Finite Group Databasebeta

← #24991483

Subgroups — #24991483

Order 11008.

530 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144052C211yesmaximal, characteristic
2#19143160C211yesmaximal, characteristic, complemented
3#19133047C211yesmaximal, characteristic, complemented
4#19132993C211yesmaximal, characteristic, complemented
5#19132978C211yesmaximal, characteristic, complemented
6#19132492C211yesmaximal, characteristic, complemented
7C43×#1277C211yesmaximal, characteristic, complemented
8C2×#13063347—21no—
9C2×#13063331—21no—
10#14583449C2211yescharacteristic
11C4×#10621898C2211yescharacteristic
12#14583122—21no—
13#14583115—21no—
14#14583110C411yescharacteristic
15#14583105C411yescharacteristic
16#14583100C411yescharacteristic
17#14583095C411yescharacteristic
18#14582952C2211yescharacteristic
19#14582925—21no—
20#14582924—22no—
21#14582923C2211yescharacteristic
22#14582921—21no—
23C4⋊C8×D43—21no—
24#14582896—21no—
25#14582631—21no—
26#14582628—21no—
27#14582628—22no—
28#14582626—21no—
29#14582626—21no—
30C2×C4⋊C8×C43C2211yescharacteristic
31C2×C4⋊C8×C43C2211yescharacteristic
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—
41#13063331—42no—
42#13063331—42no—
43C2×#10621877—21no—
44C2×#10621872—22no—
45C2×C8×D43—22no—
46#13063325C2×C411yescharacteristic
47#13063322C2×C411yescharacteristic
48#13063313—21no—
49#13063299—21no—
50#13063299—21no—
51C4×Dic86C2×C411yescharacteristic
52C4×Dic86D411yescharacteristic
53C4×D172—21no—
54C4×D172—21no—
55C4×D172C2×C411yescharacteristic
56C4×D172D411yescharacteristic
57C4×C22⋊D43—21no—
58C4×C22⋊D43—21no—
59#13063284D411yescharacteristic
60#13063282—21no—
61C42×D43—21no—
62C4⋊(C43⋊C8)—21no—
63C4⋊(C43⋊C8)—21no—
64C4⋊(C43⋊C8)D412yes—
65Dic43⋊C8—22no—
66Dic43⋊C8—22no—
67#13063250—21no—
68#13063250—21no—
69#13063247—21no—
70#13063247—21no—
71C22⋊(C43⋊C8)—21no—
72C4×C43⋊C8—21no—
73C22×C8×C43—21no—
74C22×C8×C43—21no—
75C22×C8×C43—21no—
76C2×C42×C43C2311yescharacteristic
77C4⋊C8×C43—21no—
78C4⋊C8×C43—21no—
79C4⋊C8×C43C2×C411yescharacteristic
80C4⋊C8×C43C2×C411yescharacteristic
81C4⋊C8×C43D411yescharacteristic
82C4⋊C8×C43D411yescharacteristic
83C4×C8×C43—21no—
84C4×C8×C43—21no—
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43#4111yescharacteristic
87C22×C4×C43#4111yescharacteristic
88C2×C22⋊D43—21no—
89C2×C22⋊D43—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
108C2×C8×C43—22no—
109C2×C8×C43—21no—
110C2×C8×C43—21no—
111C2×C8×C43—21no—
112C2×C8×C43—21no—
113C2×C8×C43—41no—
114C2×C8×C43—41no—
115C2×C8×C43—41no—
116C2×C8×C43—41no—
117C2×C8×C43—41no—
118C2×C8×C43—41no—
119C42×C43C22×C411yescharacteristic
120C42×C43C2×D411yescharacteristic
121C42×C43C2×D411yescharacteristic
122C42×C43C2×D411yescharacteristic
123C22⋊Dic43—21no—
124(C2×D43)⋊C4—21no—
125(C2×D43)⋊C4—21no—
126(C2×D43)⋊C4—41no—
127(C2×D43)⋊C4—41no—
128C4⋊Dic43—21no—
129C4⋊Dic43—21no—
130C4⋊Dic43C22⋊C411yescharacteristic
131C4⋊Dic43C22⋊C411yescharacteristic
132Dic43⋊C4—21no—
133Dic43⋊C4—21no—
134C4×Dic43—21no—
135C4×Dic43—21no—
136C4×Dic43—21no—
137#10621877—41no—
138#10621877—41no—
139C2×C43⋊C8—22no—
140C2×C43⋊C8—41no—
141Dic172—42no—
142D344—42no—
143#10621873—42no—
144#10621873—42no—
145#10621872—44no—
146C8×D43—44no—
147C23×C43#12311yescharacteristic
148C22×D43—21no—
149C22×D43—41no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—41no—
153C2×C4×C43C2×C22⋊C411yescharacteristic
154C2×C4×C43C4×D411yescharacteristic
155C2×C4×C43C4×D411yescharacteristic
156C2×C4×C43#12011yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43#12111yescharacteristic
159C2×C4×C43C2×D811yescharacteristic
160C2×C4×C43C2×SD1611yescharacteristic
161C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C43#13711yescharacteristic
163C22⋊D43—22no—
164C22⋊D43—22no—
165C22⋊D43—81no—
166C22⋊D43—81no—
167C2×Dic43—21no—
168C2×Dic43—21no—
169C2×Dic43—21no—
170C2×Dic43—41no—
171D172—21no—
172D172—42no—
173D172—41no—
174D172—41no—
175D172—41no—
176D172—41no—
177D172#10212yes—
178C4×D43—22no—
179C4×D43—22no—
180C4×D43—41no—
181C4×D43—41no—
182C4×D43—81no—
183C4×D43—81no—
184C4×D43—81no—
185Dic86—21no—
186Dic86—41no—
187Dic86—41no—
188Dic86#10212yes—
189C8×C43—42no—
190C8×C43—41no—
191C8×C43—41no—
192C8×C43—41no—
193C8×C43—41no—
194C43⋊C8—42no—
195C43⋊C8—81no—
196#8995—431nomaximal, Sylow
197C22×C43—21no—
198C22×C43—21no—
199C22×C43#38611yescharacteristic
200C22×C43#48011yescharacteristic
201C22×C43#48111yescharacteristic
202C2×D43—22no—
203C2×D43—41no—
204C2×D43—41no—
205C2×D43—81no—
206C2×D43—81no—
207C2×D43—81no—
208C4×C43—21no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43C2×#10211yescharacteristic
212C4×C43#41711yescharacteristic
213C4×C43#44311yescharacteristic
214C4×C43#44411yescharacteristic
215C4×C43#44711yescharacteristic
216C4×C43#44811yescharacteristic
217Dic43—22no—
218Dic43—41no—
219Dic43—41no—
220Dic43—81no—
221#3035—431no—
222#2906—431no—
223#1492—431no—
224#1480—431no—
225#1476—431no—
226#1301—431no—
227#1277D4311yescharacteristic, complemented
228C2×C43—21no—
229C2×C43—21no—
230C2×C43#187411yescharacteristic
231C2×C43#187611yescharacteristic
232C2×C43#188111yescharacteristic
233D43—42no—
234D43—161no—
235C2×#135—861no—
236C2×#131—861no—
237#532—431no—
238C4×#41—431no—
239#464—861no—
240#463—861no—
241#462—431no—
242#461—431no—
243#460—431no—
244#459—431no—
245#431—431no—
246#424—862no—
247#424—861no—
248#423—431no—
249#423—861no—
250C2×C4⋊C8—861no—
251C2×C4⋊C8C2×D4311yescharacteristic
252C2×C4⋊C8C2×D4311yescharacteristic
253#416—861no—
254C2×C4×C8C2×D4311yescharacteristic
255Q8⋊C8—861no—
256D4⋊C8—862no—
257D4⋊C8—861no—
258D4⋊C8—861no—
259D4⋊C8—861no—
260C43#899511yescharacteristic, complemented, Sylow
261C2×#41—431no—
262C2×#41—861no—
263#135—1722no—
264#135—1722no—
265C2×Q16—861no—
266C2×SD16—861no—
267C2×SD16—861no—
268C2×D8—861no—
269#131—1722no—
270#131—1722no—
271C2×M16—862no—
272C2×M16—861no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—862no—
277C4⋊Q8—431no—
278#127—431no—
279#124—861no—
280#121—861no—
281#121—861no—
282C4×Q8—431no—
283C4×Q8—431no—
284C4×D4—431no—
285C4×D4—431no—
286C4×D4—861no—
287C4×D4—861no—
288C4×D4—861no—
289C4×D4—861no—
290#117—431no—
291#117—861no—
292C2×C42—861no—
293C2×C42C22×D4311yescharacteristic
294C4⋊C8—21no—
295C4⋊C8—21no—
296C4⋊C8—432no—
297C4⋊C8—862no—
298C4⋊C8—862no—
299C4⋊C8—861no—
300C4⋊C8—861no—
301C4⋊C8C4×D4311yescharacteristic
302C4⋊C8C4×D4311yescharacteristic
303C4⋊C8D17211yescharacteristic
304C4⋊C8D17211yescharacteristic
305#103—861no—
306#103—861no—
307#102—861no—
308#102—861no—
309C22⋊C8—861no—
310C4×C8—21no—
311C4×C8—21no—
312C4×C8—861no—
313#41—432no—
314#41—432no—
315#41—861no—
316#41—861no—
317#41—1721no—
318#41—1721no—
319#41—1721no—
320#41—1721no—
321C2×Q8—431no—
322C2×Q8—861no—
323C2×D4—431no—
324C2×D4—861no—
325C2×D4—861no—
326C2×D4—861no—
327C2×D4—861no—
328C2×D4—1721no—
329C22×C4—861no—
330C22×C4—861no—
331C22×C4—861no—
332C22×C4—1721no—
333C22×C4#1062189811yescharacteristic
334C22×C4D4×D4311yescharacteristic
335C22×C4#1062190211yescharacteristic
336Q16—1722no—
337SD16—1722no—
338SD16—1722no—
339D8—1722no—
340M16—1724no—
341M16—1721no—
342M16—1721no—
343C2×C8—22no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—862no—
355C2×C8—1724no—
356C2×C8—1721no—
357C4⋊C4—431no—
358C4⋊C4—431no—
359C4⋊C4—861no—
360C4⋊C4—861no—
361C4⋊C4—861no—
362C4⋊C4—861no—
363C22⋊C4—861no—
364C22⋊C4—861no—
365C22⋊C4—861no—
366C22⋊C4—1721no—
367C22⋊C4—1721no—
368C42—861no—
369C42—861no—
370C42—861no—
371C42C2×C4×D4311yescharacteristic
372C42C2×D17211yescharacteristic
373C42D4×D4311yescharacteristic
374C42D4×D4311yescharacteristic
375C23—861no—
376C23—1721no—
377C23#1306331011yescharacteristic
378Q8—432no—
379Q8—861no—
380Q8—1721no—
381Q8—1721no—
382D4—432no—
383D4—862no—
384D4—862no—
385D4—861no—
386D4—3441no—
387D4—3441no—
388D4—1722no—
389D4—1721no—
390D4—1721no—
391D4—1721no—
392D4—1721no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—41no—
396C2×C4—861no—
397C2×C4—862no—
398C2×C4—862no—
399C2×C4—861no—
400C2×C4—861no—
401C2×C4—3441no—
402C2×C4—3441no—
403C2×C4—3441no—
404C2×C4—1721no—
405C2×C4—1721no—
406C2×C4—1721no—
407C2×C4C22⋊C4×D4311yescharacteristic
408C2×C4#1306328711yescharacteristic
409C2×C4C4×D17211yescharacteristic
410C2×C4#1306329511yescharacteristic
411C2×C4#1306329811yescharacteristic
412C2×C4#1306330011yescharacteristic
413C2×C4D8×D4311yescharacteristic
414C2×C4SD16×D4311yescharacteristic
415C2×C4#1306335211yescharacteristic
416C2×C4#1306335711yescharacteristic
417C8—42no—
418C8—41no—
419C8—41no—
420C8—41no—
421C8—41no—
422C8—3441no—
423C8—1722no—
424C22—21no—
425C22—21no—
426C22—862no—
427C22—3441no—
428C22—3441no—
429C22—3441no—
430C22—1721no—
431C22—1721no—
432C22#1458277711yescharacteristic
433C22#1458321411yescharacteristic
434C22#1458321911yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—862no—
439C4—3441no—
440C4—1721no—
441C4—1721no—
442C4#102×D4311yescharacteristic
443C4#1458289911yescharacteristic
444C4#1458301711yescharacteristic
445C4#1458302211yescharacteristic
446C4#1458303411yescharacteristic
447C4#1458303911yescharacteristic
448C2—21no—
449C2—21no—
450C2—1722no—
451C2—6881no—
452C2#1913491111yescharacteristic
453C2#1913492111yescharacteristic
454C2#1913495811yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1277C2
socleC22×C43#386
prime radical#19144052C2
cosocleC2×C42×C43C23
hypercenter#1277D43
hypocenterC43#8995
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
2. #19143160C2semidirect
3. #19133047C2semidirect
4. #19132993C2semidirect
5. #19132978C2semidirect
6. #19132492C2semidirect
7. C43×#1277C2semidirect
227. #1277D43semidirect
260. C43#8995semidirect

Maximal subgroups

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

subgroupindex
#191440522
#191431602
#191330472
#191329932
#191329782
#191324922
C43×#12772
#899543