Finite Group Databasebeta

← #24984847

Subgroups — #24984847

Order 11008.

640 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 103 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#19137103C211yesmaximal, characteristic
2#19134356C211yesmaximal, characteristic, complemented
3#19134287C211yesmaximal, characteristic, complemented
4#19132418C211yesmaximal, characteristic, complemented
5#19132415C211yesmaximal, characteristic, complemented
6#19132415C211yesmaximal, characteristic, complemented
7C43×#1271C211yesmaximal, characteristic, complemented
8C22×#10621872—21no—
9C2×#13063300C411yescharacteristic
10C2×#13063287—21no—
11C2×#13063287C411yescharacteristic
12C2×C42×D43C2211yescharacteristic
13C2×(C2×D43)⋊C8—21no—
14C2×#13063235—21no—
15#14582801C2211yescharacteristic
16#14582789—21no—
17#14582777—21no—
18#14582756C411yescharacteristic
19C4⋊C4×Dic43C411yescharacteristic
20#14582746—21no—
21#14582654C2211yescharacteristic
22#14582654C2211yescharacteristic
23#14582653—21no—
24C43×#389C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×D172—21no—
28C22×D172C2×C411yescharacteristic
29C22×C4×D43—21no—
30C22×C4×D43C2×C411yescharacteristic
31C22×C4×D43D411yescharacteristic
32C22×C4×D43D411yescharacteristic
33C2×#10621872—24no—
34C2×#10621872—42no—
35C2×#10621872—42no—
36C22×C43⋊C8—21no—
37C22×C43⋊C8—21no—
38#13063300—22no—
39#13063300—22no—
40#13063287—42no—
41#13063287—42no—
42#13063287—42no—
43C2×C4⋊Dic43C2×C411yescharacteristic
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—21no—
48C2×(C2×D43)⋊C4—21no—
49C2×C4×Dic43—21no—
50C2×C4×Dic43C2×C411yescharacteristic
51C2×C4×Dic43D411yescharacteristic
52C2×C4×Dic43D411yescharacteristic
53C42×D43—42no—
54(C2×D43)⋊C8—24no—
55#13063235—42no—
56C43⋊#95—21no—
57C43⋊#95—21no—
58C22×C8×C43—21no—
59C22×C8×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C4⋊C4×C43C2×C411yescharacteristic
62C2×C4⋊C4×C43C2×C411yescharacteristic
63C2×C42×C43C2311yescharacteristic
64#95×C43—21no—
65C23×D43—21no—
66C23×D43C22⋊C411yescharacteristic
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43C22×C411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×Dic43—21no—
73C22×Dic43C22⋊C411yescharacteristic
74C22×Dic43C22⋊C411yescharacteristic
75C22×Dic43C22⋊C411yescharacteristic
76C2×D172—24no—
77C2×D172—21no—
78C2×D172—42no—
79C2×D172—42no—
80C2×D172—41no—
81C2×D172—41no—
82C2×D172M1612yescomplemented
83C2×C4×D43—21no—
84C2×C4×D43—21no—
85C2×C4×D43—22no—
86C2×C4×D43—21no—
87C2×C4×D43—21no—
88C2×C4×D43—21no—
89C2×C4×D43—21no—
90C2×C4×D43—22no—
91C2×C4×D43—22no—
92C2×C4×D43—41no—
93C2×C4×D43—41no—
94C2×C4×D43—41no—
95C2×C4×D43—42no—
96C2×C4×D43—42no—
97C2×C4×D43—42no—
98C2×C8×C43—22no—
99C2×C8×C43—22no—
100C2×C8×C43—41no—
101C2×C8×C43—41no—
102C2×C8×C43—41no—
103C2×C8×C43—41no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—41no—
108C4⋊C4×C43M1612yescomplemented
109C42×C43—41no—
110(C2×D43)⋊C4—24no—
111(C2×D43)⋊C4—42no—
112(C2×D43)⋊C4—41no—
113(C2×D43)⋊C4—41no—
114(C2×D43)⋊C4—41no—
115(C2×D43)⋊C4—41no—
116(C2×D43)⋊C4—42no—
117C4⋊Dic43—41no—
118C4×Dic43—22no—
119C4×Dic43—22no—
120C4×Dic43—41no—
121C4×Dic43—42no—
122C2×C43⋊C8—22no—
123C2×C43⋊C8—22no—
124C2×C43⋊C8—41no—
125C2×C43⋊C8—41no—
126C2×C43⋊C8—41no—
127C2×C43⋊C8—41no—
128#10621872—48no—
129C23×C43C2×C22⋊C411yescharacteristic
130C22×D43—21no—
131C22×D43—21no—
132C22×D43—21no—
133C22×D43—21no—
134C22×D43—21no—
135C22×D43—21no—
136C22×D43—22no—
137C22×D43—41no—
138C22×D43—41no—
139C22×D43—41no—
140C22×D43—41no—
141C22×D43—41no—
142C22×D43—41no—
143C22×D43#10412yes—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—22no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43C2×M1611yescharacteristic
157C2×C4×C43C2×M1611yescharacteristic
158C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C43#13711yescharacteristic
162C2×Dic43—21no—
163C2×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—21no—
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—21no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43#9912yes—
173C2×Dic43#10412yes—
174D172—42no—
175D172—42no—
176D172—48no—
177C4×D43—24no—
178C4×D43—24no—
179C4×D43—42no—
180C4×D43—42no—
181C4×D43—42no—
182C4×D43—42no—
183C4×D43—84no—
184C8×C43—42no—
185C8×C43—42no—
186C43⋊C8—42no—
187C43⋊C8—42no—
188#7633—431nomaximal, Sylow
189C22×C43#40711yescharacteristic
190C22×C43C2×#9911yescharacteristic
191C22×C43#41311yescharacteristic
192C22×C43#41711yescharacteristic
193C22×C43#41811yescharacteristic
194C22×C43C2×#10411yescharacteristic
195C22×C43C2×#10411yescharacteristic
196C2×D43—22no—
197C2×D43—22no—
198C2×D43—22no—
199C2×D43—41no—
200C2×D43—41no—
201C2×D43—41no—
202C2×D43—41no—
203C2×D43—42no—
204C2×D43—42no—
205C2×D43—42no—
206C2×D43—81no—
207C2×D43—81no—
208C2×D43—81no—
209C2×D43—81no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—21no—
214C4×C43—21no—
215C4×C43—21no—
216C4×C43—42no—
217C4×C43—81no—
218Dic43—22no—
219Dic43—22no—
220Dic43—41no—
221Dic43—81no—
222C4×#121—431no—
223#1749—431no—
224#1728—431no—
225#1271—431no—
226#1271D4311yescharacteristic, complemented
227#1270—431no—
228#1270—431no—
229C2×C43#146511yescharacteristic
230C2×C43#148911yescharacteristic
231C2×C43#149011yescharacteristic
232C2×C43#150411yescharacteristic
233C2×C43#150711yescharacteristic
234C2×C43#152411yescharacteristic
235C2×C43#155711yescharacteristic
236D43—42no—
237D43—82no—
238C22×M16—861no—
239C2×#121—431no—
240C2×C4×D4—431no—
241C2×C4×D4—861no—
242C22×C42—431no—
243C2×C22⋊C8—861no—
244C2×#97—861no—
245#390—431no—
246#389C2×D4311yescharacteristic
247#388—861no—
248#386—861no—
249#380—431no—
250C4×C4⋊C4—431no—
251C4×C22⋊C4—861no—
252#336—431no—
253#336—431no—
254#336—861no—
255#336C2×D4311yescharacteristic
256#336C2×D4311yescharacteristic
257C43#763311yescharacteristic, complemented, Sylow
258C22×D4—431no—
259C22×D4—861no—
260C23×C4—431no—
261C23×C4—431no—
262C23×C4—431no—
263C23×C4—861no—
264C2×M16—864no—
265C2×M16—1722no—
266C2×M16—1722no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—861no—
270C22×C8—861no—
271#121—862no—
272#121—862no—
273C4×D4—1722no—
274C4×D4—1722no—
275C4×D4—1722no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—431no—
278C2×C4⋊C4C4×D4311yescharacteristic
279C2×C4⋊C4C4×D4311yescharacteristic
280C2×C22⋊C4—861no—
281C2×C22⋊C4—861no—
282C2×C22⋊C4—861no—
283C2×C22⋊C4—861no—
284C2×C22⋊C4—861no—
285C2×C42—431no—
286C2×C42—431no—
287C2×C42—431no—
288C2×C42—861no—
289C2×C42—1722no—
290C2×C42C22×D4311yescharacteristic
291C22⋊C8—864no—
292#97—1722no—
293#95—21no—
294#95—861no—
295#95—861no—
296C24—431no—
297C24—861no—
298C2×D4—432no—
299C2×D4—864no—
300C2×D4—861no—
301C2×D4—1721no—
302C2×D4—1721no—
303C2×D4—1722no—
304C2×D4—1722no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—431no—
308C22×C4—431no—
309C22×C4—431no—
310C22×C4—862no—
311C22×C4—862no—
312C22×C4—862no—
313C22×C4—861no—
314C22×C4—861no—
315C22×C4—861no—
316C22×C4—861no—
317C22×C4—861no—
318C22×C4—861no—
319C22×C4—861no—
320C22×C4—1721no—
321C22×C4—1721no—
322C22×C4—1721no—
323C22×C4—1722no—
324C22×C4—1722no—
325C22×C4—1722no—
326C22×C4C2×C4×D4311yescharacteristic
327C22×C4D4×D4311yescharacteristic
328C22×C4D4×D4311yescharacteristic
329M16—1728no—
330C2×C8—22no—
331C2×C8—22no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—862no—
337C2×C8—862no—
338C2×C8—1721no—
339C2×C8—1721no—
340C2×C8—1721no—
341C2×C8—1721no—
342C4⋊C4—21no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—1721no—
347C4⋊C4#1062187212yescomplemented
348C22⋊C4—864no—
349C22⋊C4—1722no—
350C22⋊C4—1722no—
351C22⋊C4—1721no—
352C22⋊C4—1721no—
353C22⋊C4—1721no—
354C22⋊C4—1721no—
355C42—41no—
356C42—862no—
357C42—862no—
358C42—1721no—
359C42—1722no—
360C23—432no—
361C23—861no—
362C23—861no—
363C23—861no—
364C23—861no—
365C23—861no—
366C23—861no—
367C23—862no—
368C23—1721no—
369C23—1721no—
370C23—1721no—
371C23—1721no—
372C23—1721no—
373C23—1721no—
374C23C22⋊C4×D4311yescharacteristic
375D4—1722no—
376D4—1722no—
377D4—1728no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—432no—
391C2×C4—432no—
392C2×C4—864no—
393C2×C4—864no—
394C2×C4—861no—
395C2×C4—861no—
396C2×C4—861no—
397C2×C4—861no—
398C2×C4—861no—
399C2×C4—861no—
400C2×C4—861no—
401C2×C4—3444no—
402C2×C4—1722no—
403C2×C4—1722no—
404C2×C4—1722no—
405C2×C4—1722no—
406C2×C4—1721no—
407C2×C4—1721no—
408C2×C4—1721no—
409C2×C4M16×D4311yescharacteristic
410C2×C4C2×#1062187211yescharacteristic
411C2×C4#1306334911yescharacteristic
412C2×C4#1306335211yescharacteristic
413C2×C4#1306335211yescharacteristic
414C2×C4#1306335711yescharacteristic
415C8—42no—
416C8—42no—
417C8—1722no—
418C8—1722no—
419C22—862no—
420C22—862no—
421C22—862no—
422C22—3441no—
423C22—3441no—
424C22—3441no—
425C22—3441no—
426C22—1722no—
427C22—1722no—
428C22—1722no—
429C22—1721no—
430C22—1721no—
431C22—1721no—
432C22—1721no—
433C22#1458286111yescharacteristic
434C22#99×D4311yescharacteristic
435C22#1458288211yescharacteristic
436C22#1458289911yescharacteristic
437C22#1458290211yescharacteristic
438C22#104×D4311yescharacteristic
439C22#104×D4311yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—21no—
445C4—21no—
446C4—42no—
447C4—81no—
448C4—862no—
449C4—862no—
450C4—3441no—
451C4—1721no—
452C2—3442no—
453C2—1722no—
454C2#1913293211yescharacteristic
455C2#1913303311yescharacteristic
456C2#1913303611yescharacteristic
457C2#1913309811yescharacteristic
458C2#1913310911yescharacteristic
459C2#1913318211yescharacteristic
460C2#1913331611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1271C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063300C4
cosocleC2×C42×C43C23
hypercenter#1271D43
hypocenterC43#7633
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
2. #19134356C2semidirect
3. #19134287C2semidirect
4. #19132418C2semidirect
5. #19132415C2semidirect
6. #19132415C2semidirect
7. C43×#1271C2semidirect
82. C2×D172M16semidirect
108. C4⋊C4×C43M16semidirect
226. #1271D43semidirect
257. C43#7633semidirect
347. C4⋊C4#10621872semidirect

Maximal subgroups

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

subgroupindex
#191371032
#191343562
#191342872
#191324182
#191324152
C43×#12712
#763343