Finite Group Databasebeta

← #25000990

Subgroups — #25000990

Order 11008.

532 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 99 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#19145353C211yesmaximal, characteristic
2#19135580C211yesmaximal, characteristic, complemented
3#19135431C211yesmaximal, characteristic
4#19135023C211yesmaximal, characteristic
5#19135018C211yesmaximal, characteristic, complemented
6#19132463C211yesmaximal, characteristic, complemented
7C43×#1850C211yesmaximal, characteristic, complemented
8C2×#13063304C2211yescharacteristic
9C2×#13063299C2211yescharacteristic
10#14583230—21no—
11#14583218—21no—
12#14583128—21no—
13#14583128—21no—
14#14583052—21no—
15#14583040—21no—
16C2×#13063250—21no—
17C2×#13063247—21no—
18C2×#13063239—21no—
19C2×#13063239—21no—
20#14582759C2211yescharacteristic
21#14582759C2211yescharacteristic
22#14582665—21no—
23#14582665—21no—
24#14582662—21no—
25#14582662—21no—
26C23×C8×C43C2211yescharacteristic
27C2×C4⋊C8×C43—21no—
28C2×C22⋊C8×C43C2211yescharacteristic
29C4×C22⋊C4×C43C2211yescharacteristic
30C43×#336—21no—
31C22×Dic86D411yescharacteristic
32C22×D172D411yescharacteristic
33C22×C22⋊D43—21no—
34C2×#10621873—21no—
35C2×#10621873—21no—
36#13063304—21no—
37#13063304—21no—
38#13063304—21no—
39#13063304—21no—
40#13063299—21no—
41#13063299—21no—
42#13063299—21no—
43#13063299—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43—21no—
46C2×C4⋊Dic43D411yescharacteristic
47C2×C4⋊Dic43D411yescharacteristic
48C2×Dic43⋊C4—21no—
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43—21no—
51C2×C22⋊Dic43—21no—
52C2×(C2×D43)⋊C4—21no—
53#13063257—21no—
54#13063257—21no—
55#13063250—21no—
56#13063250—21no—
57#13063250—42no—
58#13063247—21no—
59#13063247—21no—
60#13063247—42no—
61#13063239—42no—
62#13063239—42no—
63C43⋊#95—21no—
64C43⋊#95—21no—
65C23×C4×C43C2311yescharacteristic
66C22×C8×C43—21no—
67C22×C8×C43—21no—
68C22×C8×C43—21no—
69C22×C8×C43—42no—
70C22×C8×C43D411yescharacteristic
71C22×C8×C43D411yescharacteristic
72C2×C22⋊C4×C43D411yescharacteristic
73C2×C22⋊C4×C43D411yescharacteristic
74C2×C42×C43—21no—
75C4⋊C8×C43—42no—
76C22⋊C8×C43—21no—
77C22⋊C8×C43—21no—
78#95×C43—21no—
79C24×C43C2×D411yescharacteristic
80C23×D43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—41no—
84C22×C4×C43—41no—
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43#4111yescharacteristic
89C22×C4×C43#4111yescharacteristic
90C22×C4×C43#4111yescharacteristic
91C2×C22⋊D43—41no—
92C2×C22⋊D43—41no—
93C2×C22⋊D43—41no—
94C2×C22⋊D43—41no—
95C2×C22⋊D43—41no—
96C2×C22⋊D43—41no—
97C22×Dic43—21no—
98C22×Dic43—21no—
99C22×Dic43—21no—
100C22×Dic43—41no—
101C22×Dic43—41no—
102C2×D172—21no—
103C2×D172—21no—
104C2×D172—41no—
105C2×D172—41no—
106C2×Dic86—21no—
107C2×Dic86—21no—
108C2×Dic86—41no—
109C2×Dic86—41no—
110C2×C8×C43—22no—
111C2×C8×C43—22no—
112C2×C8×C43—22no—
113C2×C8×C43—21no—
114C2×C8×C43—21no—
115C2×C8×C43—41no—
116C2×C8×C43—41no—
117C2×C8×C43—41no—
118C2×C8×C43—41no—
119C2×C8×C43—41no—
120C2×C8×C43—41no—
121C22⋊C4×C43—21no—
122C22⋊C4×C43—21no—
123C22⋊C4×C43—21no—
124C22⋊C4×C43SD1612yescomplemented
125C42×C43—41no—
126C42×C43—41no—
127C22⋊Dic43—41no—
128C22⋊Dic43—41no—
129C22⋊Dic43—41no—
130C22⋊Dic43—41no—
131C22⋊Dic43—41no—
132C22⋊Dic43—41no—
133(C2×D43)⋊C4—41no—
134(C2×D43)⋊C4—41no—
135C4⋊Dic43—21no—
136C4⋊Dic43—21no—
137C4⋊Dic43—21no—
138C4⋊Dic43—21no—
139C4⋊Dic43—41no—
140C4⋊Dic43—41no—
141C4⋊Dic43—41no—
142C4⋊Dic43—41no—
143Dic43⋊C4—41no—
144Dic43⋊C4—41no—
145#10621873—81no—
146#10621873—81no—
147C23×C43—41no—
148C23×C43—41no—
149C23×C43#12111yescharacteristic
150C23×C43#12111yescharacteristic
151C23×C43#12111yescharacteristic
152C23×C43C2×SD1611yescharacteristic
153C23×C43#13511yescharacteristic
154C23×C43AGL(1,ℤ/8)11yescharacteristic
155C23×C43#13711yescharacteristic
156C22×D43—41no—
157C22×D43—41no—
158C22×D43—41no—
159C22×D43—81no—
160C22×D43—81no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—21no—
164C2×C4×C43—21no—
165C2×C4×C43—21no—
166C2×C4×C43—21no—
167C2×C4×C43—22no—
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—41no—
176C2×C4×C43#12011yescharacteristic
177C2×C4×C43#12311yescharacteristic
178C2×C4×C43#12311yescharacteristic
179C2×C4×C43#12411yescharacteristic
180C22⋊D43—81no—
181C22⋊D43—81no—
182C22⋊D43—81no—
183C22⋊D43—81no—
184C2×Dic43—41no—
185C2×Dic43—41no—
186C2×Dic43—41no—
187C2×Dic43—41no—
188C2×Dic43—41no—
189C2×Dic43—81no—
190C2×Dic43—81no—
191C2×Dic43—81no—
192C2×Dic43—81no—
193C2×Dic43—81no—
194C2×Dic43—81no—
195C2×Dic43—81no—
196C2×Dic43—81no—
197D172—42no—
198D172—41no—
199D172—41no—
200Dic86—42no—
201Dic86—41no—
202Dic86—41no—
203C8×C43—41no—
204C8×C43—42no—
205C8×C43—41no—
206#10565—431nomaximal, Sylow
207C22×C43—21no—
208C22×C43—21no—
209C22×C43—21no—
210C22×C43—21no—
211C22×C43—21no—
212C22×C43—21no—
213C22×C43—41no—
214C22×C43—41no—
215C22×C43—41no—
216C22×C43—41no—
217C22×C43#39411yescharacteristic
218C22×C43#46011yescharacteristic
219C22×C43#46111yescharacteristic
220C22×C43#46311yescharacteristic
221C22×C43#46411yescharacteristic
222C22×C43#46511yescharacteristic
223C22×C43#46811yescharacteristic
224C2×D43—81no—
225C2×D43—81no—
226C2×D43—81no—
227C2×D43—161no—
228C2×D43—161no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—42no—
233C4×C43—81no—
234C4×C43B(4,𝔽2)11yescharacteristic
235C4×C43#45811yescharacteristic
236Dic43—81no—
237Dic43—81no—
238Dic43—81no—
239Dic43—161no—
240Dic43—161no—
241#3187—431no—
242#1996—431no—
243#1964—431no—
244#1893—431no—
245#1892—431no—
246#1850D4311yescharacteristic, complemented
247#1289—431no—
248C2×C43—21no—
249C2×C43—21no—
250C2×C43—21no—
251C2×C43—21no—
252C2×C43—21no—
253C2×C43—21no—
254C2×C43#204411yescharacteristic
255C2×C43#205311yescharacteristic
256C2×C43#205511yescharacteristic
257D43—161no—
258C23×C8C2×D4311yescharacteristic
259C2×C22⋊Q8—431no—
260C2×#121—431no—
261#483—861no—
262#481—861no—
263#465—861no—
264#465—861no—
265#450—861no—
266#448—861no—
267C2×C4⋊C8—21no—
268C2×#103—861no—
269C2×#102—861no—
270C2×#99—861no—
271C2×#99—861no—
272C2×C22⋊C8C2×D4311yescharacteristic
273#380—431no—
274#380—431no—
275C4×C22⋊C4C2×D4311yescharacteristic
276#342—861no—
277#342—861no—
278#340—861no—
279#340—861no—
280#336—21no—
281C43#1056511yescharacteristic, complemented, Sylow
282C22×Q8—431no—
283C22×D4—431no—
284C22×D4—861no—
285C23×C4C22×D4311yescharacteristic
286C2×SD16—861no—
287C2×SD16—861no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—42no—
292C22×C8C22⋊D4311yescharacteristic
293C22×C8C22⋊D4311yescharacteristic
294C22⋊Q8—861no—
295C22⋊Q8—861no—
296C22⋊Q8—861no—
297C22⋊Q8—861no—
298#121—861no—
299#121—861no—
300#121—861no—
301#121—861no—
302C2×C4⋊C4—431no—
303C2×C4⋊C4—431no—
304C2×C4⋊C4—861no—
305C2×C4⋊C4—861no—
306C2×C4⋊C4—861no—
307C2×C22⋊C4—861no—
308C2×C22⋊C4—861no—
309C2×C22⋊C4—861no—
310C2×C22⋊C4—861no—
311C2×C22⋊C4D17211yescharacteristic
312C2×C22⋊C4D17211yescharacteristic
313C2×C42—21no—
314#106—861no—
315#106—861no—
316C4⋊C8—42no—
317#103—861no—
318#103—861no—
319#103—1722no—
320#102—861no—
321#102—861no—
322#102—1722no—
323#99—1722no—
324#99—1722no—
325C22⋊C8—21no—
326C22⋊C8—21no—
327#95—21no—
328#95—861no—
329#95—861no—
330C24—861no—
331C24C2×D17211yescharacteristic
332C2×Q8—861no—
333C2×Q8—861no—
334C2×Q8—1721no—
335C2×Q8—1721no—
336C2×D4—861no—
337C2×D4—861no—
338C2×D4—1721no—
339C2×D4—1721no—
340C2×D4—1721no—
341C2×D4—1721no—
342C2×D4—1721no—
343C2×D4—1721no—
344C2×D4—1721no—
345C2×D4—1721no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—861no—
351C22×C4—861no—
352C22×C4—861no—
353C22×C4—1721no—
354C22×C4—1721no—
355C22×C4#1062189811yescharacteristic
356C22×C4D4×D4311yescharacteristic
357C22×C4D4×D4311yescharacteristic
358C22×C4#1062190211yescharacteristic
359C22×C4#1062190211yescharacteristic
360C22×C4C2×C22⋊D4311yescharacteristic
361SD16—3441no—
362SD16—3441no—
363C2×C8—22no—
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—21no—
367C2×C8—21no—
368C2×C8—41no—
369C2×C8—41no—
370C2×C8—41no—
371C2×C8—41no—
372C2×C8—41no—
373C2×C8—41no—
374C4⋊C4—861no—
375C4⋊C4—861no—
376C4⋊C4—861no—
377C4⋊C4—861no—
378C4⋊C4—1721no—
379C4⋊C4—1721no—
380C4⋊C4—1721no—
381C4⋊C4—1721no—
382C4⋊C4—1721no—
383C4⋊C4—1721no—
384C22⋊C4—21no—
385C22⋊C4—21no—
386C22⋊C4—21no—
387C22⋊C4—1721no—
388C22⋊C4—1721no—
389C22⋊C4—1721no—
390C22⋊C4—1721no—
391C22⋊C4—1721no—
392C22⋊C4—1721no—
393C22⋊C4—1721no—
394C22⋊C4—1721no—
395C22⋊C4#1062187312yescomplemented
396C42—41no—
397C42—41no—
398C23—41no—
399C23—41no—
400C23—3441no—
401C23—3441no—
402C23—1721no—
403C23—1721no—
404C23—1721no—
405C23#1306329911yescharacteristic
406C23#1306330011yescharacteristic
407C23#1306330011yescharacteristic
408C23C2×#1062187311yescharacteristic
409C23#1306334711yescharacteristic
410C23#1306335311yescharacteristic
411C23#1306335811yescharacteristic
412Q8—1722no—
413Q8—1721no—
414Q8—1721no—
415D4—3441no—
416D4—3441no—
417D4—3441no—
418D4—3441no—
419D4—1722no—
420D4—1721no—
421D4—1721no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—3441no—
438C2×C4—3441no—
439C2×C4—3441no—
440C2×C4—3441no—
441C2×C4—3441no—
442C2×C4—3441no—
443C2×C4—3441no—
444C2×C4—3441no—
445C2×C4—1721no—
446C2×C4—1721no—
447C2×C4—1721no—
448C2×C4—1721no—
449C2×C4—1721no—
450C2×C4#1306329311yescharacteristic
451C2×C4#1306331011yescharacteristic
452C2×C4#1306331011yescharacteristic
453C2×C4#1306331411yescharacteristic
454C8—42no—
455C8—41no—
456C8—41no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—3441no—
468C22—3441no—
469C22—3441no—
470C22—6881no—
471C22—6881no—
472C22#1458281611yescharacteristic
473C22#1458310011yescharacteristic
474C22#1458310511yescharacteristic
475C22#1458311511yescharacteristic
476C22#1458312211yescharacteristic
477C22#1458312811yescharacteristic
478C22#1458314511yescharacteristic
479C4—21no—
480C4—21no—
481C4—21no—
482C4—42no—
483C4—81no—
484C4—3441no—
485C4—3441no—
486C4—3441no—
487C4—6881no—
488C4—6881no—
489C4#1458308511yescharacteristic
490C4#1458308811yescharacteristic
491C2—21no—
492C2—21no—
493C2—21no—
494C2—21no—
495C2—21no—
496C2—21no—
497C2—6881no—
498C2#1913584611yescharacteristic
499C2#1913590111yescharacteristic
500C2#1913591311yescharacteristic
subgroupG/H
centerC22#14582816
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1850C2
socleC22×C43#394
prime radicalC2×#13063299C22
hypercenter#1850D43
hypocenterC43#10565
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
2. #19135580C2semidirect
5. #19135018C2semidirect
6. #19132463C2semidirect
7. C43×#1850C2semidirect
124. C22⋊C4×C43SD16semidirect
246. #1850D43semidirect
281. C43#10565semidirect
395. C22⋊C4#10621873semidirect

Maximal subgroups

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

subgroupindex
#191453532
#191355802
#191354312
#191350232
#191350182
#191324632
C43×#18502
#1056543