Finite Group Databasebeta

← #24996829

Subgroups — #24996829

Order 11008.

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

normal subgroups only

This group has 716 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×#14583212C211yesmaximal, characteristic
2#19140340C211yesmaximal, characteristic
3C2×#14582830C211yesmaximal, characteristic, complemented
4C2×#14582634C211yesmaximal, characteristic
5C2×#14582624C211yesmaximal, characteristic, complemented
6#19132473C211yesmaximal, characteristic, complemented
7C43×#1823C211yesmaximal, characteristic, complemented
8C2×#13063309—21no—
9C2×#13063299C2211yescharacteristic
10C22×Dic43⋊C4—21no—
11C22×Dic43⋊C4C2211yescharacteristic
12#14583212—22no—
13#14583212—22no—
14C2×#13063258—21no—
15C2×#13063245—21no—
16C2×C22⋊(C43⋊C8)C2211yescharacteristic
17#14582831—21no—
18#14582830—22no—
19#14582830—22no—
20#14582821—22no—
21#14582817—21no—
22#14582776—21no—
23C2×C43⋊#95—21no—
24C2×C43⋊#95C2211yescharacteristic
25#14582634—22no—
26#14582624—22no—
27C22×C4⋊C4×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C43×#380C2211yescharacteristic
30C43×#340—22no—
31C22×D172D411yescharacteristic
32C22×C22⋊D43—21no—
33C23×Dic43—21no—
34C23×Dic43D411yescharacteristic
35C23×Dic43D411yescharacteristic
36C22×C43⋊C8—21no—
37#13063309—42no—
38#13063309—42no—
39#13063299—21no—
40#13063299—21no—
41#13063299—21no—
42#13063299—21no—
43C2×C4⋊Dic43—22no—
44C2×C4⋊Dic43D411yescharacteristic
45C2×Dic43⋊C4—24no—
46C2×Dic43⋊C4—21no—
47C2×Dic43⋊C4—21no—
48C2×Dic43⋊C4—21no—
49C2×Dic43⋊C4—21no—
50C2×Dic43⋊C4—21no—
51C2×Dic43⋊C4—21no—
52C2×Dic43⋊C4—42no—
53C2×Dic43⋊C4—42no—
54C2×(C2×D43)⋊C4—22no—
55C2×(C2×D43)⋊C4—21no—
56C2×(C2×D43)⋊C4—22no—
57#13063258—24no—
58#13063245—24no—
59C22⋊(C43⋊C8)—21no—
60C22⋊(C43⋊C8)D412yes—
61C43⋊#95—22no—
62C43⋊#95—24no—
63C43⋊#95—21no—
64C43⋊#95D412yes—
65C23×C4×C43—21no—
66C23×C4×C43C2311yescharacteristic
67C22×C8×C43—21no—
68C2×C4⋊C4×C43—21no—
69C2×C4⋊C4×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43—21no—
73C2×C4⋊C4×C43D412yes—
74C2×C4⋊C4×C43D412yes—
75C2×C22⋊C4×C43—21no—
76C22⋊C8×C43—21no—
77C22⋊C8×C43—21no—
78#95×C43—21no—
79C24×C43C2×D411yescharacteristic
80C23×D43—21no—
81C22×C4×C43—22no—
82C22×C4×C43—22no—
83C22×C4×C43—42no—
84C22×C4×C43—41no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43—41no—
89C22×C4×C43—41no—
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43#4111yescharacteristic
96C2×C22⋊D43—41no—
97C2×C22⋊D43—41no—
98C2×C22⋊D43—41no—
99C2×C22⋊D43—41no—
100C2×C22⋊D43—41no—
101C2×C22⋊D43—41no—
102C22×Dic43—24no—
103C22×Dic43—22no—
104C22×Dic43—21no—
105C22×Dic43—21no—
106C22×Dic43—21no—
107C22×Dic43—21no—
108C22×Dic43—21no—
109C22×Dic43—21no—
110C22×Dic43—21no—
111C22×Dic43—21no—
112C22×Dic43—21no—
113C22×Dic43—21no—
114C22×Dic43—42no—
115C22×Dic43—42no—
116C22×Dic43—41no—
117C22×Dic43—41no—
118C22×Dic43D812yes—
119C2×D172—21no—
120C2×D172—21no—
121C2×D172—42no—
122C2×C8×C43—42no—
123C2×C8×C43—41no—
124C4⋊C4×C43—22no—
125C4⋊C4×C43—22no—
126C4⋊C4×C43—42no—
127C4⋊C4×C43—41no—
128C4⋊C4×C43—41no—
129C22⋊C4×C43—41no—
130C22⋊C4×C43—41no—
131(C2×D43)⋊C4—44no—
132(C2×D43)⋊C4—41no—
133(C2×D43)⋊C4—41no—
134(C2×D43)⋊C4—82no—
135C4⋊Dic43—21no—
136C4⋊Dic43—21no—
137C4⋊Dic43—44no—
138Dic43⋊C4—48no—
139Dic43⋊C4—41no—
140Dic43⋊C4—41no—
141Dic43⋊C4—41no—
142Dic43⋊C4—41no—
143C2×C43⋊C8—22no—
144C2×C43⋊C8—42no—
145C23×C43—22no—
146C23×C43—22no—
147C23×C43#12011yescharacteristic
148C23×C43#12011yescharacteristic
149C23×C43#12111yescharacteristic
150C23×C43C2×D811yescharacteristic
151C23×C43#13511yescharacteristic
152C23×C43AGL(1,ℤ/8)11yescharacteristic
153C23×C43AGL(1,ℤ/8)11yescharacteristic
154C22×D43—41no—
155C22×D43—41no—
156C22×D43—41no—
157C22×D43—42no—
158C22×D43—42no—
159C2×C4×C43—22no—
160C2×C4×C43—22no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—42no—
166C2×C4×C43—42no—
167C2×C4×C43—42no—
168C2×C4×C43—42no—
169C2×C4×C43—42no—
170C2×C4×C43—42no—
171C2×C4×C43—81no—
172C2×C4×C43—81no—
173C2×C4×C43—81no—
174C2×C4×C43—81no—
175C2×C4×C43#12011yescharacteristic
176C2×C4×C43#12111yescharacteristic
177C2×C4×C43#12111yescharacteristic
178C2×C4×C43#12711yescharacteristic
179C22⋊D43—81no—
180C22⋊D43—81no—
181C22⋊D43—81no—
182C22⋊D43—81no—
183C2×Dic43—24no—
184C2×Dic43—22no—
185C2×Dic43—22no—
186C2×Dic43—22no—
187C2×Dic43—44no—
188C2×Dic43—44no—
189C2×Dic43—42no—
190C2×Dic43—41no—
191C2×Dic43—42no—
192C2×Dic43—41no—
193C2×Dic43—41no—
194C2×Dic43—41no—
195C2×Dic43—42no—
196C2×Dic43—41no—
197C2×Dic43—41no—
198C2×Dic43—41no—
199C2×Dic43—41no—
200C2×Dic43—42no—
201C2×Dic43—81no—
202D172—42no—
203D172—81no—
204C8×C43—81no—
205C43⋊C8—42no—
206#9919—431nomaximal, Sylow
207C22×C43—22no—
208C22×C43—22no—
209C22×C43—22no—
210C22×C43—22no—
211C22×C43—21no—
212C22×C43—21no—
213C22×C43—21no—
214C22×C43—21no—
215C22×C43#39211yescharacteristic
216C22×C43#44711yescharacteristic
217C22×C43#44711yescharacteristic
218C22×C43#44911yescharacteristic
219C22×C43#44911yescharacteristic
220C22×C43#45612yes—
221C22×C43#45812yes—
222C22×C43#46611yescharacteristic
223C22×C43#46911yescharacteristic
224C2×D43—82no—
225C2×D43—82no—
226C2×D43—81no—
227C2×D43—81no—
228C2×D43—81no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—82no—
234C4×C43—82no—
235Dic43—44no—
236Dic43—42no—
237Dic43—81no—
238Dic43—81no—
239C2×#480—431no—
240#2618—431no—
241C2×#398—431no—
242#1823D4311yescharacteristic, complemented
243C2×#327—431no—
244C2×#324—431no—
245#1294—431no—
246C2×C43—21no—
247C2×C43—21no—
248C2×C43—21no—
249C2×C43—21no—
250C2×C43#160912yes—
251C2×C43#161012yes—
252C2×C43#199911yescharacteristic
253C2×C43#200511yescharacteristic
254C2×C43#202211yescharacteristic
255D43—161no—
256C2×#123—861no—
257C2×#121—431no—
258C22×C4⋊C4—431no—
259C22×C4⋊C4—861no—
260C22×C4⋊C4C2×D4311yescharacteristic
261#480—862no—
262#480—862no—
263C2×#107—861no—
264C2×#102—861no—
265C2×C22⋊C8—431no—
266C2×C22⋊C8C2×D4311yescharacteristic
267#398—861no—
268#398—862no—
269#398—862no—
270#396—862no—
271#394—861no—
272#386—861no—
273#380C2×D4311yescharacteristic
274C2×#95—431no—
275C2×#95—861no—
276#340—22no—
277#327—862no—
278#324—862no—
279C43#991911yescharacteristic, complemented, Sylow
280C22×D4—431no—
281C22×D4—861no—
282C23×C4—21no—
283C23×C4—431no—
284C23×C4—431no—
285C23×C4—861no—
286C23×C4C22×D4311yescharacteristic
287C22×C8—21no—
288C22×C8—861no—
289#123—1722no—
290#123—1722no—
291#121—861no—
292#121—861no—
293#121—861no—
294#121—861no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—431no—
301C2×C4⋊C4—864no—
302C2×C4⋊C4—862no—
303C2×C4⋊C4—861no—
304C2×C4⋊C4—861no—
305C2×C4⋊C4—861no—
306C2×C4⋊C4—861no—
307C2×C4⋊C4—861no—
308C2×C4⋊C4—861no—
309C2×C4⋊C4—1722no—
310C2×C4⋊C4—1722no—
311C2×C4⋊C4D17212yes—
312C2×C4⋊C4C22⋊D4312yes—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—862no—
315C2×C22⋊C4—862no—
316C2×C22⋊C4—861no—
317#107—864no—
318#102—864no—
319C22⋊C8—21no—
320C22⋊C8—21no—
321C22⋊C8—432no—
322C22⋊C8—861no—
323#95—21no—
324#95—432no—
325#95—864no—
326#95—862no—
327#95—861no—
328C24—861no—
329C24D4×D4311yescharacteristic
330C2×D4—861no—
331C2×D4—861no—
332C2×D4—1722no—
333C2×D4—1721no—
334C2×D4—1721no—
335C2×D4—1721no—
336C2×D4—1721no—
337C2×D4—1721no—
338C2×D4—1721no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—42no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—432no—
349C22×C4—864no—
350C22×C4—861no—
351C22×C4—862no—
352C22×C4—861no—
353C22×C4—861no—
354C22×C4—861no—
355C22×C4—861no—
356C22×C4—861no—
357C22×C4—861no—
358C22×C4—861no—
359C22×C4—861no—
360C22×C4—861no—
361C22×C4—1722no—
362C22×C4—1722no—
363C22×C4—1721no—
364C22×C4—1721no—
365C22×C4C2×D17211yescharacteristic
366C22×C4#1062189811yescharacteristic
367C22×C4D4×D4311yescharacteristic
368C22×C4D4×D4311yescharacteristic
369C22×C4D4×D4311yescharacteristic
370C22×C4C2×C22⋊D4311yescharacteristic
371C2×C8—42no—
372C2×C8—41no—
373C2×C8—862no—
374C2×C8—1722no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—42no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—861no—
381C4⋊C4—861no—
382C4⋊C4—1728no—
383C4⋊C4—1724no—
384C4⋊C4—1721no—
385C4⋊C4—1721no—
386C4⋊C4—1721no—
387C4⋊C4—1721no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—3442no—
391C22⋊C4—1724no—
392C22⋊C4—1721no—
393C22⋊C4—1721no—
394C23—22no—
395C23—22no—
396C23—1721no—
397C23—1721no—
398C23—1722no—
399C23—1722no—
400C23—1721no—
401C23#1306329311yescharacteristic
402C23#1306329511yescharacteristic
403C23#1306329811yescharacteristic
404C23D8×D4311yescharacteristic
405C23#1306334611yescharacteristic
406C23#1306334911yescharacteristic
407C23#1306335211yescharacteristic
408D4—3441no—
409D4—3441no—
410D4—3441no—
411D4—3441no—
412D4—3441no—
413D4—1722no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—864no—
431C2×C4—862no—
432C2×C4—862no—
433C2×C4—862no—
434C2×C4—3441no—
435C2×C4—1722no—
436C2×C4—1721no—
437C2×C4—1721no—
438C2×C4—1721no—
439C2×C4—1722no—
440C2×C4—1721no—
441C2×C4—1724no—
442C2×C4—1724no—
443C2×C4—1722no—
444C2×C4—1721no—
445C2×C4—1721no—
446C2×C4—1721no—
447C2×C4—1721no—
448C2×C4—1722no—
449C2×C4#1306329511yescharacteristic
450C2×C4#1306329811yescharacteristic
451C2×C4#1306329911yescharacteristic
452C2×C4#1306332111yescharacteristic
453C8—81no—
454C8—1722no—
455C22—21no—
456C22—21no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—21no—
462C22—21no—
463C22—3441no—
464C22—3441no—
465C22—3442no—
466C22—3442no—
467C22—3441no—
468C22#1458280811yescharacteristic
469C22#1458303111yescharacteristic
470C22#1458303411yescharacteristic
471C22#1458304311yescharacteristic
472C22#1458304511yescharacteristic
473C22#1458308012yes—
474C22#1458308812yes—
475C22#1458313411yescharacteristic
476C22#1458315111yescharacteristic
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—82no—
482C4—82no—
483C4—3441no—
484C4—3441no—
485C4—1724no—
486C4—1722no—
487C2—21no—
488C2—21no—
489C2—21no—
490C2—21no—
491C2—6881no—
492C2#1913359112yes—
493C2#1913359612yes—
494C2#1913559211yescharacteristic
495C2#1913563211yescharacteristic
496C2#1913572611yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1823C2
socleC23×C43#120
prime radicalC2×#13063299C22
hypercenter#1823D43
hypocenterC43#9919
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
3. C2×#14582830C2semidirect
5. C2×#14582624C2semidirect
6. #19132473C2semidirect
7. C43×#1823C2semidirect
242. #1823D43semidirect
279. C43#9919semidirect

Maximal subgroups

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

subgroupindex
C2×#145832122
#191403402
C2×#145828302
C2×#145826342
C2×#145826242
#191324732
C43×#18232
#991943