Finite Group Databasebeta

← #24988273

Subgroups — #24988273

Order 11008.

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

normal subgroups only

This group has 844 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×#14583595C211yesmaximal, characteristic
2#19134686C212yesmaximal, complemented
3#19134583C211yesmaximal, characteristic, complemented
4#19133164C212yesmaximal, complemented
5C43×#1459C211yesmaximal, characteristic, complemented
6#14583595—24no—
7#14583595—24no—
8C2×#13063320—21no—
9C2×#13063317C411yescharacteristic, complemented
10C2×#13063307—21no—
11C2×#13063299C411yescharacteristic, complemented
12C2×#13063299C2211yescharacteristic
13C2×#13063297—21no—
14C2×C4×D172C411yescharacteristic, complemented
15C2×(C22⋊D43)⋊C4—21no—
16C2×#13063284C411yescharacteristic, complemented
17C22×C4⋊Dic43C2211yescharacteristic
18C2×#13063240—21no—
19#14582759C2212yes—
20#14582666—21no—
21#14582662—24no—
22#14582634—24no—
23C2×C4×D4×C43C2211yescharacteristic
24C2×C22⋊C8×C43C2212yes—
25C43×#324—21no—
26C43×#323—21no—
27C22×D172C2×C411yescharacteristic
28C22×C22⋊D43—21no—
29C22×C22⋊D43—21no—
30C23×Dic43—21no—
31C22×C4×D43—21no—
32#13063320—28no—
33#13063317—22no—
34#13063317—22no—
35#13063307—28no—
36#13063299—22no—
37#13063299—22no—
38#13063299—22no—
39#13063299D414yes—
40#13063297—28no—
41C4×D172—22no—
42C4×D172—22no—
43(C22⋊D43)⋊C4—28no—
44#13063284—22no—
45#13063284—22no—
46C2×C4⋊Dic43—22no—
47C2×C4⋊Dic43—21no—
48C2×C4⋊Dic43—22no—
49C2×C4⋊Dic43C2×C411yescharacteristic
50C2×C4⋊Dic43C2×C411yescharacteristic
51C2×C4⋊Dic43C2×C411yescharacteristic
52C2×C4⋊Dic43D414yes—
53C2×Dic43⋊C4—21no—
54C2×Dic43⋊C4—21no—
55C2×C22⋊Dic43—21no—
56C2×C22⋊Dic43—22no—
57C2×(C2×D43)⋊C4—21no—
58C2×(C2×D43)⋊C4—21no—
59C2×(C2×D43)⋊C4—21no—
60C2×C4×Dic43—21no—
61#13063240—42no—
62C43⋊#95—22no—
63C22×D4×C43D411yescharacteristic
64C23×C4×C43C2×C411yescharacteristic
65C23×C4×C43C2311yescharacteristic
66C22×C8×C43—22no—
67C4×D4×C43—22no—
68C4×D4×C43—22no—
69C2×C4⋊C4×C43D411yescharacteristic
70C2×C22⋊C4×C43D411yescharacteristic
71C2×C22⋊C4×C43D411yescharacteristic
72C2×C42×C43C2×C411yescharacteristic
73C22⋊C8×C43—22no—
74C22⋊C8×C43—22no—
75C24×C43C22⋊C411yescharacteristic
76C24×C43C2×D411yescharacteristic
77C23×D43—21no—
78C2×D4×C43—22no—
79C2×D4×C43—22no—
80C2×D4×C43—21no—
81C2×D4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—21no—
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—
93C2×C22⋊D43—24no—
94C2×C22⋊D43—24no—
95C2×C22⋊D43—42no—
96C2×C22⋊D43—41no—
97C2×C22⋊D43—41no—
98C2×C22⋊D43—82no—
99C22×Dic43—21no—
100C22×Dic43—21no—
101C22×Dic43—21no—
102C22×Dic43—24no—
103C22×Dic43—42no—
104C22×Dic43—82no—
105C2×D172—21no—
106C2×D172—42no—
107C2×D172C22⋊C412yes—
108C2×C4×D43—24no—
109C2×C4×D43—82no—
110C2×C8×C43—44no—
111C2×C8×C43—42no—
112C4⋊C4×C43—22no—
113C22⋊C4×C43—22no—
114C22⋊C4×C43—22no—
115C42×C43—21no—
116C42×C43—21no—
117C22⋊Dic43—24no—
118C22⋊Dic43—42no—
119C22⋊Dic43—42no—
120(C2×D43)⋊C4—24no—
121(C2×D43)⋊C4—24no—
122(C2×D43)⋊C4—24no—
123C4⋊Dic43—21no—
124C4⋊Dic43—21no—
125C4⋊Dic43—21no—
126C4⋊Dic43—24no—
127C4⋊Dic43—44no—
128C4⋊Dic43C22⋊C412yes—
129C4⋊Dic43C22⋊C412yes—
130C4⋊Dic43C22⋊C412yes—
131Dic43⋊C4—24no—
132Dic43⋊C4—24no—
133C4×Dic43—24no—
134C23×C43—21no—
135C23×C43—21no—
136C23×C43—21no—
137C23×C43—41no—
138C23×C43—41no—
139C23×C43—41no—
140C23×C43—41no—
141C23×C43C2×C22⋊C411yescharacteristic
142C23×C43#12012yes—
143C23×C43#13512yes—
144C23×C43AGL(1,ℤ/8)11yescharacteristic
145C23×C43#13711yescharacteristic
146C22×D43—22no—
147C22×D43—42no—
148C22×D43—42no—
149C22×D43—41no—
150C22×D43—41no—
151D4×C43—42no—
152D4×C43—42no—
153C2×C4×C43—24no—
154C2×C4×C43—22no—
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43—21no—
158C2×C4×C43—21no—
159C2×C4×C43—21no—
160C2×C4×C43—42no—
161C2×C4×C43—41no—
162C2×C4×C43—42no—
163C2×C4×C43—42no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43C2×C22⋊C411yescharacteristic
167C2×C4×C43C2×C22⋊C411yescharacteristic
168C2×C4×C43#12012yes—
169C22⋊D43—44no—
170C22⋊D43—44no—
171C22⋊D43—84no—
172C2×Dic43—22no—
173C2×Dic43—22no—
174C2×Dic43—22no—
175C2×Dic43—42no—
176C2×Dic43—42no—
177C2×Dic43—41no—
178C2×Dic43—41no—
179C2×Dic43—84no—
180C2×Dic43—82no—
181C2×Dic43—82no—
182C2×Dic43—82no—
183D172—42no—
184D172—42no—
185C4×D43—84no—
186C8×C43—82no—
187#8378—431nomaximal, Sylow
188C22×C43—21no—
189C22×C43—22no—
190C22×C43—21no—
191C22×C43—22no—
192C22×C43—42no—
193C22×C43—41no—
194C22×C43—41no—
195C22×C43—41no—
196C22×C43—41no—
197C22×C43—41no—
198C22×C43—81no—
199C22×C43—81no—
200C22×C43#37911yescharacteristic
201C22×C43#41611yescharacteristic
202C22×C43#41711yescharacteristic
203C22×C43#44912yes—
204C22×C43#45212yes—
205C2×D43—42no—
206C2×D43—42no—
207C2×D43—42no—
208C2×D43—82no—
209C2×D43—82no—
210C4×C43—22no—
211C4×C43—21no—
212C4×C43—41no—
213C4×C43—41no—
214C4×C43—41no—
215C4×C43#41012yes—
216Dic43—42no—
217Dic43—42no—
218Dic43—42no—
219Dic43—162no—
220C2×#553—431no—
221#1824—432no—
222#1799—431no—
223#1519—432no—
224#1459D4311yescharacteristic, complemented
225C2×C43—22no—
226C2×C43—21no—
227C2×C43—21no—
228C2×C43—22no—
229C2×C43—81no—
230C2×C43#178211yescharacteristic
231C2×C43#178811yescharacteristic
232C2×C43#179511yescharacteristic
233D43—82no—
234#553—864no—
235#553—864no—
236C2×#126—861no—
237C2×#125—431no—
238C2×#123—861no—
239C2×#121—431no—
240C2×#121—431no—
241C2×#121—861no—
242C2×C4×D4—431no—
243C2×C4×D4—861no—
244C2×C4×D4C2×D4311yescharacteristic
245C2×#117—431no—
246C22×C4⋊C4—431no—
247C2×#99—861no—
248C2×C22⋊C8C2×D4312yes—
249#380—432no—
250#342—861no—
251#340—864no—
252#327—864no—
253#324—21no—
254#323—21no—
255C43#837811yescharacteristic, complemented, Sylow
256C22×D4—431no—
257C22×D4—861no—
258C22×D4—861no—
259C22×D4D17211yescharacteristic
260C23×C4—861no—
261C23×C4—861no—
262C23×C4C4×D4311yescharacteristic
263C23×C4C22×D4311yescharacteristic
264C22×C8—22no—
265#126—868no—
266#125—862no—
267#125—862no—
268#123—868no—
269#121—434no—
270#121—862no—
271#121—862no—
272#121—868no—
273#121—862no—
274C4×D4—22no—
275C4×D4—22no—
276C4×D4—862no—
277C4×D4—862no—
278C4×D4—868no—
279#117—862no—
280#117—862no—
281C2×C4⋊C4—431no—
282C2×C4⋊C4—431no—
283C2×C4⋊C4—431no—
284C2×C4⋊C4—434no—
285C2×C4⋊C4—861no—
286C2×C4⋊C4—861no—
287C2×C4⋊C4—862no—
288C2×C4⋊C4—861no—
289C2×C4⋊C4—862no—
290C2×C4⋊C4C22⋊D4311yescharacteristic
291C2×C22⋊C4—861no—
292C2×C22⋊C4—861no—
293C2×C22⋊C4—861no—
294C2×C22⋊C4—861no—
295C2×C22⋊C4—862no—
296C2×C22⋊C4D17211yescharacteristic
297C2×C22⋊C4C22⋊D4311yescharacteristic
298C2×C42—861no—
299C2×C42C4×D4311yescharacteristic
300#99—1722no—
301C22⋊C8—22no—
302C22⋊C8—22no—
303#95—862no—
304C24—861no—
305C24(C2×D43)⋊C411yescharacteristic
306C24C2×D17211yescharacteristic
307C2×D4—22no—
308C2×D4—22no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—432no—
312C2×D4—864no—
313C2×D4—864no—
314C2×D4—861no—
315C2×D4—3442no—
316C2×D4—1722no—
317C2×D4—1722no—
318C2×D4—1721no—
319C2×D4—1721no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—864no—
325C22×C4—864no—
326C22×C4—861no—
327C22×C4—861no—
328C22×C4—861no—
329C22×C4—3442no—
330C22×C4—3442no—
331C22×C4—1722no—
332C22×C4(C2×D43)⋊C411yescharacteristic
333C22×C4(C2×D43)⋊C411yescharacteristic
334C22×C4(C2×D43)⋊C411yescharacteristic
335C22×C4C2×C4×D4311yescharacteristic
336C22×C4D4×D4312yes—
337C22×C4D4×D4312yes—
338C22×C4C2×C22⋊D4311yescharacteristic
339C2×C8—44no—
340C2×C8—42no—
341C4⋊C4—22no—
342C4⋊C4—432no—
343C4⋊C4—432no—
344C4⋊C4—432no—
345C4⋊C4—864no—
346C4⋊C4—864no—
347C4⋊C4—861no—
348C4⋊C4—861no—
349C4⋊C4—861no—
350C4⋊C4—864no—
351C4⋊C4—1724no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—864no—
355C22⋊C4—864no—
356C22⋊C4—864no—
357C22⋊C4—864no—
358C22⋊C4—1722no—
359C22⋊C4—1722no—
360C42—21no—
361C42—21no—
362C42—864no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—862no—
371C23—1722no—
372C23—1722no—
373C23—1721no—
374C23—1721no—
375C23C2×(C2×D43)⋊C411yescharacteristic
376C23#1306329512yes—
377C23#1306334712yes—
378C23#1306335311yescharacteristic
379C23#1306335811yescharacteristic
380D4—42no—
381D4—42no—
382D4—3444no—
383D4—1722no—
384D4—1724no—
385D4—1724no—
386D4—1722no—
387C2×C4—24no—
388C2×C4—22no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—862no—
401C2×C4—862no—
402C2×C4—862no—
403C2×C4—3444no—
404C2×C4—3444no—
405C2×C4—3442no—
406C2×C4—3442no—
407C2×C4—3442no—
408C2×C4—1722no—
409C2×C4—1722no—
410C2×C4—1721no—
411C2×C4—1721no—
412C2×C4C22⋊C4×D4311yescharacteristic
413C2×C4C22⋊C4×D4311yescharacteristic
414C2×C4#1306329312yes—
415C8—82no—
416C22—21no—
417C22—22no—
418C22—21no—
419C22—22no—
420C22—42no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—81no—
427C22—81no—
428C22—3442no—
429C22—3442no—
430C22—1722no—
431C22—1722no—
432C22—1722no—
433C22#1458275411yescharacteristic
434C22#1458289611yescharacteristic
435C22#1458290111yescharacteristic
436C22#1458304612yes—
437C22#1458306312yes—
438C4—22no—
439C4—21no—
440C4—41no—
441C4—41no—
442C4—41no—
443C4—1722no—
444C4—1722no—
445C4—1722no—
446C4—6882no—
447C4#1458287112yes—
448C2—22no—
449C2—21no—
450C2—21no—
451C2—22no—
452C2—81no—
453C2—3442no—
454C2#1913451111yescharacteristic
455C2#1913453611yescharacteristic
456C2#1913456611yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1459C2
socleC22×C43#379
prime radicalC2×#14583595C2
cosocleC23×C4×C43C23
hypercenter#1459D43
hypocenterC43#8378
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
2. #19134686C2semidirect
3. #19134583C2semidirect
4. #19133164C2semidirect
5. C43×#1459C2semidirect
9. C2×#13063317C4semidirect
11. C2×#13063299C4semidirect
14. C2×C4×D172C4semidirect
16. C2×#13063284C4semidirect
224. #1459D43semidirect
255. C43#8378semidirect

Maximal subgroups

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

subgroupindex
C2×#145835952
#191346862
#191345832
#191331642
C43×#14592
#837843