Finite Group Databasebeta

← #24988017

Subgroups — #24988017

Order 11008.

930 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583375C211yesmaximal, characteristic
2#19132991C211yesmaximal, characteristic, complemented
3#19132990C211yesmaximal, characteristic, complemented
4#19132989C211yesmaximal, characteristic, complemented
5#19132907C211yesmaximal, characteristic
6#19132907C211yesmaximal, characteristic
7C43×#1479C211yesmaximal, characteristic, complemented
8C22×Q8×D43C411yescharacteristic
9#14583375—22no—
10#14583375—22no—
11#14583375—22no—
12#14583375—22no—
13C2×Q8×Dic43C411yescharacteristic
14C2×C4×Dic86—21no—
15C2×C4×Dic86C2211yescharacteristic
16C2×#13063290—21no—
17C2×#13063290C411yescharacteristic
18C2×#13063283—21no—
19C2×#13063283C411yescharacteristic
20C2×#13063282—21no—
21C2×#13063282C2211yescharacteristic
22#14582952C2211yescharacteristic
23#14582952C2211yescharacteristic
24#14582631—22no—
25Q8⋊(C43⋊C8)—22no—
26#14582629—22no—
27#14582624—21no—
28#14582624—21no—
29#14582622—21no—
30#14582622—21no—
31C2×C4×Q8×C43C2211yescharacteristic
32C43×#431C2211yescharacteristic
33C43×#431C2211yescharacteristic
34C43×Q8⋊C8—22no—
35C22×Dic86—21no—
36C22×Dic86C2×C411yescharacteristic
37C2×Q8×D43—22no—
38C2×Q8×D43—22no—
39C2×Q8×D43—22no—
40C2×Q8×D43—22no—
41C2×Q8×D43—22no—
42C2×Q8×D43C814yescomplemented
43C22×C4×D43—21no—
44C22×C4×D43C2×C411yescharacteristic
45Q8×Dic43—22no—
46Q8×Dic43—22no—
47C4×Dic86—24no—
48C4×Dic86—24no—
49C4×Dic86—21no—
50C4×Dic86—21no—
51C4×Dic86D412yes—
52C4×Dic86D412yes—
53#13063290—24no—
54#13063290—24no—
55#13063290—22no—
56#13063290—22no—
57#13063283—24no—
58#13063283—24no—
59#13063283—22no—
60#13063283—22no—
61#13063282—24no—
62#13063282—24no—
63#13063282—21no—
64#13063282—21no—
65#13063282—21no—
66#13063282—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43C2×C411yescharacteristic
69C2×Dic43⋊C4—21no—
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4D411yescharacteristic
72C2×Dic43⋊C4D411yescharacteristic
73C2×(C2×D43)⋊C4—21no—
74C2×(C2×D43)⋊C4D411yescharacteristic
75C2×(C2×D43)⋊C4D411yescharacteristic
76C2×C4×Dic43—21no—
77C2×C4×Dic43—21no—
78C2×C4×Dic43—21no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43C2×C411yescharacteristic
81C4⋊(C43⋊C8)—21no—
82C4⋊(C43⋊C8)—21no—
83C22⋊(C43⋊C8)—21no—
84C22⋊(C43⋊C8)—21no—
85C4×C43⋊C8—21no—
86C4×C43⋊C8—21no—
87C22×Q8×C43C2×C411yescharacteristic
88C4×Q8×C43—21no—
89C4×Q8×C43—21no—
90C4×Q8×C43D412yes—
91C4×Q8×C43D412yes—
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43C2×C411yescharacteristic
94C2×C42×C43—21no—
95C2×C42×C43C2311yescharacteristic
96C4⋊C8×C43—21no—
97C4⋊C8×C43—21no—
98C22⋊C8×C43—21no—
99C22⋊C8×C43—21no—
100C4×C8×C43—21no—
101C4×C8×C43—21no—
102C23×D43C22⋊C411yescharacteristic
103C2×Q8×C43—21no—
104C2×Q8×C43—21no—
105C2×Q8×C43—21no—
106C2×Q8×C43C22⋊C412yes—
107C2×Q8×C43C2×C812yes—
108C2×Q8×C43M1612yes—
109C22×C4×C43—21no—
110C22×C4×C43—21no—
111C22×C4×C43C22×C411yescharacteristic
112C22×C4×C43C2×D411yescharacteristic
113C22×C4×C43C2×D411yescharacteristic
114C22×Dic43—21no—
115C22×Dic43—21no—
116C22×Dic43C22⋊C411yescharacteristic
117C22×Dic43C22⋊C411yescharacteristic
118C22×Dic43C22⋊C411yescharacteristic
119Q8×D43—28no—
120Q8×D43—28no—
121Q8×D43—28no—
122Q8×D43—28no—
123C2×C4×D43—24no—
124C2×C4×D43—24no—
125C2×C4×D43—21no—
126C2×C4×D43—21no—
127C2×C4×D43—21no—
128C2×C4×D43—21no—
129C2×C4×D43—24no—
130C2×C4×D43C2×C812yes—
131C2×C4×D43M1612yes—
132C2×Dic86—24no—
133C2×Dic86—24no—
134C2×Dic86—21no—
135C2×Dic86—21no—
136C2×Dic86—21no—
137C2×Dic86—24no—
138C2×Dic86C22⋊C412yes—
139C2×Dic86C2×C812yes—
140C2×Dic86M1612yes—
141C2×C8×C43—41no—
142C2×C8×C43—41no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—22no—
145C4⋊C4×C43—22no—
146C4⋊C4×C43C22⋊C412yes—
147C42×C43—22no—
148C42×C43—22no—
149C42×C43C2×D411yescharacteristic
150C42×C43C2×D411yescharacteristic
151C42×C43C2×D411yescharacteristic
152C42×C43C2×D411yescharacteristic
153(C2×D43)⋊C4—24no—
154(C2×D43)⋊C4—21no—
155(C2×D43)⋊C4—21no—
156(C2×D43)⋊C4—21no—
157(C2×D43)⋊C4—21no—
158C4⋊Dic43—24no—
159C4⋊Dic43—21no—
160C4⋊Dic43C22⋊C412yes—
161Dic43⋊C4—24no—
162Dic43⋊C4—22no—
163Dic43⋊C4—22no—
164Dic43⋊C4—21no—
165Dic43⋊C4—21no—
166Dic43⋊C4—21no—
167Dic43⋊C4—21no—
168C4×Dic43—24no—
169C4×Dic43—24no—
170C4×Dic43—24no—
171C4×Dic43—21no—
172C4×Dic43—21no—
173C4×Dic43—22no—
174C4×Dic43—22no—
175C2×C43⋊C8—41no—
176C2×C43⋊C8—41no—
177C23×C43C2×C22⋊C411yescharacteristic
178C22×D43—21no—
179C22×D43—21no—
180C22×D43—41no—
181C22×D43—41no—
182C22×D43C22⋊C812yes—
183Q8×C43—22no—
184Q8×C43—22no—
185Q8×C43—22no—
186Q8×C43C22⋊C814yes—
187C2×C4×C43—22no—
188C2×C4×C43—22no—
189C2×C4×C43—22no—
190C2×C4×C43—22no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—42no—
194C2×C4×C43C2×C22⋊C411yescharacteristic
195C2×C4×C43C2×C22⋊C411yescharacteristic
196C2×C4×C43#12011yescharacteristic
197C2×C4×C43#12011yescharacteristic
198C2×C4×C43#12011yescharacteristic
199C2×C4×C43#12011yescharacteristic
200C2×C4×C43C22×C811yescharacteristic
201C2×C4×C43C2×M1611yescharacteristic
202C2×C4×C43C2×M1611yescharacteristic
203C2×C4×C43C2×M1611yescharacteristic
204C2×Dic43—21no—
205C2×Dic43—22no—
206C2×Dic43—22no—
207C2×Dic43—21no—
208C2×Dic43—22no—
209C2×Dic43—21no—
210C2×Dic43—21no—
211C2×Dic43—22no—
212C2×Dic43—42no—
213C2×Dic43—41no—
214C2×Dic43—41no—
215C2×Dic43C22⋊C812yes—
216C4×D43—216no—
217C4×D43—22no—
218C4×D43—22no—
219C4×D43—22no—
220C4×D43—22no—
221Dic86—216no—
222Dic86—22no—
223Dic86—22no—
224Dic86—22no—
225Dic86C22⋊C814yes—
226C8×C43—81no—
227C8×C43—81no—
228C43⋊C8—81no—
229C43⋊C8—81no—
230#8323—431nomaximal, Sylow
231C22×C43—21no—
232C22×C43—21no—
233C22×C43#37911yescharacteristic
234C22×C43C2×C22⋊C811yescharacteristic
235C22×C43#40711yescharacteristic
236C2×D43—22no—
237C2×D43—42no—
238C2×D43—41no—
239C2×D43—41no—
240C2×D43—42no—
241C4×C43—21no—
242C4×C43—21no—
243C4×C43—21no—
244C4×C43—21no—
245C4×C43—24no—
246C4×C43—42no—
247C4×C43C2×C22⋊C811yescharacteristic
248C4×C43C2×C22⋊C811yescharacteristic
249C4×C43#40711yescharacteristic
250C4×C43#40711yescharacteristic
251Dic43—22no—
252Dic43—24no—
253Dic43—41no—
254Dic43—41no—
255Dic43—42no—
256C2×#519—431no—
257#1479—431no—
258#1479—431no—
259#1479—431no—
260#1479D4311yescharacteristic, complemented
261#1458—431no—
262#1458—431no—
263C2×C43—21no—
264C2×C43—21no—
265C2×C43#177911yescharacteristic
266C2×C43#179611yescharacteristic
267C2×C43#179611yescharacteristic
268D43—42no—
269C23×Q8—431no—
270#519—862no—
271#519—862no—
272#519—862no—
273#519—862no—
274C2×C4×Q8—431no—
275C2×C4×Q8—431no—
276C2×C4×Q8—431no—
277C2×C4×Q8—861no—
278C2×C4×Q8—861no—
279C2×C4×Q8C2×D4311yescharacteristic
280C2×#117—431no—
281C2×#117—431no—
282C2×#117—861no—
283C2×#117—861no—
284#431—431no—
285#431—431no—
286#431C2×D4311yescharacteristic
287#431C2×D4311yescharacteristic
288Q8⋊C8—22no—
289Q8⋊C8—862no—
290Q8⋊C8—862no—
291Q8⋊C8—862no—
292#324—861no—
293#324—861no—
294#323—861no—
295#323—861no—
296C43#832311yescharacteristic, complemented, Sylow
297C22×Q8—434no—
298C22×Q8—431no—
299C22×Q8—861no—
300C22×Q8—862no—
301C22×Q8—862no—
302C22×Q8—862no—
303C22×Q8—862no—
304C22×Q8—862no—
305C22×Q8C4×D4311yescharacteristic
306C23×C4—431no—
307C23×C4—861no—
308C4×Q8—21no—
309C4×Q8—21no—
310C4×Q8—432no—
311C4×Q8—432no—
312C4×Q8—864no—
313C4×Q8—864no—
314C4×Q8—862no—
315C4×Q8—864no—
316C4×Q8—864no—
317C4×Q8—862no—
318C4×Q8—862no—
319C4×Q8—862no—
320C4×Q8—861no—
321C4×Q8—861no—
322C4×Q8D17212yes—
323C4×Q8C22⋊D4312yes—
324#117—864no—
325#117—864no—
326#117—862no—
327#117—864no—
328#117—864no—
329#117—862no—
330#117—861no—
331#117—861no—
332#117—861no—
333#117—861no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—431no—
336C2×C4⋊C4—431no—
337C2×C4⋊C4—431no—
338C2×C4⋊C4—861no—
339C2×C4⋊C4—861no—
340C2×C4⋊C4—861no—
341C2×C4⋊C4C4×D4311yescharacteristic
342C2×C22⋊C4—431no—
343C2×C22⋊C4—431no—
344C2×C22⋊C4—861no—
345C2×C42—21no—
346C2×C42—431no—
347C2×C42—861no—
348C2×C42—861no—
349C2×C42—861no—
350C2×C42—861no—
351C2×C42C22×D4311yescharacteristic
352C4⋊C8—21no—
353C4⋊C8—21no—
354C4⋊C8—861no—
355C4⋊C8—861no—
356C22⋊C8—21no—
357C22⋊C8—21no—
358C22⋊C8—861no—
359C22⋊C8—861no—
360C4×C8—21no—
361C4×C8—21no—
362C4×C8—861no—
363C4×C8—861no—
364C24—431no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—432no—
369C2×Q8—432no—
370C2×Q8—432no—
371C2×Q8—864no—
372C2×Q8—864no—
373C2×Q8—864no—
374C2×Q8—868no—
375C2×Q8—868no—
376C2×Q8—868no—
377C2×Q8—868no—
378C2×Q8—861no—
379C2×Q8—861no—
380C2×Q8—861no—
381C2×Q8C8×D4312yes—
382C2×Q8#1062187212yes—
383C2×Q8(C2×D43)⋊C412yes—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—431no—
387C22×C4—432no—
388C22×C4—432no—
389C22×C4—431no—
390C22×C4—431no—
391C22×C4—864no—
392C22×C4—864no—
393C22×C4—864no—
394C22×C4—861no—
395C22×C4—861no—
396C22×C4—861no—
397C22×C4—861no—
398C22×C4—861no—
399C22×C4—861no—
400C22×C4C2×C4×D4311yescharacteristic
401C22×C4D4×D4311yescharacteristic
402C22×C4D4×D4311yescharacteristic
403C2×C8—41no—
404C2×C8—41no—
405C2×C8—1721no—
406C2×C8—1721no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—432no—
411C4⋊C4—864no—
412C4⋊C4—864no—
413C4⋊C4—861no—
414C4⋊C4—861no—
415C4⋊C4—861no—
416C4⋊C4—862no—
417C4⋊C4—861no—
418C4⋊C4—861no—
419C4⋊C4—862no—
420C4⋊C4(C2×D43)⋊C412yes—
421C22⋊C4—864no—
422C22⋊C4—861no—
423C22⋊C4—861no—
424C22⋊C4—861no—
425C22⋊C4—861no—
426C42—22no—
427C42—22no—
428C42—864no—
429C42—864no—
430C42—864no—
431C42—861no—
432C42—861no—
433C42—862no—
434C42—862no—
435C42C2×D17211yescharacteristic
436C42D4×D4311yescharacteristic
437C42D4×D4311yescharacteristic
438C42C2×C22⋊D4311yescharacteristic
439C23—432no—
440C23—861no—
441C23—861no—
442C23—1721no—
443C23—1721no—
444C23C22⋊C4×D4311yescharacteristic
445Q8—22no—
446Q8—22no—
447Q8—22no—
448Q8—434no—
449Q8—8616no—
450Q8—862no—
451Q8—862no—
452Q8—862no—
453Q8(C2×D43)⋊C814yes—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—432no—
462C2×C4—8616no—
463C2×C4—862no—
464C2×C4—861no—
465C2×C4—862no—
466C2×C4—861no—
467C2×C4—862no—
468C2×C4—862no—
469C2×C4—862no—
470C2×C4—862no—
471C2×C4—862no—
472C2×C4—862no—
473C2×C4—861no—
474C2×C4—861no—
475C2×C4—1722no—
476C2×C4—1721no—
477C2×C4—1721no—
478C2×C4C22⋊C4×D4311yescharacteristic
479C2×C4C2×(C2×D43)⋊C411yescharacteristic
480C2×C4#1306329311yescharacteristic
481C2×C4#1306329311yescharacteristic
482C2×C4#1306329511yescharacteristic
483C2×C4#1306329511yescharacteristic
484C2×C4C2×C8×D4311yescharacteristic
485C2×C4M16×D4311yescharacteristic
486C2×C4M16×D4311yescharacteristic
487C2×C4C2×#1062187211yescharacteristic
488C8—81no—
489C8—81no—
490C8—3441no—
491C8—3441no—
492C22—21no—
493C22—21no—
494C22—862no—
495C22—1722no—
496C22—1722no—
497C22—1721no—
498C22—1721no—
499C22#1458275411yescharacteristic
500C22C22⋊C8×D4311yescharacteristic
501C22#1458286111yescharacteristic
502C4—24no—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—21no—
507C4—42no—
508C4—862no—
509C4—864no—
510C4—1722no—
511C4—1721no—
512C4—1721no—
513C4C22⋊C8×D4311yescharacteristic
514C4C2×(C2×D43)⋊C811yescharacteristic
515C4#1458286111yescharacteristic
516C4#1458286211yescharacteristic
517C2—21no—
518C2—21no—
519C2—1722no—
520C2#1913450411yescharacteristic
521C2#1913456711yescharacteristic
522C2#1913456911yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1479C2
socleC22×C43#379
prime radicalC23×D43C22⋊C4
cosocleC2×C42×C43C23
hypercenter#1479D43
hypocenterC43#8323
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
2. #19132991C2semidirect
3. #19132990C2semidirect
4. #19132989C2semidirect
7. C43×#1479C2semidirect
42. C2×Q8×D43C8semidirect
260. #1479D43semidirect
296. C43#8323semidirect

Maximal subgroups

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

subgroupindex
C2×#145833752
#191329912
#191329902
#191329892
#191329072
C43×#14792
#832343