Finite Group Databasebeta

← #24984896

Subgroups — #24984896

Order 11008.

490 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 101 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#19137076C211yesmaximal, characteristic
2#19134662C211yesmaximal, characteristic
3#19134662C211yesmaximal, characteristic
4#19132419C211yesmaximal, characteristic, complemented
5#19132418C211yesmaximal, characteristic, complemented
6#19132417C211yesmaximal, characteristic, complemented
7C43×#1271C211yesmaximal, characteristic, complemented
8C2×#13063283C411yescharacteristic
9C2×#13063283C411yescharacteristic
10C2×C42×D43C2211yescharacteristic
11C2×(C2×D43)⋊C8—21no—
12C2×(C2×D43)⋊C8—21no—
13#14582798C411yescharacteristic
14#14582797C2211yescharacteristic
15#14582795C411yescharacteristic
16#14582773—21no—
17#14582770—21no—
18C4⋊C4×Dic43—21no—
19#14582750—21no—
20#14582654C2211yescharacteristic
21#14582654C2211yescharacteristic
22#14582653—21no—
23#14582653—21no—
24C43×#389C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×C4×D43C2×C411yescharacteristic
28C22×C4×D43D411yescharacteristic
29C22×C4×D43D411yescharacteristic
30C22×C43⋊C8—21no—
31C22×C43⋊C8—21no—
32#13063283—22no—
33#13063283—22no—
34#13063283—42no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43C2×C411yescharacteristic
37C2×C4⋊Dic43C2×C411yescharacteristic
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×C4×Dic43—21no—
43C2×C4×Dic43—21no—
44C2×C4×Dic43C2×C411yescharacteristic
45C2×C4×Dic43D411yescharacteristic
46C2×C4×Dic43D411yescharacteristic
47C42×D43—42no—
48(C2×D43)⋊C8—42no—
49(C2×D43)⋊C8—42no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C22×C8×C43—21no—
54C22×C8×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43C2×C411yescharacteristic
57C2×C4⋊C4×C43C2×C411yescharacteristic
58C2×C42×C43C2311yescharacteristic
59#95×C43—21no—
60C23×D43C22⋊C411yescharacteristic
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43C22×C411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×Dic43—21no—
67C22×Dic43—21no—
68C22×Dic43C22⋊C411yescharacteristic
69C22×Dic43C22⋊C411yescharacteristic
70C22×Dic43C22⋊C411yescharacteristic
71C2×C4×D43—21no—
72C2×C4×D43—21no—
73C2×C4×D43—22no—
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×C8×C43—41no—
84C2×C8×C43—41no—
85C2×C8×C43—41no—
86C2×C8×C43—41no—
87C2×C8×C43—41no—
88C2×C8×C43—41no—
89C4⋊C4×C43—21no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—41no—
93C4⋊C4×C43M1612yes—
94C42×C43—41no—
95(C2×D43)⋊C4—24no—
96(C2×D43)⋊C4—42no—
97C4⋊Dic43—21no—
98C4⋊Dic43—42no—
99C4⋊Dic43—41no—
100C4⋊Dic43M1612yes—
101Dic43⋊C4—42no—
102Dic43⋊C4—41no—
103Dic43⋊C4—41no—
104C4×Dic43—24no—
105C4×Dic43—41no—
106C4×Dic43—41no—
107C4×Dic43—41no—
108C4×Dic43—42no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8—41no—
112C2×C43⋊C8—41no—
113C2×C43⋊C8—41no—
114C2×C43⋊C8—41no—
115C23×C43C2×C22⋊C411yescharacteristic
116C22×D43—21no—
117C22×D43—21no—
118C22×D43—21no—
119C22×D43—21no—
120C22×D43—21no—
121C22×D43—21no—
122C22×D43#9912yes—
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—22no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—41no—
135C2×C4×C43C2×M1611yescharacteristic
136C2×C4×C43C2×M1611yescharacteristic
137C2×C4×C43#13511yescharacteristic
138C2×C4×C43#13511yescharacteristic
139C2×C4×C43#13511yescharacteristic
140C2×C4×C43#13511yescharacteristic
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—22no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152C2×Dic43—41no—
153C2×Dic43—41no—
154C2×Dic43—41no—
155C2×Dic43#10112yes—
156C4×D43—24no—
157C4×D43—24no—
158C4×D43—42no—
159C4×D43—42no—
160C4×D43—42no—
161C4×D43—42no—
162C8×C43—81no—
163C8×C43—81no—
164C43⋊C8—81no—
165C43⋊C8—81no—
166#7646—431nomaximal, Sylow
167C22×C43#40711yescharacteristic
168C22×C43C2×#9911yescharacteristic
169C22×C43C2×#10111yescharacteristic
170C22×C43#41611yescharacteristic
171C22×C43#41611yescharacteristic
172C22×C43#42111yescharacteristic
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—42no—
188C4×C43—81no—
189Dic43—22no—
190Dic43—42no—
191Dic43—41no—
192Dic43—41no—
193Dic43—81no—
194#2296—431no—
195#1817—431no—
196#1817—431no—
197#1271—431no—
198#1271—431no—
199#1271—431no—
200#1271D4311yescharacteristic, complemented
201C2×C43#146311yescharacteristic
202C2×C43#148811yescharacteristic
203C2×C43#148811yescharacteristic
204C2×C43#151611yescharacteristic
205C2×C43#151611yescharacteristic
206C2×C43#153711yescharacteristic
207C2×C43#154411yescharacteristic
208D43—42no—
209C2×#117—431no—
210C2×#117—431no—
211C22×C42—431no—
212C2×C22⋊C8—861no—
213C2×C22⋊C8—861no—
214#389—431no—
215#389—431no—
216#389—431no—
217#389C2×D4311yescharacteristic
218#385—861no—
219#385—861no—
220C4×C4⋊C4—861no—
221C4×C4⋊C4—861no—
222#336—431no—
223#336—431no—
224#336—861no—
225#336—861no—
226#336C2×D4311yescharacteristic
227#336C2×D4311yescharacteristic
228C43#764611yescharacteristic, complemented, Sylow
229C23×C4—431no—
230C23×C4—431no—
231C23×C4—431no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—861no—
235C22×C8—861no—
236#117—862no—
237#117—862no—
238#117—1722no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—431no—
241C2×C4⋊C4—431no—
242C2×C4⋊C4—861no—
243C2×C4⋊C4—861no—
244C2×C4⋊C4—861no—
245C2×C4⋊C4C4×D4311yescharacteristic
246C2×C4⋊C4C4×D4311yescharacteristic
247C2×C22⋊C4—861no—
248C2×C22⋊C4—861no—
249C2×C42—431no—
250C2×C42—431no—
251C2×C42—431no—
252C2×C42—861no—
253C2×C42—861no—
254C2×C42—1722no—
255C2×C42C22×D4311yescharacteristic
256C22⋊C8—1722no—
257C22⋊C8—1722no—
258#95—21no—
259#95—861no—
260#95—861no—
261#95—861no—
262C24—431no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—431no—
266C22×C4—431no—
267C22×C4—431no—
268C22×C4—862no—
269C22×C4—862no—
270C22×C4—862no—
271C22×C4—862no—
272C22×C4—861no—
273C22×C4—861no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4—861no—
278C22×C4—861no—
279C22×C4—861no—
280C22×C4—1721no—
281C22×C4—1721no—
282C22×C4C2×C4×D4311yescharacteristic
283C22×C4D4×D4311yescharacteristic
284C22×C4D4×D4311yescharacteristic
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—1721no—
292C2×C8—1721no—
293C2×C8—1721no—
294C2×C8—1721no—
295C2×C8—1721no—
296C2×C8—1721no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—432no—
302C4⋊C4—861no—
303C4⋊C4—1721no—
304C4⋊C4—1722no—
305C4⋊C4—1722no—
306C4⋊C4—1721no—
307C4⋊C4—1721no—
308C4⋊C4#1062187212yes—
309C22⋊C4—864no—
310C22⋊C4—1722no—
311C42—41no—
312C42—864no—
313C42—1721no—
314C42—1721no—
315C42—1721no—
316C42—1722no—
317C23—432no—
318C23—861no—
319C23—861no—
320C23—861no—
321C23—861no—
322C23—861no—
323C23—861no—
324C23C22⋊C4×D4311yescharacteristic
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—432no—
338C2×C4—864no—
339C2×C4—864no—
340C2×C4—861no—
341C2×C4—861no—
342C2×C4—862no—
343C2×C4—861no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—1722no—
350C2×C4—1722no—
351C2×C4—1722no—
352C2×C4—1722no—
353C2×C4—1721no—
354C2×C4—1721no—
355C2×C4—1721no—
356C2×C4—1721no—
357C2×C4—1721no—
358C2×C4M16×D4311yescharacteristic
359C2×C4C2×#1062187211yescharacteristic
360C2×C4#1306334411yescharacteristic
361C2×C4#1306334611yescharacteristic
362C2×C4#1306334611yescharacteristic
363C2×C4#1306334811yescharacteristic
364C8—81no—
365C8—81no—
366C8—3441no—
367C8—3441no—
368C22—862no—
369C22—862no—
370C22—862no—
371C22—1721no—
372C22—1721no—
373C22—1721no—
374C22—1721no—
375C22#1458286111yescharacteristic
376C22#99×D4311yescharacteristic
377C22#101×D4311yescharacteristic
378C22#1458289211yescharacteristic
379C22#1458289411yescharacteristic
380C22#1458291411yescharacteristic
381C22#1458291411yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—42no—
389C4—81no—
390C4—862no—
391C4—3441no—
392C4—1722no—
393C4—1721no—
394C4—1721no—
395C2—1722no—
396C2#1913292311yescharacteristic
397C2#1913302611yescharacteristic
398C2#1913302811yescharacteristic
399C2#1913314811yescharacteristic
400C2#1913315011yescharacteristic
401C2#1913323111yescharacteristic
402C2#1913325811yescharacteristic
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#7646
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
200. #1271D43semidirect
228. C43#7646semidirect

Maximal subgroups

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

subgroupindex
#191370762
#191346622
#191324192
#191324182
#191324172
C43×#12712
#764643