Finite Group Databasebeta

← #24997080

Subgroups — #24997080

Order 11008.

888 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 888 conjugacy classes of subgroups — too many to draw. Only its 101 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#19145367C211yesmaximal, characteristic, complemented
2C2×#14583050C211yesmaximal, characteristic
3#19135580C211yesmaximal, characteristic, complemented
4#19134526C211yesmaximal, characteristic
5#19133167C211yesmaximal, characteristic, complemented
6#19132443C211yesmaximal, characteristic, complemented
7C43×#2435C211yesmaximal, characteristic
8C22×#10621883—21no—
9C2×#13063304C2211yescharacteristic
10#14583234—21no—
11#14583232—21no—
12#14583138—22no—
13#14583055—21no—
14#14583054—21no—
15#14583050—22no—
16#14583050—22no—
17C2×#13063246—21no—
18C2×#13063246—22no—
19C2×C22⋊(C43⋊C8)C2211yescharacteristic
20C2×C22⋊(C43⋊C8)C2211yescharacteristic
21#14582759C2211yescharacteristic
22#14582665—22no—
23#14582636—22no—
24C23×D4×C43C2211yescharacteristic
25C2×#124×C43—21no—
26C2×C22⋊Q8×C43C2211yescharacteristic
27C43×#394—22no—
28C43×#390—21no—
29C43×#379—22no—
30C4×C22⋊C4×C43C2211yescharacteristic
31C22×Dic86D411yescharacteristic
32C2×#10621885—22no—
33C2×#10621883—24no—
34C2×#10621883—44no—
35C22×C43⋊C8—21no—
36C22×C43⋊C8D412yes—
37#13063304—21no—
38#13063304—21no—
39#13063304—21no—
40#13063304—21no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43D411yescharacteristic
43C2×Dic43⋊C4—21no—
44C2×C22⋊Dic43—21no—
45C2×C22⋊Dic43—21no—
46#13063258—22no—
47#13063249—22no—
48#13063248—22no—
49#13063246—24no—
50#13063246—44no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)D412yes—
55C43⋊#95—21no—
56C25×C43—21no—
57C22×Q8×C43D411yescharacteristic
58C22×D4×C43—21no—
59C22×D4×C43—21no—
60C22×D4×C43—21no—
61C22×D4×C43—21no—
62C22×D4×C43—21no—
63C22×D4×C43—44no—
64C22×D4×C43D412yes—
65C23×C4×C43C2311yescharacteristic
66#124×C43—44no—
67C22⋊Q8×C43—21no—
68C22⋊Q8×C43—21no—
69C22⋊Q8×C43—21no—
70C22⋊Q8×C43—21no—
71C2×C4⋊C4×C43—21no—
72C2×C4⋊C4×C43D411yescharacteristic
73C2×C22⋊C4×C43—24no—
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—24no—
76C2×C22⋊C4×C43D412yes—
77C2×C42×C43—21no—
78#95×C43—21no—
79C24×C43—22no—
80C24×C43—44no—
81C24×C43—41no—
82C24×C43—41no—
83C24×C43—42no—
84C24×C43—42no—
85C24×C43—82no—
86C24×C43C2×D411yescharacteristic
87C2×Q8×C43—21no—
88C2×Q8×C43—21no—
89C2×Q8×C43—42no—
90C2×D4×C43—24no—
91C2×D4×C43—24no—
92C2×D4×C43—24no—
93C2×D4×C43—22no—
94C2×D4×C43—22no—
95C2×D4×C43—44no—
96C2×D4×C43—42no—
97C2×D4×C43—42no—
98C2×D4×C43—42no—
99C2×D4×C43—44no—
100C2×D4×C43—44no—
101C2×D4×C43—41no—
102C2×D4×C43—41no—
103C22×C4×C43—22no—
104C22×C4×C43—21no—
105C22×C4×C43—21no—
106C22×C4×C43—42no—
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43C2×D411yescharacteristic
112C22×C4×C43#4111yescharacteristic
113C22×Dic43—21no—
114C22×Dic43—21no—
115C22×Dic43—41no—
116C2×Dic86—21no—
117C2×Dic86—21no—
118C2×Dic86—42no—
119C4⋊C4×C43—21no—
120C4⋊C4×C43—21no—
121C4⋊C4×C43—41no—
122C4⋊C4×C43—41no—
123C22⋊C4×C43—22no—
124C22⋊C4×C43—22no—
125C22⋊C4×C43—48no—
126C22⋊C4×C43—41no—
127C22⋊C4×C43—41no—
128C22⋊C4×C43—84no—
129C42×C43—42no—
130C22⋊Dic43—41no—
131C22⋊Dic43—41no—
132C22⋊Dic43—42no—
133#10621885—82no—
134#10621883—48no—
135C4⋊Dic43—21no—
136C4⋊Dic43—21no—
137C4⋊Dic43—42no—
138Dic43⋊C4—41no—
139Dic43⋊C4—41no—
140C2×C43⋊C8—22no—
141C2×C43⋊C8—22no—
142C2×C43⋊C8—42no—
143C2×C43⋊C8—42no—
144C23×C43—24no—
145C23×C43—41no—
146C23×C43—41no—
147C23×C43—44no—
148C23×C43—44no—
149C23×C43—44no—
150C23×C43—42no—
151C23×C43—42no—
152C23×C43—44no—
153C23×C43—82no—
154C23×C43—82no—
155C23×C43—88no—
156C23×C43—88no—
157C23×C43—82no—
158C23×C43—81no—
159C23×C43—81no—
160C23×C43#12011yescharacteristic
161C23×C43#12111yescharacteristic
162C23×C43#12711yescharacteristic
163C23×C43#13512yes—
164C23×C43#13712yes—
165Q8×C43—42no—
166Q8×C43—81no—
167D4×C43—24no—
168D4×C43—24no—
169D4×C43—42no—
170D4×C43—42no—
171D4×C43—44no—
172D4×C43—44no—
173C2×C4×C43—22no—
174C2×C4×C43—22no—
175C2×C4×C43—22no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—42no—
180C2×C4×C43—42no—
181C2×C4×C43—42no—
182C2×C4×C43—42no—
183C2×C4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43—42no—
186C2×C4×C43#12011yescharacteristic
187C2×C4×C43#12011yescharacteristic
188C2×C4×C43#12111yescharacteristic
189C2×C4×C43#12111yescharacteristic
190C2×Dic43—41no—
191C2×Dic43—41no—
192C2×Dic43—81no—
193C2×Dic43—81no—
194C2×Dic43—81no—
195C2×Dic43—81no—
196C2×Dic43—81no—
197Dic86—42no—
198Dic86—42no—
199C43⋊C8—42no—
200C43⋊C8—42no—
201#9955—431nomaximal, Sylow
202C22×C43—21no—
203C22×C43—21no—
204C22×C43—21no—
205C22×C43—21no—
206C22×C43—21no—
207C22×C43—21no—
208C22×C43—42no—
209C22×C43—42no—
210C22×C43—48no—
211C22×C43—44no—
212C22×C43—84no—
213C22×C43—84no—
214C22×C43—88no—
215C22×C43—84no—
216C22×C43—82no—
217C22×C43—82no—
218C22×C43#39211yescharacteristic
219C22×C43#45212yes—
220C22×C43#46412yes—
221C22×C43#49511yescharacteristic
222C22×C43#49711yescharacteristic
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—21no—
226C4×C43—82no—
227C4×C43—81no—
228C4×C43—81no—
229C4×C43B(4,𝔽2)12yes—
230Dic43—81no—
231Dic43—81no—
232Dic43—161no—
233#3189—431no—
234C2×#450—431no—
235#2435D4311yescharacteristic
236#1996—431no—
237#1786—431no—
238#1520—431no—
239#1282—431no—
240C2×C43—21no—
241C2×C43—22no—
242C2×C43—22no—
243C2×C43—21no—
244C2×C43—84no—
245C2×C43#200811yescharacteristic
246C2×C43#201511yescharacteristic
247C2×C43#202111yescharacteristic
248C23×D4C2×D4311yescharacteristic
249C22×SD16—861no—
250C2×#124—21no—
251C2×C22⋊Q8—431no—
252C2×C22⋊Q8C2×D4311yescharacteristic
253#484—861no—
254#484—861no—
255#467—862no—
256#451—861no—
257#451—861no—
258#450—862no—
259#450—862no—
260C2×#102—861no—
261C2×#102—862no—
262C2×C22⋊C8—431no—
263C2×C22⋊C8—431no—
264#394—22no—
265#390—21no—
266#380—431no—
267#379—22no—
268C4×C22⋊C4C2×D4311yescharacteristic
269#342—862no—
270#328—862no—
271C43#995511yescharacteristic, complemented, Sylow
272C25—21no—
273C22×Q8—431no—
274C22×Q8C22⋊D4311yescharacteristic
275C22×D4—21no—
276C22×D4—21no—
277C22×D4—21no—
278C22×D4—21no—
279C22×D4—21no—
280C22×D4—44no—
281C22×D4C22⋊D4312yes—
282C23×C4C22×D4311yescharacteristic
283C2×Q16—862no—
284C2×SD16—864no—
285C2×SD16—1724no—
286C22×C8—432no—
287C22×C8—861no—
288#124—44no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8—21no—
292C22⋊Q8—21no—
293C22⋊Q8—861no—
294C22⋊Q8—861no—
295C22⋊Q8—861no—
296C22⋊Q8—861no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—431no—
299C2×C4⋊C4—861no—
300C2×C4⋊C4—861no—
301C2×C4⋊C4C22⋊D4311yescharacteristic
302C2×C22⋊C4—24no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—861no—
306C2×C22⋊C4—861no—
307C2×C22⋊C4C22⋊D4312yes—
308C2×C42—21no—
309#107—862no—
310#103—862no—
311#103—862no—
312#102—864no—
313#102—1724no—
314C22⋊C8—432no—
315C22⋊C8—861no—
316C22⋊C8—861no—
317C22⋊C8—861no—
318#95—21no—
319#95—861no—
320C24—22no—
321C24—44no—
322C24—41no—
323C24—41no—
324C24—42no—
325C24—42no—
326C24—82no—
327C24C2×C22⋊D4311yescharacteristic
328C2×Q8—21no—
329C2×Q8—21no—
330C2×Q8—42no—
331C2×Q8—861no—
332C2×Q8—861no—
333C2×Q8—1722no—
334C2×D4—24no—
335C2×D4—24no—
336C2×D4—24no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—42no—
340C2×D4—42no—
341C2×D4—42no—
342C2×D4—44no—
343C2×D4—44no—
344C2×D4—44no—
345C2×D4—41no—
346C2×D4—41no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—42no—
351C22×C4—861no—
352C22×C4—861no—
353C22×C4—1721no—
354C22×C4D4×D4311yescharacteristic
355C22×C4D4×D4311yescharacteristic
356C22×C4D4×D4311yescharacteristic
357C22×C4#1062190011yescharacteristic
358C22×C4C2×C22⋊D4311yescharacteristic
359C22×C4C2×C22⋊D4311yescharacteristic
360Q16—3442no—
361SD16—1728no—
362C2×C8—862no—
363C2×C8—862no—
364C2×C8—1722no—
365C2×C8—1722no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—861no—
371C4⋊C4—861no—
372C4⋊C4—1722no—
373C4⋊C4—1721no—
374C4⋊C4—1721no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—48no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—84no—
381C22⋊C4—1722no—
382C22⋊C4—1721no—
383C22⋊C4—1721no—
384C42—42no—
385C23—24no—
386C23—41no—
387C23—41no—
388C23—44no—
389C23—44no—
390C23—44no—
391C23—42no—
392C23—44no—
393C23—42no—
394C23—82no—
395C23—82no—
396C23—88no—
397C23—88no—
398C23—82no—
399C23—81no—
400C23—81no—
401C23#1306329411yescharacteristic
402C23#1306329611yescharacteristic
403C23#1306332111yescharacteristic
404C23#1306334512yes—
405C23#1306335512yes—
406Q8—42no—
407Q8—81no—
408Q8—1722no—
409Q8—1722no—
410D4—24no—
411D4—24no—
412D4—42no—
413D4—42no—
414D4—44no—
415D4—44no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—3441no—
430C2×C4—3441no—
431C2×C4—3441no—
432C2×C4—3441no—
433C2×C4—3441no—
434C2×C4—1721no—
435C2×C4—1721no—
436C2×C4#1306329311yescharacteristic
437C2×C4#1306329311yescharacteristic
438C2×C4#1306329711yescharacteristic
439C2×C4#1306329711yescharacteristic
440C8—1722no—
441C8—1722no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—42no—
449C22—42no—
450C22—48no—
451C22—44no—
452C22—84no—
453C22—84no—
454C22—88no—
455C22—84no—
456C22—82no—
457C22—82no—
458C22#1458280711yescharacteristic
459C22#1458306112yes—
460C22#1458311812yes—
461C22#1458328111yescharacteristic
462C22#1458329411yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—82no—
467C4—81no—
468C4—81no—
469C4—3441no—
470C4—3441no—
471C4—6881no—
472C4#1458308512yes—
473C2—22no—
474C2—21no—
475C2—22no—
476C2—21no—
477C2—84no—
478C2#1913564811yescharacteristic
479C2#1913568911yescharacteristic
480C2#1913571811yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#2435C2
socleC22×C43#392
prime radicalC23×D4×C43C22
hypercenter#2435D43
hypocenterC43#9955
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2435

Complements

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

NH ≅ G/Ntype
1. #19145367C2semidirect
3. #19135580C2semidirect
5. #19133167C2semidirect
6. #19132443C2semidirect
271. C43#9955semidirect

Maximal subgroups

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

subgroupindex
#191453672
C2×#145830502
#191355802
#191345262
#191331672
#191324432
C43×#24352
#995543