Finite Group Databasebeta

← #25013986

Subgroups — #25013986

Order 11008.

510 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D43C211yesmaximal, characteristic, complemented
2#19144172C211yesmaximal, characteristic
3C2×#14582709C211yesmaximal, characteristic, complemented
4#19134617C211yesmaximal, characteristic, complemented
5#19132702C211yesmaximal, characteristic, complemented
6#19132701C211yesmaximal, characteristic, complemented
7C2×C43×#360C211yesmaximal, characteristic, complemented
8C22×C8×D43C2211yescharacteristic
9#14583406—21no—
10C2×#13063265C2211yescharacteristic
11C2×#13063264—21no—
12M32×D43—22no—
13M32×D43—22no—
14C2×C16×D43—21no—
15#14583137C411yescharacteristic, complemented
16#14583137C411yescharacteristic, complemented
17#14583132C411yescharacteristic, complemented
18#14583132C411yescharacteristic, complemented
19#14583125—21no—
20#14583125—21no—
21#14582937C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23#14582895—21no—
24#14582756—21no—
25#14582709—22no—
26#14582661—21no—
27C2×#135×C43C2211yescharacteristic
28C2×M32×C43C2211yescharacteristic
29C2×#106×C43C2211yescharacteristic
30C43×#360—22no—
31C22×C4×D43D411yescharacteristic
32C22×C43⋊C8D411yescharacteristic
33C2×C8×D43—21no—
34C2×C8×D43—21no—
35C2×C8×D43—21no—
36C2×C8×D43—21no—
37C2×C8×D43C2×C411yescharacteristic
38C2×C8×D43C2×C411yescharacteristic
39C2×C8×D43D411yescharacteristic
40C2×C8×D43D411yescharacteristic
41#13063306—41no—
42#13063301—21no—
43#13063301—21no—
44#13063296—21no—
45#13063296—21no—
46#13063293—41no—
47C4×C22⋊D43—41no—
48C4×C22⋊D43—41no—
49#13063284—21no—
50C2×C4⋊Dic43—21no—
51C2×(C2×D43)⋊C4—41no—
52#13063265—21no—
53#13063265D412yescomplemented
54#13063264—24no—
55C2×C43⋊C16—21no—
56C16×D43—24no—
57#13063259C2×C411yescharacteristic
58#13063259C2×C411yescharacteristic
59#13063257—21no—
60#13063257—21no—
61#13063257—21no—
62#13063249—21no—
63#13063249—21no—
64#13063246—21no—
65#13063246—21no—
66C43⋊#95—41no—
67C2×#41×C43—21no—
68#135×C43—21no—
69#135×C43—21no—
70#135×C43—21no—
71#135×C43—21no—
72C2×Q16×C43C2×C411yescharacteristic
73C2×SD16×C43—21no—
74C2×D8×C43C2×C411yescharacteristic
75C22×C8×C43C2311yescharacteristic
76C2×C4⋊C4×C43—21no—
77M32×C43—21no—
78M32×C43D412yescomplemented
79C2×C16×C43—21no—
80#106×C43—21no—
81#106×C43—21no—
82C23×D43D811yescharacteristic
83#41×C43—41no—
84#41×C43—41no—
85#41×C43—41no—
86#41×C43—41no—
87C2×Q8×C43—21no—
88C2×D4×C43—21no—
89C2×D4×C43—41no—
90C22×C4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43C2×D411yescharacteristic
93C2×C22⋊D43—41no—
94C2×C22⋊D43—41no—
95C22×Dic43—41no—
96C22×Dic43D811yescharacteristic
97C2×C4×D43—21no—
98C2×C4×D43—21no—
99C2×C4×D43—21no—
100C2×C4×D43—21no—
101C2×C4×D43C22⋊C411yescharacteristic
102C2×C4×D43C22⋊C411yescharacteristic
103C2×C4×D43SD1611yescharacteristic
104C2×C4×D43SD1611yescharacteristic
105Q16×C43—21no—
106Q16×C43—21no—
107SD16×C43—41no—
108SD16×C43—41no—
109D8×C43—21no—
110D8×C43—21no—
111C2×C8×C43C22×C411yescharacteristic
112C2×C8×C43C2×D411yescharacteristic
113C2×C8×C43C2×D411yescharacteristic
114C2×C8×C43C2×D411yescharacteristic
115C2×C8×C43#4111yescharacteristic
116C2×C8×C43#4111yescharacteristic
117C4⋊C4×C43—41no—
118C4⋊C4×C43—41no—
119C22⋊Dic43—41no—
120C22⋊Dic43—41no—
121C22⋊Dic43—41no—
122(C2×D43)⋊C4—41no—
123(C2×D43)⋊C4—41no—
124(C2×D43)⋊C4—82no—
125C4⋊Dic43—21no—
126C4⋊Dic43—21no—
127C4⋊Dic43—41no—
128C4⋊Dic43—41no—
129Dic43⋊C4—41no—
130Dic43⋊C4—41no—
131C4×Dic43—41no—
132C2×C43⋊C8—21no—
133C2×C43⋊C8—21no—
134C2×C43⋊C8C22⋊C411yescharacteristic
135C2×C43⋊C8C22⋊C411yescharacteristic
136C8×D43—21no—
137C8×D43—21no—
138C8×D43—21no—
139C8×D43—21no—
140C8×D43—21no—
141C8×D43—21no—
142C8×D43—21no—
143C8×D43—21no—
144C16×C43—22no—
145C43⋊C16—22no—
146C23×C43—41no—
147C23×C43C2×D811yescharacteristic
148C22×D43—21no—
149C22×D43—21no—
150C22×D43—22no—
151C22×D43—41no—
152C22×D43#10211yescharacteristic
153C22×D43#10211yescharacteristic
154Q8×C43—41no—
155Q8×C43—41no—
156D4×C43—41no—
157D4×C43—41no—
158D4×C43—81no—
159D4×C43—81no—
160C2×C4×C43—41no—
161C2×C4×C43—81no—
162C2×C4×C43—81no—
163C2×C4×C43—81no—
164C2×C4×C43—81no—
165C2×C4×C43—81no—
166C2×C4×C43C2×C22⋊C411yescharacteristic
167C2×C4×C43#12111yescharacteristic
168C2×C4×C43#12111yescharacteristic
169C2×C4×C43C2×SD1611yescharacteristic
170C2×C4×C43#13511yescharacteristic
171C2×C4×C43#13511yescharacteristic
172C22⋊D43—82no—
173C22⋊D43—82no—
174C2×Dic43—21no—
175C2×Dic43—21no—
176C2×Dic43—41no—
177C2×Dic43—41no—
178C2×Dic43—81no—
179C2×Dic43—81no—
180C2×Dic43—81no—
181C2×Dic43#10211yescharacteristic
182C2×Dic43#10211yescharacteristic
183C4×D43—21no—
184C4×D43—21no—
185C4×D43—21no—
186C4×D43—21no—
187C4×D43—21no—
188C4×D43—21no—
189C4×D43—21no—
190C4×D43—21no—
191C8×C43C4×D411yescharacteristic
192C8×C43C4×D411yescharacteristic
193C8×C43#12011yescharacteristic
194C8×C43#12311yescharacteristic
195C43⋊C8—21no—
196C43⋊C8—21no—
197#13065—431nomaximal, Sylow
198C22×C43—21no—
199C22×C43—21no—
200C22×C43—81no—
201C22×C43—81no—
202C22×C43—81no—
203C22×C43C2×#10211yescharacteristic
204C22×C43#46611yescharacteristic
205C22×C43#46611yescharacteristic
206C2×D43—21no—
207C2×D43—21no—
208C2×D43—21no—
209C2×D43—21no—
210C2×D43—21no—
211C2×D43—42no—
212C2×D43—42no—
213C2×D43#36012yescomplemented
214C4×C43—81no—
215C4×C43—161no—
216C4×C43#38611yescharacteristic
217C4×C43#41611yescharacteristic
218C4×C43#46511yescharacteristic
219C4×C43#46511yescharacteristic
220Dic43—21no—
221Dic43—21no—
222Dic43—81no—
223Dic43—81no—
224Dic43—161no—
225C22×M32—431no—
226#3050—431no—
227C2×#360—431no—
228C2×#360D4311yescharacteristic, complemented
229#1807—431no—
230#1386—431no—
231#1386—431no—
232C2×C43—21no—
233C2×C43—21no—
234C2×C43—161no—
235C2×C43#189311yescharacteristic
236C2×C43C2×#36011yescharacteristic
237C2×C43#214511yescharacteristic
238D43—22no—
239D43—41no—
240C2×#135C2×D4311yescharacteristic
241C23×C8—431no—
242#525—861no—
243C2×M32—431no—
244C2×M32—861no—
245C2×M32—862no—
246C2×M32—862no—
247C2×M32C2×D4311yescharacteristic
248C22×C16—861no—
249#467—431no—
250#467—431no—
251#466—431no—
252#466—431no—
253#465—861no—
254#465—861no—
255#427—431no—
256C2×#106—431no—
257C2×#106C2×D4311yescharacteristic
258#416—861no—
259#380—861no—
260#360—22no—
261#360—862no—
262#340—861no—
263C43#1306511yescharacteristic, complemented, Sylow
264C2×#41—21no—
265C23×C4—431no—
266#135—21no—
267#135—21no—
268#135—21no—
269#135—21no—
270C2×Q16C4×D4311yescharacteristic
271C2×SD16—21no—
272C2×D8C4×D4311yescharacteristic
273C22×C8—431no—
274C22×C8—431no—
275C22×C8—431no—
276C22×C8—431no—
277C22×C8—431no—
278C22×C8—861no—
279C22×C8—861no—
280C22×C8—861no—
281C22×C8—861no—
282C22×C8C22×D4311yescharacteristic
283#123—1721no—
284C22⋊Q8—861no—
285C22⋊Q8—861no—
286#121—861no—
287#121—861no—
288#120—1721no—
289C4×D4—1721no—
290C4×D4—1721no—
291#117—861no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—861no—
294C2×C22⋊C4—1721no—
295M32—21no—
296M32—432no—
297M32—864no—
298M32—861no—
299M32C22⋊D4312yescomplemented
300C2×C16—21no—
301C2×C16—864no—
302C2×C16—861no—
303#107—431no—
304#107—431no—
305#106—21no—
306#106—21no—
307#106—861no—
308#106—861no—
309#106—861no—
310#103—861no—
311#103—861no—
312#102—861no—
313#102—861no—
314#95—1721no—
315C24—431no—
316#41—41no—
317#41—41no—
318#41—41no—
319#41—41no—
320C2×Q8—21no—
321C2×D4—21no—
322C2×D4—41no—
323C2×D4—1721no—
324C2×D4—1721no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—431no—
328C22×C4—431no—
329C22×C4—431no—
330C22×C4—431no—
331C22×C4—431no—
332C22×C4—861no—
333C22×C4—861no—
334C22×C4—861no—
335C22×C4—861no—
336C22×C4—1721no—
337C22×C4D4×D4311yescharacteristic
338Q16—21no—
339Q16—21no—
340SD16—41no—
341SD16—41no—
342D8—21no—
343D8—21no—
344C2×C8—431no—
345C2×C8—431no—
346C2×C8—861no—
347C2×C8—861no—
348C2×C8—861no—
349C2×C8—861no—
350C2×C8—861no—
351C2×C8—861no—
352C2×C8—861no—
353C2×C8—861no—
354C2×C8—861no—
355C2×C8—861no—
356C2×C8C2×C4×D4311yescharacteristic
357C2×C8#1062189811yescharacteristic
358C2×C8D4×D4311yescharacteristic
359C2×C8D4×D4311yescharacteristic
360C2×C8#1062190011yescharacteristic
361C2×C8C2×C22⋊D4311yescharacteristic
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—861no—
365C4⋊C4—861no—
366C4⋊C4—1721no—
367C4⋊C4—1721no—
368C4⋊C4—1721no—
369C4⋊C4—1721no—
370C22⋊C4—3442no—
371C22⋊C4—1721no—
372C22⋊C4—1721no—
373C22⋊C4—1721no—
374C22⋊C4—1721no—
375C22⋊C4—1721no—
376C42—1721no—
377C16—22no—
378C16—862no—
379C23—41no—
380C23—431no—
381C23—431no—
382C23—862no—
383C23—861no—
384C23—861no—
385C23—1721no—
386C23D8×D4311yescharacteristic
387Q8—41no—
388Q8—41no—
389D4—41no—
390D4—41no—
391D4—81no—
392D4—81no—
393D4—3442no—
394D4—3442no—
395C2×C4—41no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—431no—
402C2×C4—431no—
403C2×C4—861no—
404C2×C4—861no—
405C2×C4—861no—
406C2×C4—861no—
407C2×C4—861no—
408C2×C4—861no—
409C2×C4—861no—
410C2×C4—861no—
411C2×C4—861no—
412C2×C4—861no—
413C2×C4—3441no—
414C2×C4—3441no—
415C2×C4—3441no—
416C2×C4—1721no—
417C2×C4—1721no—
418C2×C4C22⋊C4×D4311yescharacteristic
419C2×C4#1306329611yescharacteristic
420C2×C4#1306329811yescharacteristic
421C2×C4SD16×D4311yescharacteristic
422C2×C4#1306334411yescharacteristic
423C2×C4#1306334611yescharacteristic
424C8—861no—
425C8—861no—
426C8(C22⋊D43)⋊C411yescharacteristic
427C8C4×C22⋊D4311yescharacteristic
428C8#1306329311yescharacteristic
429C8#1306330711yescharacteristic
430C22—21no—
431C22—21no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22—432no—
436C22—861no—
437C22—861no—
438C22—861no—
439C22—861no—
440C22—861no—
441C22—1722no—
442C22—1722no—
443C22#102×D4311yescharacteristic
444C22#1458313211yescharacteristic
445C22#1458313411yescharacteristic
446C4—81no—
447C4—161no—
448C4—861no—
449C4—861no—
450C4—3441no—
451C4—3441no—
452C4—6881no—
453C4#1458277511yescharacteristic
454C4#1458289211yescharacteristic
455C4#1458312511yescharacteristic
456C4#1458312711yescharacteristic
457C2—21no—
458C2—21no—
459C2—161no—
460C2—862no—
461C2—1721no—
462C2#1913502011yescharacteristic
463C2#360×D4311yescharacteristic
464C2#1913632911yescharacteristic
subgroupG/H
centerC22#102×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#360C2
socleC22×C43C2×#102
prime radical#19144172C2
cosocleC22×C8×C43C23
hypercenterC2×#360D43
hypocenterC43#13065
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#360

Complements

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

NH ≅ G/Ntype
1. C2×M32×D43C2semidirect
3. C2×#14582709C2semidirect
4. #19134617C2semidirect
5. #19132702C2semidirect
6. #19132701C2semidirect
7. C2×C43×#360C2semidirect
15. #14583137C4semidirect
16. #14583137C4semidirect
17. #14583132C4semidirect
18. #14583132C4semidirect
53. #13063265D4semidirect
78. M32×C43D4semidirect
213. C2×D43#360semidirect
228. C2×#360D43semidirect
263. C43#13065semidirect
299. M32C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D432
#191441722
C2×#145827092
#191346172
#191327022
#191327012
C2×C43×#3602
#1306543