Finite Group Databasebeta

← #24987955

Subgroups — #24987955

Order 11008.

1174 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 1174 conjugacy classes of subgroups — too many to draw. Only its 147 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
1C22×#13063303C211yesmaximal, characteristic
2#19134504C212yesmaximal
3C2×#14582625C211yesmaximal, characteristic, complemented
4C2×#14582624C212yesmaximal, complemented
5C2×C43×#324C211yesmaximal, characteristic, complemented
6C23×Dic86C411yescharacteristic
7C23×C4×D43C2211yescharacteristic
8C2×#13063303—24no—
9C2×#13063303—24no—
10C2×#13063303—22no—
11C2×#13063303—22no—
12C22×Dic43⋊C4C411yescharacteristic
13C22×Dic43⋊C4C2211yescharacteristic
14C22×(C2×D43)⋊C4C411yescharacteristic
15C22×(C2×D43)⋊C4C411yescharacteristic
16C2×C22⋊(C43⋊C8)C2212yes—
17C2×(C2×D43)⋊C8—24no—
18#14582625—22no—
19#14582624—24no—
20C22×C4⋊C4×C43C2211yescharacteristic
21C2×C22⋊C8×C43C2212yes—
22C43×#324—22no—
23C24×D43C2×C411yescharacteristic
24C22×Dic86—22no—
25C22×Dic86—22no—
26C22×Dic86—22no—
27C22×Dic86—44no—
28C23×Dic43C2×C411yescharacteristic
29C23×Dic43C2×C411yescharacteristic
30C23×Dic43C2×C411yescharacteristic
31C22×C4×D43—21no—
32C22×C4×D43—22no—
33C22×C4×D43—21no—
34C22×C4×D43—44no—
35C22×C4×D43D414yes—
36C22×C43⋊C8—22no—
37#13063303—216no—
38#13063303—216no—
39C2×Dic43⋊C4—22no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—22no—
42C2×Dic43⋊C4—21no—
43C2×Dic43⋊C4—22no—
44C2×Dic43⋊C4—22no—
45C2×Dic43⋊C4D414yes—
46C2×(C2×D43)⋊C4—22no—
47C2×(C2×D43)⋊C4—22no—
48C2×(C2×D43)⋊C4—22no—
49C2×(C2×D43)⋊C4—22no—
50C2×(C2×D43)⋊C4—22no—
51C2×(C2×D43)⋊C4—22no—
52C22⋊(C43⋊C8)—22no—
53C22⋊(C43⋊C8)—22no—
54(C2×D43)⋊C8—48no—
55C23×C4×C43C2×C411yescharacteristic
56C23×C4×C43C2×C411yescharacteristic
57C23×C4×C43C2311yescharacteristic
58C22×C8×C43—22no—
59C2×C4⋊C4×C43—22no—
60C2×C4⋊C4×C43—22no—
61C2×C4⋊C4×C43D412yes—
62C2×C4⋊C4×C43D412yes—
63C22⋊C8×C43—22no—
64C22⋊C8×C43—22no—
65C24×C43C22×C411yescharacteristic
66C23×D43—21no—
67C23×D43—21no—
68C23×D43—24no—
69C23×D43—22no—
70C23×D43—22no—
71C23×D43—42no—
72C23×D43C22⋊C412yes—
73C22×C4×C43—21no—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43—22no—
78C22×C4×C43—22no—
79C22×C4×C43—42no—
80C22×C4×C43—42no—
81C22×C4×C43C22⋊C412yes—
82C22×C4×C43C22⋊C412yes—
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2×D412yes—
85C22×C4×C43C2×D412yes—
86C22×C4×C43C2×D411yescharacteristic
87C22×Dic43—24no—
88C22×Dic43—21no—
89C22×Dic43—21no—
90C22×Dic43—21no—
91C22×Dic43—21no—
92C22×Dic43—21no—
93C22×Dic43—21no—
94C22×Dic43—22no—
95C22×Dic43—22no—
96C22×Dic43—42no—
97C22×Dic43C22⋊C412yes—
98C22×Dic43C22⋊C412yes—
99C22×Dic43C22⋊C412yes—
100C2×C4×D43—24no—
101C2×C4×D43—24no—
102C2×C4×D43—28no—
103C2×C4×D43—44no—
104C2×C4×D43—44no—
105C2×C4×D43—48no—
106C2×C4×D43—44no—
107C2×Dic86—28no—
108C2×Dic86—48no—
109C2×Dic86—48no—
110C2×Dic86—44no—
111C2×Dic86—44no—
112C2×C8×C43—44no—
113C2×C8×C43—42no—
114C4⋊C4×C43—24no—
115C4⋊C4×C43—24no—
116(C2×D43)⋊C4—28no—
117(C2×D43)⋊C4—28no—
118Dic43⋊C4—28no—
119Dic43⋊C4—24no—
120Dic43⋊C4—24no—
121C2×C43⋊C8—44no—
122C2×C43⋊C8—42no—
123C23×C43—22no—
124C23×C43—22no—
125C23×C43C2×C22⋊C411yescharacteristic
126C23×C43C2×C22⋊C411yescharacteristic
127C23×C43C2×C22⋊C411yescharacteristic
128C23×C43#13112yes—
129C23×C43#13112yes—
130C22×D43—24no—
131C22×D43—24no—
132C22×D43—22no—
133C22×D43—24no—
134C22×D43—24no—
135C22×D43—22no—
136C22×D43—48no—
137C22×D43—48no—
138C22×D43—42no—
139C22×D43—42no—
140C22×D43—42no—
141C22×D43—41no—
142C22×D43—41no—
143C22×D43#10114yes—
144C2×C4×C43—24no—
145C2×C4×C43—22no—
146C2×C4×C43—22no—
147C2×C4×C43—22no—
148C2×C4×C43—22no—
149C2×C4×C43—41no—
150C2×C4×C43—42no—
151C2×C4×C43—41no—
152C2×C4×C43—42no—
153C2×C4×C43—42no—
154C2×C4×C43—42no—
155C2×C4×C43—42no—
156C2×C4×C43—42no—
157C2×C4×C43#12012yes—
158C2×C4×C43#12012yes—
159C2×Dic43—24no—
160C2×Dic43—24no—
161C2×Dic43—22no—
162C2×Dic43—22no—
163C2×Dic43—22no—
164C2×Dic43—22no—
165C2×Dic43—24no—
166C2×Dic43—42no—
167C2×Dic43—42no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—42no—
171C2×Dic43—42no—
172C2×Dic43#9914yes—
173C4×D43—48no—
174C4×D43—48no—
175Dic86—416no—
176C8×C43—82no—
177C43⋊C8—82no—
178#8308—431nomaximal, Sylow
179C22×C43—24no—
180C22×C43—24no—
181C22×C43—21no—
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—21no—
185C22×C43#37911yescharacteristic
186C22×C43#40812yes—
187C22×C43#40812yes—
188C22×C43#40811yescharacteristic
189C22×C43#40811yescharacteristic
190C22×C43C2×#9912yes—
191C22×C43C2×#10112yes—
192C2×D43—28no—
193C2×D43—24no—
194C2×D43—48no—
195C2×D43—44no—
196C2×D43—44no—
197C2×D43—44no—
198C2×D43—42no—
199C2×D43—42no—
200C4×C43—22no—
201C4×C43—22no—
202C4×C43—42no—
203C4×C43—42no—
204Dic43—24no—
205Dic43—42no—
206Dic43—42no—
207C22×C22⋊Q8—431no—
208#1779—432no—
209C2×#324—432no—
210C2×#324—431no—
211C2×#324D4311yescharacteristic, complemented
212C2×C43—22no—
213C2×C43—21no—
214C2×C43—21no—
215C2×C43#147214yes—
216C2×C43#178011yescharacteristic
217C2×C43#178111yescharacteristic
218C2×C43#178411yescharacteristic
219D43—44no—
220C23×Q8—431no—
221C24×C4—431no—
222C2×C22⋊Q8—864no—
223C2×C22⋊Q8—864no—
224C2×C22⋊Q8—862no—
225C2×C22⋊Q8—862no—
226C22×C4⋊C4—431no—
227C22×C4⋊C4—431no—
228C22×C4⋊C4C2×D4311yescharacteristic
229C22×C22⋊C4—431no—
230C22×C22⋊C4—431no—
231C2×C22⋊C8—432no—
232C2×C22⋊C8—864no—
233C2×C22⋊C8C2×D4312yes—
234#324—22no—
235#324—864no—
236#324—862no—
237C43#830811yescharacteristic, complemented, Sylow
238C25—431no—
239C22×Q8—862no—
240C22×Q8—862no—
241C22×Q8—862no—
242C22×Q8—1724no—
243C23×C4—431no—
244C23×C4—431no—
245C23×C4—431no—
246C23×C4—434no—
247C23×C4—861no—
248C23×C4—862no—
249C23×C4—861no—
250C23×C4—1724no—
251C23×C4C4×D4311yescharacteristic
252C23×C4C4×D4311yescharacteristic
253C23×C4C22×D4311yescharacteristic
254C22×C8—22no—
255C22×C8—862no—
256C22⋊Q8—8616no—
257C22⋊Q8—8616no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—434no—
261C2×C4⋊C4—862no—
262C2×C4⋊C4—862no—
263C2×C4⋊C4—862no—
264C2×C4⋊C4—861no—
265C2×C4⋊C4—862no—
266C2×C4⋊C4—861no—
267C2×C4⋊C4D17212yes—
268C2×C4⋊C4C22⋊D4312yes—
269C2×C22⋊C4—862no—
270C2×C22⋊C4—862no—
271C2×C22⋊C4—862no—
272C2×C22⋊C4—862no—
273C2×C22⋊C4—862no—
274C2×C22⋊C4—862no—
275C22⋊C8—22no—
276C22⋊C8—22no—
277C22⋊C8—862no—
278C22⋊C8—862no—
279C22⋊C8—1728no—
280C24—432no—
281C24—864no—
282C24—861no—
283C24—861no—
284C24—862no—
285C24—862no—
286C24—1722no—
287C24C2×C4×D4311yescharacteristic
288C2×Q8—868no—
289C2×Q8—1724no—
290C2×Q8—1728no—
291C2×Q8—1724no—
292C2×Q8—1728no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—42no—
300C22×C4—42no—
301C22×C4—432no—
302C22×C4—432no—
303C22×C4—432no—
304C22×C4—868no—
305C22×C4—864no—
306C22×C4—861no—
307C22×C4—861no—
308C22×C4—861no—
309C22×C4—861no—
310C22×C4—861no—
311C22×C4—861no—
312C22×C4—862no—
313C22×C4—862no—
314C22×C4—864no—
315C22×C4—864no—
316C22×C4—1724no—
317C22×C4—1724no—
318C22×C4—1728no—
319C22×C4—1724no—
320C22×C4—1722no—
321C22×C4(C2×D43)⋊C412yes—
322C22×C4(C2×D43)⋊C412yes—
323C22×C4C2×D17211yescharacteristic
324C22×C4D4×D4312yes—
325C22×C4D4×D4312yes—
326C22×C4C2×C22⋊D4311yescharacteristic
327C2×C8—44no—
328C2×C8—42no—
329C2×C8—1724no—
330C2×C8—1722no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—868no—
334C4⋊C4—864no—
335C4⋊C4—864no—
336C22⋊C4—868no—
337C22⋊C4—868no—
338C23—22no—
339C23—22no—
340C23—434no—
341C23—864no—
342C23—864no—
343C23—864no—
344C23—864no—
345C23—862no—
346C23—862no—
347C23—1728no—
348C23—1728no—
349C23—1722no—
350C23—1722no—
351C23—1722no—
352C23—1721no—
353C23—1721no—
354C23C22⋊C4×D4311yescharacteristic
355C23C22⋊C4×D4311yescharacteristic
356C23C2×(C2×D43)⋊C411yescharacteristic
357C23#1306333112yes—
358C23#1306333312yes—
359Q8—17216no—
360C2×C4—24no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—434no—
374C2×C4—864no—
375C2×C4—864no—
376C2×C4—862no—
377C2×C4—862no—
378C2×C4—864no—
379C2×C4—862no—
380C2×C4—862no—
381C2×C4—1728no—
382C2×C4—1728no—
383C2×C4—1722no—
384C2×C4—1722no—
385C2×C4—1721no—
386C2×C4—1721no—
387C2×C4—1722no—
388C2×C4—1722no—
389C2×C4#1306329312yes—
390C2×C4#1306329512yes—
391C8—82no—
392C8—3442no—
393C22—24no—
394C22—24no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—868no—
400C22—864no—
401C22—1728no—
402C22—1724no—
403C22—1724no—
404C22—1724no—
405C22—1722no—
406C22—1722no—
407C22#1458275411yescharacteristic
408C22#1458286412yes—
409C22#1458286412yes—
410C22#1458286511yescharacteristic
411C22#1458286711yescharacteristic
412C22#99×D4312yes—
413C22#101×D4312yes—
414C4—22no—
415C4—22no—
416C4—42no—
417C4—42no—
418C4—864no—
419C4—1722no—
420C4—1722no—
421C2—22no—
422C2—21no—
423C2—21no—
424C2—1724no—
425C2#1913295714yes—
426C2#1913450611yescharacteristic
427C2#1913450811yescharacteristic
428C2#1913451711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#324C2
socleC23×C43C2×C22⋊C4
prime radicalC24×D43C2×C4
cosocleC23×C4×C43C23
hypercenterC2×#324D43
hypocenterC43#8308
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
3. C2×#14582625C2semidirect
4. C2×#14582624C2semidirect
5. C2×C43×#324C2semidirect
211. C2×#324D43semidirect
237. C43#8308semidirect

Maximal subgroups

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

subgroupindex
C22×#130633032
#191345042
C2×#145826252
C2×#145826242
C2×C43×#3242
#830843