Finite Group Databasebeta

← #24994388

Subgroups — #24994388

Order 11008.

576 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 109 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#19143621C211yesmaximal, characteristic
2#19138897C211yesmaximal, characteristic
3#19134681C211yesmaximal, characteristic, complemented
4#19134580C211yesmaximal, characteristic
5#19132463C211yesmaximal, characteristic, complemented
6#19132462C211yesmaximal, characteristic, complemented
7C43×#1823C211yesmaximal, characteristic, complemented
8C2×#13063308—21no—
9C2×C4×C22⋊D43C2211yescharacteristic
10#14582970—22no—
11#14582967—22no—
12#14582953—21no—
13C2×#13063239—21no—
14#14582861—21no—
15C2×C22⋊(C43⋊C8)C2211yescharacteristic
16#14582830C412yescomplemented
17#14582825C412yescomplemented
18#14582795—21no—
19#14582762—21no—
20#14582759C2211yescharacteristic
21#14582759C2211yescharacteristic
22#14582756—21no—
23#14582665—21no—
24#14582661—22no—
25C22×C4⋊C4×C43C2211yescharacteristic
26C2×C22⋊C8×C43C2211yescharacteristic
27C43×#380C2211yescharacteristic
28C43×#340—22no—
29C22×C22⋊D43D411yescharacteristic
30C22×C4×D43D411yescharacteristic
31C2×#10621872—22no—
32C22×C43⋊C8D412yes—
33#13063308—42no—
34#13063308—42no—
35C4×C22⋊D43—21no—
36C4×C22⋊D43—21no—
37C4×C22⋊D43—21no—
38C4×C22⋊D43—21no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43—21no—
41C2×Dic43⋊C4—22no—
42C2×Dic43⋊C4C2×C411yescharacteristic
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43—21no—
45C2×C22⋊Dic43D411yescharacteristic
46C2×(C2×D43)⋊C4—22no—
47C2×(C2×D43)⋊C4C2×C411yescharacteristic
48C2×C4×Dic43D411yescharacteristic
49Dic43⋊C8—22no—
50#13063239—42no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53(C2×D43)⋊C8—22no—
54#13063235—22no—
55C43⋊#95—22no—
56C43⋊#95—22no—
57C43⋊#95—21no—
58C43⋊#95C2×C412yes—
59C23×C4×C43—21no—
60C23×C4×C43C2311yescharacteristic
61C22×C8×C43D412yes—
62C2×C4⋊C4×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43C2×C412yes—
69C2×C22⋊C4×C43—21no—
70C22⋊C8×C43—21no—
71C22⋊C8×C43—21no—
72#95×C43—21no—
73C24×C43C2×D411yescharacteristic
74C23×D43C22⋊C411yescharacteristic
75C22×C4×C43—22no—
76C22×C4×C43—42no—
77C22×C4×C43—41no—
78C22×C4×C43—41no—
79C22×C4×C43—41no—
80C22×C4×C43—41no—
81C22×C4×C43—41no—
82C22×C4×C43—41no—
83C22×C4×C43—41no—
84C22×C4×C43C22×C411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43#4111yescharacteristic
89C22×C4×C43#4111yescharacteristic
90C2×C22⋊D43—21no—
91C2×C22⋊D43—21no—
92C2×C22⋊D43—21no—
93C2×C22⋊D43—21no—
94C2×C22⋊D43—21no—
95C2×C22⋊D43—21no—
96C22×Dic43—22no—
97C22×Dic43—41no—
98C22×Dic43C22⋊C411yescharacteristic
99C22×Dic43C22⋊C411yescharacteristic
100C22×Dic43C22⋊C411yescharacteristic
101C2×C4×D43—21no—
102C2×C4×D43—21no—
103C2×C4×D43—42no—
104C2×C8×C43—22no—
105C2×C8×C43—42no—
106C4⋊C4×C43—22no—
107C4⋊C4×C43—22no—
108C4⋊C4×C43—42no—
109C4⋊C4×C43—41no—
110C4⋊C4×C43—41no—
111C22⋊C4×C43—41no—
112C22⋊C4×C43—41no—
113C22⋊Dic43—21no—
114C22⋊Dic43—21no—
115C22⋊Dic43—41no—
116C22⋊Dic43—41no—
117C22⋊Dic43—41no—
118C22⋊Dic43—41no—
119(C2×D43)⋊C4—21no—
120(C2×D43)⋊C4—21no—
121(C2×D43)⋊C4—44no—
122C4⋊Dic43—42no—
123C4⋊Dic43—42no—
124Dic43⋊C4—21no—
125Dic43⋊C4—21no—
126Dic43⋊C4—44no—
127C4×Dic43—21no—
128C4×Dic43—21no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—42no—
131#10621872—82no—
132C23×C43—41no—
133C23×C43—41no—
134C23×C43C2×C22⋊C411yescharacteristic
135C23×C43#12111yescharacteristic
136C23×C43#12111yescharacteristic
137C23×C43AGL(1,ℤ/8)11yescharacteristic
138C23×C43AGL(1,ℤ/8)11yescharacteristic
139C23×C43AGL(1,ℤ/8)11yescharacteristic
140C23×C43#13711yescharacteristic
141C22×D43—21no—
142C22×D43—21no—
143C22×D43—21no—
144C22×D43—41no—
145C22×D43—41no—
146C2×C4×C43—22no—
147C2×C4×C43—22no—
148C2×C4×C43—22no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—42no—
153C2×C4×C43—42no—
154C2×C4×C43—42no—
155C2×C4×C43—81no—
156C2×C4×C43—81no—
157C2×C4×C43—81no—
158C2×C4×C43—81no—
159C2×C4×C43—81no—
160C2×C4×C43—81no—
161C2×C4×C43—81no—
162C2×C4×C43C4×D411yescharacteristic
163C2×C4×C43C4×D411yescharacteristic
164C2×C4×C43#12011yescharacteristic
165C2×C4×C43#12311yescharacteristic
166C22⋊D43—41no—
167C22⋊D43—41no—
168C22⋊D43—41no—
169C22⋊D43—41no—
170C2×Dic43—21no—
171C2×Dic43—21no—
172C2×Dic43—21no—
173C2×Dic43—21no—
174C2×Dic43—21no—
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43—42no—
178C2×Dic43—42no—
179C2×Dic43—42no—
180C2×Dic43—81no—
181C2×Dic43—81no—
182C2×Dic43—81no—
183C4×D43—42no—
184C4×D43—81no—
185C8×C43—42no—
186C43⋊C8—42no—
187#9474—431nomaximal, Sylow
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—41no—
195C22×C43—41no—
196C22×C43—41no—
197C22×C43—41no—
198C22×C43#38611yescharacteristic
199C22×C43#41711yescharacteristic
200C22×C43#41811yescharacteristic
201C22×C43#46811yescharacteristic
202C22×C43#46811yescharacteristic
203C22×C43#46911yescharacteristic
204C22×C43#46911yescharacteristic
205C2×D43—42no—
206C2×D43—41no—
207C2×D43—41no—
208C2×D43—41no—
209C2×D43—81no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—21no—
213C4×C43—82no—
214C4×C43—161no—
215C4×C43#45812yes—
216Dic43—41no—
217Dic43—41no—
218Dic43—41no—
219Dic43—82no—
220Dic43—161no—
221#2973—431no—
222#2486—431no—
223#1823—431no—
224#1823D4311yescharacteristic, complemented
225#1799—431no—
226#1289—431no—
227#1289—431no—
228C2×C43—21no—
229C2×C43—21no—
230C2×C43—21no—
231C2×C43—21no—
232C2×C43—21no—
233C2×C43—21no—
234C2×C43#189011yescharacteristic
235C2×C43#189511yescharacteristic
236C2×C43#190911yescharacteristic
237D43—81no—
238C2×#123—861no—
239C2×C4×D4—431no—
240C22×C4⋊C4C2×D4311yescharacteristic
241#435—862no—
242#435—862no—
243#432—861no—
244C2×#99—861no—
245#407—861no—
246C2×C22⋊C8—431no—
247C2×C22⋊C8C2×D4311yescharacteristic
248#398—432no—
249#397—432no—
250#389—861no—
251#381—861no—
252#380—431no—
253#380—431no—
254#380—861no—
255#380C2×D4311yescharacteristic
256#342—861no—
257#340—22no—
258#340—862no—
259C43#947411yescharacteristic, complemented, Sylow
260C22×D4—431no—
261C23×C4—21no—
262C23×C4—431no—
263C23×C4C22×D4311yescharacteristic
264C2×M16—862no—
265C22×C8—432no—
266C22×C8C22⋊D4312yes—
267#123—1722no—
268#123—1722no—
269C4×D4—861no—
270C4×D4—861no—
271C4×D4—861no—
272C4×D4—861no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—431no—
280C2×C4⋊C4—862no—
281C2×C4⋊C4—861no—
282C2×C4⋊C4—861no—
283C2×C4⋊C4C4×D4312yes—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—431no—
286C2×C22⋊C4—431no—
287C2×C22⋊C4—862no—
288C2×C22⋊C4—861no—
289C2×C22⋊C4—861no—
290C2×C42—431no—
291C4⋊C8—862no—
292#99—1722no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C22⋊C8—862no—
296C22⋊C8—861no—
297C22⋊C8—861no—
298#97—862no—
299#95—21no—
300#95—432no—
301#95—862no—
302#95—862no—
303#95—861no—
304C24—431no—
305C24D4×D4311yescharacteristic
306C2×D4—861no—
307C2×D4—861no—
308C2×D4—861no—
309C2×D4—861no—
310C2×D4—861no—
311C2×D4—861no—
312C22×C4—22no—
313C22×C4—42no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—431no—
322C22×C4—431no—
323C22×C4—431no—
324C22×C4—861no—
325C22×C4—861no—
326C22×C4—862no—
327C22×C4—1722no—
328C22×C4—1721no—
329C22×C4C2×C4×D4311yescharacteristic
330C22×C4#1062189811yescharacteristic
331C22×C4D4×D4311yescharacteristic
332C22×C4D4×D4311yescharacteristic
333C22×C4#1062190011yescharacteristic
334C22×C4C2×C22⋊D4311yescharacteristic
335M16—3442no—
336C2×C8—22no—
337C2×C8—42no—
338C2×C8—862no—
339C2×C8—1722no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—42no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—861no—
346C4⋊C4—861no—
347C4⋊C4—1722no—
348C4⋊C4—1722no—
349C4⋊C4—1724no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—861no—
353C22⋊C4—861no—
354C22⋊C4—861no—
355C22⋊C4—861no—
356C22⋊C4—1724no—
357C22⋊C4—1721no—
358C22⋊C4—1721no—
359C22⋊C4—1721no—
360C22⋊C4—1721no—
361C42—861no—
362C42—861no—
363C23—41no—
364C23—41no—
365C23—861no—
366C23—861no—
367C23—861no—
368C23—1721no—
369C23—1721no—
370C23C22⋊C4×D4311yescharacteristic
371C23#1306329611yescharacteristic
372C23#1306329811yescharacteristic
373C23#1306334911yescharacteristic
374C23#1306334911yescharacteristic
375C23#1306335211yescharacteristic
376C23#1306335411yescharacteristic
377D4—1721no—
378D4—1721no—
379D4—1721no—
380D4—1721no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—861no—
398C2×C4—861no—
399C2×C4—861no—
400C2×C4—861no—
401C2×C4—861no—
402C2×C4—3441no—
403C2×C4—3441no—
404C2×C4—3441no—
405C2×C4—3441no—
406C2×C4—1722no—
407C2×C4—1722no—
408C2×C4—1722no—
409C2×C4—1722no—
410C2×C4—1721no—
411C2×C4—1721no—
412C2×C4(C22⋊D43)⋊C411yescharacteristic
413C2×C4C4×C22⋊D4311yescharacteristic
414C2×C4#1306329311yescharacteristic
415C2×C4#1306330711yescharacteristic
416C8—42no—
417C8—1722no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—3441no—
429C22—1722no—
430C22—1721no—
431C22—1721no—
432C22—1721no—
433C22#1458277511yescharacteristic
434C22#1458289711yescharacteristic
435C22#1458290211yescharacteristic
436C22#1458314211yescharacteristic
437C22#1458314411yescharacteristic
438C22#1458314911yescharacteristic
439C22#1458315111yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—82no—
444C4—161no—
445C4—3442no—
446C4—1721no—
447C4—1721no—
448C4—1721no—
449C4—6881no—
450C4#1458308812yes—
451C2—21no—
452C2—21no—
453C2—21no—
454C2—21no—
455C2—21no—
456C2—21no—
457C2—3441no—
458C2#1913500511yescharacteristic
459C2#1913503011yescharacteristic
460C2#1913511411yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1823C2
socleC22×C43#386
prime radicalC22×C22⋊D43D4
cosocleC23×C4×C43C23
hypercenter#1823D43
hypocenterC43#9474
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
3. #19134681C2semidirect
5. #19132463C2semidirect
6. #19132462C2semidirect
7. C43×#1823C2semidirect
16. #14582830C4semidirect
17. #14582825C4semidirect
224. #1823D43semidirect
259. C43#9474semidirect

Maximal subgroups

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

subgroupindex
#191436212
#191388972
#191346812
#191345802
#191324632
#191324622
C43×#18232
#947443