Finite Group Databasebeta

← #24993153

Subgroups — #24993153

Order 11008.

606 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 606 conjugacy classes of subgroups — too many to draw. Only its 107 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#19145348C211yesmaximal, characteristic
2#19137642C211yesmaximal, characteristic
3#19135581C211yesmaximal, characteristic, complemented
4#19133164C211yesmaximal, characteristic
5#19132474C211yesmaximal, characteristic, complemented
6#19132442C211yesmaximal, characteristic, complemented
7C2×C43×#328C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9C2×C4×C22⋊D43—21no—
10#14583227—21no—
11#14583217C412yescomplemented
12#14583130—22no—
13#14583049—21no—
14#14583038C412yescomplemented
15C2×C22⋊(C43⋊C8)C2211yescharacteristic
16#14582788—21no—
17#14582782—21no—
18#14582778—21no—
19#14582777—21no—
20#14582759C2211yescharacteristic
21C4×C22⋊Dic43C2211yescharacteristic
22#14582746—21no—
23#14582666—21no—
24#14582666—21no—
25#14582634—22no—
26C2×C22⋊Q8×C43C2211yescharacteristic
27C2×C22⋊C8×C43C2211yescharacteristic
28C2×#95×C43C2211yescharacteristic
29C43×#328—21no—
30C43×#328—21no—
31C22×D172D411yescharacteristic
32C22×C22⋊D43—21no—
33C22×C4×D43—21no—
34C2×#10621884—22no—
35C22×C43⋊C8—21no—
36#13063299—21no—
37#13063299—21no—
38#13063299C2×C412yes—
39#13063299D412yes—
40C4×C22⋊D43—42no—
41C4×C22⋊D43—42no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43D411yescharacteristic
44C2×Dic43⋊C4—21no—
45C2×C22⋊Dic43—21no—
46C2×C22⋊Dic43D411yescharacteristic
47C2×C22⋊Dic43D411yescharacteristic
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—21no—
50C2×(C2×D43)⋊C4—21no—
51C2×(C2×D43)⋊C4—21no—
52C2×C4×Dic43—21no—
53C2×C4×Dic43—21no—
54#13063256—22no—
55#13063249—22no—
56#13063245—22no—
57C22⋊(C43⋊C8)—21no—
58C22⋊(C43⋊C8)C2×C412yescomplemented
59C43⋊#95—21no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95—21no—
63C22×Q8×C43C2×C411yescharacteristic, complemented
64C23×C4×C43—21no—
65C23×C4×C43C2311yescharacteristic
66C22×C8×C43—21no—
67C22⋊Q8×C43—21no—
68C22⋊Q8×C43—21no—
69C22⋊Q8×C43—21no—
70C22⋊Q8×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
73C2×C22⋊C4×C43—21no—
74C22⋊C8×C43—21no—
75C22⋊C8×C43—21no—
76#95×C43—21no—
77#95×C43D411yescharacteristic
78#95×C43D411yescharacteristic
79C24×C43C2×D411yescharacteristic
80C23×D43—21no—
81C2×Q8×C43—21no—
82C2×Q8×C43—21no—
83C2×Q8×C43—81no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43—42no—
89C22×C4×C43—41no—
90C22×C4×C43—41no—
91C22×C4×C43—81no—
92C22×C4×C43—81no—
93C22×C4×C43C22×C411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43#4111yescharacteristic
98C22×C4×C43#4111yescharacteristic
99C2×C22⋊D43—22no—
100C2×C22⋊D43—22no—
101C2×C22⋊D43—41no—
102C2×C22⋊D43—41no—
103C2×C22⋊D43—41no—
104C2×C22⋊D43—41no—
105C22×Dic43—21no—
106C22×Dic43—21no—
107C22×Dic43—21no—
108C22×Dic43—41no—
109C2×D172—21no—
110C2×D172—81no—
111C2×D172C22⋊C412yes—
112C2×C4×D43—42no—
113C2×C4×D43—42no—
114C2×C4×D43—81no—
115C2×C8×C43—41no—
116C2×C8×C43—81no—
117C4⋊C4×C43—21no—
118C4⋊C4×C43—21no—
119C4⋊C4×C43—41no—
120C4⋊C4×C43—41no—
121C22⋊C4×C43—41no—
122C22⋊C4×C43—41no—
123C22⋊Dic43—21no—
124C22⋊Dic43—21no—
125C22⋊Dic43—21no—
126C22⋊Dic43—41no—
127C22⋊Dic43—41no—
128C22⋊Dic43SD1612yescomplemented
129#10621884—82no—
130(C2×D43)⋊C4—22no—
131(C2×D43)⋊C4—22no—
132(C2×D43)⋊C4—42no—
133(C2×D43)⋊C4—42no—
134(C2×D43)⋊C4—81no—
135C4⋊Dic43—21no—
136C4⋊Dic43—81no—
137C4⋊Dic43C22⋊C412yes—
138Dic43⋊C4—42no—
139C4×Dic43—42no—
140C4×Dic43—81no—
141C2×C43⋊C8—22no—
142C2×C43⋊C8—81no—
143C23×C43—41no—
144C23×C43—41no—
145C23×C43C4×D411yescharacteristic
146C23×C43#12011yescharacteristic
147C23×C43#12111yescharacteristic
148C23×C43C2×SD1611yescharacteristic
149C23×C43#13511yescharacteristic
150C23×C43AGL(1,ℤ/8)11yescharacteristic
151C23×C43#13711yescharacteristic
152C22×D43—22no—
153C22×D43—41no—
154C22×D43—41no—
155C22×D43—41no—
156C22×D43—41no—
157C22×D43—41no—
158C22×D43—41no—
159Q8×C43—42no—
160Q8×C43—81no—
161C2×C4×C43—22no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—82no—
176C2×C4×C43—82no—
177C2×C4×C43—81no—
178C2×C4×C43—81no—
179C2×C4×C43C2×C22⋊C411yescharacteristic
180C2×C4×C43C4×D411yescharacteristic
181C2×C4×C43#12111yescharacteristic
182C2×C4×C43#12311yescharacteristic
183C22⋊D43—42no—
184C22⋊D43—42no—
185C22⋊D43—42no—
186C22⋊D43—42no—
187C2×Dic43—22no—
188C2×Dic43—22no—
189C2×Dic43—41no—
190C2×Dic43—41no—
191C2×Dic43—41no—
192C2×Dic43—41no—
193C2×Dic43—41no—
194C2×Dic43—41no—
195C2×Dic43—41no—
196C2×Dic43—81no—
197C2×Dic43—81no—
198C2×Dic43—81no—
199D172—42no—
200D172—81no—
201C4×D43—84no—
202C8×C43—81no—
203C43⋊C8—42no—
204#9275—431nomaximal, Sylow
205C22×C43—21no—
206C22×C43—21no—
207C22×C43—21no—
208C22×C43—21no—
209C22×C43—21no—
210C22×C43—21no—
211C22×C43—41no—
212C22×C43—41no—
213C22×C43—41no—
214C22×C43—41no—
215C22×C43#38611yescharacteristic
216C22×C43C4×SD1611yescharacteristic
217C22×C43#44011yescharacteristic
218C22×C43#45011yescharacteristic
219C22×C43#45211yescharacteristic
220C22×C43#46111yescharacteristic
221C22×C43#46311yescharacteristic
222C2×D43—42no—
223C2×D43—42no—
224C2×D43—42no—
225C2×D43—81no—
226C2×D43—81no—
227C2×D43—81no—
228C2×D43—81no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—42no—
234C4×C43—81no—
235C4×C43—81no—
236C4×C43—81no—
237Dic43—42no—
238Dic43—42no—
239Dic43—81no—
240Dic43—161no—
241#3187—431no—
242#2364—431no—
243#1996—431no—
244#1519—431no—
245C2×#328D4311yescharacteristic, complemented
246#1294—431no—
247#1282—431no—
248C2×C43—21no—
249C2×C43—21no—
250C2×C43—21no—
251C2×C43—21no—
252C2×C43—21no—
253C2×C43—21no—
254C2×C43#187711yescharacteristic
255C2×C43#190611yescharacteristic
256C2×C43#191311yescharacteristic
257D43—82no—
258C2×C22⋊Q8C2×D4311yescharacteristic
259C2×#121—431no—
260C2×C4×D4—861no—
261#483—861no—
262#481—432no—
263#465—862no—
264#450—861no—
265#448—432no—
266C2×C22⋊C8—431no—
267C2×C22⋊C8C2×D4311yescharacteristic
268#388—861no—
269#387—861no—
270#386—861no—
271#386—861no—
272#380—431no—
273C4×C22⋊C4—431no—
274C4×C22⋊C4—861no—
275C2×#95C2×D4311yescharacteristic
276#342—861no—
277#342—861no—
278#328—21no—
279#328—21no—
280#327—862no—
281C43#927511yescharacteristic, complemented, Sylow
282C22×Q8C4×D4311yescharacteristic, complemented
283C22×D4—431no—
284C22×D4—861no—
285C23×C4—21no—
286C23×C4—861no—
287C23×C4C22×D4311yescharacteristic
288C2×SD16—862no—
289C22×C8—21no—
290C22×C8—861no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295#121—432no—
296#121—432no—
297#121—861no—
298#121—861no—
299C4×D4—1722no—
300C4×D4—1722no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—431no—
303C2×C4⋊C4—861no—
304C2×C4⋊C4—861no—
305C2×C4⋊C4C4×D4311yescharacteristic, complemented
306C2×C22⋊C4—21no—
307C2×C22⋊C4—431no—
308C2×C22⋊C4—431no—
309C2×C22⋊C4—861no—
310C2×C22⋊C4—861no—
311C2×C22⋊C4—861no—
312C2×C22⋊C4—861no—
313C2×C22⋊C4—861no—
314C2×C42—861no—
315C2×C42—861no—
316#106—862no—
317#103—862no—
318#102—862no—
319C22⋊C8—21no—
320C22⋊C8—21no—
321C22⋊C8—432no—
322C22⋊C8—861no—
323#95—21no—
324#95—861no—
325#95—861no—
326#95—861no—
327#95—861no—
328#95C22⋊D4311yescharacteristic
329#95C22⋊D4311yescharacteristic
330C24—861no—
331C24D4×D4311yescharacteristic
332C2×Q8—21no—
333C2×Q8—21no—
334C2×Q8—81no—
335C2×D4—432no—
336C2×D4—862no—
337C2×D4—862no—
338C2×D4—861no—
339C2×D4—3441no—
340C2×D4—1721no—
341C2×D4—1721no—
342C2×D4—1721no—
343C2×D4—1721no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—42no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—81no—
352C22×C4—81no—
353C22×C4—861no—
354C22×C4—861no—
355C22×C4—861no—
356C22×C4—3441no—
357C22×C4—1722no—
358C22×C4—1722no—
359C22×C4—1721no—
360C22×C4C2×C4×D4311yescharacteristic
361C22×C4#1062189811yescharacteristic
362C22×C4D4×D4311yescharacteristic
363C22×C4D4×D4311yescharacteristic
364C22×C4#1062190011yescharacteristic
365C22×C4C2×C22⋊D4311yescharacteristic
366SD16—3442no—
367C2×C8—41no—
368C2×C8—81no—
369C2×C8—862no—
370C2×C8—3441no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—432no—
376C4⋊C4—861no—
377C4⋊C4—3441no—
378C4⋊C4—1722no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—432no—
382C22⋊C4—861no—
383C22⋊C4—862no—
384C22⋊C4—862no—
385C22⋊C4—861no—
386C22⋊C4—861no—
387C22⋊C4—3441no—
388C22⋊C4—1722no—
389C22⋊C4—1722no—
390C22⋊C4—1721no—
391C22⋊C4—1721no—
392C42—3441no—
393C42—1722no—
394C23—41no—
395C23—41no—
396C23—862no—
397C23—1721no—
398C23—1721no—
399C23—1721no—
400C23—1721no—
401C23—1721no—
402C23—1721no—
403C23(C22⋊D43)⋊C411yescharacteristic
404C23#1306329311yescharacteristic
405C23#1306329811yescharacteristic
406C23SD16×D4311yescharacteristic
407C23#1306334811yescharacteristic
408C23#1306335211yescharacteristic
409C23#1306335711yescharacteristic
410Q8—42no—
411Q8—81no—
412D4—3441no—
413D4—1722no—
414D4—1722no—
415D4—1722no—
416D4—1722no—
417D4—1722no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—82no—
433C2×C4—82no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—862no—
437C2×C4—862no—
438C2×C4—3444no—
439C2×C4—3441no—
440C2×C4—3441no—
441C2×C4—3441no—
442C2×C4—1721no—
443C2×C4—1721no—
444C2×C4—1721no—
445C2×C4—1721no—
446C2×C4—1721no—
447C2×C4—1721no—
448C2×C4—1721no—
449C2×C4C22⋊C4×D4311yescharacteristic
450C2×C4C4×C22⋊D4311yescharacteristic
451C2×C4#1306329611yescharacteristic
452C2×C4#1306330711yescharacteristic
453C8—81no—
454C8—1722no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—3441no—
466C22—3441no—
467C22—3441no—
468C22—3441no—
469C22—1722no—
470C22—1722no—
471C22—1722no—
472C22#1458277511yescharacteristic
473C22#1458298411yescharacteristic
474C22#1458300211yescharacteristic
475C22#1458304811yescharacteristic
476C22#1458306011yescharacteristic
477C22#1458310311yescharacteristic
478C22#1458311711yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—42no—
484C4—81no—
485C4—81no—
486C4—81no—
487C4—3441no—
488C4—1722no—
489C4—1722no—
490C4—6881no—
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—21no—
496C2—21no—
497C2—3442no—
498C2#1913492611yescharacteristic
499C2#1913509911yescharacteristic
500C2#1913513411yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#328C2
socleC22×C43#386
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenterC2×#328D43
hypocenterC43#9275
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
3. #19135581C2semidirect
5. #19132474C2semidirect
6. #19132442C2semidirect
7. C2×C43×#328C2semidirect
11. #14583217C4semidirect
14. #14583038C4semidirect
58. C22⋊(C43⋊C8)C2×C4semidirect
63. C22×Q8×C43C2×C4semidirect
72. C2×C4⋊C4×C43C2×C4semidirect
128. C22⋊Dic43SD16semidirect
245. C2×#328D43semidirect
281. C43#9275semidirect
282. C22×Q8C4×D43semidirect
305. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191453482
#191376422
#191355812
#191331642
#191324742
#191324422
C2×C43×#3282
#927543