Finite Group Databasebeta

← #24994059

Subgroups — #24994059

Order 11008.

720 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 720 conjugacy classes of subgroups — too many to draw. Only its 93 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#19137190C211yesmaximal, 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
11#14582863C2211yescharacteristic
12#14582834C412yescomplemented
13#14582807C412yescomplemented
14#14582799—22no—
15#14582790—22no—
16#14582788—22no—
17#14582757—21no—
18#14582754—21no—
19C4×C22⋊Dic43C2211yescharacteristic
20C4×C22⋊Dic43C2211yescharacteristic
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
30C2×#10621877—21no—
31#13063306—44no—
32#13063293—44no—
33C2×Dic43⋊C4—22no—
34C2×Dic43⋊C4—22no—
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37C2×C22⋊Dic43—22no—
38C2×(C2×D43)⋊C4—21no—
39C2×(C2×D43)⋊C4—21no—
40C2×(C2×D43)⋊C4—21no—
41C2×(C2×D43)⋊C4—21no—
42C2×(C2×D43)⋊C4—22no—
43C2×(C2×D43)⋊C4—22no—
44C2×(C2×D43)⋊C4—22no—
45C2×(C2×D43)⋊C4C2×C412yes—
46C2×(C2×D43)⋊C4D412yes—
47C2×C4×Dic43—21no—
48C2×C4×Dic43—21no—
49C22⋊(C43⋊C8)—21no—
50C22⋊(C43⋊C8)—21no—
51C43⋊#95—22no—
52C43⋊#95C2×C412yes—
53C43⋊#95D412yescomplemented
54C22×D4×C43—21no—
55C22×D4×C43C2×C411yescharacteristic
56C23×C4×C43C2311yescharacteristic
57C2×M16×C43—21no—
58#121×C43—21no—
59#121×C43—21no—
60#121×C43—21no—
61#121×C43—21no—
62C2×C4⋊C4×C43C2×C411yescharacteristic
63C2×C22⋊C4×C43—21no—
64C2×C22⋊C4×C43—21no—
65C2×C42×C43—21no—
66C22⋊C8×C43—21no—
67C22⋊C8×C43—21no—
68#95×C43D412yescomplemented
69C24×C43—21no—
70C24×C43C2×D411yescharacteristic
71C23×D43—21no—
72C23×D43—21no—
73C23×D43—42no—
74C23×D43—42no—
75C23×D43—81no—
76C23×D43C22⋊C412yes—
77C2×D4×C43—21no—
78C2×D4×C43—21no—
79C2×D4×C43—42no—
80C2×D4×C43—42no—
81C2×D4×C43—41no—
82C2×D4×C43—41no—
83C2×D4×C43—81no—
84C22×C4×C43—21no—
85C22×C4×C43—22no—
86C22×C4×C43—81no—
87C22×C4×C43C22×C411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43#4111yescharacteristic
92C22×C4×C43#4111yescharacteristic
93C2×C22⋊D43—44no—
94C2×C22⋊D43—44no—
95C2×C22⋊D43—82no—
96C22×Dic43—22no—
97C22×Dic43—21no—
98C22×Dic43—22no—
99C22×Dic43—21no—
100C22×Dic43—42no—
101C22×Dic43C22⋊C412yes—
102M16×C43—81no—
103C2×C8×C43—41no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—21no—
106C22⋊C4×C43—42no—
107C22⋊C4×C43—41no—
108C22⋊C4×C43—41no—
109C42×C43—81no—
110C22⋊Dic43—24no—
111C22⋊Dic43—42no—
112C22⋊Dic43—44no—
113(C2×D43)⋊C4—22no—
114(C2×D43)⋊C4—22no—
115(C2×D43)⋊C4—22no—
116(C2×D43)⋊C4—22no—
117(C2×D43)⋊C4—44no—
118(C2×D43)⋊C4—82no—
119(C2×D43)⋊C4—82no—
120Dic43⋊C4—44no—
121Dic43⋊C4—82no—
122C4×Dic43—81no—
123C4×Dic43—81no—
124#10621877—81no—
125C2×C43⋊C8—41no—
126C23×C43—22no—
127C23×C43—22no—
128C23×C43—41no—
129C23×C43—41no—
130C23×C43—41no—
131C23×C43—42no—
132C23×C43—41no—
133C23×C43—42no—
134C23×C43C2×C22⋊C411yescharacteristic
135C23×C43#12011yescharacteristic
136C23×C43#12311yescharacteristic
137C22×D43—22no—
138C22×D43—22no—
139C22×D43—22no—
140C22×D43—42no—
141C22×D43—42no—
142C22×D43—42no—
143C22×D43—42no—
144C22×D43—42no—
145C22×D43—42no—
146C22×D43—81no—
147C22×D43—81no—
148C22×D43—88no—
149D4×C43—81no—
150D4×C43—81no—
151D4×C43—82no—
152D4×C43—82no—
153C2×C4×C43—41no—
154C2×C4×C43—41no—
155C2×C4×C43—41no—
156C2×C4×C43—41no—
157C2×C4×C43—41no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43—42no—
162C2×C4×C43—42no—
163C2×C4×C43—41no—
164C2×C4×C43—42no—
165C2×C4×C43C4×D411yescharacteristic
166C2×C4×C43C4×D411yescharacteristic
167C2×C4×C43#12111yescharacteristic
168C2×C4×C43#12111yescharacteristic
169C22⋊D43—88no—
170C2×Dic43—24no—
171C2×Dic43—22no—
172C2×Dic43—42no—
173C2×Dic43—42no—
174C2×Dic43—42no—
175C2×Dic43—42no—
176C2×Dic43—42no—
177C2×Dic43—42no—
178C2×Dic43—42no—
179C2×Dic43—81no—
180C8×C43—81no—
181C43⋊C8—81no—
182#9413—431nomaximal, Sylow
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—44no—
191C22×C43—82no—
192C22×C43—82no—
193C22×C43—81no—
194C22×C43—81no—
195C22×C43—81no—
196C22×C43#38611yescharacteristic
197C22×C43#42112yes—
198C22×C43#45312yes—
199C2×D43—44no—
200C2×D43—42no—
201C2×D43—42no—
202C2×D43—42no—
203C2×D43—84no—
204C2×D43—84no—
205C2×D43—82no—
206C4×C43—21no—
207C4×C43—21no—
208C4×C43—21no—
209C4×C43—21no—
210C4×C43—82no—
211C4×C43—81no—
212Dic43—44no—
213Dic43—42no—
214Dic43—82no—
215#2539—431no—
216#2312—431no—
217#1507—431no—
218#1507D4311yescharacteristic, complemented
219#1462—431no—
220#1297—431no—
221#1297—431no—
222C2×C43—22no—
223C2×C43—22no—
224C2×C43—41no—
225C2×C43—161no—
226C2×C43#188711yescharacteristic
227C2×C43#189711yescharacteristic
228C2×C43#191311yescharacteristic
229D43—82no—
230C2×#123—861no—
231C2×#121C2×D4311yescharacteristic
232C2×#120—861no—
233C22×C22⋊C4—431no—
234#407—431no—
235#407C2×D4311yescharacteristic
236#399—432no—
237#392—432no—
238#390—862no—
239#388—862no—
240#388—862no—
241#380—861no—
242#379—861no—
243C4×C22⋊C4—431no—
244C4×C22⋊C4—431no—
245C4×C22⋊C4C2×D4311yescharacteristic
246#327—22no—
247#327—862no—
248#323—862no—
249C43#941311yescharacteristic, complemented, Sylow
250C25—431no—
251C22×D4—21no—
252C22×D4—862no—
253C22×D4C4×D4311yescharacteristic
254C23×C4—431no—
255C23×C4C22×D4311yescharacteristic
256C2×M16—21no—
257C2×M16—861no—
258#123—1724no—
259#121—21no—
260#121—21no—
261#121—21no—
262#121—21no—
263#120—1724no—
264C2×C4⋊C4—862no—
265C2×C4⋊C4—862no—
266C2×C4⋊C4C4×D4311yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—432no—
270C2×C22⋊C4—432no—
271C2×C22⋊C4—861no—
272C2×C22⋊C4—861no—
273C2×C22⋊C4—861no—
274C2×C22⋊C4—861no—
275C2×C22⋊C4—861no—
276C2×C22⋊C4—862no—
277C2×C22⋊C4—862no—
278C2×C22⋊C4—862no—
279C2×C22⋊C4—862no—
280C2×C22⋊C4—861no—
281C2×C42—21no—
282C2×C42—861no—
283C2×C42—861no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286C22⋊C8—861no—
287C22⋊C8—861no—
288#95—432no—
289#95—432no—
290#95—862no—
291#95C22⋊D4312yescomplemented
292C24—21no—
293C24—432no—
294C24—861no—
295C24—861no—
296C24—3441no—
297C24—1722no—
298C24—1722no—
299C24D4×D4311yescharacteristic
300C2×D4—21no—
301C2×D4—21no—
302C2×D4—42no—
303C2×D4—42no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—81no—
307C2×D4—3442no—
308C2×D4—1724no—
309C2×D4—1724no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—81no—
313C22×C4—432no—
314C22×C4—861no—
315C22×C4—862no—
316C22×C4—861no—
317C22×C4—862no—
318C22×C4—1722no—
319C22×C4C2×C4×D4311yescharacteristic
320C22×C4#1062189811yescharacteristic
321C22×C4D4×D4311yescharacteristic
322C22×C4D4×D4311yescharacteristic
323C22×C4#1062190011yescharacteristic
324C22×C4C2×C22⋊D4311yescharacteristic
325M16—81no—
326M16—3441no—
327C2×C8—41no—
328C2×C8—1721no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—3442no—
332C4⋊C4—1724no—
333C22⋊C4—42no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—864no—
337C22⋊C4—862no—
338C22⋊C4—862no—
339C22⋊C4—862no—
340C22⋊C4—862no—
341C22⋊C4—3442no—
342C22⋊C4—3442no—
343C22⋊C4—1724no—
344C22⋊C4—1724no—
345C22⋊C4—1722no—
346C42—81no—
347C42—3441no—
348C42—3441no—
349C23—22no—
350C23—22no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—42no—
355C23—42no—
356C23—41no—
357C23—862no—
358C23—862no—
359C23—862no—
360C23—3441no—
361C23—3441no—
362C23—3448no—
363C23—1722no—
364C23—1722no—
365C23—1722no—
366C23—1722no—
367C23—1722no—
368C23—1722no—
369C23C22⋊C4×D4311yescharacteristic
370C23#1306329311yescharacteristic
371C23#1306330711yescharacteristic
372D4—81no—
373D4—81no—
374D4—82no—
375D4—82no—
376D4—3448no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—864no—
390C2×C4—862no—
391C2×C4—3441no—
392C2×C4—1722no—
393C2×C4—1722no—
394C2×C4—1722no—
395C2×C4—1722no—
396C2×C4—1722no—
397C2×C4—1722no—
398C2×C4—1722no—
399C2×C4(C22⋊D43)⋊C411yescharacteristic
400C2×C4C4×C22⋊D4311yescharacteristic
401C2×C4#1306329611yescharacteristic
402C2×C4#1306329811yescharacteristic
403C8—81no—
404C8—3441no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—44no—
413C22—82no—
414C22—82no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—3442no—
419C22—3444no—
420C22—3444no—
421C22—1724no—
422C22—1722no—
423C22—1722no—
424C22—1722no—
425C22#1458277511yescharacteristic
426C22#1458291412yes—
427C22#1458306512yes—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—21no—
432C4—82no—
433C4—81no—
434C4—3442no—
435C4—1724no—
436C4—1722no—
437C2—22no—
438C2—22no—
439C2—41no—
440C2—161no—
441C2—3442no—
442C2#1913499011yescharacteristic
443C2#1913504011yescharacteristic
444C2#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#9413
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. #19137190C2semidirect
3. #19133111C2semidirect
4. #19132921C2semidirect
5. #19132481C2semidirect
6. #19132480C2semidirect
7. C43×#1507C2semidirect
12. #14582834C4semidirect
13. #14582807C4semidirect
53. C43⋊#95D4semidirect
68. #95×C43D4semidirect
218. #1507D43semidirect
249. C43#9413semidirect
291. #95C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191395272
#191371902
#191331112
#191329212
#191324812
#191324802
C43×#15072
#941343