Finite Group Databasebeta

← #24988438

Subgroups — #24988438

Order 11008.

692 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147998C211yesmaximal, characteristic
2#19134576C211yesmaximal, characteristic
3#19133252C211yesmaximal, characteristic, complemented
4#19133250C211yesmaximal, characteristic, complemented
5#19132997C211yesmaximal, characteristic, complemented
6#19132907C211yesmaximal, characteristic
7C43×#1481C211yesmaximal, characteristic, complemented
8#14583529—21no—
9#14583529—21no—
10#14583528—21no—
11#14583528C412yes—
12#14583526—21no—
13#14583526—21no—
14#14583524—21no—
15#14583524C412yes—
16#14583456C2211yescharacteristic
17#14583453—22no—
18#14583453—22no—
19#14583452—21no—
20C2×#13063282C2211yescharacteristic
21#117×D43—21no—
22#14582952C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×(C2×D43)⋊C8—21no—
25#14582653—21no—
26#14582648—21no—
27#14582647—21no—
28#14582646—21no—
29#14582645—21no—
30#14582629—22no—
31#14582624—21no—
32#14582622—21no—
33C43×#533C2211yescharacteristic
34C43×#431C2211yescharacteristic
35C2×C4⋊C8×C43C2211yescharacteristic
36C43×Q8⋊C8—22no—
37C22×C4×D43D411yescharacteristic
38C22×C43⋊C8—21no—
39#13063325D411yescharacteristic
40#13063325D411yescharacteristic
41#13063324—21no—
42#13063324—21no—
43#13063324—22no—
44#13063324—22no—
45#13063323—22no—
46#13063323—22no—
47#13063317—21no—
48#13063316—21no—
49#13063316—21no—
50#13063315—22no—
51#13063315—22no—
52#13063315—22no—
53#13063315—22no—
54#13063305—22no—
55#13063305—22no—
56#13063304—21no—
57#13063304C2×C412yes—
58#13063303—22no—
59#13063303—22no—
60#13063303—22no—
61#13063303—22no—
62#13063302—22no—
63#13063302—22no—
64#13063301—22no—
65#13063301—22no—
66C4×Dic86—22no—
67C4×Dic86—22no—
68C4×Dic86—21no—
69C4×Dic86D412yes—
70#13063284—21no—
71#13063283—21no—
72#13063283—21no—
73#13063282—22no—
74#13063282—21no—
75#13063282—21no—
76#13063282—21no—
77#13063282—21no—
78#13063281—22no—
79C2×Dic43⋊C4C2×C411yescharacteristic
80C2×Dic43⋊C4D411yescharacteristic
81C4⋊C4×D43—21no—
82C4⋊C4×D43—21no—
83C2×(C2×D43)⋊C4C2×C411yescharacteristic
84C2×(C2×D43)⋊C4D411yescharacteristic
85C22⋊C4×D43—22no—
86C2×C4×Dic43D411yescharacteristic
87C42×D43—22no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)—21no—
91C22⋊(C43⋊C8)—21no—
92(C2×D43)⋊C8—42no—
93C4×C43⋊C8—21no—
94C22×C8×C43—21no—
95C4⋊Q8×C43D411yescharacteristic
96C4⋊Q8×C43D411yescharacteristic
97#125×C43—21no—
98C22⋊Q8×C43—21no—
99C22⋊Q8×C43C2×C412yes—
100C4×Q8×C43—21no—
101C4×Q8×C43D412yes—
102#117×C43—21no—
103C2×C42×C43C2311yescharacteristic
104C4⋊C8×C43—21no—
105C4⋊C8×C43—21no—
106C4⋊C8×C43—21no—
107C22⋊C8×C43—21no—
108C4×C8×C43—21no—
109C23×D43C22⋊C411yescharacteristic
110C2×Q8×C43—21no—
111C2×Q8×C43C22⋊C412yes—
112C22×C4×C43C22×C411yescharacteristic
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×Dic43C22⋊C411yescharacteristic
116C22×Dic43C22⋊C411yescharacteristic
117C22×Dic43C22⋊C411yescharacteristic
118C2×C4×D43—21no—
119C2×C4×D43—21no—
120C2×C4×D43—21no—
121C2×C4×D43—21no—
122C2×C4×D43—22no—
123C2×C4×D43—22no—
124C2×C4×D43SD1612yes—
125C2×C4×D43Q1612yes—
126C2×Dic86—22no—
127C2×Dic86—22no—
128C2×Dic86—21no—
129C2×Dic86C22⋊C412yes—
130C2×C8×C43—41no—
131C2×C8×C43—41no—
132C2×C8×C43—41no—
133C2×C8×C43—41no—
134C4⋊C4×C43—22no—
135C4⋊C4×C43—21no—
136C4⋊C4×C43—21no—
137C4⋊C4×C43—21no—
138C4⋊C4×C43—22no—
139C4⋊C4×C43C22⋊C412yes—
140C22⋊C4×C43—22no—
141C42×C43—22no—
142C42×C43C2×D411yescharacteristic
143C42×C43C2×D411yescharacteristic
144C42×C43C2×D411yescharacteristic
145C42×C43C2×D411yescharacteristic
146C22⋊Dic43—22no—
147(C2×D43)⋊C4—22no—
148(C2×D43)⋊C4—22no—
149(C2×D43)⋊C4—21no—
150(C2×D43)⋊C4—21no—
151(C2×D43)⋊C4—21no—
152(C2×D43)⋊C4—21no—
153C4⋊Dic43—22no—
154C4⋊Dic43—22no—
155C4⋊Dic43—21no—
156C4⋊Dic43—21no—
157C4⋊Dic43—21no—
158C4⋊Dic43C22⋊C412yes—
159Dic43⋊C4—22no—
160Dic43⋊C4—22no—
161Dic43⋊C4—22no—
162Dic43⋊C4—22no—
163Dic43⋊C4—22no—
164Dic43⋊C4—22no—
165Dic43⋊C4—21no—
166Dic43⋊C4—21no—
167Dic43⋊C4—22no—
168Dic43⋊C4—21no—
169Dic43⋊C4—21no—
170Dic43⋊C4—22no—
171C4×Dic43—22no—
172C4×Dic43—22no—
173C4×Dic43—22no—
174C4×Dic43—21no—
175C4×Dic43—21no—
176C2×C43⋊C8—41no—
177C2×C43⋊C8—41no—
178C2×C43⋊C8—41no—
179C2×C43⋊C8—41no—
180C23×C43C2×C22⋊C411yescharacteristic
181C22×D43—21no—
182C22×D43—21no—
183C22×D43—41no—
184C22×D43—41no—
185C22×D43#10312yes—
186Q8×C43—42no—
187Q8×C43—81no—
188C2×C4×C43—22no—
189C2×C4×C43—22no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43C2×C22⋊C411yescharacteristic
193C2×C4×C43C2×C22⋊C411yescharacteristic
194C2×C4×C43#12011yescharacteristic
195C2×C4×C43#12011yescharacteristic
196C2×C4×C43#12011yescharacteristic
197C2×C4×C43#12011yescharacteristic
198C2×C4×C43C2×SD1611yescharacteristic
199C2×C4×C43C2×Q1611yescharacteristic
200C2×C4×C43#13711yescharacteristic
201C2×C4×C43#13711yescharacteristic
202C2×Dic43—21no—
203C2×Dic43—21no—
204C2×Dic43—21no—
205C2×Dic43—21no—
206C2×Dic43—22no—
207C2×Dic43—22no—
208C2×Dic43—41no—
209C2×Dic43—41no—
210C2×Dic43#10312yes—
211C4×D43—22no—
212C4×D43—22no—
213C4×D43—22no—
214C4×D43—22no—
215C4×D43—82no—
216C4×D43—82no—
217Dic86—42no—
218Dic86—81no—
219Dic86—82no—
220Dic86—82no—
221C8×C43—81no—
222C8×C43—81no—
223C43⋊C8—81no—
224C43⋊C8—81no—
225#8410—431nomaximal, Sylow
226C22×C43—21no—
227C22×C43—21no—
228C22×C43#37911yescharacteristic
229C22×C43C2×#10311yescharacteristic
230C22×C43#41911yescharacteristic
231C2×D43—22no—
232C2×D43—41no—
233C2×D43—41no—
234C2×D43—42no—
235C2×D43—81no—
236C4×C43—21no—
237C4×C43—21no—
238C4×C43—21no—
239C4×C43—21no—
240C4×C43—42no—
241C4×C43—42no—
242C4×C43#44811yescharacteristic
243C4×C43#44811yescharacteristic
244C4×C43#45111yescharacteristic
245C4×C43#45111yescharacteristic
246Dic43—22no—
247Dic43—42no—
248Dic43—41no—
249Dic43—42no—
250Dic43—41no—
251#3458—431no—
252#1798—431no—
253#1542—431no—
254#1542—431no—
255#1481—431no—
256#1481D4311yescharacteristic, complemented
257#1458—431no—
258C2×C43—21no—
259C2×C43—21no—
260C2×C43#178711yescharacteristic
261C2×C43#179111yescharacteristic
262C2×C43#179411yescharacteristic
263D43—42no—
264#544—432no—
265#544—861no—
266#544—861no—
267#544—861no—
268#544—861no—
269#544—861no—
270#543—432no—
271#543—861no—
272#533—431no—
273#533—861no—
274#533—862no—
275#533—862no—
276#533C2×D4311yescharacteristic
277C2×#117—431no—
278C2×#117—861no—
279#431—431no—
280#431C2×D4311yescharacteristic
281C2×C4⋊C8—431no—
282C2×C4⋊C8C2×D4311yescharacteristic
283C2×C22⋊C8—861no—
284#336—861no—
285#333—861no—
286#333—861no—
287#332—861no—
288#332—861no—
289Q8⋊C8—22no—
290Q8⋊C8—862no—
291#324—861no—
292#323—861no—
293C43#841011yescharacteristic, complemented, Sylow
294C23×C4—431no—
295C22×C8—21no—
296C22×C8—861no—
297C4⋊Q8—431no—
298C4⋊Q8—431no—
299C4⋊Q8—862no—
300C4⋊Q8—862no—
301C4⋊Q8—861no—
302C4⋊Q8—861no—
303C4⋊Q8—862no—
304C4⋊Q8—862no—
305C4⋊Q8D17211yescharacteristic
306C4⋊Q8D17211yescharacteristic
307#125—21no—
308#125—862no—
309#125—862no—
310#125—862no—
311#125—861no—
312#125—861no—
313#125—862no—
314#125—861no—
315C22⋊Q8—21no—
316C22⋊Q8—432no—
317C22⋊Q8—862no—
318C22⋊Q8—862no—
319C22⋊Q8—862no—
320C22⋊Q8—862no—
321C22⋊Q8—862no—
322C22⋊Q8—862no—
323C22⋊Q8—862no—
324C22⋊Q8—862no—
325C22⋊Q8—862no—
326C22⋊Q8—861no—
327C22⋊Q8—862no—
328C22⋊Q8C4×D4312yes—
329C4×Q8—21no—
330C4×Q8—432no—
331C4×Q8—862no—
332C4×Q8—862no—
333C4×Q8—861no—
334C4×Q8C22⋊D4312yes—
335#117—21no—
336#117—862no—
337#117—862no—
338#117—861no—
339#117—861no—
340#117—861no—
341#117—861no—
342#117—861no—
343#117—861no—
344#117—861no—
345C2×C4⋊C4—431no—
346C2×C4⋊C4—431no—
347C2×C4⋊C4—861no—
348C2×C4⋊C4—861no—
349C2×C22⋊C4—431no—
350C2×C22⋊C4—431no—
351C2×C22⋊C4—862no—
352C2×C42—431no—
353C2×C42—862no—
354C2×C42C22×D4311yescharacteristic
355C4⋊C8—21no—
356C4⋊C8—21no—
357C4⋊C8—21no—
358C4⋊C8—861no—
359C4⋊C8—861no—
360C4⋊C8—861no—
361C22⋊C8—21no—
362C22⋊C8—861no—
363C22⋊C8—1722no—
364C4×C8—21no—
365C4×C8—861no—
366C24—431no—
367C2×Q8—21no—
368C2×Q8—432no—
369C2×Q8—862no—
370C2×Q8—862no—
371C2×Q8—861no—
372C2×Q8(C2×D43)⋊C412yes—
373C22×C4—431no—
374C22×C4—432no—
375C22×C4—432no—
376C22×C4—431no—
377C22×C4—431no—
378C22×C4—862no—
379C22×C4—862no—
380C22×C4—861no—
381C22×C4—861no—
382C22×C4—861no—
383C22×C4—861no—
384C22×C4C2×C4×D4311yescharacteristic
385C22×C4D4×D4311yescharacteristic
386C22×C4D4×D4311yescharacteristic
387C2×C8—41no—
388C2×C8—41no—
389C2×C8—41no—
390C2×C8—41no—
391C2×C8—1721no—
392C2×C8—1721no—
393C2×C8—1721no—
394C2×C8—1721no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—432no—
401C4⋊C4—862no—
402C4⋊C4—862no—
403C4⋊C4—862no—
404C4⋊C4—862no—
405C4⋊C4—862no—
406C4⋊C4—862no—
407C4⋊C4—862no—
408C4⋊C4—862no—
409C4⋊C4—861no—
410C4⋊C4—861no—
411C4⋊C4—862no—
412C4⋊C4—861no—
413C4⋊C4—861no—
414C4⋊C4—861no—
415C4⋊C4—861no—
416C4⋊C4—861no—
417C4⋊C4—862no—
418C4⋊C4(C2×D43)⋊C412yes—
419C22⋊C4—22no—
420C22⋊C4—862no—
421C22⋊C4—862no—
422C22⋊C4—862no—
423C22⋊C4—861no—
424C22⋊C4—861no—
425C22⋊C4—861no—
426C22⋊C4—861no—
427C42—22no—
428C42—862no—
429C42—862no—
430C42—861no—
431C42—862no—
432C42—861no—
433C42C2×D17211yescharacteristic
434C42D4×D4311yescharacteristic
435C42D4×D4311yescharacteristic
436C42C2×C22⋊D4311yescharacteristic
437C23—432no—
438C23—861no—
439C23—861no—
440C23—1721no—
441C23—1721no—
442C23C22⋊C4×D4311yescharacteristic
443Q8—42no—
444Q8—81no—
445Q8—3441no—
446Q8—3442no—
447Q8—3442no—
448Q8—1722no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—432no—
454C2×C4—861no—
455C2×C4—861no—
456C2×C4—862no—
457C2×C4—862no—
458C2×C4—862no—
459C2×C4—862no—
460C2×C4—862no—
461C2×C4—861no—
462C2×C4—861no—
463C2×C4—862no—
464C2×C4—3442no—
465C2×C4—3442no—
466C2×C4—1721no—
467C2×C4—1721no—
468C2×C4C22⋊C4×D4311yescharacteristic
469C2×C4C2×(C2×D43)⋊C411yescharacteristic
470C2×C4#1306329311yescharacteristic
471C2×C4#1306329311yescharacteristic
472C2×C4#1306329511yescharacteristic
473C2×C4#1306329511yescharacteristic
474C2×C4SD16×D4311yescharacteristic
475C2×C4Q16×D4311yescharacteristic
476C2×C4#1306335411yescharacteristic
477C2×C4#1306335711yescharacteristic
478C8—81no—
479C8—81no—
480C8—3441no—
481C8—3441no—
482C22—21no—
483C22—21no—
484C22—862no—
485C22—3441no—
486C22—1722no—
487C22—1721no—
488C22—1721no—
489C22#1458275411yescharacteristic
490C22#103×D4311yescharacteristic
491C22#1458290611yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—42no—
497C4—42no—
498C4—862no—
499C4—1722no—
500C4—1721no—
501C4—1722no—
502C4—1721no—
503C4#1458303611yescharacteristic
504C4#1458303911yescharacteristic
505C4#1458305311yescharacteristic
506C4#1458305611yescharacteristic
507C2—21no—
508C2—21no—
509C2—1722no—
510C2#1913452811yescharacteristic
511C2#1913454511yescharacteristic
512C2#1913455711yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1481C2
socleC22×C43#379
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1481D43
hypocenterC43#8410
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
3. #19133252C2semidirect
4. #19133250C2semidirect
5. #19132997C2semidirect
7. C43×#1481C2semidirect
256. #1481D43semidirect
293. C43#8410semidirect

Maximal subgroups

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

subgroupindex
#191479982
#191345762
#191332522
#191332502
#191329972
#191329072
C43×#14812
#841043