Finite Group Databasebeta

← #24994039

Subgroups — #24994039

Order 11008.

840 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 97 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#19139527C211yesmaximal, characteristic
2#19136947C211yesmaximal, characteristic, complemented
3#19133111C211yesmaximal, characteristic, complemented
4#19132921C211yesmaximal, characteristic, complemented
5#19132481C211yesmaximal, characteristic, complemented
6#19132480C211yesmaximal, characteristic, complemented
7C43×#1507C211yesmaximal, characteristic, complemented
8C2×#13063306—21no—
9C2×#13063293—21no—
10C22×(C2×D43)⋊C4C2211yescharacteristic
11C2×C22⋊C4×D43—21no—
12#14582863C2211yescharacteristic
13#14582834C412yescomplemented
14#14582807C412yescomplemented
15#14582799—22no—
16C22⋊C4×Dic43—21no—
17C4×(C2×D43)⋊C4—22no—
18C4×C22⋊Dic43C2211yescharacteristic
19C4×C22⋊Dic43C2211yescharacteristic
20#14582746—22no—
21#14582633—22no—
22#14582622—22no—
23C2×#121×C43C2211yescharacteristic
24C43×#407C2211yescharacteristic
25C4×C22⋊C4×C43C2211yescharacteristic
26C43×#327—22no—
27C24×D43D411yescharacteristic
28C22×C22⋊D43—22no—
29C23×Dic43D411yescharacteristic
30C22×C4×D43—22no—
31C2×#10621877—21no—
32#13063306—44no—
33#13063293—44no—
34C2×Dic43⋊C4—22no—
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37C2×C22⋊Dic43—22no—
38C2×(C2×D43)⋊C4—22no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—22no—
44C2×(C2×D43)⋊C4C2×C412yes—
45C2×(C2×D43)⋊C4D412yes—
46C22⋊C4×D43—28no—
47C2×C4×Dic43—22no—
48C2×C4×Dic43—21no—
49C2×C4×Dic43—21no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C43⋊#95—22no—
53C43⋊#95C2×C412yescomplemented
54C43⋊#95D412yescomplemented
55C22×D4×C43—21no—
56C22×D4×C43C2×C411yescharacteristic, complemented
57C23×C4×C43C2311yescharacteristic
58C2×M16×C43—21no—
59#121×C43—21no—
60#121×C43—21no—
61#121×C43—21no—
62#121×C43—21no—
63C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
64C2×C22⋊C4×C43—21no—
65C2×C22⋊C4×C43—21no—
66C2×C42×C43—21no—
67C22⋊C8×C43—21no—
68C22⋊C8×C43—21no—
69#95×C43D412yescomplemented
70C24×C43—21no—
71C24×C43C2×D411yescharacteristic
72C23×D43—21no—
73C23×D43—21no—
74C23×D43—24no—
75C23×D43—42no—
76C23×D43—81no—
77C23×D43C22⋊C412yes—
78C2×D4×C43—21no—
79C2×D4×C43—21no—
80C2×D4×C43—42no—
81C2×D4×C43—42no—
82C2×D4×C43—41no—
83C2×D4×C43—41no—
84C2×D4×C43—81no—
85C22×C4×C43—21no—
86C22×C4×C43—22no—
87C22×C4×C43—81no—
88C22×C4×C43C22×C411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43#4111yescharacteristic
93C22×C4×C43#4111yescharacteristic
94C2×C22⋊D43—44no—
95C2×C22⋊D43—44no—
96C2×C22⋊D43—82no—
97C22×Dic43—22no—
98C22×Dic43—21no—
99C22×Dic43—22no—
100C22×Dic43—21no—
101C22×Dic43—42no—
102C22×Dic43C22⋊C412yes—
103C2×C4×D43—28no—
104C2×C4×D43—82no—
105C2×C4×D43—82no—
106M16×C43—81no—
107C2×C8×C43—41no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—21no—
110C22⋊C4×C43—24no—
111C22⋊C4×C43—41no—
112C22⋊C4×C43—41no—
113C42×C43—81no—
114C22⋊Dic43—24no—
115C22⋊Dic43—24no—
116C22⋊Dic43—44no—
117(C2×D43)⋊C4—28no—
118(C2×D43)⋊C4—22no—
119(C2×D43)⋊C4—22no—
120(C2×D43)⋊C4—22no—
121(C2×D43)⋊C4—22no—
122(C2×D43)⋊C4—44no—
123Dic43⋊C4—44no—
124C4×Dic43—81no—
125C4×Dic43—81no—
126C4×Dic43—82no—
127#10621877—81no—
128C2×C43⋊C8—41no—
129C23×C43—22no—
130C23×C43—22no—
131C23×C43—41no—
132C23×C43—41no—
133C23×C43—41no—
134C23×C43—42no—
135C23×C43—41no—
136C23×C43—42no—
137C23×C43C2×C22⋊C411yescharacteristic
138C23×C43#12011yescharacteristic
139C23×C43#12311yescharacteristic
140C22×D43—22no—
141C22×D43—22no—
142C22×D43—22no—
143C22×D43—24no—
144C22×D43—22no—
145C22×D43—42no—
146C22×D43—42no—
147C22×D43—42no—
148C22×D43—42no—
149C22×D43—88no—
150C22×D43—81no—
151C22×D43—81no—
152C22×D43#10414yes—
153D4×C43—81no—
154D4×C43—81no—
155D4×C43—82no—
156D4×C43—82no—
157C2×C4×C43—24no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—42no—
165C2×C4×C43—42no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43C4×D411yescharacteristic
170C2×C4×C43C4×D411yescharacteristic
171C2×C4×C43#12111yescharacteristic
172C2×C4×C43#12111yescharacteristic
173C22⋊D43—88no—
174C2×Dic43—24no—
175C2×Dic43—24no—
176C2×Dic43—22no—
177C2×Dic43—42no—
178C2×Dic43—42no—
179C2×Dic43—42no—
180C2×Dic43—42no—
181C2×Dic43—42no—
182C2×Dic43—42no—
183C2×Dic43—81no—
184C4×D43—88no—
185C8×C43—81no—
186C43⋊C8—81no—
187#9409—431nomaximal, Sylow
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43—21no—
194C22×C43—21no—
195C22×C43—44no—
196C22×C43—82no—
197C22×C43—82no—
198C22×C43—81no—
199C22×C43—81no—
200C22×C43—81no—
201C22×C43#38611yescharacteristic
202C22×C43C2×#10412yes—
203C22×C43#45312yes—
204C2×D43—24no—
205C2×D43—44no—
206C2×D43—44no—
207C2×D43—42no—
208C2×D43—42no—
209C2×D43—44no—
210C2×D43—82no—
211C2×D43—84no—
212C4×C43—21no—
213C4×C43—21no—
214C4×C43—21no—
215C4×C43—21no—
216C4×C43—44no—
217C4×C43—81no—
218Dic43—44no—
219Dic43—44no—
220Dic43—42no—
221#2539—431no—
222#2273—431no—
223#1507—431no—
224#1507D4311yescharacteristic, complemented
225#1462—431no—
226#1297—431no—
227#1297—431no—
228C2×C43—22no—
229C2×C43—22no—
230C2×C43—41no—
231C2×C43—161no—
232C2×C43#188711yescharacteristic
233C2×C43#189611yescharacteristic
234C2×C43#191311yescharacteristic
235D43—44no—
236C2×#123—861no—
237C2×#121C2×D4311yescharacteristic
238C2×#120—861no—
239C22×C22⋊C4—431no—
240C22×C22⋊C4—861no—
241#407—431no—
242#407C2×D4311yescharacteristic
243#399—432no—
244#392—432no—
245#390—862no—
246C4×C22⋊C4—431no—
247C4×C22⋊C4—431no—
248C4×C22⋊C4—862no—
249C4×C22⋊C4—861no—
250C4×C22⋊C4—862no—
251C4×C22⋊C4C2×D4311yescharacteristic
252#327—22no—
253#327—862no—
254#323—862no—
255C43#940911yescharacteristic, complemented, Sylow
256C25—431no—
257C22×D4—21no—
258C22×D4—862no—
259C22×D4C4×D4311yescharacteristic, complemented
260C23×C4—431no—
261C23×C4—862no—
262C23×C4C22×D4311yescharacteristic
263C2×M16—21no—
264C2×M16—861no—
265#123—1724no—
266#121—21no—
267#121—21no—
268#121—21no—
269#121—21no—
270#120—1724no—
271C2×C4⋊C4—862no—
272C2×C4⋊C4C4×D4311yescharacteristic, complemented
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—432no—
276C2×C22⋊C4—432no—
277C2×C22⋊C4—868no—
278C2×C22⋊C4—862no—
279C2×C22⋊C4—861no—
280C2×C22⋊C4—861no—
281C2×C22⋊C4—861no—
282C2×C22⋊C4—861no—
283C2×C22⋊C4—861no—
284C2×C22⋊C4—861no—
285C2×C22⋊C4—862no—
286C2×C22⋊C4—862no—
287C2×C42—21no—
288C2×C42—862no—
289C2×C42—861no—
290C2×C42—861no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8—861no—
294C22⋊C8—861no—
295#95—432no—
296#95—432no—
297#95—862no—
298#95C22⋊D4312yescomplemented
299C24—21no—
300C24—432no—
301C24—864no—
302C24—861no—
303C24—861no—
304C24—3441no—
305C24—1722no—
306C24D4×D4311yescharacteristic
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—42no—
310C2×D4—42no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—81no—
314C2×D4—3442no—
315C2×D4—1724no—
316C2×D4—1724no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—81no—
320C22×C4—432no—
321C22×C4—868no—
322C22×C4—861no—
323C22×C4—862no—
324C22×C4—862no—
325C22×C4—861no—
326C22×C4—3442no—
327C22×C4—3442no—
328C22×C4—1722no—
329C22×C4C2×C4×D4311yescharacteristic
330C22×C4#1062189811yescharacteristic
331C22×C4D4×D4311yescharacteristic
332C22×C4D4×D4311yescharacteristic
333C22×C4#1062190011yescharacteristic
334C22×C4C2×C22⋊D4311yescharacteristic
335M16—81no—
336M16—3441no—
337C2×C8—41no—
338C2×C8—1721no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—1724no—
342C22⋊C4—24no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—868no—
346C22⋊C4—864no—
347C22⋊C4—864no—
348C22⋊C4—862no—
349C22⋊C4—862no—
350C22⋊C4—862no—
351C22⋊C4—862no—
352C22⋊C4—1724no—
353C22⋊C4—1724no—
354C42—81no—
355C42—3441no—
356C42—3441no—
357C42—3442no—
358C23—22no—
359C23—22no—
360C23—41no—
361C23—41no—
362C23—41no—
363C23—42no—
364C23—42no—
365C23—41no—
366C23—434no—
367C23—864no—
368C23—862no—
369C23—862no—
370C23—862no—
371C23—862no—
372C23—3441no—
373C23—3441no—
374C23—3448no—
375C23—1722no—
376C23—1722no—
377C23—1722no—
378C23—1722no—
379C23C22⋊C4×D4311yescharacteristic
380C23#1306329311yescharacteristic
381C23#1306330711yescharacteristic
382D4—81no—
383D4—81no—
384D4—82no—
385D4—82no—
386D4—3448no—
387C2×C4—24no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—864no—
400C2×C4—864no—
401C2×C4—862no—
402C2×C4—3448no—
403C2×C4—3441no—
404C2×C4—1722no—
405C2×C4—1722no—
406C2×C4—1722no—
407C2×C4—1722no—
408C2×C4—1722no—
409C2×C4—1722no—
410C2×C4(C22⋊D43)⋊C411yescharacteristic
411C2×C4C4×C22⋊D4311yescharacteristic
412C2×C4#1306329611yescharacteristic
413C2×C4#1306329811yescharacteristic
414C8—81no—
415C8—3441no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—44no—
424C22—82no—
425C22—82no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22—864no—
430C22—3442no—
431C22—3444no—
432C22—1724no—
433C22—1724no—
434C22—1724no—
435C22—1722no—
436C22—1722no—
437C22#1458277511yescharacteristic
438C22#104×D4312yes—
439C22#1458306512yes—
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—44no—
445C4—81no—
446C4—1724no—
447C4—1724no—
448C4—1722no—
449C2—22no—
450C2—22no—
451C2—41no—
452C2—161no—
453C2—1724no—
454C2#1913499011yescharacteristic
455C2#1913503511yescharacteristic
456C2#1913513411yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1507C2
socleC22×C43#386
prime radical#19139527C2
cosocleC23×C4×C43C23
hypercenter#1507D43
hypocenterC43#9409
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
2. #19136947C2semidirect
3. #19133111C2semidirect
4. #19132921C2semidirect
5. #19132481C2semidirect
6. #19132480C2semidirect
7. C43×#1507C2semidirect
13. #14582834C4semidirect
14. #14582807C4semidirect
53. C43⋊#95C2×C4semidirect
54. C43⋊#95D4semidirect
56. C22×D4×C43C2×C4semidirect
63. C2×C4⋊C4×C43C2×C4semidirect
69. #95×C43D4semidirect
224. #1507D43semidirect
255. C43#9409semidirect
259. C22×D4C4×D43semidirect
272. C2×C4⋊C4C4×D43semidirect
298. #95C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191395272
#191369472
#191331112
#191329212
#191324812
#191324802
C43×#15072
#940943