Finite Group Databasebeta

← #24992475

Subgroups — #24992475

Order 11008.

510 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144083C211yesmaximal, characteristic
2#19143160C211yesmaximal, characteristic
3#19133266C211yesmaximal, characteristic, complemented
4C2×#14582646C211yesmaximal, characteristic, complemented
5#19132983C211yesmaximal, characteristic
6#19132469C211yesmaximal, characteristic, complemented
7C43×#1301C211yesmaximal, characteristic, complemented
8C2×#13063358—21no—
9C2×#13063331—21no—
10C2×#13063325C2211yescharacteristic
11C4×#10621898C2211yescharacteristic
12#14583110—21no—
13#14583110C412yes—
14#14583105—21no—
15#14583105C412yes—
16#14582925—21no—
17#14582924—22no—
18#14582923C2211yescharacteristic
19#14582921—21no—
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C4⋊C8×D43—21no—
22#14582909—21no—
23#14582646—21no—
24#14582646—21no—
25#14582644—22no—
26#14582631—21no—
27#14582628—21no—
28C43×#431C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C2×C4⋊C8×C43C2211yescharacteristic
31C2×#10621898D411yescharacteristic
32C22×Dic86—21no—
33#13063358—42no—
34#13063358—42no—
35C2×Dic172—22no—
36C2×#10621873—22no—
37#13063331—42no—
38#13063331—42no—
39C2×#10621877—21no—
40C2×#10621872—22no—
41C22×C43⋊C8—21no—
42C2×C8×D43—22no—
43#13063325—21no—
44#13063325—21no—
45#13063325—21no—
46#13063325C2×C412yes—
47C4×Dic86C2×C411yescharacteristic
48C4×Dic86D411yescharacteristic
49C4×D172C2×C411yescharacteristic
50C4×D172D411yescharacteristic
51C4×C22⋊D43—21no—
52C4×C22⋊D43—21no—
53#13063284D411yescharacteristic
54#13063282—21no—
55C2×C4⋊Dic43—21no—
56C2×C4⋊Dic43—21no—
57C42×D43—21no—
58C4⋊(C43⋊C8)—21no—
59C4⋊(C43⋊C8)—21no—
60C4⋊(C43⋊C8)—21no—
61C4⋊(C43⋊C8)D412yes—
62Dic43⋊C8—22no—
63Dic43⋊C8—22no—
64#13063250—22no—
65#13063250—22no—
66C2×M16×C43—21no—
67C22×C8×C43—21no—
68C2×C42×C43C2311yescharacteristic
69C4⋊C8×C43—21no—
70C4⋊C8×C43—21no—
71C4⋊C8×C43—21no—
72C4⋊C8×C43C2×C412yes—
73C4⋊C8×C43D411yescharacteristic
74C4⋊C8×C43D411yescharacteristic
75C22⋊C8×C43—21no—
76C4×C8×C43—21no—
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43#4111yescharacteristic
79C22×C4×C43#4111yescharacteristic
80C2×C22⋊D43—21no—
81C22×Dic43—41no—
82#10621898—21no—
83#10621898—21no—
84#10621898D812yes—
85#10621898SD1612yes—
86C2×D172C22⋊C411yescharacteristic
87C2×C4×D43—21no—
88C2×C4×D43—21no—
89C2×C4×D43—21no—
90C2×Dic86—22no—
91C2×Dic86—41no—
92C2×Dic86—41no—
93C2×Dic86—41no—
94C2×Dic86—41no—
95C2×Dic86—41no—
96C2×Dic86C22⋊C411yescharacteristic
97M16×C43—41no—
98M16×C43—41no—
99C2×C8×C43—22no—
100C2×C8×C43—21no—
101C2×C8×C43—21no—
102C2×C8×C43—41no—
103C2×C8×C43—41no—
104C2×C8×C43—41no—
105C42×C43C22×C411yescharacteristic
106C42×C43C2×D411yescharacteristic
107C42×C43C2×D411yescharacteristic
108C42×C43C2×D411yescharacteristic
109C22⋊Dic43—21no—
110(C2×D43)⋊C4—21no—
111(C2×D43)⋊C4—21no—
112C4⋊Dic43—22no—
113C4⋊Dic43—22no—
114C4⋊Dic43—41no—
115C4⋊Dic43—41no—
116C4⋊Dic43C22⋊C411yescharacteristic
117C4⋊Dic43C22⋊C411yescharacteristic
118Dic43⋊C4—21no—
119Dic43⋊C4—21no—
120C4×Dic43—21no—
121C4×Dic43—21no—
122C4×Dic43—21no—
123#10621877—41no—
124#10621877—41no—
125C2×C43⋊C8—22no—
126C2×C43⋊C8—41no—
127C2×C43⋊C8—81no—
128Dic172—44no—
129#10621873—44no—
130#10621872—44no—
131C8×D43—44no—
132C23×C43#12311yescharacteristic
133C22×D43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—41no—
137C2×C4×C43C2×C22⋊C411yescharacteristic
138C2×C4×C43C4×D411yescharacteristic
139C2×C4×C43C4×D411yescharacteristic
140C2×C4×C43#12011yescharacteristic
141C2×C4×C43#12111yescharacteristic
142C2×C4×C43#12111yescharacteristic
143C2×C4×C43C2×D811yescharacteristic
144C2×C4×C43C2×SD1611yescharacteristic
145C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C43#13711yescharacteristic
147C22⋊D43—22no—
148C22⋊D43—22no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—21no—
152C2×Dic43—42no—
153C2×Dic43—81no—
154C2×Dic43—81no—
155D172—21no—
156D172#10212yes—
157C4×D43—22no—
158C4×D43—22no—
159C4×D43—41no—
160C4×D43—41no—
161C4×D43—81no—
162Dic86—21no—
163Dic86—42no—
164Dic86—42no—
165Dic86—81no—
166Dic86—81no—
167Dic86#10212yes—
168C8×C43—42no—
169C8×C43—41no—
170C8×C43—41no—
171C8×C43—81no—
172C43⋊C8—42no—
173C43⋊C8—81no—
174#9171—431nomaximal, Sylow
175C22×C43—21no—
176C22×C43—21no—
177C22×C43#38611yescharacteristic
178C22×C43#48011yescharacteristic
179C22×C43#48111yescharacteristic
180C2×D43—22no—
181C2×D43—41no—
182C2×D43—41no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43C2×#10211yescharacteristic
187C4×C43#41711yescharacteristic
188C4×C43#44711yescharacteristic
189C4×C43#44811yescharacteristic
190C4×C43#47111yescharacteristic
191C4×C43#47311yescharacteristic
192Dic43—22no—
193Dic43—41no—
194Dic43—41no—
195Dic43—82no—
196#3039—431no—
197#2906—431no—
198#1546—431no—
199C2×#332—431no—
200#1477—431no—
201#1301D4311yescharacteristic, complemented
202#1292—431no—
203C2×C43—21no—
204C2×C43—21no—
205C2×C43#187411yescharacteristic
206C2×C43#190211yescharacteristic
207C2×C43#190811yescharacteristic
208D43—42no—
209C2×#137—861no—
210C2×#131—861no—
211C2×C4⋊Q8—431no—
212C4×#41—431no—
213#462—432no—
214#462—861no—
215#461—432no—
216#461—861no—
217#431C2×D4311yescharacteristic
218#424—862no—
219#424—861no—
220#423—431no—
221#423—861no—
222#423C2×D4311yescharacteristic
223C2×C4⋊C8—431no—
224C2×C4⋊C8—861no—
225C2×C4⋊C8C2×D4311yescharacteristic
226#419—861no—
227#332—862no—
228#332—861no—
229#332—861no—
230Q8⋊C8—861no—
231D4⋊C8—861no—
232C43#917111yescharacteristic, complemented, Sylow
233C2×#41—431no—
234C22×Q8—861no—
235#137—1722no—
236#137—1722no—
237C2×Q16—862no—
238C2×SD16—862no—
239#131—1722no—
240#131—1722no—
241C2×M16—21no—
242C2×M16—862no—
243C2×M16—861no—
244C22×C8—21no—
245C22×C8—862no—
246C22×C8—861no—
247C4⋊Q8—432no—
248C4⋊Q8—861no—
249C4⋊Q8—861no—
250C4⋊Q8—861no—
251C4×Q8—431no—
252C4×Q8—431no—
253C4×D4—431no—
254C4×D4—431no—
255C4×D4—861no—
256C4×D4—861no—
257#117—431no—
258#117—861no—
259C2×C4⋊C4—861no—
260C2×C4⋊C4—861no—
261C2×C42—861no—
262C2×C42C22×D4311yescharacteristic
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—432no—
267C4⋊C8—862no—
268C4⋊C8—862no—
269C4⋊C8—861no—
270C4⋊C8—861no—
271C4⋊C8—861no—
272C4⋊C8C4×D4312yes—
273C4⋊C8D17211yescharacteristic
274C4⋊C8D17211yescharacteristic
275#103—862no—
276#103—862no—
277C22⋊C8—21no—
278C4×C8—21no—
279#41—432no—
280#41—432no—
281#41—861no—
282#41—861no—
283C2×Q8—431no—
284C2×Q8—862no—
285C2×Q8—1721no—
286C2×Q8—1721no—
287C2×Q8—1721no—
288C2×Q8—1721no—
289C2×Q8—1721no—
290C2×D4—431no—
291C2×D4—861no—
292C22×C4—861no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—1721no—
296C22×C4#1062189811yescharacteristic
297C22×C4D4×D4311yescharacteristic
298C22×C4#1062190211yescharacteristic
299Q16—1724no—
300SD16—1724no—
301M16—41no—
302M16—41no—
303M16—1724no—
304M16—1721no—
305M16—1721no—
306C2×C8—22no—
307C2×C8—21no—
308C2×C8—21no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—862no—
313C2×C8—3441no—
314C2×C8—1724no—
315C2×C8—1721no—
316C4⋊C4—431no—
317C4⋊C4—431no—
318C4⋊C4—861no—
319C4⋊C4—861no—
320C4⋊C4—862no—
321C4⋊C4—862no—
322C4⋊C4—1721no—
323C4⋊C4—1721no—
324C22⋊C4—861no—
325C22⋊C4—861no—
326C22⋊C4—861no—
327C42—861no—
328C42—861no—
329C42—861no—
330C42C2×C4×D4311yescharacteristic
331C42C2×D17211yescharacteristic
332C42D4×D4311yescharacteristic
333C42D4×D4311yescharacteristic
334C23—861no—
335C23#1306331011yescharacteristic
336Q8—432no—
337Q8—861no—
338Q8—3441no—
339Q8—3441no—
340Q8—1722no—
341Q8—1722no—
342D4—432no—
343D4—862no—
344D4—862no—
345D4—861no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—861no—
350C2×C4—862no—
351C2×C4—862no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—3441no—
355C2×C4—3441no—
356C2×C4—3441no—
357C2×C4—1722no—
358C2×C4—1721no—
359C2×C4—1721no—
360C2×C4C22⋊C4×D4311yescharacteristic
361C2×C4#1306328711yescharacteristic
362C2×C4C4×D17211yescharacteristic
363C2×C4#1306329511yescharacteristic
364C2×C4#1306329811yescharacteristic
365C2×C4#1306330011yescharacteristic
366C2×C4D8×D4311yescharacteristic
367C2×C4SD16×D4311yescharacteristic
368C2×C4#1306335211yescharacteristic
369C2×C4#1306335711yescharacteristic
370C8—42no—
371C8—41no—
372C8—41no—
373C8—81no—
374C8—3441no—
375C8—1722no—
376C22—21no—
377C22—21no—
378C22—862no—
379C22—1721no—
380C22—1721no—
381C22#1458277711yescharacteristic
382C22#1458321411yescharacteristic
383C22#1458321911yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—862no—
388C4—3442no—
389C4—1721no—
390C4—1721no—
391C4#102×D4311yescharacteristic
392C4#1458289911yescharacteristic
393C4#1458303411yescharacteristic
394C4#1458303911yescharacteristic
395C4#1458316311yescharacteristic
396C4#1458317511yescharacteristic
397C2—21no—
398C2—21no—
399C2—1722no—
400C2#1913491111yescharacteristic
401C2#1913506711yescharacteristic
402C2#1913510911yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1301C2
socleC22×C43#386
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenter#1301D43
hypocenterC43#9171
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
3. #19133266C2semidirect
4. C2×#14582646C2semidirect
6. #19132469C2semidirect
7. C43×#1301C2semidirect
201. #1301D43semidirect
232. C43#9171semidirect

Maximal subgroups

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

subgroupindex
#191440832
#191431602
#191332662
C2×#145826462
#191329832
#191324692
C43×#13012
#917143