Finite Group Databasebeta

← #25012408

Subgroups — #25012408

Order 11008.

936 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 936 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C2×#14582694C211yesmaximal, characteristic, complemented
2C2×#14582689C211yesmaximal, characteristic, complemented
3C2×#14582686C211yesmaximal, characteristic
4#19135009C211yesmaximal, characteristic, complemented
5#19135004C211yesmaximal, characteristic
6#19134984C211yesmaximal, characteristic, complemented
7C2×C43×#551C211yesmaximal, characteristic
8#14583374C2211yescharacteristic
9#14582908—21no—
10C2×#13063242C2211yescharacteristic
11C2×#13063240C2211yescharacteristic
12C2×#13063240C2211yescharacteristic
13#14582762—21no—
14#14582755—21no—
15#14582694—22no—
16#14582689—22no—
17#14582686—22no—
18#14582665—21no—
19#14582665—21no—
20#14582659—21no—
21C43×#551—22no—
22C43×#551—22no—
23C43×#551—22no—
24C43×#551C414yescomplemented
25C2×#126×C43—21no—
26C2×#124×C43C2211yescharacteristic
27C2×#123×C43—21no—
28C2×#123×C43C2211yescharacteristic
29C2×C22⋊Q8×C43—21no—
30C2×#120×C43C2211yescharacteristic
31C2×C4×D4×C43—21no—
32C2×#117×C43—21no—
33C22×C22⋊C4×C43—21no—
34C2×#10621877—21no—
35D4×Dic43—42no—
36#13063284—21no—
37C2×C22⋊Dic43—21no—
38C2×C22⋊Dic43—21no—
39C2×C22⋊Dic43—21no—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43—42no—
42#13063249—42no—
43#13063242—21no—
44#13063242—21no—
45#13063240—21no—
46#13063240—21no—
47#13063240—21no—
48#13063240—21no—
49C43⋊#95—42no—
50C25×C43D411yescharacteristic
51C22×Q8×C43D411yescharacteristic
52C22×D4×C43—21no—
53C22×D4×C43C2311yescharacteristic
54C23×C4×C43—21no—
55C23×C4×C43—21no—
56C23×C4×C43D411yescharacteristic
57#126×C43—24no—
58#126×C43—24no—
59#124×C43—21no—
60#124×C43—21no—
61#124×C43C2×C412yes—
62#124×C43D412yes—
63#123×C43—24no—
64#123×C43—21no—
65#123×C43—21no—
66#123×C43—24no—
67#123×C43C2×C412yes—
68#123×C43D412yes—
69C22⋊Q8×C43—24no—
70C22⋊Q8×C43—24no—
71#120×C43—21no—
72#120×C43—21no—
73#120×C43C2×C412yes—
74#120×C43D412yes—
75C4×D4×C43—24no—
76C4×D4×C43—24no—
77#117×C43—24no—
78#117×C43—24no—
79C2×C4⋊C4×C43—21no—
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43—21no—
82C2×C4⋊C4×C43—21no—
83C2×C22⋊C4×C43—21no—
84C2×C22⋊C4×C43—21no—
85C2×C22⋊C4×C43—24no—
86C2×C22⋊C4×C43—24no—
87C2×C22⋊C4×C43—21no—
88C2×C22⋊C4×C43—21no—
89C2×C22⋊C4×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43D411yescharacteristic
92C2×C22⋊C4×C43D411yescharacteristic
93C2×C42×C43—21no—
94C2×C42×C43D411yescharacteristic
95C24×C43—21no—
96C24×C43—21no—
97C24×C43—44no—
98C24×C43—41no—
99C24×C43—41no—
100C24×C43C22⋊C412yes—
101C24×C43C2×D411yescharacteristic
102C24×C43C2×D411yescharacteristic
103C2×Q8×C43—21no—
104C2×Q8×C43—41no—
105C2×Q8×C43—41no—
106C2×Q8×C43C22⋊C412yescomplemented
107C2×D4×C43—22no—
108C2×D4×C43—22no—
109C2×D4×C43—41no—
110C2×D4×C43—41no—
111C2×D4×C43—44no—
112C2×D4×C43C22×C411yescharacteristic
113C2×D4×C43C2×D411yescharacteristic
114C2×D4×C43C2×D411yescharacteristic
115C2×D4×C43C2×D411yescharacteristic
116C22×C4×C43—24no—
117C22×C4×C43—24no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—44no—
125C22×C4×C43—41no—
126C22×C4×C43—41no—
127C22×C4×C43—81no—
128C22×C4×C43—81no—
129C22×C4×C43C22⋊C412yescomplemented
130C22×C4×C43C2×D411yescharacteristic
131C22×Dic43—22no—
132C22×Dic43—22no—
133C22×Dic43—41no—
134C22×Dic43—41no—
135C4⋊C4×C43—24no—
136C4⋊C4×C43—24no—
137C4⋊C4×C43—24no—
138C4⋊C4×C43—22no—
139C4⋊C4×C43—22no—
140C22⋊C4×C43—24no—
141C22⋊C4×C43—24no—
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×C43—22no—
149C22⋊C4×C43—22no—
150C22⋊C4×C43—21no—
151C22⋊C4×C43—21no—
152C22⋊C4×C43C22⋊C412yes—
153C22⋊C4×C43C22⋊C412yescomplemented
154C42×C43—24no—
155C42×C43—21no—
156C42×C43C22⋊C412yescomplemented
157C22⋊Dic43—41no—
158C22⋊Dic43—41no—
159C22⋊Dic43—41no—
160C22⋊Dic43—41no—
161C22⋊Dic43—41no—
162C22⋊Dic43—41no—
163C22⋊Dic43—41no—
164C22⋊Dic43—84no—
165C4⋊Dic43—22no—
166C4×Dic43—41no—
167#10621877—41no—
168#10621877—41no—
169C2×C43⋊C8—41no—
170C23×C43—24no—
171C23×C43—22no—
172C23×C43—21no—
173C23×C43—21no—
174C23×C43—21no—
175C23×C43—21no—
176C23×C43—42no—
177C23×C43—42no—
178C23×C43—44no—
179C23×C43—42no—
180C23×C43—42no—
181C23×C43—44no—
182C23×C43—41no—
183C23×C43—41no—
184C23×C43—44no—
185C23×C43—81no—
186C23×C43—84no—
187C23×C43—82no—
188C23×C43C2×C22⋊C411yescharacteristic
189C23×C43C2×C22⋊C411yescharacteristic
190C23×C43#12011yescharacteristic
191C23×C43#12011yescharacteristic
192C23×C43#12011yescharacteristic
193Q8×C43—42no—
194Q8×C43—81no—
195D4×C43—41no—
196D4×C43—41no—
197D4×C43—41no—
198D4×C43—41no—
199D4×C43—44no—
200D4×C43—44no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—22no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—42no—
209C2×C4×C43—42no—
210C2×C4×C43—48no—
211C2×C4×C43—42no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—42no—
217C2×C4×C43—81no—
218C2×C4×C43—84no—
219C2×C4×C43C2×C22⋊C411yescharacteristic
220C2×C4×C43#12011yescharacteristic
221C2×Dic43—42no—
222C2×Dic43—82no—
223C2×Dic43—82no—
224C2×Dic43—81no—
225C2×Dic43—81no—
226C2×Dic43—82no—
227C2×Dic43—82no—
228C43⋊C8—81no—
229#12761—431nomaximal, Sylow
230C22×C43—22no—
231C22×C43—24no—
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—21no—
236C22×C43—41no—
237C22×C43—41no—
238C22×C43—41no—
239C22×C43—41no—
240C22×C43—42no—
241C22×C43—44no—
242C22×C43—44no—
243C22×C43—44no—
244C22×C43—42no—
245C22×C43—42no—
246C22×C43—42no—
247C22×C43—81no—
248C22×C43—81no—
249C22×C43—84no—
250C22×C43—82no—
251C22×C43#37911yescharacteristic
252C22×C43B(4,𝔽2)11yescharacteristic
253C22×C43#45811yescharacteristic
254C4×C43—21no—
255C4×C43—21no—
256C4×C43—42no—
257C4×C43—42no—
258C4×C43—42no—
259C4×C43—42no—
260C4×C43—42no—
261Dic43—82no—
262Dic43—161no—
263Dic43—161no—
264C2×#551D4311yescharacteristic
265C2×#354—431no—
266C2×#352—431no—
267C2×AΣL(1,𝔽16)—431no—
268#1890—431no—
269#1889—431no—
270#1885—431no—
271C2×C43—21no—
272C2×C43—21no—
273C2×C43—41no—
274C2×C43—41no—
275C2×C43—44no—
276C2×C43—41no—
277C2×C43—41no—
278C2×C43#179011yescharacteristic
279C2×C43#219712yes—
280#551—22no—
281#551—22no—
282#551—22no—
283#551Dic4314yescomplemented
284C2×#126—21no—
285C2×#124C2×D4311yescharacteristic
286C2×#123—21no—
287C2×#123C2×D4311yescharacteristic
288C2×C22⋊Q8—21no—
289C2×#120C2×D4311yescharacteristic
290#518—431no—
291C2×C4×D4—21no—
292C2×#117—21no—
293C22×C22⋊C4—21no—
294#419—861no—
295C2×#100—431no—
296C2×#99—431no—
297C2×#99—431no—
298#381—861no—
299#379—861no—
300#354—862no—
301#352—862no—
302AΣL(1,𝔽16)—862no—
303#342—861no—
304#342—861no—
305#339—861no—
306C43#1276111yescharacteristic, complemented, Sylow
307C25C22⋊D4311yescharacteristic
308C22×Q8C22⋊D4311yescharacteristic
309C22×D4—21no—
310C22×D4C22×D4311yescharacteristic
311C23×C4—21no—
312C23×C4—21no—
313C23×C4C22⋊D4311yescharacteristic
314C2×M16—861no—
315#126—24no—
316#126—24no—
317#124—21no—
318#124—21no—
319#124C2×Dic4312yes—
320#124C22⋊D4312yes—
321#123—24no—
322#123—21no—
323#123—21no—
324#123—24no—
325#123C2×Dic4312yes—
326#123C22⋊D4312yes—
327C22⋊Q8—24no—
328C22⋊Q8—24no—
329#120—21no—
330#120—21no—
331#120C2×Dic4312yes—
332#120C22⋊D4312yes—
333C4×D4—24no—
334C4×D4—24no—
335C4×D4—1722no—
336#117—24no—
337#117—24no—
338#117—861no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—861no—
352C2×C22⋊C4—861no—
353C2×C22⋊C4—861no—
354C2×C22⋊C4—861no—
355C2×C22⋊C4—1722no—
356C2×C22⋊C4C22⋊D4311yescharacteristic
357C2×C22⋊C4C22⋊D4311yescharacteristic
358C2×C42—21no—
359C2×C42C22⋊D4311yescharacteristic
360#103—1722no—
361#100—861no—
362#100—861no—
363#99—861no—
364#99—861no—
365#99—861no—
366#99—861no—
367#95—1722no—
368C24—21no—
369C24—21no—
370C24—41no—
371C24—44no—
372C24—41no—
373C24C22⋊Dic4312yes—
374C24C2×C22⋊D4311yescharacteristic
375C24C2×C22⋊D4311yescharacteristic
376C2×Q8—21no—
377C2×Q8—41no—
378C2×Q8—41no—
379C2×Q8C22⋊Dic4312yescomplemented
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4—44no—
385C2×D4C22×Dic4311yescharacteristic
386C2×D4C2×C22⋊D4311yescharacteristic
387C2×D4C2×C22⋊D4311yescharacteristic
388C2×D4C2×C22⋊D4311yescharacteristic
389C22×C4—24no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—24no—
396C22×C4—21no—
397C22×C4—44no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—81no—
401C22×C4—81no—
402C22×C4—862no—
403C22×C4—862no—
404C22×C4—1721no—
405C22×C4—1721no—
406C22×C4C22⋊Dic4312yescomplemented
407C22×C4C2×C22⋊D4311yescharacteristic
408M16—1721no—
409M16—1721no—
410C2×C8—1721no—
411C4⋊C4—24no—
412C4⋊C4—24no—
413C4⋊C4—24no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—862no—
417C22⋊C4—24no—
418C22⋊C4—24no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—21no—
426C22⋊C4—21no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—3444no—
430C22⋊C4—1721no—
431C22⋊C4—1721no—
432C22⋊C4—1721no—
433C22⋊C4—1721no—
434C22⋊C4—1721no—
435C22⋊C4—1721no—
436C22⋊C4—1721no—
437C22⋊C4C22⋊Dic4312yes—
438C22⋊C4C22⋊Dic4312yescomplemented
439C42—24no—
440C42—21no—
441C42—1721no—
442C42C22⋊Dic4312yescomplemented
443C23—24no—
444C23—21no—
445C23—21no—
446C23—22no—
447C23—21no—
448C23—21no—
449C23—42no—
450C23—42no—
451C23—44no—
452C23—42no—
453C23—42no—
454C23—44no—
455C23—41no—
456C23—41no—
457C23—44no—
458C23—81no—
459C23—84no—
460C23—82no—
461C23C2×C22⋊Dic4311yescharacteristic
462C23C2×C22⋊Dic4311yescharacteristic
463C23#1306329411yescharacteristic
464C23#1306329411yescharacteristic
465C23#1306329411yescharacteristic
466Q8—42no—
467Q8—81no—
468D4—41no—
469D4—41no—
470D4—41no—
471D4—41no—
472D4—44no—
473D4—44no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—48no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—81no—
491C2×C4—84no—
492C2×C4—3442no—
493C2×C4—3442no—
494C2×C4—3441no—
495C2×C4—3441no—
496C2×C4—3442no—
497C2×C4—3442no—
498C2×C4—1722no—
499C2×C4C2×C22⋊Dic4311yescharacteristic
500C2×C4#1306329411yescharacteristic
501C8—3441no—
502C22—22no—
503C22—24no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—42no—
513C22—44no—
514C22—44no—
515C22—42no—
516C22—42no—
517C22—44no—
518C22—42no—
519C22—81no—
520C22—81no—
521C22—84no—
522C22—82no—
523C22#1458275511yescharacteristic
524C22#1458308611yescharacteristic
525C22#1458308911yescharacteristic
526C4—21no—
527C4—21no—
528C4—42no—
529C4—42no—
530C4—42no—
531C4—42no—
532C4—42no—
533C4—3442no—
534C4—6881no—
535C4—6881no—
536C2—21no—
537C2—21no—
538C2—41no—
539C2—41no—
540C2—44no—
541C2—41no—
542C2—41no—
543C2#1913454311yescharacteristic
544C2#1913658512yes—
subgroupG/H
centerC22#14583086
commutatorC2×D4×C43C22×C4
FrattiniC22×D4C22×D43
FittingC2×C43×#551C2
socleC22×C43B(4,𝔽2)
prime radicalC2×#120×C43C22
cosocleC22×D4×C43C23
hypercenterC2×#551D43
hypocenterC43#12761
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#551

Complements

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

NH ≅ G/Ntype
1. C2×#14582694C2semidirect
2. C2×#14582689C2semidirect
4. #19135009C2semidirect
6. #19134984C2semidirect
24. C43×#551C4semidirect
106. C2×Q8×C43C22⋊C4semidirect
129. C22×C4×C43C22⋊C4semidirect
153. C22⋊C4×C43C22⋊C4semidirect
156. C42×C43C22⋊C4semidirect
283. #551Dic43semidirect
306. C43#12761semidirect
379. C2×Q8C22⋊Dic43semidirect
406. C22×C4C22⋊Dic43semidirect
438. C22⋊C4C22⋊Dic43semidirect
442. C42C22⋊Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145826942
C2×#145826892
C2×#145826862
#191350092
#191350042
#191349842
C2×C43×#5512
#1276143