Finite Group Databasebeta

← #24988296

Subgroups — #24988296

Order 11008.

780 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C2×#14583589C211yesmaximal, characteristic
2#19134679C212yesmaximal, complemented
3#19133166C212yesmaximal, complemented
4#19132913C211yesmaximal, characteristic
5C43×#1799C211yesmaximal, characteristic
6#14583589—24no—
7#14583589—24no—
8C2×#13063318—21no—
9C2×#13063317C411yescharacteristic, complemented
10C2×#13063315—21no—
11C2×#13063306—21no—
12C2×#13063304C411yescharacteristic, complemented
13C2×#13063304C2211yescharacteristic
14C2×C4×Dic86C411yescharacteristic, complemented
15C2×#13063284C411yescharacteristic, complemented
16C2×#13063281—21no—
17C22×C4⋊Dic43C2211yescharacteristic
18C2×C22⋊(C43⋊C8)C2212yes—
19#14582661—24no—
20#14582635—24no—
21#14582625—21no—
22#14582623—21no—
23C2×C4×D4×C43C2211yescharacteristic
24C2×#99×C43—21no—
25C43×#380C2212yes—
26C43×#342—21no—
27C22×Dic86C2×C411yescharacteristic
28C23×Dic43—21no—
29C22×C43⋊C8—22no—
30#13063318—28no—
31#13063317—22no—
32#13063317—22no—
33#13063315—28no—
34#13063306—28no—
35#13063304—22no—
36#13063304—22no—
37#13063304—22no—
38#13063304D414yes—
39C4×Dic86—22no—
40C4×Dic86—22no—
41#13063284—22no—
42#13063284—22no—
43#13063281—28no—
44C2×C4⋊Dic43—22no—
45C2×C4⋊Dic43—21no—
46C2×C4⋊Dic43C2×C411yescharacteristic
47C2×C4⋊Dic43C2×C411yescharacteristic
48C2×C4⋊Dic43C2×C411yescharacteristic
49C2×C4⋊Dic43D414yes—
50C2×Dic43⋊C4—21no—
51C2×Dic43⋊C4—21no—
52C2×Dic43⋊C4—21no—
53C2×Dic43⋊C4—21no—
54C2×Dic43⋊C4—21no—
55C2×C22⋊Dic43—21no—
56C2×C22⋊Dic43—21no—
57C2×C22⋊Dic43—21no—
58C2×C4×Dic43—21no—
59C2×C4×Dic43—21no—
60C22⋊(C43⋊C8)—22no—
61C22⋊(C43⋊C8)—22no—
62C22×D4×C43D411yescharacteristic
63C23×C4×C43C2×C411yescharacteristic
64C23×C4×C43C2311yescharacteristic
65C4×D4×C43—22no—
66C4×D4×C43—22no—
67C2×C4⋊C4×C43—22no—
68C2×C4⋊C4×C43D411yescharacteristic
69C2×C22⋊C4×C43—22no—
70C2×C22⋊C4×C43D411yescharacteristic
71C2×C22⋊C4×C43D411yescharacteristic
72C2×C42×C43C2×C411yescharacteristic
73#99×C43—42no—
74#95×C43—22no—
75C24×C43C22⋊C411yescharacteristic
76C24×C43C2×D411yescharacteristic
77C2×D4×C43—22no—
78C2×D4×C43—22no—
79C2×D4×C43—21no—
80C2×D4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—42no—
84C22×C4×C43—42no—
85C22×C4×C43—42no—
86C22×C4×C43C22⋊C411yescharacteristic
87C22×C4×C43C22⋊C411yescharacteristic
88C22×C4×C43C22⋊C411yescharacteristic
89C22×C4×C43C22×C411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D412yes—
92C22×C4×C43C2×D412yes—
93C22×Dic43—21no—
94C22×Dic43—21no—
95C22×Dic43—21no—
96C22×Dic43—21no—
97C22×Dic43—24no—
98C22×Dic43—42no—
99C22×Dic43—41no—
100C22×Dic43—41no—
101C2×Dic86—21no—
102C2×Dic86—42no—
103C2×Dic86C22⋊C412yes—
104C4⋊C4×C43—22no—
105C4⋊C4×C43—44no—
106C22⋊C4×C43—22no—
107C22⋊C4×C43—22no—
108C22⋊C4×C43—42no—
109C22⋊C4×C43—42no—
110C42×C43—21no—
111C42×C43—21no—
112C22⋊Dic43—24no—
113C22⋊Dic43—24no—
114C22⋊Dic43—24no—
115C4⋊Dic43—21no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118C4⋊Dic43—24no—
119C4⋊Dic43C22⋊C412yes—
120C4⋊Dic43C22⋊C412yes—
121C4⋊Dic43C22⋊C412yes—
122Dic43⋊C4—24no—
123Dic43⋊C4—24no—
124Dic43⋊C4—24no—
125Dic43⋊C4—24no—
126Dic43⋊C4—24no—
127C4×Dic43—24no—
128C4×Dic43—24no—
129C2×C43⋊C8—44no—
130C2×C43⋊C8—42no—
131C23×C43—21no—
132C23×C43—21no—
133C23×C43—21no—
134C23×C43—41no—
135C23×C43—41no—
136C23×C43—41no—
137C23×C43—41no—
138C23×C43C2×C22⋊C411yescharacteristic
139C23×C43#12012yes—
140C23×C43#13512yes—
141C23×C43AGL(1,ℤ/8)11yescharacteristic
142C23×C43#13711yescharacteristic
143D4×C43—42no—
144D4×C43—42no—
145C2×C4×C43—24no—
146C2×C4×C43—22no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—41no—
153C2×C4×C43—42no—
154C2×C4×C43—42no—
155C2×C4×C43—42no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—82no—
159C2×C4×C43—82no—
160C2×C4×C43—82no—
161C2×C4×C43C2×C22⋊C411yescharacteristic
162C2×C4×C43C2×C22⋊C411yescharacteristic
163C2×C4×C43#12012yes—
164C2×Dic43—22no—
165C2×Dic43—22no—
166C2×Dic43—22no—
167C2×Dic43—22no—
168C2×Dic43—42no—
169C2×Dic43—42no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—44no—
175C2×Dic43—44no—
176Dic86—42no—
177Dic86—42no—
178C43⋊C8—82no—
179#8382—431nomaximal, Sylow
180C22×C43—21no—
181C22×C43—22no—
182C22×C43—21no—
183C22×C43—22no—
184C22×C43—42no—
185C22×C43—41no—
186C22×C43—41no—
187C22×C43—41no—
188C22×C43—41no—
189C22×C43—41no—
190C22×C43—81no—
191C22×C43—81no—
192C22×C43#37911yescharacteristic
193C22×C43#41611yescharacteristic
194C22×C43#41711yescharacteristic
195C22×C43#44912yes—
196C22×C43#45212yes—
197C4×C43—22no—
198C4×C43—21no—
199C4×C43—41no—
200C4×C43—41no—
201C4×C43—41no—
202C4×C43—162no—
203C4×C43#41012yes—
204Dic43—42no—
205Dic43—42no—
206Dic43—42no—
207Dic43—42no—
208C2×#552—431no—
209#1823—432no—
210#1799D4311yescharacteristic
211#1520—432no—
212#1459—431no—
213C2×C43—22no—
214C2×C43—21no—
215C2×C43—21no—
216C2×C43—22no—
217C2×C43—81no—
218C2×C43#178211yescharacteristic
219C2×C43#178811yescharacteristic
220C2×C43#179611yescharacteristic
221#552—864no—
222#552—864no—
223C2×#126—861no—
224C2×#125—431no—
225C2×#125—861no—
226C2×#123—861no—
227C2×C22⋊Q8—431no—
228C2×C22⋊Q8—431no—
229C2×C4×Q8—431no—
230C2×C4×D4C2×D4311yescharacteristic
231C2×#117—431no—
232C2×#117—861no—
233C22×C4⋊C4—431no—
234C2×#99—21no—
235C2×C22⋊C8—432no—
236#380C2×D4312yes—
237#342—21no—
238#340—864no—
239#328—864no—
240#324—861no—
241#323—861no—
242C43#838211yescharacteristic, complemented, Sylow
243C22×Q8—431no—
244C22×D4C22⋊D4311yescharacteristic
245C23×C4—861no—
246C23×C4C4×D4311yescharacteristic
247C23×C4C22×D4311yescharacteristic
248C22×C8—862no—
249#126—868no—
250#125—862no—
251#125—862no—
252#125—868no—
253#123—868no—
254C22⋊Q8—434no—
255C22⋊Q8—862no—
256C22⋊Q8—862no—
257C22⋊Q8—862no—
258C4×Q8—862no—
259C4×Q8—862no—
260C4×D4—22no—
261C4×D4—22no—
262#117—868no—
263#117—862no—
264#117—862no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—431no—
267C2×C4⋊C4—431no—
268C2×C4⋊C4—431no—
269C2×C4⋊C4—434no—
270C2×C4⋊C4—861no—
271C2×C4⋊C4—861no—
272C2×C4⋊C4—861no—
273C2×C4⋊C4—861no—
274C2×C4⋊C4—861no—
275C2×C4⋊C4—861no—
276C2×C4⋊C4—862no—
277C2×C4⋊C4D17211yescharacteristic
278C2×C22⋊C4—22no—
279C2×C22⋊C4—861no—
280C2×C22⋊C4—861no—
281C2×C22⋊C4—861no—
282C2×C22⋊C4D17211yescharacteristic
283C2×C22⋊C4C22⋊D4311yescharacteristic
284C2×C42—861no—
285C2×C42—861no—
286C2×C42C4×D4311yescharacteristic
287#99—42no—
288C22⋊C8—862no—
289C22⋊C8—862no—
290#95—22no—
291C24(C2×D43)⋊C411yescharacteristic
292C24C2×C22⋊D4311yescharacteristic
293C2×Q8—432no—
294C2×Q8—861no—
295C2×Q8—1722no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—21no—
299C2×D4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—861no—
306C22×C4—861no—
307C22×C4—861no—
308C22×C4—861no—
309C22×C4—864no—
310C22×C4—1722no—
311C22×C4—1721no—
312C22×C4—1721no—
313C22×C4(C2×D43)⋊C411yescharacteristic
314C22×C4(C2×D43)⋊C411yescharacteristic
315C22×C4(C2×D43)⋊C411yescharacteristic
316C22×C4C2×C4×D4311yescharacteristic
317C22×C4C2×D17211yescharacteristic
318C22×C4D4×D4312yes—
319C22×C4D4×D4312yes—
320C2×C8—1724no—
321C2×C8—1722no—
322C4⋊C4—22no—
323C4⋊C4—44no—
324C4⋊C4—432no—
325C4⋊C4—432no—
326C4⋊C4—432no—
327C4⋊C4—864no—
328C4⋊C4—864no—
329C4⋊C4—864no—
330C4⋊C4—864no—
331C4⋊C4—861no—
332C4⋊C4—861no—
333C4⋊C4—861no—
334C4⋊C4—864no—
335C4⋊C4—864no—
336C22⋊C4—22no—
337C22⋊C4—22no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C22⋊C4—864no—
341C22⋊C4—864no—
342C22⋊C4—864no—
343C42—21no—
344C42—21no—
345C42—864no—
346C42—864no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23C2×(C2×D43)⋊C411yescharacteristic
355C23#1306329312yes—
356C23#1306334512yes—
357C23#1306335111yescharacteristic
358C23#1306335611yescharacteristic
359Q8—1722no—
360Q8—1722no—
361D4—42no—
362D4—42no—
363C2×C4—24no—
364C2×C4—22no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—82no—
379C2×C4—862no—
380C2×C4—862no—
381C2×C4—862no—
382C2×C4—862no—
383C2×C4—1722no—
384C2×C4—1722no—
385C2×C4—1724no—
386C2×C4—1724no—
387C2×C4—1721no—
388C2×C4—1721no—
389C2×C4—1721no—
390C2×C4—1721no—
391C2×C4C22⋊C4×D4311yescharacteristic
392C2×C4C22⋊C4×D4311yescharacteristic
393C2×C4#1306329512yes—
394C8—3442no—
395C22—21no—
396C22—22no—
397C22—21no—
398C22—22no—
399C22—42no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—81no—
406C22—81no—
407C22#1458275411yescharacteristic
408C22#1458289311yescharacteristic
409C22#1458289811yescharacteristic
410C22#1458304212yes—
411C22#1458305912yes—
412C4—22no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—41no—
417C4—162no—
418C4—1722no—
419C4—1722no—
420C4—1722no—
421C4—1722no—
422C4#1458287112yes—
423C2—22no—
424C2—21no—
425C2—21no—
426C2—22no—
427C2—81no—
428C2#1913451111yescharacteristic
429C2#1913453311yescharacteristic
430C2#1913456811yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1799C2
socleC22×C43#379
prime radicalC22×D4×C43D4
cosocleC23×C4×C43C23
hypercenter#1799D43
hypocenterC43#8382
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #19134679C2semidirect
3. #19133166C2semidirect
9. C2×#13063317C4semidirect
12. C2×#13063304C4semidirect
14. C2×C4×Dic86C4semidirect
15. C2×#13063284C4semidirect
242. C43#8382semidirect

Maximal subgroups

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

subgroupindex
C2×#145835892
#191346792
#191331662
#191329132
C43×#17992
#838243