Finite Group Databasebeta

← #24985160

Subgroups — #24985160

Order 11008.

500 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142946C211yesmaximal, characteristic
2#19134662C211yesmaximal, characteristic
3#19134356C211yesmaximal, characteristic
4#19132419C211yesmaximal, characteristic, complemented
5#19132418C211yesmaximal, characteristic, complemented
6#19132417C211yesmaximal, characteristic, complemented
7C43×#1271C211yesmaximal, characteristic, complemented
8C2×#13063324C411yescharacteristic
9C2×#13063303—21no—
10C2×C42×D43C2211yescharacteristic
11C2×(C2×D43)⋊C8—21no—
12C2×(C2×D43)⋊C8—21no—
13C2×#13063235—21no—
14#14582803—21no—
15#14582797C2211yescharacteristic
16#14582794—21no—
17#14582768C411yescharacteristic
18#14582758—21no—
19#14582756C411yescharacteristic
20#14582756C411yescharacteristic
21#14582654C2211yescharacteristic
22#14582654C2211yescharacteristic
23#14582653—21no—
24C43×#389C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×Dic86—21no—
28C22×C4×D43C2×C411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C22×C43⋊C8—21no—
32C22×C43⋊C8—21no—
33#13063324—42no—
34#13063303—42no—
35#13063303—42no—
36C2×C4⋊Dic43C2×C411yescharacteristic
37C2×C4⋊Dic43C2×C411yescharacteristic
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×C4×Dic43C2×C411yescharacteristic
45C2×C4×Dic43D411yescharacteristic
46C2×C4×Dic43D411yescharacteristic
47C42×D43—42no—
48(C2×D43)⋊C8—24no—
49(C2×D43)⋊C8—42no—
50#13063235—42no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C22×C8×C43—21no—
55C22×C8×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43C2×C411yescharacteristic
58C2×C4⋊C4×C43C2×C411yescharacteristic
59C2×C42×C43C2311yescharacteristic
60#95×C43—21no—
61C23×D43C22⋊C411yescharacteristic
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43C22×C411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—21no—
68C22×Dic43—21no—
69C22×Dic43C22⋊C411yescharacteristic
70C22×Dic43C22⋊C411yescharacteristic
71C22×Dic43C22⋊C411yescharacteristic
72C2×C4×D43—21no—
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43—22no—
79C2×C4×D43—22no—
80C2×C4×D43—22no—
81C2×C4×D43—41no—
82C2×C4×D43—41no—
83C2×C4×D43—41no—
84C2×Dic86—42no—
85C2×Dic86—42no—
86C2×Dic86—42no—
87C2×C8×C43—22no—
88C2×C8×C43—41no—
89C2×C8×C43—41no—
90C2×C8×C43—41no—
91C2×C8×C43—41no—
92C2×C8×C43—41no—
93C4⋊C4×C43—21no—
94C4⋊C4×C43—21no—
95C4⋊C4×C43—41no—
96C4⋊C4×C43—41no—
97C4⋊C4×C43—41no—
98C42×C43—41no—
99(C2×D43)⋊C4—42no—
100(C2×D43)⋊C4—42no—
101C4⋊Dic43—21no—
102C4⋊Dic43—21no—
103C4⋊Dic43—41no—
104Dic43⋊C4—42no—
105Dic43⋊C4—42no—
106Dic43⋊C4—41no—
107Dic43⋊C4—41no—
108Dic43⋊C4—42no—
109C4×Dic43—22no—
110C4×Dic43—22no—
111C4×Dic43—41no—
112C2×C43⋊C8—22no—
113C2×C43⋊C8—41no—
114C2×C43⋊C8—41no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—41no—
117C2×C43⋊C8—41no—
118C23×C43C2×C22⋊C411yescharacteristic
119C22×D43—21no—
120C22×D43—21no—
121C22×D43—21no—
122C22×D43—21no—
123C22×D43—21no—
124C22×D43—21no—
125C22×D43#10112yes—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43—41no—
136C2×C4×C43—41no—
137C2×C4×C43—41no—
138C2×C4×C43#13111yescharacteristic
139C2×C4×C43#13111yescharacteristic
140C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C43#13711yescharacteristic
143C2×C4×C43#13711yescharacteristic
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43—41no—
156C2×Dic43—41no—
157C2×Dic43#9912yes—
158C2×Dic43#10412yes—
159C4×D43—42no—
160C4×D43—42no—
161C4×D43—42no—
162C4×D43—42no—
163C4×D43—42no—
164C4×D43—42no—
165Dic86—84no—
166C8×C43—42no—
167C8×C43—81no—
168C43⋊C8—42no—
169C43⋊C8—81no—
170#7705—431nomaximal, Sylow
171C22×C43#40811yescharacteristic
172C22×C43C2×#9911yescharacteristic
173C22×C43C2×#10111yescharacteristic
174C22×C43#41811yescharacteristic
175C22×C43#41911yescharacteristic
176C22×C43C2×#10411yescharacteristic
177C22×C43#42111yescharacteristic
178C2×D43—22no—
179C2×D43—22no—
180C2×D43—22no—
181C2×D43—41no—
182C2×D43—41no—
183C2×D43—41no—
184C2×D43—41no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—21no—
188C4×C43—21no—
189C4×C43—21no—
190C4×C43—21no—
191C4×C43—81no—
192C4×C43—81no—
193Dic43—22no—
194Dic43—22no—
195Dic43—41no—
196Dic43—81no—
197Dic43—81no—
198#2857—431no—
199#1817—431no—
200#1749—431no—
201#1271—431no—
202#1271—431no—
203#1271—431no—
204#1271D4311yescharacteristic, complemented
205C2×C43#147211yescharacteristic
206C2×C43#148511yescharacteristic
207C2×C43#149611yescharacteristic
208C2×C43#150711yescharacteristic
209C2×C43#151111yescharacteristic
210C2×C43#153111yescharacteristic
211C2×C43#155611yescharacteristic
212D43—42no—
213C2×C4⋊Q8—431no—
214C2×C22⋊Q8—861no—
215C22×C42—431no—
216C2×C22⋊C8—861no—
217C2×C22⋊C8—861no—
218C2×#97—861no—
219#391—861no—
220#389—431no—
221#389—861no—
222#389C2×D4311yescharacteristic
223#384—431no—
224#380—431no—
225#380—431no—
226#380—861no—
227#336—431no—
228#336—431no—
229#336—861no—
230#336C2×D4311yescharacteristic
231#336C2×D4311yescharacteristic
232C43#770511yescharacteristic, complemented, Sylow
233C22×Q8—861no—
234C23×C4—431no—
235C23×C4—431no—
236C23×C4—431no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—861no—
240C22×C8—861no—
241C4⋊Q8—1722no—
242C22⋊Q8—1722no—
243C22⋊Q8—1722no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—431no—
246C2×C4⋊C4—431no—
247C2×C4⋊C4—861no—
248C2×C4⋊C4—861no—
249C2×C4⋊C4—861no—
250C2×C4⋊C4—861no—
251C2×C4⋊C4C4×D4311yescharacteristic
252C2×C4⋊C4C4×D4311yescharacteristic
253C2×C22⋊C4—861no—
254C2×C22⋊C4—861no—
255C2×C42—431no—
256C2×C42—431no—
257C2×C42—431no—
258C2×C42—1722no—
259C2×C42C22×D4311yescharacteristic
260C22⋊C8—864no—
261C22⋊C8—1722no—
262#97—1722no—
263#95—21no—
264#95—861no—
265#95—861no—
266#95—861no—
267C24—431no—
268C2×Q8—1722no—
269C2×Q8—1722no—
270C2×Q8—1722no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—431no—
274C22×C4—431no—
275C22×C4—431no—
276C22×C4—862no—
277C22×C4—862no—
278C22×C4—862no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4—861no—
284C22×C4—861no—
285C22×C4—861no—
286C22×C4—861no—
287C22×C4—1721no—
288C22×C4—1721no—
289C22×C4—1721no—
290C22×C4C2×C4×D4311yescharacteristic
291C22×C4D4×D4311yescharacteristic
292C22×C4D4×D4311yescharacteristic
293C2×C8—22no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—862no—
300C2×C8—1721no—
301C2×C8—1721no—
302C2×C8—1721no—
303C2×C8—1721no—
304C2×C8—1721no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—861no—
311C4⋊C4—861no—
312C4⋊C4—1721no—
313C4⋊C4—1722no—
314C4⋊C4—1722no—
315C4⋊C4—1722no—
316C4⋊C4—1721no—
317C4⋊C4—1721no—
318C22⋊C4—1722no—
319C22⋊C4—1722no—
320C42—41no—
321C42—862no—
322C42—862no—
323C42—1721no—
324C23—432no—
325C23—861no—
326C23—861no—
327C23—861no—
328C23—861no—
329C23—861no—
330C23—861no—
331C23C22⋊C4×D4311yescharacteristic
332Q8—3444no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—432no—
346C2×C4—432no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—861no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—1722no—
355C2×C4—1722no—
356C2×C4—1722no—
357C2×C4—1722no—
358C2×C4—1722no—
359C2×C4—1722no—
360C2×C4—1721no—
361C2×C4—1721no—
362C2×C4—1721no—
363C2×C4—1721no—
364C2×C4—1721no—
365C2×C4—1721no—
366C2×C4#1306333111yescharacteristic
367C2×C4#1306333311yescharacteristic
368C2×C4#1306334911yescharacteristic
369C2×C4#1306335211yescharacteristic
370C2×C4#1306335411yescharacteristic
371C2×C4#1306335711yescharacteristic
372C8—42no—
373C8—81no—
374C8—3441no—
375C8—1722no—
376C22—862no—
377C22—862no—
378C22—862no—
379C22—1721no—
380C22—1721no—
381C22—1721no—
382C22—1721no—
383C22#1458286411yescharacteristic
384C22#99×D4311yescharacteristic
385C22#101×D4311yescharacteristic
386C22#1458290211yescharacteristic
387C22#1458290611yescharacteristic
388C22#104×D4311yescharacteristic
389C22#1458291411yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—81no—
397C4—81no—
398C4—862no—
399C4—862no—
400C4—3441no—
401C4—3441no—
402C4—1721no—
403C2—1722no—
404C2#1913295711yescharacteristic
405C2#1913301411yescharacteristic
406C2#1913306211yescharacteristic
407C2#1913310911yescharacteristic
408C2#1913312611yescharacteristic
409C2#1913320811yescharacteristic
410C2#1913331011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1271C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1271D43
hypocenterC43#7705
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
4. #19132419C2semidirect
5. #19132418C2semidirect
6. #19132417C2semidirect
7. C43×#1271C2semidirect
204. #1271D43semidirect
232. C43#7705semidirect

Maximal subgroups

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

subgroupindex
#191429462
#191346622
#191343562
#191324192
#191324182
#191324172
C43×#12712
#770543