Finite Group Databasebeta

← #24985143

Subgroups — #24985143

Order 11008.

470 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 95 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#19142936C211yesmaximal, characteristic
2#19134574C211yesmaximal, characteristic
3#19134356C211yesmaximal, characteristic
4#19132421C211yesmaximal, characteristic, complemented
5#19132419C211yesmaximal, characteristic, complemented
6#19132417C211yesmaximal, characteristic, complemented
7C43×#1272C211yesmaximal, characteristic, complemented
8C2×#13063301C411yescharacteristic
9C2×C42×D43C2211yescharacteristic
10C2×Dic43⋊C8—21no—
11C2×(C2×D43)⋊C8—21no—
12C2×(C2×D43)⋊C8—21no—
13C2×#13063235—21no—
14#14582806C411yescharacteristic
15#14582798C411yescharacteristic
16#14582797C2211yescharacteristic
17#14582782—21no—
18#14582781—21no—
19#14582773—21no—
20#14582761—21no—
21#14582756C411yescharacteristic
22#14582654C2211yescharacteristic
23#14582654C2211yescharacteristic
24C43×#391C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×C4×D43C2×C411yescharacteristic
28C22×C4×D43D411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C22×C43⋊C8—21no—
31C22×C43⋊C8—21no—
32#13063301—42no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43C2×C411yescharacteristic
35C2×C4⋊Dic43C2×C411yescharacteristic
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×C4×Dic43C2×C411yescharacteristic
41C2×C4×Dic43D411yescharacteristic
42C2×C4×Dic43D411yescharacteristic
43C42×D43—42no—
44Dic43⋊C8—42no—
45(C2×D43)⋊C8—24no—
46(C2×D43)⋊C8—42no—
47#13063235—42no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C22×Q8×C43C2×C411yescharacteristic
54C22×C8×C43—21no—
55C22×C8×C43—21no—
56C2×C4⋊C4×C43C2×C411yescharacteristic
57C2×C42×C43C2311yescharacteristic
58#95×C43—21no—
59#95×C43—21no—
60C23×D43C22⋊C411yescharacteristic
61C2×Q8×C43—21no—
62C2×Q8×C43—21no—
63C2×Q8×C43—41no—
64C2×Q8×C43—41no—
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43C22×C411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43C22⋊C411yescharacteristic
73C22×Dic43C22⋊C411yescharacteristic
74C22×Dic43C22⋊C411yescharacteristic
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—22no—
82C2×C4×D43—22no—
83C2×C4×D43—41no—
84C2×C4×D43—41no—
85C2×C4×D43—41no—
86C2×C4×D43—41no—
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—41no—
94C42×C43—41no—
95(C2×D43)⋊C4—42no—
96(C2×D43)⋊C4—42no—
97C4⋊Dic43—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43—42no—
100C4⋊Dic43—41no—
101Dic43⋊C4—41no—
102Dic43⋊C4—41no—
103Dic43⋊C4—42no—
104C4×Dic43—22no—
105C4×Dic43—22no—
106C4×Dic43—41no—
107C2×C43⋊C8—22no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8—41no—
112C2×C43⋊C8—41no—
113C23×C43C2×C22⋊C411yescharacteristic
114C22×D43—21no—
115C22×D43—21no—
116C22×D43—21no—
117C22×D43—21no—
118C22×D43—21no—
119C22×D43—21no—
120C22×D43#10412yes—
121Q8×C43—81no—
122Q8×C43—81no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43#13111yescharacteristic
136C2×C4×C43#13111yescharacteristic
137C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C43#13711yescharacteristic
139C2×C4×C43#13711yescharacteristic
140C2×C4×C43#13711yescharacteristic
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43#9912yes—
156C4×D43—42no—
157C4×D43—42no—
158C4×D43—42no—
159C4×D43—42no—
160C4×D43—42no—
161C4×D43—42no—
162C8×C43—42no—
163C8×C43—81no—
164C43⋊C8—42no—
165C43⋊C8—81no—
166#7701—431nomaximal, Sylow
167C22×C43#40811yescharacteristic
168C22×C43C2×#9911yescharacteristic
169C22×C43#41311yescharacteristic
170C22×C43#41711yescharacteristic
171C22×C43#41911yescharacteristic
172C22×C43C2×#10411yescharacteristic
173C22×C43#42111yescharacteristic
174C2×D43—22no—
175C2×D43—22no—
176C2×D43—22no—
177C2×D43—41no—
178C2×D43—41no—
179C2×D43—41no—
180C2×D43—41no—
181C4×C43—21no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43—21no—
187C4×C43—81no—
188C4×C43—81no—
189Dic43—22no—
190Dic43—41no—
191Dic43—41no—
192Dic43—81no—
193Dic43—81no—
194#2855—431no—
195#1797—431no—
196#1749—431no—
197#1272—431no—
198#1272D4311yescharacteristic, complemented
199#1271—431no—
200#1271—431no—
201C2×C43#146811yescharacteristic
202C2×C43#148311yescharacteristic
203C2×C43#149711yescharacteristic
204C2×C43#150811yescharacteristic
205C2×C43#151311yescharacteristic
206C2×C43#153211yescharacteristic
207C2×C43#155911yescharacteristic
208D43—42no—
209C2×C22⋊Q8—431no—
210C22×C42—431no—
211C2×C4⋊C8—861no—
212C2×C22⋊C8—861no—
213C2×C22⋊C8—861no—
214C2×#97—861no—
215#391—431no—
216#391C2×D4311yescharacteristic
217#389—431no—
218#389—431no—
219#387—861no—
220#387—861no—
221#385—861no—
222#381—861no—
223#380—431no—
224#336—431no—
225#336—431no—
226#336C2×D4311yescharacteristic
227#336C2×D4311yescharacteristic
228C43#770111yescharacteristic, complemented, Sylow
229C22×Q8C4×D4311yescharacteristic
230C23×C4—431no—
231C23×C4—431no—
232C23×C4—431no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—861no—
236C22×C8—861no—
237C22⋊Q8—1722no—
238C2×C4⋊C4—431no—
239C2×C4⋊C4—431no—
240C2×C4⋊C4—861no—
241C2×C4⋊C4—861no—
242C2×C4⋊C4—861no—
243C2×C4⋊C4C4×D4311yescharacteristic
244C2×C22⋊C4—861no—
245C2×C22⋊C4—861no—
246C2×C42—431no—
247C2×C42—431no—
248C2×C42—431no—
249C2×C42—1722no—
250C2×C42C22×D4311yescharacteristic
251C4⋊C8—1722no—
252C22⋊C8—864no—
253C22⋊C8—1722no—
254#97—1722no—
255#95—21no—
256#95—21no—
257#95—861no—
258#95—861no—
259#95—861no—
260#95—861no—
261#95—861no—
262C24—431no—
263C2×Q8—21no—
264C2×Q8—21no—
265C2×Q8—41no—
266C2×Q8—41no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—431no—
270C22×C4—431no—
271C22×C4—431no—
272C22×C4—862no—
273C22×C4—862no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4—861no—
278C22×C4—861no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4—1721no—
283C22×C4—1721no—
284C22×C4—1721no—
285C22×C4—1721no—
286C22×C4C2×C4×D4311yescharacteristic
287C22×C4D4×D4311yescharacteristic
288C22×C4D4×D4311yescharacteristic
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—862no—
296C2×C8—1721no—
297C2×C8—1721no—
298C2×C8—1721no—
299C2×C8—1721no—
300C2×C8—1721no—
301C4⋊C4—41no—
302C4⋊C4—861no—
303C4⋊C4—861no—
304C4⋊C4—1721no—
305C4⋊C4—1722no—
306C4⋊C4—1722no—
307C4⋊C4—1721no—
308C4⋊C4—1721no—
309C22⋊C4—1722no—
310C22⋊C4—1722no—
311C42—41no—
312C42—862no—
313C42—862no—
314C42—1721no—
315C23—432no—
316C23—861no—
317C23—861no—
318C23—861no—
319C23—861no—
320C23—861no—
321C23—861no—
322C23C22⋊C4×D4311yescharacteristic
323Q8—81no—
324Q8—81no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—432no—
338C2×C4—861no—
339C2×C4—861no—
340C2×C4—861no—
341C2×C4—861no—
342C2×C4—861no—
343C2×C4—861no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—1722no—
347C2×C4—1722no—
348C2×C4—1722no—
349C2×C4—1722no—
350C2×C4—1722no—
351C2×C4—1722no—
352C2×C4—1721no—
353C2×C4—1721no—
354C2×C4—1721no—
355C2×C4—1721no—
356C2×C4—1721no—
357C2×C4—1721no—
358C2×C4#1306333111yescharacteristic
359C2×C4#1306333311yescharacteristic
360C2×C4#1306335211yescharacteristic
361C2×C4#1306335411yescharacteristic
362C2×C4#1306335711yescharacteristic
363C2×C4#1306335711yescharacteristic
364C8—42no—
365C8—81no—
366C8—3441no—
367C8—1722no—
368C22—862no—
369C22—862no—
370C22—862no—
371C22—1721no—
372C22—1721no—
373C22—1721no—
374C22—1721no—
375C22#1458286411yescharacteristic
376C22#99×D4311yescharacteristic
377C22#1458288011yescharacteristic
378C22#1458289911yescharacteristic
379C22#1458290611yescharacteristic
380C22#104×D4311yescharacteristic
381C22#1458291411yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—81no—
389C4—81no—
390C4—862no—
391C4—3441no—
392C4—3441no—
393C4—1721no—
394C4—1721no—
395C2—1722no—
396C2#1913294011yescharacteristic
397C2#1913300711yescharacteristic
398C2#1913306611yescharacteristic
399C2#1913311311yescharacteristic
400C2#1913313711yescharacteristic
401C2#1913321211yescharacteristic
402C2#1913332211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1272C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1272D43
hypocenterC43#7701
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
4. #19132421C2semidirect
5. #19132419C2semidirect
6. #19132417C2semidirect
7. C43×#1272C2semidirect
198. #1272D43semidirect
228. C43#7701semidirect

Maximal subgroups

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

subgroupindex
#191429362
#191345742
#191343562
#191324212
#191324192
#191324172
C43×#12722
#770143