Finite Group Databasebeta

← #25012415

Subgroups — #25012415

Order 11008.

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

normal subgroups only

This group has 944 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×#14582692C211yesmaximal, characteristic, complemented
2C2×#14582689C211yesmaximal, characteristic, complemented
3C2×#14582686C211yesmaximal, characteristic, complemented
4#19135009C211yesmaximal, characteristic, complemented
5#19135004C211yesmaximal, characteristic, complemented
6#19134994C211yesmaximal, characteristic, complemented
7C2×C43×#560C211yesmaximal, characteristic
8#14583374C2211yescharacteristic
9#14582904—21no—
10C2×#13063242C2211yescharacteristic
11C2×#13063240C2211yescharacteristic
12C2×#13063240C2211yescharacteristic
13#14582762—21no—
14#14582755—21no—
15#14582692—22no—
16#14582689—22no—
17#14582686—22no—
18#14582665—21no—
19#14582665—21no—
20#14582659—21no—
21C43×#560—22no—
22C43×#560—22no—
23C43×#560—22no—
24C43×#560C414yescomplemented
25C2×#127×C43C2211yescharacteristic
26C2×#126×C43—21no—
27C2×#123×C43—21no—
28C2×#123×C43C2211yescharacteristic
29C2×#121×C43—21no—
30C2×#121×C43—21no—
31C2×#121×C43—21no—
32C2×#120×C43—21no—
33C2×#120×C43C2211yescharacteristic
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#13063246—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×D4×C43—21no—
52C22×D4×C43—21no—
53C22×D4×C43—21no—
54C22×D4×C43—21no—
55C22×D4×C43—21no—
56C22×D4×C43D411yescharacteristic
57C22×D4×C43C2311yescharacteristic
58C23×C4×C43—21no—
59C23×C4×C43D411yescharacteristic
60#127×C43—21no—
61#127×C43—21no—
62#127×C43C2×C412yes—
63#127×C43D412yes—
64#126×C43—24no—
65#126×C43—24no—
66#123×C43—24no—
67#123×C43—21no—
68#123×C43—21no—
69#123×C43—24no—
70#123×C43C2×C412yes—
71#123×C43D412yes—
72#121×C43—24no—
73#121×C43—24no—
74#121×C43—24no—
75#121×C43—24no—
76#121×C43—24no—
77#121×C43—24no—
78#120×C43—24no—
79#120×C43—24no—
80#120×C43—21no—
81#120×C43—21no—
82#120×C43C2×C412yes—
83#120×C43D412yes—
84C2×C4⋊C4×C43—21no—
85C2×C4⋊C4×C43—21no—
86C2×C4⋊C4×C43—21no—
87C2×C22⋊C4×C43—21no—
88C2×C22⋊C4×C43—21no—
89C2×C22⋊C4×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43D411yescharacteristic
93C2×C22⋊C4×C43D411yescharacteristic
94C2×C42×C43D411yescharacteristic
95C24×C43—21no—
96C24×C43—21no—
97C24×C43—21no—
98C24×C43—41no—
99C24×C43—41no—
100C24×C43—82no—
101C24×C43C22⋊C412yes—
102C24×C43C2×D411yescharacteristic
103C24×C43C2×D411yescharacteristic
104C2×D4×C43—24no—
105C2×D4×C43—24no—
106C2×D4×C43—21no—
107C2×D4×C43—22no—
108C2×D4×C43—22no—
109C2×D4×C43—22no—
110C2×D4×C43—22no—
111C2×D4×C43—22no—
112C2×D4×C43—22no—
113C2×D4×C43—41no—
114C2×D4×C43—41no—
115C2×D4×C43—41no—
116C2×D4×C43—41no—
117C2×D4×C43—82no—
118C2×D4×C43—82no—
119C2×D4×C43—82no—
120C2×D4×C43—82no—
121C2×D4×C43—81no—
122C2×D4×C43—81no—
123C2×D4×C43C22⋊C412yescomplemented
124C2×D4×C43C22×C411yescharacteristic
125C2×D4×C43C2×D411yescharacteristic
126C2×D4×C43C2×D411yescharacteristic
127C2×D4×C43C2×D411yescharacteristic
128C22×C4×C43—24no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—41no—
135C22×C4×C43—41no—
136C22×C4×C43—82no—
137C22×C4×C43C22⋊C412yescomplemented
138C22×C4×C43C2×D411yescharacteristic
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—41no—
142C22×Dic43—41no—
143C4⋊C4×C43—24no—
144C4⋊C4×C43—24no—
145C4⋊C4×C43—22no—
146C4⋊C4×C43—22no—
147C22⋊C4×C43—24no—
148C22⋊C4×C43—24no—
149C22⋊C4×C43—24no—
150C22⋊C4×C43—22no—
151C22⋊C4×C43—22no—
152C22⋊C4×C43—22no—
153C22⋊C4×C43—22no—
154C22⋊C4×C43—21no—
155C22⋊C4×C43—21no—
156C22⋊C4×C43C22⋊C412yes—
157C22⋊C4×C43C22⋊C412yescomplemented
158C42×C43—21no—
159C42×C43C22⋊C412yescomplemented
160C22⋊Dic43—41no—
161C22⋊Dic43—41no—
162C22⋊Dic43—41no—
163C22⋊Dic43—41no—
164C22⋊Dic43—41no—
165C22⋊Dic43—41no—
166C22⋊Dic43—41no—
167C22⋊Dic43—84no—
168C4⋊Dic43—22no—
169C4×Dic43—41no—
170#10621877—41no—
171#10621877—41no—
172C2×C43⋊C8—41no—
173C23×C43—21no—
174C23×C43—21no—
175C23×C43—21no—
176C23×C43—21no—
177C23×C43—22no—
178C23×C43—22no—
179C23×C43—42no—
180C23×C43—42no—
181C23×C43—42no—
182C23×C43—42no—
183C23×C43—42no—
184C23×C43—42no—
185C23×C43—42no—
186C23×C43—44no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43—41no—
190C23×C43—41no—
191C23×C43—81no—
192C23×C43—82no—
193C23×C43—82no—
194C23×C43—82no—
195C23×C43—84no—
196C23×C43C2×C22⋊C411yescharacteristic
197C23×C43C2×C22⋊C411yescharacteristic
198C23×C43#12011yescharacteristic
199C23×C43#12011yescharacteristic
200C23×C43#12011yescharacteristic
201D4×C43—41no—
202D4×C43—41no—
203D4×C43—41no—
204D4×C43—41no—
205D4×C43—42no—
206D4×C43—81no—
207D4×C43—82no—
208D4×C43—82no—
209D4×C43—84no—
210D4×C43—82no—
211D4×C43—82no—
212D4×C43—82no—
213D4×C43—82no—
214D4×C43—84no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—42no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—42no—
227C2×C4×C43—81no—
228C2×C4×C43—84no—
229C2×C4×C43C2×C22⋊C411yescharacteristic
230C2×C4×C43#12011yescharacteristic
231C2×Dic43—42no—
232C2×Dic43—82no—
233C2×Dic43—82no—
234C2×Dic43—81no—
235C2×Dic43—81no—
236C2×Dic43—82no—
237C2×Dic43—82no—
238C43⋊C8—81no—
239#12762—431nomaximal, Sylow
240C22×C43—22no—
241C22×C43—21no—
242C22×C43—21no—
243C22×C43—21no—
244C22×C43—21no—
245C22×C43—41no—
246C22×C43—41no—
247C22×C43—41no—
248C22×C43—41no—
249C22×C43—42no—
250C22×C43—42no—
251C22×C43—42no—
252C22×C43—42no—
253C22×C43—42no—
254C22×C43—42no—
255C22×C43—44no—
256C22×C43—42no—
257C22×C43—42no—
258C22×C43—81no—
259C22×C43—81no—
260C22×C43—82no—
261C22×C43—82no—
262C22×C43—82no—
263C22×C43—84no—
264C22×C43—82no—
265C22×C43—82no—
266C22×C43#37911yescharacteristic
267C22×C43B(4,𝔽2)11yescharacteristic
268C22×C43#45811yescharacteristic
269C4×C43—21no—
270C4×C43—21no—
271C4×C43—42no—
272C4×C43—42no—
273C4×C43—42no—
274C4×C43—42no—
275Dic43—82no—
276Dic43—161no—
277Dic43—161no—
278C2×#560D4311yescharacteristic
279C2×#353—431no—
280C2×#352—431no—
281C2×AΣL(1,𝔽16)—431no—
282#1890—431no—
283#1889—431no—
284#1887—431no—
285C2×C43—21no—
286C2×C43—21no—
287C2×C43—41no—
288C2×C43—41no—
289C2×C43—41no—
290C2×C43—41no—
291C2×C43—82no—
292C2×C43—82no—
293C2×C43#179011yescharacteristic
294C2×C43#220012yes—
295#560—22no—
296#560—22no—
297#560—22no—
298#560Dic4314yescomplemented
299C2×#127C2×D4311yescharacteristic
300C2×#126—21no—
301C2×#123—21no—
302C2×#123C2×D4311yescharacteristic
303C2×#121—21no—
304C2×#121—21no—
305C2×#121—21no—
306C2×#120—21no—
307C2×#120C2×D4311yescharacteristic
308#518—431no—
309#418—861no—
310C2×#100—431no—
311C2×#99—431no—
312C2×#99—431no—
313#381—861no—
314#379—861no—
315#353—862no—
316#352—862no—
317AΣL(1,𝔽16)—862no—
318#342—861no—
319#342—861no—
320#339—861no—
321C43#1276211yescharacteristic, complemented, Sylow
322C25C22⋊D4311yescharacteristic
323C22×D4—21no—
324C22×D4—21no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—21no—
328C22×D4C22⋊D4311yescharacteristic
329C22×D4C22×D4311yescharacteristic
330C23×C4—21no—
331C23×C4C22⋊D4311yescharacteristic
332C2×M16—861no—
333#127—21no—
334#127—21no—
335#127C2×Dic4312yes—
336#127C22⋊D4312yes—
337#126—24no—
338#126—24no—
339#123—24no—
340#123—21no—
341#123—21no—
342#123—24no—
343#123C2×Dic4312yes—
344#123C22⋊D4312yes—
345#121—24no—
346#121—24no—
347#121—24no—
348#121—24no—
349#121—24no—
350#121—24no—
351#120—24no—
352#120—24no—
353#120—21no—
354#120—21no—
355#120C2×Dic4312yes—
356#120C22⋊D4312yes—
357C4×D4—1722no—
358#117—861no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—861no—
368C2×C22⋊C4—861no—
369C2×C22⋊C4—861no—
370C2×C22⋊C4—861no—
371C2×C22⋊C4—1722no—
372C2×C22⋊C4C22⋊D4311yescharacteristic
373C2×C22⋊C4C22⋊D4311yescharacteristic
374C2×C42C22⋊D4311yescharacteristic
375#102—1722no—
376#100—861no—
377#100—861no—
378#99—861no—
379#99—861no—
380#99—861no—
381#99—861no—
382#95—1722no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—41no—
387C24—41no—
388C24—82no—
389C24C22⋊Dic4312yes—
390C24C2×C22⋊D4311yescharacteristic
391C24C2×C22⋊D4311yescharacteristic
392C2×D4—24no—
393C2×D4—24no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—21no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—82no—
406C2×D4—82no—
407C2×D4—82no—
408C2×D4—82no—
409C2×D4—81no—
410C2×D4—81no—
411C2×D4C22⋊Dic4312yescomplemented
412C2×D4C22×Dic4311yescharacteristic
413C2×D4C2×C22⋊D4311yescharacteristic
414C2×D4C2×C22⋊D4311yescharacteristic
415C2×D4C2×C22⋊D4311yescharacteristic
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—24no—
421C22×C4—21no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—82no—
425C22×C4—862no—
426C22×C4—862no—
427C22×C4—1721no—
428C22×C4—1721no—
429C22×C4C22⋊Dic4312yescomplemented
430C22×C4C2×C22⋊D4311yescharacteristic
431M16—1721no—
432M16—1721no—
433C2×C8—1721no—
434C4⋊C4—24no—
435C4⋊C4—24no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—862no—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4—24no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—21no—
445C22⋊C4—21no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—3444no—
449C22⋊C4—1721no—
450C22⋊C4—1721no—
451C22⋊C4—1721no—
452C22⋊C4—1721no—
453C22⋊C4—1721no—
454C22⋊C4—1721no—
455C22⋊C4—1721no—
456C22⋊C4C22⋊Dic4312yes—
457C22⋊C4C22⋊Dic4312yescomplemented
458C42—21no—
459C42—1721no—
460C42C22⋊Dic4312yescomplemented
461C23—21no—
462C23—21no—
463C23—21no—
464C23—21no—
465C23—22no—
466C23—22no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23—42no—
473C23—42no—
474C23—44no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—81no—
480C23—82no—
481C23—82no—
482C23—82no—
483C23—84no—
484C23C2×C22⋊Dic4311yescharacteristic
485C23C2×C22⋊Dic4311yescharacteristic
486C23#1306329411yescharacteristic
487C23#1306329411yescharacteristic
488C23#1306329411yescharacteristic
489D4—41no—
490D4—41no—
491D4—41no—
492D4—41no—
493D4—42no—
494D4—81no—
495D4—82no—
496D4—82no—
497D4—84no—
498D4—82no—
499D4—82no—
500D4—82no—
501D4—82no—
502D4—84no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—81no—
516C2×C4—84no—
517C2×C4—3442no—
518C2×C4—3442no—
519C2×C4—3441no—
520C2×C4—3441no—
521C2×C4—3442no—
522C2×C4—3442no—
523C2×C4—1722no—
524C2×C4C2×C22⋊Dic4311yescharacteristic
525C2×C4#1306329411yescharacteristic
526C8—3441no—
527C22—22no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—44no—
543C22—42no—
544C22—42no—
545C22—81no—
546C22—81no—
547C22—82no—
548C22—82no—
549C22—82no—
550C22—84no—
551C22—82no—
552C22—82no—
553C22#1458275511yescharacteristic
554C22#1458308611yescharacteristic
555C22#1458308911yescharacteristic
556C4—21no—
557C4—21no—
558C4—42no—
559C4—42no—
560C4—42no—
561C4—42no—
562C4—3442no—
563C4—6881no—
564C4—6881no—
565C2—21no—
566C2—21no—
567C2—41no—
568C2—41no—
569C2—41no—
570C2—41no—
571C2—82no—
572C2—82no—
573C2#1913454311yescharacteristic
574C2#1913660212yes—
subgroupG/H
centerC22#14583086
commutatorC2×D4×C43C22×C4
FrattiniC22×D4C22×D43
Fitting, prime radicalC2×C43×#560C2
socleC22×C43B(4,𝔽2)
cosocleC22×D4×C43C23
hypercenterC2×#560D43
hypocenterC43#12762
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#560

Complements

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

NH ≅ G/Ntype
1. C2×#14582692C2semidirect
2. C2×#14582689C2semidirect
3. C2×#14582686C2semidirect
4. #19135009C2semidirect
5. #19135004C2semidirect
6. #19134994C2semidirect
24. C43×#560C4semidirect
123. C2×D4×C43C22⋊C4semidirect
137. C22×C4×C43C22⋊C4semidirect
157. C22⋊C4×C43C22⋊C4semidirect
159. C42×C43C22⋊C4semidirect
298. #560Dic43semidirect
321. C43#12762semidirect
411. C2×D4C22⋊Dic43semidirect
429. C22×C4C22⋊Dic43semidirect
457. C22⋊C4C22⋊Dic43semidirect
460. C42C22⋊Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×#145826922
C2×#145826892
C2×#145826862
#191350092
#191350042
#191349942
C2×C43×#5602
#1276243