Finite Group Databasebeta

← #25007723

Subgroups — #25007723

Order 11008.

452 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 79 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#19138905C211yesmaximal, characteristic
2#19134582C211yesmaximal, characteristic
3#19132914C211yesmaximal, characteristic
4#19132620C211yesmaximal, characteristic, complemented
5#19132619C211yesmaximal, characteristic, complemented
6#19132618C211yesmaximal, characteristic, complemented
7C43×#1352C211yesmaximal, characteristic, complemented
8C2×(C22⋊D43)⋊C4C2211yescharacteristic
9C2×C4⋊C4×D43C411yescharacteristic, complemented
10#14582949—21no—
11C2×#13063239—21no—
12#14582839C411yescharacteristic, complemented
13#14582837C411yescharacteristic, complemented
14#14582835C2211yescharacteristic
15#14582794—21no—
16#14582775—21no—
17#14582770—21no—
18#14582758C411yescharacteristic, complemented
19#14582757—21no—
20#14582757—21no—
21#14582666C2211yescharacteristic
22#14582623C2211yescharacteristic
23#14582622—21no—
24C43×#399C2211yescharacteristic
25C43×#342C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C22×C22⋊D43D411yescharacteristic
28C23×Dic43D411yescharacteristic
29C22×C4×D43—21no—
30C22×C4×D43C2×C411yescharacteristic
31(C22⋊D43)⋊C4—41no—
32(C22⋊D43)⋊C4—41no—
33C2×C4⋊Dic43C2×C411yescharacteristic
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—41no—
38C2×Dic43⋊C4C2×C411yescharacteristic
39C4⋊C4×D43—41no—
40C4⋊C4×D43—41no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4D411yescharacteristic
45C2×C4×Dic43D411yescharacteristic
46Dic43⋊C8—41no—
47#13063239—42no—
48C22⋊(C43⋊C8)—21no—
49C8×Dic43—41no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—41no—
55C43⋊#95C2×C411yescharacteristic
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43C2×C411yescharacteristic
58C2×C22⋊C4×C43—21no—
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43C2311yescharacteristic
61C22⋊C8×C43—21no—
62#95×C43C2×C411yescharacteristic
63C24×C43C2×D411yescharacteristic
64C23×D43C22⋊C411yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—41no—
68C22×C4×C43C22×C411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C2×C22⋊D43—41no—
71C2×C22⋊D43—41no—
72C2×C22⋊D43SD1612yes—
73C2×C22⋊D43Q1612yes—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—41no—
79C22×Dic43—42no—
80C22×Dic43C22⋊C411yescharacteristic
81C22×Dic43C22⋊C411yescharacteristic
82C22×Dic43C22⋊C411yescharacteristic
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43—42no—
86C2×C4×D43—42no—
87C2×C4×D43—81no—
88C2×C4×D43—81no—
89C2×C8×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—81no—
92C22⋊C4×C43—41no—
93C22⋊C4×C43—41no—
94C22⋊C4×C43—41no—
95C22⋊C4×C43—81no—
96C22⋊Dic43—41no—
97C22⋊Dic43—41no—
98C22⋊Dic43—81no—
99(C2×D43)⋊C4—41no—
100(C2×D43)⋊C4—42no—
101C4⋊Dic43—41no—
102Dic43⋊C4—41no—
103Dic43⋊C4—42no—
104Dic43⋊C4—41no—
105Dic43⋊C4—41no—
106Dic43⋊C4—81no—
107Dic43⋊C4—82no—
108C4×Dic43—21no—
109C4×Dic43—21no—
110C2×C43⋊C8—41no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—41no—
114C23×C43—41no—
115C23×C43C2×C22⋊C411yescharacteristic
116C23×C43C2×SD1611yescharacteristic
117C23×C43C2×Q1611yescharacteristic
118C22×D43—21no—
119C22×D43—21no—
120C22×D43—41no—
121C22×D43—41no—
122C22×D43#10312yes—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—81no—
134C2×C4×C43—81no—
135C2×C4×C43—81no—
136C22⋊D43—42no—
137C22⋊D43—42no—
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43—22no—
141C2×Dic43—21no—
142C2×Dic43—42no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—81no—
151C2×Dic43—81no—
152C2×Dic43—81no—
153C2×Dic43—81no—
154C2×Dic43#9911yescharacteristic
155C2×Dic43#9911yescharacteristic
156C2×Dic43#10312yes—
157C4×D43—42no—
158C4×D43—42no—
159C4×D43—84no—
160C8×C43—81no—
161C43⋊C8—81no—
162#11899—431nomaximal, Sylow
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43—81no—
172C22×C43C2×#9911yescharacteristic
173C22×C43C2×#10311yescharacteristic
174C22×C43#42111yescharacteristic
175C2×D43—22no—
176C2×D43—42no—
177C2×D43—41no—
178C2×D43—41no—
179C2×D43—42no—
180C4×C43—41no—
181C4×C43—41no—
182C4×C43—81no—
183C4×C43—81no—
184C4×C43—161no—
185Dic43—21no—
186Dic43—22no—
187Dic43—41no—
188Dic43—81no—
189Dic43—81no—
190Dic43—161no—
191Dic43#35212yes—
192#2487—431no—
193#1799—431no—
194#1460—431no—
195#1352—431no—
196#1352—431no—
197#1352—431no—
198#1352D4311yescharacteristic, complemented
199C2×C43—21no—
200C2×C43—21no—
201C2×C43—41no—
202C2×C43—41no—
203C2×C43#152011yescharacteristic
204C2×C43C2×#35211yescharacteristic
205C2×C43#212811yescharacteristic
206D43—42no—
207C2×C4×D4—431no—
208C22×C4⋊C4—431no—
209#431—861no—
210C2×#99—861no—
211#400—431no—
212#400—431no—
213#399—431no—
214#399C2×D4311yescharacteristic
215#389—861no—
216#386—861no—
217#385—861no—
218#380—431no—
219#380—861no—
220#380—861no—
221#342—431no—
222#342C2×D4311yescharacteristic
223#323—431no—
224#323—861no—
225#323C2×D4311yescharacteristic
226C43#1189911yescharacteristic, complemented, Sylow
227C22×D4—431no—
228C23×C4—431no—
229C23×C4—431no—
230C23×C4—861no—
231C4×D4—1721no—
232C4×D4—1721no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—431no—
235C2×C4⋊C4—431no—
236C2×C4⋊C4—861no—
237C2×C4⋊C4—861no—
238C2×C4⋊C4—861no—
239C2×C4⋊C4—1721no—
240C2×C4⋊C4—1721no—
241C2×C4⋊C4—1721no—
242C2×C4⋊C4C4×D4311yescharacteristic
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—431no—
246C2×C22⋊C4—861no—
247C2×C22⋊C4—861no—
248C2×C22⋊C4—861no—
249C2×C22⋊C4C22×D4311yescharacteristic
250C2×C42—431no—
251C4⋊C8—1721no—
252#99—1722no—
253C22⋊C8—21no—
254C22⋊C8—861no—
255C4×C8—1721no—
256#95—431no—
257#95—861no—
258#95—861no—
259#95—861no—
260#95—861no—
261#95—1721no—
262#95C4×D4311yescharacteristic
263C24—431no—
264C24D4×D4311yescharacteristic
265C2×D4—432no—
266C2×D4—432no—
267C2×D4—1721no—
268C2×D4—1721no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—41no—
272C22×C4—431no—
273C22×C4—431no—
274C22×C4—431no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4—861no—
278C22×C4—861no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4—3441no—
282C22×C4—3441no—
283C22×C4—1722no—
284C22×C4—1722no—
285C22×C4—1722no—
286C22×C4—1721no—
287C22×C4C2×C4×D4311yescharacteristic
288C22×C4D4×D4311yescharacteristic
289C2×C8—41no—
290C2×C8—1721no—
291C4⋊C4—41no—
292C4⋊C4—81no—
293C4⋊C4—3441no—
294C4⋊C4—3442no—
295C4⋊C4—1721no—
296C4⋊C4—1721no—
297C4⋊C4—1721no—
298C4⋊C4—1721no—
299C4⋊C4—1722no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—81no—
304C22⋊C4—3441no—
305C22⋊C4—1721no—
306C22⋊C4—1722no—
307C22⋊C4—1721no—
308C22⋊C4—1721no—
309C42—861no—
310C42—861no—
311C23—21no—
312C23—21no—
313C23—41no—
314C23—41no—
315C23—432no—
316C23—861no—
317C23—861no—
318C23—1721no—
319C23—1721no—
320C23C22⋊C4×D4311yescharacteristic
321C23SD16×D4311yescharacteristic
322C23Q16×D4311yescharacteristic
323D4—1722no—
324D4—1722no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—431no—
339C2×C4—431no—
340C2×C4—432no—
341C2×C4—862no—
342C2×C4—861no—
343C2×C4—861no—
344C2×C4—861no—
345C2×C4—3444no—
346C2×C4—3441no—
347C2×C4—3441no—
348C2×C4—3441no—
349C2×C4—3441no—
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×C4—1721no—
359C2×C4—1721no—
360C8—81no—
361C8—3441no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—81no—
371C22—862no—
372C22—1722no—
373C22—1722no—
374C22—1721no—
375C22—1721no—
376C22#99×D4311yescharacteristic
377C22#103×D4311yescharacteristic
378C22#1458291411yescharacteristic
379C4—41no—
380C4—41no—
381C4—81no—
382C4—81no—
383C4—161no—
384C4—432no—
385C4—861no—
386C4—862no—
387C4—3441no—
388C4—3441no—
389C4—1721no—
390C4—6881no—
391C2—21no—
392C2—21no—
393C2—41no—
394C2—41no—
395C2—1722no—
396C2#1913316511yescharacteristic
397C2#352×D4311yescharacteristic
398C2#1913626511yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1352C2
socleC22×C43C2×#99
prime radicalC22×C22⋊D43D4
cosocleC2×C22⋊C4×C43C23
hypercenter#1352D43
hypocenterC43#11899
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

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

NH ≅ G/Ntype
4. #19132620C2semidirect
5. #19132619C2semidirect
6. #19132618C2semidirect
7. C43×#1352C2semidirect
9. C2×C4⋊C4×D43C4semidirect
12. #14582839C4semidirect
13. #14582837C4semidirect
18. #14582758C4semidirect
198. #1352D43semidirect
226. C43#11899semidirect

Maximal subgroups

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

subgroupindex
#191389052
#191345822
#191329142
#191326202
#191326192
#191326182
C43×#13522
#1189943