Finite Group Databasebeta

← #24991578

Subgroups — #24991578

Order 11008.

558 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 95 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#19143634C211yesmaximal, characteristic
2#19137852C211yesmaximal, characteristic
3#19134694C211yesmaximal, characteristic, complemented
4C4×#13063239C211yesmaximal, characteristic
5#19132481C211yesmaximal, characteristic, complemented
6#19132480C211yesmaximal, characteristic, complemented
7C43×#1826C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D43C2211yescharacteristic
9#14582975—22no—
10#14582974—22no—
11#14582949—21no—
12C2×#13063239—21no—
13#14582863C2211yescharacteristic
14#14582861—21no—
15#14582837C411yescharacteristic, complemented
16#14582834C411yescharacteristic, complemented
17#14582830C411yescharacteristic, complemented
18#14582827—21no—
19#14582825C411yescharacteristic, complemented
20#14582814—21no—
21C4×Dic43⋊C4—21no—
22C4×(C2×D43)⋊C4—21no—
23C4×C22⋊Dic43C2211yescharacteristic
24C4×C22⋊Dic43C2211yescharacteristic
25#14582665—21no—
26#14582658—22no—
27C2×#117×C43C2211yescharacteristic
28C43×#407C2211yescharacteristic
29C4×C22⋊C4×C43C2211yescharacteristic
30C43×#339—22no—
31C22×C22⋊D43D411yescharacteristic
32C22×C4×D43D411yescharacteristic
33C2×#10621877D412yes—
34C2×#10621872—22no—
35C4×C22⋊D43—21no—
36C4×C22⋊D43—21no—
37C4×C22⋊D43—21no—
38C4×C22⋊D43—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4C2×C411yescharacteristic
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43D411yescharacteristic
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4C2×C411yescharacteristic
48C2×C4×Dic43—21no—
49C2×C4×Dic43—21no—
50C2×C4×Dic43D411yescharacteristic
51Dic43⋊C8—22no—
52#13063239—24no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)—21no—
55(C2×D43)⋊C8—22no—
56C8×Dic43—22no—
57C43⋊#95—21no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95C2×C411yescharacteristic
63C43⋊#95C2×C411yescharacteristic
64C23×C4×C43C2311yescharacteristic
65C2×M16×C43D412yes—
66#117×C43—21no—
67#117×C43—21no—
68#117×C43—21no—
69#117×C43—21no—
70C2×C4⋊C4×C43C2×C411yescharacteristic
71C2×C4⋊C4×C43C2×C411yescharacteristic
72C2×C22⋊C4×C43—21no—
73C2×C22⋊C4×C43—21no—
74C2×C42×C43—21no—
75C2×C42×C43—21no—
76C22⋊C8×C43—21no—
77C22⋊C8×C43—21no—
78#95×C43—21no—
79C24×C43C2×D411yescharacteristic
80C23×D43C22⋊C411yescharacteristic
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—42no—
84C22×C4×C43—41no—
85C22×C4×C43C22×C411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43#4111yescharacteristic
90C22×C4×C43#4111yescharacteristic
91C2×C22⋊D43—22no—
92C2×C22⋊D43—21no—
93C2×C22⋊D43—21no—
94C2×C22⋊D43—41no—
95C22×Dic43—21no—
96C22×Dic43—21no—
97C22×Dic43—41no—
98C22×Dic43C22⋊C411yescharacteristic
99C22×Dic43C22⋊C411yescharacteristic
100C22×Dic43C22⋊C411yescharacteristic
101C2×C4×D43—21no—
102C2×C4×D43—21no—
103C2×C4×D43—42no—
104M16×C43—42no—
105C2×C8×C43—22no—
106C4⋊C4×C43—21no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—21no—
110C22⋊C4×C43—22no—
111C22⋊C4×C43—41no—
112C22⋊C4×C43—41no—
113C22⋊C4×C43—41no—
114C42×C43—42no—
115C42×C43—41no—
116C42×C43—41no—
117C22⋊Dic43—22no—
118C22⋊Dic43—21no—
119C22⋊Dic43—21no—
120C22⋊Dic43—41no—
121C22⋊Dic43—42no—
122(C2×D43)⋊C4—21no—
123(C2×D43)⋊C4—21no—
124(C2×D43)⋊C4—42no—
125(C2×D43)⋊C4—42no—
126Dic43⋊C4—21no—
127Dic43⋊C4—21no—
128Dic43⋊C4—42no—
129Dic43⋊C4—42no—
130C4×Dic43—21no—
131C4×Dic43—21no—
132C4×Dic43—42no—
133C4×Dic43—42no—
134#10621877—42no—
135C2×C43⋊C8—22no—
136#10621872—82no—
137C23×C43—21no—
138C23×C43—21no—
139C23×C43—41no—
140C23×C43—41no—
141C23×C43C2×C22⋊C411yescharacteristic
142C23×C43#12111yescharacteristic
143C23×C43#12111yescharacteristic
144C22×D43—21no—
145C22×D43—21no—
146C22×D43—21no—
147C22×D43—41no—
148C22×D43—41no—
149C2×C4×C43—22no—
150C2×C4×C43—22no—
151C2×C4×C43—22no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—42no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—81no—
163C2×C4×C43—81no—
164C2×C4×C43C4×D411yescharacteristic
165C2×C4×C43C4×D411yescharacteristic
166C2×C4×C43#12011yescharacteristic
167C2×C4×C43#12311yescharacteristic
168C22⋊D43—42no—
169C22⋊D43—42no—
170C2×Dic43—21no—
171C2×Dic43—21no—
172C2×Dic43—22no—
173C2×Dic43—21no—
174C2×Dic43—21no—
175C2×Dic43—41no—
176C2×Dic43—41no—
177C2×Dic43—41no—
178C2×Dic43—41no—
179C2×Dic43—41no—
180C2×Dic43—42no—
181C2×Dic43—41no—
182C2×Dic43—41no—
183C2×Dic43—81no—
184C2×Dic43—81no—
185C2×Dic43#10412yes—
186C4×D43—42no—
187C4×D43—81no—
188C8×C43—42no—
189C43⋊C8—42no—
190#9012—431nomaximal, Sylow
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—21no—
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—81no—
200C22×C43—81no—
201C22×C43#38611yescharacteristic
202C22×C43C2×#10411yescharacteristic
203C22×C43#42111yescharacteristic
204C2×D43—42no—
205C2×D43—41no—
206C2×D43—41no—
207C2×D43—41no—
208C2×D43—81no—
209C4×C43—21no—
210C4×C43—21no—
211C4×C43—21no—
212C4×C43—82no—
213C4×C43—81no—
214C4×C43—81no—
215C4×C43#45812yes—
216Dic43—22no—
217Dic43—42no—
218Dic43—41no—
219Dic43—41no—
220Dic43—81no—
221Dic43—82no—
222#2975—431no—
223#2395—431no—
224#1826—431no—
225#1826D4311yescharacteristic, complemented
226C4×#99—431no—
227#1297—431no—
228#1297—431no—
229C2×C43—21no—
230C2×C43—21no—
231C2×C43—41no—
232C2×C43—41no—
233C2×C43#187111yescharacteristic
234C2×C43#188411yescharacteristic
235C2×C43#189011yescharacteristic
236D43—81no—
237C2×C4×D4—431no—
238C2×#117C2×D4311yescharacteristic
239#436—862no—
240#436—862no—
241#431—861no—
242C2×#99—861no—
243#407—431no—
244#407—861no—
245#407C2×D4311yescharacteristic
246#400—431no—
247#399—431no—
248#398—431no—
249#397—431no—
250#397—861no—
251#394—861no—
252C4×C4⋊C4—861no—
253C4×C22⋊C4—431no—
254C4×C22⋊C4—431no—
255C4×C22⋊C4—861no—
256C4×C22⋊C4C2×D4311yescharacteristic
257#342—861no—
258#339—22no—
259#339—862no—
260C43#901211yescharacteristic, complemented, Sylow
261C22×D4—431no—
262C23×C4—431no—
263C23×C4C22×D4311yescharacteristic
264C2×M16—432no—
265C2×M16—862no—
266C2×M16C22⋊D4312yes—
267C4×D4—861no—
268C4×D4—861no—
269C4×D4—861no—
270C4×D4—861no—
271#117—21no—
272#117—21no—
273#117—21no—
274#117—21no—
275C2×C4⋊C4—431no—
276C2×C4⋊C4—861no—
277C2×C4⋊C4—861no—
278C2×C4⋊C4C4×D4311yescharacteristic
279C2×C4⋊C4C4×D4311yescharacteristic
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—431no—
283C2×C22⋊C4—431no—
284C2×C22⋊C4—861no—
285C2×C22⋊C4—861no—
286C2×C22⋊C4—861no—
287C2×C22⋊C4—861no—
288C2×C42—21no—
289C2×C42—21no—
290C2×C42—431no—
291C2×C42—861no—
292C2×C42—861no—
293C4⋊C8—862no—
294#99—864no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C22⋊C8—862no—
298C22⋊C8—861no—
299C22⋊C8—861no—
300C4×C8—862no—
301#95—21no—
302#95—431no—
303#95—431no—
304#95—861no—
305#95—861no—
306#95—861no—
307#95—861no—
308#95—861no—
309C24—431no—
310C24D4×D4311yescharacteristic
311C2×D4—862no—
312C2×D4—861no—
313C2×D4—861no—
314C2×D4—1721no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—42no—
318C22×C4—41no—
319C22×C4—431no—
320C22×C4—431no—
321C22×C4—431no—
322C22×C4—861no—
323C22×C4—861no—
324C22×C4—861no—
325C22×C4—861no—
326C22×C4—1722no—
327C22×C4—1721no—
328C22×C4C2×C4×D4311yescharacteristic
329C22×C4#1062189811yescharacteristic
330C22×C4D4×D4311yescharacteristic
331C22×C4D4×D4311yescharacteristic
332C22×C4#1062190011yescharacteristic
333C22×C4C2×C22⋊D4311yescharacteristic
334M16—42no—
335M16—3442no—
336M16—1722no—
337C2×C8—22no—
338C2×C8—862no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—21no—
343C4⋊C4—861no—
344C4⋊C4—861no—
345C4⋊C4—1722no—
346C4⋊C4—1722no—
347C22⋊C4—22no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—861no—
352C22⋊C4—861no—
353C22⋊C4—861no—
354C22⋊C4—861no—
355C22⋊C4—862no—
356C22⋊C4—1722no—
357C22⋊C4—1722no—
358C22⋊C4—1722no—
359C22⋊C4—1721no—
360C42—42no—
361C42—41no—
362C42—41no—
363C42—861no—
364C42—861no—
365C42—1722no—
366C42—1722no—
367C23—21no—
368C23—21no—
369C23—41no—
370C23—41no—
371C23—861no—
372C23—861no—
373C23—861no—
374C23—1721no—
375C23—1721no—
376C23C22⋊C4×D4311yescharacteristic
377C23#1306329611yescharacteristic
378C23#1306329811yescharacteristic
379D4—1722no—
380D4—1722no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—432no—
397C2×C4—861no—
398C2×C4—861no—
399C2×C4—862no—
400C2×C4—861no—
401C2×C4—861no—
402C2×C4—3441no—
403C2×C4—3441no—
404C2×C4—3441no—
405C2×C4—1721no—
406C2×C4—1722no—
407C2×C4—1721no—
408C2×C4—1721no—
409C2×C4—1721no—
410C2×C4—1721no—
411C2×C4—1722no—
412C2×C4—1721no—
413C2×C4—1721no—
414C2×C4(C22⋊D43)⋊C411yescharacteristic
415C2×C4C4×C22⋊D4311yescharacteristic
416C2×C4#1306329311yescharacteristic
417C2×C4#1306330711yescharacteristic
418C8—42no—
419C8—1722no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—81no—
429C22—81no—
430C22—3441no—
431C22—1722no—
432C22—1721no—
433C22—1721no—
434C22—1721no—
435C22#1458277511yescharacteristic
436C22#104×D4311yescharacteristic
437C22#1458291411yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—82no—
442C4—81no—
443C4—81no—
444C4—862no—
445C4—3441no—
446C4—3442no—
447C4—1722no—
448C4—1721no—
449C4—1721no—
450C4#1458308812yes—
451C2—21no—
452C2—21no—
453C2—41no—
454C2—41no—
455C2—3441no—
456C2#1913489411yescharacteristic
457C2#1913497511yescharacteristic
458C2#1913500511yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1826C2
socleC22×C43#386
prime radicalC22×C22⋊D43D4
cosocleC23×C4×C43C23
hypercenter#1826D43
hypocenterC43#9012
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
3. #19134694C2semidirect
5. #19132481C2semidirect
6. #19132480C2semidirect
7. C43×#1826C2semidirect
15. #14582837C4semidirect
16. #14582834C4semidirect
17. #14582830C4semidirect
19. #14582825C4semidirect
225. #1826D43semidirect
260. C43#9012semidirect

Maximal subgroups

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

subgroupindex
#191436342
#191378522
#191346942
C4×#130632392
#191324812
#191324802
C43×#18262
#901243