Finite Group Databasebeta

← #24992473

Subgroups — #24992473

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#19144078C211yesmaximal, characteristic
2#19143164C211yesmaximal, characteristic
3C2×#14582645C211yesmaximal, characteristic, complemented
4#19132983C211yesmaximal, characteristic
5#19132491C211yesmaximal, characteristic, complemented
6#19132469C211yesmaximal, characteristic, complemented
7C43×#1546C211yesmaximal, characteristic, complemented
8C2×#13063356—21no—
9C2×#13063333—21no—
10C4×#10621898C2211yescharacteristic
11#14583106—21no—
12#14583106C412yes—
13#14583101—21no—
14#14583101C412yes—
15#14582927—21no—
16#14582924—22no—
17#14582923C2211yescharacteristic
18#14582921—21no—
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C4⋊C8×D43—21no—
22#14582908—21no—
23#14582645—21no—
24#14582645—21no—
25#14582631—21no—
26#14582628—21no—
27C2×C4⋊Q8×C43C2211yescharacteristic
28C43×#431C2211yescharacteristic
29C43×#423C2211yescharacteristic
30C43×#332—22no—
31C2×#10621898D411yescharacteristic
32#13063356—42no—
33#13063356—42no—
34C2×#10621885—22no—
35C2×#10621884—22no—
36#13063333—42no—
37#13063333—42no—
38C2×#10621877—21no—
39C2×#10621872—22no—
40C22×C43⋊C8—21no—
41C22×C43⋊C8—21no—
42C2×C8×D43—22no—
43C4×Dic86C2×C411yescharacteristic
44C4×Dic86D411yescharacteristic
45C4×D172C2×C411yescharacteristic
46C4×D172D411yescharacteristic
47C4×C22⋊D43—21no—
48C4×C22⋊D43—21no—
49#13063284D411yescharacteristic
50#13063282—21no—
51C42×D43—21no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)—21no—
55C4⋊(C43⋊C8)—21no—
56C4⋊(C43⋊C8)C2×C412yes—
57C4⋊(C43⋊C8)D411yescharacteristic
58C4⋊(C43⋊C8)D411yescharacteristic
59Dic43⋊C8—22no—
60Dic43⋊C8—22no—
61#13063249—22no—
62#13063249—22no—
63C22×Q8×C43—21no—
64C2×M16×C43—21no—
65C4⋊Q8×C43—21no—
66C4⋊Q8×C43—21no—
67C4⋊Q8×C43—21no—
68C4⋊Q8×C43C2×C412yes—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C42×C43C2311yescharacteristic
72C4⋊C8×C43—21no—
73C4⋊C8×C43—21no—
74C4⋊C8×C43D412yes—
75C22⋊C8×C43—21no—
76C4×C8×C43—21no—
77C2×Q8×C43—22no—
78C2×Q8×C43—41no—
79C2×Q8×C43—41no—
80C2×Q8×C43—41no—
81C2×Q8×C43—41no—
82C2×Q8×C43—41no—
83C22×C4×C43—41no—
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43#4111yescharacteristic
86C22×C4×C43#4111yescharacteristic
87C2×C22⋊D43—21no—
88#10621898—21no—
89#10621898—21no—
90#10621898D812yes—
91#10621898SD1612yes—
92C2×D172C22⋊C411yescharacteristic
93C2×C4×D43—21no—
94C2×C4×D43—21no—
95C2×C4×D43—21no—
96C2×Dic86C22⋊C411yescharacteristic
97M16×C43—41no—
98M16×C43—41no—
99C2×C8×C43—22no—
100C2×C8×C43—41no—
101C4⋊C4×C43—22no—
102C4⋊C4×C43—22no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43—41no—
105C42×C43C22×C411yescharacteristic
106C42×C43C2×D411yescharacteristic
107C42×C43C2×D411yescharacteristic
108C42×C43C2×D411yescharacteristic
109C22⋊Dic43—21no—
110#10621885—44no—
111#10621884—44no—
112(C2×D43)⋊C4—21no—
113(C2×D43)⋊C4—21no—
114C4⋊Dic43C22⋊C411yescharacteristic
115C4⋊Dic43C22⋊C411yescharacteristic
116Dic43⋊C4—21no—
117Dic43⋊C4—21no—
118C4×Dic43—21no—
119C4×Dic43—21no—
120C4×Dic43—21no—
121#10621877—41no—
122#10621877—41no—
123C2×C43⋊C8—22no—
124C2×C43⋊C8—21no—
125C2×C43⋊C8—21no—
126C2×C43⋊C8—41no—
127C2×C43⋊C8—41no—
128C2×C43⋊C8—41no—
129C2×C43⋊C8—81no—
130#10621872—44no—
131C8×D43—44no—
132C23×C43#12311yescharacteristic
133C22×D43—21no—
134Q8×C43—42no—
135Q8×C43—42no—
136Q8×C43—81no—
137Q8×C43—81no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—41no—
141C2×C4×C43—42no—
142C2×C4×C43—81no—
143C2×C4×C43—81no—
144C2×C4×C43C2×C22⋊C411yescharacteristic
145C2×C4×C43C4×D411yescharacteristic
146C2×C4×C43C4×D411yescharacteristic
147C2×C4×C43#12011yescharacteristic
148C2×C4×C43#12111yescharacteristic
149C2×C4×C43#12111yescharacteristic
150C2×C4×C43C2×D811yescharacteristic
151C2×C4×C43C2×SD1611yescharacteristic
152C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C43#13711yescharacteristic
154C22⋊D43—22no—
155C22⋊D43—22no—
156C2×Dic43—21no—
157C2×Dic43—21no—
158C2×Dic43—21no—
159D172—21no—
160D172#10212yes—
161C4×D43—22no—
162C4×D43—22no—
163C4×D43—41no—
164C4×D43—41no—
165C4×D43—81no—
166Dic86—21no—
167Dic86#10212yes—
168C8×C43—42no—
169C8×C43—81no—
170C43⋊C8—42no—
171C43⋊C8—41no—
172C43⋊C8—41no—
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×C43—82no—
187C4×C43C2×#10211yescharacteristic
188C4×C43#41711yescharacteristic
189C4×C43#44711yescharacteristic
190C4×C43#44811yescharacteristic
191C4×C43#47111yescharacteristic
192C4×C43#47311yescharacteristic
193Dic43—22no—
194Dic43—41no—
195Dic43—41no—
196#3039—431no—
197#2906—431no—
198#1546D4311yescharacteristic, complemented
199C2×#332—431no—
200#1477—431no—
201#1301—431no—
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⋊Q8C2×D4311yescharacteristic
212C4×#41—431no—
213#462—432no—
214#462—861no—
215#461—432no—
216#461—861no—
217#431C2×D4311yescharacteristic
218#424—861no—
219#424—862no—
220#423—431no—
221#423—861no—
222#423C2×D4311yescharacteristic
223C2×C4⋊C8—431no—
224C2×C4⋊C8—431no—
225C2×C4⋊C8—861no—
226#419—861no—
227#332—22no—
228#332—861no—
229#332—861no—
230Q8⋊C8—861no—
231D4⋊C8—861no—
232C43#917111yescharacteristic, complemented, Sylow
233C2×#41—431no—
234C22×Q8—21no—
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—862no—
245C22×C8—861no—
246C22×C8—861no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8C4×D4312yes—
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—21no—
260C2×C4⋊C4—21no—
261C2×C42—861no—
262C2×C42C22×D4311yescharacteristic
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—432no—
266C4⋊C8—431no—
267C4⋊C8—431no—
268C4⋊C8—862no—
269C4⋊C8—862no—
270C4⋊C8—861no—
271C4⋊C8—861no—
272C4⋊C8—861no—
273C4⋊C8—861no—
274C4⋊C8C22⋊D4312yes—
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—22no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—431no—
290C2×D4—431no—
291C2×D4—861no—
292C22×C4—41no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4#1062189811yescharacteristic
297C22×C4D4×D4311yescharacteristic
298C22×C4#1062190011yescharacteristic
299Q16—1724no—
300SD16—1724no—
301M16—41no—
302M16—41no—
303M16—1724no—
304M16—1721no—
305M16—1721no—
306C2×C8—22no—
307C2×C8—41no—
308C2×C8—862no—
309C2×C8—861no—
310C2×C8—861no—
311C2×C8—3441no—
312C2×C8—1724no—
313C2×C8—1721no—
314C2×C8—1721no—
315C2×C8—1721no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—431no—
321C4⋊C4—431no—
322C4⋊C4—861no—
323C4⋊C4—861no—
324C22⋊C4—861no—
325C22⋊C4—861no—
326C22⋊C4—861no—
327C42—861no—
328C42—861no—
329C42—861no—
330C42C2×C4×D4311yescharacteristic
331C42D4×D4311yescharacteristic
332C42D4×D4311yescharacteristic
333C42C2×C22⋊D4311yescharacteristic
334C23—861no—
335C23#1306330711yescharacteristic
336Q8—42no—
337Q8—42no—
338Q8—81no—
339Q8—81no—
340Q8—432no—
341Q8—861no—
342D4—432no—
343D4—862no—
344D4—862no—
345D4—861no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—861no—
353C2×C4—862no—
354C2×C4—862no—
355C2×C4—861no—
356C2×C4—861no—
357C2×C4—3441no—
358C2×C4—1721no—
359C2×C4—1721no—
360C2×C4C22⋊C4×D4311yescharacteristic
361C2×C4(C22⋊D43)⋊C411yescharacteristic
362C2×C4C4×C22⋊D4311yescharacteristic
363C2×C4#1306329311yescharacteristic
364C2×C4#1306329611yescharacteristic
365C2×C4#1306329811yescharacteristic
366C2×C4D8×D4311yescharacteristic
367C2×C4SD16×D4311yescharacteristic
368C2×C4#1306334911yescharacteristic
369C2×C4#1306335411yescharacteristic
370C8—42no—
371C8—81no—
372C8—3441no—
373C8—1722no—
374C8—1721no—
375C8—1721no—
376C22—21no—
377C22—21no—
378C22—862no—
379C22—1721no—
380C22—1721no—
381C22#1458277511yescharacteristic
382C22#1458321111yescharacteristic
383C22#1458321611yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—82no—
388C4—862no—
389C4—1721no—
390C4—1721no—
391C4#102×D4311yescharacteristic
392C4#1458289711yescharacteristic
393C4#1458303111yescharacteristic
394C4#1458303611yescharacteristic
395C4#1458316511yescharacteristic
396C4#1458317311yescharacteristic
397C2—21no—
398C2—21no—
399C2—1722no—
400C2#1913490911yescharacteristic
401C2#1913506511yescharacteristic
402C2#1913510711yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1546C2
socleC22×C43#386
prime radicalC2×#10621898D4
cosocleC2×C42×C43C23
hypercenter#1546D43
hypocenterC43#9171
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
3. C2×#14582645C2semidirect
5. #19132491C2semidirect
6. #19132469C2semidirect
7. C43×#1546C2semidirect
198. #1546D43semidirect
232. C43#9171semidirect

Maximal subgroups

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

subgroupindex
#191440782
#191431642
C2×#145826452
#191329832
#191324912
#191324692
C43×#15462
#917143