Finite Group Databasebeta

← #24992657

Subgroups — #24992657

Order 11008.

762 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 113 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#19140331C211yesmaximal, characteristic
2#19137208C211yesmaximal, characteristic, complemented
3#19133163C211yesmaximal, characteristic, complemented
4C2×#14582622C211yesmaximal, characteristic, complemented
5#19132463C211yesmaximal, characteristic, complemented
6#19132462C211yesmaximal, characteristic, complemented
7C43×#1519C211yesmaximal, characteristic, complemented
8C2×#13063293—21no—
9C22×(C2×D43)⋊C4C2211yescharacteristic
10C2×C22⋊C4×D43—21no—
11C2×C22⋊(C43⋊C8)C2211yescharacteristic
12#14582825C412yescomplemented
13#14582815—22no—
14#14582807C412yescomplemented
15#14582779—21no—
16#14582773—22no—
17#14582770—22no—
18#14582759C2211yescharacteristic
19#14582759C2211yescharacteristic
20#14582757—21no—
21#14582633—22no—
22#14582622—22no—
23C2×#121×C43C2211yescharacteristic
24C2×C22⋊C8×C43C2211yescharacteristic
25C43×#380C2211yescharacteristic
26C43×#327—22no—
27C24×D43D411yescharacteristic
28C22×C22⋊D43—22no—
29C23×Dic43D411yescharacteristic
30C22×C4×D43—22no—
31C22×C43⋊C8—21no—
32#13063293—42no—
33#13063293—42no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43—21no—
36C2×Dic43⋊C4—22no—
37C2×C22⋊Dic43—21no—
38C2×C22⋊Dic43—21no—
39C2×C22⋊Dic43—22no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—22no—
45C2×(C2×D43)⋊C4—22no—
46C2×(C2×D43)⋊C4C2×C412yes—
47C2×(C2×D43)⋊C4D412yes—
48C22⋊C4×D43—42no—
49C22⋊C4×D43—42no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C43⋊#95—22no—
53C43⋊#95—22no—
54C43⋊#95C2×C412yescomplemented
55C43⋊#95D412yescomplemented
56C22×D4×C43—21no—
57C22×D4×C43C2×C411yescharacteristic, complemented
58C23×C4×C43C2311yescharacteristic
59C22×C8×C43—21no—
60#121×C43—21no—
61#121×C43—21no—
62#121×C43—21no—
63#121×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
66C2×C22⋊C4×C43—21no—
67C2×C22⋊C4×C43—21no—
68C22⋊C8×C43—21no—
69C22⋊C8×C43—21no—
70#95×C43D412yescomplemented
71C24×C43—21no—
72C24×C43C2×D411yescharacteristic
73C23×D43—21no—
74C23×D43—21no—
75C23×D43—21no—
76C23×D43—21no—
77C23×D43—81no—
78C23×D43—81no—
79C23×D43C22⋊C412yes—
80C23×D43D812yes—
81C23×D43SD1612yes—
82C2×D4×C43—21no—
83C2×D4×C43—21no—
84C2×D4×C43—41no—
85C2×D4×C43—41no—
86C2×D4×C43—41no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C2×D4×C43—41no—
90C2×D4×C43—81no—
91C22×C4×C43—21no—
92C22×C4×C43—22no—
93C22×C4×C43—81no—
94C22×C4×C43C22×C411yescharacteristic
95C22×C4×C43C2×D411yescharacteristic
96C22×C4×C43C2×D411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43#4111yescharacteristic
99C22×C4×C43#4111yescharacteristic
100C2×C22⋊D43—44no—
101C2×C22⋊D43—82no—
102C2×C22⋊D43—82no—
103C22×Dic43—22no—
104C22×Dic43—21no—
105C22×Dic43—22no—
106C22×Dic43—21no—
107C22×Dic43—81no—
108C22×Dic43C22⋊C412yes—
109C2×C4×D43—44no—
110C2×C4×D43—82no—
111C2×C4×D43—82no—
112C2×C8×C43—41no—
113C2×C8×C43—81no—
114C4⋊C4×C43—21no—
115C4⋊C4×C43—21no—
116C4⋊C4×C43—81no—
117C22⋊C4×C43—41no—
118C22⋊C4×C43—41no—
119C22⋊C4×C43—41no—
120C22⋊C4×C43—41no—
121C22⋊Dic43—41no—
122C22⋊Dic43—41no—
123C22⋊Dic43—41no—
124C22⋊Dic43—41no—
125C22⋊Dic43—82no—
126(C2×D43)⋊C4—22no—
127(C2×D43)⋊C4—22no—
128(C2×D43)⋊C4—22no—
129(C2×D43)⋊C4—22no—
130(C2×D43)⋊C4—44no—
131(C2×D43)⋊C4—44no—
132C4⋊Dic43—81no—
133C4⋊Dic43—81no—
134Dic43⋊C4—82no—
135C2×C43⋊C8—41no—
136C2×C43⋊C8—81no—
137C23×C43—41no—
138C23×C43—41no—
139C23×C43—42no—
140C23×C43—42no—
141C23×C43—41no—
142C23×C43—41no—
143C23×C43—41no—
144C23×C43C2×C22⋊C411yescharacteristic
145C23×C43#12011yescharacteristic
146C23×C43#12311yescharacteristic
147C23×C43C2×D811yescharacteristic
148C23×C43C2×SD1611yescharacteristic
149C23×C43AGL(1,ℤ/8)11yescharacteristic
150C23×C43#13711yescharacteristic
151C22×D43—22no—
152C22×D43—22no—
153C22×D43—22no—
154C22×D43—22no—
155C22×D43—22no—
156C22×D43—22no—
157C22×D43—42no—
158C22×D43—42no—
159C22×D43—42no—
160C22×D43—42no—
161C22×D43—82no—
162C22×D43—82no—
163C22×D43—81no—
164C22×D43—81no—
165C22×D43—82no—
166C22×D43—82no—
167C22×D43#10214yes—
168D4×C43—81no—
169D4×C43—81no—
170D4×C43—81no—
171D4×C43—81no—
172D4×C43—81no—
173D4×C43—81no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43—42no—
181C2×C4×C43—42no—
182C2×C4×C43—41no—
183C2×C4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43—42no—
186C2×C4×C43C4×D411yescharacteristic
187C2×C4×C43C4×D411yescharacteristic
188C2×C4×C43#12111yescharacteristic
189C2×C4×C43#12111yescharacteristic
190C22⋊D43—88no—
191C2×Dic43—22no—
192C2×Dic43—42no—
193C2×Dic43—42no—
194C2×Dic43—42no—
195C2×Dic43—42no—
196C2×Dic43—42no—
197C2×Dic43—42no—
198C2×Dic43—42no—
199C2×Dic43—42no—
200C2×Dic43—81no—
201C4×D43—88no—
202C8×C43—81no—
203C43⋊C8—81no—
204#9203—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—82no—
216C22×C43—82no—
217C22×C43—81no—
218C22×C43—81no—
219C22×C43—81no—
220C22×C43#38611yescharacteristic
221C22×C43C2×#10211yescharacteristic
222C22×C43#41711yescharacteristic
223C22×C43#44711yescharacteristic
224C22×C43#44811yescharacteristic
225C22×C43#48011yescharacteristic
226C22×C43#48111yescharacteristic
227C2×D43—24no—
228C2×D43—44no—
229C2×D43—44no—
230C2×D43—42no—
231C2×D43—42no—
232C2×D43—44no—
233C2×D43—82no—
234C2×D43—82no—
235C2×D43—82no—
236C4×C43—21no—
237C4×C43—21no—
238C4×C43—21no—
239C4×C43—21no—
240C4×C43—82no—
241C4×C43—81no—
242Dic43—42no—
243Dic43—82no—
244Dic43—82no—
245#2617—431no—
246#2315—431no—
247#1519—431no—
248#1519D4311yescharacteristic, complemented
249C2×#323—431no—
250#1289—431no—
251#1289—431no—
252C2×C43—21no—
253C2×C43—21no—
254C2×C43—21no—
255C2×C43—21no—
256C2×C43—21no—
257C2×C43—21no—
258C2×C43—161no—
259C2×C43#187411yescharacteristic
260C2×C43#191111yescharacteristic
261C2×C43#191311yescharacteristic
262D43—44no—
263C2×#121C2×D4311yescharacteristic
264C2×#120—861no—
265C22×C22⋊C4—431no—
266C22×C22⋊C4—861no—
267C2×C22⋊C8—431no—
268C2×C22⋊C8C2×D4311yescharacteristic
269#397—432no—
270#394—862no—
271#392—432no—
272#386—861no—
273#385—862no—
274#385—862no—
275#380—431no—
276#380—431no—
277#380—861no—
278#380C2×D4311yescharacteristic
279#327—22no—
280#327—862no—
281#323—862no—
282C43#920311yescharacteristic, complemented, Sylow
283C25—431no—
284C22×D4—21no—
285C22×D4—862no—
286C22×D4C4×D4311yescharacteristic, complemented
287C23×C4—431no—
288C23×C4—862no—
289C23×C4C22×D4311yescharacteristic
290C22×C8—21no—
291C22×C8—861no—
292#121—21no—
293#121—21no—
294#121—21no—
295#121—21no—
296#120—1722no—
297#120—1722no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—862no—
300C2×C4⋊C4—861no—
301C2×C4⋊C4—861no—
302C2×C4⋊C4C4×D4311yescharacteristic, complemented
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—432no—
306C2×C22⋊C4—432no—
307C2×C22⋊C4—861no—
308C2×C22⋊C4—861no—
309C2×C22⋊C4—861no—
310C2×C22⋊C4—861no—
311C2×C22⋊C4—862no—
312C2×C22⋊C4—862no—
313C2×C22⋊C4—862no—
314C2×C22⋊C4—861no—
315C2×C22⋊C4—861no—
316C2×C22⋊C4—1722no—
317C2×C22⋊C4—1722no—
318C22⋊C8—21no—
319C22⋊C8—21no—
320C22⋊C8—861no—
321C22⋊C8—861no—
322#95—432no—
323#95—432no—
324#95—862no—
325#95—862no—
326#95C22⋊D4312yescomplemented
327C24—21no—
328C24—432no—
329C24—432no—
330C24—432no—
331C24—861no—
332C24—861no—
333C24—861no—
334C24—861no—
335C24—3441no—
336C24—3441no—
337C24D4×D4311yescharacteristic
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—81no—
347C2×D4—3442no—
348C2×D4—3442no—
349C2×D4—1724no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—81no—
353C22×C4—432no—
354C22×C4—861no—
355C22×C4—861no—
356C22×C4—862no—
357C22×C4—862no—
358C22×C4—3442no—
359C22×C4—3442no—
360C22×C4—3441no—
361C22×C4—1724no—
362C22×C4C2×C4×D4311yescharacteristic
363C22×C4#1062189811yescharacteristic
364C22×C4D4×D4311yescharacteristic
365C22×C4D4×D4311yescharacteristic
366C22×C4#1062190011yescharacteristic
367C22×C4C2×C22⋊D4311yescharacteristic
368C2×C8—41no—
369C2×C8—81no—
370C2×C8—3441no—
371C2×C8—1721no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—81no—
375C4⋊C4—3442no—
376C4⋊C4—3441no—
377C4⋊C4—3441no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—862no—
383C22⋊C4—862no—
384C22⋊C4—862no—
385C22⋊C4—862no—
386C22⋊C4—3442no—
387C22⋊C4—1724no—
388C22⋊C4—1724no—
389C22⋊C4—1721no—
390C22⋊C4—1721no—
391C22⋊C4—1721no—
392C22⋊C4—1721no—
393C23—41no—
394C23—41no—
395C23—42no—
396C23—42no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—434no—
401C23—862no—
402C23—862no—
403C23—862no—
404C23—862no—
405C23—862no—
406C23—862no—
407C23—3441no—
408C23—3441no—
409C23—3442no—
410C23—3442no—
411C23—3442no—
412C23—3442no—
413C23—1722no—
414C23—1722no—
415C23—1722no—
416C23—1722no—
417C23C22⋊C4×D4311yescharacteristic
418C23#1306329311yescharacteristic
419C23#1306330711yescharacteristic
420C23D8×D4311yescharacteristic
421C23SD16×D4311yescharacteristic
422C23#1306334911yescharacteristic
423C23#1306335411yescharacteristic
424D4—81no—
425D4—81no—
426D4—81no—
427D4—81no—
428D4—81no—
429D4—81no—
430D4—3448no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—42no—
443C2×C4—862no—
444C2×C4—3448no—
445C2×C4—3441no—
446C2×C4—1722no—
447C2×C4—1722no—
448C2×C4—1722no—
449C2×C4—1722no—
450C2×C4—1722no—
451C2×C4—1722no—
452C2×C4—1722no—
453C2×C4—1722no—
454C2×C4(C22⋊D43)⋊C411yescharacteristic
455C2×C4C4×C22⋊D4311yescharacteristic
456C2×C4#1306329611yescharacteristic
457C2×C4#1306329811yescharacteristic
458C8—81no—
459C8—3441no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—82no—
471C22—82no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22—864no—
476C22—3442no—
477C22—3442no—
478C22—3442no—
479C22—1724no—
480C22—1724no—
481C22—1724no—
482C22—1722no—
483C22—1722no—
484C22#1458277511yescharacteristic
485C22#102×D4311yescharacteristic
486C22#1458289711yescharacteristic
487C22#1458303111yescharacteristic
488C22#1458303611yescharacteristic
489C22#1458321111yescharacteristic
490C22#1458321611yescharacteristic
491C4—21no—
492C4—21no—
493C4—21no—
494C4—21no—
495C4—82no—
496C4—81no—
497C4—3442no—
498C4—3442no—
499C4—1722no—
500C2—21no—
501C2—21no—
502C2—21no—
503C2—21no—
504C2—21no—
505C2—21no—
506C2—161no—
507C2—1724no—
508C2#1913490911yescharacteristic
509C2#1913512411yescharacteristic
510C2#1913513411yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1519C2
socleC22×C43#386
prime radical#19140331C2
cosocleC23×C4×C43C23
hypercenter#1519D43
hypocenterC43#9203
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
2. #19137208C2semidirect
3. #19133163C2semidirect
4. C2×#14582622C2semidirect
5. #19132463C2semidirect
6. #19132462C2semidirect
7. C43×#1519C2semidirect
12. #14582825C4semidirect
14. #14582807C4semidirect
54. C43⋊#95C2×C4semidirect
55. C43⋊#95D4semidirect
57. C22×D4×C43C2×C4semidirect
65. C2×C4⋊C4×C43C2×C4semidirect
70. #95×C43D4semidirect
248. #1519D43semidirect
282. C43#9203semidirect
286. C22×D4C4×D43semidirect
302. C2×C4⋊C4C4×D43semidirect
326. #95C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191403312
#191372082
#191331632
C2×#145826222
#191324632
#191324622
C43×#15192
#920343