Finite Group Databasebeta

← #24989013

Subgroups — #24989013

Order 11008.

616 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 103 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#19149083C211yesmaximal, characteristic
2#19133305C211yesmaximal, characteristic, complemented
3#19133224C211yesmaximal, characteristic
4#19133170C211yesmaximal, characteristic
5#19133145C211yesmaximal, characteristic, complemented
6#19133067C211yesmaximal, characteristic, complemented
7C43×#1515C211yesmaximal, characteristic, complemented
8#14583650—22no—
9Q8×Dic86C411yescharacteristic, complemented
10#14583628C411yescharacteristic, complemented
11#14583627—21no—
12#14583622—21no—
13#14583622C411yescharacteristic, complemented
14#14583620—21no—
15#14583609C411yescharacteristic, complemented
16#14583583—21no—
17#14583526—21no—
18#14583520—21no—
19#14583511—21no—
20#14583510—21no—
21#14583508—22no—
22#14583456C2211yescharacteristic
23#14583433C2211yescharacteristic
24#14582956C2211yescharacteristic
25#14582952C2211yescharacteristic
26#14582648—21no—
27#14582645—21no—
28#14582640—21no—
29#14582638—21no—
30#14582635—22no—
31#14582635—21no—
32#14582632—21no—
33#14582629—22no—
34C43×#533C2211yescharacteristic
35C43×#432C2211yescharacteristic
36C43×#383C2211yescharacteristic
37C43×#328—21no—
38C43×#328—21no—
39#13063325—21no—
40#13063325—21no—
41#13063325C2×C411yescharacteristic
42#13063325C2×C411yescharacteristic
43#13063324—22no—
44#13063324—21no—
45#13063323—22no—
46#13063320—22no—
47#13063320—22no—
48#13063320—22no—
49#13063320—22no—
50#13063319—21no—
51#13063318—22no—
52#13063318—22no—
53#13063317—21no—
54#13063317—21no—
55#13063317D411yescharacteristic
56#13063316—21no—
57#13063316—22no—
58#13063315—22no—
59#13063315—22no—
60#13063315—22no—
61#13063315—22no—
62#13063313—21no—
63#13063313D411yescharacteristic
64#13063311—22no—
65#13063308—21no—
66#13063307—22no—
67#13063304—21no—
68#13063304D412yes—
69#13063304D411yescharacteristic
70#13063303—22no—
71#13063303—22no—
72#13063301—22no—
73#13063301—21no—
74#13063301—21no—
75#13063299D411yescharacteristic
76Q8×Dic43—21no—
77Q8×Dic43—21no—
78C4×Dic86—21no—
79C4×Dic86—21no—
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×Dic86C2×C411yescharacteristic
83C4×Dic86D412yes—
84#13063290—22no—
85C4×D172—21no—
86C4×D172C2×C411yescharacteristic
87C4×C22⋊D43—21no—
88#13063284—21no—
89#13063283—22no—
90#13063283—21no—
91#13063282—21no—
92C4⋊C4×D43—21no—
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)—21no—
95C22⋊(C43⋊C8)—21no—
96C22⋊(C43⋊C8)—21no—
97#13063236—21no—
98C4×C43⋊C8—21no—
99C4⋊Q8×C43D411yescharacteristic
100C4⋊Q8×C43D411yescharacteristic
101#125×C43—21no—
102C22⋊Q8×C43—21no—
103C22⋊Q8×C43D411yescharacteristic
104C22⋊Q8×C43D411yescharacteristic
105C4×Q8×C43—21no—
106C4×Q8×C43C2×C411yescharacteristic
107C4×Q8×C43C2×C411yescharacteristic
108#117×C43—21no—
109C2×C42×C43C2311yescharacteristic
110C4⋊C8×C43—21no—
111C22⋊C8×C43—21no—
112#97×C43—21no—
113#95×C43—21no—
114#95×C43—21no—
115#95×C43—21no—
116C2×Q8×C43—21no—
117C2×Q8×C43C22⋊C411yescharacteristic
118C2×Q8×C43C22⋊C411yescharacteristic
119C22×C4×C43—41no—
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C2×C22⋊D43—21no—
124C2×D172C22⋊C411yescharacteristic
125C2×C4×D43—21no—
126C2×C4×D43—22no—
127C2×Dic86—21no—
128C2×Dic86—22no—
129C2×Dic86C22⋊C411yescharacteristic
130C2×Dic86C22⋊C412yes—
131C2×C8×C43—41no—
132C4⋊C4×C43—21no—
133C4⋊C4×C43—21no—
134C4⋊C4×C43—21no—
135C4⋊C4×C43—21no—
136C4⋊C4×C43—21no—
137C4⋊C4×C43—21no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43C22⋊C411yescharacteristic
140C4⋊C4×C43C22⋊C411yescharacteristic
141C22⋊C4×C43—21no—
142C22⋊C4×C43—21no—
143C42×C43—21no—
144C42×C43—21no—
145C42×C43C22×C411yescharacteristic
146C42×C43C2×D411yescharacteristic
147C42×C43C2×D411yescharacteristic
148C42×C43C2×D411yescharacteristic
149C22⋊Dic43—22no—
150C22⋊Dic43—21no—
151(C2×D43)⋊C4—22no—
152(C2×D43)⋊C4—22no—
153(C2×D43)⋊C4—22no—
154(C2×D43)⋊C4—21no—
155(C2×D43)⋊C4—21no—
156(C2×D43)⋊C4—21no—
157(C2×D43)⋊C4—21no—
158C4⋊Dic43—22no—
159C4⋊Dic43—22no—
160C4⋊Dic43—22no—
161C4⋊Dic43—21no—
162C4⋊Dic43—21no—
163C4⋊Dic43—21no—
164C4⋊Dic43C22⋊C411yescharacteristic
165C4⋊Dic43C22⋊C411yescharacteristic
166C4⋊Dic43C22⋊C412yes—
167Dic43⋊C4—22no—
168Dic43⋊C4—22no—
169Dic43⋊C4—22no—
170Dic43⋊C4—22no—
171Dic43⋊C4—22no—
172Dic43⋊C4—21no—
173Dic43⋊C4—21no—
174Dic43⋊C4—21no—
175Dic43⋊C4—21no—
176Dic43⋊C4—22no—
177Dic43⋊C4—22no—
178C4×Dic43—22no—
179C4×Dic43—22no—
180C4×Dic43—22no—
181C4×Dic43—21no—
182C4×Dic43—22no—
183C2×C43⋊C8—41no—
184C2×C43⋊C8—41no—
185C23×C43#12011yescharacteristic
186C22×D43—21no—
187Q8×C43—41no—
188Q8×C43—41no—
189Q8×C43—81no—
190C2×C4×C43—21no—
191C2×C4×C43—21no—
192C2×C4×C43—21no—
193C2×C4×C43—21no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—81no—
198C2×C4×C43—81no—
199C2×C4×C43—81no—
200C2×C4×C43C2×C22⋊C411yescharacteristic
201C2×C4×C43C2×C22⋊C411yescharacteristic
202C2×C4×C43C2×C22⋊C411yescharacteristic
203C2×C4×C43#12011yescharacteristic
204C2×C4×C43#12011yescharacteristic
205C2×C4×C43#12011yescharacteristic
206C22⋊D43—81no—
207C2×Dic43—21no—
208C2×Dic43—21no—
209C2×Dic43—22no—
210C2×Dic43—21no—
211C2×Dic43—22no—
212D172—41no—
213C4×D43—42no—
214C4×D43—82no—
215Dic86—42no—
216Dic86—42no—
217Dic86—41no—
218Dic86—82no—
219C8×C43—81no—
220C43⋊C8—81no—
221C43⋊C8—81no—
222#8501—431nomaximal, Sylow
223C22×C43—21no—
224C22×C43—21no—
225C22×C43—21no—
226C22×C43#37911yescharacteristic
227C2×D43—41no—
228C2×D43—41no—
229C2×D43—41no—
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—21no—
235C4×C43—21no—
236C4×C43—41no—
237C4×C43—41no—
238C4×C43—41no—
239C4×C43—41no—
240C4×C43—161no—
241Dic43—42no—
242Dic43—41no—
243Dic43—42no—
244Dic43—41no—
245Dic43—41no—
246#3555—431no—
247#1554—431no—
248#1535—431no—
249#1521—431no—
250#1515—431no—
251#1515D4311yescharacteristic, complemented
252#1497—431no—
253C2×C43—41no—
254C2×C43#179411yescharacteristic
255C2×C43#179611yescharacteristic
256C2×C43#179611yescharacteristic
257D43—81no—
258#563—862no—
259Q82—431no—
260#557—431no—
261#557—861no—
262#556—431no—
263#556—861no—
264#556—861no—
265#554—431no—
266#552—861no—
267#544—861no—
268#542—861no—
269#541—861no—
270#541—862no—
271#541—861no—
272#533—431no—
273#533C2×D4311yescharacteristic
274#529—431no—
275#432—431no—
276#432C2×D4311yescharacteristic
277#431—431no—
278#383C2×D4311yescharacteristic
279#333—861no—
280#332—861no—
281#330—861no—
282#329—861no—
283#328—21no—
284#328—21no—
285#328—862no—
286#328—861no—
287#327—861no—
288Q8⋊C8—862no—
289C43#850111yescharacteristic, complemented, Sylow
290C4⋊Q8—431no—
291C4⋊Q8—431no—
292C4⋊Q8—861no—
293C4⋊Q8—861no—
294C4⋊Q8—862no—
295C4⋊Q8—862no—
296C4⋊Q8—861no—
297C4⋊Q8D17211yescharacteristic
298C4⋊Q8D17211yescharacteristic
299#126—862no—
300#126—862no—
301#126—862no—
302#126—862no—
303#126—862no—
304#126—862no—
305#126—861no—
306#125—21no—
307#125—431no—
308#125—861no—
309#125—862no—
310#125—862no—
311#125—862no—
312#125—862no—
313#125—862no—
314#125—861no—
315#125—861no—
316#124—431no—
317#124—861no—
318#124—862no—
319#123—862no—
320#123—861no—
321C22⋊Q8—21no—
322C22⋊Q8—431no—
323C22⋊Q8—432no—
324C22⋊Q8—862no—
325C22⋊Q8—862no—
326C22⋊Q8—862no—
327C22⋊Q8—861no—
328C22⋊Q8—861no—
329C22⋊Q8—861no—
330C22⋊Q8C22⋊D4311yescharacteristic
331C22⋊Q8C22⋊D4311yescharacteristic
332#121—431no—
333C4×Q8—21no—
334C4×Q8—431no—
335C4×Q8—432no—
336C4×Q8—861no—
337C4×Q8—861no—
338C4×Q8—861no—
339C4×Q8—862no—
340C4×Q8—861no—
341C4×Q8—861no—
342C4×Q8—861no—
343C4×Q8C4×D4311yescharacteristic
344C4×Q8C4×D4311yescharacteristic
345C4×D4—431no—
346C4×D4—861no—
347C4×D4—861no—
348#117—21no—
349#117—862no—
350#117—861no—
351#117—861no—
352#117—861no—
353C2×C4⋊C4—861no—
354C2×C42C22×D4311yescharacteristic
355C4⋊C8—21no—
356C4⋊C8—861no—
357C4⋊C8—861no—
358C22⋊C8—21no—
359C22⋊C8—861no—
360C22⋊C8—861no—
361#97—21no—
362#97—861no—
363C4×C8—861no—
364#95—21no—
365#95—21no—
366#95—21no—
367C2×Q8—21no—
368C2×Q8—431no—
369C2×Q8—432no—
370C2×Q8—862no—
371C2×Q8—861no—
372C2×Q8(C2×D43)⋊C411yescharacteristic
373C2×Q8(C2×D43)⋊C411yescharacteristic
374C2×D4—431no—
375C2×D4—861no—
376C22×C4—41no—
377C22×C4—862no—
378C22×C4—861no—
379C22×C4D4×D4311yescharacteristic
380C22×C4D4×D4311yescharacteristic
381C22×C4C2×C22⋊D4311yescharacteristic
382C2×C8—41no—
383C2×C8—1721no—
384C2×C8—1721no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—431no—
393C4⋊C4—431no—
394C4⋊C4—432no—
395C4⋊C4—862no—
396C4⋊C4—862no—
397C4⋊C4—862no—
398C4⋊C4—862no—
399C4⋊C4—862no—
400C4⋊C4—862no—
401C4⋊C4—862no—
402C4⋊C4—862no—
403C4⋊C4—861no—
404C4⋊C4—861no—
405C4⋊C4—861no—
406C4⋊C4—861no—
407C4⋊C4—861no—
408C4⋊C4—861no—
409C4⋊C4—861no—
410C4⋊C4—862no—
411C4⋊C4—862no—
412C4⋊C4(C2×D43)⋊C411yescharacteristic
413C4⋊C4(C2×D43)⋊C411yescharacteristic
414C22⋊C4—21no—
415C22⋊C4—21no—
416C22⋊C4—862no—
417C22⋊C4—862no—
418C22⋊C4—862no—
419C22⋊C4—862no—
420C22⋊C4—861no—
421C22⋊C4—861no—
422C22⋊C4—861no—
423C22⋊C4—861no—
424C22⋊C4—861no—
425C42—21no—
426C42—21no—
427C42—862no—
428C42—862no—
429C42—862no—
430C42—861no—
431C42—862no—
432C42C2×C4×D4311yescharacteristic
433C42C2×D17211yescharacteristic
434C42D4×D4311yescharacteristic
435C42D4×D4311yescharacteristic
436C23—861no—
437C23#1306329311yescharacteristic
438Q8—41no—
439Q8—41no—
440Q8—81no—
441Q8—3442no—
442Q8—1722no—
443Q8—1721no—
444Q8—1722no—
445D4—3441no—
446D4—1721no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—81no—
455C2×C4—81no—
456C2×C4—81no—
457C2×C4—862no—
458C2×C4—861no—
459C2×C4—861no—
460C2×C4—861no—
461C2×C4—862no—
462C2×C4—3442no—
463C2×C4—1722no—
464C2×C4C22⋊C4×D4311yescharacteristic
465C2×C4C22⋊C4×D4311yescharacteristic
466C2×C4C2×(C2×D43)⋊C411yescharacteristic
467C2×C4#1306329311yescharacteristic
468C2×C4#1306329511yescharacteristic
469C2×C4#1306329511yescharacteristic
470C8—81no—
471C8—3441no—
472C8—3441no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—1721no—
477C22—1721no—
478C22—1721no—
479C22#1458275411yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—41no—
487C4—41no—
488C4—41no—
489C4—41no—
490C4—161no—
491C4—1722no—
492C4—1721no—
493C4—1722no—
494C4—1721no—
495C4—1721no—
496C2—41no—
497C2—3441no—
498C2#1913455711yescharacteristic
499C2#1913456711yescharacteristic
500C2#1913456811yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1515C2
socleC22×C43#379
prime radical#13063299D4
cosocleC2×C42×C43C23
hypercenter#1515D43
hypocenterC43#8501
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1515

Complements

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

NH ≅ G/Ntype
2. #19133305C2semidirect
5. #19133145C2semidirect
6. #19133067C2semidirect
7. C43×#1515C2semidirect
9. Q8×Dic86C4semidirect
10. #14583628C4semidirect
13. #14583622C4semidirect
15. #14583609C4semidirect
251. #1515D43semidirect
289. C43#8501semidirect

Maximal subgroups

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

subgroupindex
#191490832
#191333052
#191332242
#191331702
#191331452
#191330672
C43×#15152
#850143