Finite Group Databasebeta

← #25007716

Subgroups — #25007716

Order 11008.

452 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 77 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#19139950C211yesmaximal, characteristic
2#19134582C211yesmaximal, characteristic
3#19132910C211yesmaximal, characteristic
4#19132619C211yesmaximal, characteristic, complemented
5#19132617C211yesmaximal, characteristic, complemented
6#19132615C211yesmaximal, characteristic, complemented
7C43×#1352C211yesmaximal, characteristic, complemented
8C2×#13063290C411yescharacteristic, complemented
9C2×(C22⋊D43)⋊C4C2211yescharacteristic
10C2×#13063239—21no—
11C22⋊C8×D43—21no—
12#14582834C411yescharacteristic, complemented
13#14582812C411yescharacteristic, complemented
14#14582811C2211yescharacteristic
15#14582799—21no—
16#14582794—21no—
17#14582771—21no—
18#14582770—21no—
19#14582763C411yescharacteristic, complemented
20#14582757—21no—
21#14582666C2211yescharacteristic
22#14582624—21no—
23#14582623C2211yescharacteristic
24C43×#399C2211yescharacteristic
25C43×#342C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C22×Dic86C2×C411yescharacteristic
28C22×C22⋊D43D411yescharacteristic
29C23×Dic43D411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C2×C8×D43—41no—
32#13063290—41no—
33#13063290—41no—
34(C22⋊D43)⋊C4—41no—
35(C22⋊D43)⋊C4—41no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—41no—
40C2×Dic43⋊C4D411yescharacteristic
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4C2×C411yescharacteristic
46C2×C4×Dic43—21no—
47C2×C4×Dic43C2×C411yescharacteristic
48#13063239—42no—
49C22⋊(C43⋊C8)—21no—
50(C2×D43)⋊C8—41no—
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—81no—
80C22×Dic43C22⋊C411yescharacteristic
81C22×Dic43C22⋊C411yescharacteristic
82C22×Dic43C22⋊C411yescharacteristic
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43—81no—
86C2×Dic86—41no—
87C2×Dic86—42no—
88C2×C8×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—81no—
91C22⋊C4×C43—41no—
92C22⋊C4×C43—41no—
93C22⋊C4×C43—41no—
94C22⋊C4×C43—81no—
95C22⋊Dic43—41no—
96C22⋊Dic43—42no—
97C22⋊Dic43—41no—
98(C2×D43)⋊C4—41no—
99(C2×D43)⋊C4—42no—
100(C2×D43)⋊C4—81no—
101Dic43⋊C4—41no—
102Dic43⋊C4—42no—
103Dic43⋊C4—41no—
104Dic43⋊C4—41no—
105Dic43⋊C4—81no—
106Dic43⋊C4—82no—
107C4×Dic43—21no—
108C4×Dic43—21no—
109C4×Dic43—42no—
110C2×C43⋊C8—41no—
111C8×D43—82no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43—41no—
115C23×C43—41no—
116C23×C43C2×C22⋊C411yescharacteristic
117C23×C43C2×SD1611yescharacteristic
118C23×C43C2×Q1611yescharacteristic
119C22×D43—21no—
120C22×D43—21no—
121C22×D43—41no—
122C22×D43—41no—
123C22×D43#10312yes—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
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—41no—
134C2×C4×C43—81no—
135C2×C4×C43—81no—
136C2×C4×C43—81no—
137C22⋊D43—42no—
138C22⋊D43—42no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—22no—
142C2×Dic43—21no—
143C2×Dic43—41no—
144C2×Dic43—42no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—81no—
152C2×Dic43—81no—
153C2×Dic43—81no—
154C2×Dic43—81no—
155C2×Dic43#9911yescharacteristic
156C2×Dic43#9911yescharacteristic
157C2×Dic43#10312yes—
158C4×D43—42no—
159C4×D43—81no—
160Dic86—42no—
161Dic86—42no—
162C8×C43—81no—
163C43⋊C8—81no—
164#11897—431nomaximal, Sylow
165C22×C43—21no—
166C22×C43—21no—
167C22×C43—21no—
168C22×C43—21no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43—81no—
174C22×C43C2×#9911yescharacteristic
175C22×C43C2×#10311yescharacteristic
176C22×C43#42111yescharacteristic
177C2×D43—22no—
178C2×D43—41no—
179C2×D43—41no—
180C2×D43—42no—
181C2×D43—81no—
182C4×C43—41no—
183C4×C43—41no—
184C4×C43—81no—
185C4×C43—81no—
186C4×C43—161no—
187Dic43—21no—
188Dic43—21no—
189Dic43—22no—
190Dic43—42no—
191Dic43—41no—
192Dic43—81no—
193Dic43—161no—
194#2580—431no—
195#1799—431no—
196#1459—431no—
197#1352—431no—
198#1352D4311yescharacteristic, complemented
199#1351—431no—
200#1351—431no—
201C2×C43—21no—
202C2×C43—21no—
203C2×C43—41no—
204C2×C43—41no—
205C2×C43#152011yescharacteristic
206C2×C43#212011yescharacteristic
207C2×C43#212711yescharacteristic
208D43—42no—
209C2×C4×Q8—431no—
210C2×C4×D4—431no—
211C2×#99—861no—
212C2×C22⋊C8—861no—
213#399—431no—
214#399C2×D4311yescharacteristic
215#393—431no—
216#393—431no—
217#390—861no—
218#389—861no—
219#385—861no—
220#385—861no—
221#382—431no—
222#380—861no—
223#342—431no—
224#342C2×D4311yescharacteristic
225#324—861no—
226#323—431no—
227#323C2×D4311yescharacteristic
228C43#1189711yescharacteristic, complemented, Sylow
229C22×Q8—431no—
230C22×D4—431no—
231C23×C4—431no—
232C23×C4—431no—
233C22×C8—1721no—
234C4×Q8—1721no—
235C4×Q8—1721no—
236C4×D4—1721no—
237C4×D4—1721no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—431no—
240C2×C4⋊C4—861no—
241C2×C4⋊C4—861no—
242C2×C4⋊C4—861no—
243C2×C4⋊C4—1721no—
244C2×C4⋊C4C4×D4311yescharacteristic
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—431no—
248C2×C22⋊C4—861no—
249C2×C22⋊C4—861no—
250C2×C22⋊C4—861no—
251C2×C22⋊C4—861no—
252C2×C22⋊C4C22×D4311yescharacteristic
253C2×C42—431no—
254C2×C42—861no—
255#99—1722no—
256C22⋊C8—21no—
257C22⋊C8—861no—
258C22⋊C8—1721no—
259#95—431no—
260#95—861no—
261#95—861no—
262#95—861no—
263#95—1721no—
264#95C4×D4311yescharacteristic
265C24—431no—
266C24D4×D4311yescharacteristic
267C2×Q8—1721no—
268C2×Q8—1722no—
269C2×D4—432no—
270C2×D4—432no—
271C2×D4—1721no—
272C2×D4—1721no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—41no—
276C22×C4—431no—
277C22×C4—431no—
278C22×C4—431no—
279C22×C4—861no—
280C22×C4—861no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4—861no—
284C22×C4—861no—
285C22×C4—3441no—
286C22×C4—3441no—
287C22×C4—1721no—
288C22×C4C2×C4×D4311yescharacteristic
289C22×C4D4×D4311yescharacteristic
290C2×C8—41no—
291C2×C8—3442no—
292C2×C8—1721no—
293C4⋊C4—41no—
294C4⋊C4—81no—
295C4⋊C4—3441no—
296C4⋊C4—3442no—
297C4⋊C4—1721no—
298C4⋊C4—1721no—
299C4⋊C4—1721no—
300C4⋊C4—1722no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—81no—
305C22⋊C4—3441no—
306C22⋊C4—1721no—
307C22⋊C4—1722no—
308C22⋊C4—1722no—
309C22⋊C4—1721no—
310C22⋊C4—1721no—
311C42—861no—
312C42—861no—
313C42—1722no—
314C23—21no—
315C23—21no—
316C23—41no—
317C23—41no—
318C23—432no—
319C23—861no—
320C23—861no—
321C23—1721no—
322C23—1721no—
323C23C22⋊C4×D4311yescharacteristic
324C23SD16×D4311yescharacteristic
325C23Q16×D4311yescharacteristic
326Q8—1722no—
327Q8—1722no—
328D4—1722no—
329D4—1722no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—431no—
344C2×C4—431no—
345C2×C4—432no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—862no—
349C2×C4—861no—
350C2×C4—3441no—
351C2×C4—3441no—
352C2×C4—3441no—
353C2×C4—3441no—
354C2×C4—3441no—
355C2×C4—1722no—
356C2×C4—1721no—
357C2×C4—1722no—
358C2×C4—1721no—
359C2×C4—1721no—
360C2×C4—1721no—
361C2×C4—1721no—
362C2×C4—1721no—
363C2×C4—1721no—
364C8—81no—
365C8—3441no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—81no—
375C22—862no—
376C22—3441no—
377C22—1722no—
378C22—1721no—
379C22—1721no—
380C22#99×D4311yescharacteristic
381C22#103×D4311yescharacteristic
382C22#1458291411yescharacteristic
383C4—41no—
384C4—41no—
385C4—81no—
386C4—81no—
387C4—161no—
388C4—861no—
389C4—861no—
390C4—862no—
391C4—3441no—
392C4—1721no—
393C4—1722no—
394C4—6881no—
395C2—21no—
396C2—21no—
397C2—41no—
398C2—41no—
399C2—1722no—
400C2#1913316511yescharacteristic
401C2#1913623511yescharacteristic
402C2#1913626111yescharacteristic
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#11897
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. #19132619C2semidirect
5. #19132617C2semidirect
6. #19132615C2semidirect
7. C43×#1352C2semidirect
8. C2×#13063290C4semidirect
12. #14582834C4semidirect
13. #14582812C4semidirect
19. #14582763C4semidirect
198. #1352D43semidirect
228. C43#11897semidirect

Maximal subgroups

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

subgroupindex
#191399502
#191345822
#191329102
#191326192
#191326172
#191326152
C43×#13522
#1189743