Finite Group Databasebeta

← #24992140

Subgroups — #24992140

Order 11008.

648 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 115 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#19143624C211yesmaximal, characteristic, complemented
2#19137249C211yesmaximal, characteristic
3C2×#14582622C212yesmaximal, complemented
4#19132442C212yesmaximal, complemented
5C43×#1459C211yesmaximal, characteristic, complemented
6C2×#13063293C411yescharacteristic
7C22×(C2×D43)⋊C4C2211yescharacteristic
8#14582971—24no—
9#14582956—21no—
10#14582863—21no—
11C2×C22⋊(C43⋊C8)C2212yes—
12#14582799—21no—
13#14582790—21no—
14#14582789—21no—
15#14582779C411yescharacteristic
16#14582778—21no—
17#14582771C411yescharacteristic
18#14582754C411yescharacteristic
19C4×C22⋊Dic43C2211yescharacteristic
20#14582622—24no—
21C2×C4×D4×C43C2211yescharacteristic
22C2×C22⋊C8×C43C2212yes—
23C43×#324—21no—
24C43×#323—21no—
25C24×D43C2×C411yescharacteristic
26C22×C22⋊D43—21no—
27C23×Dic43C2×C411yescharacteristic
28C2×#10621877—22no—
29C22×C43⋊C8—22no—
30#13063293—22no—
31#13063293—22no—
32C2×Dic43⋊C4—21no—
33C2×C22⋊Dic43—21no—
34C2×C22⋊Dic43C2×C411yescharacteristic
35C2×C22⋊Dic43C2×C411yescharacteristic
36C2×(C2×D43)⋊C4—21no—
37C2×(C2×D43)⋊C4—21no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—22no—
40C2×(C2×D43)⋊C4—22no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×C4×Dic43—21no—
44C4⋊(C43⋊C8)—22no—
45C22⋊(C43⋊C8)—22no—
46C22⋊(C43⋊C8)—22no—
47C22⋊(C43⋊C8)D414yescomplemented
48#13063236—22no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C22×D4×C43C2×C411yescharacteristic
53C23×C4×C43D411yescharacteristic
54C23×C4×C43C2311yescharacteristic
55C22×C8×C43—22no—
56C4×D4×C43—22no—
57C4×D4×C43—22no—
58C2×C4⋊C4×C43D411yescharacteristic
59C2×C22⋊C4×C43C2×C411yescharacteristic
60C2×C22⋊C4×C43D411yescharacteristic
61C2×C42×C43D411yescharacteristic
62C22⋊C8×C43—22no—
63C22⋊C8×C43—22no—
64C24×C43C22⋊C411yescharacteristic
65C24×C43C22×C411yescharacteristic
66C23×D43—21no—
67C23×D43—22no—
68C23×D43—21no—
69C23×D43—22no—
70C23×D43—81no—
71C23×D43—81no—
72C23×D43M1612yescomplemented
73C2×D4×C43—22no—
74C2×D4×C43—21no—
75C2×D4×C43—21no—
76C2×D4×C43—22no—
77C22×C4×C43—21no—
78C22×C4×C43—21no—
79C22×C4×C43—81no—
80C22×C4×C43—81no—
81C22×C4×C43C22⋊C411yescharacteristic
82C22×C4×C43C22⋊C411yescharacteristic
83C22×C4×C43C22⋊C411yescharacteristic
84C22×C4×C43C2×D411yescharacteristic
85C22×C4×C43C2×D411yescharacteristic
86C22×C4×C43C2×D412yes—
87C22×C4×C43#4112yes—
88C2×C22⋊D43—24no—
89C2×C22⋊D43—81no—
90C2×C22⋊D43—81no—
91C22×Dic43—21no—
92C22×Dic43—21no—
93C22×Dic43—21no—
94C22×Dic43—22no—
95C22×Dic43—81no—
96C2×C8×C43—42no—
97C2×C8×C43—82no—
98C4⋊C4×C43—22no—
99C22⋊C4×C43—22no—
100C22⋊C4×C43—22no—
101C42×C43—21no—
102C42×C43—21no—
103C22⋊Dic43—21no—
104C22⋊Dic43—22no—
105C22⋊Dic43—81no—
106C22⋊Dic43M1612yescomplemented
107(C2×D43)⋊C4—24no—
108(C2×D43)⋊C4—41no—
109(C2×D43)⋊C4—42no—
110(C2×D43)⋊C4—41no—
111(C2×D43)⋊C4—81no—
112(C2×D43)⋊C4—81no—
113Dic43⋊C4—81no—
114C4×Dic43—81no—
115#10621877—82no—
116C2×C43⋊C8—24no—
117C2×C43⋊C8—82no—
118C23×C43—21no—
119C23×C43—21no—
120C23×C43—21no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43C2×C22⋊C411yescharacteristic
126C23×C43C4×D412yes—
127C23×C43C2×M1611yescharacteristic
128C23×C43C2×M1611yescharacteristic
129C23×C43#13112yes—
130C22×D43—22no—
131C22×D43—24no—
132C22×D43—41no—
133C22×D43—41no—
134C22×D43—41no—
135C22×D43—41no—
136C22×D43—41no—
137C22×D43—41no—
138C22×D43—42no—
139C22×D43—82no—
140C22×D43—82no—
141C22×D43—82no—
142C22×D43—82no—
143C22×D43—84no—
144D4×C43—42no—
145D4×C43—42no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—42no—
152C2×C4×C43—41no—
153C2×C4×C43—42no—
154C2×C4×C43—41no—
155C2×C4×C43—42no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—81no—
159C2×C4×C43#12011yescharacteristic
160C2×C4×C43#12112yes—
161C2×C4×C43#12311yescharacteristic
162C22⋊D43—84no—
163C2×Dic43—22no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—82no—
173C8×C43—82no—
174C43⋊C8—44no—
175#9109—431nomaximal, Sylow
176C22×C43—21no—
177C22×C43—22no—
178C22×C43—21no—
179C22×C43—22no—
180C22×C43—41no—
181C22×C43—41no—
182C22×C43—42no—
183C22×C43—42no—
184C22×C43—41no—
185C22×C43—41no—
186C22×C43—41no—
187C22×C43—81no—
188C22×C43#38611yescharacteristic
189C22×C43#40711yescharacteristic
190C22×C43#40811yescharacteristic
191C22×C43#43512yes—
192C22×C43#43612yes—
193C2×D43—42no—
194C2×D43—42no—
195C2×D43—42no—
196C2×D43—81no—
197C2×D43—81no—
198C2×D43—84no—
199C2×D43—81no—
200C2×D43—81no—
201C2×D43—84no—
202C4×C43—21no—
203C4×C43—22no—
204C4×C43—21no—
205C4×C43—41no—
206C4×C43—41no—
207C4×C43—41no—
208Dic43—42no—
209Dic43—81no—
210Dic43—81no—
211#2973—431no—
212#2321—431no—
213#1459D4311yescharacteristic, complemented
214C2×#323—432no—
215#1282—432no—
216C2×C43—21no—
217C2×C43—21no—
218C2×C43—22no—
219C2×C43—22no—
220C2×C43—81no—
221C2×C43#187011yescharacteristic
222C2×C43#191311yescharacteristic
223C2×C43#191411yescharacteristic
224D43—82no—
225C2×#120—431no—
226C2×C4×D4C2×D4311yescharacteristic
227C22×C22⋊C4—431no—
228#435—864no—
229#432—861no—
230#407—861no—
231C2×C22⋊C8—432no—
232C2×C22⋊C8C2×D4312yes—
233#390—861no—
234#388—861no—
235#388—861no—
236#386—431no—
237#386—861no—
238#385—431no—
239#379—431no—
240C4×C22⋊C4—431no—
241#324—21no—
242#323—21no—
243#323—864no—
244C43#910911yescharacteristic, complemented, Sylow
245C25—431no—
246C22×D4—861no—
247C22×D4C4×D4311yescharacteristic
248C23×C4—431no—
249C23×C4D17211yescharacteristic
250C23×C4C22×D4311yescharacteristic
251C2×M16—862no—
252C22×C8—22no—
253C22×C8—862no—
254#120—862no—
255#120—862no—
256C4×D4—22no—
257C4×D4—22no—
258C2×C4⋊C4—861no—
259C2×C4⋊C4C22⋊D4311yescharacteristic
260C2×C22⋊C4—431no—
261C2×C22⋊C4—431no—
262C2×C22⋊C4—861no—
263C2×C22⋊C4—861no—
264C2×C22⋊C4—861no—
265C2×C22⋊C4—861no—
266C2×C22⋊C4—861no—
267C2×C22⋊C4—862no—
268C2×C22⋊C4—862no—
269C2×C22⋊C4—861no—
270C2×C22⋊C4C4×D4311yescharacteristic
271C2×C22⋊C4C22⋊D4311yescharacteristic
272C2×C42—861no—
273C2×C42D17211yescharacteristic
274C4⋊C8—862no—
275C22⋊C8—22no—
276C22⋊C8—22no—
277C22⋊C8—434no—
278C22⋊C8—862no—
279C22⋊C8—862no—
280#97—862no—
281#95—861no—
282#95—861no—
283#95—861no—
284C24—432no—
285C24—862no—
286C24—861no—
287C24—862no—
288C24—861no—
289C24—3441no—
290C24—3441no—
291C24(C2×D43)⋊C411yescharacteristic
292C24C2×C4×D4311yescharacteristic
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—22no—
297C2×D4—864no—
298C2×D4—3441no—
299C2×D4—3441no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—81no—
303C22×C4—81no—
304C22×C4—861no—
305C22×C4—862no—
306C22×C4—861no—
307C22×C4—861no—
308C22×C4—3441no—
309C22×C4(C2×D43)⋊C411yescharacteristic
310C22×C4(C2×D43)⋊C411yescharacteristic
311C22×C4(C2×D43)⋊C411yescharacteristic
312C22×C4C2×D17211yescharacteristic
313C22×C4D4×D4312yes—
314C22×C4#1062190012yes—
315C22×C4C2×C22⋊D4311yescharacteristic
316M16—3442no—
317C2×C8—42no—
318C2×C8—82no—
319C2×C8—864no—
320C2×C8—3442no—
321C4⋊C4—22no—
322C4⋊C4—3441no—
323C22⋊C4—22no—
324C22⋊C4—22no—
325C22⋊C4—432no—
326C22⋊C4—864no—
327C22⋊C4—861no—
328C22⋊C4—862no—
329C22⋊C4—3441no—
330C22⋊C4—3441no—
331C22⋊C4—3441no—
332C22⋊C4—1721no—
333C22⋊C4—1722no—
334C22⋊C4—1721no—
335C42—21no—
336C42—21no—
337C42—3441no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—864no—
346C23—862no—
347C23—3442no—
348C23—3442no—
349C23—3444no—
350C23—3442no—
351C23—3442no—
352C23—1721no—
353C23—1721no—
354C23—1721no—
355C23—1721no—
356C23—1721no—
357C23—1722no—
358C23—1721no—
359C23C2×(C2×D43)⋊C411yescharacteristic
360C23(C22⋊D43)⋊C412yes—
361C23M16×D4311yescharacteristic
362C23M16×D4311yescharacteristic
363C23#1306333112yes—
364D4—42no—
365D4—42no—
366D4—3444no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—81no—
380C2×C4—862no—
381C2×C4—3442no—
382C2×C4—1721no—
383C2×C4—1721no—
384C2×C4—1721no—
385C2×C4—1721no—
386C2×C4—1721no—
387C2×C4—1721no—
388C2×C4—1721no—
389C2×C4—1721no—
390C2×C4#1306329511yescharacteristic
391C2×C4#1306329712yes—
392C2×C4#1306330911yescharacteristic
393C8—82no—
394C8—1724no—
395C22—21no—
396C22—22no—
397C22—21no—
398C22—22no—
399C22—41no—
400C22—41no—
401C22—42no—
402C22—42no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—81no—
407C22—3444no—
408C22—3444no—
409C22—3441no—
410C22—3441no—
411C22—3441no—
412C22—3441no—
413C22—1722no—
414C22—1722no—
415C22—1722no—
416C22#1458277611yescharacteristic
417C22#1458286211yescharacteristic
418C22#1458286511yescharacteristic
419C22#1458297312yes—
420C22#1458297412yes—
421C4—22no—
422C4—21no—
423C4—21no—
424C4—41no—
425C4—41no—
426C4—41no—
427C4—3441no—
428C4—3441no—
429C4—1722no—
430C2—21no—
431C2—21no—
432C2—22no—
433C2—22no—
434C2—81no—
435C2—3442no—
436C2#1913489011yescharacteristic
437C2#1913513511yescharacteristic
438C2#1913514011yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1459C2
socleC22×C43#386
prime radicalC2×#13063293C4
cosocleC23×C4×C43C23
hypercenter#1459D43
hypocenterC43#9109
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
1. #19143624C2semidirect
3. C2×#14582622C2semidirect
4. #19132442C2semidirect
5. C43×#1459C2semidirect
47. C22⋊(C43⋊C8)D4semidirect
72. C23×D43M16semidirect
106. C22⋊Dic43M16semidirect
213. #1459D43semidirect
244. C43#9109semidirect

Maximal subgroups

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

subgroupindex
#191436242
#191372492
C2×#145826222
#191324422
C43×#14592
#910943