescharacteristic
337C22×C4#1062190211yescharacteristic
338Q16—1722no—
339SD16—1722no—
340SD16—1722no—
341D8—1722no—
342M16—41no—
343M16—41no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—22no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—861no—
351C2×C8—861no—
352C2×C8—1724no—
353C2×C8—1722no—
354C4⋊C4—431no—
355C4⋊C4—431no—
356C4⋊C4—862no—
357C4⋊C4—861no—
358C4⋊C4—861no—
359C4⋊C4—861no—
360C4⋊C4—861no—
361C4⋊C4—1721no—
362C22⋊C4—861no—
363C22⋊C4—861no—
364C22⋊C4—861no—
365C22⋊C4—1721no—
366C22⋊C4—1721no—
367C42—861no—
368C42—861no—
369C42—861no—
370C42—1721no—
371C42—1721no—
372C42C2×C4×D4311yescharacteristic
373C42#1062189811yescharacteristic
374C42D4×D4311yescharacteristic
375C42D4×D4311yescharacteristic
376C23—861no—
377C23—1721no—
378C23#1306330011yescharacteristic
379Q8—432no—
380Q8—861no—
381Q8—1721no—
382Q8—1721no—
383D4—432no—
384D4—862no—
385D4—862no—
386D4—861no—
387D4—3441no—
388D4—3441no—
389D4—3441no—
390D4—1721no—
391D4—1721no—
392D4—1721no—
393D4—1721no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—41no—
397C2×C4—861no—
398C2×C4—862no—
399C2×C4—862no—
400C2×C4—861no—
401C2×C4—861no—
402C2×C4—3441no—
403C2×C4—3441no—
404C2×C4—3441no—
405C2×C4—3441no—
406C2×C4—1722no—
407C2×C4—1722no—
408C2×C4—1721no—
409C2×C4—1721no—
410C2×C4—1721no—
411C2×C4C22⋊C4×D4311yescharacteristic
412C2×C4#1306328711yescharacteristic
413C2×C4C4×D17211yescharacteristic
414C2×C4#1306329511yescharacteristic
415C2×C4#1306329811yescharacteristic
416C2×C4#1306331011yescharacteristic
417C2×C4D8×D4311yescharacteristic
418C2×C4SD16×D4311yescharacteristic
419C2×C4#1306334611yescharacteristic
420C2×C4#1306334811yescharacteristic
421C8—42no—
422C8—41no—
423C8—41no—
424C8—81no—
425C8—862no—
426C8—1721no—
427C22—21no—
428C22—21no—
429C22—862no—
430C22—3441no—
431C22—3441no—
432C22—3441no—
433C22—1721no—
434C22—1721no—
435C22#1458277711yescharacteristic
436C22#1458312911yescharacteristic
437C22#1458313611yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—862no—
442C4—3442no—
443C4—3441no—
444C4—1721no—
445C4—1721no—
446C4#102×D4311yescharacteristic
447C4#1458289411yescharacteristic
448C4#1458301511yescharacteristic
449C4#1458302011yescharacteristic
450C4#1458313111yescharacteristic
451C4#1458313411yescharacteristic
452C2—21no—
453C2—21no—
454C2—1722no—
455C2—6881no—
456C2#1913492311yescharacteristic
457C2#1913502211yescharacteristic
458C2#1913509711yescharacteristic
subgroupG/H
centerC2×C4#13063298
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1301C2
socleC22×C43#386
prime radical#19144052C2
cosocleC2×C42×C43C23
hypercenter#1301D43
hypocenterC43#9208
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
2. #19143551C2semidirect
3. #19134612C2semidirect
4. #19133091C2semidirect
5. #19133045C2semidirect
6. #19132434C2semidirect
7. C43×#1301C2semidirect
13. #14583110C4semidirect
14. #14583105C4semidirect
15. #14583100C4semidirect
16. #14583095C4semidirect
228. #1301D43semidirect
262. C43#9208semidirect

Maximal subgroups

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

subgroupindex
#191440522
#191435512
#191346122
#191330912
#191330452
#191324342
C43×#13012
#920843