Finite Group Databasebeta

← #24989070

Subgroups — #24989070

Order 11008.

652 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 652 conjugacy classes of subgroups — too many to draw. Only its 111 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#19149205C211yesmaximal, characteristic
2#19135552C211yesmaximal, characteristic, complemented
3#19133295C211yesmaximal, characteristic, complemented
4#19133196C211yesmaximal, characteristic, complemented
5#19133118C211yesmaximal, characteristic
6#19133009C211yesmaximal, characteristic
7C43×#1986C211yesmaximal, characteristic, complemented
8C43⋊#564C412yescomplemented
9#14583653C412yescomplemented
10#14583625—21no—
11#14583607—21no—
12#14583591—21no—
13#14583590—21no—
14#14583582—22no—
15#14583528—21no—
16#14583526—21no—
17#14583510—21no—
18#14583507—22no—
19#14583498—21no—
20#14583433C2211yescharacteristic
21C2×#13063317C2211yescharacteristic
22#14582956C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24#14582661—21no—
25#14582661—21no—
26#14582645—21no—
27#14582645—21no—
28#14582640—22no—
29#14582635—21no—
30#14582632—21no—
31#14582631—21no—
32#14582628—21no—
33C43×#533C2211yescharacteristic
34C4×M16×C43C2211yescharacteristic
35C4×C4⋊C4×C43C2211yescharacteristic
36C43×#339—22no—
37C22×C43⋊C8—21no—
38#13063324—21no—
39#13063324—22no—
40#13063323—22no—
41#13063320—22no—
42#13063320—22no—
43#13063320—22no—
44#13063319—22no—
45#13063319—21no—
46#13063317—22no—
47#13063317—21no—
48#13063317—21no—
49#13063317C2×C412yes—
50#13063317C2×C411yescharacteristic
51#13063317D412yes—
52#13063316—21no—
53#13063316—22no—
54#13063316—22no—
55#13063315—22no—
56#13063315—22no—
57#13063315—22no—
58#13063315—22no—
59#13063315—22no—
60#13063313C2×C411yescharacteristic
61#13063310—22no—
62#13063309—22no—
63#13063308—21no—
64#13063305—22no—
65#13063304D411yescharacteristic
66#13063303—22no—
67#13063302—22no—
68#13063301—21no—
69#13063301—21no—
70#13063301—22no—
71#13063299D411yescharacteristic
72Q8×Dic43—21no—
73Q8×Dic43—21no—
74C4×Dic86—22no—
75C4×Dic86D411yescharacteristic
76C4×D172D411yescharacteristic
77C4×C22⋊D43—21no—
78(C22⋊D43)⋊C4—22no—
79#13063283—21no—
80#13063282—22no—
81#13063282—21no—
82#13063281—22no—
83C2×C4⋊Dic43D411yescharacteristic
84C2×C4⋊Dic43D411yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C4⋊C4×D43—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)—21no—
91C22⋊(C43⋊C8)—21no—
92#13063236—21no—
93C2×M16×C43—21no—
94C4⋊Q8×C43D411yescharacteristic
95C4⋊Q8×C43D411yescharacteristic
96#125×C43C2×C412yes—
97C22⋊Q8×C43—21no—
98C22⋊Q8×C43—21no—
99C4×Q8×C43—21no—
100C4×Q8×C43—21no—
101#117×C43D412yes—
102C2×C4⋊C4×C43—21no—
103C2×C42×C43—21no—
104C2×C42×C43C2311yescharacteristic
105#97×C43—21no—
106C4×C8×C43—21no—
107#95×C43—21no—
108C2×Q8×C43—21no—
109C2×Q8×C43—21no—
110C22×C4×C43—41no—
111C22×C4×C43C2×D411yescharacteristic
112C22×C4×C43C2×D411yescharacteristic
113C22×C4×C43C2×D411yescharacteristic
114C2×C22⋊D43—21no—
115C22×Dic43—21no—
116C22×Dic43—21no—
117C2×D172C22⋊C411yescharacteristic
118C2×C4×D43—21no—
119C2×C4×D43—22no—
120C2×Dic86—22no—
121C2×Dic86C22⋊C411yescharacteristic
122M16×C43—22no—
123M16×C43—41no—
124C2×C8×C43—41no—
125C4⋊C4×C43—22no—
126C4⋊C4×C43—22no—
127C4⋊C4×C43—21no—
128C4⋊C4×C43—21no—
129C4⋊C4×C43—22no—
130C4⋊C4×C43—41no—
131C4⋊C4×C43C22⋊C412yes—
132C4⋊C4×C43C22⋊C412yes—
133C22⋊C4×C43—22no—
134C42×C43—22no—
135C42×C43—42no—
136C42×C43C22×C411yescharacteristic
137C42×C43C2×D411yescharacteristic
138C42×C43C2×D411yescharacteristic
139C42×C43C2×D411yescharacteristic
140C22⋊Dic43—21no—
141(C2×D43)⋊C4—22no—
142(C2×D43)⋊C4—22no—
143(C2×D43)⋊C4—22no—
144(C2×D43)⋊C4—21no—
145(C2×D43)⋊C4—21no—
146(C2×D43)⋊C4—21no—
147(C2×D43)⋊C4—21no—
148C4⋊Dic43—22no—
149C4⋊Dic43—22no—
150C4⋊Dic43—22no—
151C4⋊Dic43—21no—
152C4⋊Dic43—21no—
153C4⋊Dic43C22⋊C412yes—
154C4⋊Dic43C22⋊C412yes—
155C4⋊Dic43C22⋊C411yescharacteristic
156C4⋊Dic43C22⋊C411yescharacteristic
157Dic43⋊C4—22no—
158Dic43⋊C4—22no—
159Dic43⋊C4—22no—
160Dic43⋊C4—22no—
161Dic43⋊C4—22no—
162Dic43⋊C4—22no—
163Dic43⋊C4—22no—
164Dic43⋊C4—21no—
165Dic43⋊C4—21no—
166Dic43⋊C4—22no—
167Dic43⋊C4—22no—
168Dic43⋊C4—21no—
169Dic43⋊C4—21no—
170C4×Dic43—22no—
171C4×Dic43—22no—
172C4×Dic43—22no—
173C4×Dic43—21no—
174C2×C43⋊C8—42no—
175C2×C43⋊C8—41no—
176C2×C43⋊C8—41no—
177C23×C43#12011yescharacteristic
178C22×D43—21no—
179Q8×C43—41no—
180Q8×C43—41no—
181Q8×C43—81no—
182C2×C4×C43—21no—
183C2×C4×C43—21no—
184C2×C4×C43—21no—
185C2×C4×C43—21no—
186C2×C4×C43—22no—
187C2×C4×C43—22no—
188C2×C4×C43—41no—
189C2×C4×C43—42no—
190C2×C4×C43—81no—
191C2×C4×C43—81no—
192C2×C4×C43C2×C22⋊C411yescharacteristic
193C2×C4×C43C2×C22⋊C411yescharacteristic
194C2×C4×C43C2×C22⋊C411yescharacteristic
195C2×C4×C43#12011yescharacteristic
196C2×C4×C43#12011yescharacteristic
197C2×C4×C43#12011yescharacteristic
198C22⋊D43—41no—
199C22⋊D43—41no—
200C2×Dic43—21no—
201C2×Dic43—21no—
202C2×Dic43—21no—
203C2×Dic43—22no—
204C2×Dic43—22no—
205C2×Dic43—41no—
206C2×Dic43—41no—
207C2×Dic43—81no—
208D172—41no—
209C4×D43—41no—
210C4×D43—41no—
211C4×D43—82no—
212Dic86—41no—
213Dic86—82no—
214C8×C43—42no—
215C43⋊C8—81no—
216C43⋊C8—81no—
217#8512—431nomaximal, Sylow
218C22×C43—21no—
219C22×C43—21no—
220C22×C43#37911yescharacteristic
221C22×C43#45411yescharacteristic
222C22×C43#45611yescharacteristic
223C2×D43—41no—
224C2×D43—41no—
225C2×D43—41no—
226C4×C43—21no—
227C4×C43—21no—
228C4×C43—21no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—42no—
232C4×C43—42no—
233C4×C43—82no—
234C4×C43#45411yescharacteristic
235C4×C43#45611yescharacteristic
236Dic43—41no—
237Dic43—42no—
238Dic43—41no—
239Dic43—41no—
240Dic43—42no—
241#3563—431no—
242#1989—431no—
243#1986D4311yescharacteristic, complemented
244#1552—431no—
245#1528—431no—
246#1509—431no—
247#1483—431no—
248C2×C43—21no—
249C2×C43—21no—
250C2×C43#179311yescharacteristic
251C2×C43#179311yescharacteristic
252C2×C43#179411yescharacteristic
253D43—81no—
254#564—432no—
255#563—432no—
256#557—861no—
257#554—861no—
258#552—861no—
259#552—861no—
260#552—862no—
261#544—861no—
262#544—861no—
263#541—862no—
264#541—861no—
265#539—861no—
266#533C2×D4311yescharacteristic
267#529—431no—
268C2×#125—431no—
269#432—431no—
270C2×C4⋊C8—431no—
271C4×M16C2×D4311yescharacteristic
272C4×C4⋊C4C2×D4311yescharacteristic
273#340—861no—
274#340—861no—
275#339—22no—
276#332—861no—
277#332—861no—
278#330—862no—
279#328—861no—
280#327—861no—
281Q8⋊C8—861no—
282D4⋊C8—861no—
283C43#851211yescharacteristic, complemented, Sylow
284C2×M16—21no—
285C22×C8—861no—
286C4⋊Q8—862no—
287C4⋊Q8—861no—
288C4⋊Q8—862no—
289C4⋊Q8D17211yescharacteristic
290C4⋊Q8D17211yescharacteristic
291#126—862no—
292#126—862no—
293#126—862no—
294#126—862no—
295#126—861no—
296#125—432no—
297#125—431no—
298#125—432no—
299#125—862no—
300#125—862no—
301#125—862no—
302#125—862no—
303#125—862no—
304#125—862no—
305#125—861no—
306#125—862no—
307#125—862no—
308#125—861no—
309#125—861no—
310#125C4×D4312yes—
311#124—431no—
312#123—862no—
313#123—862no—
314#123—861no—
315C22⋊Q8—21no—
316C22⋊Q8—21no—
317C22⋊Q8—431no—
318C22⋊Q8—862no—
319C22⋊Q8—862no—
320C22⋊Q8—862no—
321C22⋊Q8—861no—
322C22⋊Q8—861no—
323C22⋊Q8—862no—
324#121—431no—
325C4×Q8—21no—
326C4×Q8—21no—
327C4×Q8—431no—
328C4×Q8—862no—
329C4×Q8—861no—
330C4×Q8—861no—
331C4×D4—431no—
332C4×D4—862no—
333C4×D4—861no—
334#117—862no—
335#117—862no—
336#117—861no—
337#117—861no—
338#117C22⋊D4312yes—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—431no—
341C2×C4⋊C4—431no—
342C2×C4⋊C4—861no—
343C2×C4⋊C4—861no—
344C2×C4⋊C4—861no—
345C2×C42—21no—
346C2×C42C22×D4311yescharacteristic
347C4⋊C8—861no—
348C4⋊C8—861no—
349C4⋊C8—861no—
350C22⋊C8—861no—
351#97—21no—
352#97—861no—
353C4×C8—21no—
354#95—21no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—431no—
358C2×Q8—862no—
359C2×D4—431no—
360C2×D4—861no—
361C22×C4—41no—
362C22×C4—862no—
363C22×C4—861no—
364C22×C4—861no—
365C22×C4—861no—
366C22×C4D4×D4311yescharacteristic
367C22×C4D4×D4311yescharacteristic
368C22×C4C2×C22⋊D4311yescharacteristic
369M16—22no—
370M16—41no—
371C2×C8—41no—
372C2×C8—1722no—
373C2×C8—1721no—
374C2×C8—1721no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—41no—
381C4⋊C4—432no—
382C4⋊C4—432no—
383C4⋊C4—431no—
384C4⋊C4—431no—
385C4⋊C4—862no—
386C4⋊C4—862no—
387C4⋊C4—862no—
388C4⋊C4—862no—
389C4⋊C4—862no—
390C4⋊C4—862no—
391C4⋊C4—862no—
392C4⋊C4—862no—
393C4⋊C4—862no—
394C4⋊C4—861no—
395C4⋊C4—862no—
396C4⋊C4—861no—
397C4⋊C4—862no—
398C4⋊C4—861no—
399C4⋊C4—861no—
400C4⋊C4—861no—
401C4⋊C4—862no—
402C4⋊C4—861no—
403C4⋊C4(C2×D43)⋊C412yes—
404C4⋊C4(C2×D43)⋊C412yes—
405C22⋊C4—22no—
406C22⋊C4—862no—
407C22⋊C4—862no—
408C22⋊C4—862no—
409C22⋊C4—861no—
410C22⋊C4—861no—
411C22⋊C4—861no—
412C22⋊C4—861no—
413C22⋊C4—861no—
414C42—22no—
415C42—42no—
416C42—862no—
417C42—862no—
418C42—862no—
419C42—861no—
420C42C2×C4×D4311yescharacteristic
421C42C2×D17211yescharacteristic
422C42D4×D4311yescharacteristic
423C42D4×D4311yescharacteristic
424C23—861no—
425C23#1306329311yescharacteristic
426Q8—41no—
427Q8—41no—
428Q8—81no—
429Q8—3442no—
430Q8—1721no—
431D4—1721no—
432D4—1721no—
433D4—1721no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4—861no—
445C2×C4—861no—
446C2×C4—862no—
447C2×C4—861no—
448C2×C4—862no—
449C2×C4—3442no—
450C2×C4—3441no—
451C2×C4—1721no—
452C2×C4—1721no—
453C2×C4—1721no—
454C2×C4—1721no—
455C2×C4C22⋊C4×D4311yescharacteristic
456C2×C4C22⋊C4×D4311yescharacteristic
457C2×C4C2×(C2×D43)⋊C411yescharacteristic
458C2×C4#1306329311yescharacteristic
459C2×C4#1306329511yescharacteristic
460C2×C4#1306329511yescharacteristic
461C8—42no—
462C8—3441no—
463C8—3441no—
464C22—21no—
465C22—21no—
466C22—1721no—
467C22—1721no—
468C22—1721no—
469C22#1458275411yescharacteristic
470C22#1458307111yescharacteristic
471C22#1458308111yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—42no—
478C4—42no—
479C4—82no—
480C4—1722no—
481C4—1721no—
482C4—1721no—
483C4—1722no—
484C4—1721no—
485C4#1458307311yescharacteristic
486C4#1458308311yescharacteristic
487C2—21no—
488C2—21no—
489C2—3441no—
490C2#1913455311yescharacteristic
491C2#1913455511yescharacteristic
492C2#1913455711yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1986C2
socleC22×C43#379
prime radical#13063299D4
cosocleC2×C42×C43C23
hypercenter#1986D43
hypocenterC43#8512
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
2. #19135552C2semidirect
3. #19133295C2semidirect
4. #19133196C2semidirect
7. C43×#1986C2semidirect
8. C43⋊#564C4semidirect
9. #14583653C4semidirect
243. #1986D43semidirect
283. C43#8512semidirect

Maximal subgroups

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

subgroupindex
#191492052
#191355522
#191332952
#191331962
#191331182
#191330092
C43×#19862
#851243