Finite Group Databasebeta

← #25012432

Subgroups — #25012432

Order 11008.

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

normal subgroups only

This group has 852 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
1#19136280C211yesmaximal, characteristic, complemented
2#19136236C212yesmaximal, complemented
3#19135014C212yesmaximal, complemented
4#19134979C211yesmaximal, characteristic, complemented
5C43×#3481C211yesmaximal, characteristic
6#14583666C2211yescharacteristic, complemented
7#14582916—21no—
8#14582883C2212yescomplemented
9#14582873C2211yescharacteristic, complemented
10#14582863—22no—
11#14582698—21no—
12#14582696—21no—
13#14582689—22no—
14#14582686—22no—
15#14582669—22no—
16#14582659—21no—
17C43×#559C411yescharacteristic, complemented
18C43×#554—21no—
19C43×#553—22no—
20C43×#551—21no—
21C43×#551C412yescomplemented
22C43×#546—22no—
23D42×C43C411yescharacteristic, complemented
24C43×#532C2211yescharacteristic
25C43×#529—22no—
26C43×#525—21no—
27C43×#525C2212yes—
28C4×#41×C43—21no—
29C2×C4×D4×C43—22no—
30#13063332—42no—
31C2×#10621877—22no—
32C2×#10621877—21no—
33C2×#10621877—22no—
34#13063284—21no—
35#13063252—42no—
36#13063244—22no—
37#13063242—22no—
38#13063240—22no—
39C22⋊(C43⋊C8)—44no—
40C2×#41×C43—21no—
41C2×#41×C43D411yescharacteristic
42C2×#41×C43C2311yescharacteristic
43C22×D4×C43—22no—
44C23×C4×C43—21no—
45C23×C4×C43D412yes—
46C4⋊Q8×C43D411yescharacteristic
47#127×C43C2×C411yescharacteristic
48#126×C43—22no—
49#126×C43—22no—
50#125×C43—22no—
51#124×C43—22no—
52#124×C43C2×C411yescharacteristic
53#124×C43D411yescharacteristic
54#123×C43—21no—
55#123×C43—22no—
56#123×C43—21no—
57#123×C43—22no—
58#123×C43C2×C412yes—
59#123×C43D412yes—
60C22⋊Q8×C43—22no—
61C22⋊Q8×C43—22no—
62C22⋊Q8×C43—22no—
63#121×C43—22no—
64#121×C43—22no—
65#121×C43—22no—
66#121×C43—22no—
67#120×C43—21no—
68#120×C43—21no—
69#120×C43C2×C412yes—
70#120×C43D412yes—
71C4×Q8×C43—21no—
72C4×Q8×C43—21no—
73C4×D4×C43—21no—
74C4×D4×C43—22no—
75C4×D4×C43—22no—
76C4×D4×C43—22no—
77C4×D4×C43—22no—
78C4×D4×C43—22no—
79C4×D4×C43—22no—
80C4×D4×C43—22no—
81C4×D4×C43—22no—
82C4×D4×C43—22no—
83C4×D4×C43—21no—
84#117×C43—21no—
85#117×C43—21no—
86#117×C43—22no—
87#117×C43D412yes—
88C2×C4⋊C4×C43—22no—
89C2×C22⋊C4×C43—22no—
90C2×C22⋊C4×C43—22no—
91C2×C42×C43—22no—
92C2×C42×C43D411yescharacteristic
93C24×C43—21no—
94C24×C43C22⋊C412yes—
95#41×C43—41no—
96#41×C43—41no—
97#41×C43—41no—
98#41×C43—41no—
99#41×C43—44no—
100C2×Q8×C43—21no—
101C2×Q8×C43C22⋊C411yescharacteristic
102C2×Q8×C43C2×D411yescharacteristic
103C2×D4×C43—21no—
104C2×D4×C43—22no—
105C2×D4×C43—22no—
106C2×D4×C43—22no—
107C2×D4×C43—22no—
108C2×D4×C43—21no—
109C2×D4×C43—48no—
110C2×D4×C43C22⋊C411yescharacteristic
111C2×D4×C43C22×C411yescharacteristic
112C2×D4×C43C2×D412yes—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—21no—
117C22×C4×C43—22no—
118C22×C4×C43—21no—
119C22×C4×C43—22no—
120C22×C4×C43—21no—
121C22×C4×C43—42no—
122C22×C4×C43—42no—
123C22×C4×C43—81no—
124C22×C4×C43—81no—
125C22×C4×C43C22⋊C412yes—
126C22×C4×C43C2×D412yes—
127C22×C4×C43C2×D411yescharacteristic
128C4⋊C4×C43—21no—
129C4⋊C4×C43—22no—
130C4⋊C4×C43—21no—
131C4⋊C4×C43—22no—
132C4⋊C4×C43—22no—
133C4⋊C4×C43—22no—
134C4⋊C4×C43—22no—
135C4⋊C4×C43—22no—
136C4⋊C4×C43—22no—
137C22⋊C4×C43—22no—
138C22⋊C4×C43—22no—
139C22⋊C4×C43—22no—
140C22⋊C4×C43—21no—
141C22⋊C4×C43—21no—
142C22⋊C4×C43—22no—
143C22⋊C4×C43—22no—
144C22⋊C4×C43—22no—
145C22⋊C4×C43—22no—
146C22⋊C4×C43—22no—
147C22⋊C4×C43—22no—
148C22⋊C4×C43C22⋊C412yes—
149C22⋊C4×C43C22⋊C412yes—
150C42×C43—22no—
151C42×C43—22no—
152C42×C43—21no—
153C42×C43—22no—
154C42×C43C22⋊C411yescharacteristic
155C42×C43C22⋊C411yescharacteristic
156C22⋊Dic43—41no—
157C4⋊Dic43—41no—
158C4×Dic43—41no—
159#10621877—22no—
160#10621877—42no—
161#10621877—41no—
162#10621877—42no—
163#10621877—42no—
164C2×C43⋊C8—24no—
165C2×C43⋊C8—41no—
166C2×C43⋊C8—42no—
167C23×C43—22no—
168C23×C43—21no—
169C23×C43—42no—
170C23×C43—44no—
171C23×C43—44no—
172C23×C43—81no—
173C23×C43C2×C22⋊C412yes—
174C23×C43#12011yescharacteristic
175Q8×C43—41no—
176Q8×C43—41no—
177Q8×C43—42no—
178D4×C43—24no—
179D4×C43—41no—
180D4×C43—42no—
181D4×C43—41no—
182D4×C43—44no—
183D4×C43—44no—
184D4×C43—44no—
185D4×C43—44no—
186D4×C43—81no—
187C2×C4×C43—21no—
188C2×C4×C43—22no—
189C2×C4×C43—21no—
190C2×C4×C43—22no—
191C2×C4×C43—21no—
192C2×C4×C43—21no—
193C2×C4×C43—22no—
194C2×C4×C43—22no—
195C2×C4×C43—22no—
196C2×C4×C43—21no—
197C2×C4×C43—44no—
198C2×C4×C43—42no—
199C2×C4×C43—44no—
200C2×C4×C43—42no—
201C2×C4×C43—41no—
202C2×C4×C43—42no—
203C2×C4×C43—41no—
204C2×C4×C43—42no—
205C2×C4×C43—82no—
206C2×C4×C43—81no—
207C2×C4×C43—82no—
208C2×C4×C43C2×C22⋊C411yescharacteristic
209C2×C4×C43#12012yes—
210C2×C4×C43#12011yescharacteristic
211C2×Dic43—81no—
212C43⋊C8—42no—
213C43⋊C8—82no—
214#12765—431nomaximal, Sylow
215C22×C43—24no—
216C22×C43—22no—
217C22×C43—21no—
218C22×C43—42no—
219C22×C43—41no—
220C22×C43—42no—
221C22×C43—42no—
222C22×C43—44no—
223C22×C43—42no—
224C22×C43—41no—
225C22×C43—82no—
226C22×C43—84no—
227C22×C43#37911yescharacteristic
228C4×C43—22no—
229C4×C43—22no—
230C4×C43—21no—
231C4×C43—41no—
232C4×C43—42no—
233C4×C43—42no—
234C4×C43—42no—
235C4×C43—41no—
236C4×C43B(4,𝔽2)11yescharacteristic
237C4×C43#45811yescharacteristic
238Dic43—161no—
239#3481D4311yescharacteristic
240#2132—431no—
241#2120—432no—
242#1891—432no—
243#1884—431no—
244C2×C43—21no—
245C2×C43—41no—
246C2×C43—42no—
247C2×C43—44no—
248C2×C43—81no—
249C2×C43#179011yescharacteristic
250#568—431no—
251#559Dic4311yescharacteristic, complemented
252#554—21no—
253#553—22no—
254#551—21no—
255#551Dic4312yescomplemented
256#546—22no—
257D42Dic4311yescharacteristic, complemented
258#532C2×D4311yescharacteristic
259#529—22no—
260#525—21no—
261#525C2×D4312yes—
262C4×#41—21no—
263C2×C4×D4—22no—
264#421—861no—
265#413—432no—
266#410—431no—
267#407—862no—
268#356—861no—
269#355—861no—
270#352—862no—
271AΣL(1,𝔽16)—862no—
272#344—862no—
273#339—861no—
274C43#1276511yescharacteristic, complemented, Sylow
275C2×#41—21no—
276C2×#41C22⋊D4311yescharacteristic
277C2×#41C22×D4311yescharacteristic
278C22×D4—22no—
279C23×C4—21no—
280C23×C4C22⋊D4312yes—
281#131—1722no—
282C2×M16—862no—
283C2×M16—861no—
284C2×M16—862no—
285C4⋊Q8C22⋊D4311yescharacteristic
286#127C2×Dic4311yescharacteristic
287#126—22no—
288#126—22no—
289#125—22no—
290#124—22no—
291#124C2×Dic4311yescharacteristic
292#124C22⋊D4311yescharacteristic
293#123—21no—
294#123—22no—
295#123—21no—
296#123—22no—
297#123C2×Dic4312yes—
298#123C22⋊D4312yes—
299C22⋊Q8—22no—
300C22⋊Q8—22no—
301C22⋊Q8—22no—
302#121—22no—
303#121—22no—
304#121—22no—
305#121—22no—
306#120—21no—
307#120—21no—
308#120C2×Dic4312yes—
309#120C22⋊D4312yes—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×D4—21no—
313C4×D4—22no—
314C4×D4—22no—
315C4×D4—22no—
316C4×D4—22no—
317C4×D4—22no—
318C4×D4—22no—
319C4×D4—22no—
320C4×D4—22no—
321C4×D4—22no—
322C4×D4—21no—
323#117—21no—
324#117—21no—
325#117—22no—
326#117—861no—
327#117C22⋊D4312yes—
328C2×C4⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C42—22no—
332C2×C42C22⋊D4311yescharacteristic
333#104—1722no—
334#101—862no—
335#100—862no—
336#99—862no—
337C22⋊C8—1724no—
338C24—21no—
339C24C22⋊Dic4312yes—
340#41—41no—
341#41—41no—
342#41—41no—
343#41—41no—
344#41—44no—
345C2×Q8—21no—
346C2×Q8C22⋊Dic4311yescharacteristic
347C2×Q8C2×C22⋊D4311yescharacteristic
348C2×D4—21no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—21no—
354C2×D4—48no—
355C2×D4C22⋊Dic4311yescharacteristic
356C2×D4C22×Dic4311yescharacteristic
357C2×D4C2×C22⋊D4312yes—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—81no—
369C22×C4—81no—
370C22×C4C22⋊Dic4312yes—
371C22×C4C2×C22⋊D4311yescharacteristic
372C22×C4C2×C22⋊D4312yes—
373M16—862no—
374M16—1722no—
375M16—1722no—
376M16—1722no—
377M16—1721no—
378C2×C8—864no—
379C2×C8—1722no—
380C2×C8—1721no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—1721no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—22no—
394C22⋊C4—21no—
395C22⋊C4—21no—
396C22⋊C4—22no—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—22no—
400C22⋊C4—22no—
401C22⋊C4—22no—
402C22⋊C4—1721no—
403C22⋊C4C22⋊Dic4312yes—
404C22⋊C4C22⋊Dic4312yes—
405C42—22no—
406C42—22no—
407C42—21no—
408C42—22no—
409C42—1721no—
410C42C22⋊Dic4311yescharacteristic
411C42C22⋊Dic4311yescharacteristic
412C23—22no—
413C23—21no—
414C23—42no—
415C23—44no—
416C23—44no—
417C23—81no—
418C23C2×C22⋊Dic4312yes—
419C23#1306329411yescharacteristic
420Q8—41no—
421Q8—41no—
422Q8—42no—
423D4—24no—
424D4—41no—
425D4—42no—
426D4—41no—
427D4—44no—
428D4—44no—
429D4—44no—
430D4—44no—
431D4—81no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—21no—
436C2×C4—22no—
437C2×C4—21no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—21no—
442C2×C4—44no—
443C2×C4—42no—
444C2×C4—44no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—82no—
451C2×C4—81no—
452C2×C4—82no—
453C2×C4—3441no—
454C2×C4C2×C22⋊Dic4311yescharacteristic
455C2×C4#1306329412yes—
456C2×C4#1306329411yescharacteristic
457C8—3442no—
458C8—1722no—
459C22—24no—
460C22—22no—
461C22—21no—
462C22—41no—
463C22—42no—
464C22—42no—
465C22—42no—
466C22—44no—
467C22—42no—
468C22—41no—
469C22—82no—
470C22—84no—
471C22#1458275511yescharacteristic
472C4—22no—
473C4—22no—
474C4—21no—
475C4—41no—
476C4—42no—
477C4—42no—
478C4—42no—
479C4—41no—
480C4—6881no—
481C4#1458308611yescharacteristic
482C4#1458308911yescharacteristic
483C2—21no—
484C2—41no—
485C2—44no—
486C2—42no—
487C2—81no—
488C2#1913454311yescharacteristic
subgroupG/H
centerC4#14583086
commutatorC2×D4×C43C22×C4
FrattiniC2×#41C22×D43
Fitting, prime radicalC43×#3481C2
socleC2×C43#1790
cosocleC2×#41×C43C23
hypercenter#3481D43
hypocenterC43#12765
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #3481

Complements

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

NH ≅ G/Ntype
1. #19136280C2semidirect
2. #19136236C2semidirect
3. #19135014C2semidirect
4. #19134979C2semidirect
6. #14583666C22semidirect
8. #14582883C22semidirect
9. #14582873C22semidirect
17. C43×#559C4semidirect
21. C43×#551C4semidirect
23. D42×C43C4semidirect
251. #559Dic43semidirect
255. #551Dic43semidirect
257. D42Dic43semidirect
274. C43#12765semidirect

Maximal subgroups

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

subgroupindex
#191362802
#191362362
#191350142
#191349792
C43×#34812
#1276543