Finite Group Databasebeta

← #25013894

Subgroups — #25013894

Order 11008.

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

normal subgroups only

This group has 644 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#19143657C211yesmaximal, characteristic, complemented
2#19136236C211yesmaximal, characteristic, complemented
3#19134559C211yesmaximal, characteristic, complemented
4#19134546C211yesmaximal, characteristic, complemented
5#19132723C211yesmaximal, characteristic, complemented
6#19132715C211yesmaximal, characteristic, complemented
7C43×#3025C211yesmaximal, characteristic
8#14582977—21no—
9#14582977—21no—
10#14582971—21no—
11#14582971—21no—
12#14582960—21no—
13#14582916—21no—
14#14582895—21no—
15#14582883—21no—
16#14582883C2211yescharacteristic
17#14582873C2211yescharacteristic
18#14582866—21no—
19#14582866C2211yescharacteristic
20#14582866C2211yescharacteristic
21#14582863—21no—
22#14582689—21no—
23#14582686—21no—
24C43×#585C2211yescharacteristic
25C43×#525—21no—
26C43×#525C2211yescharacteristic
27C43×#458—21no—
28C43×#458C412yescomplemented
29C43×B(4,𝔽2)—21no—
30C43×B(4,𝔽2)C412yescomplemented
31C43×#410—21no—
32C43×#410C2211yescharacteristic
33C2×#10621877—21no—
34C2×#10621877—21no—
35C2×#10621877—21no—
36C2×#10621877D411yescharacteristic, complemented
37C2×#10621877D411yescharacteristic, complemented
38C22×C43⋊C8D411yescharacteristic, complemented
39C22×C43⋊C8D411yescharacteristic, complemented
40#13063284—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43#13063252—42no—
44#13063249—41no—
45#13063246—41no—
46#13063244—21no—
47#13063244—41no—
48#13063242—21no—
49#13063242—41no—
50#13063240—21no—
51#13063240—21no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)—21no—
58C22⋊(C43⋊C8)—42no—
59#13063236—21no—
60C4×C43⋊C8—21no—
612−1+4×C43—21no—
622−1+4×C43—41no—
63H(5,𝔽2)×C43—21no—
64H(5,𝔽2)×C43—21no—
65H(5,𝔽2)×C43—41no—
66H(5,𝔽2)×C43C2×C412yes—
67C2×#41×C43—21no—
68C2×#41×C43—21no—
69C2×#41×C43—21no—
70C2×#41×C43—42no—
71C2×#41×C43C2311yescharacteristic
72C23×C4×C43D411yescharacteristic
73#123×C43—22no—
74#123×C43C2×C411yescharacteristic
75#123×C43D411yescharacteristic
76C22⋊Q8×C43—21no—
77C22⋊Q8×C43—41no—
78#121×C43—21no—
79#121×C43—41no—
80#120×C43—22no—
81#120×C43C2×C411yescharacteristic
82#120×C43D411yescharacteristic
83C4×D4×C43—21no—
84C4×D4×C43—21no—
85C4×D4×C43—42no—
86#117×C43—21no—
87#117×C43D411yescharacteristic
88#99×C43—21no—
89#99×C43—22no—
90#99×C43—22no—
91#99×C43C2×C412yes—
92C24×C43C22⋊C411yescharacteristic
93#41×C43—22no—
94#41×C43—22no—
95#41×C43—41no—
96#41×C43—41no—
97#41×C43—42no—
98#41×C43—41no—
99#41×C43—41no—
100#41×C43—41no—
101#41×C43—41no—
102#41×C43—41no—
103#41×C43—42no—
104#41×C43—42no—
105#41×C43—42no—
106#41×C43—41no—
107#41×C43—41no—
108#41×C43—41no—
109C2×Q8×C43—21no—
110C2×Q8×C43—21no—
111C2×Q8×C43—21no—
112C2×Q8×C43—42no—
113C2×Q8×C43#4111yescharacteristic
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—22no—
117C2×D4×C43—22no—
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—42no—
122C2×D4×C43—42no—
123C2×D4×C43—42no—
124C2×D4×C43—42no—
125C2×D4×C43—41no—
126C2×D4×C43C22×C411yescharacteristic
127C2×D4×C43C2×D411yescharacteristic
128C2×D4×C43#4111yescharacteristic
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—41no—
134C22×C4×C43—41no—
135C22×C4×C43—41no—
136C22×C4×C43C22⋊C411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C4⋊C4×C43—21no—
141C4⋊C4×C43—21no—
142C4⋊C4×C43—21no—
143C4⋊C4×C43—41no—
144C4⋊C4×C43—42no—
145C22⋊C4×C43—21no—
146C22⋊C4×C43—21no—
147C22⋊C4×C43—22no—
148C22⋊C4×C43—21no—
149C22⋊C4×C43—21no—
150C22⋊C4×C43—42no—
151C22⋊C4×C43—42no—
152C22⋊C4×C43C22⋊C411yescharacteristic
153C22⋊C4×C43C22⋊C411yescharacteristic
154C42×C43—21no—
155C42×C43—41no—
156C22⋊Dic43—41no—
157C4⋊Dic43—41no—
158C4×Dic43—41no—
159#10621877—41no—
160#10621877—41no—
161#10621877—41no—
162#10621877—41no—
163#10621877—81no—
164#10621877—81no—
165C2×C43⋊C8—21no—
166C2×C43⋊C8—21no—
167C2×C43⋊C8—21no—
168C2×C43⋊C8—21no—
169C2×C43⋊C8—41no—
170C2×C43⋊C8—41no—
171C2×C43⋊C8—41no—
172C23×C43—22no—
173C23×C43—22no—
174C23×C43—21no—
175C23×C43—41no—
176C23×C43—41no—
177C23×C43—81no—
178C23×C43C2×C22⋊C411yescharacteristic
179C23×C43C4×D411yescharacteristic
180C23×C43#12111yescharacteristic
181Q8×C43—22no—
182Q8×C43—41no—
183Q8×C43—41no—
184Q8×C43—41no—
185Q8×C43—41no—
186D4×C43—22no—
187D4×C43—41no—
188D4×C43—41no—
189D4×C43—41no—
190D4×C43—41no—
191D4×C43—41no—
192D4×C43—42no—
193D4×C43—42no—
194D4×C43—42no—
195D4×C43—42no—
196D4×C43—41no—
197D4×C43—81no—
198D4×C43—81no—
199D4×C43—84no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—42no—
218C2×C4×C43—41no—
219C2×C4×C43—42no—
220C2×C4×C43—81no—
221C2×C4×C43C4×D411yescharacteristic
222C2×C4×C43#12011yescharacteristic
223C2×C4×C43#12111yescharacteristic
224C2×C4×C43#12311yescharacteristic
225C2×Dic43—81no—
226C43⋊C8—41no—
227C43⋊C8—41no—
228C43⋊C8—41no—
229C43⋊C8—41no—
230C43⋊C8—81no—
231#13046—431nomaximal, Sylow
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—41no—
236C22×C43—41no—
237C22×C43—41no—
238C22×C43—41no—
239C22×C43—41no—
240C22×C43—42no—
241C22×C43—42no—
242C22×C43—41no—
243C22×C43—82no—
244C22×C43—82no—
245C22×C43—81no—
246C22×C43—161no—
247C22×C43#38611yescharacteristic
248C4×C43—21no—
249C4×C43—21no—
250C4×C43—21no—
251C4×C43—41no—
252C4×C43—41no—
253C4×C43—42no—
254C4×C43—41no—
255C4×C43—82no—
256C4×C43B(4,𝔽2)11yescharacteristic
257C4×C43B(4,𝔽2)11yescharacteristic
258Dic43—161no—
259#3025D4311yescharacteristic
260#2978—431no—
261#2120—431no—
262#1794—431no—
263#1791—431no—
264#1395—431no—
265#1391—431no—
266C2×C43—21no—
267C2×C43—41no—
268C2×C43—41no—
269C2×C43—41no—
270C2×C43—81no—
271C2×C43—82no—
272C2×C43#188911yescharacteristic
273#585C2×D4311yescharacteristic
274#525—21no—
275#525C2×D4311yescharacteristic
276#458—21no—
277#458Dic4312yescomplemented
278B(4,𝔽2)—21no—
279B(4,𝔽2)Dic4312yescomplemented
280#436—861no—
281#436—861no—
282#435—861no—
283#435—861no—
284#433—861no—
285#421—861no—
286#416—861no—
287#413—431no—
288#413—861no—
289#410—21no—
290#410—431no—
291#410C2×D4311yescharacteristic
292#408—431no—
293#408—431no—
294#408—861no—
295#407—861no—
296#352—861no—
297AΣL(1,𝔽16)—861no—
298C43#1304611yescharacteristic, complemented, Sylow
2992−1+4—21no—
3002−1+4—41no—
301H(5,𝔽2)—21no—
302H(5,𝔽2)—21no—
303H(5,𝔽2)—41no—
304H(5,𝔽2)C2×Dic4312yes—
305C2×#41—21no—
306C2×#41—21no—
307C2×#41—21no—
308C2×#41—42no—
309C2×#41C22×D4311yescharacteristic
310C23×C4C22⋊D4311yescharacteristic
311C2×M16—431no—
312C2×M16—431no—
313C2×M16—861no—
314C2×M16—861no—
315C2×M16—861no—
316C22×C8—431no—
317C22×C8—431no—
318#123—22no—
319#123C2×Dic4311yescharacteristic
320#123C22⋊D4311yescharacteristic
321C22⋊Q8—21no—
322C22⋊Q8—41no—
323#121—21no—
324#121—41no—
325#120—22no—
326#120C2×Dic4311yescharacteristic
327#120C22⋊D4311yescharacteristic
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—42no—
331#117—21no—
332#117—861no—
333#117C22⋊D4311yescharacteristic
334C4⋊C8—861no—
335C4⋊C8—861no—
336#104—1722no—
337#103—1721no—
338#102—1721no—
339#101—861no—
340#101—1721no—
341#100—861no—
342#100—1721no—
343#99—21no—
344#99—22no—
345#99—22no—
346#99—861no—
347#99—861no—
348#99C2×Dic4312yes—
349C22⋊C8—861no—
350C22⋊C8—861no—
351C22⋊C8—861no—
352C22⋊C8—861no—
353C22⋊C8—861no—
354C22⋊C8—861no—
355C22⋊C8—1722no—
356#97—861no—
357C4×C8—861no—
358C24C22⋊Dic4311yescharacteristic
359#41—22no—
360#41—22no—
361#41—41no—
362#41—41no—
363#41—42no—
364#41—41no—
365#41—41no—
366#41—41no—
367#41—41no—
368#41—41no—
369#41—42no—
370#41—42no—
371#41—42no—
372#41—41no—
373#41—41no—
374#41—41no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—42no—
379C2×Q8#1062190011yescharacteristic
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—42no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—41no—
391C2×D4—42no—
392C2×D4#1062190011yescharacteristic
393C2×D4C22×Dic4311yescharacteristic
394C2×D4C2×C22⋊D4311yescharacteristic
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4C22⋊Dic4311yescharacteristic
403C22×C4D4×D4311yescharacteristic
404C22×C4D4×D4311yescharacteristic
405C22×C4C2×C22⋊D4311yescharacteristic
406M16—3441no—
407M16—3441no—
408M16—1721no—
409M16—1721no—
410M16—1721no—
411M16—1721no—
412C2×C8—861no—
413C2×C8—861no—
414C2×C8—861no—
415C2×C8—861no—
416C2×C8—1721no—
417C2×C8—1721no—
418C2×C8—1721no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—41no—
423C4⋊C4—42no—
424C4⋊C4—1721no—
425C22⋊C4—21no—
426C22⋊C4—21no—
427C22⋊C4—21no—
428C22⋊C4—21no—
429C22⋊C4—22no—
430C22⋊C4—42no—
431C22⋊C4—42no—
432C22⋊C4—1721no—
433C22⋊C4C22⋊Dic4311yescharacteristic
434C22⋊C4C22⋊Dic4311yescharacteristic
435C42—21no—
436C42—41no—
437C42—1721no—
438C23—22no—
439C23—22no—
440C23—21no—
441C23—41no—
442C23—41no—
443C23—81no—
444C23C2×C22⋊Dic4311yescharacteristic
445C23D4×Dic4311yescharacteristic
446C23#1306329711yescharacteristic
447Q8—22no—
448Q8—41no—
449Q8—41no—
450Q8—41no—
451Q8—41no—
452D4—22no—
453D4—41no—
454D4—41no—
455D4—41no—
456D4—41no—
457D4—41no—
458D4—42no—
459D4—42no—
460D4—42no—
461D4—42no—
462D4—41no—
463D4—81no—
464D4—81no—
465D4—84no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—81no—
487C2×C4—3441no—
488C2×C4D4×Dic4311yescharacteristic
489C2×C4#1306329311yescharacteristic
490C2×C4#1306329711yescharacteristic
491C2×C4#1306330611yescharacteristic
492C8—3441no—
493C8—1721no—
494C8—1721no—
495C8—1721no—
496C8—1721no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—42no—
506C22—42no—
507C22—41no—
508C22—82no—
509C22—82no—
510C22—81no—
511C22—161no—
512C22#1458277911yescharacteristic
513C4—21no—
514C4—21no—
515C4—21no—
516C4—41no—
517C4—41no—
518C4—42no—
519C4—41no—
520C4—82no—
521C4—6881no—
522C4#1458308511yescharacteristic
523C4#1458308511yescharacteristic
524C2—21no—
525C2—41no—
526C2—41no—
527C2—41no—
528C2—81no—
529C2—82no—
530C2#1913500411yescharacteristic
subgroupG/H
centerC4#14583085
commutatorC2×D4×C43C22×C4
FrattiniC2×#41C22×D43
Fitting, prime radicalC43×#3025C2
socleC2×C43#1889
cosocleC2×#41×C43C23
hypercenter#3025D43
hypocenterC43#13046
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #3025

Complements

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

NH ≅ G/Ntype
1. #19143657C2semidirect
2. #19136236C2semidirect
3. #19134559C2semidirect
4. #19134546C2semidirect
5. #19132723C2semidirect
6. #19132715C2semidirect
28. C43×#458C4semidirect
30. C43×B(4,𝔽2)C4semidirect
36. C2×#10621877D4semidirect
37. C2×#10621877D4semidirect
38. C22×C43⋊C8D4semidirect
39. C22×C43⋊C8D4semidirect
277. #458Dic43semidirect
279. B(4,𝔽2)Dic43semidirect
298. C43#13046semidirect

Maximal subgroups

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

subgroupindex
#191436572
#191362362
#191345592
#191345462
#191327232
#191327152
C43×#30252
#1304643