Finite Group Databasebeta

← #24996820

Subgroups — #24996820

Order 11008.

812 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 113 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×#14583210C211yesmaximal, characteristic, complemented
2#19140331C211yesmaximal, characteristic
3C2×#14582826C211yesmaximal, characteristic, complemented
4#19134682C211yesmaximal, characteristic, complemented
5C2×#14582622C211yesmaximal, characteristic, complemented
6#19132474C211yesmaximal, characteristic, complemented
7C2×C43×#327C211yesmaximal, characteristic, complemented
8C2×#13063293—21no—
9C22×C4⋊Dic43C2211yescharacteristic
10C22×(C2×D43)⋊C4—21no—
11C22×(C2×D43)⋊C4C2211yescharacteristic
12#14583210—22no—
13#14583210—22no—
14C2×#13063258—21no—
15C2×#13063246—21no—
16C2×C22⋊(C43⋊C8)C2211yescharacteristic
17#14582826—22no—
18#14582826—22no—
19#14582825—21no—
20#14582815—22no—
21#14582807—21no—
22#14582779—21no—
23#14582759C2211yescharacteristic
24C2×C43⋊#95—21no—
25#14582662—22no—
26#14582622—22no—
27C2×#121×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C2×#95×C43C2211yescharacteristic
30C43×#327—22no—
31C24×D43D411yescharacteristic
32C22×C22⋊D43—22no—
33C23×Dic43—21no—
34C23×Dic43D411yescharacteristic
35C22×C43⋊C8—21no—
36#13063293—42no—
37#13063293—42no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43D412yes—
44C2×C4⋊Dic43D412yescomplemented
45C2×C22⋊Dic43—21no—
46C2×C22⋊Dic43—22no—
47C2×(C2×D43)⋊C4—22no—
48C2×(C2×D43)⋊C4—24no—
49C2×(C2×D43)⋊C4—21no—
50C2×(C2×D43)⋊C4—21no—
51C2×(C2×D43)⋊C4—21no—
52C2×(C2×D43)⋊C4—21no—
53C2×(C2×D43)⋊C4—21no—
54C2×(C2×D43)⋊C4—21no—
55C2×(C2×D43)⋊C4—42no—
56C2×(C2×D43)⋊C4—42no—
57#13063258—24no—
58#13063246—24no—
59C22⋊(C43⋊C8)—21no—
60C22⋊(C43⋊C8)D412yescomplemented
61C43⋊#95—22no—
62C43⋊#95—24no—
63C43⋊#95—21no—
64C22×D4×C43—21no—
65C22×D4×C43D411yescharacteristic
66C23×C4×C43—21no—
67C23×C4×C43C2311yescharacteristic
68C22×C8×C43—21no—
69#121×C43—21no—
70#121×C43—21no—
71#121×C43—21no—
72#121×C43—21no—
73C2×C4⋊C4×C43D411yescharacteristic
74C2×C22⋊C4×C43—21no—
75C22⋊C8×C43—21no—
76C22⋊C8×C43—21no—
77#95×C43—21no—
78#95×C43D412yescomplemented
79C24×C43—21no—
80C24×C43C2×D411yescharacteristic
81C23×D43—21no—
82C23×D43—21no—
83C23×D43—21no—
84C23×D43—21no—
85C23×D43—21no—
86C23×D43—21no—
87C23×D43—42no—
88C23×D43—42no—
89C23×D43D812yes—
90C2×D4×C43—21no—
91C2×D4×C43—21no—
92C2×D4×C43—41no—
93C2×D4×C43—41no—
94C2×D4×C43—41no—
95C2×D4×C43—41no—
96C2×D4×C43—41no—
97C2×D4×C43—41no—
98C2×D4×C43—42no—
99C22×C4×C43—22no—
100C22×C4×C43—21no—
101C22×C4×C43—42no—
102C22×C4×C43—42no—
103C22×C4×C43—42no—
104C22×C4×C43—41no—
105C22×C4×C43—41no—
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43#4111yescharacteristic
112C2×C22⋊D43—44no—
113C2×C22⋊D43—82no—
114C2×C22⋊D43—82no—
115C22×Dic43—21no—
116C22×Dic43—21no—
117C22×Dic43—22no—
118C22×Dic43—22no—
119C22×Dic43—21no—
120C22×Dic43—42no—
121C22×Dic43—41no—
122C22×Dic43—41no—
123C22×Dic43—41no—
124C22×Dic43—41no—
125C22×Dic43—41no—
126C22×Dic43—41no—
127C2×C8×C43—42no—
128C2×C8×C43—41no—
129C4⋊C4×C43—21no—
130C4⋊C4×C43—21no—
131C22⋊C4×C43—41no—
132C22⋊C4×C43—41no—
133C22⋊Dic43—41no—
134C22⋊Dic43—41no—
135C22⋊Dic43—82no—
136(C2×D43)⋊C4—48no—
137(C2×D43)⋊C4—44no—
138(C2×D43)⋊C4—41no—
139(C2×D43)⋊C4—41no—
140(C2×D43)⋊C4—41no—
141(C2×D43)⋊C4—41no—
142C4⋊Dic43—22no—
143C4⋊Dic43—22no—
144C4⋊Dic43—41no—
145C4⋊Dic43—41no—
146C4⋊Dic43—42no—
147C2×C43⋊C8—22no—
148C2×C43⋊C8—42no—
149C23×C43—22no—
150C23×C43—22no—
151C23×C43—41no—
152C23×C43—41no—
153C23×C43—41no—
154C23×C43—42no—
155C23×C43—42no—
156C23×C43#12011yescharacteristic
157C23×C43#12011yescharacteristic
158C23×C43#12111yescharacteristic
159C23×C43C2×D811yescharacteristic
160C23×C43#13511yescharacteristic
161C23×C43AGL(1,ℤ/8)11yescharacteristic
162C23×C43AGL(1,ℤ/8)11yescharacteristic
163C22×D43—22no—
164C22×D43—22no—
165C22×D43—22no—
166C22×D43—44no—
167C22×D43—44no—
168C22×D43—42no—
169C22×D43—42no—
170C22×D43—41no—
171C22×D43—41no—
172C22×D43—41no—
173C22×D43—42no—
174C22×D43—42no—
175C22×D43—41no—
176C22×D43—82no—
177C22×D43—82no—
178C22×D43—81no—
179C22×D43—81no—
180D4×C43—42no—
181D4×C43—81no—
182D4×C43—81no—
183D4×C43—81no—
184D4×C43—81no—
185D4×C43—81no—
186C2×C4×C43—22no—
187C2×C4×C43—22no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—42no—
193C2×C4×C43—42no—
194C2×C4×C43—41no—
195C2×C4×C43—42no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—82no—
199C2×C4×C43—82no—
200C2×C4×C43#12011yescharacteristic
201C2×C4×C43#12111yescharacteristic
202C2×C4×C43#12111yescharacteristic
203C2×C4×C43#12711yescharacteristic
204C22⋊D43—88no—
205C2×Dic43—42no—
206C2×Dic43—42no—
207C2×Dic43—41no—
208C2×Dic43—42no—
209C2×Dic43—42no—
210C2×Dic43—42no—
211C2×Dic43—42no—
212C2×Dic43—42no—
213C2×Dic43—42no—
214C2×Dic43—81no—
215C2×Dic43—81no—
216C2×Dic43—81no—
217C2×Dic43—81no—
218C2×Dic43—81no—
219C8×C43—81no—
220C43⋊C8—42no—
221#9918—431nomaximal, Sylow
222C22×C43—22no—
223C22×C43—22no—
224C22×C43—22no—
225C22×C43—22no—
226C22×C43—21no—
227C22×C43—21no—
228C22×C43—21no—
229C22×C43—21no—
230C22×C43—82no—
231C22×C43—82no—
232C22×C43—81no—
233C22×C43—81no—
234C22×C43—81no—
235C22×C43#39211yescharacteristic
236C22×C43#44711yescharacteristic
237C22×C43#44711yescharacteristic
238C22×C43#44911yescharacteristic
239C22×C43#44911yescharacteristic
240C22×C43#45512yes—
241C22×C43#45812yes—
242C22×C43#46611yescharacteristic
243C22×C43#46911yescharacteristic
244C2×D43—44no—
245C2×D43—44no—
246C2×D43—42no—
247C2×D43—82no—
248C2×D43—82no—
249C2×D43—82no—
250C2×D43—81no—
251C2×D43—81no—
252C2×D43—82no—
253C4×C43—21no—
254C4×C43—21no—
255C4×C43—21no—
256C4×C43—21no—
257C4×C43—82no—
258C4×C43—81no—
259Dic43—82no—
260Dic43—82no—
261Dic43—81no—
262C2×#480—431no—
263#2617—431no—
264C2×#397—431no—
265#1823—431no—
266C2×#327D4311yescharacteristic, complemented
267C2×#323—431no—
268#1294—431no—
269C2×C43—21no—
270C2×C43—21no—
271C2×C43—21no—
272C2×C43—21no—
273C2×C43—161no—
274C2×C43#160712yes—
275C2×C43#161212yes—
276C2×C43#199911yescharacteristic
277C2×C43#200411yescharacteristic
278C2×C43#202211yescharacteristic
279D43—82no—
280C2×#121C2×D4311yescharacteristic
281C2×#120—861no—
282C22×C4⋊C4—431no—
283C22×C22⋊C4—431no—
284C22×C22⋊C4—861no—
285#480—862no—
286#480—862no—
287C2×#107—861no—
288C2×#102—861no—
289C2×C22⋊C8—431no—
290C2×C22⋊C8C2×D4311yescharacteristic
291#397—862no—
292#397—861no—
293#397—862no—
294#394—862no—
295#392—861no—
296#386—861no—
297#380—431no—
298C2×#95—861no—
299C2×#95C2×D4311yescharacteristic
300#340—862no—
301#327—22no—
302#323—862no—
303C43#991811yescharacteristic, complemented, Sylow
304C25—431no—
305C22×D4—21no—
306C22×D4—862no—
307C22×D4D17211yescharacteristic
308C23×C4—21no—
309C23×C4—431no—
310C23×C4—861no—
311C23×C4C22×D4311yescharacteristic
312C22×C8—21no—
313C22×C8—861no—
314#121—21no—
315#121—21no—
316#121—21no—
317#121—21no—
318#120—1722no—
319#120—1722no—
320C2×C4⋊C4—432no—
321C2×C4⋊C4—432no—
322C2×C4⋊C4—861no—
323C2×C4⋊C4—861no—
324C2×C4⋊C4—861no—
325C2×C4⋊C4—861no—
326C2×C4⋊C4—861no—
327C2×C4⋊C4D17211yescharacteristic
328C2×C22⋊C4—21no—
329C2×C22⋊C4—862no—
330C2×C22⋊C4—864no—
331C2×C22⋊C4—862no—
332C2×C22⋊C4—861no—
333C2×C22⋊C4—861no—
334C2×C22⋊C4—861no—
335C2×C22⋊C4—861no—
336C2×C22⋊C4—861no—
337C2×C22⋊C4—861no—
338C2×C22⋊C4—861no—
339C2×C22⋊C4—1722no—
340C2×C22⋊C4—1722no—
341#107—864no—
342#102—864no—
343C22⋊C8—21no—
344C22⋊C8—21no—
345C22⋊C8—432no—
346C22⋊C8—861no—
347#95—21no—
348#95—864no—
349#95—862no—
350#95—861no—
351#95C22⋊D4312yescomplemented
352C24—21no—
353C24—432no—
354C24—861no—
355C24—861no—
356C24—861no—
357C24—861no—
358C24—861no—
359C24—861no—
360C24—1722no—
361C24—1722no—
362C24D4×D4311yescharacteristic
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—42no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—3442no—
373C2×D4—3442no—
374C2×D4—1724no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—861no—
383C22×C4—861no—
384C22×C4—862no—
385C22×C4—861no—
386C22×C4—862no—
387C22×C4—1721no—
388C22×C4—1721no—
389C22×C4—1721no—
390C22×C4—1721no—
391C22×C4—1721no—
392C22×C4—1721no—
393C22×C4—1722no—
394C22×C4C2×D17211yescharacteristic
395C22×C4#1062189811yescharacteristic
396C22×C4D4×D4311yescharacteristic
397C22×C4D4×D4311yescharacteristic
398C22×C4D4×D4311yescharacteristic
399C22×C4C2×C22⋊D4311yescharacteristic
400C2×C8—42no—
401C2×C8—41no—
402C2×C8—862no—
403C2×C8—1722no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—862no—
407C4⋊C4—862no—
408C4⋊C4—1722no—
409C4⋊C4—1721no—
410C4⋊C4—1721no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—3442no—
414C22⋊C4—1728no—
415C22⋊C4—1724no—
416C22⋊C4—1721no—
417C22⋊C4—1721no—
418C22⋊C4—1721no—
419C22⋊C4—1721no—
420C22⋊C4—1721no—
421C22⋊C4—1721no—
422C23—22no—
423C23—22no—
424C23—41no—
425C23—41no—
426C23—42no—
427C23—42no—
428C23—41no—
429C23—862no—
430C23—862no—
431C23—862no—
432C23—3441no—
433C23—3442no—
434C23—3441no—
435C23—3442no—
436C23—1722no—
437C23—1724no—
438C23—1722no—
439C23—1724no—
440C23—1721no—
441C23—1721no—
442C23—1721no—
443C23—1722no—
444C23—1722no—
445C23—1721no—
446C23#1306329311yescharacteristic
447C23#1306329511yescharacteristic
448C23#1306329811yescharacteristic
449C23D8×D4311yescharacteristic
450C23#1306334611yescharacteristic
451C23#1306334911yescharacteristic
452C23#1306335211yescharacteristic
453D4—42no—
454D4—81no—
455D4—81no—
456D4—81no—
457D4—81no—
458D4—81no—
459D4—3448no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—82no—
473C2×C4—82no—
474C2×C4—3441no—
475C2×C4—3441no—
476C2×C4—3441no—
477C2×C4—3441no—
478C2×C4—3441no—
479C2×C4—1722no—
480C2×C4—1722no—
481C2×C4—1721no—
482C2×C4—1722no—
483C2×C4—1722no—
484C2×C4—1722no—
485C2×C4—1722no—
486C2×C4—1722no—
487C2×C4—1722no—
488C2×C4#1306329511yescharacteristic
489C2×C4#1306329811yescharacteristic
490C2×C4#1306329911yescharacteristic
491C2×C4#1306332111yescharacteristic
492C8—81no—
493C8—1722no—
494C22—21no—
495C22—21no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22—21no—
501C22—21no—
502C22—81no—
503C22—81no—
504C22—82no—
505C22—82no—
506C22—81no—
507C22—3442no—
508C22—3442no—
509C22—3442no—
510C22—3441no—
511C22—3442no—
512C22—3441no—
513C22—1724no—
514C22—1722no—
515C22—1724no—
516C22#1458280811yescharacteristic
517C22#1458303111yescharacteristic
518C22#1458303411yescharacteristic
519C22#1458304311yescharacteristic
520C22#1458304511yescharacteristic
521C22#1458307812yes—
522C22#1458309012yes—
523C22#1458313411yescharacteristic
524C22#1458315111yescharacteristic
525C4—21no—
526C4—21no—
527C4—21no—
528C4—21no—
529C4—82no—
530C4—81no—
531C4—3442no—
532C4—3441no—
533C4—3442no—
534C2—21no—
535C2—21no—
536C2—21no—
537C2—21no—
538C2—161no—
539C2—3442no—
540C2#1913358212yes—
541C2#1913361012yes—
542C2#1913559211yescharacteristic
543C2#1913562311yescharacteristic
544C2#1913572511yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC2×C43×#327C2
socleC23×C43#120
prime radical#19140331C2
hypercenterC2×#327D43
hypocenterC43#9918
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
1. C2×#14583210C2semidirect
3. C2×#14582826C2semidirect
4. #19134682C2semidirect
5. C2×#14582622C2semidirect
6. #19132474C2semidirect
7. C2×C43×#327C2semidirect
44. C2×C4⋊Dic43D4semidirect
60. C22⋊(C43⋊C8)D4semidirect
78. #95×C43D4semidirect
266. C2×#327D43semidirect
303. C43#9918semidirect
351. #95C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832102
#191403312
C2×#145828262
#191346822
C2×#145826222
#191324742
C2×C43×#3272
#991843