Finite Group Databasebeta

← #25008797

Subgroups — #25008797

Order 11008.

664 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 664 conjugacy classes of subgroups — too many to draw. Only its 63 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#19135721C211yesmaximal, characteristic
2#19133614C211yesmaximal, characteristic, complemented
3#19133546C211yesmaximal, characteristic, complemented
4#19132619C211yesmaximal, characteristic, complemented
5#19132616C211yesmaximal, characteristic, complemented
6#19132523C211yesmaximal, characteristic, complemented
7C43×#2437C211yesmaximal, characteristic, complemented
8#14583461C2211yescharacteristic
9C2×#13063294—21no—
10#14583217—21no—
11#14583038—21no—
12C2×#13063239—21no—
13#14582666C2211yescharacteristic
14#14582632—21no—
15#14582632—21no—
16#14582623C2211yescharacteristic
17#14582623C2211yescharacteristic
18C2×C22⋊Q8×C43—21no—
19C22×C22⋊C4×C43—21no—
20C43×#399C2211yescharacteristic
21C43×#396—21no—
22C43×#393C2211yescharacteristic
23C43×#385—21no—
24C43×#385—21no—
25C43×#380—21no—
26C43×#379C2211yescharacteristic
27C22×C22⋊D43—21no—
28C22×C22⋊D43—41no—
29C2×#10621884—41no—
30#13063309—41no—
31#13063299—21no—
32#13063299—21no—
33#13063295—41no—
34#13063294—42no—
35#13063294—42no—
36C2×C22⋊Dic43—21no—
37C2×C22⋊Dic43—41no—
38#13063256—41no—
39#13063249—41no—
40#13063245—41no—
41#13063239—42no—
42C22⋊(C43⋊C8)—21no—
43C22⋊(C43⋊C8)—21no—
44C25×C43D411yescharacteristic
45C22×Q8×C43D411yescharacteristic, complemented
46C23×C4×C43—21no—
47C23×C4×C43—21no—
48C22⋊Q8×C43—44no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43—21no—
51C2×C4⋊C4×C43—21no—
52C2×C4⋊C4×C43—21no—
53C2×C4⋊C4×C43D411yescharacteristic, complemented
54C2×C22⋊C4×C43—21no—
55C2×C22⋊C4×C43—21no—
56C2×C22⋊C4×C43—21no—
57C2×C22⋊C4×C43—21no—
58C2×C22⋊C4×C43—21no—
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43—44no—
61C2×C22⋊C4×C43D411yescharacteristic
62C2×C22⋊C4×C43C2311yescharacteristic
63#95×C43—21no—
64#95×C43—21no—
65#95×C43D411yescharacteristic, complemented
66#95×C43D411yescharacteristic, complemented
67C24×C43—21no—
68C24×C43—21no—
69C24×C43—42no—
70C24×C43—42no—
71C24×C43—41no—
72C24×C43—41no—
73C24×C43SD1612yescomplemented
74C24×C43C2×D411yescharacteristic
75C23×D43—21no—
76C2×Q8×C43—42no—
77C2×Q8×C43—41no—
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—21no—
81C22×C4×C43—21no—
82C22×C4×C43—21no—
83C22×C4×C43—42no—
84C22×C4×C43—42no—
85C22×C4×C43—42no—
86C22×C4×C43—42no—
87C22×C4×C43—81no—
88C22×C4×C43—81no—
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C2×C22⋊D43—41no—
92C2×C22⋊D43—41no—
93C2×C22⋊D43—41no—
94C2×C22⋊D43—44no—
95C2×C22⋊D43—41no—
96C2×C22⋊D43—41no—
97C2×C22⋊D43—41no—
98C2×C22⋊D43—82no—
99C2×C22⋊D43—82no—
100C22×Dic43—21no—
101C22×Dic43—41no—
102C2×D172—21no—
103C2×D172—21no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—42no—
106C4⋊C4×C43—42no—
107C4⋊C4×C43—42no—
108C4⋊C4×C43—81no—
109C22⋊C4×C43—24no—
110C22⋊C4×C43—41no—
111C22⋊C4×C43—41no—
112C22⋊C4×C43—42no—
113C22⋊C4×C43—42no—
114C22⋊C4×C43—42no—
115C22⋊C4×C43—42no—
116C22⋊C4×C43—42no—
117C22⋊Dic43—22no—
118C22⋊Dic43—44no—
119C22⋊Dic43—41no—
120#10621884—82no—
121(C2×D43)⋊C4—41no—
122(C2×D43)⋊C4—41no—
123C4⋊Dic43—21no—
124C4⋊Dic43—21no—
125C2×C43⋊C8—41no—
126C2×C43⋊C8—41no—
127C23×C43—22no—
128C23×C43—22no—
129C23×C43—22no—
130C23×C43—21no—
131C23×C43—21no—
132C23×C43—41no—
133C23×C43—41no—
134C23×C43—42no—
135C23×C43—41no—
136C23×C43—44no—
137C23×C43—41no—
138C23×C43—44no—
139C23×C43—41no—
140C23×C43—41no—
141C23×C43—42no—
142C23×C43—42no—
143C23×C43—81no—
144C23×C43—84no—
145C23×C43—81no—
146C23×C43—81no—
147C23×C43#12011yescharacteristic
148C23×C43C2×SD1611yescharacteristic
149C23×C43#13711yescharacteristic
150C22×D43—41no—
151C22×D43—41no—
152C22×D43—41no—
153C22×D43—81no—
154C22×D43—81no—
155Q8×C43—42no—
156Q8×C43—81no—
157C2×C4×C43—22no—
158C2×C4×C43—22no—
159C2×C4×C43—21no—
160C2×C4×C43—21no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43—84no—
177C2×C4×C43—84no—
178C22⋊D43—81no—
179C22⋊D43—81no—
180C22⋊D43—88no—
181C22⋊D43—81no—
182C22⋊D43—81no—
183C2×Dic43—42no—
184C2×Dic43—41no—
185C2×Dic43—41no—
186C2×Dic43—41no—
187C2×Dic43—81no—
188C2×Dic43—81no—
189D172—81no—
190D172—81no—
191C43⋊C8—81no—
192C43⋊C8—81no—
193#12120—431nomaximal, Sylow
194C22×C43—21no—
195C22×C43—21no—
196C22×C43—24no—
197C22×C43—21no—
198C22×C43—21no—
199C22×C43—41no—
200C22×C43—41no—
201C22×C43—42no—
202C22×C43—42no—
203C22×C43—42no—
204C22×C43—44no—
205C22×C43—42no—
206C22×C43—41no—
207C22×C43—42no—
208C22×C43—41no—
209C22×C43—42no—
210C22×C43—81no—
211C22×C43—82no—
212C22×C43—82no—
213C22×C43—82no—
214C22×C43#44811yescharacteristic
215C22×C43#45311yescharacteristic
216C22×C43B(4,𝔽2)11yescharacteristic
217C2×D43—82no—
218C2×D43—81no—
219C2×D43—81no—
220C2×D43—81no—
221C2×D43—161no—
222C4×C43—42no—
223C4×C43—41no—
224C4×C43—42no—
225C4×C43—41no—
226C4×C43—81no—
227C4×C43—81no—
228C4×C43—81no—
229Dic43—82no—
230Dic43—81no—
231#2437D4311yescharacteristic, complemented
232#2021—431no—
233#1613—431no—
234#1601—431no—
235#1352—431no—
236#1351—431no—
237#1316—431no—
238C2×C43—21no—
239C2×C43—21no—
240C2×C43—41no—
241C2×C43—41no—
242C2×C43—44no—
243C2×C43#159611yescharacteristic
244C2×C43#219611yescharacteristic
245C2×C43#219711yescharacteristic
246D43—161no—
247#534—431no—
248C2×C22⋊Q8—21no—
249C2×#120—861no—
250C22×C22⋊C4—21no—
251#481—861no—
252#448—861no—
253C2×#99—861no—
254#399C2×D4311yescharacteristic
255#396—21no—
256#393C2×D4311yescharacteristic
257#385—21no—
258#385—21no—
259#380—21no—
260#379C2×D4311yescharacteristic
261#342—431no—
262#327—861no—
263#327—861no—
264#323—431no—
265#323—431no—
266C43#1212011yescharacteristic, complemented, Sylow
267C25C22⋊D4311yescharacteristic
268C22×Q8C22⋊D4311yescharacteristic, complemented
269C22×D4—861no—
270C22×D4—1721no—
271C23×C4—21no—
272C23×C4—21no—
273C2×SD16—1721no—
274#123—1721no—
275C22⋊Q8—44no—
276#121—861no—
277#121—861no—
278#120—1721no—
279#120—1722no—
280#120—1722no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4C22⋊D4311yescharacteristic, complemented
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—21no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—44no—
293C2×C22⋊C4—861no—
294C2×C22⋊C4—1721no—
295C2×C22⋊C4C22⋊D4311yescharacteristic
296C2×C22⋊C4C22×D4311yescharacteristic
297#106—1721no—
298#103—1721no—
299#102—1721no—
300#99—1722no—
301C22⋊C8—861no—
302C22⋊C8—861no—
303#95—21no—
304#95—21no—
305#95C22⋊D4311yescharacteristic, complemented
306#95C22⋊D4311yescharacteristic, complemented
307C24—21no—
308C24—21no—
309C24—42no—
310C24—41no—
311C24—42no—
312C24—41no—
313C24—861no—
314C24#1062188412yescomplemented
315C24C2×C22⋊D4311yescharacteristic
316C2×Q8—42no—
317C2×Q8—41no—
318C2×D4—861no—
319C2×D4—861no—
320C2×D4—3442no—
321C2×D4—3442no—
322C2×D4—1721no—
323C2×D4—1721no—
324C2×D4—1721no—
325C2×D4—1724no—
326C2×D4—1721no—
327C2×D4—1721no—
328C2×D4—1721no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—81no—
339C22×C4—81no—
340C22×C4—861no—
341C22×C4—1721no—
342C22×C4C2×C22⋊D4311yescharacteristic
343C22×C4C2×C22⋊D4311yescharacteristic
344SD16—3442no—
345C2×C8—1721no—
346C2×C8—1721no—
347C4⋊C4—41no—
348C4⋊C4—42no—
349C4⋊C4—42no—
350C4⋊C4—42no—
351C4⋊C4—81no—
352C4⋊C4—861no—
353C4⋊C4—861no—
354C22⋊C4—24no—
355C22⋊C4—41no—
356C22⋊C4—42no—
357C22⋊C4—42no—
358C22⋊C4—42no—
359C22⋊C4—42no—
360C22⋊C4—42no—
361C22⋊C4—41no—
362C22⋊C4—862no—
363C22⋊C4—1721no—
364C22⋊C4—1721no—
365C22⋊C4—1724no—
366C22⋊C4—1721no—
367C23—22no—
368C23—22no—
369C23—21no—
370C23—22no—
371C23—21no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23—42no—
376C23—44no—
377C23—41no—
378C23—44no—
379C23—41no—
380C23—41no—
381C23—42no—
382C23—42no—
383C23—81no—
384C23—84no—
385C23—81no—
386C23—81no—
387C23—3441no—
388C23—3441no—
389C23—1721no—
390C23—1721no—
391C23—1721no—
392C23#1306329411yescharacteristic
393C23C2×#1062188411yescharacteristic
394C23#1306335611yescharacteristic
395Q8—42no—
396Q8—81no—
397D4—3441no—
398D4—3441no—
399D4—3441no—
400D4—3441no—
401D4—3448no—
402D4—3441no—
403D4—3441no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—84no—
424C2×C4—84no—
425C2×C4—3441no—
426C2×C4—3441no—
427C2×C4—1722no—
428C2×C4—1721no—
429C2×C4—1721no—
430C2×C4—1721no—
431C8—3441no—
432C8—3441no—
433C22—21no—
434C22—21no—
435C22—24no—
436C22—21no—
437C22—21no—
438C22—41no—
439C22—41no—
440C22—42no—
441C22—42no—
442C22—42no—
443C22—44no—
444C22—42no—
445C22—41no—
446C22—41no—
447C22—42no—
448C22—42no—
449C22—81no—
450C22—82no—
451C22—82no—
452C22—82no—
453C22—3442no—
454C22—3441no—
455C22—3441no—
456C22—3441no—
457C22—6881no—
458C22#1458303811yescharacteristic
459C22#1458306711yescharacteristic
460C22#1458308611yescharacteristic
461C4—42no—
462C4—41no—
463C4—42no—
464C4—41no—
465C4—81no—
466C4—81no—
467C4—81no—
468C4—3442no—
469C4—3441no—
470C2—21no—
471C2—21no—
472C2—41no—
473C2—44no—
474C2—41no—
475C2—6881no—
476C2#1913351811yescharacteristic
477C2#1913657911yescharacteristic
478C2#1913658511yescharacteristic
subgroupG/H
centerC22#14583086
commutator, cosocleC2×C22⋊C4×C43C23
FrattiniC2×C22⋊C4C22×D43
FittingC43×#2437C2
socleC22×C43B(4,𝔽2)
prime radical#19135721C2
hypercenter#2437D43
hypocenterC43#12120
LCSG ▷ C2×C22⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2437

Complements

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

NH ≅ G/Ntype
2. #19133614C2semidirect
3. #19133546C2semidirect
4. #19132619C2semidirect
5. #19132616C2semidirect
6. #19132523C2semidirect
7. C43×#2437C2semidirect
45. C22×Q8×C43D4semidirect
53. C2×C4⋊C4×C43D4semidirect
65. #95×C43D4semidirect
66. #95×C43D4semidirect
73. C24×C43SD16semidirect
231. #2437D43semidirect
266. C43#12120semidirect
268. C22×Q8C22⋊D43semidirect
285. C2×C4⋊C4C22⋊D43semidirect
305. #95C22⋊D43semidirect
306. #95C22⋊D43semidirect
314. C24#10621884semidirect

Maximal subgroups

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

subgroupindex
#191357212
#191336142
#191335462
#191326192
#191326162
#191325232
C43×#24372
#1212043